Handbook of Magnetic Materials, Volume 3 North-Holland Publishing Company, 1982 Edited by: E.P Wohlfarth ISBN: 978-0-444-86378-2
by kmno4
PREFACE This H a n d b o o k on the Properties of Magnetically Ordered Substances, Ferromagnetic Materials, is intended as a comprehensive work of reference and textbook at the same time. As such it aims to encompass the achievements both of earlier compilations of tables and of earlier monographs. In fact, one aim of those who have helped to prepare this work has been to produce a worthy successor to Bozorth's classical and monumental book on Ferromagnetism, published some 30 years ago. This older book contained a mass of information, some of which is still valuable and which has been used very widely as a work of reference. It also contained in its text a remarkably broad coverage of the scientific and technological background. One man can no longer prepare a work of this nature and the only possibility was to produce several edited volumes containing review articles. The authors of these articles were intended to be those who are still active in research and development and sufficiently devoted to their calling and to their fellow scientists and technologists to be prepared to engage in the heavy tasks facing them. The reader and user of the H a n d b o o k will have to judge as to the success of the choice made. Each author had before him the task of producing a description of material properties in graphical and tabular form in a broad background of discussion of the physics, chemistry, metallurgy, structure and, to a lesser extent, engineering aspects of these properties. In this way, it was hoped to produce the required combined comprehensive work of reference and textbook. The success of the work will be judged perhaps more on the former than on the latter aspect. Ferromagnetic materials are used in remarkably many technological fields, but those engaged on research and development in this fascinating subject often feel themselves as if in strife for superiority against an opposition based on other physical phenomena such as semiconductivity. Let the present H a n d b o o k be a suitable and effective weapon in this strife! The publication of Volumes 1 and 2 took place in 1980 and produced entirely satisfactory results. Many of the articles have already been widely quoted in the scientific literature as giving authoritative accounts of the modern status of the
vi
PREFACE
subject. One book reviewer paid us the compliment of calling the work a champion although with the proviso that the remaining two volumes be published within a reasonable time. The present Volume 3 goes halfway towards this event and contains articles on a variety of subjects. There is a certain degree o f coherence in the topics treated here but this i s not ideal due to the somewhat random arrival of articles. The same will be the case for the remaining Volume 4 as such, although this will then complete the work so as to finally produce a fully coherent account of all aspects of this subject. Three of the authors of Volume 3 are members of the Philips Research Laboratories, Eindhoven and, as already noted in the Preface to Volumes 1 and 2, this organization has been of immense help in making this enterprise possible. The North-Holland Publishing Company has continued to bring its professionalism to bear on this project and Dr. W. Montgomery, in particular, has been of the greatest help with Volume 3. Finally, I would like to thank all the authors of Volume 3 for their co-operation, with the profoundest hope that those of Volume 4 will shortly do likewise! E.P. Wohlfarth
Imperial College
TABLE OF CONTENTS Preface
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T a b l e of C o n t e n t s
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vii
List of C o n t r i b u t o r s
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1. M a g n e t i s m a n d M a g n e t i c M a t e r i a l s : H i s t o r i c a l D e v e l o p m e n t s a n d P r e s e n t R o l e in I n d u s t r y a n d T e c h n o l o g y U. E N Z . . . . . . . . . . . . . . . . . . . . . 2. P e r m a n e n t M a g n e t s ; T h e o r y H. Z I J L S T R A . . . . . . . . . . . . . . . . . . 3. T h e S t r u c t u r e a n d P r o p e r t i e s of A l n i c o P e r m a n e n t M a g n e t A l l o y s R.A. McCURRIE . . . . . . . . . . . . . . . . . . 4. O x i d e S p i n e l s S. K R U P I C K A a n d P. N O V A K . . . . . . . . . . . . 5. F u n d a m e n t a l P r o p e r t i e s of H e x a g o n a l F e r r i t e s with M a g n e t o p l u m b i t e Structure H. K O J I M A . . . . . . . . . . . . . . . . . . . 6. P r o p e r t i e s of F e r r o x p l a n a - T y p e H e x a g o n a l F e r r i t e s M. S U G I M O T O . . . . . . . . . . . . . . . . . . 7. H a r d F e r r i t e s a n d P l a s t o f e r r i t e s H. S T J i d ~ L E I N . . . . . . . . . . . . . . . . . . 8. S u l p h o s p i n e l s R.P. V A N S T A P E L E . . . . . . . . . . . . . . . . . 9. T r a n s p o r t P r o p e r t i e s of F e r r o m a g n e t s I.A. CAMPBELL and A. FERT . . . . . . . . . . . .
1 37 107 189
305 393 441 603 747
Author Index
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805
Subject Index
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833
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845
Materials Index
vii
chapter 1 MAGNETISM AND MAGNETIC MATERIALS" HISTORICAL DEVELOPMENTS AND PRESENT ROLE IN INDUSTRY AND TECHNOLOGY
U. ENZ Philips Research Laboratories Eindhoven The Netherlands
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982
CONTENTS Introduction 1. F r o m l o d e s t o n e to f e r r i t e : a s u r v e y of t h e h i s t o r y of m a g n e t i s m . . . . . . . . . 2. T h e r o l e of m a g n e t i s m in p r e s e n t - d a y t e c h n o l o g y a n d i n d u s t r y . . . . . . . . . . 3. D e v e l o p m e n t o f s o m e classes of m a g n e t i c m a t e r i a l s . . . . . . . . . . . . . . 3.1. I r o n - s i l i c o n a l l o y s . . . . . . . . . . . . . . . . . . . . . . . . 3.2. F e r r i t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. G a r n e t s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. P e r m a n e n t m a g n e t s . . . . . . . . . . . . . . . . . . . . . . . 4. T r e n d s in m a g n e t i s m r e s e a r c h a n d t e c h n o l o g y . . . . . . . . . . . . . . . . 4.1. M a g n e t i s m r e s e a r c h b e t w e e n p h y s i c s , c h e m i s t r y a n d e l e c t r o n i c s . . . . . . . . 4.2. T r e n d s in a p p l i e d m a g n e t i s m . . . . . . . . . . . . . . . . . . . . 4.3. O u t l o o k a n d a c k n o w l e d g e m e n t . . . . . . . . . . . . . . . . . : References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 3 6 10 10 12 20 24 30 30 31 34 35
Introduction
In this contribution we attempt to trace a few main developments of the history of magnetism and to give an account of the present role of ferromagnetic materials in industry and technology. The treatment of a subject as broad as the present one must necessarily be limited and incomplete; nevertheless, we may give an impression how the large body of knowledge on magnetism accumulated in the past, and how important it is at present. The first section gives a short sketch of some early historical developments and inventions. Such a flash back to history may be useful to place the m o d e r n activities and achievements in a wider context. The next section deals with the role of magnetism and magnetic materials in modern technology, especially in the context of power generation and distribution, telecommunication and data storage. Some statistical figures on the economic significance of magnetic materials are included. The third-section gives a somewhat more detailed account of the development lines~i~f a few selected classes of materials, whereas in the last section an attempt is made to indicate the trends in applied magnetism.
1. F r o m lodestone to ferrite: a survey of the history of m a g n e t i s m
The notion of magnetism dates back to the Ancient World, where magnets were known in the form of lodestone, consisting of the ore magnetite. The name of the ore, and hence that of the whole science of magnetism, is said to be derived from the G r e e k province of Magnesia in Thessaly, where magnetite was found as a natural mineral. It seems very likely that the early observers were fascinated by the attractive and repulsive force between lodestones. Thales of Miletus (624-547 BC) reports that the interaction at a distance between magnets was known before 800 BC. Another, probably m o r e apocryphal account is due to Pliny the Elder, who ascribes the n a m e magnet to its discoverer, the shepherd Magnes "the nails of whose shoes and the tip of whose staff stuck fast in a magnetic field while he pastored his flocks". From such modest beginnings grew the science of magnetism, which may be represented as a tree on whose growing trunk new shoots and branches continuously appeared (see fig. 1). The trunk represents the mag-
4
u. ENZ
netic materials such as metals, alloys or oxides, because history shows that the use and study of materials have been the main sources of discoveries and progress. T h e new branches which developed in the course of time f o r m e d scientific fields in themselves. A brief account of s o m e of these d e v e l o p m e n t s is given in the following pages (Encyclopedia Britannica: Magnetism; see also, Mattis (1965)). Magnets f o u n d their first application in compasses, which were m a d e from a lodestone b u o y a n t on a disc of cork. W e k n o w that the compass was used by Vikings and, of course, by Columbus, but the art of navigation guided by compasses m a y be much older. T h e invention is p r o b a b l y of Italian or A r a b i c origin. T h e earliest extant E u r o p e a n reference to the compass is attributed to the English scholar A l e x a n d e r N e c k a m (died 1217). T h e influence of this simple device was far-reaching in every respect: it m a d e it possible to navigate on the high seas. T h e principle of the compass has r e m a i n e d unchanged, the device is still in full use. T h e invention of the compass is characteristic of m a n y later developments in magnetism: seemingly marginal effects turned out to be very i m p o r t a n t and to have had a t r e m e n d o u s impact on later technological developments. A milestone in the history of magnetism was William Gilbert's De Magnete, electro- high neutroncritical materials spin structures magnetic fields diffr, phenom metals semi- amorphous micromagnetism radiation , magn. M6ssbauer para- alloys cond. mogn. J spin I domains I inductio~ moment ;NI~R ;mogn. gl~ss ~'
;sp;e'Ig° ne i
ro~
I
I I bb,es
leomac netism stellar magnetism
F?Curi~
I Jalloys
I L oxides
Maxwell
~
~-
~
I
Faraday,
A~ere,1 8 0 O r ~ ert' tedr2[lmeognete 1269 Peregrinus de Maricourt 1200 Neckarn describes compass
J J J 800 b ~ r l d
: magnesian stones
Fig. 1. Development of the modern branches of magnetism from a common root. A few names and dates are indicated to mark some of the most crucial moments in this development. The modern fields of magnetism, ranging from basic entities like magnetic fields and particles to more complex ensembles, emanate in quite a straightforward way from a few basic branches. A central position is reserved to the various classes of materials, reflecting the central position of materials in magnetism research.
MAGNETISM AND MAGNETIC MATERIALS
5
Magneticisque Corporibus, et de Magno Magnete Tellure (1600, "Concerning Magnetism, Magnetic Bodies and the Great Magnet Earth") which summarized all the available knowledge of magnetism up to that time, notably that of Petrus Peregrinus de Maricour (1269). In addition Gilbert describes his own experiments: he measured the direction of the magnetic field and its strength around spheres of magnetite with the aid of small compass needles. For this purpose he introduced notions like magnetic poles and lines of force. Gilbert found that the distribution of the magnetic field on the surface of his sphere or terella ("microworld") was much like that of the earth as a whole and concluded that the earth is a giant magnet with its two magnetic poles situated in regions near the geographical poles. This observation made him the founder of geomagnetism. Gilbert's work not only strongly influenced the later development of magnetism, but also contributed to the development of the idea of universal gravitation: it was believed, for some period of time before Newton, that the planets were held in their orbits by magnetic forces in some form or other. Gilbert also discovered that lodestone, when heated to bright red heat, loses its magnetic properties, but regains them on cooling. In this way he anticipated the existence of the Curie temperature. For more than two centuries after Gilbert little progress was made in the understanding of magnetism, and its origin remained a mystery. The early nineteenth century marked the beginning of a series of major contributions. Hans Christian Orsted discovered in 1820 that an electric current flowing in a wire affected a nearby magnet. Andr6 Marie Amp6re established quantitative laws of the magnetic force between electric currents and demonstrated the equivalence of the field of a bar magnet and that of a current-carrying coil. Michael Faraday discovered magnetic induction in 1831, his most celebrated achievement, and introduced the concept of the magnetic field as an independent physical entity. Guided by his feeling for symmetry and harmony he suspected that an influence of magnetic fields on electric conduction should exist as a counterpart to Orsted's magnetic action of currents. After a long period of unsuccessful experiments with static fields and stationary magnets, he discovered the induction effects of changing fields and moving magnets. This line of investigation culminated in Maxwell's equations, establishing the synthesis between electric and magnetic fields. Progress in the understanding of the microscopic origin of magnetism was initiated by Amp6re, who suggested that internal electric currents circulating on a molecular scale were responsible for the magnetic moment of a ferromagnetic material. Amp6re's hypothesis enabled Wilhelm Eduard Weber to explain how a substance may be in an unmagnetized state when the molecular magnets point in random directions, and how they are oriented by the action of an external field. This idea also explained the occurrence of saturation of a magnetic material, a state reached when all elementary magnets are oriented parallel to the applied field. This line of thinking led to the studies of Pierre Curie and Paul Langevin on paramagnetic substances, and also to the work of Pierre Weiss (1907) on ferromagnetic materials. Pierre Curie described the paramagnetic substances as an en-
6
u. ENZ
semble of uncoupled elementary magnetic dipoles subjected to thermal agitation, the orienting action of the external field being counteracted by the thermal agitation. Such a description was also applied successfully to ferromagnetic materials at temperatures higher than the Curie temperature. The modern discipline of critical phenomena is, for the time being, the end point of this branch. Weiss, in turn, postulated the existence of a hypothetical internal magnetic field of great strength in ferromagnets, resulting in a spontaneous magnetization even in the absence of an external field. Amongst his other contributions is the notion of a magnetic domain, a small saturated region inside a ferromagnet, and the notion of domain walls. Weiss's work can be viewed as the starting point of the branch leading to the modern disciplines of micromagnetism and domain theory, and also as the point of departure of N6el's work on interactions, leading to the fields of ferrimagnetism and antiferromagnetism, including the actual disciplines of spin structures and spin glasses. A branch of its own, the study of the magnetic aspects of particles is perhaps a less obvious offshoot from the common source, but it nevertheless forms a very important part of magnetism. Indeed fields like electron spin resonance and nuclear spin resonance, M6ssbauer spectroscopy and structure analysis by neutron diffraction are at the same time indispensable tools and important disciplines of magnetism. The modern disciplines of magnetism as represented at the top of fig. 1 range from the fundamental entities like fields and particles on the left to more complex systems on the right. Critical phenomena, magnetic phase diagrams and spin structures in various materials including spin glasses are important fields of modern research. The classical discipline of domains, domain walls and micromagnetism is still being actively studied, and has even received renewed attention stimulated by the modern investigations on bubbles. The various materials appear in the centre of the three, thus confirming their central role in magnetism. The few materials that are named represent just a very small fraction of the magnetic materials known at the present time. The study of the magnetic properties of materials is the subject of the present handbook, and the present article is intended to give a general introduction to the remaining chapters of this work.
2. The role of magnetism in present-day technology and industry Having outlined the early developments of magnetism as well as the subsequent accumulation of knowledge on magnetic phenomena and materials, we now turn to the description of the role of magnetism in present-day technology and industry. Magnetic materials occupy a key position in many essential areas of interest to society. The most important of these, which depend in an essential way on magnetic materials, are the generation and distribution of electrical power, the storage and processing of information, and of course communication in all its forms, including telephony, radio and television. Apart from these major fields, many other industrial machines and devices, including motors for numerous applications, depend on magnetic materials or magnetic forces. Figure 2 gives a
MAGNETISM AND MAGNETIC MATERIALS
7
Industrally and economicallyrelwant fields of application of matlneticmaterial= Function
Physicaleffect, important parameters
power generators, power transformers magnetic induction, recording heads, medium frequency transformers, inductors, particle accelerator electric motors, small motors with permanentmagnets
Material classes
high induction material, silicon-iron sheet, oriented sheet
Permalloysheet, amorphousmetals, ferrites I ~
[ magnetomotive ~ior~teS~linduction
permanentmagnets, Ticonal, Ferroxdure~ SmCo-magnets
latching devices, levitation (trains) television,radio, resonantband pass filters
self-induction, high Q
ferrites
unidirectional microwavedevices gyrators
ferromagnetic resonance, low damping
garnet crystals, hexagonal ferrites
storageof digital information in cores, plated wires
squarehysteresis loop, fast switching time
l smallparticlesof
massstorage in magnetic tapes, magnetic discs and floppy discs
information storage in magneto-optic stores compact digital massstorage
I square-loop ferrites, plated wires, permalloy
remanenceand coerciveforce of small particles and thin magnetic films
1
3'- Fe203, CrO2, Fe
thin metallic films, Co-based
high Faradayand Kerr effect
amorphous films, MnBi, GdFe
stability and mobility of bubbles
monocrystalline garnet films
Fig. 2. Industrially and economically relevant fields of application of magnetic materials. T h e central column lists the basic physical effects together with the important parameters. T h e left-hand column gives the useful functions and the right-hand one the classes of materials most commonly used to fulfil these functions. The arrows indicate the various interrelations.
8
u. ENZ
survey of the use of magnetic materials in various areas of application. The left-hand column shows the type of application or the function realized with the aid of magnetism. The central column lists the various physical effects and the parameters most relevant to a specific application. The right-hand column displays the classes of materials used to accomplish the various functions. The variety of physical effects, applications and materials is impressive, even in this necessarily incomplete survey. Most of the applications are based on magnetic induction, magnetomotive forces or the specific properties of the hysteresis loop such as squareness or coercive field, but other effects like ferromagnetic resonance or the Faraday effect also find their applications. The useful materials are in general restricted to those classes which are ferromagnetic or ferrimagnetic at room temperature and which possess a sizable saturation magnetization. Although magnetic materials are indispensable for the listed and for many other applications, their role remains to some extent hidden because the ultimate practical function is not associated with magnetism. The public at large is often unaware of the role of magnetism in everyday life. Occasionally one gets the impression that the same holds even for some professionals! The economic impact of magnetism is very considerable. Jacobs (1969) estimates the total value of processed magnetic material produced in the United States in 1967 at about 680 million dollars, which represents about 0.1% of the American gross national product. In 1976 the corresponding amount was 2140 million dollars (Luborsky et al. 1978, Snyderman 1977). These figures apply to magnetic materials as such and do not take into account that magnetic materials are nearly always components of more elaborate products such as electric motors, transformers, loudspeakers, microwave isolators or computer memories. Jacobs estimates that for such products a "multiplication factor" of the order of 15 is appropriate, so that the total economic impact of magnetism was of the order of 1.5% of the American gross national product in 1969. This figure has not changed much since, and probably applies to other economies as well. In table 1 some economic data on magnetic materials are given, split up into various classes of materials to be discussed below. The largest quantities of magnetic material enter the field of electric power generation and distribution, a field which is historically the major application of magnetism. For this function the aim is to reach the highest possible saturation magnetization and the lowest possible total loss, properties which are best met in iron-based alloys such as silicon-iron sheet and grain-oriented sheet. More recently amorphous metals have become competitive for some specific applications in this field. Although power generation and distribution have now achieved the status of well-established and mature technologies, progress towards reduced losses is still going on. As a result the amount of power handled by a transformer of constant size has increased continuously, resulting in the last 40 years in a tenfold increase in power-handling performance. A second area of great and rapidly increasing importance is that of magnetic materials for information storage and processing. The amount of material involved in these fields is much smaller, but their economical significance is larger
MAGNETISM AND MAGNETIC MATERIALS TABLE 1 Annual magnetic materials market in millions of dollars (not corrected for inflation) 196%1968 US Electrical steel Magnetic recording tapes Magnetic discs and drums Soft ferrites (communication, entertainment and professional) Square-loop ferrites Permanent magnets
World (17
1976-1977 US
World 07
180(27
4400)
180(27
45007
1300(3/
100(~)
900(37
3000(37
110(2) 55(2) 55(27
130 70(67
535(4)
1 5 0 (3,6)
1979-1980 US
World 07
148 57(7) 170(5)
600(4) 960(5)
(1/Western world including Japan. (2)Jacobs (1969). (3)Luborski et al. (1978). (4)De Bruyn and Verlinde (1980). (s)Hornsveld (1980). (6)Snijderman (1977). (7)Electronics, 3, Jan. 1980.
than that of electrical steels. T h e leading e c o n o m i c position was taken over by information storage about ten years ago. A m o n g s t information-storing materials, magnetic tapes and discs are the most i m p o r t a n t groups. T a p e and disc techniques are both based on the same physical principle, the association of a bit of information with the direction of the magnetization in a small area of the material. T h e merits of this storage principle are simplicity, p e r m a n e n c e (or non-volatility) of information, and a high information density per unit surface of the (film-like) material. T h e progress of these techniques has been entirely directed towards higher information densities and thus towards lower prices per bit of information, and further progress in this direction is expected. Square-loop ferrites or bubble d o m a i n m e m o r i e s are also based on the association of inf o r m a t i o n with the direction of the magnetization in the material, in the f o r m e r case in a small sintered core, in the latter case in a single domain, a bubble, which is able to m o v e in a single-crystal film. Magnetic cores have been the basic m e t h o d of information storage in c o m p u t e r s for m o r e than 25 years, but have now r e a c h e d a level of saturation, which is i m p o s e d by the limitations of handling ever smaller (and faster) cores. T h e bubble d o m a i n memories, on the o t h e r hand, are in full d e v e l o p m e n t and m a y find a p e r m a n e n t position in the hierarchy of information storage. N u m e r o u s other magnetic information storage principles have been p r o p o s e d and realized, including thin permalloy films and permalloyplated wire, but their total e c o n o m i c impact has r e m a i n e d small. C o m m u n i c a t i o n is the third i m p o r t a n t field of application of magnetic materials. This field includes telephony, radio and television broadcasting and receivers, and radar, all of which techniques use m e d i u m to very high frequencies. D u e to their
10
u. ENZ
high resistivity and consequently low eddy-current losses, ferrites are the best suited materials for communication. In telephony the medium frequency channel filters are based on resonant circuits using high-O ferrite cores, one of the first applications of ferrites and the standard technique till now. Every broadcast receiver contains many ferrite parts, such as inductors, deflection units, line transformers and antenna rods.
3. Development of some classes of magnetic materials
In this section the development of a few selected classes of magnetic materials is described. These case histories relate to iron-silicon alloys, ferrites, garnets and permanent magnets. The emphasis will be on the chronology of events, the improvement of performance and the technical relevance.
3.1. Iron-silicon alloys Electrical grade steel is the magnetic material produced in the largest quantities of all; hundreds of thousands of tons are annually needed by the electrical industry. The bulk of this material is used for the generation and distribution of electrical energy and for motors. High magnetic induction and low losses are of prime importance in these applications. Alloys of iron and silicon meet the above conditions well and therefore take a prominent position with the product category of electrical steels. Here we confine ourselves to some historical remarks and to give some recent figures on silicon-iron alloys. The starting point of the development of silicon-iron alloys of suitable quality is marked by the work of Barrett et al. (1900). These authors found that the addition of about 3% of silicon in iron increased the electrical resistance and reduced the coercive force as compared to unalloyed iron. The slight reduction in saturation magnetization due to silicon was far outweighted by the improvement in the other properties. Some years later, in 1903, the industrial production of these alloys started in Germany and in the U n i t e d States. The promotion and subsequent improvement of this technique is, to a considerable extent, the merit of Gumlich and Goerens (1912). The material was used in the form of hot rolled polycrystalline sheets having random grain orientation. Due to the higher permeability and the reduced hysteresis and eddy-current losses, iron-silicon sheet replaced the conventional materials within a few years, in spite of the initial difficulties of production and the higher price, and was used in this form for about three decades. However, these random oriented materials were still imperfect because saturation was only reached by applying magnetic fields well above the coercive field, which limits the useful maximum induction to about 10 kG. The hysteresis loops of single crystals or of well oriented samples, on the other hand, are nearly rectangular. Fields slightly higher than the coercive field are therefore sufficient to drive the core close to saturation. The useful maximum induction is thus higher,
MAGNETISM AND MAGNETIC MATERIALS
ll
reaching 15 to 1 7 k G (1.5 to 1.7Wb/m 2) (fig. 3). An ideal transformer would consist of single crystal sheets oriented such that a closed rectangular flux path along [100] directions, the preferential directions, results. Progress towards this goal was achieved by Goss (1935) who showed that grain oriented sheets can be obtained by certain cold rolling and annealing procedures. This so called Goss texture is characterized by crystallites having their [110] planes oriented parallel to the plane of the sheet, with common [100] direction in this plane. The magnetic properties of such materials are characterized by coercive fields around 0.1 Oe and maximum permeabilities up to 70.000 (fig. 3). Data obtained by Williams and Shockley (1949) on a oriented single crystal frame of high purily 3.85% silicon iron with limbs parallel to [100] directions are included in fig. 3 for comparison. The coercive field of this single crystal was as low as 0.028 Oe (2.2 A/m) and the maximum permeability exceeded 10 6. Grain orientation contributed to a further decrease of the magnetic core losses. Loss figures dropped to about 0.6 Watt per kg at 60 cycles and an induction of 10 kG (1 Wb/m 2) for commercial grade oriented silicon-iron sheet. An additional advantage was that maximum induction up to 17 kG (1.7 Wb/m 2) became practical. Another more recent step towards higher quality is related to even more perfect crystalline orientation combined with the introduction of a controlled tensile stress in the sheet (Taguchi et al. 1974). The composition of the material remained unchanged i.e. the silicon content is still around 3%. The tensile stress is introduced by a surface coating consisting of a glass film and an inorganic film applied on both surfaces of the sheet. This procedure leads, by magnetoelastic
Magnetization (kG) 18
Br.=17 kG
~kO
t
'°r i/ill'
l I
-0.2
0
0.2
I
I
I
0.L
0.6
Magnetic field (Oe)
Fig. 3. Static hysteresis loops of grain oriented silicon-iron sheet (Goss texture). For comparison the loop of a single crystal (broken line, Williams and Shockley 1949) is shown (after Tehble and Craik 1969).
12
U. E N Z
interactions, to improved properties of the hysteresis loop and thus to still lower magnetic losses. The improvement of the quality of electrical grade steel since 1880 is shown in fig. 4. In a time span of 100 years the core loss decreased from 8 W/kg to about 0.4 W/kg for an induction of 10 k G and a frequency of 60 Hz. The innovations described above clearly show up as marked steps: the introduction of silicon-iron alloys after 1900, causing the loss figure to drop from 8 to 2 W/kg and also the use of grain-oriented material in the late thirties. The latter innovation enabled higher induction ratings: new branches with maximum induction of 15 kG and 1 7 k G appear after 1940. The dramatic increase of the power handled by a transformer of equal size is also shown. co. e toss ( W a t t / k g )
transforrnator power { MVA)
6 4.
17 kG 15kG
2
1000
! 10 kG
1 0.8 0.6
I ' /t
o.4
/ 0.2
50
//
If
188o
1900
1920
194.0
I
/
I I
1960
I
1980
2000 year
Fig. 4. Core loss of electrical grade steel (after Luborsky et al. 1978). Since 1880 the core loss decreased from 8 W / k g to 0 . 4 W / k g at an induction of 1 0 k G and a frequency of 6 0 H z . T h e introduction of textured sheet around 1940 led to the use of higher m a x i m u m induction (up to 17 k G (1.7 Wb/m2)). T h e broken line shows the increase in power handled by a transformer of constant size.
3.2. Ferrites Ferrites are mixed oxides of the general chemical composition MeOFe203, where Me represents a divalent metal ion such as Ni, Mn or Zn. The crystallographic structure of ferrites, and also that of the closely related ore magnetite (FeOFe203) is the spinel structure. Ferrites can therefore be seen as direct descendants of magnetite (see fig. 1). Many simple or mixed ferrites are magnetic at room temperature, but due to their ferrimagnetic character the saturation magnetization is only a fraction of that of iron. The outstanding property of ferrites, which makes them suitable for many applications, is their high electrical resistivity as compared to that of metals. Their specific resistivity ranges from 102 to 101° f~ cm, which is up to 15 orders of magnitude higher than that of iron. In most high frequency applications of ferrites eddy currents are therefore absent or negligibly small, whereas at such frequencies eddy currents are the main drawback of
MAGNETISM A N D M A G N E T I C M A T E R I A L S
13
metals, even in laminated form. Such intrinsic properties make the ferrites indispensable materials in telecommunications and in the electronics industry, where frequencies in the range of 109 to 1011Hz have to be handled. The potential usefulness of magnetic oxides for high frequency applications was realized as early as 1909 by S. Hilpert, who investigated the magnetic properties Of various oxides including some simple ferrites. In 1915 the crystallographic structure of ferrites, which had remained unknown until then, was determined independently by W.H. Bragg in England and S. Nishikawa in Japan. Contributions to the understanding of the chemistry of ferrites were also made by Forestier (1928) in France. All of this early work remained without a direct follow-up; at that time there was apparently no technological need yet for such materials. The situation remained unchanged until 1933, when Snoek of the Philips Research Laboratories started a systematic investigation (Snoek 1936) into the magnetic properties of oxides. In the same period of time ferrites were independently investigated by Takai (1937) in Japan. Snoek's working hypothesis in his search for high permeability materials was to look for cubic oxides which, for symmetry reasons, could be expected to have a low crystalline anisotropy. Simultaneously he aimed at finding materials with low magnetostriction values to minimize the adverse effects of the unavoidable internal stresses present in polycrystalline materials. Snoek's approach turned out to be fruitful: he found suitable materials in the form of mixed spinels of the type (MeZn)Fe204, where Me is a metal of the group Cu, Mg, Ni or Mn. Permeabilities up to 4000 were reached (Snoek 1947). Snoek's achievement may again have remained of more academic interest, but this time there was a clear demand for magnetic materials from the telephone industry, which felt the need to improve the load coils of their long-distance lines and to use bandpass filters based on low-loss magnetic materials. Ferrite inductors proved to be well suited for these purposes, and so ferrites and telephone technology developed in close cooperation. Six (1952) was the inventive and leading promotor of this development, which did not, however, proceed without a great deal of effort from chemists, physicists and electrical engineers, who cooperated in achieving adequate material properties and practical technical designs. Before 1948, when most of this work was done, little was known about the cause of the low saturation magnetization of ferrites or of the origin of their anisotropy. This changed when N6el (1948), who had already explained the behaviour of antiferromagnets, introduced his concept of partially compensated antiferromagnetism, which he called ferrimagnetism. The essential point of N6el's explanation is the antiparallel orientation of the spins of the ions in the two sublattices, octahedral and tetrahedral, of the spinel structure. N6el's model revealed directly the cause of the low saturation of ferrites. The work of Verwey and Heilman (1947) on the distribution of the various ions over these lattice sites was undoubtedly of great help. N6el's model was directly verified by neutron diffraction work done by Shull et al. (1951) only a few years after the invention of this powerful method of analysis. Further proof was derived from a study of the temperature dependence of the saturation magnetization in some spinel ferrites
14
u. ENZ
(Gorter et al. 1953). A n o t h e r fundamental mechanism, ferromagnetic resonance, was extensively studied in ferrites (Snoek 1947) shortly after its discovery by Griffiths (1946). The main difficulty encountered in the early use of ferrites was their high level of magnetic losses and disaccommodation. It was found that even in the absence of eddy currents there were still appreciable residual losses, which prevented the design of high quality resonance circuits. It is now well known that quite a large number of electronic and ionic relaxation processes can cause magnetic aftereffects in magnetic materials subjected to alternating fields. These processes are the main cause of the losses in magnetic cores. Snoek (1947) tried to minimize these after-effects by controlling the presence of relaxing ions with the aid of special sintering procedures in suitable oxidizing or reducing atmospheres. A n important insight concerning the use of ferrites in resonant filter circuits was that the relevant quantity to be considered is the ratio between the loss factor tan6 and the initial permeability/x rather than tan~ as such. This ratio can be controlled by introducing air gaps in the magnetic circuits. Therefore a high initial permeability is as important as a low loss factor. A reduced loss level in the ferrite material made it possible to reduce the physical size of the inductors, a successful development vizualized in fig. 5. Ferrite cores having about equal quality factors are shown in a sequence ranging from 1946 to 1974. The volume of the inductors was reduced by a factor of 32 during this time span. Compared with an air coil of
Fig. 5. Development of pot cores between 1946 and 1974. Reduction of the loss level of ferrite materials led to the reduction of the physical size of these components, all of which fulfil the same technical function. The quality factor Q of the ferrite components remained, as indicated, about constant during this time span. An air coil and a Fernico coil of much lower quality, representing the state of the art in 1936 and 1939, are shown for comparison. The total reduction in volume is nearly a factor of 400.
MAGNETISM AND MAGNETIC MATERIALS
15
much lower quality representing the state of the art in 1936, the reduction in volume is nearly a factor of 400. Similar, albeit less spectacular progress was also made in another ferrite application, i.e., that in power transformers where a high saturation induction and low hysteresis losses are of principal importance (see fig. 6). The total losses are shown to be reduced by a factor of three, while the maximum usable inductance nearly doubled in the indicated period of time. This type of material, a high saturation MnZn ferrite, is at present finding increasing application in switched-mode power supplies for small to medium power levels. loss P (Watt cm-3)
\
0.2
Induction 8 (kG)
"°"3c'3c5 ...---tt
I
"~..3c8 2
0.1
J
1950
L
i
1960
1970
0
1980 year
Fig. 6. Reduction of loss factor and increase of usable maximum induction of ferrite cores for power applications from 1950 to 1980.
A new and rather unexpected application of ferrites emerged with the invention of the gyrator, a non-reciprocal network element. The impedance of signals passing through such an element in the forward direction differs from that in the backward direction. The gyrator was conceived by Tellegen (1948) on theoretical grounds as a possible but not yet realized network element. Hogan (1952) was the first to realize a non-reciprocal microwave device consisting of a ferrite-loaded waveguide. The physical effect on which the device is based is analogous to the well-known Faraday effect, i.e., the rotation of the plane of polarization of a light wave passing through a magnetized body. One form of the non-reciprocal device thus consists of a circular wave-guide carrying a central ferrite rod magnetized along its axis. If the rotation of the plane of polarization of the microwave equals 45 ° and coupling in or out also occurs with an offset angle of 45 ° the microwaves pass through the device in the forward direction while propagation in the backward direction is suppressed. A similar device functions as a microwave switch (see fig. 7) controlled by the bias field. Other devices based on this principle, which have found wide application in microwave technology, are circulators, resonance isolators and power limiters. The discovery that some polycrystalline spinel ferrites can have a rectangular hysteresis loop and therefore can be used as computer memory elements was of paramount importance for computer technology. Until 1970 nearly all main-frame
16
U. E N Z
Rectangular waveguide Cylindrical waveguide'-k~" ~ IX Rectangular ~ ~..,/', waveguide -x~.r~.~ ~ ,.~1"~,, !/
". L~ ~ I t ', , "':."l'-'~4"-"
]
I I I L___ I
Fig. 7. Microwave switch based on the rotation of the plane of polarization of microwaves propagating along the magnetized ferrite rod in the central cylindrical part of the device.
Fig. 8. Core array of a ferrite core m e m o r y in 3D organization showing word, bit and sense lines. T h e ferrite core matrix is shown together with the preceding storage technology, based on electron tubes, and the succeeding technology, the semiconductor memory.
MAGNETISM AND MAGNETIC MATERIALS
17
computer memories consisted of ferrite cores, so that it is fair to say that the whole computer development was closely connected with the development of the ferrite core memory. A r o u n d 1968 the yearly,world production of ferrite cores was about 2 x 10 l° cores (Jacobs 1969). J.W. Forrester and W.N. Papion, both at that time at MIT, are generally considered to be the inventors of the principle of coincident current selection of a core (Forrester 1951). The first square-loop cores consisted of nickel-iron alloys, the switching speed of which suffered from an inherent limitation due to eddy currents. Both Forrester and Rajchman (1952) suggested the use of non-metallic cores to avoid this shortcoming. At about the same time, Albers-Schoenberg (1954) observed the square-loop properties of some ferrite compositions. A link with system requirements was immediately made. This revolutionary challenge materialized in Whirlwind I, the first experimental computer based on a ferrite core memory, built at the Lincoln laboratory at MIT in 1953. Figure 8 shows a wired ferrite core matrix consisting of 1024 ferrite cores. A stack of such matrix planes forms the memory. Two individual cores are shown in fig. 9. Ferrites also p l a y e d an unexpected role in particle accelerators constructed to study elementary particles (Brockman et al. 1969). The operation of these large
Fig. 9. Two individual ferrite memory cores (20 mil and 14 mil) are shown on the wings of a fly.
18
U. E N Z
machines is based on accelerating units consisting of large transformers designed as resonance cavities. These elements accelerate the charged particles (protons) by feeding energy into the particle beam circulating in the machine. The stations act in such a way that the particle beam represents the secondary winding of the transformers. During one acceleration sequence the increasing frequency has to be followed by controlling the self-induction of the core of the transformer with the aid of a bias field. Again, the demand for low losses, especially low eddy current losses, favoured ferrites above other materials for this application, and so ferrites entered this field as essential elements and played a continued role in the subsequent stages of the development of these machines. Figure 10 shows an acceleration unit of the alternating gradient synchrotron in Brookhaven. The synchrotron contains 12 of such cavities, and each unit Contains about 500 kg of ferrite.
Fig. 10. Accelerator unit of the alternating gradient synchrotron at Brookhaven, containing a hollow cylindrical ferrite core assembled from a large number of rings. The total weight of the core is about 500 kg (after Brockman et al. 1969).
Apart from these few examples of specific implementations of ferrites we recall that the bulk of ferrite material is used in telecommunication and consumer applications, with roughly equal turnover in these two fields. The main consumer products are television and radio sets, in which such parts as line transformers, deflection coils, tuners and rod antennas contain ferrite materials. About 0.7 kg of ferrite enters a black-and-white television set, and about 2 kg a colour set. Figure 11 gives an impression of the diversity of ferrite products for such applications.
MAGNETISM AND MAGNETIC MATERIALS
19
Fig. 11. Various ferrite componentsas used in radio and televisionsets.
Hand in hand with the implementation of ferrites and with the tailoring and perfection of their technically relevant parameters, the investigation of their fundamental properties continued, resulting in a considerable deepening of the understanding of their chemical and physical properties. The main lines of investigation concerned: (a) crystal structures, chemical miscibility regions and preferential site occupation of the various ions in the spinel lattice; (b) the experimental determination of data relating to spontaneous magnetization, Curie temperature, anisotropy and magnetostriction constants; (c) micromagnetic properties such as domain walls and domain configuration in polycrysta!line and monocrystalline materials; (d) the dynamics of the magnetization process, and damping and resonance phenomena; and (e) the theoretical description, discussion and understanding of these properties in atomic terms, i.e., the arrangement of the ionic magnetic moments in sublattices, the quantum mechanics of magnetic interactions between localized moments, the spin-orbit interaction and dipole-dipole interaction as a cause of anisotropy. These methods of studying the properties of ferrites have acquired ~he status of a scientific standard, i.e., a paradigm, which has since been applied to many other materials. Garnets and hexagonal ferrites are examples of materials of industrial importance discovered and investigated along such lines. Other compounds of as yet more academic interest include sulphospinels and rare-earth chalcogenides.
20
U. ENZ
3.3. Garnets
The prototype of the family of garnets is the compound Mn3A12Si3012, a mineral and esteemed gemstone occurring in nature. The crystal structure of garnets is cubic with three different types of sublattices occupied by the three metals of the above compound. The garnets existing in nature often contain other ions as well and are in most cases non-magnetic. It is interesting to note that it was precisely the ferrimagnetic properties, discovered by Pauthenet (1956) and Bertaut et al. (1956) of some synthetic rare-earth iron garnets that attracted attention and opened up a new field of research in magnetism. Since then, a wealth of scientific and technological information on garnets has been produced. For more than two decades, publications on garnets have been appearing at a rate of about 200 papers a year, so that garnets and especially yttrium iron garnet (YIG), are now amongst the best known magnetic materials. One may agree with J.H. van Vleck who compared the role of Y I G for magneticians to that of the fruit fly to geneticists. Pioneering work on the chemical, crystallographic and magnetic properties of garnet was done by Geller et al. (1957), while Pauthenet (1957) investigated the magnetism of mixed rare-earth iron garnets, Re3FesO12, some of which were found to have compensation temperatures of the magnetization. These findings demonstrated directly their ferrimagnetic character and indicated that the magnetic moment of the rare-earth sublattice is oriented oppositely to the resulting moment of the two iron sublattices. The total magnetization of garnets is therefore relatively low as compared with that of magnetic metals or ferrites. The Curie temperatures, dominated by the iron-iron interaction, are of the order of 300°C, reflecting the same type of interaction mechanisms as those active in ferrites. Because the magnetization of garnets is lower than that of ferrites, garnets have not found bulk applications competing with ferrites, such as in transformers, coils, etc. One of the outstanding properties of YIG, which was discovered by Spencer et al. (1956) and Dillon (1957) shortly after the publication of the first papers on garnets, is its extremely low ferromagnetic resonance linewidth. Values of the linewidth A H of some oersteds were then measured, but subsequent improvements of crystal quality and purity yielded figures as low as A H = 0 . 1 0 e (8 A/m) at 10 MHz for carefully polished samples of Y I G (LeCraw et al. 1958). These exceptional resonance properties made Y I G very useful as a microwave device material, with loss figures one or two orders of magnitude lower than those of corresponding spinel ferrites. Moreover, Y I G also proved to have acoustic losses lower than quartz, thus opening up prospects for magneto-acoustic devices such as adjustable delay lines. Small amounts of rare-earth ions substituted into Y I G produced a dramatic increase in both anisotropy and linewidths. Such substituted materials were ideal objects on which to study the fundamentals of anisotropy (Kittel 1959) and relaxation processes (Dillon 1962, Teale et al. 1962), studies which contributed considerably to progress in the understanding of these mechanisms.
MAGNETISM AND MAGNETIC MATERIALS
21
Garnets are also outstanding in their optical properties: Y I G shows a low optical absorption in the range of visible light, so that layers up to several microns thick are transparent. With the aid of the magneto-optical Faraday effect, domain structures can be directly observed (Dillon 1958). Y I G m o r e o v e r exhibits a "window" of extremely low optical absorption in the infrared region. Optical absorption coefficients as low as c~ = 0.03 cm -1 for wavelengths between A = 1.2 ~ m and A = 4.4 p~m have been observed. The Faraday rotation of some garnets is large enough to m a k e the material suitable for magneto-optical devices such as light modulators and magneto-optical memories. In particular, garnets containing bismuth show a very high specific Faraday rotation, e.g., 0 = 3°/~m at A = 0.5 ~m for Y2.6Bi0.4Fe4Oa2 (Robertson et al. 1973). Bismuth-doped garnets have also proved to be suitable for use as fast switching magneto-optical display components (Hill et al. 1978). The non-magnetic yttrium aluminium garnet (YAG), was found to be an excellent laser host (Geusic et al. 1964). Garnets, especially Si-doped Y I G , are also interesting for their photomagnetic properties, i.e., the light-induced change of magnetic properties as a consequence of a light-stimulated redistribution of electrons or Fe 2+ ions (see Teale et al. 1967, Enz et al. 1971). Even greater prominence was achieved by the granets in their application as the leading magnetic bubble device material. Two basic contributions, both m a d e by Bobeck, opened up this new field. The first was the invention of the principle of high-density information storage with the aid of bubble domains (Bobeck 1967); the second was his observation of a growth-induced uniaxial anisotropy energy in garnets (Bobeck et al. 1970). B o b e c k ' s basic idea was to associate a bit of information, a digital one or zero, with the presence or absence of a bubble at some defined location and time. Bubbles are cylindrical domains of reversed magnetization occurring in nearly magnetized thin films having a sufficiently large uniaxial anisotropy. The dimensions of bubbles are mainly determined by the length l = trw/47rM2s, a material constant depending on the specific Bloch wall energy O-w and the saturation magnetization Ms. By controlling the magnetization of the garnet material the bubble diameters can be adjusted in a wide range from submicron size to tens of microns. The first observation of stable bubbles, which were in fact submicron bubbles, was made by Kooy et al. in 1960 in the hexagonal material BaFe120~9, a material with a rather high magnetization and a large uniaxial anisotropy. D u e to the microscopic dimensions of the bubbles, the packing density of the bubbles and thus the density of information can be very high; values of 1 0 6 bits cm -2 have been achieved, and densities higher than 1 0 7 bits c m -2 a r e considered to be attainable in the future. An extensive review of the physical and chemical properties of garnets has been given by Wang (1973) and a survey of garnet materials for bubble devices has been published by Nielsen (1976). The advent of bubble domain devices stimulated work in the field of crystal growth, both of bulk garnet crystals and of thin monocrystalline films grown by liquid phase epitaxy, known as the L P E method. Flux-grown bulk crystals were
22
U. E N Z
first prepared by Remeika in 1956, mainly for the purpose of studying fundamental properties. This art developed rapidly and the growth of large crystals of high perfection was finally mastered (Tolksdorf et al. 1978). L P E growth experienced a similar evolution, starting with the work of Shick et al. 1971, who grew films suitable for bubble devices. This method of preparation, which is an extension of flux growth, has now become the standard method of growing bubble device films. The growth procedure is as follows: a carefully polished wafer of a non-magnetic garnet crystal is immersed in a liquid consisting of a flux and the dissolved garnet. If the lattice misfit is controlled, the magnetic garnet grows isostructurally and without dislocations on the substrate. The films made in this way meet high standards of quality and reproducibility: composition and film thickness can be controlled within narrow limits and the remaining level of defects is low, which is reflected in the low values of the coercive fields achieved. Figure 12 shows bubbles and stripe domains in a Y G d T m epitaxial garnet film as observed with the aid of the Faraday effect. Figure 13 shows an overlay Y-bar structure of a shift register as processed on a garnet film (Bobeck and Della Torre 1975). A second scientific discipline which was greatly stimulated by the success of bubbles is that of the dynamics of domain walls and bubbles. Domain wall motion
U •
•
•
• •
•
•
•
•
..
i •
•
Fig. 12. Bubbles and stripe domains in a Y G d T m epitaxial garnet film 7 Ixm thick. The bias field is near to the run-out field. The bubble diameter is about 7 ixm (after Bobeck and Della Torre 1975).
MAGNETISM AND MAGNETIC MATERIALS
23
Fig. 13. Bubbles moving in a Y-bar pattern of a bubble shift register. Some propagation loops and the bubble generator (heavy black square) are shown (after Bobeck and Della Torre 1975).
has been studied in the past in the context of magnetization processes of magnetic bodies caused by domain wall displacements. A detailed understanding of the dynamic wall properties had not been reached along such lines owing to the extreme complexity of the process. This situation changed when perfect monocrystalline layers of garnets for bubble devices became available, which made it possible to study the motion of domain walls and bubbles by direct optical observation. As a result of this development, the body of experimental data on wall dynamics has greatly increased and the theoretical understanding of the mechanisms involved has deepened considerably. Amongst the new results is the insight that there is an upper limit to the velocity of a domain wall, a velocity limit which also marks a limit to the speed, i.e., the data rate of bubble devices. Extended reviews on the subject of wall and bubble dynamics have been published by Malozemoff and Slonczewski (1980) and also by de Leeuw et al. (1980).
24
U. ENZ
3.4. Permanent magnets
Permanent magnets, i.e., the magnesian stones, marked the beginning of magnetism. It is interesting to observe that, at present, permanent magnets are still being investigated, improved and increasingly applied. They are essential to modern life as components of a wide variety of electromechanical and electronic devices. It has been estimated that the average home contains more than fifty permanent magnets and every car uses an average about eight of them. The applications of permanent magnets range from loudspeakers, small electric motors and generators, door latches and toys, to ore separators, water filters, electric watches and microwave tubes. The function of a permanent magnet in these and other applications is to generate a magnetic field in an air gap of a magnet system. The air gap may either be fixed to accommodate moving electric conductors which exert external forces, a function performed by loudspeakers and electric motors, or it may be variable as it is in movable armatures on which the magnet exerts the force. The latter application is found in door latches, relays, telephone sets, magnetic levitation and contactless couplings between rotating shafts. Another typical application of permanent magnets is the alignment of an object by exerting a magnetic torque on it, as in a compass. A special application is found in electron tubes where permanent magnets are used for controlling the orbits of electron beams or for focussing them. Table 2 shows a number of functions performed by permanent magnets together with the corresponding applications. The four functions described cover the main applications of permanent magnets; they include the conversion of electrical into mechanical energy and vice versa, and the exertion of mechanical forces on material bodies and on moving charge carriers. Figures 14 and 15 give an impression of two of the most common applications of permanent magnets, the loudspeaker and the small motor (after Zijlstra 1976). The early development of permanent magnet materials proceeded entirely by trial and error. Nevertheless 100 years ago bar and horseshoe magnets made from TABLE 2 Typical functions and applications of permanent magnets with some examples of machines, devices and components (after Zijlstra 1974) Function
Application
Conversion of electrical into mechanical energy and vice versa
Small electric motors, dynamos, loudspeakers, microphones, eddy-current brakes, speedometers, magnetos
Exerting a force on a ferromagnetically soft body
Relays, couplings, bearings, clutches, magnetic chucks and clamps, separators (extraction of iron impurities, concentration of ores)
Alignment with respect to a field
Positioning mechanisms (e.g. stepping motors), compasses, some ammeters
Exerting a force on moving charge carriers
Magnetrons, travelling-wave tubes, some cathode-ray tubes, Hall plate
MAGNETISM AND MAGNETIC MATERIALS
25
Fig. 14. Cut-away view of a loudspeaker containing a Ferroxdure ring.
Fig. 15. Cut-away view of a windscreen wiper. The stator field is provided by two Ferroxdure segments.
26
U. ENZ
carbon steel were well known and widely used. Since then an unparallelled development has taken place; new permanent magnet materials have been discovered and the existing ones improved. The foundations for the scientific understanding of permanent magnets have also been laid in this period. The relevant figure of merit expressing the quality of a permanent magnet is its maximum energy product (BH).... This figure describes the ability of a permanent magnet to withstand the influence of a counteracting magnetic field. Moreover the energy product is a measure of the useful magnetic flux that can be produced by the magnet in a given volume. Figure 16 shows the magnetic flux density B plotted as a function of the magnetic field H, i.e., the well-known hysteresis loop. The shaded area represents the (BH)max product; the optimum working point of the loop is that which defines the largest area. As an illustration of the achievements of the past, the energy product is plotted in fig. 17 as a function of time, starting in 1880. Since then, the (BH)max values have increased by a factor of more than 100. This great achievement was not realized by improving a single material, but rather by the discovery of new classes of material. Each new finding was followed by a period of technological improvement, which in turn was followed by a new discovery. The figure gives the top values reached in any year. The sequence starts with carbon steels and tungsten steels at the end of the last century and is continued with cobalt-containing steels around 1920. A major advance in magnetic materials was made in 1932, when the development of the Alnico magnets started with Mishima's AINiFe alloy (Mishima 1932). In the illustration the various members of this family are indicated as Tic II, Tic G (Jonas et al. 1941) etc. The coercive force of Alnico magnets was essentially doubled as compared with earlier materials; these magnets were the first to be truly p e r m a n e n t under adverse conditions such as stray fields, shock and elevated temperature. The magnetic and mechanical hardness of the Alnico alloy is due to
Fig. 16. Hysteresis loop showing the optimum working point of a permanent magnet. The hatched rectangle represents the maximum energy product of the material.
MAGNETISM AND MAGNETIC MATERIALS
27
(BHlrnax (MG Oe) 100
// / /
50
/
20
(Sin, Pr) Cos (.1/ Sm C o 5 / ~
10 5 // 2
//
/
oFxd 330
tlTic lI
//M is~j.I, el* FxdlO0
1
0.5 0.2
,/ I W-steel C-steel
0.1 i
i
i
i
/
I
1880 1900 1920 19~0 1960 1980 = year Fig. 17. Development of the maximum energy products of permanent magnets between 1880 and 1980. Most data are due to Van den Broek and Stuijts (1977). 7
a thermal treatment leading to the precipitation of a second phase in a finely dispersed form. This development culminated with Ticonal XX, an Alnico alloy hardened in the presence of a magnetic field which leads to the precipitation of oriented second-phase particles of elongated shape (fig. 18). The maximum energy product reached was about 11 M G O e (90 kJm -3) (Fast a n d r e Jong 19591)/. The next breakthrough in the development of high energy product materials was made with rare-earth transition metal compounds. The systematic investigation of the physical and magnetic properties of these alloys and compounds started around 1960 at Bell Laboratories (Nesbitt et al. 1961). However it was Strnat who realized the potential of these compounds for high energy-product magnets and vigorously promoted their development (Strnat et al. 1966). In 1969, Das of the Raytheon Company announced that he had made a magnet having an energy product of 20 M G O e (160 kJm -3) by sintering SmCos. Even higher values, up to 35 M G O e (280 kJm-3), were recently reported to have been obtained in a related material of the formula (RE)2(CoFe)17 (Wheeler report, 1979)*. This quasi-binary intermetallic phase was again prepared by sintering. It is interesting * Wheeler Associates, Inc., 1979, Rare Earth-Cobalt permanent magnets, Elizabethtown, Kentucky, USA.
28
U. ENZ
Fig. 18. Micrograph of Ticonal XX (after De Vos, thesis, Delft, 1966). to note in fig. 17, that the energy product, plotted as a function of time, follows an approximately linear dependence throughout the period reported. The material quoted last yields the top value of the energy product reached up till now. It is possible to reach still higher values of (BH)max? Rathenau (1974) discussed this 1 2 question in detail and showed that the limit of (BH)max is given by ~Bs for any material, provided the coercive field and the anisotropy can be made strong enough. The saturation magnetization of iron or iron cobalt alloys is high enough to allow for a further increase of (BH)max by a factor of four. In addition to the materials discussed, which follow a straight line, fig. 17 also contains materials indicated as Fxd 100 and Fxd 300. The energy products of these materials fall clearly below the general trend. They are typical representatives of the family of low cost permanent magnet materials having a medium energy product, the hexagonal oxides. If we plot the price per unit energy product of various materials (fig. 19) we observe another systematic correlation, the continuous progress made in improving the economy of permanent magnets. In this plot the hexagonal oxides occupy a leading position and are the end point of a long development. The importance of ferrimagnetic hexagonal oxides for permanent magnets was first pointed out in 1952 by Went et al. A detailed account of these magnetically hard materials, called Ferroxdure, and their history has been given recently by Van den Broek and Stuijts (1977). The opinion expressed at the time of discovery was that these new materials were of great economic importance. That opinion has been fully confirmed: the total world production of magnetically hard f e r r i t e s - which, in composition and crystal structure, all belong
MAGNETISM A N D M A G N E T I C M A T E R I A L S
l
100
29
T S'mCo5
50 price per unit of energy 20
' P t Co I Tic xx /
C-steel
•___. W.-steel •~ ,~,~ Co-steel
10 Q
%
5
Tic ff X
2
Tic
1
0.5
Tic GG
\NPZFxd 100 \ \ \ \ ~ F x d 330 \
0.2 0.1
1800 '90 1900 '10
'20
'30
%0 '50
'60 '70 '80 '9 2 = year
0
Fig. 19. Price per unit of energy product (after Rathenau 1974). to the same g r o u p - is now estimated at about 100,000 tonnes a year (1980), with a value of some 400 million dollars. Figure 20 shows how these ferrites have acquired an ever increasing share of the world production of p e r m a n e n t magnets, measured in tonnes per annum. C o m p a r e d with other materials for p e r m a n e n t magnets, Ferroxdure is characterized by an exceptionally high coercivity, combined with a r e m a n e n c e which, though not very high, is valuable for practical purposes. With such a material it became possible to produce magnets of shapes such that would have almost completely demagnetized themselves if made of a different material. Typical shapes were flat ring magnets, magnetized perpendicular to the plane of the ring, or transversely magnetized rods with m a n y north and south poles closely adjacent to each other. Ferroxdure is also highly resistant to external demagnetizing fields, as encountered in D C motors, for example. These novel properties were exploited on a large scale, e.g., for making flat loudspeakers and compact D C motors (see figs. 14 and 15). The great economic success of Ferroxdure is due in the first place, however, to the low price per unit of available magnetic energy (fig. 19). The material is therefore mainly used not so much as a technical i m p r o v e m e n t but m o r e as a substitute for m o r e expensive components, such as Ticonal magnets in loudspeakers or stator coils of windscreen-wiper motors. Ferroxdure is inexpensive because it does not contain any rare material such as nickel or cobalt, and it is relatively easy to manufacture: it is only necessary to "mix a few cheap oxides" and to " b a k e them to the right shape". Finally, Ferroxdure - an oxide - has a high electrical resistivity, so that there are
30
U. ENZ
)roduction (kt) 100
tot 20
10
//~lloys
5
I
L
I
I
I
I
L
I
1900 '10 '20 '30 '/.0 '50 '60 '70 '80 year Fig. 20. Estimate of the world production of permanent magnets (after Rathenau 1974). hardly any eddy-current losses. This is an important advantage in radio-frequency applications and also in certain types of electric motors. A disadvantage is the relatively high temperature coefficient of the remanence and the coercivity. This makes the material less suitable for certain professional applications. In 1954 the material was substantially improved by orienting the crystallites (Stuijts et al. 1954, 1955). In isotropic material the magnetic moments of the crystallites, in zero field after saturation, are randomly distributed over a hemisphere. In anisotropic Ferroxdure, on the other hand, which is the material now most widely used, the c-axes and hence the moments after saturation are approximately parallel. Consequently the remanence is about twice as great and (BH)max is about four times higher. At the time it was a surprise that the attempts to produce crystal-oriented Ferroxdure were so successful. It was feared, quite reasonably, that the orientation of the crystallites, achieved with much difficulty in the compacted product, would be lost during sintering. The result exceeded all expectations: the texture was not only preserved but was even greatly improved.
4. Trends in magnetism research and technology
4.1. Magnetism research between physics, chemistry and electronics On studying the ways to progress in magnetism one observes that magnetism research has an interdisciplinary character and depends in an essential way on the
MAGNETISM AND MAGNETIC MATERIALS
31
cooperation of scientists and engineers working in fields quite different from each other. The various disciplines relevant for magnetism research range from fundamental theoretical physics through chemistry to electric and electronic engineering. The cooperation of these disciplines is of such a type that the preparation and chemical or crystallographical study of new materials may stimulate physical work, or alternatively that the discovery of a physical effect in one material may stimulate the search for other classes of material showing analogous effects. A similar mutual relation is observed between engineering efforts facing material problems and basic material studies concentrating on the relevant critical parameters. Last but not least, and most commonly recognized, the discovery of new materials or of new physical effects may stimulate new engineering applications. This special character of magnetism research has consequences for the organization of research and development laboratories. An organizational structure concentrating the various disciplines in multidisciplinary units or groups is probably the most adequate form. Indeed, the study of the case histories of m a j o r innovations seems to show that those research laboratories which have such an organization are most likely to produce outstanding results. This applies equally for university laboratories organized as "material centers", government institutes and industrial laboratories. In the last category the multidisciplinary approach has an even stronger weight as engineering aspects are included. Examples of research successes obtained by the cooperation of experts in different disciplines are easily at hand. In fact some have already been described in this chapter. The early industrialization of ferrites is an example in which chemistry, crystallography, physics and telecommunication technology were equally indispensable for success. Other examples are the discovery of garnets, the invention of the gyrator or the development of bubble devices. In all cases the study of materials played a central role. Some remarks concerning the growth of magnetism research may be made here. Before the second world war only few laboratories were active in this field, and with some famous exceptions, magnetism was not usually a subject of research at universities. Since then the n u m b e r of laboratories occupied with magnetism has largely increased. In particular many new or existing university institutes turned to studies in this field. As a consequence the n u m b e r of investigations has much increased and more and more detailed studies of materials were made. The industrial laboratories, on the other hand, did not much grow in n u m b e r or size, so that their share, especially concerning fundamental studies, has diminished. The few government or national research centers which were traditionally active in magnetism research maintained their position and continued their important role.
4.2. Trends in applied magnetism In this outlook into the future of applied magnetism we try to indicate some trends which are discernable at this m o m e n t and which will probably be of importance for some time to come (see, Wijn 1976). We have seen that magnetic materials
32
U. ENZ
are used for a wide variety of different functions such as transformers, various types of inductive elements or m e m o r y cores. C o m m o n to most of these applications is the use of materials prepared separately in bulk form. The processed material is then assembled into the magnetic device as a separate part. Since some years, however, there seems to be a tendency towards the use of materials as an integrated part of the device. In m a n y cases the magnetic material is present in the form of a thin layer, having a monocrystalline, polycrystalline or amorphous structure. The layers are often structured or shaped by methods known from integrated circuit technology. The purpose is to reach a miniaturization also in the case of magnetic materials and to give it its shape in situ. Modification or control of the local compositions and the local magnetic properties of a thin film, e.g., by means of ion implantation, is another aspect of the tendency described here. A second development is aimed at the control of the position and displacement of individual domain walls in monocrystalline or oriented polycrystalline layers. The bubble devices are a good example for this tendency. Such devices depend, apart from a successful miniaturization, in an essential way on the mastering of the material properties, the material perfection and the internal stress distribution. Some examples of these tendencies in device development will now be given, starting with the magnetoresistive reading heads used in magnetic recording. Reading of the information recorded on a magnetic tape is usually achieved by picking up the stray flux passing the air gap of an inductive reading head. T h e electric signal induced in the windings of the head is proportional to the rate of change of the flux. In the magnetoresistive reading head proposed some time ago (Hunt 1971), the flux itself is measured with the aid of the magnetoresistive effect in a thin film of Permalloy. The effect depends on the angle 0 between the direction of the current flowing through the film and the direction of the magnetization. The latter is modulated by the stray flux of the tape. To obtain a linear characteristic the equilibrium angle 0 should be 45 °. An elegant solution is achieved in the so-called " B a r b e r pole configuration" (Kuijk et al. 1975) in which the direction of the current flow is forced into the desired direction with the aid of parallel conductor strips (see fig. 21).
i Ni'Fe
// z - - current flow
Fig. 21. Magnetoresistive reading head based on the "Barberpole configuration". The magnetization of the NiFe film is parallel to the vector M, the current is forced, by conducting bars, into a direction parallel to the vector I. The optimum angle 0 is 45° (after Kuijk et al. 1975).
MAGNETISM AND MAGNETIC MATERIALS
33
Closely related to this example are the thin film integrated recording heads of the inductive variety. Here the emphasis is on reading and writing many tracks on the tape or disc simultaneously. Accordingly the heads are made in large number in integrated form by a batch process using thin film and photolithographic techniques (Romankiw 1970). In combination with solid state integrated circuits a new and very attractive approach of magnetic recording becomes feasible in such a way (fig. 22). A similar development toward miniaturization can be observed with inductors. The L-chip, a miniaturized self inductance based on multiple coils printed on ferrite substrates, is being developed at present. The second main trend, the control of magnetic domain walls and domain structures at a micromagnetic level is manifest in bubble domain devices and domain control in Fe-Si sheet. Both fields have already been discussed in the present survey. Also thermomagnetic recording can be viewed as an example of this line. The basic idea of this storage principle has been proposed long ago (Mayer 1958), but new interest has arisen recently (Berkowitz and Meiklejohn 1975). The information is stored in small regions of reversed magnetization in a thin magnetic film. Unlike the situation with bubbles, these domains remain fixed. Reversal of the magnetization is achieved by reducing locally the coercive force of the film by heating with the aid of a focussed light beam. The information is read by using the Faraday effect. The bits of information are accessed by mechanical motion. Film materials include GdFe, MnBi and garnet films. The
Fig. 22. Array of integrated recording heads shown in a fabrication stage prior to cutting off the front part. The individual heads carry 6 windings (courtesy of W.F. Druyvesteyn, Philips Research Laboratories).
34
U. ENZ
large Faraday effect of some substituted garnets is also used in a different type of device, proposed recently (Hill 1980), the integrated light modulation matrix. The matrix consists of isolated islands etched from a garnet film (fig. 23), which can be switched individually by a cross bar system. The switching of an island occurs by a single Bloch wall, and is initiated by local heating of the island. These examples sufficiently demonstrate the trend mentioned and show that magnetic materials provide an environment in which rather naturally we can build and control certain kinds of objects having dimensions in the micron or submicron range, a region which is generally not readily accessible. The examples also show that applied magnetism is still very much alive.
~ranspareniresis]Gnce,J
q
d
'
I
subsirate
y-bus
Fig. 23. Light modulating matrix based on switching cells of iron garnet single crystal films, with x-y addressed resistance network (after Hill 1980).
4.3. Outlook and acknowledgement In this contribution we have sketched the early historical lines leading to the present edifice of magnetism, and indicated its importance for modern industry and society as a whole. Some material classes received more detailed attention in both the way they developed and their achievements. These materials represent only a very small fraction of those which have been studied. Moreover, many achievements in the explanation of material properties and their theoretical understanding have hardly been touched upon. In this context we note that the amount of knowledge and detailed information on the properties of magnetic
MAGNETISM AND MAGNETIC MATERIALS
35
m a t e r i a l s has a c c u m u l a t e d t o s u c h a d e g r e e , t h a t it is b e c o m i n g i n c r e a s i n g l y difficult t o k e e p sight o n t h e w h o l e of i n f o r m a t i o n . P e r h a p s it is w o r t h w h i l e t o c o n s i d e r t h e f e a s i b i l i t y of t h e i n s t a l l a t i o n of a d a t a b a n k c o n t a i n i n g i n f o r m a t i o n o n magnetic materials. T h e a u t h o r w o u l d l i k e to t h a n k P r o f . G . W . R a t h e n a u , P r o f . H . P . J . W i j n , D r . R . P . v . S t a p e l e , D r . D . J . B r e e d a n d D r . P . F . B o n g e r s of this l a b o r a t o r y , f o r a d v i c e a n d c r i t i c a l r e a d i n g of t h e m a n u s c r i p t of this c o n t r i b u t i o n .
References Albers-Schoenberg, E., 1954, J.A.P. 25, 152. Barrett, W.F., W. Brown and R.A. Hadfield, 1900, Sci. Trans. Roy. Dublin Soc. 7, 67. Berkowitz, A.E. and W.H. Meiklejohn, 1975, IEEE-MAG 11,997. Bertaut, F. and F. Forrat, 1956, C.R. Acad. Sc. 242, 382. Bobeck, A.H., 1967, Bell Syst. Tech. J. 46, 1901. Bobeck, A.H. and E. Della Torre, 1975, Magnetic Bubbles (North-Holland, Amsterdam). Bobeck, A.H., E.G. Spencer, L.G. van Uitert, S.C. Abrahams, R.L. Barnes, W.H. Grodkiewicz, R.C. Sherwood, P.H. Schmidt, D.H. Smith and E.M. Waiters, 1970, Appl. Phys. Lett. 17, 131. Bragg, W.H., 1915, Phil. Mag. 30, 305. Brockmann, F.G., H. van der Heide and M.W. Louwerse, 1969, Philips Tech. R. 30, 323. Das, D.K., 1969, IEEE-MAG 5, 214. De Bruyn, R. and G.J. Verlinde, 1980, Philips Elcoma Division, Eindhoven, private communication. Dillon, J.F., 1957, Phys. Rev. 105, 759. Dillon, J.F., 1958, J.A.P. 29, 539. Dillon, J.F., 1962, Phys. Rev. 127, 1495. Enz, U., R. Metselaar and P.J. Rijnierse, 1971, J. de Phys. 32, C1-703. Fast, J.D. and J.J. de Jong, 1959, J. de Phys. Radium 20, 371. Forestier, H., 1928, Ann. de Chim. 10e srr. 9, 316. Forrester, J.W., 1951, J.A.P. 22, 44. Geller, S. and M.A. Gilleo, 1957, Acta Cryst. 10, 239. Geusic, J.E., H.M. Marcos and L.G. van Uitert, 1964, Appl. Phys. Lett. 4, 182. Gorter, E.W. and J.A. Schulkes, 1953, Phys. Rev. 90, 487. Goss, N.P., 1935, Trans. Am. Soc. Metals, 23, 511.
Griffiths, J.H.E., 1946, Nature, 158, 670. Gumlich, E. and P. Goerens, 1912, Trans. Farad. Soc. 8, 98. Hill, B., 1980, IEEE-ED 27, 1825. Hill, B. and K.P. Schmidt, 1978, Philips J. Res. 33, 211. Hilpert, S., 1909, Ber. Deutsch. Chem. Ges. Bd 2, 42, 2248. Hogan, C.L., 1952, Bell Syst. Tech. J. 31, 1. Hornsveld, L., 1980, Philips Elcoma Division, private communication. Hunt, R.P, 1971, IEEE-MAG 7, 150. Jacobs, I.S., 1969, J.A.P. 40, 917. Jonas, B. and H.J. Meerkamp van Embden, 1941, Philips Tech. Rev. 6, 8. Kittel, C., 1959, Phys. Rev. Lett. 3, 169. Kooy, C. and U. Enz, 1960, Philips Res. Rep. 15, 7. Kuijk, K.E., W.J. van Gestel and F.W. Gorter, 1975, IEEE-MAG 11, 1215. LeGraw, R.C., E.G. Spencer and C.S. Porter, 1958, Phys. Rev. 110, 1311. Leeuw, F.H. de, R. van den Doel and U. Enz, 1980, Rept. Progr. Phys. 43, 689. Luborsky, F.E., P.G. Frischmann and L.A. Johnson, 1978, J. Magn. Mag. Mat. 8, 318. Malozemoff, A.P. and J.C. Slonczewski, 1979, Physics of magnetic domain walls in bubble materials (Academic Press, New York). Mattis, D.C., 1965, Theory of Magnetism (Harper and Row, New York). Mayer, L., 1958, J.A.P. 29, 1454. Mishima, T., 1932, Iron Age, 130, 346. N6el, L., 1948, Ann. de Phys. 3, 137. Nesbitt, E.A., H.J. Williams, J.H. Wernick and R.C. Sherwood, 1961, J.A.P. 32, 342 S. Nielsen, J.W., 1976, IEEE-MAG 12, 327. Nishikawa, S., 1915, Proc. Tokyo Math. Phys. Soc. 8, 199. Pauthenet, R., 1956, C.R. Acad. Sc. 242, 1859. Pauthenet, R., 1957, Thesis, Grenoble, France.
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Rajchman, J.A., 1952, RCA Rev. 13, 183. Rathenau, G.W., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam (Bond voor Materialenkennis, P.O. Box 9321, Den Haag, The Netherlands) p. 7. Remeika, J.P., 1956, J. Am. Chem. Soc. 78, 4259. Robertson, J.M., S.W. Wittekoek, Th.J.A. Popma and P.F. Bongers, 1973, Appl. Phys. 2, 219. Romankiw, L.T., I.M. Croll and M. Hatzakis, 1970, IEEE-MAG 6, 597. Shick, L.K. and J.W. Nielsen, 1971, J.A.P. 42, 1554. Shull, C.G., E.O. Wollan and W.C. Koeler, 1951, Phys. Rev. 84, 912. Six, W., 1952, Philips Tech. Rev. 13, 301. Snoek, J.L., 1936, Physica, 3, 463. Snoek, J.L., 1947, New Devel. in Ferromagn. Materials (Elsevier, Amsterdam). Snyderman, N., 1977, Electronics News, 28 November. Spencer, E.G., R.C. LeCraw and F. Reggia, 1956, Proc. IRE 44, 790. Strnat, KJ., G.J. Hoffer, W. Ostertag and I.C. Olson, 1966, J.A.P. 37, 1252. Stuijts, A.L., G.W. Rathenau and G.H. Weber, 1954/1955, Philips Tech. Rev. 16, 141. Taguchi, S., T. Yamamoto and A. Sakakura, 1974, IEEE-MAG 10, 123. Takai, T., 1937, J. Electrochem. Japan, 5, 411.
Teale, R.W. and D.W. Temple, 1967, Phys. Rev. Lett. 19, 904. Teale, R.W. and Tweedale K., 1962, Phys. Lett. 1,298. Tebble, R.S. and D.J. Craik, 1969, Magnetic Materials (Wiley, London) 520. Tellegen, B.D.H., 1948, Philips Res. Rep. 3, 81. Tolksdorf, W. and F. Welz, 1978, Crystal growth of magnetic garnets from high temperature solutions, in Crystals Vol. 1 (Springer, Berlin). Van den Broek, C.A.M. and A.L. Stuijts, 1977, Philips Techn. Rev. 37, 157. Verwey, E.J.W. and E.L. Heilmann, 1947, J. Chem. Phys. 15, 174. Vos, K.J. de, 1966, Thesis, Delft. Wang, F.Y., 1973, in: Treatise on Materials Science and Technology, ed., H. Herman (Academic Press, New York) 279. Weiss, P., 1907, J. Phys. 6, 661. Went, JJ., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/1952, Philips Techn. Rev. 13, 194. Wijn, H.P.J., 1970, Proc. Int. Conf. Ferrites, Kyoto. Wijn, H.P.J., 1976, Physics in Industry (Pergamon, Oxford) 69. Williams, H.J. and W. Shockley, 1949, Phys. Rev. 75, 178. Zijlstra, H., 1974, Philips Tech. Rev. 34, 193. Zijlstra, H., 1976, Physics in Technology (May), 98.
chapter 2 PERMANENT MAGNETS; THEORY
H. ZlJLSTRA Philips Research Laboratories Eindhoven The Netherlands
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-HollandPublishing Company, 1982 37
CONTENTS 1. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. G e n e r a l p r o p e r t i e s a n d a p p l i c a t i o n s . . . . . . . . . . . . . . . . 1.2. T h e h y s t e r e s i s l o o p . . . . . . . . . . . . . . . . . . . . . 2. Suitability criteria for a p p l i c a t i o n s . . . . . . . . . . . . . . . . . . 2.1. T h e e n e r g y p r o d u c t . . . . . . . . . . . . . . . . . . . . . 2.2. T h e m a g n e t i c free e n e r g y . . . . . . . . . . . . . . . . . . . 3. M a g n e t i c a n i s o t r o p y . . . . . . . . . . . . . . . . . . . . . . 3.1. A n i s o t r o p y field a n d coercivity a s s o c i a t e d w i t h m a g n e t i c a n i s o t r o p y . . . . . 3.2. S h a p e a n i s o t r o p y . . . . . . . . . . . . . . . . . . . . . . 3.3. M a g n e t o c r y s t a l l i n e a n i s o t r o p y . . . . . . . . . . . . . . . . . . 4. F i n e p a r t i c l e s . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Critical r a d i u s for s i n g l e - d o m a i n particles . . . . . . . . . . . . . . 4.2. B r o w n ' s p a r a d o x . . . . . . . . . . . . . . . . . . . . . . 5. C o e r c i v i t y a s s o c i a t e d w i t h s h a p e a n i s o t r o p y . . . . . . . . . . . . . . 5.1. P r o l a t e s p h e r o i d . . . . . . . . . . . . . . . . . . . . . . 5.2. C h a i n of s p h e r e s . . . . . . . . . . . . . . . . . . . . . . 6. C o e r c i v i t y a s s o c i a t e d with m a g n e t o c r y s t a l l i n e a n i s o t r o p y . . . . . . . . . . 6.1. M a g n e t i z a t i o n r e v e r s a l by d o m a i n wall p r o c e s s e s f o r / * 0 / / A > Js . . . . . . 6.2. T h e 180 ° d o m a i n wall . . . . . . . . . . . . . . . . . . . . 6.2.1. E n e r g y a n d w i d t h of a 180 ° d o m a i n wall . . . . . . . . . . . . 6.2.2. T h e e x c h a n g e e n e r g y coefficient A . . . . . . . . . . . . . . 6.3. I n t e r a c t i o n of d o m a i n walls w i t h cavities a n d n o n - f e r r o m a g n e t i c i n c l u s i o n s 6.3.1. D o m a i n - w a l l p i n n i n g at l a r g e i n c l u s i o n s . . . . . . . . . . . . 6.3.2. N u c l e a t i o n of r e v e r s e d o m a i n s at l a r g e i n c l u s i o n s . . . . . . . . . 6.3.3. D o m a i n - w a l l p i n n i n g at small i n c l u s i o n s . . . . . . . . . . . . 6.4. D o m a i n - w a l l n u c l e a t i o n at surface defects . . . . . . . . . . . . . 6.5. I n t e r a c t i o n of d o m a i n walls w i t h the crystal lattice . . . . . . . . . . 6.5.1. W a l l p i n n i n g at r e g i o n s w i t h d e v i a t i n g K and A . . . . . . . . . 6.5.2. P i n n i n g of a d o m a i n wall by an a n t i p h a s e b o u n d a r y . . . . . . . . 6.5.3. N u c l e a t i o n of a d o m a i n wall at an a n t i p h a s e b o u n d a r y . . . . . . . 6.5.4. T h i n - w a l l c o e r c i v i t y in a perfect crystal . . . . . . . . . . . . 6.5.5. P a r t i a l wall p i n n i n g at d i s c r e t e sites . . . . . . . . . . . . . 7. I n f l u e n c e of t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
39 39 4O 42 42 46 49 49 52 53 55 55 6O 6O 60 64 66 66 67 67 69 74 76 78 78 80 81 81 88 93 94 98 100 104
1. Introduction
1.1. General properties and applications The appearance of permanent-magnet materials such as alnico (Jonas et al. 1941) and hexaferrite (Went et al. 1951) with much better properties than materials previously in use was followed by a great increase in the applications of the permanent magnet. Compared with electromagnets (including power supplies) permanent magnets offer the advantage of a larger ratio of the useful magnetic field volume to the volume of the magnet system. Their usefulness is of course particularly apparent where a constant magnetic field is required. As is widely known, the constancy of the externally generated field is related to the magnetic "hardness" of the material, that is to say the extent to which the material retains its magnetization in opposing fields. In this way the p o l a r i z a t i o n - a n d therefore the external f i e l d - of a p e r m a n e n t magnet is maintained. A particular example of an opposing field is the internal field of the poles of the magnet itself. In this case the demagnetizing action is again unable to destroy the polarization of the magnet. The present increasing interest in the further development of hard magnetic materials is explained in part by the growing demand for miniaturization in modern technology. The problem of heat dissipation is inseparable from miniaturization, and the substitution of permanent magnets for electromagnets obviously goes a long way towards solving that problem. To ensure the most effective development it is desirable to start by investigating the likely applications of permanent magnets. The next step is to decide on the criteria that indicate suitability for these applications. These criteria can then provide a pattern for the production of tailor-made magnetic materials. This calls for insight into the effects that variation of such properties as remanence and coercivity has on the suitability of the materials for a particular application, and it also requires knowledge of the physical background. This will be the main subject of the present chapter. Table 1 lists various machines, devices and components in which permanent magnets are nowadays used. The classification is based on four principles: - m e c h a n i c a l energy is converted into electrical energy (or vice versa) in the magnetic field; - t h e permanent magnet exerts a force on a ferromagnetically soft body; 39
40
H. ZIJLSTRA
TABLE 1 Examples of machines, devices and components using permanent magnets, classified by four functions which the magnet can perform. Function
Application
Conversion of electrical in'~o mechanical energy and vice versa
Small electric motors, dynamos, loudspeakers, microphone% eddy-current brakes, speedometers, magnetos
Exerting a force on a ferromagneticaUy soft body
Relays, couplings, bearings, clutches, magnetic chucks and clamps, separators (extraction of iron impurities, concentration of ores)
Alignment with respect to a field
Positioning mechanisms (e.g., stepping motors), compasses, some ammeters
Exerting a force on moving charge carriers
Magnetrons, travelling-wave cathode-ray tubes, Hall plates
tubes,
some
- t h e permanent magnet is subjected to a directional force exerted by a magnetic field; - t h e permanent magnet exerts a force on moving charge carriers, e.g., a beam of electrons in a vacuum. In sections 2.1 and 2.2 the two main suitability criteria are discussed which together cover almost the entire field of applications. They are the maximum energy product and the maximum change in the magnetic free energy. Applications not covered by these criteria can be found among the positioning mechanisms in table 1. Apart from the fact that the existing applications provide an incentive to search for better magnetic materials, the converse is of course equally true: better magnets lead to applications that had not previously been thought of or did not seem feasible.
1.2. The hysteresis loop Permanent magnet materials are characterized by high coercivities and high remanent magnetizations. Before proceeding with the discussion of the structural parameters that determine the hard magnetic properties, we must first define the parameters that are generally used to specify the magnetic properties of permanent magnets. We employ the International System of Units (SI) in which the magnetic flux density B is expressed as either B =/~o(H + M ) , or
B =/~oH + J ,
PERMANENT MAGNETS; THEORY
41
where M and J are are the local material contributions to the flux density, respectively called magnetization and magnetic polarization, and H is the con: tribution from all other sources and is called magnetic field strength. The quantities H and M are measured in A m -1 (1 A m -1 = 4~r x 10 - 3 0 e ) . The quantities B and J are measured in Vsm -2 or tesla (1 T = 10 4 Gauss). The vacuum permeability ~0 is equal to 47r x 10 -7 V s A -1 m -t (or Hm-1). Both expressions for B will be used in this chapter. Although magnetic polarization is the official n a m e for J it will often be called magnetization. If the magnetization M or J of a p e r m a n e n t magnet material is plotted as a function of the applied field H a hysteresis loop is obtained in which the magnetization is not a unique function of H, but depends on the direction and magnitude of previously applied fields. A typical hysteresis loop is shown in fig. 1. The initial magnetization curve starting at the origin is obtained when the material is in a thermally demagnetized state. If the m a x i m u m applied field H m is sufficient to saturate the material the loop is referred to as a saturation loop. When the applied field is reduced the magnetization decreases to the r e m a n e n t magnetization J,, which is generally less than the saturation magnetization Js. In an efficient p e r m a n e n t magnet material Jr is usually 0.8-1.0Js. If the material is subjected to a demagnetizing field (i.e. a negative applied field H ) the magnetization is gradually reduced and at a critical field - H = jHc the magnetization is zero. This critical field jHc is known as the magnetization coercivity and is defined as the reverse field required to reduce the net magnetization of the material to zero in the presence of the field. The latter qualifying statement is necessary because if the field is r e m o v e d the specimen may return to a small positive r e m a n e n t magnetization J; < Jr. Instead of J we can plot the magnetic
/Z jHc k
/]I//] .,11] /
Fig. 1. Saturation hysteresis loop for magnetic flux density B as a function of H (drawn) and for magnetization J as a function of H with initial magnetization curve (dashed).
42
H. ZIJLSTRA
flux density B = / x 0 H + J as a function of H (drawn line in fig. 1). We then obtain the flux hysteresis loop with remanence Br = Jr and with a smaller value of the coercivity which is here called the flux coercivity ~Hc. Note that by these definitions the coercivities are positive numbers quantifying negative field strengths. It should be emphasized that the coercivities jHc and BHc are assumed to correspond to demagnetization of the saturated material, though we shall see later that permanent magnet materials are rarely if ever absolutely saturated even in exceptionally high fields. Unless otherwise stated, it can usually be safely assumed that the values of Hc quoted in the various scientific journals, books and papers refer to the "saturation" values as defined above. In the following the prefix J will be omitted when jH~ is discussed.
2. Suitability criteria for applications 2.1. The energy product
The extent to which a material will be suitable for applications in which electrical energy plays a part (the first groups in table 1) depends on the amount of magnetic flux linkage per metre squared and the maximum opposing field that can be tolerated without loss of polarization. The product of the flux density B and the associated opposing field H, referred to as the energy product, is a useful measure of the performance of a particular magnet, since it is proportional to the potential energy of the field in the air gap. It is useful only, however, when the magnet is not disturbed by fields from another source. To determine the energy product it is of course necessary to have information about the hysteresis loop of the material (fig. 2). A permanent magnet that is subject only to the influence of its own field will be in a state represented by a working point in the second (or the fourth) quadrant of the hysteresis loop. In these quadrants the field is opposed to the flux density, and is referred to as the demagnetizing field. It can be shown quite generally that the occurrence of a magnetic field outside the permanent magnet does in fact relate to a field inside the magnet with B and B
Fig. 2. Part of a magnetic hysteresis loop for magnetic flux density B; the shaded area is equal to the maximum energy product (BH)....
PERMANENT MAGNETS; THEORY
43
/ - / i n opposition. To do this, we have to apply Maxwell's equations to a situation in which there are no electric currents (apart from the circular currents on an atomic scale, which are the carriers of the magnetization of the material). The magnetic field strength H then satisfies curl H = O, and for the flux density B we always have div B = 0. For a permanent magnet of finite dimensions we may therefore deduce (Brown 1962a)
fn(H.
B ) d V = 0,
(2.1)
where the integration is performed over the complete space R. If this integral is written as the sum of the integral over the volume (Rrnagn) of the permanent magnet and the integral over the rest of the complete space (Rrest), then
~Rmagn (/~r B)
dV
= --fRrest(H- B) dV.
Assuming that the space Rrest is " e m p t y " , i.e., contains no magnetic substances, then the flux density there is given by B =/x0H. The right-hand side of the last equation is then negative, which is possible only if B and H inside the magnet are of opposite sense or at least include an obtuse angle at least somewhere. This result is not affected if Rrest contains soft magnetic material in which B and H always have the same direction. It can also be shown directly from what we have said above why the product is a good criterion of quality for the applications considered in this section. If we assume that any field present in soft magnetic material is negligible, we may write:
BH
fRmagn(lt.B)dV=-tXo f nrestH2dV.
(2.2)
The right-hand side of this equation is twice the potential energy of the field outside the magnet (i.e. in the air gap). This is proportional to H • B. The exact location of the operating p o i n t - a n d hence the value of the energy p r o d u c t - d e p e n d s on the relative dimensions of the magnet and the magnetic circuit in which it is used. In the limiting cases of an infinitely long needle of a closed circuit ( H = 0) or of an infinitely extensive plate (B = 0) the energy product is equal to zero; then there
44
H. Z I J L S T R A
is no external field. Between these two extremes a situation exists in which the energy product has its maximum magnitude. In the case of the needle-shaped magnet the demagnetizing field is very weak and the working point is close to the point Br in fig. 2. The value of the flux density at this point is the remanence. If the magnet is made shorter and thicker, the working point then moves along the loop in the direction of the point sHe, which it reaches if the magnet is given the form of a thin plate magnetized perpendicular to its plane. The demagnetizing field then has its maximum value and exactly compensates the magnetization. In a properly dimensioned design the energy product will thus assume a maximum value, ( B H ) .... which is determined solely by the material used. The suitability criterion sought has thus been found. The product can be represented by the area of the shaded rectangle in fig. 2; its magnitude is equal to twice the total potential energy of the field produced outside the magnet divided by the volume of the magnet. The higher the remanence, the greater the coercive force and the more convex the hysteresis loop, the greater is the value of the product. For an ideal magnet, i.e., a magnet that maintains the saturation value Js of its polarization in spite of the presence of an opposing field H, the hysteresis loop in the second quadrant is formed by a straight line going from the point where H = 0, i.e., where B = Br = Js, to the point where - H = BHc = Js/l~o. The maximum energy product is then given by: 1 (BH)max = 4/x~ j 2 .
(2.3)
To reach this maximum it is sufficient if the magnet maintains its saturation until the opposing field reaches the value -½JJl~o. A further improvement in the energy product is then only possible with materials that have a higher saturation value J~. The highest known saturation value at room temperature is shown by an FeCo alloy (2.4 T); from this value the theoretical energy product could be as much as 1150 kJm -3 (144 MGOe). However, the coercive force of this alloy is very low, which makes it unsuitable for permanent magnets. Figure 3 shows the improvements achieved in maximum energy products over the years, the record values being indicated on a logarithmic scale. It is interesting to note how closely the curve approximates to an exponential development. Once the material and thus the hysteresis loop and the (BH)max value are given, the magnet system has to be designed to make optimum use of the material parameters. Very schematically this is done as follows: Consider a permanent magnet system as drawn in fig. 4. The magnet has a length Im and cross-sectional area Sin. The air gap has a length Ig and crosssectional area Sg. The pole pieces are assumed to have infinite permeability ( H = 0 at finite B). The fields H and B are assumed to be uniform in the magnet body and in the air gap. For simplicity the field spread outside the magnet and the air gap is taken to be zero, although this is certainly not true in the given arrangement. We then have from flux continuity BmSm = - B g S g ,
PERMANENT MAGNETS; THEORY I00C k Jim 3 50C
45
// /
/
j11
20C (BH)mox 100
,
50
j
~10
zt ~
20 10 //
5
/
/
/
//
1 I
880 19'00 1920 19 0,960 1 80 Fig. 3. Historical trend of the maximum energy product (BH)mx achieved experimentally since the year 1880; (1) carbon steel, (2) tungsten steel, (3) cobalt steel, (4) Fe-Ni-AI alloy, (5) 'Ticonal II', (6) 'Ticonal G', (7) 'Ticonal GG', (8) 'Ticonal XX' (laboratory value, Luteijn and de Vos 1956), (9) SmCos, (10) (Sin, Pr)Co5 (laboratory value, Martin and Benz 1971), (11) Sm2(Co0.85Fe0.11Mn0.04)17 (laboratory value, Ojima et al. 1977). The energy in MGOe is found by dividing the value in kJm -3 by 7.96.
1 Ig
s/[ Fig. 4. Permanent magnet system with pole pieces. S m and Sg are the cross-sectional areas of the magnet and the air gap respectively, and Im and lg their respective lengths.
46
H. ZIJLSTRA
and, since no currents are present, Hmlm - G i g = O,
where the positive direction for H and B is taken to the right. From these equations it is easily found that H m = Hglg/Im,
and B m = - tzoHgSg/ Sm B m / H m = - tZoSglm / Smlg .
The latter expression shows that the reluctance of the system and hence the working point of the magnet is entirely determined by the dimensional ratios of the yoke. Allowance for finite permeability of the pole pieces and for flux leakage can be made by factors o~ (resistance factor) and /3 (leakage factor) so that the equations for magnetomotoric force and the flux in the air gap are written as HgLg = otHmLm,
BgSg = - /3BmSm .
For good designs c~ may have values between 0.7 and 0.95 and/3 between 0.1 and 0.8. Detailed discussions of these factors have been published by Edwards (1962) and by Schiller and Brinkmann (1970). 2.2. T h e m a g n e t i c free energy
In applications involving clamping ability, lifting power or pull of the magnet (ponderomotive force, the second category in table 1) the working point is also in the second quadrant of the hysteresis loop. Whereas in the previous group of applications it was the location of the working point that mattered, the important thing now is how the working point moves. If, for example, the application is of a cyclical nature, it is usually necessary for the working point to "stay well on the loop" during the cyclical motion, so that good reversibility is important. The amount of mechanical work spent in going anticlockwise round part of the loop and completely recovered on going back again is used as a criterion for measuring the performance of a magnet system for applications of this type. In these applications there is generally a particular configuration of permanent magnets and magnetizable objects, which are capable of relative movement. Leaving aside the work required to overcome friction, the mechanical work required to produce an isothermal change in the configuration is equal to the increase in its magnetic free energy. Conversely, a decrease in the magnetic free energy will result in the same amount of mechanical work becoming available.
PERMANENT MAGNETS; THEORY
47
According to the first law of thermodynamics (conservation of energy) a system in which a reversible process takes place can be described by the equation TdS
+ dA = dU.
The term T dS, the product of the absolute temperature T of the system and the change of its entropy S, is equal to the amount of heat supplied to the system from the environment. In addition the environment performs on the system an amount of mechanical work dA, taken as positive. This sign convention for the mechanical work performed is employed for systems in which magnetic effects occur. Both amounts of energy are spent on the increment d U of the internal energy of the system. The free energy F of the system is defined by F=U-TS.
It follows from these two relations that dF = dA- S dT. If the state of the system changes isothermally (i.e. d T = 0), then dF = dA. In a system that contains magnetic material the main problem is to find the correct expression for the mechanical work. The criterion used for the suitability of a magnetic material for applications of the type we are now considering is the maximum possible reversible change of its magnetic free energy. This value is usually calculated per unit volume of the magnet. The mechanical work d A associated with an infinitesimal change of the configuration is equal to dA
½f_
(H. dS - S . d H ) d V, magn
where the integration is performed over the part Rmagn of the space occupied by the material. T o derive this expression for the mechanical work, let us imagine a number of bodies of various magnetizations arranged in a particular configuration. We assume that the bodies are situated in each other's magnetic field and that their temperature remains constant. A slight change in the configuration causes a change in the fields and hence in the polarizations. For each body the increase in the magnetic free energy consists of a quantity dFp, connected with the build-up of the polarization in the material, and a quantity of interaction energy dF~, since in a field H a piece of material with the polarization vector J possesses the potential energy, - ( J • H). For the body considered we can now write: d F = dFp+ d E = H . d d - d ( J - H ) .
48
H. ZIJLSTRA
T o find the change in the free energy of the whole system we must perform a summation over all the bodies. The contributions from the interaction energy would then be counted twice, but putting a factor 1 in front of them corrects for this. The total increase in the free energy is therefore dFsystem = E
dVp+½E
dFi,
where both summations are made over all the bodies. Using the above expressions for dFp and dF~ and applying the expression d F = d A for isothermal changes, we obtain the required expression for the mechanical work, calculated per unit volume of the material. W e should note here that the energy change H - d J is positive, because the structure of the material offers a certain resistance to the change of the polarization. The interaction energy, - ( J • H ) , has a minus sign because it is customary to take this energy by definition equal to zero for two bodies that are an infinite distance apart. If the polarization vector in the expression for the mechanical work is replaced by the equivalent quantity B -/~0H, then, after integration, d A = ½fu
( H . dB - B . dH) d V. magi
T o evaluate this integral it is necessary to bear in mind that during a change in the configuration the working point moves along the hysteresis loop in the second quadrant from P to Q (fig. 5). It is then found that the work d A is equal to the area of the sector O P Q . One configuration (point P) cannot move farther to the right than point Br, where H is zero, and therefore the magnetic circuit must be closed. The other configuration (point Q) cannot m o v e farther to the left than the point BHc, where B and the force exerted are zero. W h e r e possible, cyclical processes will be carried out in such a way that the working region in the second quadrant extends to the vertical axis (Br). T h e magnetic circuit there is closed, which corresponds to a state of lowest energy. In general the material chosen for
B/ P
Br
S Fig. 5. Part of a B hysteresis curve in the second quadrant. The area of the sector OPQ represents the change in magnetic free energy when the working point moves from P to Q.
PERMANENT MAGNETS; THEORY
49
these applications is one in which the working point can move reversibly from remanence over the greatest possible extent of the hysteresis loop. For an ideal magnet, where the complete (linear) hysteresis branch in the second quadrant is transversed reversibly, the maximum mechanical work made available per unit volume during a change of configuration is given by: ½B~BH~ = (1/2/Xo)J 2 • It will be evident t h a t the magnet must be capable of maintaining its saturation polarization Js until the opposing field reaches the value -JJtxo. This imposes a stronger requirement on the coercivity than when the magnet is used for static field generation. The hexaferrite materials with their (for that time) high coercivity of the order of 3 x 10SAm -a ( ~ 4 k O e ) made many of these dynamic applications possible. Today there are many materials with much higher coercivities, notably the rare-earth alloys, whose coercivities are of the order of 106 A m -1 (104 Oe).
3. Magnetic anisotropy
3.1. Anisotropy field and coercivity associated with magnetic anisotropy Consider a single-crystal sphere of a material with uniaxial magnetic anisotropy, uniformly magnetized to saturation parallel to the easy axis of magnetization. We assume that changes in the magnetization occur by a uniform or coherent rotation of the magnetization Ms and that the anisotropy energy density is given by Wk = K sin 2 q~, where ~0 is the angle between the easy axis and the magnetization vector. In the presence of a f i e l d / - / a l o n g the easy axis we assume that the magnetization vector is rotated through an angle ~p as shown in fig. 6. In this state the total magnetic energy is 1 2 W = g/x0Ms + K sin 2 q~ +/x0HMs(1 - cos q~).
Note that the first term, which is the magnetostatic energy of the magnetized sphere, is independent of the angle q~ because the demagnetization factor of the sphere is isotropic and equal to ½. For a minimum in the energy W corresponding to a stable position of the magnetization vector we require dW d~ - 0
and
d2W > 0. d~ 2
Thus q~ = 0 is a stable position of Ms when
H. ZIJLSTRA
50
easy
axis
Ms
Fig. 6. Uniaxial crystal with easy axis for the magnetization.
H > -2K/IxoMs. However, if the field H<-2K/l~oMs the position q~ = 0 is unstable and the magnetization reverses discontinuously to ~0 = ~-. The critical field 2K/~oMs is defined as the anisotropy field HA. It is important to note that the coercivity/arc of this model of uniform rotation is equal to HA. W e shall see later that in real materials the coercivity is smaller than HA and depends on the microstructural features of the magnetic crystals. However, in any case the anisotropy field is the upper limit for the coercivity, and magnetic anisotropy is therefore a prerequisite for coercivity to occur. When the easy axis does not coincide with the field direction the magnetization reverses by a reversible rotation followed by an irreversible jump. The hysteresis loop is no longer rectangular and the coercivity depends on the orientation angle of the easy axis. These cases have been calculated by Stoner and Wohlfarth (1948) and are summarized in fig. 7. The hysteresis loop of an array of non-interacting identical particles with uniaxial anisotropy oriented at r a n d o m is given in fig. 8. The coercivity of this array is Hc = 0.48HA if coherent rotation is assumed. Magnetic anisotropy can have various causes. The most important in p e r m a n e n t magnet materials are: (a) shape anisotropy, associated with the geometrical shape of a magnetized body; (b) magnetocrystalline anisotropy, associated with the crystal symmetry of the material. They are discussed in sections 3.2 and 3.3. A p a r t from these types of anisotropies, there are a few of less importance for p e r m a n e n t magnets, but nevertheless worth mentioning. At the surface of a crystal the atoms are in a position of deviating symmetry as compared with the
PERMANENT MAGNETS; THEORY -1 I
I
I
0 r
I
I
51 1
I
I
I
I
I
I
[
0
I
0,10,90
1
M/M s
T
¢'
0
I
-1
0
0,10,90 I
I
I
I
I
-1
I
I
0
I
~
I
h
I
I
1
Fig. 7. Hysteresis loops for uniform rotation of the magnetization in a crystal with one easy axis for the magnetization, with the orientation angle (in degrees) between easy axis and direction of applied field as a parameter (Stoner and Wohlfarth 1948).
1.0
Sf
-0.5
-1.0 :-1.5
Y
f
0.5
f -1.0
M/Ms
J ~ 0..=
0
0.5
1.0
1.5
Fig. 8. Hysteresis loop and initial curve for an array of non-interacting identical particles with one easy axis, oriented at random (Stoner and Wohlfarth 1948).
52
H. ZIJLSTRA
interior. This may give rise to a magnetic anisotropy experienced only by these superficial atoms, causing the spins to be oriented normal to the surface, or in other cases, tangential to the surface. In a non-spherical crystal this leads to a net anisotropy effect which, of course, becomes smaller with increasing size of the crystal. The underlying theory has been treated by N6el (1954) and the effect may contribute somewhat to the shape anisotropy of heterogeneous elongated particle magnets like alnico. A similar kind of "surface anisotropy" has been observed by Berkowitz et al. (1975) on fine ferrite particles covered with a monomolecular layer of oleic acid. Another interfacial type of anisotropy was discussed by Meiklejohn and Bean (1957), namely, exchange anisotropy. It occurs when an antiferromagnetic crystal with high anisotropy and a ferromagnetic crystal constitute one solid body such that the spins on either side of the interface are coupled by exchange forces. The (non-magnetic) antiferromagnetic crystal then imparts its anisotropy to the ferromagnetic crystal. The effect has been observed with small cobalt spheres covered by an anisotropic antiferromagnetic oxide layer.
3.2. Shape anisotropy Shape anisotropy refers to the preference that the polarization in a long body has for the direction of the major axis. The effect, which does not arise from an intrinsic property of the material, can easily be described in the case of a prolate ellipsoid. It is assumed that the ellipsoid is homogeneously magnetized in a direction that makes an angle ~0 with the major axis (fig. 9). The demagnetizing / /
I
I
÷
I I !
I I I
Fig. 9. Magnetized prolate spheroid.
PERMANENT MAGNETS; THEORY
53
field Ha due to the magnetic poles at the surface is also homogeneous within the ellipsoid. Along each of the three principal axes of the ellipsoid we can apply one of the relations
I.l"ondi = -- NiJi , where i is the number of the principal axis; the coefficients N~ are the demagnetization factors. In the case of a prolate spheroid we have the "parallel" demagnetization factor NIl for the direction parallel to the axis of revolution and two "perpendicular" demagnetization factors Na, which, for reasons of symmetry, are identical. Using eq. (2.1)
f
(H.B) dV=O,
it can easily be shown that the energy Em of the demagnetizing field, which is given by
Em = II.~OIR n 2 d V , depends in the following way on the parameters that describe the situation: Em = ~ 0 {]~lJ2 + (NL - ]~l)J 2 sin 2 ~p}Rmagn • In this expression Rmagnis the volume of the ellipsoid. The coefficient of the directionally dependent part of the equation describes the shape anisotropy. For small values of the angle ~0 we find from this an effective anisotropy field HA = (N±-
Nfl/~0
•
In the case of a long bar (needle) this field HA approximates to the value J/2l~o. If the bar consists of iron (Js ~ 2 Wbm -2) it follows from the foregoing that HA 106Am -1 (~104Oe). This is the value of the coercive force when the magnetization is rotated uniformly. Magnetic materials which derive their hardness from shape anisotropy consist of a fine dispersion of magnetic needles in a matrix of non-magnetic or weakly magnetic material, like alnico (fig. 10).
3.3. Magnetocrystalline anisotropy There are three situations that give rise to magnetic anisotropy as an intrinsic crystal property. The first and most important one is that in which the atoms possess an electron-orbital moment in addition to an electron-spin moment. In
54
H. ZIJLSTRA
Fig. 10. Microstructure of an alnico magnet. The alloy consists of a precipitate of elongated particles (approx. composition FeCo, average thickness 30 nm) in a matrix of approx, composition NiA1. Left: plane of observation parallel to the easy axis. Right: perpendicular to the easy axis. (Electron micrograph of 'Ticonal XX' magnet steel (De Vos 1966).) such a situation the spin direction may be coupled to the crystal axes. This arises through the coupling between spin and orbital moments and the interaction between the charge distribution over the orbit and the electrostatic field of the surrounding atoms. There will then be one or more axes or surfaces along which magnetization requires relatively little work. The crystal will then be preferentially magnetized along such an easy axis or plane. The second situation is encountered in non-cubic crystal lattices. In these crystals the magnetostatic interaction between the atomic moments is also anisotropic, which may give rise to easy directions or planes of magnetization. The third possibility of crystal anisotropy is found in the directional ordering of atoms as described by N6el (1954). This typically involves solid solutions of atoms of two kinds, A and B, linked by the atomic bonds A - A , A - B and B-B. In the presence of a strong external magnetic field the internal energy of these bonds may be to some extent direction-dependent. Given a sufficient degree of atomic diffuson - as a result of raising the temperature, for example - a certain ordering can be brought about in the distribution of the bonds; in this way it is possible to " b a k e " the direction of this field into the material as the easy axis of magnetization. In addition to these sources of magnetocrystalline anisotropy mechanical stresses may contribute through the magnetoelastic (magnetostrictive) properties of
55
PERMANENT MAGNETS; THEORY
the crystal. This contribution, however, is considered to be negligible in hard magnetic materials. Examples of materials with magnetocrystalline anisotropy are Ba- or Sr-hexaferrite with H A ~ I . 3 X 106Am -1 (17kOe), MnAI with HA ~ 3.2 X 106 A m -1 (40 kOe) and SmCo5 with H a ~ 24 x 106 A m a (300 kOe).
4. Fine particles
4.1. Critical radius for single-domain particles In section 3.1 the coercivity is calculated in a model assuming uniform rotation of the magnetization. The result Hc = HA however is in disagreement with experiment, as illustrated by a few examples in table 2. Obviously the assumption of uniform rotation is not realistic and we have to consider other modes of reversal. This section deals with the conditions under which uniform magnetization is stable and with the non-uniform states that may occur otherwise. Consider a uniformly magnetized sphere. It contains a certain amount of magnetostatic free energy due to its magnetic dipole field. This energy can be reduced by allowing a non-uniform magnetization. By this the magnetic field acquires multipole components at the expense of the dipole field with a general reduction in magnetostatic energy. The field even vanishes altogether when the magnetization vectors form closed loops inside the sphere. However, non-uniform magnetization requires work due to the exchange interaction and the magneti c anisotropy, and the trade-off of these energies with the magnetostatic energy determines which mode of magnetization the sphere will have. In general the mode depends on the radius of the sphere, and in some cases a critical radius can be calculated below which a sphere is uniformly magnetized in its lowest state. A rigorous determination of the critical radius for a uniformly magnetized sphere using the micromagnetic equations (Brown 1957, Frei et al. 1957) would be extremely difficult because the micromagnetic theory contains non-linear differential equations. However, a simplified approach to the problem has been made by Kittel (1949) who calculated approximate values of the critical radius Rc while Brown (1969) calculated exact values for the upper and lower bounds for TABLE 2 Comparison of anisotropy field HA and coercivityshe of various permanent magnet materials. HA
Material Ticonal 900 Ferroxdure SmCo5 MnAI
jnc
(kAm-1)
(kOe)
(kAm-l)
(kOe)
370 1200 24000 3400
4.6 15 300 40
100 400 5500 400
1.3 5 70 5
56
H. ZIJLSTRA
Re. T h e following calculations are based on B r o w n ' s a p p r o a c h with the following assumptions: (1) T h e m a g n e t i z a t i o n is continuous with the magnetic polarization IJs[ constant (2) T h e energy density due to the e x c h a n g e coupling is (see section 6.2.1): We = A(V~p) 2 . (3) T h e f e r r o m a g n e t i c material is uniaxial and the magnetocrystalline anisotropy energy density is (apart f r o m a constant term): W r = K sin 2 ~ , w h e r e ~0 is the angle b e t w e e n the easy axis of magnetization and the magnetization vector. According to B r o w n the critical radius Rc0 b e l o w which a sphere is certainly uniformly m a g n e t i z e d is / I.l,o A \ 1/2
Rco = 5.099~-~s2 )
•
If we assume that for iron (Kittel 1949) A ~ 2 x 10 -11Jm -1 , we find that Rc0(iron) = 13 n m (130 ~ ) .
O
b
Fig. 11. Demagnetization modes of a sphere. (a) Magnetization curling. (b) Two-domain state.
PERMANENT MAGNETS; THEORY
57
In order to calculate the critical radius above which the magnetization is nonuniform we must distinguish between two cases: (1) The material has a low magnetocrystalline anisotropy energy density. In this case the energy associated with the uniform magnetization state is compared with the non-uniform magnetization state known as "curling". The latter is considered to have the l o w e s t energy because the curling mode (shown in fig. ll(a)) minimizes the sum of the magnetostatic, anisotropy and exchange energies. (2) The material has a high magnetocrystalline anisotropy energy density. In this case the energy associated with the uniform-magnetization state is compared with the two-domain state having a single plane wall as shown in fig. ll(b). Unfortunately the micromagnetic theory does not generate the magnetization configuration that has the lowest energy, so that the non-uniform states as mentioned have been chosen on the assumption that they have the lowest energy. Simple calculations suggest that this is probably correct. (1) Low magnetocrystalline anisotropy energy density. According to Brown (1969) this condition is defined by
K
K < 1.0686Wm, Wm =
where
(1/6/x0)J 2 .
The latter expression, Win, is of course the magnetostatic energy of a uniformly magnetized sphere. If the above condition is satisfied the curling mode has a lower energy than the uniform magnetization mode provided that the particle radius R >
RCl ,
where 64053 ~---~ m 1 - 5 . 6 1 5 0 ~ 2 K ) -1 If K = 0 then Rcl = 1.2562Rc0. If K = 0.1781JsZ//x0 then Rcl = ~. (2) High magnetocrystalline anisotropy energy density. According to Brown (1969) this condition is defined by K > 0.1781J~/~0, in which case the two-domain state shown in fig. 11(b) has a lower energy than the uniformly magnetized state provided that the particle radius
58
H. ZIJLSTRA
R > Rc2, where /x0A ~/: /x0K Rc2= 56.129 ( J~s ) ( --77-+ Js 1.5708)
1/2
Note that when R > Rc2 the two-domain state has a lower energy than the uniformly magnetized state even when the material has a low magnetocrystalline anisotropy density. When K = 0, R c l = 1.2562Rc0 and Rc2 = 13.7965Rc0 ; when K = 0.1781J~//z0, Rcl = ~ and Rc2 = 14.5576Rc0 ; when K = 0.1627J~/Iz0, Rca = Rc2 = 14.5Rc0. and R c j R c 0 as functions of the parameter Graphs of the ratio R c l / R c o are shown in fig. 12. The calculations of the critical radius made by Kittel (1949) are also shown for comparison. Kittel's calculations are based on a comparison of the approximate energy of a two-domain sphere having a plane wall through the centre with the energy of a x = txoK/J~
102
two doma ~s
b
10
curling
1o.2
lo-~---~ x =.uo K/J~
10
Fig. 12. Ratios of upper bounds beyond which magnetization curling occurs, Rcl (curve a) or the two-domain state has the lowest energy, Rc2 (curve b), both with respect to the lower bound Rc0, below which the uniform state is stable, as a function of the reduced magnetocrystalline anisotropy x = t.LoK/J~. T h e critical radius separating uniform from non-uniform behaviour (Kittel's approximation) is also given as its ratio with Rc0 (curve c).
PERMANENTMAGNETS;THEORY
59
uniformly magnetized sphere. H e finds the latter to have lowest energy when #0A 1/2 /z0K 1/2
R<9tx°2Y Js =36(js)~
(Js)
where the domain wall energy 3' = 4X/A-K. H e has assumed that the magnetostatic energy of the two-domain state is approximately half of that of the uniformly magnetized state. The critical radius as determined by Kittel (1949) can be compared with Rc0 as determined by Brown as follows: R (Kittel) _ 3 6 / x 0 X / ~ / 5 . 0 9 9 ~ / / x 0 A Re0 " / Z / p, o K \ 1/2
= 7.06~-2 )
.
The ratio R(Kittel)/Rco is also shown in fig. 12 and plotted as a function of the parameter x = t~oK/J~. This line fits reasonably well between Brown's upper and lower bounds but is certainly incorrect for values of x < 0.02. Note that in all the above calculations of ratios of Rc~, Re2 and R (Kittel) with respect to Rc0 no assumption has been made about the value of A. From the above discussion it will readily be appreciated that single domain particles, i.e., particles with radius R < Rc0, are necessarily uniformly magnetized but that particles with R >Rc~ or R > R c 2 are not necessarily non-uniformly magnetized. Although the latter particles can be uniformly magnetized, the energy of that state is higher than that for the non-uniform state. Thus the uniformly magnetized state may persist if there is an energy barrier between this and the non-uniform state. This is true for a perfect single crystal in which the nucleation of a domain wall requires a finite energy for nucleation (see section 4.2). It is also possible for particles with R < R c 0 to contain domain walls provided they contain lattice defects where the domain wall energy is lower than that in the surrounding matrix. The coercivity is determined by the height of the nucleation energy barrier and hence by the presence of lattice defects and the particular magnetic spin structure of the material (see section 6.5.3). The presence of superficial features, such as scratches and sharp edges, may also influence the coercivity owing to the associated local demagnetizing fields, which may assist domain wall nucleation (see section 6.4). The coercivity can also be determined by domain wall pinning at the lattice defect (see section 6.5.2). The behaviour of the sphere for radii between Rc0 and Rcl or Rc2 is unknown, but it cannot be excluded that the magnetization alternates from the uniform to the non-uniform states. The region between Rc0 and Rcl or Rc2 is associated with the upper and lower bounds to the magnetostatic energy of the non-uniform states (Brown 1962b). If this energy is zero as is indeed the case for a cylindrical bar which demagnetizes by the curling mode, the calculation is exact, and Rc0 and Rc~ coincide and therefore correspond to a single critical rod radius (Frei et al. 1957) (see also section 5.1).
60
H. ZIJLSTRA
4.2. Brown's paradox For high anisotropy a supercritical (R > Rc2) sphere has the non-uniform multidomain mode as the lowest energy state. However, if the particle happens to be in a uniform state it cannot spontaneously transform to the lower energy state. For this a wall has to be nucleated, which means that one or several spins must start rotating. Consider one particular spin. It is subjected to an effective field H which is composed of H = HA + Hw+ Ha+ He, H A is the anisotropy field; Hw is the Weiss field, accounting for the exchange interaction between the spin and its neighbours; Ha is the demagnetizing field; He is the externally applied field. For instability of the spin it is required that
where
- (Ha + He) > HA + H w .
Now Hw is of the order of 10 9 A m -1 which far outweighs any practical value that Ha or He could reach. The conclusion is that the uniform magnetization is maintained under all circumstances and that when - H e > HA the magnetization reverses by uniform rotation. The coercivity of a spherical crystal is thus always H~=Ha, which is in obvious contradiction with experiment (see table 2). This inconsistency which is referred to as "Brown's paradox" (Shtrikman and Treves 1960) is solved by considering that lattice defects are able to reduce Hw considerably and even reverse it locally. Also HA can be influenced by a defect as the symmetry of the crystal is disturbed locally. Finally sharp edges and scratches can locally increase Ha. These matters are discussed in more detail in sections 6.4 and 6.5.
5. Coercivity associated with shape anisotropy
5.1. Prolate spheroid From calculations using micromagnetic theory Frei et al. (1957) and Aharoni and Shtrikman (1958) have shown that magnetization reversal of a prolate spheroid may occur by three basic mechanisms. These are:
PERMANENT MAGNETS; THEORY
61
(a) Uniform rotation of the magnetization for which the coercivity is equal to the anisotropy field Ho = HA = !
/Xo
(N. - N)J~,
(5.1)
where N~ and N]I are the demagnetization factors perpendicular and parallel to the major axis of the spheroid (see also sections 3.1 and 3.2). (b) Magnetization curling (see figs. l l ( a ) and 13(a)) for which the coercivity is Hc=k
Js 1 2/Zo p2,
(5.2)
where p = R/Ro, R is the minor half axis of the spheroid, R0 is a fundamental length defined by R0 = (47rtxoA/J2)1/2 and A is the exchange energy coefficient as discussed in sections 4.1 and 6.2.1. The factor k depends on the axial ratio of the spheroid and is equal to 1.08 for the infinitely long spheroid or the infinite cylinder. For the sphere k = 1.39. However, a sphere will rotate its magnetization uniformly under any applied field. Therefore its coercivity is zero. The sphere can perform a transition in zero applied field from the uniformly magnetized state to a non-uniform one by the curling process under its own demagnetizing field. The condition for this is
Js > 1 . 3 9 Js 1 3tZo 2/Xo p 2,
(5.3)
where the left-hand member is the self-demagnetizing field of the sphere and the
£1
b
c
Fig. 13. Demagnetization modes of the infinite cylinder: (a) curling; (b) twisting; (c) buckling.
62
H.' ZIJLSTRA
right-hand member follows from eq. (5.2) with k = 1.39. This is rewritten as p2 > 2.09, or
/ lzoA \ 1/2
R > 5.121--=~/
which is about the result obtained by Brown (1969) for the critical radius of a sphere (see section 4.1). It is interesting to note the similarity between the quantity R0 and the thickness of a domain wall. As discussed in section 6.2.1, the wall thickness 6 is determined by the exchange energy competing with the anisotropy energy, so that 3 c~ ~/--A/K. In the present discussion we deal with a balance between exchange energy and magnetostatic self-demagnetization energy, the latter being proportional to J2/iXo. If we substitute this for K in 6 we obtain
{ l~oA "ll/2 6 oc\ j2 ] o:Ro. (c) Magnetization buckling. This mechanism of magnetization change is shown in fig. 13(c) and is degenerate with magnetization twisting (fig. 13(b)) as first described by Kondorsky (1952). Both of these mechanisms are nearly degenerate with uniform rotation of the magnetization of an infinite cylinder with R < R0 and represent a higher energy barrier than curling does for R > R0. This is illustrated in fig. 14 where the coercivities of an infinite cylinder due to these mechanisms is shown as a function of R/Ro. The buckling and twisting mechanisms will be ignored in the present discussion. When the magnetization changes by uniform rotation the associated anisotropy energy is entirely of magnetostatic origin, whereas for magnetization curling the associated energy is entirely due to changes in the ferromagnetic exchange energy. In the latter case there is no magnetic flux leakage from the surface of the spheroid so that the magnetostatic energy is zero. This result implies that for the curling mode the coercivity is independent of the particle packing density. For the uniform rotation of the magnetization the coercivity depends on the particle packing density p (p is the ratio of the volume occupied by the particles compared with the total volume of the specimen) i.e., for a system of parallel infinite cylinders Hc = ~
1
/-/xo
Js(1 - p ) .
(5.4)
For a derivation of this result see Compaan and Zijlstra (1962). Thus in any assembly of particles the hysteretic behaviour will be determined by the magnetization reversal mechanism which has the lowest coercivity (see fig. 14). In all the above cases the particles remain uniformly magnetized until the reverse field
PERMANENT MAGNETS; THEORY
63
2 Uniform r o t a t i o n
Buckling or twisting 0.2
HC/HA
l
o,
Curling
0.05
0.02 ~- R / R o
0.01 0.2
I 0.5
i 1
i 2
t 5
10
20
50
Fig. 14. R e d u c e d coercivity He/HA due to various demagnetization m o d e s of the infinite cylinder as a function of reduced radius R/Ro.
nucleates an instability in the magnetization, which is then reversed either by a sudden uniform rotation or a curling of the magnetization. In this case the nucleation field is the same as the coercivity and the hysteresis loops are all symmetrical and rectangular. Which mechanism of magnetization reversal occurs depends on both R and p. The uniform rotation mode changes to the curling mode for a system of parallel infinite cylinders when R e > I ~~13.6 ( ~ 2A ) ,
(5.5)
which is obtained by putting Hc of eq. (5.4) greater than Hc of eq. (5.2). The critical radius for an isolated cylinder is / i,~oA \ l/2
Rc = 3.68~---f{-2)
.
If we assume that for iron A = 2 x 10-'1 Jm -1 (Kittel 1949) and Js = 2 T, the critical radius for an isolated infinite cylinder is 9 x 10-9m. For an assembly of iron cylinders with a packing density p = 2 (as it occurs for example in alnico 5) Rc ~ 16 x 10-9 m. The measured coercivity Hc for alnico 5 is about 5.5 X 104 A m -1.
64
H. ZIJLSTRA
F r o m measurements with a torque m a g n e t o m e t e r the anisotropy field H A -~ 2 x 105Am -1. The latter value is the coercivity which would be expected for uniform rotation of the magnetization. According to measurements m a d e by D e Jong et al. (1958) the rod diameters in alnico 5 are about 3 x 10 -8 m, which is too close to the calculated critical diameter to determine whether the difference between HA and Hc is due to curling or to the fact that the elongated particles are not regular in shape. More convincing evidence in support of the above theory has been provided by Luborsky and Morelock (1964) who measured the coercivities of Fe and FeCo whiskers of various diameters. The coercivities varied from 4 x 104Am -1 to 25 × 10 4 A m -1 for whisker diameters in the range 65 nm to 5 nm and are in very good agreement with the theoretical curve for the curling mechanism. For whiskers with larger diameters the experimental results deviate from the theoretical curve, due presumably to the presence of a finite magnetocrystalline anisotropy energy and to the non-circular cross section of the whiskers.
5.2. Chain of spheres The appearance of electrodeposited particles in a mercury cathode, as observed by Paine et al. (1955), inspired Jacobs and Bean (1955) to investigate theoretically the hysteretic properties of a chain of ferromagnetic spheres, consisting of an intrinsically isotropic material. The spheres touch each other but have only magnetostatic interaction. Two mechanisms of reversal are considered: (a) symmetric fanning, and (b) parallel rotation.
a
b
c
Fig. 15. Demagnetization modes of the chain of spheres: (a) symmetric fanning; (b) parallel rotation. For comparison the uniform rotation mode of the prolate spheroid of the same dimensional ratio is also indicated (c).
PERMANENT MAGNETS; THEORY
65
The coercivities of these models are compared with those of prolate spheroids of the same length-to-diameter ratio. The three models are shown in fig. 15. The symmetric fanning appears not to provide the lowest energy barrier owing to end effects that have been ignored. Taking these into account leads to a modified fanning process, called asymmetric fanning. The results of the calculations for a system of non-interacting elongated particles oriented at random are given for the various mechanisms mentioned as a function of the length-to-diameter ratio (fig. 16). The experimental points refer to samples consisting of electrodeposited elongated particles (Paine et al. 1955) with diameters lying between 14 and 18 nm. Coercivities are in good agreement with the asymmetric fanning model. However, this might be a fortuitous agreement, since the experimental spheres have certainly more than a point-like contact, and possibily exchange interaction between the spheres has to be reckoned with. The mechanism must then be something between symmetrical fanning and magnetization buckling as described in section 5.1.
a
b 0
T I
I
I
~- Elongation
Fig. 16. Coercivity of fine-particle iron oriented at random as a function of particle elongation. Chain of spheres model: (a) parallel rotation; (b) symmetric fanning; (c) asymmetric fanning. Prolate spheroid model: (d) uniform rotation. The points refer to experiments (Jacobs and Bean 1955).
66
H. ZIJLSTRA
The magnetization reversal in elongated particles has been thoroughly analyzed theoretically by Aharoni (1966).
6. Coercivity associated with magnetocrystalline anisotropy 6.1. Magnetization reversal by domain wall processes for tXoHA > Js The fundamental requirements for magnetization reversal by domain wall processes are: (a) The nucleation of a domain wall (or a reverse domain) by a nucleation field Ha which may be either positive or negative, though for high coercivities we require Ha to be large and negative.
Hn
~H
IHnl>lHpl
b
J Hp
Hn
~H
J
IHnl
Fig. 17. Hysteresis loops in relation to nucleation field H. and pinning field Hp: (a) Coercivity determined by H.; (b) Coercivitydetermined by Hp.
PERMANENT MAGNETS; THEORY
67
m
,~ B
-115
-1.10
C
P
oo-o.--=
':"
I
0.~
H 1'10
L (MA/rn) 1.5
Fig. 18. Hysteresis loop of a SmCo5 particle of 5 i~m size. After magnetizing in a strong positive field a wall is nucleated at an applied field of about -0.6MAre -1 (point A) or at an internal field of -0.8 MAm-1 (due to the self-demagnetizing field of -0.2 MAm-1). The internal curve measured after applying a weaker positive field reveals wall nucleation at zero applied field and subsequent wall detachment at about -0.35 MAre-1 applied field (point B) which means a pinning field of 0.55 MAm-~ for this particular pinning site. The curve C demonstrates the absence of strong pinning sites in a large part of the crystal (Zijlstra 1974). (b) T h e d i s p l a c e m e n t of the wall by a reverse field, if necessary by d e t a c h i n g it from its p i n n i n g sites, in which case a reverse field Hp k n o w n as the p i n n i n g field m u s t be applied. T h e resulting hysteresis loop d e p e n d s o n which of these two processes is d o m i n a n t . Schematic hysteresis loops for m a t e r i a l s in which the coercivities are principally d e t e r m i n e d by d o m a i n wall n u c l e a t i o n a n d p i n n i n g are s h o w n in fig. 17(a) a n d (b) respectively. A hysteresis loop which shows m a g n e t i z a t i o n changes c o n t r o l l e d by either n u c l e a t i o n or p i n n i n g is s h o w n in fig. 18.
6.2. The 180" domain wall 6.2.1. Energy and width of a 180 ° domain wall C o n s i d e r a 180 ° d o m a i n wall in a uniaxial f e r r o m a g n e t as d e p i c t e d in fig. 19. T h e o r i e n t a t i o n angle of the m a g n e t i z a t i o n is 0 at x = -co a n d 7r at x = +oo. T h e x-axis is n o r m a l to the wall plane. T h e m a g n e t i z a t i o n has its easy axis along the z-axis. T h e c e n t r e of the wall is at x = 0. Inside the wall the m a g n e t i z a t i o n vectors deviate from the easy axis by an angle ~, giving rise to an a n i s o t r o p y e n e r g y density WK = K sin 2 q~,
(6.1)
w h e r e ~0 d e p e n d s o n x a n d K is the a n i s o t r o p y constant. T h e m a g n e t i z a t i o n inside
68
H. Z I J L S T R A
easy axis I I
Fig. 19. Perspective view of 180 ° domain wall.
the wall is not uniform, giving rise to an exchange energy density
We=A/d ] 2
(6.2)
where A is the exchange energy coefficient. Here it is assumed that no higher terms than K occur in the anisotropy energy and that the ferromagnetic coupling is adequately described by nearest neighbour interaction. The wall energy per unit area then is Y = f_7=(W~; + We) dx,
(6.3)
with ~0 depending on x in such a way that the energy is a minimum. By using variational calculus (see e.g. Margenau and Murphy 1956), we find the Euler equation as the minimizing condition for this problem to be
d2~
K sin 2q~ - 2A ~
= 0,
stating that the torque is zero everywhere. Multiplying by dq~/dx and integrating from -oo to x we find K s i n 2~0=
A{d~] 2 \~-x] '
(6.4)
stating that the energy density due to magnetic anisotropy equals that due to exchange interaction everywhere. The relation between q~ and x follows by integration to be tan ½~o= e ~'/~ ,
PERMANENT MAGNETS; THEORY ------7------
69 y~
Y 0 6
Ii-
Fig. 20. Distribution of spin orientation angle q~across a 180° domain wall (schematic). The width 6 of the wall is defined after Lilley (1950). where x0 = X/--A/K is called the wall thickness parameter. According to this relation a wall is infinitely thick. However, the m a j o r part of the orientation change and hence the energy is concentrated near x = 0. Following Lilley (1950) we define the wall thickness 6 as the distance between the intersections of the tangent to ~ at x = 0, with ~p = 0 and ~ = zr (fig. 20). We then find
6 = 7r~/~4/K = 7rXo.
(6.5)
The wall energy is calculated by substituting WK for We in eq. (6.3) and shifting from x to ~0 as a variable using eq. (6.4): y = 2V'A-K
L
sin ~ dq~ = 4X/A--K.
(6.6)
Equations (6.5) and (6.6) are derived under the assumption m a d e in eq. (6.2) that the magnetization is continuous, i.e., the discreteness of the lattice of magnetic atoms is ignored. This is generally allowed provided that x0 is large c o m p a r e d with the lattice p a r a m e t e r or the distance between magnetic nearest neighbours. However, this approximation gives rise to errors when x0 approaches the lattice p a r a m e t e r a, i.e., when a2K becomes comparable with A. This case of very strong anisotropy is treated in section 6.5.4. When a wall is pinned an applied field causes a contribution to the wall energy which is treated in section 6.5.2.
6.2.2. The exchange energy coefficient A 6.2.2.1. Determination of the exchange energy coefficient A fro m the Weiss internal field model of ferromagnetism. The Weiss internal field model describes the ferromagnetic interaction between localized spins in a regular lattice. A particular spin i is aligned with its nearest neighbours by an effective field per nearest neighbour j H,,j = N M / Z ,
70
H. Z I J L S T R A
where N is the Weiss field constant, M the magnetization of the crystal and Z the n u m b e r of nearest neighbours or coordination number. Consider the spin pair i, L each spin having a magnetic m o m e n t / z . They differ in orientation by an angle Aq~. The exchange energy change associated with this orientation difference can be written as wij = ~ j ~ (1 - c o s a ~ ) =
(NM/Z)tx (1 - cos 2~q~),
which for A~ ~ 1 approaches
N M , ,t ,,2 wi~ = ~ - / x t a q ~ ) . Suppose an angular gradient d~p/dx is to be present along the x direction. With a distance ~ between the two spins and an angle h between their connecting line and the x-axis we then have
NM wij = - ~ -
*2 ~t
[d~o'~2 c o s 2 ,~ \ ~ x x ]
"
This expression will be applied to various crystal lattices: (a) Body-centred cubic (bcc, fig. 21). For a bcc lattice the n u m b e r of nearest neighbours is 8, all with cos2A = ½ if the x-axis is coinciding with a cube edge.
13
Fig. 21. Body-centred cubic crystal lattice. With a being the lattice p a r a m e t e r we have ~2 = 3a2 and NM a 2 [dq~ ,~2 w,j = ---fg- ~ T Td;x ] " Per unit cell of volume a 3 there are 8 such pair interactions and two atoms contributing with 2~//z0 to the magnetization M. Substituting this and dividing by the cell volume results in the exchange energy density We due to the angular gradient d~/dx:
N M 2 az{d~ ~2
We= ~ o ~
\~xl "
PERMANENT MAGNETS; THEORY
71
Cl Fig. 22. Face-centred cubic crystal lattice.
(b) Face-centred cubic (fcc, fig. 22). For an fcc lattice the n u m b e r of nearest neighbours is 12, of which 8 with cos2A = ½ and 4 with cos2A = 0. The nearest neighbour distance is ~: = ½a~/2 in all cases. Per unit cell there are 24 pair interactions and 4 atoms. Weighting the interactions with their proper values of cos2A we find the exchange energy per unit volume NM 2
We =/z0 ~
2/d~\ 2 a I~x-x,] .
(c) Simple cubic (sc, fig. 23). For an sc lattice the n u m b e r of nearest neighbours 9i i i i i O--
•
i i - :g-'-
Q,,
PF -
-O
~×
6 Fig. 23. Simple cubic crystal lattice.
is 6, of which 2 with COS2A = 1 and 4 with COS2A = 0. The nearest neighbour distance ~: = a in all cases. Per unit cell there are six half interactions (the other halves to be attributed to adjacent cells) and only one atom. The exchange energy per unit volume is then NM 2
We = ~ o - i ~
a2{d~o'~2 \dx-x/ "
(d) Hexagonal close-packed (hcp, fig. 24). For an hcp lattice the coordination n u m b e r is 12. The nearest neighbour distance sc = a in all cases. Per unit cell there are 23 pairs, which are tabulated below together with the proper value of cos2A and the part p for which they have to be attributed to the unit cell under consideration (table 3). There are two atoms in this cell contributing 2/x/~0 to the
72
H. Z I J L S T R A
-~ - -..-- - i- ; . ~
O- . . . . .
-O-/- - / f ' -
0 /
~\ ¢_~J
\
~X
Fig. 24. Hexagonal close-packed crystal lattice.
magnetization. With these data we find for the exchange energy density
N M 2 a2[ d~o,~2 w° = ~°-J3--
\TX-x] "
If we express We in terms of the nearest neighbour distance ~: rather than the lattice p a r a m e t e r a we obtain for all four structures the same result (N6el 1944a)
NM2.2{d~ \2 we
=
.
This is not the case when we expand the structures along the vertical axis in order to obtain tetragonal symmetries from the cubic structures or to deviate from the close packing in the hexagonal case. In all these cases, however, the expressions TABLE 3 Interactions in an hcp cell. Location in cell
Number
cos2A
p
Contribution
F r o m centre plane to upper and lower planes
4
¼
1
1
2
0
1
0
In centre plane
3 2 2
1 ¼ ¼
1 ~ 1 _2
1 g 1
2 g
1 ¼
g ½
In upper and lower planes
3
1
Total contribution
3
1 1
4
PERMANENT MAGNETS; THEORY
73
for We in terms of a remain unchanged, because the expansion is perpendicular to the x-axis. If we introduce the Weiss-field energy
Ew = ½1~oNM2 we have for the coefficient A of eq. (6.2): bcc: A = ~a2Ew = l~2Ew, fcc:
A = ~2a2Ew= ~2.Ew ,
sc:
A = la2Ew = ~2Ew,
hcp:
A = {a2Ew = {sC2Ew.
6.2.2.2. Determination of the exchange energy coefficient A from the Heisenberg model of ferromagnetism. According to the Heisenberg model the ferromagnetic coupling between two spins is expressed as w~j = -2J$~ • ~ , where St and Sj are spin vectors of two neighbouring atoms and J is a coefficient called the exchange integral. For J > 0 parallel spins have minimum energy, resulting in ferromagnetic coupling. We suppose an angular gradient d~/dx to be present along the x-axis. The coupling energy between spins i and j can then be written as (d~'~ 2 Wi] = J S 2 ~ 2 COS2 a \ ~ X ] '
where sc is the distance between the spins, A is the angle between their connecting line and the x-axis, and the moduli of the spin vectors are assumed equal. In the same way as in the previous section these energy contributions are added for the various spin pairs in a crystallographic unit cell. We then find for the exchange energy density, 2 J S 2 {d~o'~ 2 bcc: We = - - 7 - ',~X ] '
4JS z {d~o"~2
fcc:
We = - - 7 - - \d--x-x) '
SC:
JS 2 {dq~'~2 we = --a- \ ~ x x j , JS22~/ 2 [ d~o'~2
hcp: W e -
a
k~xx] "
Expansion by a factor a of the vertical axis divides the coefficient of (dq~/dx) 2 by
74
H. ZIJLSTRA
the same factor a, as only the cell volume increases by this factor and the rest remains the same. The coefficients thus derived are usually written as A, e.g., by N6el and Kittel, or as C = 2A by Brown. They are associated with the Curie t e m p e r a t u r e Tc and can be determined by calorimetry, spin-wave resonance m e a s u r e m e n t s or t e m p e r a t u r e dependence of magnetization. A difficulty is that the models discussed here are based on nearest neighbour interaction, although there is much experimental evidence that interactions at a longer range cannot be ignored. Therefore determination of A will seldom be better than an indication of the order of magnitude. Using the approximate relation A~105~ZTc,
(SI),
with A in J/m, ~ the nearest neighbour distance in meters and Tc the Curie temperature in Kelvin, fulfills most requirements in the present context. In cgs units we have A in erg/cm, ~ in cm and Tc in Kelvin, for which the relation becomes A ~ 106~2Tc,
(cgs).
6.3. Interaction of domain walls with cavities and non-ferromagnetic inclusions Consider an array of non-ferromagnetic spheres on a simple cubic lattice as shown in fig. 25, and assume that the spheres have a radius p and occupy a fraction a of
radius p
0 © ©
0 0
) d
0
) t
Domain Wall
Fig. 25. Cubic array of spherical cavities interacting with a rigid domain wall.
PERMANENT
MAGNETS; THEORY
75
the total volume of the material. The n u m b e r n of spheres per unit volume is
3 n = 0, 4 . / r p 3 ,
so that the n u m b e r of spheres which are intersected by a (100) plane is given by /./2/3= { 3 ~ 2/3 0,2/3 \4~r/ p2 " The distance d between the centres of the spheres on any (100) plane is given by /4,B-'~ 1/3
If we assume that a (100) plane of these spheres is intersected by a domain wall and that the wall m a x i m u m pinning force per sphere is fm, the m a x i m u m pinning force on the wall is F = r~ .~2/3g Jm
•
If the wall is m o v e d through an infinitesimally small distance dx in the presence of an external field H, the change in magnetostatic energy is 2J~H dx. The total change in energy is d W = n2/3fm dx + 2J~H d x . T h e wall will actually m o v e if d W / d x <~O, i.e., if H ~ < - H e where
( 3 )2/3fm0,2/3 ~.
Hc = \~-~]
(6.7)
The above model has been used by Kersten (1943) as the basis of a simple theory of coercivity. Kersten assumed radii of the spheres to be much larger than the domain wall width, i.e., p ~> 6, so that the wall can be regarded as a plane of zero thickness. When a sphere is intersected by a planar domain wall, which is also assumed to be rigid, the pinning force is due to the change in the wall energy which occurs because an area ~rp2 is r e m o v e d when the wall intersects a sphere through a diameter. However, it should be appreciated that the pinning force is a m a x i m u m at the edge of the sphere where the rate of change of the wall energy with position d y / d x is a maximum. For a sphere of radius p the area of intersection with a plane domain wall changes at a m a x i m u m rate of 2~p so that the m a x i m u m pinning force fm per sphere is f~ = 2~-py.
76
H. Z I J L S T R A
Hence the coercivity for a simple cubic lattice of these spheres is given by _
He=
3 )2/3 ~-y _
4~r
_
_
^
2/3
pJs 'x
"
(6.8)
Unfortunately the above result does not agree with the experimental values for ferromagnetic materials which contain dispersions of non-ferromagnetic particles, principally because the effect of the magnetostatic energy due to the surface poles has been omitted. When the spheres, each of volume V, are not intersected by a domain wall the magnetostatic energy is 1 2 m = g/toMs V,
but when they are intersected across their major diameters the above magnetostatic energy is reduced by a factor of about 2 (N6el 1944b). This magnetostatic energy variation may not be negligible in comparison with the change in the domain wall energy. Furthermore the assumption that the domain walls are rigid is unrealistic and makes the model strongly dependent on the shape of the inclusions. 6.3.1. D o m a i n - w a l l p i n n i n g at large inclusions
N6el (1944b) has extended Kersten's theory and has developed a theory of the coercivity of an array of identical non-ferromagnetic spheres which includes the effects of their magnetostatic energies. The resulting expressions for the coercivities depend on the size of the inclusions compared with the width 6 of the domain wall. We consider large inclusions first (p >>6). Consider a non-ferromagnetic sphere in a uniformly magnetized material. The associated magnetostatic energy of the sphere due to the magnetic charges on its surface is W m = l g/x0Ms47rp/3. 2 3
When the sphere is intersected by a plane domain wall through its centre the above magnetostatic energy is reduced by a factor of about 2, i.e., AW m
. # 2s P 9171"[.ZoIVl
3•
A rigid wall moving through the crystal will have minimum energy when it intersects the spherical hole just through the centre. The force required to move it away from the centre is
f = d(Wm+ W~) dx where W~ is the contribution of the wall energy to the total energy. N6el (1944b) has numerically calculated the energy Wm as a function of wall position x and the
PERMANENT MAGNETS; T H E O R Y
77
maximum value of its derivative with respect to x, d Wm')
dx
= 0.600 j2p2,
,/max
/~0
which maximum is attained when the wall is just tangent to the sphere• With eqs. (6.7) and (6.8) we then find for the rigid wall pinned by a cubic array of spheres He = 0 385o:2/3(0 3Ms+ •
\ "
"rr'y "~
(6.9)
/xopMs]"
Note that the magnetostatic term is independent of sphere radius and that the wall energy term is inversely proportional to p. There is a critical radius pc, below which the surface energy term is dominant, and thus Kerstens theory becomes applicable. Above pe the magnetostatic term is dominant and N6eI's theory must be applied. The critical radius is pe ~
~o~/Y~
•
This value is exactly the same as that derived by Kittel (1949) for the radius below which a ferromagnetic sphere is uniformly magnetized in its lowest state (see section 4.1). In order to test the validity of eq. (6.9) we substitute the parameter values of a typical rare-earth magnet and of iron (see table 4). We then obtain for the rare-earth magnet, with a = 0 . 1 and p = 1 0 - 6 m , H e ~ 1 0 4 A m -1, which is by several orders of magnitude too low as compared with experiment. The coercivity of these magnets is obviously not determined by wall pinning at large inclusions• More likely models are discussed in sections 6.3.3 and 6.5. For iron with the same dispersion of inclusions we find He ~ 105 Am -1, which is far too high. A possible explanation for the latter discrepancy is discussed in the next section.
TABLE 4 Intrinsic properties (order of magnitude) of a typical hard magnetic material (lanthanide-cobalt alloy) and a soft magnetic material (iron). La--Co Anisotropy field HA 107 Anisotropy constant K 5 × 106 Saturation magnetization Js 1 Saturation magnetization Ms 106 Exchange parameter A 10-11 Wall energy 3' 5 x 1 0 -2 Wall thickness 6 5 x 10 -9
Fe
(SI)
La-Co
Fe
(cgs)
5 × 104 5 × 104 2 2 × 106 10-11 5 x 1 0 -3 5 x 10-8
(Am -1) (Jm -3) (T) (Am -1) (Jm -1) (Jm -2) (m)
10s 5 × 107 103
5 x 102 5 x 105 2 × 103
(Oe) (erg cm -3) (erg Oe -1 cm -3)
10-6 10-6 50 5 5 × 10-7 5 × 10 -6
(erg cm -1) (erg cm -2) (cm)
78
H. ZIJLSTRA
Fig. 26. Spherical cavity in a ferromagnetic crystal with reverse-domain spikes. The arrows indicate the domain magnetization. Concentrations of surface charges are indicated by their respective signs.
6.3.2. Nucleation of reverse domains at large inclusions If the spherical cavity is larger than the critical radius it becomes energetically favourable to provide it with a pair of reverse domain spikes as shown in fig. 26. The (dominant) magnetostatic energy is then appreciably reduced at the expense of some wall energy. The latter energy becomes less important the larger the sphere. Therefore in the magnetized crystal reverse domains may occur spontaneously at non-ferromagnetic inclusions or cavities. N6el (1944b) has shown that these reverse domains expand indefinitely when the applied field H = -H~, where Hc = 1.23y/tzopMs.
(6.10)
For the same two examples of the previous section (table 4) we calculate the nucleation coercivity at an inclusion of radius p = 10-6m and find Hc(La-Co) 5 × 104Am -1 and H c ( F e ) ~ 103 A m -1. The nucleation at an inclusion in a hard magnetic material is thus relatively easyl Inclusions of cavities should therefore be avoided or indefinite expansion of a nucleated domain should be prevented by some pinning mechanism. The spike formation at a cavity is analogous to the formation of reverse domain spikes at the flat end face of a long magnetized crystal, where as mentioned in section 6.4 the local demagnetizing field is Hd = -½Ms (see also fig. 29). 6.3.3. Domain-wall pinning at small inclusions If the inclusions are small (p ~ ~), the pinning force is due to the change in the energy of a wall which occurs when part of its volume is occupied by nonferromagnetic inclusions. Consider a spherical cavity of volume V and radius p in the magnetized crystal. If this is located inside a wall the wall energy is reduced by the following quantities: (a) (b)
exchange energy
We = a ( dq~'~2 \ d x ] V; magnetocrystalline anisotropy energy
WK = K V s i n 2 ~ .
The inhomogeneous magnetization requires a correction Wn of the order which may be neglected here since p ~ 6.
p2/t~2,
PERMANENT MAGNETS; THEORY
79
The presence of the sphere adds a certain amount of magnetostatic energy, calculated by N6el (1944b) to be (c)
2_ 2//dq~ 2] g Wa = _~/x0Ms2[1-25P \ dx ] J '
where the second term is due to the inhomogeneous magnetization with angular gradient dq~/dx. Outside the wall the magnetization is uniform and oriented along the easy axis. Hence the energies WK and We are zero and
1 2 Wd = gtx0Ms V. The difference in energy between the two situations: sphere outside wall and sphere inside wall then is
[
A W = - / K sin 2 ~0 + A
-~
dq~ 2
or using eqs. (6.3) and (6.5),
A W
=
-
[
2K +
75
B21 V sin 2 q~.
Under the present approximations, K > / x 0 M ~ and p ~ B, we may ignore the second term and find A W = -2KV
sin 2 q~.
The pinning force (using eq. (6.3) for the relation between ~0 and x) is f-
d(zX dxW ) _ 4 K V 3 / K~ sin 2 p cos p .
This is maximum for cos 2 ~ = ½so that with eq. (6.5)
sV5 K V Im-- ~ - - 'TT~-Substituting this result into eq. (6.7) we find the coercivity due to a cubic array of spheres with radius p ~ 8 as 2 K a2/3 V 1 Hc = 0.47-----0-~s p 28 = 1.95/-/1 ~ ol 2/s , where H a = 2K/~oMs, the anisotropy field.
(6.11)
80
H. ZIJLSTRA
The numerical factor of 1.95 depends on the geometry of the inclusions and their distribution, but is expected to be of the same order of magnitude for a variety of probable inclusion shapes and distributions. Using the parameters of the two examples mentioned in section 6.3.1 (table 4), we find for a dispersion of inclusions with a radius of 10 -9 m, occupying 0.1 of the material Volume H c ( L a - C o ) ~ 106Am -1 and H c ( F e ) ~ 5 0 0 A m -1. Both orders of magnitude agree well with experiment, which suggests that pinning at small inclusions might be an explanation for the observed coercivities. For this pinning mechanism it is assumed that the wall is rigid and moves through a cubic array of spheres (see fig. 25). A non-rigid wall in a random distribution of spheres is able to arrange itself so that it contains a maximum number of inclusions. The latter, a more likely picture of a pinned wall is expected to obey eq. (6.11) as well.
6.4. Domain-wall nucleation at surface defects Domain-wall nucleation may occur at surface defects such as pits, protrusions, scratches or sharp edges, where the magnetization reversal is assisted by the locally increased demagnetizing fields (Shtrikman and Treves 1960). Consider, for example, a surface defect such as a pit (fig. 27) in the form of a truncated cone with an apex semi-angle ~b, base radius r± and face radius r2. It can be shown (Zijlstra 1967) that the axial demagnetizing field Ha at the apex point P is Ha = 1Ms sin 2 q5 cos ~b ln(rl/r2).
,,//I////////////l z
\
\
Fig. 27. Surface defect.
PERMANENT MAGNETS; THEORY
81
At an infinitely sharp point, i.e., when r2 = 0, the demagnetizing field at the point P is infinite. However, as pointed out by Aharoni (1962), this is physically unrealistic since a point cannot be sharper than the atomic radius --~10-1° m. For a conical pit with a base radius of 1 p~m and sin 2 ~p cos ~b = 0.4 (i.e. ~b ~ 60 °) Ha ~ 1.8Ms. Similar demagnetizing field concentrations arise at sharp corners and edges and at the bottom of cracks and scratches. Although they are appreciably stronger than the overall demagnetizing field of a magnetized body and perfectly capable of explaining the persistence of reverse domains in soft magnetic materials (De Blois and Bean 1959) they are not sufficient to account for nucleation of reverse domains in hard magnetic crystals. However, there is experimental evidence that sharp edges do play a role in nucleating reverse domains, as demonstrated by the following experiments on SmCo5 and related compounds. Becker (1969) has measured a coercivity of 8.3kAm -1 (105 Oe) on a YCo5 powder made by mechanical grinding. Subsequent treatment in a chemical polishing solution increased the coercivity to 266 kAm -1 (3340 Oe). Becker attributed the increase to the rounding off of the initially sharp edges of the powder particles, which he observed by microscope. Ermolenko et al. (1973) prepared a single-crystal sphere of 8mCo5.3 of about 2 mm diameter. After chemical polishing the sphere had a coercivity of 460 kAm -1 (5800 Oe). Scratching the sphere reduced the coercivity to practically zero (Shur 1973) and subsequent polishing restored it again. The influence on the nature of the hysteresis loop was shown by Zijlstra (1974) who compared the hysteresis loops of two single particles taken from a ground SmCo5 powder before and after annealing (fig. 28). The coercivity of the particle as ground appeared to be determined by easy nucleation and subsequent pinning of domain walls. For the annealed particle the nucleation proved much less easy. The annealing process may have removed internal defects which also have their influence on the hysteresis. However, McCurrie and Willmore (1979) have ~hown that a similar behaviour is obtained when the particles are smoothed by chemical polishing rather than by heat treatment. A special case is the long body with a flat end face. The local demagnetization factor equals ½ at this end face, although the average demagnetization factor approaches zero for longitudinal magnetization. The associated superficial demagnetizing field may give rise to homogeneous nucleation of reverse domains as shown in fig. 29. 6.5. Interaction of domain walls with the crystal lattice 6.5.1. Wall pinning at regions with deviating K and A The nucleation of domain walls at regions with reduced K has been treated by Aharoni (1960, 1962) and Brown (1963) using micromagnetic theory, but although a nucleation field Hn of the order of one tenth of the anisotropy field HA could be derived, their model was not able to explain the many orders of magnitude
H. ZIJLSTRA
82
r~
e..
""
O
,-
©
E
o~
~E
E
r.~
r~
O
=2 o
PERMANENT MAGNETS; THEORY
83
/
/ a
Fig. 29. End surface of a magnetized body. (a) The body in cross section. Reverse-domain spikes penetrate from the surface into the body (schematic). The arrows indicate the domain magnetization. (b) Micrograph of a Sm2Co17single-crystal surface with the spikes seen from above. reduction of Hn with respect to HA f o u n d experimentally. Calculations of the pinning of d o m a i n walls at regions with r e d u c e d K and A were m o r e successfully carried out by A h a r o n i (1960), Mitzek and S e m y a n n i k o v (1969), Hilzinger (1977) and Craik and Hill (1974). W e will discuss the p r o b l e m on the basis of the t h e o r y by Friedberg and Paul (1975) of d o m a i n wall pinning at a planar defect region. Consider the crystal shown in fig. 30 in which there are three distinct regions a, b and c defined by a f r o m - ~ to Xl , b f r o m xl to x2, c from x2 to + ~ . Their magnetic properties J, K and A are identified by subscripts i = a, b and c where
Ja=Jc¢Jb, A a = A~ ¢ A b ,
g . = K ~ gu.
84
H. ZIJLSTRA Z
I
I
x
,/
c ,¸ , /
b
I a
,
\
I X2
I I Xl
Fig. 30. Domain wall distributed in three zones a, b and c of the ferromagnetic crystal.
The easy axis of the uniaxial crystal is along the z-axis; the planar defect is in the yz plane. A field H is applied along the z-axis. A 180 ° domain wall parallel to the planar defect has an energy per unit area of
f~[Ai\{d~2 d x ] + Ki sin 2 ~ - H J / c o s ~ ] dx,
Y = -~ L
(6.12)
where ~ is the angle between the magnetization vector and the z direction, and the subscript i applies to the appropriate region where the wall is located. Minimizing Y by variational calculus and integrating Euler's equations in the three regions yields the following three equations: - A i ( d ~ ' ~ 2 + Ki sin 2 ~ - HJ~ cos ~p = C~, \dx]
(6.13)
for i = a, b and c, where C~ are constants to be determined by the boundary conditions. Imposing the conditions ~ ( - ~ ) = 0 and ~p(+~)--~- and noting that d~/dx = 0 at x = _+0%determines Ca = -HJa and Cc = HJa. The'continuum approach inherent in micromagnetic methods requires continuity of ~ at the interfaces at xl and x2, where ~ has the values ~1 and q2 respectively. Stability of the wall requires zero torque everywhere and thus minimum local energy density. This requirement implies continuity of A d~/dx at the interfaces xl and x2, which can be seen from the following argument. Consider the interface of xl and a narrow zone of width Ax on either side (fig. 31). The value of z~x is so small that dq/dx may be taken as constant in each zone. The energy content of this slab is then (to a first approximation) A T = A a (~Pl - ~0a)2 ~. ( K a sin 2 f~l -- HJa c o s ~/)1) A x
Ax
+ Ab (~Pb-- ~)2 4- (Kb sin 2 ~p~-- HJb cos ~1) Ax. Ax
PERMANENT MAGNETS; THEORY
85
i i [ I
i I
i
1
I I
I I
×
Fig. 31. Orientation angle ~0as a function of distance x near the interface between zone a and zone b. Minimizing this with respect to q~l with fixed values of ~0a,~b and Ax and subsequently letting Ax approach to zero, yields
A.(~x) = Ab(~-~-~X)b at x= Xl. The difference ~ b - ~Oahas a fixed value for fixed Ax, since it determines the local exchange energy density. This must be equal to the anisotropy energy density, which is fixed by ~1 lying between ~0, and q~b,which interval can be taken arbitrarily small. Continuity of q~ and A d~p/dx at the interfaces xl and x2 produces four equations from which dq~/dx and Cb are eliminated to give a relation between q~ and ~02 with coefficients expressed in the parameters A, K, J and H : H(AaJ~ - A J b ) ]2
[cos ~, + ~ -
A--/~uJ -
[cos
H ( A a J , - AbJb) ]2
~,2 ~ 2(--X~Ka- A---~3]
(6.14)
2HAaJa - O. AaKa - AbKb
This equation describes a hyperbola shown in fig. 32. Only the upper right hand branch applies to our model. For H = 0 this curve degenerates to its asymptote cos ~j = cos ¢2. The width of the defect determines which point of the curve represents the actual situation. Narrower defects shift the point to the right. In the small-deviations approximation, A a ~ . A b , K a ~ K b and Ja-~Jb, eq. (6.14) can be written as
7)/t-x-+-k-)j = -4h
/(A_k- ,,÷) +
,
-
[cos
K,12I (6.15)
86
H. ZIJLSTRA cos %
J cos "P2 -p
\ \\
Fig. 32. The hyperbola (cos ¢1 + p)2 _ (cos ~2 + p)2_ Q = 0.
w h e r e A A = A b - - Aa, A K = Kb = K a , A J = J b - - J a and h = H/HA with H A = 2KJJa, the anisotropy field of the undisturbed crystal. T h e relation b e t w e e n go1, go2 and the width x 2 - xl of the defect is calculated by integrating eq. (6.13) for i = b:
f
x: dx = f~i2 dgo [A~ sin z go - ~
Cb 1-1/2 ' cos go - AbJ
(6.16)
dX 1
with -- AaKa sin2 gol -- ~H (AbJb -- AaJa) cos ~1 - H AAabJ Cb - AbKb Ab
H o w e v e r , this integral cannot be solved analytically and has to be approximated. First consider the case H = 0. F r o m eq. (6.14) we see that cos: go1= cos 2 go2,which means that for finite width of the defect go1 = ~ ' - ~ 2 and the wall is located symmetrically with respect to the defect (see fig. 33). Since the width of the defect is not specified this m e a n s that in zero field a wall finds an equilibrium position at a defect of any size different f r o m zero; there is no critical size for defects of this kind. M o r e o v e r this m e a n s that a field, h o w e v e r small, is n e e d e d to detach the wall f r o m the defect. N o w assume that the width D of the defect is small c o m p a r e d to the wall width 6 defined by eq. (6.5). T h e angular gradient dgo/dx m a y then be assumed constant inside the defect. F r o m eq. (6.4) in section 6.2.1 we see that d_~_~= 4 K b dx ~ sin ~ ,
PERMANENT MAGNETS; THEORY "it-- --
--
--
87
[
0 . . . . .
I
XI
X2
--
~ X
Fig. 33. Orientation angle ~0 as a function of x of a pinned d o m a i n wall in zero field (drawn line) and
in a small positive applied field (dotted line). w h e r e we take for ~0 the average value 1(~1 + ~pz). Integrating this gives
(Abl Kb) 112 D
=
x2 -
Xl =
sin
(6.17)
l ( ~ o I -it- ~D2) (~2}2 - - ~ 0 1 ) "
N o w suppose that a small field H ~ HA is applied. F r o m eq. (6.15) we see that in the small-field, small-deviations a p p r o x i m a t i o n
COS2 ~1 -- COS2 ~2 =
-4h
/?A ~
+T
"
T h e small-defect-width a p p r o x i m a t i o n w h e r e ~92~'~-~1 allows cos 2 q~l - cos 2 ~2 ~ (~02- ~pl) sin(~j + ~2), so that by substituting this into eq. (6.17) we find
h-
7r D / A A
AK\
~- 6b t--A---+--K--) sin(qh + ¢2)sinl(qh+ ~2).
(6.18)
L o o k i n g at fig. 33 we see that u n d e r increasing field h the wall will shift to the right thus steadily decreasing the average angle of orientation ~p inside the defect. Starting from ~p = ~-/2, the position at H = 0, we see that the angular function of eq. (6.18) starts at zero and increases to a m a x i m u m of the o r d e r o n e at a certain critical value of h. F u r t h e r increase of h will give no solutions for ~1 and ~2 so that no stable wall will exist. W e identify this critical field with the unpinning field or coercive force (6.19)
88
H. ZIJLSTRA
The minus sign in eq. (6.18) implies that pinning occurs only if the form between brackets in eq. (6.19) is negative, i.e., the wall energy inside the defect is lower than if the defect were not present. If the form in brackets is positive a wall will be repelled, and the defect will form a barrier rather than a trap. It should be noted that eq. (6.19) is valid only in the small-field, small-deviations, small-defect-width approximation. If deviations become larger the symmetry in AA and AK will be lost. In particular a substantial lowering of A will contract most of the wall inside the defect so that the condition 6 >> D is no longer satisfied. This particular situation is discussed in secion 6.5.2. In the small-deviations approximation ~b may be replaed by 6a, the wall thickness in the undisturbed crystal. Note that hc falls within the small-field approximation as a direct consequence of the small-defect-width, small-deviations approximation. In this approximation a deviation of J has no influence on he. In the case where D >> ~b the wall will be almost entirely within the defect region at H = 0. With field increasing from zero we deal with a wall penetrating from region b into region c, i.e., a wall pinned by a phase boundary. Using eq. (6.13) with i = b, we impose boundary conditions ~ = 0 and d~/dx = 0 for the far left-hand end of the wall, which yields Cb = -HJb. Similarly we find with q~(+~) = 7r and d p / d x ( + ~ ) = 0 in eq. (6.13) with i = c the integration constant Cc = HJa, recalling that region c has the s a m e properties as region a. Eliminating d~o/dx from these equations we find H=
(KaAa - KbAb) sin 2 q?2 (AaJa - AbJb) COS q~2+ (AaJa -{-AbJb) '
which in the small-deviations approximation becomes
(AA/A + AK/K) sin 2 ~2 H = ½Ha(b) 2 + (AA/A + AJ/J)(1 + cos ¢2)" Looking at fig. 33 we expect that the highest rate of energy change will be found at about ¢2 = ~-/2, so that the coercivity becomes _
hc
He
HA(b)~
AK\ ~-A--+--K--)'
1/AA
(6.20)
which is the pinning force exerted upon a wall that penetrates from a phase with low A and K into a phase with high A and K. In a material as SmCo5 with HA = 2.5 x 1 0 7 A m -1 (300 kOe) this pinning mechanism could account for a coercivity of the order of 1 0 6 A m i (~104 Oe) with a 10% variation in A and K.
6.5.2. Pinning of a domain wall by an antiphase boundary This section treats a theoretical model of the interaction of a plane domain wall with a certain type of plane lattice defect, namely the antiphase boundary (APB). The A P B occurs in ordered crystals where the atomic order on either side of the
PERMANENT MAGNETS; THEORY
89
I
X X X I0 0 0 I~ I~ I~III'IX'XI'X ~ X I
x x × f×?×?×?×
~x~x~×~?x?x?×? x I
APB Fig. 34. Ferromagnetic ordered crystal with magnetically active antiphase boundary (APB). A P B is opposite in phase. This is clarified in fig. 34 for a two-dimensional binary crystal consisting of A atoms (circles) and B atoms (crosses). The crystal lattice is continuous, but on the right-hand side of the defect B atoms occupy what would have been A sites without the presence of the APB, and vice versa. Suppose now that only the A atoms carry a magnetic m o m e n t and that these are coupled ferromagnetically in the undisturbed crystal. However, across the A P B the much shorter A - A distance might give rise to antiferromagnetic coupling, thus dividing the crystal into two ferromagnetic parts which, in the lowest state and zero field, are antiparallel as indicated in fig. 34. It has been suggested by Zijlstra (1966) that such magnetically active A P B s are responsible for the easy nucleation of reverse domains in MnA1 crystals. On the other hand it was expected that moving domain walls would encounter strong pinning, which was indeed found to exist in MnA1 crystals (Zijlstra and Haanstra 1966). Consider a magnetic domain wall as described in section 6.2.1 with its plane parallel to an A P B as described above. T h e orientation angle of the magnetization is 0 at x = - ~ and ~r at x = + ~ . The A P B is located at x = 0 and coincides with the y z plane. The ferromagnet has uniaxial anisotropy with the z-axis as easy axis. The energy densities due to anisotropy and to exchange interaction are described by eqs. (6.1) and (6.2), respectively. T h e coefficients K and A are assumed to be the same throughout the crystal, except for the APB. The situation at the A P B is described as two layers of atoms, at a distance ~, one belonging to the left-hand side of the crystal and the other to the right-hand side. The coupling energy density between these two adjacent lattice planes, is different from the coupling energy density in the undisturbed crystal owing to shorter A - A distance and is given by At w~ = g ~ - [1 - c o s ( ~ , 2 - ~ , ) ] ,
(6.21)
where pl is the orientation of the left-hand layer and ~2 that of the right-hand layer. The coefficient A ' is different from A and can be negative, in which case antiparallel coupling across the A P B is favoured. The structure of the wall in an arbitrary position with respect to the A P B is shown in fig. 35 by the orientation
90
H. Z I J L S T R A
J
0
-×
Fig. 35. Orientation angle p as a function of distance x normal to a domain wall pinned at APB.
angle q~ as a function of x. T h e wall energy per unit area can then be written as 3' = 2X/)-K(1 - cos q~,) + 2 X / ~ ( 1
+ cos q~2)
+ (A'/sc)[1 - cos(~2 - ~01)] nt- ½K~(sin 2 ~, + sin 2 (P2).
(6.22)
T h e first two terms follow by integrating eq. (6.6) from 0 to ~1 and f r o m q~2 to ~, respectively. T h e third term is the exchange coupling energy in the slab of thickness ~ at the A P B and the last term accounts for the anisotropy energy in the same slab. N o w approximating to continuous magnetization with the A P B as a mathematical plane of zero thickness (~: ~ 0) where the j u m p in p is concentrated, we can ignore the anisotropy energy term and write (omitting constant terms) 3' = x/)-g
2(cos q~2- cos ~1) - r/cos(r/2
-- ~1)
(6.23)
where the coefficient r / = A'/~X/--A-K can take values f r o m -oo to 0 for antiparallel coupling, and f r o m 0 to +o0 for parallel coupling across the A P B . F o r r / ~ oo the difference between q~l and q~2 vanishes and we have the undisturbed wall with 3' = 4X/A--K following from eq. (6.22). Using standard differential calculus with respect to the two variables ~pl and q~2 we find for r / > 1 stability at cos qh = l/r/ and cos ~0z = - l / r / , i.e., the wall is pinned with its centre coinciding with the A P B . F o r r / < 1 the wall collapses into the A P B with q~l = 0 and ~2 = ~r. Such a d e g e n e r a t e d wall will still be called a wall here. T h e energy of the pinned wall follows f r o m eq. (6.22) with the a p p r o p r i a t e values of cos ~01 and cos q~2 substituted as
y = 4 ( 1 - 1/2r/)N/)--K,
for
and T=2r/X/A--K,
for
r/
r/> 1
PERMANENT MAGNETS; THEORY
91
-5
I
1'0
"-5
--10
Fig. 36. Energy ~/of domain wall pinned at A P B in zero field as a function of the coupling p a r a m e t e r ~7 across the APB.
These relations are shown in fig. 36. N o t e that there is no discontinuity at r / = 1, neither in value, nor in slope. Since we have chosen the uniformly magnetized state with q~l = ~02 = 0 as the g r o u n d state with zero energy, the wall e n e r g y goes to - ~ when ~ / ~ - ~ . This m e a n s that eventually the pinning b e c o m e s infinitely strong. T h e d o m a i n wall is thus pinned at the A P B for any value of r/ in zero field. To calculate the field that must be applied to detach the wall, we first have to see h o w the pinned wall behaves in an applied field.
Energy of a pinned wall in an applied field. Consider a part of a wall stretching f r o m x = - w where q~ = 0, to x = 0 w h e r e q~ = ~00. T h e angle ~0 is kept fixed and the wall e n e r g y is calculated as a function of the f i e l d / - / a p p l i e d along the positive z direction. T h e energy of this partial wall is Y(~o, H ) =
F[
K sin e ~ + HJ(1 - cos ~ ) + A [ d~'~2]
\ d x ] J dx,
(6.24)
where J is the saturation magnetization and the o t h e r symbols are as m e n t i o n e d before. With variational calculus we find the condition for m i n i m u m energy to be
d2~p
2 K sin ~ cos ~ + H J sin ~p - 2 A ~
= 0,
which states that the t o r q u e is zero everywhere. Multiplication by dq~/dx and integration f r o m - ~ to 0 give
92
H. ZIJLSTRA
{dq~ ,~2 K sin 2 q~0+ HJ(1 - cos q~0)= A \d-x-x] " Substituting this into eq. (6.24) and switching f r o m x to ¢ as variable we have Y(q~o, h) = 2 ~/ A K
(1 - -
fO~°
COS 2 ~ - -
2h cos q~ + 2h) u2 d~o
= -2{[cos 2 Po + 2(h + 1) cos q~0+ 2h + 1] 1/2- 2(h + 1) 1/2 + h ln[(cos 2 ~o + 2(h + 1) cos q~o+ 2h + 1) 1/2 + cos ¢o + h + 1] - h In[2(h + 1) 1/2+ h + 2]}, where h
=
(6.25)
H/HA, and HA = 2 K / J is the anisotropy field.
Detachment of a pinned wall. Consider the wall in zero field symmetrically pinned at x = 0 with q~2= ~" - qh. A field applied along the z axis will rotate ~Pl and q~2 towards 0, i.e., the centre of the wall will be shifted from x = 0 to the right in fig. 35. If the field is varied f r o m zero to increasing positive values, the force exerted on the wall will increase, at first being in equilibrium with the rate of change of wall energy. But as the latter quantity reaches a m a x i m u m a further increase of the field detaches the wall from its pinning site and makes it travel to infinity. T h e total energy of the wall when pinned is
3' : 3'(~1, h)+ 3'(¢2, h ) - n V ~
cos(~2- ~1),
where 7(qh, h) follows from eq. (6.25) with qh substituted for q~0, and 7(qh, h) follows by substituting 7r - q~2 for ~0 and - h for h. T h e m i n i m u m of 3' with respect 1
0.5
\
\
0.2
0.1
\
\
0.05
\
\
0.02
\
0.01 0.1
0.2
0.5
1
2 _
F i g . 37. R e d u c e d
c o e r c i v i t y h0 =
5 ~
Ho/HA d u e
10
20
50
100
r]
to pinning at APB
a s a f u n c t i o n o f 7.
PERMANENT MAGNETS; THEORY
93
to the independent variables ~01 and ~02 is sought and the critical value h~ of h where this extreme ceases to be a minimum is determined. This critical value h~ is identified with the unpinning field or the coercivity and its relation with r/ is shown in fig. 37. The curve applies only to positive values of ~7. At negative 7/ the zero field values of q~l and ~2 are 0 and ~-, respectively, and it would take a stronger field than h = 1 to detach the wall. However, at h = 1 uniform rotation occurs and the whole concept of wall detachment becomes irrelevant. 6.5.3. Nucleation of a domain wall at an antiphase boundary Consider the crystal of fig. 34 with the coupling p a r a m e t e r ~7 at its A P B smaller than zero. If a strong positive field is applied a situation occurs as depicted in fig. 38(a). This is a m o r e or less saturated state which is stable, though not always of the lowest energy, for all positive values of h including zero. If a counter field of increasing strength is applied tO this state there is a critical value hc of - h at which the symmetric configuration becomes unstable and a wall is emitted from the defect, leaving the defect itself with an antiparallel magnetization orientation as given in fig. 38(b). The relation between the critical field hc and the coupling constant is calculated in the following. Consider the configuration of fig. 38(a) in a field h. Near the A P B there are two partial domain walls separated by an angle (~;2-~pl). The energy of this configuration is T = Y(~I, h ) + T(q~2, h ) - 7/N/A--K cos(~2 - ~1), where ~/ is a negative n u m b e r and Y(q~l, h) and 7(q~2, h) are given by eq. (6.25) with @1 and q~2 respectively substituted for ~P0. For equilibrium the partial derivatives of y with respect to the independent variables ~/91and q~2 must be zero. Since in equilibrium q)l --@2 for symmetry reasons, these two conditions reduce to one: ~
2(1 - cos 2 q~l- 2h cos ~pl+ 2h) 1/2+ ~ sin 2q~1 = 0.
(6.26) q~
q01
-~ x
r
a Fig. 38. (a) Magnetization orientation near A P B after saturation in a strong positive field. (b) Wall emitted from A P B by a negative field moves to the right, leaving the A P B in antiparallel configuration.
94
H. Z I J L S T R A
The value of q~a in the remanent state (h = 0) is given by cos ¢~ = 1
for
0 > 7 > -1
cosqh=-l/7
for
7<-1-
By investigating second derivatives we find that the equilibrium of eq. (6.26) loses its stability when cos q~l + h ~<0. This gives a simple relation between the critical field hc and the critical angle qh: he
=
cos q~l •
Elimination of ~1 from this formula and eq. (6.26) then gives the relation between hc and 7 as shown in fig. 39. The nucleation described here occurs only for negative values of 7 and at a negative field which approaches zero for large negative values of 7/. The Lorentz microscope observations by Lapworth and Jakubovics (1974) and by Van Landuyt et al. (1978) of the APBs in thin slices of MnA1 crystals being always decorated by a domain wall are explained by assuming that a strong negative coupling at the APB is present. 6.5.4. Thin-wall coercivity in a perfect crystal In crystals with a very high magnetocrystalline anisotropy constant K, comparable to the energy density A / a 2 due to the exchange coupling, the wall thickness t~ = 7r~v/A/K according to eq. (6.5) becomes of the order of the lattice parameter a. In this case we must abandon the continuum approach of section 6.2.1 and take into account the discreteness of the crystal lattice. It then turns out that there is a difference in energy between a wall with its centre coinciding with a lattice 1 0.5
02
\
ho l
0.1
"..
0.05
0.02 0.01
0.1
\ 0.2
0.5
1
2
5
10
20
50
100
Fig. 39. R e d u c e d c o e r c i v i t y hc d u e to n u c l e a t i o n of a wall at A P B as a function of - 7 .
PERMANENT MAGNETS; THEORY
9_
95
b
Fig. 40. Spin orientation in domain wall of fig. 19 viewed along a row of atoms normal to the wall plane. (a) High-energy transitional position. (b) Low-energy stable position. plane and a wall with its centre just b e t w e e n two lattice planes. T h e two situations are shown in fig. 40(a) and (b), where the (b) configuration has the lowest energy. T h e energy difference gives rise to pinning of the wall (Zijlstra 1970a). T o calculate the wall e n e r g y we divide the wall along its thickness into three zones: two continuous zones away from the centre, where the angle b e t w e e n adjacent spins is small, and a central zone of N + 2 discrete magnetic m o m e n t s . T h e continuous zones end in the first (or, as the case m a y be, the last) discrete m o m e n t (fig. 41). T h e energy of this wall in a field h along the z-axis is 7 = y(q~0, h ) + ')/(~DN+I,h)
hK(2- cos q~0- cos q~N+I) + ~, [aKsin2~i+2~A{1-cos(¢i-~oi-1)}+2 h K ( 1 - cos ~i)l + laK(sin2 q~0+ sin 2 q~N+l)+
i=1
-1-
a
2A a
{1 -- COS(@N+
I
i
i
I
t
1
(6.27)
1 -- qON)} ,
I
I
I
I
x\
Fig. 41. Domain-wall model consisting of centre part with discrete spins sandwiched between continuous zones.
96
H. Z I J L S T R A
where y(q~0, h) is given by eq. (6.25) and 7(~Pl, h) follows from eq. (6.25) by substituting (Tr - ~N+I) for ¢P0 and - h for h. The third term accounts for half of the anisotropy energy of the spins 0 and N + 1, the other half being included in the continuous zones. Similarly the fourth term accounts for the magnetostatic energy of the same spins in the field h = HJ/2K (where J is the saturation magnetization per unit volume). The fifth term is the sum of the anisotropy energy and the magnetostatic energy of the spins 1 to N and the exchange-coupling energy between spins 0 to N. The last term adds the exchange-coupling energy between spins (N + 1) and N. The energy difference between the two spin configurations of fig. 40 in zero field has been calculated by Van den Broek and Zijlstra (1971) by minimizing eq. (6.27) with h = 0 for variations of ~i. The result is given in fig. 42 where the energy barrier is plotted as a function of ~7 = a2K/A. The angle between the two central spins of the wall in its lowest state is shown in fig. 43 as a function of ~7. For values of ~7 greater than 4 the wall collapses to a configuration with one part of the spins oriented in the + z direction and the rest in the - z direction. The critical field hc required to let the wall pass the energy barrier is calculated by minimizing eq. (6.26) and finding the value of h for which the equilibrium becomes unstable. The result is given in fig. 44 where log hc is plotted as a function of r/. With increasing ~7 we see that a sharp rise occurs at r / ~ 1. This phenomenon is indeed found to occur in a family of lanthanide-transition metal compounds investigated by Buschow and Brouha (1975) and Brouha and Buschow
v
10-1 aK
10-2
10.3
10-~
10-5 t o
1
2
3
/.
_-~rt
Fig. 42. Energy difference between configurations of fig. 40(a) and (b) as a function of ~t =
a2K/A.
PERMANENT
MAGNETS;
THEORY
97
TC
3
&,.p
1
0
I
I
I
I
I
I
1
I
~
~
I
2
~-rt F i g . 43. A n g l e b e t w e e n
t h e t w o c e n t r a l s p i n s in t h e c o n f i g u r a t i o n field.
o f fig. 4 0 ( b ) as a f u n c t i o n o f r/ a t z e r o
1
f 0.5 hc 0.2
j
O.OE
0.02
O.Ol o.1
0.2
0.5
5
1
10
20
50
100
Dq.
F i g . 44. R e d u c e d
c o e r c i v i t y hc =
He~HA as a f u n c t i o n o~ r/.
(1975). Their results are summarized in fig. 45, in which the coercivities of various compounds measured at 4 K are plotted as a function of HA/Ixs, where /zs is the magnetic m o m e n t per formula unit. This variable can be rewritten as HAI.~J~, in which expression the n u m e r a t o r is proportional to K and the denominator is proportional to A. There is only qualitative agreement since the proportionality factor between K/A in the model and HA/I~ in the experiment is not known.
98
H. ZIJLSTRA 30 - [kOe)
/A
o y (Co,Ni)s x Th {Co,Ni)s ,, Lo (Co,Ni)5
/
/ / /
2c
I I,,
"1
ac
I ~o
I I 4 I
°o
i
10
°° ':'~
x ~
I
2 50 30 0 (kOe/jaB ) HA/-IJs / F.U./
20
"
Fig. 45, Coercivity of various lanthanide-transition metal compounds at liquid helium temperature, as a function of HA/t~s, which variable is proportional to ~7 (Buschow and Brouha 1975, Brouha and Buschow 1975). Thin-wall pinning is a homogeneous process where the wall is stationary below the critical field and moves to disappear beyond this field. This gives rise to typical rectangular hysteresis loops as observed by Barbara et al. (1971) on Dy3A12 and by Buschow and Brouha (1975). The similarity between thin-wall pinning at the atomic lattice and the Peierls force in the description of moving dislocations in crystals has been discussed by Weiner (1973) and by Hilzinger and Kronmfiller (1973). Thin-wall pinning in dysprosium crystals was observed and discussed by Egami and G r a h a m (1971). Hilzinger and Kronmfiller (1972) applied the model to the lattice of RCo5 compounds (R = rare-earth element) taking into account various orientations of the wall plane with respect to the crystal axes. Quantitative comparison with experiment is h a m p e r e d by insufficient knowledge of the magnitude of A and is particularly difficult when m o r e than one kind of magnetic atom or m o r e than one nearest neighbour distance is present. Also exchange coupling between other than adjacent atoms, which is not u n c o m m o n in intermetallic compounds, complicates the matter considerably. 6.5.5. Partial wall pinning at discrete sites When a wall is pinned at discrete sites with the parts in between free to move like a stretched m e m b r a n e the coercivity is determined by the competition between the magnetic pressure on the entire wall and the local pinning forces at the pinning sites. Consider a wall pinned at certain sites (fig. 46). Between the pinning sites the wall is free to move under the influence of a field H to form cylindrical
PERMANENT MAGNETS; THEORY
99
Q7 Fig. 46. Wall pinned at discrete sites and bulging under the pressure of an applied field. surfaces if it is pinned to parallel line defects, or look like a padded surface if it is pinned to point defects. In both cases its area S varies by an amount (per unit S ) ,
A S = o l ( x / a )2
where x is the m a x i m u m displacement, a is the distance between the pinning sites, and a is a geometrical factor of the order one. At the same time a volume A V reverses its magnetization direction: AV=/3x
(per unit S),
where /3 is another geometrical factor of the order one. The energy of the magnetic system varies by AE
= yAS
- 2HJ
= ay(x/a)
A V
2 - 2flHJx,
(6.28)
where J is the saturation magnetization and y is the wall energy. If the wall is not parallel to the magnetization direction a magnetostatic term is contributed to the wall energy. This situation occurs with the " p a d d e d surface" and also with cylindrical surfaces whose axes deviate from the magnetization direction. However, when the anisotropy field is large compared with the demagnetizing field, i.e., K > 210 J2 ,
100
H. ZIJLSTRA
as is the case in the hard magnetic materials discussed here, the magnetostatic contribution is small compared with the wall energy and may be ignored (Zijlstra 1970b, Hilzinger and Kronmfiller 1976). The equilibrium position of the wall follows by minimizing h E with respect to x for fixed H : (6.29)
x = HYa2/y,
where a and/3 are taken equal to one. When H is increased until it reaches the pinning field strength Hp the wall is about to leave its pinning sites. The force exerted on these sites by the wall is determined by the wall energy y and by the boundary angle ~0 (see fig. 46). This angle is geometrically connected with the ratio x/a, and the pinning field strength Hp can thus be related to a critical value (x/a)~rit which is a property of the pinning sites. The coercivity H~ then follows from eq. (6.29)
Hc = ~aa
(x)
crit"
(6.30)
This formula is not to be taken too seriously in view of the many assumptions made. However, the inverse proportionality of Hc with the distance a between the defects implies n c o( /,/1/3
where n is the density of point defects distributed in a regular array. If the defects are distributed at random one might expect different results. Hilzinger and Kronmiiller (1976) have made computer simulations of a moving wall pinned by randomly distributed centres and found empirical proportionalities of Hc with n x, with x ranging from 0.5 for weak pinning to 1.5 for strong pinning. Any distribution of the inter-defect distance will give rise to a lowest unpinning field, at which the wall will be detached somewhere. In the new wall position there will again be a lowest unpinning field, which is not necessarily stronger than the previous one. By this the observed coercivity will be lower than which follows from the average a. Moreover, thermal fluctuations will cause wall creep at fields weaker than the coercivity. Small applied-field fluctuations may have the same effect. For this reason permanent magnets with their coercivity based upon wall pinning at point or line defects must be considered as less stable than other magnets. Substantial wall creep has been observed in copper-containing rare-earth permanent magnet alloys which, indeed, have their coercivity determined by wall-pinning at precipitates (Mildrum et al. 1970).
7. Influence of temperature In the foregoing sections relations between coercivity and intrinsic properties like anisotropy, magnetization and exchange coupling energy have been discussed.
PERMANENT
MAGNETS;
THEORY
101
The t e m p e r a t u r e dependence of the coercivity can be determined by measuring the t e m p e r a t u r e dependences of the relevant intrinsic properties and using these in the appropriate equations. However, by this procedure the discussion remains essentially at zero t e m p e r a t u r e in the sense that thermal agitation of magnetization orientation or wall position is ignored. This thermal agitation may lower the coercivity and, moreover, give rise to time effects like wall creep or magnetic viscosity. These time effects render a magnet unstable and should thus be avoided. In this section we shall discuss and estimate roughly where the danger zones are. For a critical review of theories pertaining to magnetic fluctuations the reader is referred to Brown (1965, 1979). The n u m b e r of thermally excited events to occur per second is given by p = v e -aE/kr,
(7.1)
where v is a frequency factor, indicating how m a n y times per second the event could occur and AE is the energy barrier which the system under consideration has to overcome for the event to occur. The barrier AE is c o m p a r e d with the average energy of thermal motion kT, where k is Boltzmann's constant and T the absolute temperature. At r o o m t e m p e r a t u r e k T ~ 4 x 1 0 -21 J. First we consider the case of an isolated particle with shape or magnetocrystalline anisotropy as discussed in sections 3.2 and 3.3. The thermal motion of the magnetization orientation is expected to have peak amplitude at the precessional resonance of the magnetic vector in the anisotropy field. This field will be of the order of 105-107 A m -1, thus giving rise to ferromagnetic resonance at 101°-1012 s -1. W e take these frequencies as the frequency v in eq. (7.1). W e now compare two situations: a highly unstable one with p = 10 s-1 and a practically stable one with p = 1 0 . 7 s -1. For these situations we calculate the required barrier height AE using the values for u and k T mentioned (table 5). There are two points worth noting: (a) The value of AE is not sensitive to the choice of v and (b) p has a very strong dependence on AE, establishing a critical value AE-~ 10 19j below which the system is thermally unstable at r o o m t e m p e r a t u r e and beyond which it is stable. The barrier A E against rotation of the magnetization vector is associated with the anisotropy constant K and the particle volume v AE = Kv.
TABLE 5 I n s t a b i l i t y of m a g n e t i c particle d u e to t h e r m a l a g i t a t i o n at r o o m t e m p e r a t u r e .
p (S 1) 10 10 -7
/,' (s-l) 101° 1012 101° 1012
AE (j) 0.8 1.0 1.6 1.7
x 10 -19 X 10 19 X 10 -lv x 10 -19
102
H. Z I J L S T R A
For shape anisotropy K = 1 0 6 J m -3, which determines a lower limit for v = 10 -25 m 3 for stability. In alnico the elongated precipitates have a v o l u m e of the order of 10 -24 m 3, which is above the critical value. H o w e v e r , Street and W o o l l e y (1949) have o b s e r v e d viscosity effects in alnico which might be ascribed to this relaxation effect. In any case, the barrier is lowered by an applied counter-field as discussed in section 3.1 and b e c o m e s zero at He. So viscosity effects, h o w e v e r small, are to be expected near the coercive field strength. F o r magnetocrystalline anisotropy, K ~ 107jm -3, which determines a lower limit of v = 10-26m 3 for stability. M a g n e t s based on magnetocrystalline anisotropy always consist of fine powders, often sintered to a dense body. T h e crystallite size of these magnets is typically 10-7-10 -6 m, which means a particle volume of 10-21-10 -18 m 3, well a b o v e the critical volume. A n o t h e r case to consider is the thermal activation of wall displacement. A wall pinned over its entire area has in its potential well a resonance frequency given by
{dZY/m)l/2 w = \dx2 / ,
(7.2)
where 3' is the wall energy as a function of the distance x from its pinning site and m is the wall mass associated with the precessional m o t i o n of spins inside a moving wall. For 3' we write arbitrarily
y(x) = a70
+ (1 - a ) y 0 ,
(7.3)
which means that 3' is lowered by a fraction a at the pinning site and is equal to its undisturbed value 3'o when it is displaced by half the thickness 6 of the undisturbed wall. T h e effective mass of a wall has been discussed by D 6 r i n g (1948). F r o m his work we have the relation
47r/z0 (
m - 2c~26
1
)
= 2 a 2 6 , cgs ,
(7.4)
where a is the g y r o m a g n e t i c ratio of the spins in the wall. Substituting eqs. (7.3) and (7.4) into eq. (7.2) and using eqs. (6.5) and (6.6) we have o) ~- ( a o l 2 K X 106) 1/2 ,
where K is the magnetocrystalline anisotropy constant. With K = 107 Jm -3, a = 2 × 105 m A -1 s -1 and a = 0.1 we calculate w ~6x
10 ~°s -~,
or ~ 10 lo s-1 ,
P E R M A N E N T MAGNETS; T H E O R Y
103
to be used in eq. (7.1). Now consider a part of the wall of area S displaced by a distance ½6 from its pinning site (fig. 47). This excitation requires an energy of A E = 7 ( a S + 28X/S),
(7.5)
in which the second term accounts for the peripheral wall that has to be made. W e may safely assume that an excitation with S < 62 will not give rise to an increasing unpinning of the wall. We thus take the energy of an excitation with S = 62 as the minimum 2~E for wall detachment and see whether this may occur at r o o m temperature. The activation energy for this excitation is A E = 23/6 2 ~ 20A6,
where the fraction a is ignored with respect to 2 and y6 is replaced by the exchange p a r a m e t e r A times 10 (eqs. (6.5) and (6.6)). With A ~ 10 -11Jm -1 and a ~ 10 -s m, as it is in highly anisotropic materials like SmCos, we have AE 10 -18 J. Substituting this into eq. (7.1) with the value of v = 10 l° s -1 we obtain the n u m b e r of these excitations per second: p=
10 -207S 1,
which means that in this example no thermal instability will occur. In materials with extremely high anisotropy we have very thin walls of the order of the lattice p a r a m e t e r as discussed in section 6.5.4. These walls are pinned by the atomic lattice and we consider the excitation of a wall area with S large
\, UFeU
S
pinning site Fig. 47. Part of wall area S displaced by half its thickness ~ from its pinning site.
104
H. ZIJLSTRA
c o m p a r e d with the lattice p a r a m e t e r squared, S>> ~2. W e e s t i m a t e the wall r e s o n a n c e f r e q u e n c y . T h e e n e r g y as a f u n c t i o n of wall position x is, to a first approximation,
[2X\ 2
3'(x) = a3"o~--~.-) + (1 - a)3'0 ,
(7.6)
a n a l o g o u s to eq. (7.3) b u t n o w with half the lattice p a r a m e t e r ~: as the excursion for which 3' has the value 3'0. W i t h 6 = 10 -9 m, ~ = 3 x 10 -20 m, 3'0 = 10 -2 J m -2 a n d a = 0.1 we calculate, using eqs. (7.2), (7.4) a n d (7.6), that w ~ 3 x 10 22s -1 or 1-'~'1012S 1. T h e activation e n e r g y for the excitation is
A E = a3"oS, which has to b e smaller t h a n 10-29J to p e r m i t m o r e t h a n o n e excitation per second. W i t h the a s s u m e d values for a a n d 3'0 this gives a m a x i m u m value for the wall area i n v o l v e d of S = 10-27 m 2 , which is by two orders of m a g n i t u d e m o r e t h a n ~2 a n d thus c o n s i s t e n t with o u r p r e s u p p o s i t i o n . T h e c o n c l u s i o n is that in materials with thin wall coercivity t h e r m a l excitations m a y well occur that give rise to wall creep. Such creep has b e e n observed, a.o., by B a r b a r a a n d U e h a r a (1976) a n d H u n t e r a n d T a y l o r (1977). E g a m i (1973) has w r i t t e n an extensive theoretical t r e a t m e n t of the creep of thin walls, taking into a c c o u n t b o t h t u n n e l l i n g a n d t h e r m a l excitation.
References Aharoni, A. and S. Shtrikman, 1978, Phys. Rev. 109, 1522. Aharoni, A., 1960, Phys. Rev. 119, 127. Aharoni, A., 1966, Phys. Stat. Sol. 16, 3. Aharoni, A., 1962, Rev. Mod. Phys. 34, 227. Barbara, B., B. B6cle, R. Lemaire and D. Paccard, 1971, J. Physique, C1-1971, 299. Barbara, B. and M. Uehara, 1977, Physica (Netherlands) 86-88 B + C, 1477, (Proc. Int. Conf. Magn., Amsterdam, 1976). Becket, J.J., 1969, IEEE Trans. Magn. MAG-5, 211. Berkowitz, A.E., J.A. Lahut, I.S. Jacobs, L.M.
Levinson and D.W. Forrester, 1975, Phys. Rev. Lett. 34, 594. Brouha, M. and K.H.J. Buschow, 1975, IEEE Trans. Magn. MAG-11, 1358. Brown Jr., W.F., 1957, Phys. Rev. 105, 1479. Brown Jr., W.F., 1962a, Magnetostatic Principles in Ferromagnetism (North-Holland, Amsterdam). Brown Jr., W.F., 1962b, J. Phys. Soc. Japan, 17, Suppl. B-I, 540. Brown Jr., W.F., 1963, Micromagnetics (Interscience/Wiley, New York).
PERMANENT MAGNETS; THEORY Brown Jr., W.F., 1965, in: Fluctuation Phenomena in Solids, ed., R.E. Burgess (Academic Press, New York) p. 37. Brown Jr., W.F., 1969, Ann. New York Acad. Sci. 147, 463. Brown Jr., W.F., 1979, IEEE Trans. Magn. MAG-15, 1196. Buschow, K.H.J. and M. Brouha, 1975, AIP Conf. Proc. 29, 618. Compaan, K. and H. Zijlstra, 1962, Phys. Rev. 126, 1722. Craik, D.J. and E. Hill, 1974, Phys. Lett. 48A, 157. De Blois, R.W. and C.P. Bean, 1959, J. Appl. Phys. 30, 225S. De Jong, J.J., J.M.G. Smeets and H.B. Haanstra, 1958, J. Appl. Phys. 29, 297. De Vos, K.J., 1966, Thesis Tech. Univ. Delft. D6ring, W., 1948, Z. Naturf. 3a, 373. Edwards, A., 1962, Magnet Design and Selection of Material, in: Permanent Magnets, ed., D. Hadfield (Iliffe, London) p. 191. Egami, T. 1973, Phys. Status Solidi (13) 57, 211. Egami, T. and C.D. Graham Jr., 1971, J. Appl. Phys. 42, 1299. Ermolenko, A.S., A.V. Korolev and Y.S. Shur, 1973, Proc. Int. Conf. on Magn., Moskow, 1973, Vol. I(2), p. 236. Frei, E.H., S. Shtrikman and D. Treves, 1957, Phys. Rev. 106, 446. Friedberg, R. and D.I. Paul, 1975, Phys. Rev. Lett. 34, 1234. Hilzinger, H.R., 1977, Appl. Phys. 12, 253. Hilzinger, H.R. and H. Kronmfiller, 1972, Phys. Status Solidi (B) 54, 593. Hilzinger, H.R. and H. Kronmfiller, 1973, Phys. Status Solidi (B) 59, 71. Hilzinger, H.R. and H. Kronmfiller, 1976, J. Magn. Magn. Mat. 2, 11. Hunter, J. and K.N.R. Taylor, 1977, Physica (Netherlands) 86-88 B + C (1), 161 0aroc. Int. Conf. Magn., Amsterdam, 1976). Jacobs, I.S. and C.P. Bean, 1955, Phys. Rev. 100, 1060. Jonas, B. and H.J. Meerkamp van Embden, 1941, Philips Tech. Rev. 6, 8. Kersten, M., 1943, Phys. Z. 44, 63. Kittel, C., 1949, Rev. Mod. Phys. 21, 541. Kondorsky, E., 1952, Dokl. Akad. Nauk SSSR, 80, 197 and 82, 365. Lapworth, A.J. and J.P. Jakubovics, 1974, Proc. 3rd. Eur. Conf. on Hard Magn. Mat., Amsterdam, 1974, p. 174. Lilley, B.A., 1950, Phil. Mag. 41, 792.
105
Luborsky, F.E. and C.R. Morelock, 1964, J. Appl. Phys. 35, 2055. Luteijn, A.I. and K.J. de Vos, 1956, Philips Res. Rep. 11, 489. McCurrie, R.A. and L.E. Willmore, 1979, J. Appl. Phys. 50, 3560. Margenau, H. and G.M. Murphy, 1956, The Mathematics of Physics and Chemistry (2nd ed.) (Van Nostrand, Princeton) p. 198. Martin, D.L. and M.G. Benz, 1971, Cobalt No. 50, 11. Meiklejohn, W.H. and C.P. Bean, 1957, Phys. Rev. 105, 904. Mildrum, H., A.E. Ray and K. Strnat, 1970, Proc. 8th Rare Earth Research Conf., Reno, 1970, p. 21. Mitzek, A.I. and S.S. Semyannikov, 1969, Soviet Physics-Solid State 11, 899. N6el, L., 1944a, Cahiers de Physique, No. 25, 1. N6el, L., 1944b, Cahiers de Physique, No. 25, 21. N6el, L., 1954, J. Phys. Radium 15, 225. Ojima, T., S. Tomizawa, T. Yoneyma and T. Hori, 1977, Japan J. Appl. Phys. 16, 671. Paine, T.O., L.I. Mendelsohn and F.E. Luborsky, 1955, Phys. Rev. 100, 1055. Schiller, K. and K. Brinkmann, 1970, Dauermagnete (Springer, Berlin) p. 74. Shtrikman, S. and D. Treves, 1960, J. Appl. Phys. 31, 72 S. Shur, Y.S., 1973, private communication. Stoner, E.C. and E.P. Wohlfarth, 1948, Phil. Trans. Roy. Soc. (London) 240A, 599. Street, R. and J.C. Woolley, 1949, Proc. Roy. Soc. (London) A62, 562. Van den Broek, J.J. and H. Zijlstra, 1971, IEEE Trans. Magn. MAG-7, 226. Van Landuyt, J, G. van Tendeloo, J.J. van den Broek, H. Donkersloot and H. Zijlstra, 1978, IEEE Trans. Magn. MAG-14, 679. Weiner, J.H., 1973, IEEE Trans. Magn. MAG9, 602. Went, J.J., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/52, Philips Tech. Rev. 13, 194. Zijlstra, H., 1966, Z. Angew. Phys. 21, 6. Zijlstra, H., 1967, Experimental Methods in Magnetism, Vol. I (North-Holland, Amsterdam) p. 135. Zijlstra, H., 1970a, IEEE Trans. Magn. MAG-6, 179. Zijlstra, H., 1970b, J. Appl. Phys. 41, 4881. Zijlstra, H., 1974, Philips Tech. Rev. 34, 193. Zijlstra, H. and H.B. Haanstra, 1966, J. Appl. Phys. 37, 2853:
chapter 3 THE STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
R.A. McCURRIE School of Materials Science and Technology University of Bradford Bradford, W Yorks BD7 1DP UK
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 107
CONTENTS 1, Isotropic alnicos 1-4 . . . . . . . . . . . . . . . . . . . . . . 1.1. Fe2NiA1 and the isotropic alnicos 1-4 . . . . . . . . . . . . . . . 1.2. Microstructure and origin of the coercivity in Fe2NiA1 and the isotropic alnicos 1-4 . . . . . . . . . . . . . . . . . . . . . . . . 2, Anisotropic alnicos 5 and 6 . . . . . . . . . . . . . . . . . . . . 2.1. Thermomagnetic treatment of anisotropic alnico 5 . . . . . . . . . . 2.2. Cyclic heat treatment of alnico 5 . . . . . . . . . . . . . . . . 2.3. Anisotropic cast alnico 5 with grain orientation (alnico 5 D G or alnico 5-7) . 2.4. Shape anisotropy of alnico 5 and alnico 5 D G (alnico 5-7) . . . . . . . . 2.5. Magnetostriction of alnico 5 and alnico 5 D G (alnico 5-7) . . . . . . . 2.6. Microstructures of alnico 5 alloys . . . . . . . . . . . . . . . . 2.7. Alnico 6 . . . . . . . . . . . . . . . . . . . . . . . . . 3. Anisotropic alnicos 8 and 9 . . . . . . . . . . . . . . . . . . . . 3.1. Thermomagnetic treatment of anisotropic alnico 8 . . . . . . . . . . 3.2. Extra high coercivity alnico 8 . . . . . . . . . . . . . . . . . 3.3, Anisotropic alnico 9 with fully columnar grains . . . . . . . . . . . 3.4. Shape anisotropy of alnicos 8 and 9 . . . . . . . . . . . . . . . 3.5. Microstructures of alnicos 8 and 9 . . . . . . . . . . . . . . . . 4. M6ssbauer spectroscopy of alnicos 5 and 8 . . . . . . . . . . . . . . 5. Sintered alnicos . . . . . . . . . . . . . . . . . . . . . . . . 6. Moulded, pressed or bonded alnico magnets . . . . . . . . . . . . . . 7. Effects of thermomagnetic treatment on the magnetic properties of alnicos 5-9 7.1. Factors controlling development of am particle shape anisotropy . . . . . 7.2. Relationship between the preferred or easy direction of magnetization and the direction of the applied field during thermomagnetic treatment 7.3. Dependence of the magnetic properties on the direction of the applied field during thermomagnetic treatment . . . . . . . . . . . . . . 8. Effects of cobalt on' the magnetic properties of the alnicos . . . . . . . . . 9. Effects of titanium on the magnetic properties of the alnicos (mainly 6, 8 and 9) . . . . . . . . . . . . . . . . . . . . . . . 10. Dependence of the magnetic properties on the angle between the direction of measurement and the preferred or easy axis of magnetization . . . . . . . 11. Relationship between magnetic properties and crystallographic texture . . . . . 12. Effects of particle misalignment on the rcmanence and coercivity of the anisotropic field-treated alnicos . . . . . . . . . . . . . . . . . . . . . . 12.1. Remanence . . . . . . . . . . . . . . . . . . . . . . . 12.2. Coercivity . . . . . . . . . . . . . . . . . . . . . . . . 108
111 111 113 121 121 129 129 131 133 134 137 137 137 141 142 145 146 148 148 149 149 149 151 151 154 155 158 161 161 161 163
13. Determination of the optimum volume fraction of the F e - C o rich particles 14. Interpretation of the magnetic properties in terms of the Stoner-Wohlfarth theory of hysteresis in single domain particles . . . . . . . . . . . . . . . . 15. Interpretation of the magnetic properties in terms of magnetization reversal by the curling mechanism . . . . . . . . . . . . . . . . . . . . 16. Magnetostatic interaction domains in alnicos . . . . . . . . . . . . . . 17. Comparison of the N6el-Zijlstra and Cahn theories of magnetic annealing in alnico alloys . . . . . . . . . . . . . . . . . . . . . . . . 17.1. N6el-Zijlstra theory . . . . . . . . . . . . . . . . . . . . 17.2. Cahn's theory . . . . . . . . . . . . . . . . . . . . . . 17.3. Discussion of the N6el-Zijlstra and Cahn theories . . . . . . . . . . 18. Rotational hysteresis . . . . . . . . . . . . . . . . . . . . . . 19. Anhysteretic magnetization . . . . . . . . . . . . . . . . . . . . 20. Magnetic viscosity . . . . . . . . . . . . . . . . . . . . . . . 21. Temperature dependence of magnetic properties . . . . . . . . . . . . 22. Dynamic excitation (AC magnetization) . . . . . . . . . . . . . . . 23. Prospects for impi-ovement in the magnetic properties . . . . . . . . . . 24. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
109
164 166 169 170 171 172 173 174 177 179 179 181 181 181 182 184
1. Isotropic alnicos 1-4
1.i. Fe2NiAl and the isotropic alnicos 1-4 The alnicos are an important group of p e r m a n e n t magnet alloys. They contain Fe, Co, Ni and A1 with minor additions of Cu and Ti. The first m e m b e r s of the series, which do not contain cobalt, were discovered by Mishima (1932) and are known as the Mishima alloys. They have a composition in the range 55-63% Fe, 25-30% Ni and 12-15% A1, an energy product of ~ 8 kJm -3 and a coercivity of 4.8 x 1 0 4 A m which is m o r e than twice the coercivity of the magnet steels which were available in 1931. Because of their commercial importance the alnico alloys have been studied in great detail by m a n y researchers. Burgers and Snoek (1935) found that when an alloy containing 59% F e - 28% N i - 1 3 % A1 was slowly cooled at a controlled rate from 1200°C to 700°C the coercivity rose to a m a x i m u m of about 48 k A m 1 (600 Oe) as the cooling time was extended and then decreased to about 16 k A m -~ (200 Oe) as the cooling time was prolonged. X-ray investigation showed that in the o p t i m u m high coercivity state a precipitation reaction had occurred. F r o m m e a s u r e m e n t s of the internal demagnetization coefficient Snoek (1938, 1939) suggested that the alloys were heterogeneous and that in the optimum high coercivity state there were two ferromagnetic phases a~ and c~2. The phase segregation process in Fe2NiAI has been investigated by Sucksmith (1939) who measured the magnetization versus t e m p e r a t u r e curves of the single and two-phase alloy. The latter was formed by quenching from 800°C and the magnetization versus t e m p e r a t u r e curve showed a dip at 450°C which indicated that the alloy was indeed two-phase. Sucksmith (1939) found that the phase segregation occurred according to the reaction: 3.25 FesoNi25A125~ Fe9sNizsAlz5 + 2.25 Fe30Ni35A13s, and that the saturation magnetizations of the two phases are, respectively 2 1 2 J T -1 kg -1 (212emu/g or 212erg Oe -1 g-a) and 6 1 J T 1 kg 1(61emu/g or 6 1 e r g O e -1 g-l). Since the densities of the two phases were not known the saturation magnetic polarizations in teslas (T) could not be determined. Details of the o p t i m u m composition and heat treatment of these isotropic iii
112
R.A. M c C U R R I E
Fe-Ni-A1 alloys have been given by Betteridge (1939). The best properties were obtained for an alloy containing 59.5% F e - 2 7 . 6 % Ni and 12.9% A1 which had been quenched at 28°Cs I from the single phase state at l l00°C and then tempered for 4 hours at 650°C. This treatment gave a coercivity BHc = 4 1 k A m - 1 ( 5 1 5 O e ) and a maximum energy product ( B H ) m ~ = 1 0 . 8 k J m -3 (1.35 x 106G Oe). The coercivity was shown to depend very critically on the A1 content while the remanence depended more on the Ni content. Betteridge (1939) also investigated the effects of adding Cu to the Fe-Ni-A1 alloys and found a Cu addition of 3.5% increased (BH)max to 12kJm -3 (1.5 x 1 0 6 G O e ) after quenching from above 950°C and tempering at 550°C. The Cu addition increased the rate of precipitation so that the Fe-Ni-A1-Cu alloys required more rapid cooling or quenching. The effects of elastic stress on the precipitation and magnetic properties of Fe-Ni-A1 alloys with additions of Cu and Ti have been investigated by Yermolenko and Korolyov (1970) who obtained improved optimum permanent magnet properties of ( B H ) m a x = 16.8 k J m -3, BHc = 63 kAm 1 and Br = 0.67 T. The permanent magnet alloys with compositions close to Fe2NiA1 are usually prepared commercially by cooling from above 1250°C at an approximately controlled rate. Rapidly cooled castings can be improved by annealing at 600°C for several hours. These alloys, which usually have small additions of Cu, are known as alni or alnico 3, in spite of the fact that they contain no cobalt; they are still produced in small quantities. Betteridge (1939), Zumbusch (1942a) and others also found that the magnetic properties of the Fe-Ni-A1 alloys could be significantly improved by the addition of cobalt as shown in fig. 1. The increase in remanence follows the increase in the saturation magnetic polarization of the alloys while the larger relative increase in the coercivity BHo can be attributed to an increase in the difference between the
100 -
1"Or
20 Br
~ 80- 0"8I
16
~6o -,-°= ~.6
12 "J
,ff
BH(max)
g 8
40 -
0-4 f
20 -
0.2
0
--0
0
E
I
-r Ill
4
5
10 15 Wt % Cobalt
20
25
Fig. 1. Dependence of coercivity, remanence and energy product on cobalt content (after Zumbusch 1942b).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 113 saturation magnetic polarization of the F e - C o rich precipitate particles and the Ni-A1 rich matrix. The addition of cobalt has the further beneficial effect of raising the Curie temperature. The cobalt-containing alloys are produced by controlled cooling from above !250°C and subsequent annealing for several hours in the range 600-650°C. Since cobalt decreases the rate of precipitation of the c~1 and ~2 phases it was found essential to add small quantities of copper (Betteridge 1939) and to reduce both the nickel and aluminium contents as the cobalt content was increased. It was also shown (Betteridge 1939, Edwards 1957) that the magnetic properties of these isotropic alloys (alnicos 1, 2, 3 and 4) could be significantly improved by the addition of 4-5% Ti provided that the cobalt content was increased to 17-20%. These extra high BHc isotropic alnicos (alnico 2) have coercivities in the range 60-72 kAm 2 compared with 36-56 kAm -1 for the isotropic alnicos 1, 2, 3 and 4. The energy product of the high coercivity form of isotropic alnico 2 is also slightly higher. Although the Ti addition reduces the remanence this is more than compensated by the much higher coercivities. Details of the optimum composition and heat treatments of the isotropic alnicos have been given by Betteridge (1939) and Edwards (1957). The magnetic properties and compositions of the alnicos 1-4 are summarized in table 1 and typical demagnetization B - H curves are shown in fig. 2.
0.8 0.6
lib
>2
0"4
u) "0 X -I m
0.2 u.
I1
60
I
50
/
!
I
I
I
I
40 30 20 Applied field,H (kAm-1)
I
10
0
0
Fig. 2. Demagnetization curves for isotropic alnicos 1, 2, 3 and 4.
1.2. Microstructure and origin of the coercivity in Fe2NiAl and the isotropic alnicos 1--4 The compositions of the alnicos are complex and the F e - N i - A I system is the only one for which the phase diagram has been investigated in detail. Bradley and Taylor (1938a, b) and Bradley, (1949a, b, 1951, 1952) established the positions of the phase boundaries and the general metallurgical behaviour of the Fe-Ni-A1 system and showed that the alloys with potentially interesting permanent magnet properties lay close to the line from Fe to NiA1 and were centered round the
114
R.A. M c C U R R I E
~
_'2
~
t--
©
,q.
tt~
t--
e., ©
©
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c~ <
0
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?
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ii
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5 II E"
z
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 115 composition Fe2NiAI. The isothermal section of the Fe-Ni-A1 phase diagram at 750°C is shown in fig. 3. D e Vos (1966, 1969) has suggested that for the alloys which are of most interest as permanent magnets the phase diagram for the alnicos can be considerably simplified if it is assumed that they are pseudobinaries of Fe and NiA1 or F e - C o and Ni-AI. Marcon et al. (1978a) have shown that in the Fe-Ni-A1 system this is not strictly correct because of the extension of the a + T phase boundary below 9 1 0 ° C - t h e a ~ 7 allotropic transformation temperature for Fe. The approximate pseudo-binary phase diagram shown in fig. 4 (Marcon et al. 1978a) is that for a vertical section cut through the line with full circles in the phase diagram shown in fig. 3. Since the permanent magnet alloys contain at least 50 wt % Fe it can be seen from fig. 4 that below about 800°C alloys containing 25-75% Fe are two-phase (al and a2). When the sub-division into the al and o~2phases occurs on a sufficiently fine scale the Fe or F e - C o rich particles have a significant shape anisotropy, which gives rise to high coercivities according to the Stoner and Wohlfarth (1948) model in which the magnetization is assumed to reverse by coherent rotation, though we shall see later that this simple process is unlikely to occur.
The Fe or F e - C o rich particles (o~1phase) and the non-ferromagnetic or weakly ferromagnetic Ni-A1 rich matrix (c~2phase) have bcc structures and are formed by spinodal decomposition (Cahn and Hilliard 1958, 1959, Cahn 1961-1963, 1968, Hillert 1961) rather than a nucleation and growth process. We shall see that this has important effects on the microstructure and magnetic properties of the alloys. The spinodal decomposition of the c~ phase into the c~ and c~2 phases, although spontaneous, is of course diffusion limited and can occur only at relatively high temperatures ~850°C. The concentrations of the Fe or Fe and Co atoms in the two phases vary periodically (assumed to be sinusoidal by Cahn (1962)) and the
Ni
7 5 0 °C
70 80
Fe
to
20
3o
~o
so
so
m
so
9o
AI
At % AI
Fig. 3. Ternary equilibrium phase diagrams for Fe-Ni-A1 at 750°C (after Bradley 1949, 1951, 1952).
116
R.A. McCURRIE
1800[ 1 6 0 1400~--~
0
\
0oov/ oor/ oor/'
o
o,.o
oor/' O0 02 I.
Fe
~
=
0'I 4
i
Composition
01.6
I
01.8
I NiA
Fig. 4. Pseudo binary equilibrium phase diagram for Fe-NiA1 (after Marcon et al. 1978a). amplitudes of the composition fluctuations increases with time until the phase separation is complete; the whole process takes a very short time - seconds or minutes. Cahn (1962) has demonstrated theoretically that for alloys in which the elastic constants obey the relation 2C44 -
C l l ~- C12 > 0 ,
the spinodal decomposition waves are parallel to the three {100} planes. This results in an initial microstructure which consists of a simple cubic array of regions rich in one component (e.g. Fe or Fe-Co) connected along the (100) directions by rods similarly enriched. The 'body centres' of this array are regions enriched in Ni-A1 and are connected by similarly enriched (100) rods. This produces two interlocking 3 dimensional systems of (100) rods, one enriched in Fe or F e - C o and other enriched in Ni-A1. Such a micros~ructure is typical of the periodic distribution of the phases in spinodally decomposed systems and may be contrasted with the irregular distribution of the phases in systems which decompose by nucleation and growth. Cahn (1962) also predicted that the relative volume fractions of the two phases also affects the final microstructure. If the volume fraction of one phase is much smaller than the other the final microstructure will consist of nearly equiaxed particles aligned along (100) directions. As the volume fraction of this phase increases elongated particles are formed with their axes of elongation parallel to the (100) directions, and these are of course the directions of easy magnetization, though the alloys are macroscopically isotropic. Since the
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
117
volume fraction of the al phase is usually in the range 0.5-0.7, the observed microstructures (figs. 6 and 7 and De Vos, 1966, 1969) are in very good agreement with those predicted by Cahn's (1962) theory. The formation and growth of the particles to their final shape and size occurs almost entirely during the spinodal decomposition at 800-850°C. The driving force for this reaction is of course the reduction in the interracial energy between the particles (~1) and the matrix (a2). Although the interfacial energy is small 10-3-10 -1Jm -2 (1-102erg cm -2) this is sufficient to favour particle growth. The principal effect of the heat treatment at 600°C is to increase the difference between the saturation magnetic polarization of the Fe or F e - C o rich particles and the surrounding matrix (Ni-A1 rich) by a continuous change in their composition due to the diffusion of Fe and Co atoms to the particles. The spinodal decomposition into two phases does not, however, produce a very large shape anisotropy in the ferromagnetic o~ phase particles and since the difference in the saturation magnetizations of the a~ particles and the matrix is relatively small the effective shape anisotropy field of the particles (proportional to Js(al)-Js(o~2)) is also small in spite of the elongation (e.g. fig. 6 (De Vos 1966, 1969)). Further heat treatment is necessary in order to increase the shape anisotropy and hence to obtain the highest coercivities and the best permanent magnet properties. This heat treatment usually consists of an anneal at about 600°C for several hours, though this is sometimes omitted in the case of the cobalt free alnico 3 alloys with compositions close to Fe2NiA1. The variation of the intrinsic coercivity (He) with composition and heat treatment for Fe-NiA1 alloys (De Vos 1966, 1969) is shown in fig. 5. The coercivities were measured (a) after quenching and tempering to give the optimum coercivity and (b) after continuous controlled cooling of the alloys. Since the interfacial energy depends on the crystallographic orientation of the boundary between the a~ and o~2 phases the particle growth is anisotropic (though
Fe-NiAI ~'~6 I E <¢
a
b
*¢
24 O
2
o
i
I
o Fe
20
40 60 8O Composition, At.%
lOO NiAI
Fig. 5. Dependence of coercivity of Fe-NiAI alloys on composition and heat treatment (a) after quenching and tempering for optimum properties (b) after continuous cooling (after De Vos 1969).
118
R.A. McCURRIE
only slightly so in Fe2NiA1) which results in an elongation parallel to the {100) directions. The microstructures of the alnicos have been studied in considerable detail by D e Vos (1966, 1969) who used replication electron microscopy. An example of the microstructure of Fe2NiA1 after o p t i m u m cooling ( H c ~ 56 k A m -1) is shown in fig, 6 though the shape anisotropy is not very pronounced. If the alloy is given an isothermal heat treatment for 2 h a t 850°C followed by quenching the preferential particle growth along the {100) directions is clearly visible (fig. 7), though this microstructure does not give o p t i m u m p e r m a n e n t magnet properties because the particles are too coarse and hence magnetization reversal occurs by curling (see Zijlstra, chapter 2 of this handbook) or by a m o r e complex mechanism. F r o m fig. 7 we may assume that the particles are mainly rod-like (~500 nm long and 100 nm in diameter) though particle coalescence and the presence of plate-like particles gives rise to the observed more complex microstructure. Since the Bloch-Lifshitz domain wall width in Fe or F e - C o alloys is of the order of 200 nm the particles are probably 'single domains' though they are not expected to
Fig. 6. Electron micrograph of the oq + a2 structure in an arbitrary plane, for an alloy containing 50 at. % Fe, 25 at. % Ni and 25 at. % AI, after optimum cooling (magnification 45000 x) (De Vos 1969).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
119
Fig. 7. Electron micrograph of the o~l + ~e2 structure for an alloy containing 50 at. % Fe, 25 at. % Ni and 25 at. % A1, after annealing for 2 h at 8500C followed by quenching (magnification 30000 x) (De Vos 1969).
behave as ideal isolated single domain particles with uniaxial shape anisotropy. Even if Bloch-Lifshitz domain walls could be nucleated in the alloys it seems most unlikely that they could move freely in such a complex interconnected microstructure, so, even this mechanism of magnetization change could lead to significant coercivities. Assuming that the relatively high coercivities and remanences in the alnicos l - 4 are due principally to shape anisotropy of elongated Fe or F e - C o rich particles in a non-ferromagnetic matrix the Stoner-Wohlfarth (1948) theory (for a summary see e.g. Zijlstra, chapter 2 of this handbook) predicts that the coercivity is proportional to the saturation magnetization, Ms, of the Fe or F e - C o rich particles and to a factor related to the difference in the effective demagnetization factors perpendicular (Dz) and parallel (Dx) to the preferred direction of magnetization in the particles, i.e., Hc = f(O)(Dz - D x ) M ~ ,
where f(O) is an averaging factor which takes account of the various orientations of the preferred axes of the particles with respect to the direction of measurement
120
R.A. McCURRIE
of He. According to Stoner and Wohlfarth (1948) the coercivity of a random array of non-interacting uniaxial single domain particles which reverse their magnetization by coherent rotation of the magnetization vector Ms is Hc = 0.479(Dz -
D,)Ms.
However, since the microstructures of Fe2NiA1 and the cobalt containing alnicos 1, 2 and 4 - p r e s u m a b l y similar to those of FezNiA1-are so complex, a detailed quantitative interpretation of the magnetic properties has not yet been attempted. In any case it is clear that a simple Stoner-Wohlfarth coherent rotation mechanism of magnetization reversal is very unlikely to occur. Although the particles have dimensions small enough to be single domains they are close to the size where magnetization reversal is likely to occur by curling. The irregular shape anisotropy of the interconnected particles may result in more complex mechanisms of magnetization reversal due to the complex spatial variation of the associated demagnetizing fields. The magnetization reversal is further complicated by particle interactions (Wohlfarth 1955), interaction domains (Bates et al. 1962) and the ferromagnetism of the Ni-AI rich a2 phase (see section 16). The suggestion by Stoner and Wohlfarth (1947, 1948) that the relatively high coercivities of the alloy FezNiA1 and the other isotropic alnicos, could be due essentially to the shape anisotropy of elongated single domain particles has been confirmed by Nesbitt et al. (1954). The magnetic behaviour of the material was simulated by embedding fine wires of Ni-Fe-Mo permalloy (which have a predominant shape anisotropy) in a non-magnetic matrix, with their axes in the three mutually perpendicular (100) directions viz. [100], [010] and [001]. By comparing the field dependence of the torque curves for single crystals of Fe2NiA1 with those of the simulated specimen Nesbitt et al. (1954) were able to show that the structures of the two materials were essentially the same although the interpretation of the results was complicated by the magnetocrystalline anisotropy of the FezNiA1. Further complications arise because the particles in Fe2NiA1 often coalesce to form very complex structures and shapes, as shown in figs. 6 and 7. Since the microstructures of the cobalt-containing alnicos are very similar to those observed in Fe2NiA1 it seems reasonable to assume that the coercivities of these alloys are also due to shape anisotropy. Apart from the dipole field interactions between the particles which depend on the volume fraction p, the magnetic behaviour is further complicated by the fact that in some alnico alloys the Ni-A1 rich a2 matrix phase is weakly ferromagnetic so that there is an exchange coupling between the Fe-Co rich al phase and the Ni-A1 rich a2 phase. Thus magnetization change may occur by some kind of 'wall motion' through the complex interconnected al and Og2 phases. The domain walls may of course only be 'interaction domain walls' as described in section 16 rather than Bloch-Lifshitz walls, but the motion of these interaction domain walls still requires magnetization reversal in the individual al phase particles and in view of the particle interaction effects this itself will be a co-operative process. The magnetization reversal may occur by an incoherent process such as curling but in
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 121 view of the complex shapes of the particles and the exchange coupling to the matrix phase even more complex reversal processes may occur. In the high cobalt and high titanium alloys where the particles are very regular in shape and are isolated single domains embedded in a non-ferromagnetic matrix (c~2 phase), it seems that magnetization reversal is likely to occur by the curling mechanism in individual particles although these are still expected to act co-operatively and hence give rise to domains or regions of reversed magnetization interaction domains. A fuller discussion of the physical concepts briefly described here is given in sections 14, 15 and 16 as well as by Zijlstra, in chapter 2 of this handbook.
2. Anisotropic alnicos 5 and 6
2.1. Thermomagnetic treatment of anisotropic alnico 5 The most important advance in the technology of alnico magnets was the discovery by Oliver and Shedden (1938) of the beneficial effect of thermomagnetic treatment and its development by Jonas and Meerkamp van E m b d e n (1941). Oliver and Shedden (1938) found that when an alloy containing 54% Fe, 18% Ni, 10% A1, 12% Co and 6% Cu was cooled from 1200°C in a magnetic field of 352 kAm -1 the resulting magnet was anisotropic and that the value of (BH)max was increased from 12 kJm -3 (1.5 x 106 G Oe) in the isotropic alloy to 14.4 kJm -3 (1.8 x 106G Oe) parallel to the field direction. Perpendicular to the field (BH)max decreased to 10.8 kJm -3 (1.35 x 1066 Oe). The anisotropy in (BH)max was due entirely to changes in the remanence and fullness factor ((BH)max/BrHc) of the demagnetizing B - H curves; the coercivity remained isotropic. Following this discovery by Oliver and Shedden (1938), Jonas and Meerkamp van Embden (1941) heat treated an alloy with a higher cobalt content (viz. 51.5% Fe, 14% Ni, 8.5% A1, 23% Co and 3% Cu) by cooling from 1200°C to 600°C in a magnetic field of 240 kAm -1 and then annealing for several hours at 600°C. They obtained a maximum energy product of 41.6 kJm -3 parallel to the field direction and only 5.6 kJm -3 perpendicular to it. For an isotropic alloy of the same composition the maximum energy product was 17.6 kJm -3. Most of the improvement in the energy product parallel to the field direction could be attributed to an increase in the fullness factor though there was also a significant increase in the remanence from 0.87 T to 1.24 T. The increase in the coercivity BHc was s m a l l - f r o m 47 kAm -1 to 52 kAm -1. Jonas and Meerkamp van Embden (1941) also found that the application of a magnetic field during the anneal at 600°C had no beneficial effect. More detailed investigations of these anisotropic alnico 5 alloys were made by Jellinghaus (1943) who studied the effects of varying the aluminium content in alloys with the composition Fe, 15% Ni, 5.7-16.6% A1, 23% Co and 3% Cu. H e found that good magnetic properties could be obtained only in the narrow range of A1 content, about 8-9%, where the coercivitY , remanence and maximum energy product were all high and that at the composition 50% F e - 23% C o - 15%
122
R.A. McCURRIE
N i - 9 % A 1 - 3 % Cu the application of a magnetic field during cooling increased (BH)max very substantially from 12 kJm -3 (no field) to 40 kJm -3 (with field). The dependence of (BH)m~x on the aluminium content and the effect of the thermomagnetic field is shown in fig. 8. This conclusion is supported by Lange (1968). The presence of the deleterious fcc Y phase (Jellinghaus 1943) was detected only for very low A1 contents and was absent above 6% A1 where the whole alloy had a bcc structure. Extensive investigations of alnico 5 alloys were made by Zumbusch (1942a, b) who studied alloys with a wider range of compositions including an addition of up to 4% Ti. H e found that the best magnetic properties were obtained for alloys with compositions in the range Fe, 14-15.5% Ni, 7.8-9.2% A1, 21.5-23.5% Co, 3-4% Cu and less than 1% Ti. The heat treatment recommended by Zumbusch (1942a, b) consists of cooling fro.m 1250°C at about l°Cs -1 to 500°C in a field well above 160 kAm -1, followed by tempering at 550°C for 10 hours. The precipitation processes in alnico 5 have been investigated by Heimke et al. (1966) who measured the saturation magnetic polarization, the remanence and coercivity as a function of tim e using a modified thermomagnetic treatment. They concluded that when the O/1 (Fe-Co) particles are first formed they are spherical but just below the Curie temperature and under the influence of the applied field they soon become elongated and form larger interconnected particles with their long axes parallel to the applied field direction. Later or at lower temperatures more cross links are formed between the particles. The effect of the Cu content of alnico 5 has been investigated by Van der Steeg and De Vos (1964) who showed that increasing the Cu content raised the homogenization temperature, stabilized the 3' fcc phase and lowered the Curie temperature and hence the temperature for effective heat treatment in a magnetic field. They also found that the annealing process was accelerated by the addition 40 O o
"~" 30 I E ~=
(b)
¢x 20 E 10 -
//
0
~1 6
4.
(a)
8 10 12 Wt % AluminFum
14
16
i 18
Fig. 8. Dependence of maximum energy product on the aluminium content of alloys containing Fe-23% Co-15% Ni-3% Cu (a) without thermomagnetic treatment (b) with thermomagnetic treatment (after Jellinghaus 1943).
STRUCTURE AND PROPERTIES OF ALNICOPERMANENTMAGNETALLOYS
123
of copper and that above 2.5% Cu the coercivity increased. Ritzow and Ebert (1957) have shown that the presence of Cu decreased the rate of cooling through the y fcc region necessary to prevent the precipitation of the magnetically deleterious y fcc phase which must be avoided if the best magnetic properties are to be obtained. All the anisotr0pic alloys (including alnicos 6-9) are single phase above about 1200°C but if they are held in the temperature range 1000-1200°C for more than a very short time the resulting magnetic properties are inferior due to the precipitation of the ~ fcc phase. The formation of the latter phase is favoured if the composition deviates significantly from the 'ideal' or if the alloys are incompletely homogenized by soaking at 1250-1300°C. The a-~ y phase transformation has been investigated by Koch et al. (1957, 1959), Koshiba and Nishinuma (1957, 1960), Pater et al. (1963), Van der Steeg and De Vos (1964), Planchard et al. (1964a-1966a), Heimke and Kohlhaas (1966). Koch et al. (1957, 1959) have shown by high temperature X-ray studies that the fcc y phase can coexist with the bcc a phase in the temperature range 1250-800°C and that on cooling below 800°C this fcc y phase transforms, by an apparently diffusionless reaction to another bcc phase c~. The magnetic properties of alnico 5 as a function of heat treatment have also been measured by many other authors (see e.g. Clegg and McCaig (1957), Tenzer and Kronenberg (1958), Yermolenko and Shur (1964), De Vos (1966, 1969), Bronner et al. (1968-1970)). The temperature dependence of the coercivity of alnico 5 (Clegg and McCaig 1957) after various heat treatments is shown in fig. 9. Curves (c) and (g) represent specimens with optimum permanent magnet properties. The saturation magnetic polarization of these specimens decreased almost linearly by 20-35% in the temperature range 0-550°C. Above 550°C up to the Curie temperature (--~850°C) the decrease in Js was very rapid. For heat treatments above about 500°C the magnetic properties are not reversible on cooling because at high temperatures fundamental structural changes occur. The temperature stability of alnico alloys is discussed in section 21. By considering magnetization versus temperature curves (for a review of this technique see e.g. Berkowitz (1969)) Tenzer and Kronenberg (1958) concluded that in the optimum permanent magnet state alnico 5 (52% Fe, 23% Co, 14% Ni, 8% A1, 3% Cu) consists of two ferromagnetic phases, one is mainly Fe2Co with some A1, Ni and Cu (Js ~ 1.4 T) in solid solution and the other is mainly NiA1 with a small Fe content. By means of a similar study on alnico 5 (51% Fe, 24% Co, 14% Ni, 8% A1, 3% Cu) Yermolenko and Shut (1964) concluded that in the optimum state the saturation magnetic polarizations of the ~1 (Fe-Co) and a2 (Ni-A1) phases were respectively 1.6 T and 0.1 T. De Vos (1966, 1969) found that when the controlled cooling was terminated by quenching from different temperatures the resulting magnetic properties were nearly independent of the quenching temperature, provided the latter was below about 775°C. The variation of the coercivity of alnico 5 with quenching temperature before and after tempering at 585°C is shown in fig. 10.
124
R.A. M c C U R R I E
0
0
0
0
,! O
o
o
~
(L-tu~M) °H8
~.~
~ - , r,- O
OE
~b N
~N
0
0
0
(~-,,,~) 0~
0
;" +
"~
~sU
s~
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 125 6
c
r.
~
~
5
Alnico 5 •
After for
tempering 14
hr
r- 2 o
1 !
500
600
700
800
900
Quenching Temperature (°C )
Fig. 10. Dependence of coercivity of alnico 5 on quenching temperature before and after tempering at 585°C (De Vos 1969).
Wittig (1962) attempted to obtain high energy product, titanium-free alnico 5 magnets by isothermal heat treatment in a magnetic field at temperatures between 800 and 870°C for 2-20 min but found that the (BH)max products were lower than those obtained with the conventional thermomagnetic treatment in agreement with the earlier results obtained by Koch et al. (1957). However, Wittig (1962) also found that a (BH)max = 40 kJm -3 (equal to that obtained by the conventional thermomagnetic treatment) could be obtained if the alnico 5 was given a twostage isothermal heat treatment in a magnetic field as follows: (1) 4 rain at 860°C in a magnetic field (presumably of saturating strength) (2) 2min at 830°C in a magnetic field (3) tempering for 2 h at 650°C (4) tempering for 16 h at 585°C. The heat treatment of alnico 5 varies according to the composition and manufacturer; a typical heat treatment is as follows (Marcon et al. 1978b): (1) Homogenization at 1350°C to obtain the a phase. (2) Fast cooling at 4 ° C s -1 down to about 900°C to prevent the parasitic precipitation of the fcc 3' phase. (3) Controlled cooling in a magnetic field (ideally of saturating strength ~320 kAm -1) down to 600°C. This treatment results in the spinodal decomposition of the a phase into the al (Fe-Co) and (1' 2 (Ni-A1) phases and the formation of elongated a~ (Fe-Co) particles. (4) Tempering for 6 h at 650°C followed by 24h at 550°C. This treatment produces the equilibrium al and a2 phases which have a maximum in the difference between their saturation magnetic polarizations AJ = J~l - JR. Many variations in the above process can be made without producing significant changes in the magnetic properties; e.g., average cooling rates in the range 0.5-4°Cs -1 have b e e n quoted by many authors (see, e.g., Nesbitt and Williams 1957, Clegg and McCaig 1957, Povolotskii et al. 1963, Marcon et al. 1978b). Marcon et al. (1978b) have also investigated the effects of varying the applied
126
R.A. M c C U R R I E
field during cooling (from 900 to 600°C) over the range 0 - 5 7 6 k A m -1. They found that for polycrystalline alnico 5 (50.6% Fe, 13.9% Ni, 8.2% AI, 24.3% Co, 3% Cu) the optimum permanent magnet properties could be obtained by cooling in a field of 80kAm-1; cooling in larger fields up to a maximum 5 7 6 k A m -1 produced no significant improvement in Br, BH¢ or ( B H ) . . . . The thermomagnetic treatment of the alnico 5 alloys is most effective when they contain about 23% Co or more. The high cobalt content is essential because it raises the Curie temperature to about 850°C so that when the spinodal decomposition occurs in the temperature range 700-850°C the shape and growth of the particles can be influenced by the applied field because they are already ferromagnetic. The effects and theory of magnetic annealing and the relationship between the preferred direction of magnetization in alnico 5 and the applied field during cooling are discussed later in sections 7 and 17. The improvement in the magnetic properties of alnico 5 occurs only in the direction of the applied field and there is an accompanying deterioration of the properties in other directions. These alloys, though polycrystalline, are anisotropic owing to the preferential growth of the particles along the field direction or as near to it as possible depending on the orientation of the [100] directions in the grains. We can see from table 2 that the improvement in the remanence and energy product of alnico 5 compared with those alnicos 1-4 (table 1) is very significant. A typical demagnetization curve for alnico 5 (random grain) is shown in fig. 11: (the demagnetization curves for columnar and single crystal alnico 5 are also shown in fig. 11). In dynamic applications of alnico 5 where the working point of the magnet
B. 80
(kJn -3) 60 40
11.4
..~"
H
1.0~ >~
"
16.1"~~~
0-40"6"o; •'=
-%
Alnico 5
80
I
70
I
~ i
'
60 50t''- 40 30 20 Applied field, H (kAm-1)
'
10
0-2 0
0
Fig. 11. Demagnetization curves for various forms of alnico 5: (a) equiaxed alnico 5, (b) grain orientated alnico 5-7, (c) single crystal alnico 5.
S T R U C T U R E A N D P R O P E R T I E S OF A L N I C O P E R M A N E N T M A G N E T A L L O Y S
tt3 k~
"7
"2.
m.
"7
©
E C~
6
C4
~5 '~ eq
0 eq
03 eq
eq ¢¢3
P~ ¢¢3
eq
tt~
~
,.~
tt~
tt3
0
H ,....,
-4
.,
e~
o
b~
0 oq.
zq.
p.,
p..
r--
r--
oq.
l
G,
If
Go
<
tt')
T
C~
d
z
0
q;
tl
"-6 t:'-6 ~. , " ~ ~'rca ~ k~
127
128
R.A. McCURRIE
changes, details of the recoil hysteresis loops and the recoil energy contours are essential if the material is to be used efficiently. Hysteresis loops and their associated recoil curves for various alnico alloys have b e e n published by Stfiblein (1968). T h e recoil energy c o n t o u r s for various alnicos can be f o u n d in the b o o k by Parker and Studders (1962). Typical recoil loops for alnico 5 are shown in fig. 12 which also shows various load lines and working points. T h e recoil energy contours for alnico 5 are shown in fig. 13. N o t e that the recoil energies given in
29~2~ I
J
r
=
2
~
BIT] 11"0 0.8 0"6 0"4 0"2
60
0 0
40 20 H I kAm-l]
Fig. 12. Typical recoil loops for alnico 5, and various load lines and working points (after Stiiblein 1968).
B (T) 1.2 1.0 0-8 0.6 0.4 0-2 -5
-4
-3 -2 -1 H (10 4 Am - 1 )
0
0
Fig. 13. Recoil energy contours for alnico 5 (after Parker and Studders 1962).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 129 fig. 13 (usually referred to as the useful recoil energies) are those obtained by using the more practical definition used by permanent magnet designers (Edwards 1962, Parker and Studders 1962, Schiller and Brinkmann 1970) rather than the fundamental definition given by Zijlstra in chapter 2 of this handbook. The technological importance of alnico 5 alloys is reflected by the large number of published papers which have appeared since their discovery. For further details the reader is referred to the papers by Bronner et al. (1967-1969, 1970a) and Gould (1971) who have attempted to interpret the magnetic properties in terms of the Stoner-Wohlfarth (1948) theory. Kolbe.and Martin (1960) have shown that alnico 5 can be successfully shaped into rod, wire or strip by hot working at high temperatures. They have also shown that alnico 5 can be extruded swaged and rolled.
2.2. Cyclic heat treatment of alnico 5 Hansen (1955) showed that the magnetic properties of alnico 5 were impaired by heat treating at 620-790°C but could be restored by re-tempering at 585°C provided the spoiling heat treatment temperature was below 675°C. After spoiling heat treatment above this temperature the coercivity could only be partially restored. Similar observations were made by Koch et al. (1957) and Fujiwara and Kato (1960). D e Vos (1966) investigated the microstructures of an alnico 5 alloy after it had been given the following treatments: (1) after optimum cooling in a magnetic field (BHc = 44 kAm -1) (2) treatment (1) followed by spoiling at 750°C for 3 min (Uric = 8.8 kAm -1) (3) treatments (1) and (2) followed by re-tempering at 585°C (BHc = 54 kAm-1). By observing the microstructure in a plane parallel to the direction of the field during cooling, De Vos (1966, 1969) found that there was no significant change in the morphology of the structure after each stage of the above cyclical heat treatment. According to De Vos ( 1 9 6 6 ) t h e best magnetic properties of alnico 5 are obtained when optimally field cooled magnets are aged below 600°C. The magnetic properties as a function of heat treatment in the range 550-750°C have been tabulated by De Vos (1966). H e found that the optimum permanent magnet properties: (BH)~ax = 48 kJm -3, BHc = 52 kAm -1, Br = 1.3 T and Bs = 1.4 T can be obtained by optimum field cooling followed by heat treatment for 8 h at 585°C.
2.3. Anisotropic cast alnico 5 with grain orientation (alnico 5 D G or alnico 5-7) It has been established by Ebeling and Burr (1953) and Zijlstra (1956) that the best magnetic properties of alnico 5 are obtained when single crystals are given a thermomagnetic treatment with the applied field parallel to one of the [100] directions. Hoselitz and McCaig (1949b) showed that a further improvement in the magnetic properties of field cooled polycrystalline alnico 5 can be obtained if the grains have a preferred orientation so that the al (Fe-Co) particle axes in the whole alloy are as nearly aligned as possible. Fortunately, if iron-base alloys such as the alnicos are allowed to solidify on a
130
R.A. McCURRIE
cold surface the [100] axes tend to grow preferentially perpendicular to the cold surface so that the desired grain orientation or columnar grain structure can be produced relatively easily. Thus when alnico 5 alloys are cast with a columnar crystallization or preferred grain orientation thermomagnetic treatment with the applied field parallel to the preferred or columnar axis results in a significant improvement in the magnetic properties compared with the alnico 5 alloys with randomly oriented grains. This result can be readily appreciated by comparing the demagnetization curves shown in fig. 11. In order to obtain well oriented columnar magnets it is necessary to use pre-heated or exothermic moulds and to cast the magnets on steel or copper slabs (preferably water cooled). A typical columnar grain structure of an alnico 5-7 casting is shown in fig. 14 from which it can be seen that there is a high degree of alignment but this is by no means fully columnar. The production and magnetic properties of alnico 5-7 have been described and investigated by Ebeling and Burr (1953), McCaig and Wright (1960), Makino (1962), Makino et al. (1963), Makino and Kimura (1965), Lindner et al. (1963) and Gould (1964, 1971). The compositions and magnetic properties of alnico 5-7 columnar alloys (laboratory specimens) are shown in table 3. Unfortunately magnets with energy products as high as 70 kJm -3 do not appear to be available commercially. Typical magnetic properties of commercial alnico 5-7 are shown in table 3. Alnico 5 and alnico 5-7 or their equivalents are among the most widely used permanent magnet alloys. Many millions are used as loudspeaker magnets, though
Fig. 14. Typical columnar grain structure of alnico5 D G (alnico 5-7) (Gould 1971). (Magnification: ~2x.)
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
131
TABLE 3 Magnetic properties of alnico 5-7 (columnar) alloys (after Gould 1964). Composition (wt %) Fe
Ni
Co
Al
Cu
Br
BH¢
(BH)m.x
Nb
(T)
(kAm ~)
(kJm -3)
51
14
24
8
3
-
1.33
56
51
50.7
13.5
24
8
3
0.8
1.33
59
57
50.3
13.8
24.3
8.4
3.2
-
1.33
58
64
49.7
13.5
25
8
3
0.8
1.43
62
70
49.7
13.5
25
8
3
0.8
1.35
63
65
49.7
13.5
25
8
3
0.8
1.38
57
58
50.5
13.5
25
8
3
-
1.4
56
64
49.7
13.5
25
8
3
0.8
1.4
60
69
48.5
13.5
25
8
3
2.0
1.37
66
69
47.3
17.7
24
8
3
-
1.4
59
64
N.B. 1 T = 104 G; 1 A m -a = (4~-/1000) Oe; 1 Jm -3 = 407r GOe.
they are gradually being replaced in this application by oriented BaFel20~9 and SrFe~2019 magnets, which are very much cheaper. It can be seen from fig. 11 that the demagnetization curve for single crystal alnico 5 gives the best magnetic properties with an energy product of 80 kJm -3 compared with ~60 kJm -3 for columnar alnico 5-7 and ~42 kJm 3 for equiaxed polycrystalline alnico 5 (Cronk 1966). By using a technique involving secondary recrystallization of large grained alnico 5 (~51% Fe, 24% Co, 14% Ni, 8% A1, 3% Cu, contaminated with 0.08% C or 0.35% Mn) Steinort et al. (1962) succeeded in obtaining a single crystal of mass ~0.11 kg with a maximum energy product of 88 kJm -3. From fig. 11, demagnetization curve (c), it is clear that the single crystal alnico 5 has significantly better magnetic properties than alnico 5 and alnico 5-7, but unfortunately single crystals are difficult to produce on a commercial scale.
2.4. Shape anisotropy of alnico 5 and alnico 5 D G (alnico 5-7) From torque curve measurements on alnico 5 and alnico 5 D G (i.e. alnico 5 with a columnar grain structure also known as alnico 7) Hoselitz and McCaig (1951, 1952) have concluded that the materials are magnetically uniaxial with an anisotropy coefficient of Ku ~ 105 Jm -3 (106 erg cm-3). A similar result was obtained by
132
R.A. McCURRIE
Nesbitt and Heidenreich (1952). From electron micrographs and torque curve measurements on single crystals of alnico 5 Nesbitt and Williams (1955) concluded that the high coercivity was due to the shape anisotropy of small elongated particles (approximately 0.41xm long and 0.061xm in diameter) and that the magnetocrystalline anisotropy was negligible. Typical torque curves for a disc with a (110) plane as surface are shown in fig. 15 from which can be concluded that the uniaxial shape anisotropy coefficient Ku is 1.08 x 105 Jm -3 with [001] as the easy direction of magnetization. Similar torque curve measurements of the anisotropy constants Ku for various thermomagnetic treatments of single crystals of alnico 5 have been made by Yermolenko et al. (1964). Instead of the conventional thermomagnetic treatment (i.e. controlled cooling in a magnetic field) they used isothermal heat treatment for various times in a field of 720 kAm -1 (9000 Oe) on specimens which had been quenched from 1300°C. This procedure followed by more complex tempering schedules did not produce specimens with optimum permanent magnet properties. However, for an alnico 5 alloy which had been heat treated in a field parallel to the [001] direction (which became the preferred direction) they obtained from the torque curve in the (110) plane a value of Ku = 0.84× 105jm -3, Sergeyev and Bulygina (1970) investigated the magnetic properties and the magnetic anisotropy at various stages in the heat treatment of single crystals of alnico 5. Some of their results are summarized in table 4 from which it can be seen that the increases in the coercivity and the energy product after tempering are accompanied by an increase in the anisotropy constant Ku, which can be attributed to an increased elongation of the particles and to changes
12 8
Alnico 5
[E 4 O m-
I,,.
0
= O I---4
-8
I
|
i
20
40
60
/
I /
801
i
I
100
120
Angle 0 from
o i
I
b
140
160
180
01]
Applied field = I ' 6 M A m
-1
-12 I
Fig. 15. Torque curve in the (ll(I) plane of a single crystal of alnico 5 (after Nesbitt and Williams 1955).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
133
TABLE 4 Magnetic properties and anisotropy constant Ku at various stages in the heat treatment of alnico 5 single crystals. Heat treatment A
Homogenization at 1300°C, followed by cooling to 9 0 0 ° C at a rate of 3.5°Cs-1.
1 A and cooling in a field from 900°C to 600°C at a rate of 0.5oCs i.
B (T) .
BHc (kAm-1) .
.
(BH)max (kJm-3)
Ku (Jm 3)
.
1.4
38.4
38.4
1.07
1 and tempering at 640°C for 2 h.
1.38
.47.2
43.2
1.30
3 2 and tempering at 560°C for 10 h.
1.37
52.8
60
1.52
2
N.B. 1 T =
10 4
G; 1 Am-1 = (4~r/1000) Oe; 1 J m
-3 =
407r GOe.
in their composition and hence the difference in the saturation magnetic polarizations of the al particles and the matrix, i.e. A J = Jal - Ja2. M o r e recently T a k e u c h i and I w a m a (1976) cooled a single crystal of alnico 5 (containing 51.31% Fe, 14.04% Ni, 7.69% A1, 23.88% C o and 3.08% Cu) in a magnetic field of 6 4 0 k A m -1 parallel to the [100] direction (which of course b e c a m e the preferred direction of magnetization) and obtained a value of Ku = 1.56× 105 Jm -3 and an associated magnetocrystalline anisotropy constant K1 = 0.15 × 105 J m -3, a result which suggests that the p e r m a n e n t m a g n e t properties of alnico are due principally to the shape anisotropy of the a~ ( F e - C o ) particles and that the contribution f r o m the magnetocrystalline anisotropy is relatively small. A technique for determining the magnetic anisotropy energy of alnico magnets has been developed by Allec (1971). This is based on a m e t h o d originally used on single crystals by Guillaud (1953) and enables the anisotropy constants to be d e t e r m i n e d f r o m the magnetization curves in various directions for single crystal, c o l u m n a r and polycrystalline specimens.
2.5. Magnetostriction of alnico 5 and alnico 5 D G (Alnico 5-7) T h e magnetostriction in alnico 5 has been investigated in considerable detail by Hoselitz and McCaig (1949) and McCaig (1949). T h e y m e a s u r e d the magnetostriction as a function of the direction of magnetization and the direction of m e a s u r e m e n t for specimens of alnico 5-7 which had been cooled from 1300°C in a magnetic field (a) parallel to the c o l u m n a r crystal axis and (b) perpendicular to the c o l u m n a r axis. T h e saturation magnetostriction, hs, was shown to d e p e n d very strongly on the particular set of angular relationships (angles were either 0 ° or 90 °)
134
R.A. McCURRIE
between the columnar axis, the field direction during cooling, the direction of magnetization and the direction of m e a s u r e m e n t of &. The observed values of A~ (McCaig 1949) ranged from - 6 1 x 10 -6 to 54 x 10 -6. McCaig (1949) also made measurements of As as a function of the direction of magnetization and the direction of m e a s u r e m e n t for alnico 5 specimens with (a) columnar crystals (anisotropic) and (b) randomly oriented crystals (isotropic) which had n o t been cooled in a magnetic field. The observed values of A~ for (a) also depended very strongly on the angular relationship (angles either 0 ° or 90 °) between the columnar axis, the direction of magnetization and the direction of m e a s u r e m e n t of As and ranged from - 7 . 5 × 10 .6 to 34.2× 10 .6 . For the (b) specimen with randomly oriented crystals (i.e. isotropic) the longitudinal saturation magnetostriction was 20 x 10 .6 while that measured perpendicular to the direction of magnetization, i.e., the transverse saturation magnetostriction was --8 X 10 -6. An extensive investigation of the magnetostriction of alnico alloys has been made by Nesbitt (1950) who showed that for polycrystalline alnico 5 alloys the saturation magnetostriction constants As depended very strongly on the heat treatment; the observed values of As were in the range 2.5 to 43 x 10 -6 which includes both longitudinal (i.e. parallel to the direction of the field applied during cooling) and transverse measurements of &. The low longitudinal value (2.5 × 10 -6) is due to the fact that the magnetization vectors in most of the interaction domains (see section 16) are either parallel or antiparallel to the applied field and hence at an angle of 180 ° to the domain magnetization and therefore do not contribute to a change in length of the specimen as a whole. The high transverse value (43 x 10 -6) is due to the fact that after cooling in a transverse field (i.e. in the direction perpendicular to that in which the magnetostriction is measured) most of the magnetization vectors of the interaction domains are perpendicular to the direction of m e a s u r e m e n t of As and so after magnetization in the measuring field each domain contributes to the overall change in length of the specimen. For an alnico 5 which was cooled from 1300°C at 2°Cs -1 (i.e. at the rate necessary to give o p t i m u m p e r m a n e n t magnet properties) the saturation magnetostriction & after tempering was 35 x 10 -6, whereas a specimen of alnico 5 which was given the commercial thermomagnetic and tempering treatment for o p t i m u m permanent magnet properties was found to have a saturation magnetostriction ),s of only 7.5 × 10 -6. 2.6. Microstructures of alnico 5 alloys The first attempts to determine the microstructures of alnico 5 alloys were made by Heidenreich and Nesbitt (1952) who used an oxide replica technique and electron microscopy. Unfortunately they were unable to resolve the microstructure in the optimum permanent magnet state. The microstructures and particle dimensions which they reported were obtained from specimens which had been over-aged by heat treatment at 800°C in order to m a k e the microstructure visible. Heidenreich and Nesbitt (1952) observed a rod-like precipitate which
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
135
tended to grow along (100) directions and to group into plate-like arrays. When there was no applied field during the heat treatment the cubic symmetry of the rods (i.e. their long axes were parallel to the (100) directions) was very clearly discernible. However, when the alnico 5 was heat treated in an applied field the long axes of the particles were confined to a single (100) direction when the field was parallel to that direction. By extrapolating their results to zero time at 800°C, Heidenreich and Nesbitt (1952) estimated that the particle dimensions were 7.5 × 7.5 × 40 nm. They also concluded that the particles were F e - C o rich and had a Curie temperature higher than that of the Ni-A1 rich matrix. By using very thin thermally grown oxide replicas and electron microscopy Kronenberg (1954) was able to observe the microstructure of alnico 5 in the optimum permanent magnet state but the results were inconclusive. Fahlenbrach (1954, 1955, 1956) used a refinement of the oxide replica technique and was able to show that after cooling in a magnetic field and tempering to give optimum permanent magnet properties the particles (Fe-Co) were rods 40 nm in diameter and 100rim long. Similar results were also obtained by Schulze (1956) who estimated the particle dimensions to be 36nm in diameter and 120nm long. Further improvements were made by Haanstra et al. (1957) and de Jong et al. (1958) who obtained very clear electron micrographs of alnico 5 and alnico 8 in the optimum permanent magnet state by using carbon replicas. They also concluded that the F e - C o rich particles were rods (approximately 30 nm x 30 n m × 120 nm) and that their long axes were parallel to the [100] direction which was closest to the direction of the applied field during the thermomagnetic treatment. The most comprehensive study of the microstructures of the alnicos (including Fe2NiA1) has been made by D e Vos (1966, 1969) who confirmed all the above conclusions concerning the microstructure of alnico 5 - an example of the latter is shown in fig. 16, from which it can be seen that the particles are about 150 nm long and about 40 nm in diameter. De Vos also showed that the higher coercivities which are observed in alnicos 8 and 9 can be attributed to the very high degree of particle elongation, perfection and alignment which results from the higher Co content and hence their greater sensitivity to thermomagnetic treatment (Zijlstra 1960-1962). Further confirmation of these microstructures has been made by Granovsky et al. (1967) and Pashkov et al. (1970). The microstructures of alnico 5 alloys have also been investigated by Pfeiffer (1969), Bronner et al. (1967), Mason et al. (1970), Nicholson and Tufton (1966) and Kronenberg (1960, 1961) who used transmission electron microscopy. From the above electron microscopy studies of alnico 5 it can be concluded that the volume fraction, p, of the o~1 (Fe-Co) phase is in the range 0.6-0.7, and that the degree of elongation (i.e. the ratio of the length to the diameter of the particles, l/d) is in the range ~ 4 - 6 . The observed values of p and I/d depend of course on the composition, thermomagnetic treatment and the temperature and time for which the alloys are annealed. According to Arbuzov and Pavlyukov (1965) both the c~1 (Fe-Co) and O~2 (Ni-A1) phases are ordered and have the bcc structure. However, Granovsky et al. (1967) and Pashkov et al. (1969) have shown by very careful X-ray diffraction
136
R.A. McCURRIE
H
l a
b Fig. 16. Microstructures of alnico 5; (a) in a plane parallel to applied field H and (b) in a plane perpendicular to H (magnification 45500 x) (De Vos 1966).
studies t h a t b o t h t h e a~ a n d og2 p h a s e s a r e very slightly t e t r a g o n a l . F o r alnico 5 the l a t t e r a u t h o r s f o u n d for t h e a l ( F e - C o ) p h a s e a = 0.2876 nm, c = 0.2872 n m a n d c/a = 0.998 a n d for t h e a 2 (Ni-A1) phase, a = 0.2870 nm, c = 0.2872 n m a n d c/a = 1.001. H o w e v e r , f r o m t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y Pfeiffer (1969) a n d B r o n n e r et al. (1967) c o n c l u d e d , in d i s a g r e e m e n t with the X - r a y diffraction results, t h a t only the a2 ( N i - A I ) p h a s e is o r d e r e d a n d that the a l ( F e - C o ) p h a s e is a d i s o r d e r e d solid solution. F r o m m e a s u r e m e n t s of t h e m a g n e t i c p r o p e r t i e s of alnico 5 S e r g e y e v a n d B u l y g i n a (1970) a n d B u l y g i n a a n d S e r g e y e v (1969) c o n c l u d e d t h a t t h e v o l u m e fraction, p, of the c~1 ( F e - C o ) p h a s e a r e in the r a n g e 0.62-0.67, d e p e n d i n g on t h e t h e r m o m a g -
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 137 netic heat treatment, and hence are in excellent agreement with those observed directly from the electron microscopical studies.
2.Z Alnico 6 This is a high coercivity form of random grain alnico 5. The higher coercivity is due to a Ti or Nb addition but is achieved, unfortunately, at the expense of a lower energy product (see table 2). A typical demagnetization curve for alnico 6 is shown in fig. 17. 1"2
I-
Alnicos 6,7,8
d 0"8
0"4 6
-12
-8
- 4 H (~104Am - 1 )
0
0
Fig. 17. Demagnetization curves for anisotropic alnicos 6, 7 and 8.
3. Anisotropic alnicos 8 and 9
3.1. Thermomagnetic treatment of anisotropic alnico 8 The high energy products of alnico 5-7 (alnico 5DG, alnico 7) are achieved principally as a result of" the increased remanence parallel to the 'thermomagnetic field' direction and the preferred or columnar crystal axis. The coercivity on the other hand remains almost the same as that in alnico 5 with randomly oriented grains. It can be seen from fig. 11 that the various forms of alnico 5 all have nearly rectangular demagnetization curves so that the alloys are used at m a x i m u m efficiency only if the load line or load permeance B / H intersects the demagnetization curve at a point corresponding to the (BH)maxenergy product. A slight shift of the load permeance results in a significant decrease in the available energy. Since the composition of the alloy limits the m a x i m u m remanence to about 1.4T, further squaring of the demagnetization curve will not result in a significant increase in the m a x i m u m energy product. In view of this limitation considerable research effort has been expended to increase the coercivity, and this has been achieved by increasing the cobalt content to 32-36wt % and adding
138
R.A. McCURRIE
4-5 wt % titanium. The addition of Ti alone was found to increase the coercivity but this was, unfortunately, accompanied by a decrease in the remanence (Honda 1934). To compensate for the latter Koch et al. (1957) found that it is necessary to increase the cobalt content to ~ 3 5 % . Koch et al. (1957) found that if the alnico 8 alloy containing 35.5% Fe, 34% Co, 14.5% Ni, 7% A1, 5% Ti, 4% Cu was cooled from 1260°C in a saturating magnetic field and subsequently tempered at 585°C the following properties were obtained: Br = 0.85 T, BHc = 92 kAm -1 and (BH)max--28 kJm -3. When the same alloy was given an isothermal heat treatment at ~800°C for several minutes (precise details not specified) in a saturating magnetic field there was a significant improvement in the magnetic properties to: Br = 0.9 T, BH~ = 112 k A m -1 and ( B H ) ~ = 40kJm -~. Koch et al. (1957) concluded that for Ti-containing alnicos the best magnetic properties are obtained by isothermal heat treatment in a saturating magnetic field (~200-300 kAm -1) followed by tempering for several hours at 585°C. De Vos (1966, 1969) suggested that because the Ti ion has a large radius it has a low rate of diffusion and therefore requires a longer time at high temperatures for the phase separation to occur. From electron microscopy Koch et al. (1959) showed that for alnico 5 which had been isothermally heat treated in a magnetic field the a l (Fe-Co) particles were much more elongated than those which had been given the conventional thermomagnetic treatment (i.e. cooling in a magnetic field). Koch et al. (1959) also found that even higher coercivities could be obtained with a cobalt content >34% Co and a Ti content > 5 % Ti. For alnico 8 alloys with 34-40% Co and 5-8% Ti, Wyrwich (1963), Stfiblein (1963), Planchard et al. (1964b), Bronner et al. (1966a, b) and Vallier et al, (1967), Livshitz et al. (1970a) have shown that coercivities BHc --~ 176 kAm -1 and energy products up to ~48 kJm -3 can be obtained. Bronner et al. (1966a, b) found that the energy product of 48 kJm -3 was constant up to about 45% Co. Wright (1970) and Bronner et al. (1970a) have shown that the addition of niobium as well as titanium also has beneficial effects on the magnetic properties of alnicos 5, 6, 8 and 9, though alnico 5-7 should contain a small addition of niobium only. Typical compositions and magnetic properties of alnico 8 alloys are given in table 5. Koch et al. (1959) found that for the alloy 35.5% Fe, 34% Co, 14.5% Ni, 7% A1, 4% Cu, 5% Ti, the homogeneous bcc ce phase is stable only above about 1250°C and that between 1250°C and 845°C it decomposed to form another bcc c~ phase and an fcc y phase with lattice parameter, a0 = 0.365nm. In the range 845-800°C, the c~ phase decomposes spinodally to form a bcc F e - C o rich al phase and a bcc Ni-A1 rich a2 phase. A small amount of the y phase is also present at this stage but below 800°C this transforms by an apparently diffusionless reaction to another bcc phase, c~v with lattice parameter 0.359 nm. Ritzow (1963) suggested that the difficulties encountered in controlling the heat treatment of the high Ti alloys is probably due to the fact that the Curie temperature is practically in the y region (see section 9) so that the isothermal thermomagnetic treatment temperature is very critical. Julien and Jones (1965a, b)
S T R U C F U R E A N D P R O P E R T I E S OF A L N I C O P E R M A N E N T M A G N E T A L L O Y S
139
TABLE 5 High coercivity field-treated anisotropic alnico 8 alloys. Composition Fe
Ni
A1
Co
Cu
Ti
Nb
B, (T)
BHc (kAm -l)
(BH)max (Jm -3)
40.8
14.6
6.9
28.5
3
4.2
2
0.95
97
40
35
14.9
7
34
4.5
5
-
0.96
103
41
34.5
14.3
6,9
34
3.8
5.5
1
0,88
117
41
36
14
7,5
34
3
5
0.5
0.93
119
46 48
35
13
7.5
34
3
6
1.5
0.83
/ ' 150
29.5
14
7.5
38
3
8
-
0.74
167
48
35.5
14
7.5
34
3
4.5
1.5
0.8
162
48
33
15
7.5
34
3
7
0.5 Hf
0.8
154
49
N.B. 1 T = 10 4 G ; 1 A m -~ = (4:7/1000) Oe; 1 Jm -3 = 40~ GOe.
have shown that if an alloy of alnico 8 with 32% Co and 6.5% Ti is held at 900°C for about 15 rain the 3' phase is produced which lowers the (BH)max product by 50% compared with the same alloy which had not been annealed at 900°C, They also found that the tendency to precipitate the 3' phase was increased when the Cu content was increased (a similar effect was observed in alnico 5) while the Ti suppressed its formation. The homogenization temperature was just below the melting point. If alnico 8 alloys are cooled too slowly the appearance of the 3' phase results in a deterioration in magnetic properties which manifests itself in a concave demagnetization curve just as occurs in alnico 5 (see fig. 18). Such concave demagnetization curves can be synthesised from three normal demagnetization curves. The effects of the a~ phase on the hysteresis loops have also been discussed by Julien and Jones (1965b). In view of the tendency of Ticontaining alnico 8 alloys to form the fcc Y phase their heat treatment must be Carefully controlled in order to obtain optimum magnetic properties. This inevitably increases the cost of their p r o d u c t i o n - though this is largely due to the high cobalt content. The kinetics of the a ~ 3, transformation in alnico 8 (and alnico 5) alloys have also been investigated by Planchard et al. (1964a, 1965, 1966a). A study of the influence of cobalt on the c~ ~ 3, transformation has been made by Marcon et al. (1971) who showed that for alnicos containing more than 28% Co it is practically impossible to avoid the precipitation of the deleterious y phase during thermomagnetic treatment unless appropriate amounts of a-stabilizing elements such as silicon or titanium are added. A typical heat treatment for alnico 8 alloys is as follows. After controlled
140
R.A. McCURRIE
1"2
Alnico 5
1.0
0.8 ~ m 0.6 O "O
0"4 x
_= I.I.
0"2
t
0
60
50
40 30 20 10 Applied field,H (kAm-1.)
0
Fig. 18. Demagnetization curve for alnico 5 showing deleterious effect of the presence of the o~ fcc phase on the shape of the curve.
(BH) max (k Jrn-3) 80 60 40 //
/I
¢I
~
//
1.2
/I
,
/ i/./
1-4
i
1I
//
1"0 ~ "
ii
0"8
m ¢n c
0.6 ¢~ qD X
0.4 0.2 !
160
140
120 100 80 Applied field, H
60 40 CkAm-1)
I
20
0
Fig. 19. Demagnetization curve for alnicos 8, 9 and 5-7. The latter two curves are given for comparison. The alloy 8(b), which has the highest coercivity is also known as sermalloy A1 (Bronner et al. 1966b). c o o l i n g f r o m a b o v e 1250°C, t h e a l l o y is h e a t t r e a t e d f o r a f e w m i n u t e s at a b o u t 820°C in a s a t u r a t i n g m a g n e t i c field ( ~ 3 0 0 k A m -1) a n d t e m p e r e d f o r a b o u t 6 h at 650°C f o l l o w e d by a b o u t 24 h at 550°C.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 141 A typical B - H demagnetization curve for alnico 8 is shown in fig. 19, the compositions and magnetic properties of various alnico 8 alloys are given in table 5.
3.2. Extra high coercivity alnico 8 A higher coercivity field-treated random grain form of alnico 8 can be produced by increasing the cobalt and titanium contents still further to 37-40% Co and 7-8% Ti. Sometimes a little (0.5 to 1.5%) of the titanium is replaced by niobium. The maximum coercivity of these extra high coercivity alnico 8 alloys is about 180 kAm -1 which is higher than that of any other alnico. The production and properties of extra high coercivity alnico 8 alloys have been described and investigated by Wyrwich (1963), Planchard et al. (1964b, 1966b), Bronner et al. (1966a, b), Vallier et al. (1967) and Bronner et al. (1970a). Planchard et al. (1964b) and Bronner et al. (1966a) studied the dependence of the magnetic properties on the Ni, Ti, A1 and Cu content for alloys containing 40% Co. Planchard et al. (1964b) obtained a maximum coercivity BHc = 161 kAm -1 with Br = 0.71 T and (BH)m~ = 44 kJm -3, for an alloy containing 27.5% F e - 4 0 % C o - 14% N i - 8 % A 1 - 7 . 5 % T i - 3 % Cu. The alloy was homogenized at 1250°C for 1 h and then heat treated isothermally for 5 minutes at 810°C in a magnetic field of 336 kAm -1. After this treatment the alloy was annealed for 6 h at 650°C and then for 24 h at 550°C. In a later investigation Bronner et al. (1966b) developed an alloy containing 29.5% F e - 3 8 % C o - 1 4 % N i - 7 . 5 % A 1 - 8 % T i - 3 % Cu with a coercivity BHo = 168 kAm -I with Br = 0.74 T and (BH)max = 48 kJm -3. These properties were obtained by homogenization at 1250°C in a neutral or reducing atmosphere followed by cooling in compressed air to 600°C in order to avoid the precipitation of the deleterious 3, phase. The alloy was then isothermally annealed for a few minutes at 820°C in a magnetic field ~336 kAm 1 and then tempered for 6 h at 640°C and finally for 24 h at 550°C. This alloy, which is an extra high coercivity alnico 8, is also known as sermalloy A1. Apart from its high coercivity and energy product, sermalloy A1 has high useful recoil energy (a maximum Erec ~ 20 kJm -3) and a high Curie temPerature Tc = 874°C so that it is very stable under demagnetizing conditions and at temperatures up to about 550°C. An alloy, with almost identical properties to sermalloy A~, also known as hycomax IV has also been developed by Harrison and Wright (1967). A typical demagnetization curve for this special alnico 8 alloy (A1) is shown in fig. 19. Koch et al. (1957) investigated the effectiveness of Ti and Nb additions in increasing the coercivity of alnico 8 alloys and concluded that Ti was more effective. However, Bronner et al. (1970a) and Bronner (1970) found that the addition of Nb (0.5-2.0%) to alnico 8 alloys containing 4.5-6.5% Ti could be beneficial. For example the alloy 35.5% F e - 34% C o - 14% N i - 7.5% A 1 - 4.5% T i - 3 % C u - 1 . 5 % Nb B H c = 1 6 2 k A m -1, B r = 0 . 8 T and (BH)max=48kJm -3. Bronner (1970) reported that the addition of hafnium was also beneficial and found that the alloy 33% F e - 3 4 % C o - 15% N i - 7.5% A 1 - 7% T i - 3% Cu with 0.5% Hf had a coercivity td-/c = 154 k A m -1, a Br = 0.8 T and a (BH)m~ = 49 kJm -3.
142
R.A. McCURRIE
Similar investigations of extra high coercivity alnico 8 alloys have been made by Livshitz et al. (1970a) who used a wide variety of thermomagnetic and tempering treatments. They obtained magnetic properties in the ranges Hc = 160-176 kAm -1, Br = 0.65-0.75 T and (BH)m~x = 36-44 kJm -3 for alloys containing 38% Co and 8.0-8.5% Ti after optimum thermomagnetic and tempering treatments. The compositions and magnetic properties of some typical extra high coercivity alnico 8 alloys are given in table 5. A simplified heat treatment, using continuous cooling, rather than isothermal heat treatment in a magnetic field (240 kAm -1) for alnico 8 alloys has been developed by Wright (1970). He showed that by cooling alloys with compositions in the range 34-35% Co, 14-15% Ni, 6.8-7.2% A1, 5-5.4% Ti, 0.8-1.1% Nb, 3 - 4 % Cu, balance Fe from 1250°C (at average rates of 2, 1.2, and 0.6°Cs -I from 1200-600°C) in a magnetic field of 240 kAm 1 followed by tempering for 4 h at 640°C and then for 16h at 570°C, magnetic properties better than Br = 0.85 T BHc = l l 2 k A m -~ and (BH)max = 36kJm -3 can be obtained. Wright (1970) also showed that if 0.25% S is added to the alloys, magnets with columnar crystals can be produced by casting in a mould with heated sides and chilled at the end faces. For these columnar magnets typical properties are, Br = 1.03 T, BHc = 118 kAm -~, and (BH)max = 58 kJm -3. Columnar alnico 8 alloys i.e. alnico 9 alloys are discussed in section 3.3.
3.3. Anisotropic alnico 9 with fully columnar grains Alnico 9 is produced by the columnar crystallization of alnico 8. Unfortunately, the high Ti content of the latter reduces the grain size (Luteijn and De Vos 1956) so that columnar crystallization of alnico 8 is difficult. Luteijn and De Vos (1956) succeeded in producing a grain oriented alnico 9 magnet by using special techniques. For the alloy containing 35% Fe, 34% Co, 15% Ni, 7% A1, 5% Ti and 4% Cu by weight, they obtained a magnet with Br = 1.18 T, BHc =- 105 kAm -1 and (BH)max = 88 kJm -3. These very high values were obtained by using very pure starting materials and isothermal heat treatment parallel to the [100] axis of the columnar grains. The demagnetization curves for the alloy are shown in fig. 19. Gould (1964), Makino and Kimura (1965), Wittig (1966) and Harrison and Wright (1967) have shown that these difficulties in producing fully columnar alnico 9 magnets can be overcome by the addition of small quantities of S, Se or Te. Alnico 9 can be prepared as follows. After melting an alnico 8 alloy with a small addition of S, Se or Te (sometimes two of these elements are added) the fully columnar structure is obtained by casting the alloy in a heated or exothermic mould in which the end faces are chilled so that grains with (100) axes grow perpendicularly to the chilled surfaces. The alloy is then solution treated at 1250°C cooled at a controlled rate and heat treated in a saturating magnetic field (~300 kAm -1) for a few minutes at about 820°C and finally given a two-stage tempering treatment for several hours at 650°C and at 550°C. The grain structure of a fully columnar alnico 9 magnet is shown in fig. 20.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 143
Fig. 20. Grain structure of fully columnar alnico 9 (Gould 1964) (magnification: ~2x).
The production of columnar alnico 9 has also been described and investigated by Fahlenbrach and Stfiblein (1964), Naastepad (1966), Harrison (1966), Hoffmann and Stfiblein (1966, 1967, 1970), Palmer and Shaw (1969), Dean and Mason (1969), Hoffmann and Pant (1970) and Pant (1974). Hoffmann and Pant (1970) produced magnets (containing 7.7% Ti) with coercivities up to a m a x i m u m of Uric = 1 7 1 k A m -1, iHc = 1 7 9 k A m -l, B r = 0 . 8 7 T and (BH)max = 7 7 k J m -3. They also produced a magnet (containing 7.1% Ti) with an energy product (BH)max = 98 kJm -3 in combination with ~Hc = 136 k A m -1, i S c ~ 138 k A m -~ and Br = 1.03 T. Pant (1974) produced alnico 9 magnets having diameters ~ 1 5 - 8 0 m m with a columnar crystallization length of ~120 m m for which (BH)max ~ 90 kJm -3 (with BHo = 150 k A m -1) and (BH)max ~ 80 k J m -3 (with BHc ~ 160 kAm-1). Although the coercivity of alnico 9 is nearly the same as that of alnico 8 the higher energy product is due to the increased remanence parallel to the columnar axis i.e. [100]. The improved properties of alnico 9 parallel to the columnar axis are of course achieved at the expense of those perpendicular to the columnar axis but in many applications this is not a serious disadvantage. Demagnetization curves for alnicos, 8 and 9 are shown in fig. 19 from which it can be seen that the magnetic properties of alnico 9 are considerably better than those for alnico 8; the m a x i m u m energy products for alnico 9 are typically in the range 60-75 kJm -3. The higher energy products of alnicos 8 and 9 compared with alnico 5-7 are, unfortunately, obtained at the expense of a reduced remanence. T h e relationship between the magnetic properties and the crystal textures of alnico 9 alloys have been investigated by Higuchi and Miyamoto (1970) and D u r a n d - C h a r r e et al. (1978). T h e latter used Schulz's (1949) X-ray diffraction method and found that the observed metallurgical texture could be correlated with the solidification rates. Grain growth by solid state recrystallization in various alnico 9 alloys has been
144
R.A. M c C U R R I E
investigated by Wright and Ogden (1964) but although some large crystals were grown the technique was not considered to be very successful. The dependence of the magnetic properties of columnar alnico 9 on the angle between the columnar axis and the direction of thermomagnetic treatment, and the angle of measurement is discussed in section 7.3. The development and chronology of alnico magnets are shown in fig. 21 (Cronk 1966). The best magnetic properties are of course obtained for single crystal alnicos. Naastepad (1966) showed that a single crystal containing 35 wt % Fe, 34.8% Co, 14.9% Ni, 7.5% A1, 5.4% Ti and 2.4% Cu had a coercivity 8He of 122kAm -1 and an energy product (BH)max of 107kJm -3. The latter energy product is the highest yet reported for any alnico. A summary of the magnetic properties and compositions of columnar alnico 9 alloys is given in table 6. 120 Alnicos DG -- Directed grain MC - Monocrystal
100 ¢0 I
E
-~
MC9
MC5
80
5-7 x
60
5DG
E
.,p m
40
2
20
II I I 1940 1950 Calendar year
o
1930
!
I
1960
1970
Fig. 21. Development and chronology of alnico magnets (after Cronk 1966),
TABLE 6 Compositions and magnetic properties of anisotropic field-treated alnico 9 columnar alloys. Composition Fe
Ni
A1
Co
Cu
Ti
Nb
Others
26.1
14.7
6.8
40.3
2.9
8,2
-
35.2 35 36.1 29
14.8 15 14.5 14
7 7 7 7
33.1 34 34 38.9
4.5 4 3 3,5
5.5 5 5.2 7.1
-
35
14.9
7.5
34.8
2.4
5.4
-
0.77 Te O.22 S 0.22 S 0,2S 0.45 S 0.05 C -
N.B. 1 T
=
10 4
G; 1 A m -1 = (4~'/1000) Oe; 1 Jm -3 = 40~r GOe.
Br (T)
BEe (kAm -1)
(BH)max (kJm -3)
0.895
160
67
1.095 1,18 1.11 1.03
123 104.5 129 136
83.5 87.5 91.5 97
1.15
121
106
STRUCTURE
AND PROPERTIES
OF ALNICO PERMANENT
MAGNET
ALLOYS
145
3.4. Shape anisotropy of alnicos 8 and 9 The effects of varying the cobalt and titanium contents on the induced shape anisotropy constant K. of alnico alloys have been studied by Takeuchi and Iwama (1976) (see also section 2.4). They found that for an alnico 8 alloy (29.5% F e - 39% C o - 14% N i - 7% A1- 7.5% T i - 3% Cu) Ku = 2.4 × 105 Jm -3 and a magnetocrystalline anisotropy constant K1 = 0.26 x 105 Jm -3, thus confirming that the anisotropy and hence the coercivity of alnico alloys is due predominantly to the shape anisotropy of the individual Fe-Co rich particles. The induced anisotropy constant K. was of course measured on single crystal specimens in which the individual particles were almost fully aligned by the thermomagnetic treatment. TABLE 7
Compositions of single crystal alnicos. Specimen No.
Fe
1
51.4
2
Ni
Al
Co
Cu
Ti
14
7.7
23.9
3
0
47.9
14.4
7.9
26
2.5
1.3
3
43.5
14
7.6
29
2.9
3
4
29.5
14
7
39
3
7.5
TABLE 8
Apparent anisotropy constants Ku and K,] ( x 104 J m -3) determined by torque measurements, volume fraction, p, particle diameter d, elongation l/d intrinsic coercivity iHc and flux coercivity BHc (K" = Ku/p) (Takeuchi and Iwama 1976). Specimen No.
Ti (wt % )
Ku (104Jm -3)
p
d (nm)
lid
inc (kAm-1)
BH¢ (kAm-1)
K" ( 1 0 4 j m 3)
1
0
15.6
0.68
44
4-5
57
-
22.9
2
1.3
16.1
0.67
42
6-7
59
-
24
3
3.0
17.3
0.63
37
8-12
67
-
27.5
4
7.5
24.2
0.46 ~
30
30-50
167
-
52.6
Alnico 5*
0.0
15.2
0.67
40
4-6
-
53
22.7
Alnico 8*
5.0
23
0.54
30
13-16
-
114
42.6
Alnico 8"*
7.5
-
-
20
30-35
-
147
-
*Sergeyev and Bulygina (1970) and **Granovsky et al. (1967). N.B. 1 T = 104 G ; 1 A m -1 = (47r/1000) O e ; 1 J m -3 = 40~" G O e .
146
R.A. McCURRIE
This is clearly shown by the electron micrographs obtained by Takeuchi and Iwama (1976). Their value of Ku = 2.4 x 105 Jm -3 is in very good agreement with that obtained by Sergeyev and Bulygina (1970) who found a Ku = 2.3 x 105 Jm -3 for an alnico 8 alloy containing 26.5% F e - 40% C o - 1 4 % N i - 7.5% A 1 - 7.5% T i - 4 . 5 % Cu. The alloy was homogenized at 1240°C, cooled to 800°C at 5°Cs -1 and then annealed for about 12 rain at 820°C in a magnetic field of 160 kAm -1 after which the alloy was tempered for 5 h at 650°C and 20 h at 560°C. The compositions and properties of the alloys used in the above investigations are summarized in tables 7 and 8. The high coercivities of alnico 8 (and alnico 9) can be attributed to the increased shape anisotropy energy resulting from the high cobalt content and the addition of titanium. The effects of cobalt and titanium contents on the magnetic properties are discussed in sections 8 and 9 respectively.
3.5. Microstructures of.alnicos 8 and 9 Replication electron micrographs of the highly oriented microstructure of an alnico 8 alloy were obtained by De Vos (1966, 1969). Typical microstructures in planes parallel and perpendicular to the thermomagnetic field direction are shown in figs. 22(a) and (b). The regular distribution of the precipitated particles in both orientations is characteristic of a system in which phase separation has occurred by spinodal decomposition. From measurements on the electron micrographs the average dimensional length to diameter ratio 1/d is >10 and from the application of quantitative metallography (Hilliard 1962, 1967, 1968, Hilliard and Cahn 1961, Underwood 1970, 1973, Saltykov 1970) the volume fraction of the particles is ~0.65. Although the volume fraction of the particles is comparable to that of the other alnicos there is a marked increase in the dimensional ratio, degree of particle alignment and particle perfection; all of these factors contribute to the increased coercivity of the alnico 8 alloys compared with alnico 5 alloys. Since alnico 9 alloys have similar compositions to the alnico 8 alloys (alnico 9 is simply a columnar crystallized alnico 8) it may be assumed that the microstructures are similar to those of alnico 8. The microstructures of alnico 8 alloys have also been investigated by Bronner et al. (1967), Granovsky et al. (1967), Pfeiffer (1969), Mason et al. (1970), Livshitz et al. (1970b), Iwama et al. (1970) and Takeuchi and Iwama (1976). From the electron micrographs obtained by the above authors it can be seen that the F e - C o rich particles have length to diameter ratios l/d in the range 10-50 where l ~ 400-1000 nm and d is in the range 20-40 nm. The application of quantitative metallography to the electron micrographs shows that the volume fraction of the F e - C o rich particles is ~0.65. Although the volume fraction of the particles in alnico 8 is comparable to that in the other alnicos, there is a marked increase in the elongation (l/d), the degree of particle alignment and particle perfection; all of these factors contribute to the increased coercivity of alnico 8 alloys compared with alnico 5 alloys. By using X-ray electron diffraction Pashkov et al. (1969) measured the lattice parameters of the bcc a~ and a2 phases in three alnico 8 alloys containing
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
147
Fig. 22. Electron micrograpti of the al + ~2 structure of alnico 8 after an isothermal heat treatment at 800°C for 9 min; (a) in a plane parallel to the direction of the applied field during heat treatment, (b) in a plane perpendicular to the field direction (magnification 45500 ×) (after De Vos 1966).
TABLE 9 Lattice parameters of the bcc oq and c~2 phases in alnico 8 alloys (A). c~1 phase (Fe-Co) Alnico 8
a
c
35% Co, 5% Ti
2.909
2.873
40% Co, 7% Ti
2.909
42% Co, 8% Ti
2.915
c~2 phase (Ni-A1) c/a
a
c
c/a
0.99
2.855
2.873
1.006
2.872
0.987
2.850
2.872
1.008
2.872
0.985
2.852
2.872
1.007
148
R.A. McCURRIE
respectively, 35, 40, 42% Co and 5, 7, and 8% Ti; their results are shown in table 9, from which it can be seen that both the eel and O~2 phases are very slightly tetragonal with c/a < 1 and c/a > 1 respectively.
4. M6ssbauer spectroscopy of alnicos 5 and 8
From M6ssbauer spectroscopy measurements on alnico 5, Shtrikman and Treves (1966) have concluded that in the optimum permanent magnet state, the alloy consists of two phases one of which is an Fe-rich ferromagnetic phase and the other is a Ni and Cu rich paramagnetic phase. M6ssbauer measurements on alnico 8 made by Albanese et al. (1970) show that 7-8% of the total Fe content is paramagnetic. From the quadrupole splitting of the M6ssbauer spectra it was also concluded that the two phases have a small tetragonal distortion in agreement with the X-ray work of Bulygina and Sergeyev (1969). Van Wieringen and Rensen (1966) also detected the presence of Fe in both the al and Og2 phases. They have also shown that after continuous cooling of alnico 5 all the Fe atoms have a ferromagnetic environment suggesting that both the c~1 and O~2 phases are ferromagnetic, whereas after tempering (Ho = 50 kAm -1) 5% of the total iron content is in a non-ferromagnetic phase. The M6ssbauer spectra of alnico 5 and alnico 8, particularly the latter, have also been investigated in detail by Makarov et al. (1967), Belova et al. (1969), Povitsky et al. (1970), Belozersky et al. (1971) and Makarov et al. (1972). A short review of M6ssbauer measurements on the alnicos has been published by Schwartz (1976).
5. Sintered alnicos
The alnico alloys whether isotropic or anisotropic can also be made by mixing suitably fine metal powders, pressing to a green compact followed by a sintering heat treatment at about 1250-1350°C to produce a homogeneous solid with low porosity. The solid compact is then given a heat treatment appropriate to the particular composition. The resulting magnetic properties of the sintered alloys are comparable, though slightly inferior, to those of the cast alloys. The energy product for anisotropic sintered magnets may sometimes be as much as 20% lower than that for the cast magnets but for isotropic cast magnets the difference is usually smaller than this. A comparison of the magnetic properties of various sintered and cast alnicos has been given by Bronner et al. (1970b). Typical demagnetization curves for four sintered alnicos are shown in fig. 23. The advantage of the sintering process is that very small magnets of intricate shape can be made which is not possible or very expensive by the usual casting and grinding process. However, sintered alnicos have a very small share of the market. The production and magnetic properties of sintered alnicos have been discussed by Schiller (1968), Schiller and Brinkmann (1970) and Heck (1974).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 149 - 1-2
Sinteredalnicos/~~
1.0
6
0.8~ 0.6
D'4
(D "0
I,I.
D.2 n 70
0 60
50
40
30
20
10
0
Applied field, H (kAm-1) Fig. 23. Typical B-H demagnetization curves for sintered alnicos 2, 5, 6 and 8.
6. Moulded, pressed or bonded alnico m a g n e t s
Alnico alloys can be milled to fine powders without a marked deterioration in their magnetic properties. If the powders are then bonded into a thermosetting resin they can be accurately pressed or moulded to the required magnet shape. The properties of the bonded magnets are inferior (Dehler 1942, Heck 1974) to those of the cast or sintered magnets. This is due to the fact that the volume fraction of the powder cannot exceed about 60% so that there is a corresponding reduction in the remanence.
7. Effects of t h e r m o m a g n e t i c t r e a t m e n t on the magnetic properties of alnicos 5 - 9
7.1. Factors controlling development of Ol 1 particle shape anisotropy The factors which control the development of the magnetic anisotropy of alnico 5 during thermomagnetic treatment have been studied in detail by Zijlstra (19601962) following a suggestion made by N6el (1947b). H e found that the rate of elongation of the particles is related to the difference between the decrease in the magnetic free energy of the particles in the magnetic field and the simultaneous increase in the interfacial or surface free energy. The equilibrium value of the elongation is high when the magnetic free energy is large compared with the interfacial free energy between the particles and the matrix. Since the former is measured as energy per unit volume and thus independent of particle size and the
150
R.A. McCURRIE
latter is a surface energy and hence inversely proportional to the particle size, the particles will always become considerably elongated when they are sufficiently large. The efficacy of the thermomagnetic treatment on alnico 5 can be attributed to the particularly low value of the interfacial energy or surface free e n e r g y typically this is ~10-3Jm -2 (1 erg cm-2). This enables the particles to become elongated when they are still small enough to display single domain behaviour and thus to form a magnet with high shape anisotropy together with a high coercivity. Zijlstra (1961) suggested that the same reasoning leads to the conclusion that the Mishima alloy Fe2NiAI, which is usually not considered to respond to magnetic annealing owing to its much larger interfacial free energy, may be expected to do so only when the particles are large enough. He verified this conclusion by heat treating a specimen of Fe2NiA1 in a magnetic field for two weeks at 725°C during which it developed a uniaxial magnetic anisotropy of 4.5 x 10 4 Jm 3 which is of the same order of magnitude as that observed in alnico 5. This Fe2NiA1 alloy did not, however, have a high coercivity because after the long thermomagnetic treatment the particles were too large to be single domains. Thus it appears that the function of the cobalt in the alnico alloys, apart from increasing the saturation magnetic polarization and the Curie temperature, is to decrease the interfacial free energy between the Fe-Co rich particles and the Ni-A1 rich matrix and hence to enable the alloys to respond to thermomagnetic treatment with a resulting improvement in their magnetic properties. If the magnetic field is applied only during the cooling over the narrow temperature range 840-790°C with subsequent tempering at 600°C without an applied field, the resulting magnetic properties are only slightly inferior to alloys which have been given the full thermomagnetic treatment. If the field is applied only below 790°C the anisotropy is less than half that of the fully thermomagnetically treated specimens. If the specimen is cooled to 790°C in the presence of the field and then allowed to cool with the field off, the maximum energy product is lower than the value obtained by quenching the alloy from 790°C. The decrease is due presumably to a partial destruction of the shape anisotropy by inhomogeneous demagnetizing fields and thermal fluctuations. The most effective temperature range for the particle elongation and alignment in a magnetic field is therefore 840°C to 790°C; the lower limit is particularly critical. Nesbitt and Williams (1957) suggested that in the temperature range 850-790°C only nucleation takes place, while particle growth occurs at 600°C. However, Zijlstra's (1960-1962) and De Vos' (1966, 1969) experiments showed that in the field cooling treatment the final particle shape is attained in the very first stage (i.e. in the range 850-790°C) and that subsequent heat treatments did not alter the shape or size of the particles. As was mentioned earlier tempering at 600°C increases the difference in the saturation magnetic polarization between the c~1 (Fe-Co rich) and c~2 (Ni-A1 rich) phases and leads to an increase in the coercivity and remanence.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 151
7.2. Relationship between the preferred or easy direction of magnetization and the direction of the applied field during thermomagnetic treatment The relationship between the orientation of the particles and the direction of the magnetic field during heat treatment has been investigated by Heidenreich and Nesbitt (1952). They found that the orientation of the particles is not strictly bound to the (100) directions, but could be forced into other directions by the thermomagnetic treatment. In a later paper Nesbitt and Heidenreich (1952a) deduced from magnetic torque measurements that the magnetic anisotropy of alnico 5 was a maximum when the magnetic field was directed along a (100) direction of a single crystal sample during the thermomagnetic treatment. If the field was applied in another direction the anisotropy was lower and the preferred direction of magnetization appeared to lie between the field direction and the nearest (100) direction. Similar results were obtained by Hoselitz and McCaig (1951) but they found that the preferred direction of magnetization was closer to the [100] direction than was indicated by the experiments of Heidenreich and Nesbitt (1952). These differences may be attributable to difference in the magnitudes of the applied fields which were chosen for the thermomagnetic treatments. In another series of experiments McCaig (1953) found that the uniaxial anisotropy of alnico 5 was approximately 105 Jm 3 and that for normal cooling rates (~l.4°Cs -1) and angles less than about 45 ° between the crystal and field directions, the easy direction of magnetization was close to the columnar axis. However, for faster cooling rates, larger angles and less than optimum heat treatments the easy direction of magnetization may be closer to the field direction with a correspondingly lower value of the anisotropy coefficient. An extensive investigation has also been made by Yermolenko et al. (1964) who found that when the thermomagnetic field was parallel to the [100] direction the O/1 (Fe-Co) particles were elongated parallel to this direction but for other angles between the applied field and the [100] direction, the axes of elongation of the particles were not parallel to the field direction. They concluded in contrast to the theory proposed by N6el (1947b) and later developed by Zijlstra (1960-1962) that the axes of elongation are not entirely determined by the minimization of the magnetic and interface energies of the particles in the thermomagnetic field but that their shapes and orientations are partly determined by their elastic energies. It should be mentioned that Yermolenko et al. (1964) used isothermal heat treatment in a magnetic field (720 kAm 1) but this enabled them to study the microstructures of the alloy at different stages in the formation and growth of the particles.
7.3. Dependence of the magnetic properties of the alnicos on the direction of the applied field during thermomagnetic treatment The dependence of the magnetic properties of columnar and single crystal alnico 5 (and alnico 6) on grain orientation and the direction of the thermomagnetic field have been investigated in detail by Ebeling and Burr (1953). They found that the
152
R.A. McCURRIE
best magnetic properties are obtained when the direction of the thermomagnetic field is as close as possible to the [100] direction in the single crystals or to the long axis of the columnar single crystals- i.e., approximately parallel to the [100] direction. When the thermomagnetic field was applied at other angles to [100] or to the [100] columnar axis the maximum energy product decreased according to the cosine of the angle between the thermomagnetic field direction and the [100] or the [100] columnar axis:
(BH)max(O)=
(BH)max(0)cos 0.
The variation of (BH)max with the angle 0 for various sintered single crystals of alnico 5 is shown in fig. 24. From measurements of the energy products of single crystal alnico 5 (51 wt % F e - 24% C o - 14% N i - 8% A 1 - 3% Cu) after heat treatment in a magnetic field parallel to the directions [100], [110] and [111] Zijlstra (1956) showed that the energy product could be expressed as a power series of the direction cosines/31,/32 and/33 measured with respect to the cube axes of the crystal. This was used to calculate the energy product for polycrystalline alnico 5 as a function of crystal orientation. The columnar texture of the magnet was represented by assuming that there was a constant density of [100] axes inside a cone of revolution around the measuring direction which enclosed an angle 2,/. By averaging the above power series for (BH)max Zijlstra obtained an expression for (BH)max in terms of r/. The energy product was shown to decrease almost linearly from 60.8 kJm -3 for ~7 = 0° to 40 kJm -3 for r / = 45 °. The calculated value of the energy product for a
50-
0
~3o
\cosO
"--"20
0
I 0
I
I 30
I
I 60
90
Angle 0 °
Fig. 24. Dependence of (BH)max energy product on the angle between the field applied during thermomagnetic treatment and the [100] preferred or easy axis of magnetization (after Ebeling and Burr 1953).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
153
polycrystalline alnico 5 magnet (i.e. one for which ~/= 180 °) was 39.2 kJm -3 which was in good agreement with experiment and suggests that the analysis was essentially correct. An expression for the energy product as a function of ~/ was also developed for magnets in which the crystals are radially oriented in a plane perpendicular to the magnet axis. Magnets with this texture are significantly better than those with randomly oriented grains. The magnetic properties of equiaxed and columnar alnico 5 have been investigated in detail by Makino et al. (1963) and Makino and Kimura (1965). They measured the demagnetization curves parallel and perpendicular to the columnar axis (a) as a function of the angle 0 between the columnar axis and the direction of the 'thermomagnetic field', and (b) as a function of the angle 0' (0' = 90 - 0) between the direction of measurement perpendicular to the columnar axis and the direction of the thermomagnetic field. The results of these measurements are shown in fig. 25 from which it can be seen that the maximum coercivity (58 kAm-1), remanence (1.35 T) and energy product (64 kJm -3) are obtained when the 'thermomagnetic field' is applied parallel to the columnar axis. For the measurements in the direction perpendicular to the columnar axis the maximum coercivity (50kAm-1), remanence (1.32 T) and energy product (42 kJm -3) are obtained when the thermomagnetic field is parallel to the direction of measurement, i.e., perpendicular to the columnar axis. Although the maximum energy product for (b) of 42 kJm -3 is lower than that of 64 kJm -3 for (a) the fact that such a high value was obtained for (b) is an important result because it provides further evidence for the theory that - 1-4
~
0=0¢
I
60
50
1
40 30 Applied field, H
.
20
2
10
(kAm-1}
0
Fig. 25. B - H demagnetization curves measured in the direction M of the columnar axis after heat treatment in a magnetic field at an angle 0 to the columnar axis c (after Makino and Kimura 1965 and Makino et al. 1963).
154
R.A. McCURRIE
15
45
~"~'I0
.
[010] . H ~ ~ . , . 4 ~...Ku " ~
/
/
ool 0~ 0
30
e.ol, I
1 15
I
I 30
I
I 0 45
Angle [30
Fig. 26. Variations of uniaxial anisotropy constant Ku and its direction o~ with direction/9 of the heat treatment field H.
the preferred direction of magnetization is largely determined by the direction of the thermomagnetic field (N6el 1947(b), Zijlstra 1960, 1961) and that crystallographic anisotropy is of secondary importance. Zijlstra (1960, 1961) has shown by experiments on Fe2NiA1 that the time for which the alloy is subjected to the thermomagnetic field treatment is also of fundamental importance in determining the results. (The theories of the effects of thermomagnetic treatment of the alnicos are discussed in section 17.) Iwama et al. (1976) measured the anisotropy constant Ku of single crystal alnico 5 after cooling in a magnetic field at angles 0 °, 15°, 30 ° and 45 ° to the [100] direction. The results are shown in fig. 26; Ko decreased from 15.6× 104Jm -3 parallel to the [100] direction to 4.5 x 104 Jm s at 45 ° to [100]. Figure 26 also shows the variation of the angle a between the preferred axis of Ku and the [100] direction as a function of the angle/3 between the direction of the heat treatment field and the [100] direction. It can be seen that only when /3 = 45 ° does the preferred direction of magnetization (i.e. the Ku axis) follow that of the heat treatment field, i.e., a 2 4 5 °. At lower values of /3 the Ku axis lies between the direction of the heat treatment field and the [100] direction. These results are in good agreement with those obtained by McCaig (1953).
8. Effects of cobalt on the magnetic properties of the alnicos
The addition of cobalt to both the isotropic and anisotropic alnicos has several beneficial effects. In the isotropic alloys it increases the saturation magnetic
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 155 polarization Js and hence the remanence Jr. Since the cobalt is precipitated in the c~1 phase particles (i.e. the F e - C o rich phase) this increases the difference between the magnetic polarizations of the al and a2 phases and hence increases the coercivity due to the resulting increase in the shape anisotropy. The same improvements are also observed in the anisotropic alnicos 5-9 but in these alloys the cobalt content is in the range 23-40%. The high cobalt content also increases the Curie temperature Tc which has the beneficial effect of increasing the sensitivity (of the alnicos 5-9) to magnetic annealing. This is due to the fact that the spinodal decomposition temperature Ts is then further below Tc so that the magnetic polarization of the particles at Tc is higher, and therefore increases the elongation of the particles in the magnetic field direction because their magnetic free energy is thereby lowered. Cahn (1963) has shown the magnetic energy is proportional to the square of the rate of change of the saturation magnetic polarization with composition i.e. (OJs/Oc)2 and that the latter is very large when the spinodal decomposition temperature is close to the Curie temperature. Thus heat treatment in a magnetic field is expected to be most effective when T~ is close to but lower than To. According to Zijlstra (1960, 1961) the high cobalt content also decreases the interfacial energy ,,/between the F e - C o rich c~i phase and the Ni-A1 rich a2 phase so that the increase in the total surface energy which results from the particle elongation is reduced. N6el (1947b) and Zijlstra (1960, 1961) have suggested that the sensitivity of alnico alloys is proportional to (A J)2~3, where AJ is the difference between the saturation magnetic polarizations of the F e - C o rich c~ phase and the Ni-A1 rich a2 phase. Thus when AJ is high and 3' low the rate of elongation of the particles in the thermomagnetic field is high. This results in an increase in the coercivity, the remanence and the energy product parallel to the direction of the applied field. From tables 2, 3, 5, and 6 it can be seen that there is a substantial improvement in BHc, Br and (BH),nax in the cobalt containing alloys compared with the original F e - N i - A I alloy (table t). Unfortunately the increased cobalt content, particularly in the anisotropic alnicos 5-9, favours the precipitation of the magnetically deleterious fcc phase so that more carefully controlled cooling through the range 1200°C to 850°C is required. Detailed investigations of the effects of cobalt on the magnetic properties of the alnicos have been made by many authors, see e.g., Betteridge (1939), Jellinghaus (1943), Zumbusch (1942a, b), Bronner et al. (1966a-1970). According to Wyrwich (1963) the best magnetic properties are obtained with a cobalt content -~38%.
9. Effects of titanium on the magnetic properties of the alnicos (mainly 6, 8 and 9) The effects of titanium additions on the magnetic properties of the alnico 8 are summarized in fig. 27 from which it can be seen that titanium increases the coercivity and the energy product and the time required to form the undesirable fcc 3, phase at 1050°C, though there is unfortunately a rapid decrease in the remanence with increasing Ti content (Vallier et al. 1967). Similar results were obtained by Iwama et al. (1970) who also showed that the Curie temperature of
156
R.A. M c C U R R I E oO. 120
m
1 " 1 --
O O
1"0--
~" E
4~,16
3C
®
0-9 - ~
3 E
Br
12 0
0
o
toO'8
2
= 8
C
E
[~'mlc
c
0"7-
1 ® E
0 . 6 [-
0
I--
2
4 6 Wt % Ti
8
I
[0
Fig. 27. Effects of titanium additions on the magnetic properties of alnico 8 (41% F e - 3 4 % C o - 15% N i - 7% A I - 3% Cu) (after Vallier et al. 1967).
the Ni-A1 rich OL2 phase decreased linearly with increasing Ti content as shown in fig. 28 from which it can be seen that if the alnico 8 alloy containing more than 5% Ti is annealed at 600°C the Curie temperature falls below room temperature. This increases the coercivity because in normal use (~20°C) the F e - C o rich
6 0 0 I-
.
~,AnneaEed
o
for 48hr at T C
I "~
0 "~_
0.200
0
I
I
I
I
2
4
6
8
Wt % titanium Fig. 28. Variations of Curie temperature of the Ni-AI rich o~2 phase with Ti content for alnico specimens annealed at various temperatures (after Iwama et al. 1970).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 157 particles are then surrounded by a non-ferromagnetic matrix and are not therefore in exchange contact so that the difference between the saturation magnetic polarizations of the F e - C o rich al phase and the Ni-AI rich ~2 phase is as large as possible; the latter therefore increases the shape anisotropy energy of the particles and hence the coercivity. The effects of Ti additions on the magnetic properties of various thermomagnetically treated alnico single crystals have been investigated by Takeuchi and Iwama (1976). They measured the anisotropy coefficient Ku, the volume fraction of the F e - C o rich particles, p, the particle diameter d, the elongation l/d and the intrinsic coercivity iHc. Their results are summarized in tables 7 and 8. The latter includes results obtained by Sergeyev and Bulygina (1970) and Granovsky et al. (1967) for comparison. These results show that the anisotropy Ku (and K ' , the anisotropy per unit volume of the F e - C o rich particles), the particle elongation l/d and the coercivity increase as the Ti content increases. The increase in coercivity is also accompanied by a decrease in the volume fraction p and the particle diameter d. If we can assume that the coercivity dependence on the packing fraction is given by, He(p) = He(0)(1 - p ) , an increase in Hc is to be expected if p decreases. The increase in the coercivity due to the titanium addition can also be partly attributed to an increase in the elastic and surface energy associated with the spinodal decomposition which increases the smoothness, perfection and regularity of the particle s p a c i n g - s e e e.g. electron micrographs of alnico 8 (fig. 22(a), (b)) obtained by De Vos (1966, 1969), and those obtained by Granovsky et al. (1967) and Takeuchi and Iwama (1976). While Ti inhibits the a ~ y transformation Vallier et al. (1967) have shown that it restricts the temperature ranges for homogenization and thermomagnetic treatment so th~it the choice of the heat treatment schedule is critical. De Vos (1966, 1969) has suggested that the necessity to give titanium containing alnicos an isothermal anneal in a magnetic field is due to the fact that the Ti 2+ ion has a large radius and a low rate of diffusion so that longer times are required for the phase separation and particle elongation to occur. Marcon et al. (1971) have shown, for alnicos containing more than 28% Co, that it is practically impossible to avoid the precipitation of the deleterious y phase during thermomagnetic treatment unless appropriate amounts of a-stabilizing elements such as silicon or titanium are added. Unfortunately titanium inhibits the formation of the columnar grain structure. However, Gould (1964), McCaig (1964) and Harrison and Wright (1967) have shown that the addition of small quantities of sulphur, selenium or tellurium facilitates the formation and growth of columnar grains. Thus the addition of titanium to the alnicos, although beneficial, means that much more careful control of the composition and heat treatment of the alloys is required. It is for this reason and the higher cobalt content that the high coercivity alnicos 8 and 9 are generally more expensive than the other alnicos. The effects of additions of Ti, S, Nb, and other elements on the magnetic and metallurgical properties of the
158
R.A. McCURRIE
alnicos have been investigated by Clegg (1966, 1970), Palmer and Shaw (1969), Higuchi (1966), Hoffmann and St/iblein (1970) and Wright (1970).
10. Dependence of the magnetic properties on the angle between the direction of measurement and the preferred or easy axis of magnetization The variation of the coercivity with angle 0 to the preferred axis in alnico 9 and ticonal 900 (single crystal) has been measured by McCurrie and Jackson (1980) who observed small maxima at 0 = 60 ° followed by a rapid decrease to zero at 90 ° (fig. 29). According to Shtrikman and Treves (1959) the reduced coercivity hc as a function of the angle of m e a s u r e m e n t 0 and the reduced radius for infinitely long cyclindrical rods with shape anisotropy only is given by Hc hc = 2XMs- $2[(1 _
1.08(1- 1.08S 2) ( 1 - 2.16S -2) sin 2 0] 1/2'
1.08S_2)2
where S = R/Ro (Ro = (4"n't.zoA/JZs)1/2) and 0 is the angle between the easy axis of magnetization (i.e., the axis of the cylinder) and the direction of m e a s u r e m e n t of He. Comparison of the results shown in fig. 29 with the theoretical curves obtained from the above relation shown in fig. 30 suggests that the observed angular variation of Hc in these alloys is due to magnetization reversal by the curling mechanism. The coercivities of alnico 9 and ticona1900 are - 0 . 2 5 H A (HA is the anisotropy field) which are in good agreement with the values to be expected if the magnetization reverses by curling (Shtrikman and Treves 1959). The angular variation of the r e m a n e n c e coercivity Hr (Hr is the reverse field required to reduce the r e m a n e n c e to zero) showed even m o r e pronounced maxima at 0 ~ 80 ° followed by a rapid decrease to zero at 0 ~ 90 °. Unfortunately no detailed theory of the variation of Hr with 0 is available for comparison, though Kneller (1966, 1969) has suggested that Hr(O)/Hc(O) varies between the limits:
1 (0 = 0 °) <~H,-(O)/Hc(O) ~< o~ (0 = 90°). Paine and Luborsky (1960) have measured the angular variation of the intrinsic coercivity of alnico 5DG, columnar alnico, which was found to be almost independent of the angle up to about 40 ° after which Hc decreased and at 0 = 90 ° it was about half the value at 0 = 0 °. For a specimen of alnico 9 the coercivity decreased with the angle 0 and at 0 = 90 °, it was about a quarter of the value at 0 = 0 °. Bate (1961) found that for partially aligned y-Fe203 particles Hr(O)/Hc(O) increased from 1.25 at 0 = 0 ° to 2.3 at 0 = 90 °. The dependence of the magnetic properties on the crystal orientations (i.e., crystallographic texture) in columnar alnico 5-7 has been investigated in considerable detail by McCaig and Wright (1960), Makino and Kimura (1965) and
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS AHrT tXHrA • HcT
3,0
10 I 0-9
i 2.5 E
0"8 ~ S < 1 O'7 ~
,~,
3
2.0 0.6
"r" e-
159
j¢
1"5
..r" ~, 1.0
S=1"47
o,+
0"3
>
o= 0.5 0~ O
o.1 0
+ I I I I 15 30 45 60 75 90 Angle 0 ° from easy axis in degrees
Fig. 29. Dependence of the coercivity Hc and remanence coercivity Hr on the angle 0 between the preferred axis and the direction of measurement for columnar alnico 9 (A) and single crystal alnico 9 (T) (McCurrie and Jackson 1980).
S--6,0
0
0
_
.
~
I
I
1
I
[
I
I
I
\ ~1
10
20
30
40
50
60
70
80
90
0o Fig. 30. Reduced coercivity hc for an aligned array of infinitely long single domain cylindrical particles with shape anisotropy only as a function of the angle 0 between the easy axis (i.e. the cylindrical axis) and the direction of measurement. S is the reduced particle radius. (S ~ R/Ro where R0 = (4~A)l/2//z~/2Ms and A is the exchange constant.) The curve for S < 1 is identical to that for the Stoner-Wohlfarth coherent rotation theory (after Shtrikman and Treves 1959).
M o o n (1974), M c C a i g a n d W r i g h t (1960) h a v e m a d e m e a s u r e m e n t s of t h e m a g netic p r o p e r t i e s at v a r i o u s angles to the p r e f e r r e d d i r e c t i o n in t h r e e c o l u m n a r alnico m a g n e t s (49.7 wt % F e - 25% C o - 13.5% N i - 8% A 1 - 3% C u - 0.8% N b ) a n d h a v e s h o w n t h a t t h e d e c r e a s e in r e m a n e n c e with angle is in g o o d q u a l i t a t i v e a g r e e m e n t with results p r e d i c t e d f r o m t h e S t o n e r - W o h l f a r t h (1948) t h e o r y . F o r an a l i g n e d a s s e m b l y of e l o n g a t e d p a r t i c l e s t h e r e m a n e n c e at an angle 0 to t h e p r e f e r r e d d i r e c t i o n of m a g n e t i z a t i o n , i.e., t h e c o l u m n a r a x i s - n o m i n a l l y p a r a l l e l to the [100] d i r e c t i o n , is given by B~ : L = J+ cos O.
F o r angles > 7 5 ° t h e m e a s u r e d v a l u e s of Jr ( M c C a i g a n d W r i g h t 1960) are l a r g e r t h a n t h o s e p r e d i c t e d by t h e a b o v e e x p r e s s i o n (fig. 31). T h e v a r i a t i o n of t h e c o e r c i v i t y with t h e a n g l e b e t w e e n t h e p r e f e r r e d d i r e c t i o n a n d t h e d i r e c t i o n of m e a s u r e m e n t is shown in fig. 32 f r o m which it can b e seen that the coercivities are a l m o s t c o n s t a n t up to an angle of 20 ° . T h e l a t t e r lack of a g r e e m e n t with t h e
160
R.A. McCURRIE
1 0 0 ~ l ~ ~ o C o l u m n a r alnico5 r,
.\ '
60
°~ =
E 20 0
.~
- ~-~sw
~
Theory
'~ r
SW Theory ~ , ,
0
I
I
~
I
30
, ~
6O
~ ~
v ~--'~R41
90
Angle e °
Fig. 31. Variation of remanence Br and maximum energy product (BH)max with angle 0 to the preferred axis in columnar alnico, 5DG (alnico 5-7) and comparison with Stoner-Wohlfarth (1948) theory (after McCaig and Wright 1960).
100 8O 60 m
•~- 4O ._> @ O
(3 20
0
0
30
60
90
Angle e °
Fig. 32. Variation of coercivity ~ with angle 0 to the preferred axis in columnar alnico 5DG (alnico 5-7) and comparison with Stoner-Wohlfarth (1948) theory (after McCaig and Wright 1960).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 161 Stoner-Wohlfarth (1948) theory is due to incomplete alignment of the particles, magnetostatic interaction between the particles and to incoherent magnetization reversal by curling (see Zijlstra, chapter 2 of this handbook). The variation of the (BH)ma~ product with angle to the preferred direction is shown in fig. 31 from which it can be seen that the decrease in (BH)r~ax with increasing angle is much less rapid than that predicted from the Stoner±Wohlfarth (1948) theory.
11. Relationship between magnetic properties and crystallographic texture The relationship between the crystal texture and the magnetic properties of alnico 8 (33 wt % F e - 36% C o - 1 5 % N i - 7% A 1 - 5 % T i - 4% C u ) h a s been studied by Higuchi and Miyamoto (1970). The magnets were solution heat treated for 30 min at 1250°C and then annealed in a magnetic field of 240 kAm -1 for 8 min at 810°C, after which they were given a two-step anneal at about 600°C. Unlike the previous studies discussed above the crystal textures of the specimens were determined from their magnetization curves assuming that changes in the magnetization occurred by coherent rotation of the magnetization vector. Higuchi and Miyamoto (1970) showed that there was very good agreement between the measured values of Br, Hc and (BH)m~x and the values calculated from their model. The highest observed energy product was 89 kJm -3. The relationship between magnetic properties and crystallographic texture of alnico 5 has also been investigated by Moon (1974). In this work measurements of the orientation (by an X-ray diffractometer) and magnetic properties were made on several specimens from a series of columnar magnets with a nominal composition 50.4wt % F e - 2 4 . 5 % C o - 1 3 . 5 % N i - 8 % A 1 - 3 % C u - 0 . 6 % Nb. The magnets were cooled from 1250°C at 1.2°Cs -1 in a magnetic field - 2 2 0 kAm -~ parallel to the direction of solidification, annealed at 590°C for 48 h and then annealed for a further 48 h at 560°C. Moon showed that the energy product (BH)max decreased rapidly with increase in the standard deviation of the angle 0 between the [100] direction and the axis of the magnet and suggested that small improvements in the casting techniques and hence the crystallographic texture might lead to a significant improvement in the (BH)ma× product.
12. Effects of particle misalignment on the remanence and coercivity of the anisotropic field-treated alnicos 12.1. R e m a n e n c e
Although the magnetic properties of the alnicos depend on the degree of particle alignment, a considerable deviation from complete alignment can be tolerated without a very significant deterioration in the magnetic properties. Suppose that the axes of elongation of the particles in a given specimen all lie within a cone of
162
R.A. M c C U R R I E Z
0
~X
Fig. 33. Definition of solid angle dO for determination of r e m a n e n c e of an array of uniaxial single domain particles whose preferred axes of magnetization lie within the cone with semi-vertical angle 0.
semi-solid angle 0 m a s shown in fig. 33 where 0 m is the maximum deviation from the preferred axis. The number of particles with their axes at an angle 0 is proportional to the solid angle contained within the interval 0 and 0 + dO viz. 27r sin 0 dO. So that the remanence is given by IOOm27r sin 0 cos 0 dO Jr=L"
_ Js(1 + cos 0m)
or.
(1)
fo 2~- sin 0 dO so that even when 0m = 30 °, Jr/Js = 0.933. Unfortunately it is difficult to compare this simple theory with experimental measurements because of the difficulty in obtaining samples which have their particle axes included in a suitable range of measurable 0m angles. Furthermore the cosine function is relatively insensitive to changes in 0m (fig. 34). McCurrie (1981) has suggested that a more accurate
Jr
1.0
Js 0.8 0.6
0-4
0.2
0
I
0
I
I
I
I
30
I
60
I
I
I
90
Angle e m Fig. 34. D e p e n d e n c e of r e m a n e n c e on m a x i m u m angle of'deviation 0m of the particle axes from preferred axis of magnetization (McCurrie 1981).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
163
estimate of the degree of alignment can be o b t a i n e d by measuring the saturation r e m a n e n c e at 90 ° to the preferred or easy axis. In this case,
Jr _ (Om -- 1 sin 2Ore) J~ vr(1 -- COS Om) ' or
J~/Js ~ ~ sin Ore. These functions, which are shown in fig. 35, are m u c h m o r e sensitive to changes in 0m than the function given in eq. (1). 0.5
_~sinem,,,~,/
Js
,,;,/
0'3
/ g ~
/,,/\ (.em~ _ ~ ' .~Sin2ern) _ 2
,~'
0-1 0
0
' i
~1 2c-'~SOm) !
!
30
i
I
l
60
|
!
i
90
Angle 0 m Fig. 35. D e p e n d e n c e of r e m a n e n c e m e a s u r e d perpendicular to preferred axis and the m a x i m u m angle of deviation 0m of the particle axes from the preferred axis of the magnet (McCurrie 198l).
12.2. Coercivity
T h e coercivity is also decreased when the axes of elongation of the particles are at angles in the range 0 to 0m to the preferred axis. F r o m the S t o n e r - W o h l f a r t h (1948) theory of hysteresis in single domain particles it can be shown that for a single particle whose axis of elongation is at an angle 180-0 to the applied field (i.e. a demagnetizing field) the coercivity is given by: Hc = (Dz - Dx)Ms (1 - tan 2/3 0 + tan 4/3 0) 1/2 ( 1 + t a n 2/30) ,
for0<0~<45 ° ,
and He = }(Dz - Dx)Ms sin 20,
for 45 ° ~ 0 ~< 90 ° .
164
R.A. McCURRIE
The variation of the coercivity with angle 0 is shown in fig. 32, where the ordinate has been plotted in reduced units (% of He at 0 = 0°). From fig. 32 it can be seen that the coercivity decreases rapidly for 0 up to about 15° after which the decrease with increasing 0 is m u c h less rapid. For a reasonably well aligned array of particles in an alnico alloy 0 is unlikely to be greater than about 30 ° at the maximum.
13. Determination of the optimum volume fraction of the F e - C o rich particles
Since the F e - C o rich particles are required to be elongated single domains they must not be precipitated in a quantity sufficient to cause coalescence. This means that the composition of the alloys must be chosen so that the volume fraction of the F e - C o rich cq phase is surrounded by the non-ferromagnetic or weakly ferromagnetic Ni-A1 rich ~2 phase. A further restriction is placed on the volume fraction, p, of the F e - C o rich al phase because the coercivities of the alloys are reduced by particle interaction effects which are usually assumed to be proportional to ( 1 - p). If we assume that for a packing fraction p and coherent magnetization reversal, the coercivity is given by (see for example, Ndel 1947a, Kittel 1949, Kittel and Galt 1956, Brown 1962, Compaan and Zijlstra 1962): H e ( p ) = H~(O)(1 - p ) ,
where He(0) is the extrapolated coercivity when p = 0, then the value of p for which the energy product is a maximum can be determined as follows. Since the maximum possible coercivity Hc(0) is given by He(p) = [(Dz - Dx)(1 - p ) M ~ ] / p , and taking (Dz - Dx) ~ ½, 1
1
He(p) - 5(1 - p ) M ~ _ (1 - p) Js, p 2p, o where Ms~ is the average or overall saturation magnetization of the alloy and Js is the saturation magnetic polarization of the particles. (Note that if the magnetization reversal occurs entirely by curling then Hc is independent of p because curling produces no interaction fields (Kneller 1969)i) However, since magnetostatic interaction domains (section 16) are observed during the demagnetization of the alnicos it appears that the particles do produce interaction fields so that some coherent magnetization reversal must also occur. Thus for the present approximate calculation it seems that the use of the above relation for He(p) is justified. Consider an alnico alloy with a rectangular M - H hysteresis loop with an
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
165
intrinsic coercivity H¢(p) as shown in fig. 36(a). The corresponding B - H demagnetization curve is shown in fig. 36(b). The flux coercivity ,Hc = He(p) because the M - H loop is rectangular so that the discontinuous magnetization and flux reversals take place in the same reverse field. The maximum energy product for this B - H demagnetization curve is given by the area OPQR, i.e., (BH)max = (PJs - ½(1 - p)Js)(1 - p)Js/ZI-Lo. Note that the saturation magnetic polarization of the alloy as a whole is Jm = PJs. From the above expression we find that (BH)m,x = (J~/4tzo)(-3p 2 + 4p - 1), which has a maximum value when
d(BH)max/dp = 0
and
d2(BH)m,x/dp 2< O,
i.e., when 6p=4,
or
p=2.
Thus (BH)max is equal to J~/12/x0. This value of (BH)max is obtainable only when the intrinsic coercivity, He, satisfies the condition H~ = (1 - p)JJ2/x0. For the magnetically annealed alnicos the absolute maximum in the (BH)max product is obtained when p = 0.6-0.7 which is in good agreement with both the
i
~
Mr=Ms
B Br=Jm=PJs
-H
Hc
?,
H / / / /
/
/ Z
'H
(a)
/ He
R BHc
O
(b)
Fig. 36. (a) Ideal rectangular M - H hysteresis loop with intrinsic coercivity iH¢. (b) Corresponding B - H demagnetization curve for M - H loop in (a). (NB: The flux coercivity BHc=iH¢, the intrinsic coercivity because the M - H loop is rectangular.)
166
R.A. McCURRIE
above theories. The packing fraction p can be determined by quantitative metallography (see for example, Hilliard 1962, 1967, 1968, Hilliard and Cahn 1961, Underwood 1970, 1973, Saltykov 1970) of the two phases which are clearly visible on the replication electron micrographs such as those shown in figs. 22(a) and (b). Another estimate of p can be obtained from the measured value of the saturation magnetic polarization, Jm, of the magnet alloy as a whole if it is assumed that the individual particles have a saturation magnetic polarization Js, equal to that of FeCo and by using the relationship Jm = PJ~.
For field heat treated grain oriented alnico 5-7 the saturation magnetic polarization is approximately 1.4 T. Since Js = 2.4 T for FeCo we find that p = 0.6 which is very close to the values determined by quantitative metallography (De Vos 1966, 1969, Granovsky et al. 1967, Takeuchi and Iwama 1976) and from magnetic measurements (Bulygina and Sergeyev 1969, Sergeyev and Bulygina 1970). Apart from the reduction in the coercivity due to the packing fraction p of the particles (H~(p)= H~(0)(I-p)), Kondorsky (1952a, b) and Aharoni (1959) have shown that the critical diameter for infinitely long single domain particles is given by:
Re(p) = Re(0) (1 - p)-l/e, so that R~(p) increases with the packing fraction. For materials such as the alnicos in which the coercivity is due almost entirely to the shape anisotropy of elongated single domain particles of Fe-Co the critical radius Re(0) (for an infinitely long cylinder) is given by Rc(0) = (1.08/2Dz )1/2(47"rtzoA/J2s)1,2 , i.e., Rc(0) = 1.04(4 7"rtzoA/J~) ~/2 , since the demagnetization factor Dz for an infinitely long cylinder is 0.5. In the above relation A is the exchange energy coefficient, Js the saturation magnetic polarization and/z0 = 47r x 10 -7 Hm -1 is the magnetic constant. A more detailed discussion of the critical sizes for single domain particles is given by Zijlstra in chapter 2 of this handbook.
14. Interpretation of the magnetic properties in terms of the Stoner-Wohifarth theory of hysteresis in single domain particles The magnetic hysteresis of non-interacting single domain particles with uniaxial shape anisotropy has been investigated theoretically by Stoner and Wohlfarth (1948). They investigated the behaviour of a single domain ellipsoid of revolution when subjected to increasing magnetic fields at various angles to the easy axis of
S T R U C T U R E A N D P R O P E R T I E S O F A L N I C O P E R M A N E N T M A G N E T ALLOYS
167
magnetization of the ellipsoid assuming that changes in magnetization occurred by coherent rotation of the magnetization vector. The relationship between the applied field, the easy axis and the magnetization is shown in fig. 37. For a particle with a saturation magnetization of Ms the total magnetic free energy is 1 2 E = ½1xo(Dz - D x ) M 2 sin 2 ~ + gl.xoDxMs + IxoHMs cos qS.
(2)
where Dx and Dz are the demagnetization factors parallel and perpendicular to the axis of elongation of the particle. The particle is assumed to be a prolate ellipsoid of revolution so that Dy = D~ and Dy > Dx. Thus in a given field H the stable positions of the magnetization vector are those which correspond to the minima of eq. (2). The solutions, for various values of the field and the angle 0, have been tabulated by Stoner and Wohlfarth (1948) who have also plotted several representative hysteresis loops notably those for 0 = 0, 45 ° and 90 °. For a survey of the results the reader is referred to Zijlstra, (chapter 2 in this handbook). One of the most important conclusions from the Stoner-Wohlfarth theory is that the coercivity of an aligned assembly of identical non-interacting (i.e., infinitely dilute) single domain particles with uniaxial shape anisotropy is Hc = (D: - D x ) M s ,
i.e., the coercivity is directly proportional to the saturation magnetization and to the difference in the demagnetization factors perpendicular and parallel to the easy axis. For a randomly orientated array of such particles the coercivity is reduced to Hc = 0.479(Dz - D x ) M s . The dependence of ( D z - Dx) on the degree of elongation, i.e., the ratio of the lengths of the x- and z-axes of the particle, is shown in fig. 38. It has already been mentioned in section 1.2 that in view of the complex microstructures and particle shapes in the isotropic alnicos 1-4 it is not possible to give a quantitative comparison or interpretation of their magnetic properties in terms of the StonerWohlfarth (1948) theory though their magnetic properties can be understood Ms
H
Fig. 37. Relationship between the applied field, easy axis and magnetization vector in a prolate ellipsoidal single domain particle with uniaxial shape anisotropy.
168
R.A. M c C U R R I E
0.5 0"4
Dz
~0-3 I
N
0'2
Dx
0"1 0
1
I
I
2
3
I
I
4 5 Dimensional
I
I
6 7 8 ratio m = a / b
I
I
9
10
Fig. 38. Difference (Dz- Dx) between demagnetization factors perpendicular and parallel to the preferred axis of magnetization as a function of the particle elongation or dimensional ratio m = a/b, where a is the semi-major and b the semi-minor axis of the prolate ellipsoid of revolution.
qualitatively. In any case in the alnicos 1-4 both the al and a2 phases are ferromagnetic so that magnetization changes by domain wall movement may also occur.
From the electron micrographs of alnico 5 and alnico 5-7, the precipitated F e - C o rich particles are rod-like (i.e., they approximate to prolate ellipsoids of revolution) and have dimensions ~150 nm long and ~40 nm in diameter. From fig. 38 the corresponding value of Dz - Dx is ~0.5 and hence if we take the saturation magnetization of the particles Ms = 1.7x 106Am -1 which is considerably larger than the observed value of 60 kAm -1. Although the particles are not fully aligned this is insufficient to account for the difference in the two values. Since the coercivity depends on the presence of demagnetizing fields it is clear that particle interactions cannot be neglected. Many authors (see e.g., N6el 1947a, Compaan and Zijlstra 1962) suggest that the effects of particle interactions on the coercivity are best described by the relation
He(p)= H o ( O ) ( 1 - p ) , where He(p) is the coercivity for a particle packing fraction p and He(0) is the coercivity for a packing fraction of zero. Thus if the effects of particle interactions are included the coercivity of a fully aligned array of single domain particles with uniaxial shape anisotropy is Ho= (1-p)(Dz -Dx)Ms,
(3)
or
Hc = (1 - p ) ( D z - Dx)M's/p, where M'~ is the average saturation magnetization of the alloy. The packing factor
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 169 p is usually in the range 0.6-0.7 and (Dz-D~) approaches 0.5 so that the theoretical value of Hc ~ 300 kAm -~. Thus even if particle interaction effects are included there is still a very significant difference between the theoretical and observed coercivities (-~60 kAm-1). Baran (1959) has derived a more general expression for the coercivity of a fully aligned array of particles which takes account of the reduction in coercivity due to particle interactions and the possibility that the matrix is also ferromagnetic, viz. Hc = p(1
-
p)(Dz
-
Dx)(MI
-
M2)2/M's,
(4)
where p is the volume fraction of the most strongly ferromagnetic phase, M1 and M2 the saturation magnetizations of this phase and the matrix phase respectively, M's the overall saturation magnetization of the alloy and Dz and Dx are the demagnetization factors Of the particles perpendicular and parallel to the axis of elongation respectively. For the maximum coercivity it is clear from eq. (4) that the difference M 1 - M 2 should be as" large as possible. If it is assumed that the alloy is fully heat treated, i.e., sufficient time has been allowed for all the Fe and Co atoms to diffuse to the precipitated particles, then the matrix saturation magnetization M2 ~ 0 and the saturation magnetization of the Fe--Co rich particles M1 = Ms = M's/p, so that eq. (4) reduces to eq. (3). From the electron micrographs of alnico 8 shown in figs. 22(a) and (b) (De Vos 1966, 1969) the F e - C o rich particles are very long rods and approximate to prolate ellipsoids of revolution with length to diameter ratios l/d ~-16 corresponding to D z - D~--~ 0.5. Quantitative metallography shows that the volume fraction of the F e - C o rich particles p ~ 0.65. Since there is a very high degree of particle alignment we may calculate the coercivity from eq. (1). If Ms is taken to be at least equal to the value for pure iron viz. 1.7 MAre -1 (the saturation magnetization for Fe-30% Co is about 10% higher than that of pure iron) the theoretical coercivity as derived from eq. (3) is ~300 kAm -1 which compares very favourably with the highest experimental value of 180 kAm -~ for alnico 8. The discrepancy between the observed value of the coercivity and that calculated according to the Stoner-Wohlfarth (1948) theory suggest that the assumption that changes in the magnetization occur by coherent rotation is invalid (see Zijlstra, chapter 2 in this handbook).
15. Interpretation of the magnetic properties in terms of magnetization reversal by the curling mechanism According to calculations by Kondorsky (1952a), Brown (1957, 1963, 1969), Frei et al. (1957) and Aharoni and Shtrikman (1958) magnetization reversal by coherent rotation in infinitely long cylinders with shape anisotropy only, should occur only when the cylinder radius R is less than a critical radius R0 = (4zrA)llZ/Izaol2Ms where A is the exchange constant,/z0 is the magnetic constant 4~- × 10 -7 H m -1 and Ms the saturation magnetization. Above this radius magnetization reversal occurs by the curling mechanism (apart from a very small range of radii for which magnetization
170
R.A. McCURRIE
reversal occurs by a process known as buckling). According to Aharoni and Shtrikman (1958) the dependence of the coercivity on the cylinder radius R is given by Hc = 1.08(Ro/R )ZMs/2 ,
(5)
where it is of course assumed that D z - Dx has its maximum value of 0.5 for an infinitely long cylinder. The curling mechanism is discussed in chapter 2 of this handbook by Zijlstra who has also included a diagram showing the configuration of the magnetic Spins during the reversal process. From measurements on the electron micrographs of alnico 8 obtained by De Vos (1966, 1969) (see figs. 22(a) and (b)) the particles have radii ~15 nm. Although the particles are obviously not infinitely long cylinders their length to diameter ratio l/d ~ 16 so that assuming magnetization reversals occur by curling we may estimate the coercivity from eq. (5) from which we find that Hc ~ 2.4 × 105 A m -1 (McCurrie and Jackson 1980). The highest observed flux coercivity for alnico 8 BHo ~ 1.8 × 105 A m -1 (this is slightly less than the intrinsic coercivity He) so that the theoretical and observed coercivities are in reasonable agreement. When the magnetization reversal occurs entirely by curling there are no particle interaction effects so that the coercivity is independent of the packing fraction p. However, the appearance of magnetostatic interaction domains (discussed below) during demagnetization suggests that some interparticle interaction does occur. From measurements of the angular variation of the coercivity and rotational hysteresis in columnar and single crystal alnico 9 (see sections 10 and 18) McCurrie and Jackson (1980) have concluded that magnetization reversal does occur by the curling mechanism and that the quantitative results are in reasonable agreement with those predicted on the basis of the theory proposed by Shtrikman and Treves (1959).
16. Magnetostatic interaction domains in alnicos Magnetization reversal in the alnicos is further complicated by the formation of magnetostatic interaction domains which are due to interparticle interactions. Although it is well established that the alnicos contain single domain particles, macroscopic surface domain structures known as magnetostatic interaction domains, can sometimes be observed by the Bitter colloid technique, as shown by Nesbitt and Williams (1950), Bates (1955), Bates and Martin (1955), Kussmann and Wollenberger (1956), Schulze (1956), Andr/i (1956), Kronenberg and Tenzer (1958), Bates et al. (1962) and Iwama (1968). This apparently contradictory observation can be explained as follows. Consider the demagnetization process of an alnico magnet. As the magnetization of the particles is gradually reversed we should expect that as a result of the long-range interaction fields, particles in a particular region which have already reversed their magnetization will tend to assist the reversal of those in adjacent regions. Thus in the demagnetized state, when just half the total magnetization has been reversed, the magnet is effectively
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 171
Fig. 39. Magnetostatic interaction domains in alnico 5 (Bates et al. 1962). divided up into a domain structure as shown in fig. 39. At the boundaries between the various regions or interaction domains there are stray magnetic fields and gradients which attract the colloidal particles and so delineate the domain structure. These boundaries are of course quite different from the conventional Bloch-Lifshitz walls (Kittel 1949, Kittel and Galt 1956). Similar magnetostatic interaction domains have also been observed on elongated single domain magnets by Craik and Isaac (1960). For detailed discussions of magnetostatic interaction domains and the mechanism of their formation the reader is referred to the papers by Craik and Lane (1967, 1969). The effects of particle interactions have also been discussed by Wohlfarth (1955).
17. Comparison of the N6ei-Zijlstra and Cahn theories of magnetic annealing in alnico alloys The improvements in the magnetic properties of alnico alloys by heat treatment in a magnetic field were first observed in alnico 5 (see section 2) but the following discussion also includes the effects which are observed when alnicos 6, 8 and 9 are given an isothermal heat treatment in a magnetic field.
172
R.A. McCURRIE
17.1. Ndel-Zijlstra theory In the theory of magnetic annealing proposed by N6el (1947b) and later developed by Zijlstra (1960-1962) the spinodal decomposition at high temperatures results in the formation of very small spherical particles and is considered to be complete before the elongation of the particles begins. If the decomposition takes place in a magnetic field the spherical particles develop into ellipsoids with their axes of elongation parallel to the applied field thereby reducing their total magnetic free energy. During the thermomagnetic treatment the particles increase their size and elongation very rapidly because at high temperatures the rate of atomic diffusion is high. The applied field should of course be sufficient to saturate the Fe-Co rich particles in order to achieve the maximum possible alignment during the relatively short thermomagnetic heat treatment. The relevant counteracting energies are the interfacial energy F~ between the a~ and a2 phases and the difference in the magnetostatic energy Fm between the decomposition waves parallel and perpendicular to the applied field. During the elongation of the particles there is arl increase in the interfacial energy but this is accompanied by a larger reduction in the magnetic energy of the particles in the applied field. Thus the elongation is energetically favourable when the ratio Fm/Fs is large. In the N6el-Zijlstra theory F~ is defined as the product of the interface tension and the amount of interface per unit volume. Thus the ratio Fm/Fs will increase in a coarsening structure so that the interfacial free energy is of great importance in determining the efficacy of magnetic annealing. According to Zijlstra (1960-1962) the rates of elongation and coarsening of the particles are proportional to the square of the difference in the saturation magnetic polarizations of the OgI and a2 phases (AJs)2 and inversely proportional to the interfacial energy Y, i.e., the efficacy of the thermomagnetic treatment is proportional to (AJs)2/T. This theory explains why thermomagnetic treatment is most effective in alnico alloys with a high cobalt content (i.e. alnicos 5-9) which raises the Curie temperature and AJs and lowers the interfacial energy Y. From measurements on alnico 5 Zijlstra (1960) concluded that 3' ~0.1 Jm -2, a result which confirms an earlier suggestion by Kittel et al. (1950) who also suggested that since the interfacial energy is small the particles should develop a shape anisotropy in order to minimize their magnetic energy in the applied field. Thus according to the N6el-Zijlstra theory the axes of elongation of the particles should be parallel to the applied field irrespective of its orientation relative to particular crystallographic directions in the alloy. This conclusion suggests that the shape anisotropy for finite annealing time at a given temperature should give the same result for both polycrystalline and single crystal specimens. However, Zijlstra's (1960) experiments show that the anisotropy of the single crystal specimens is considerably larger than that for the polycrystalline specimens. Zijlstra (1960) suggested that this difference could be due to a contribution from magnetocrystalline anisotropy, but the magnitude of the difference makes this unlikely.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 173 17.2. C a h n ' s theory
The spinodal decomposition of the alnico alloys into two phases al and Ol2 occurs because it is accompanied by a reduction in the total free energy FT of the alloy. The effect of the magnetic field in producing elongated particles with their axes of elongation parallel to the field direction has been investigated theoretically by Cahn (1963). He suggested that the effect of the magnetic field is to suppress the spinodal decomposition waves along the magnetic field direction and that this is due to the difference in the magnetic energy Fm of the spinodal waves parallel and perpendicular to the field direction which favours the formation of long rods parallel to the field direction. In the absence of the magnetic field the spinodally decomposed system consists of three mutually perpendicular spinodal decomposition waves, i.e., a cubic array of isotropic particles. Cahn (1963) stated that the two main sources of anisotropy are the magnetic and elastic energies. The former favours compositional waves parallel to the internal field direction while the latter favours compositional waves parallel to particular crystallographic directions. Waves parallel to the (100) directions in the {100} planes in cubic crystals are favoured when 2C44- Cl1+
C12>0
,
where the Cii coefficients are elastic energy constants from the stress tensor. If the anisotropy in the magnetic energy is much larger than the anisotropy in the elastic energy then the geometry of the decomposition will be independent of the crystallographic orientation so that the axes of elongation of the particles will be parallel to the applied field direction. However, if the anisotropy in the elastic energy predominates then the axes of elongation of the particles will be parallel to the crystallographic direction which minimizes the elastic energy. When the elastic and magnetic anisotropy energies are of comparable magnitude the axes of elongation of the particles lie between the field direction and the nearest (100) direction. In particular if the applied field is parallel to a (100) direction then the axes of elongation of the particles are parallel to the chosen (100) direction. Cahn (1963) also suggested that for a solid solution with a composition fluctuation ( x - x 0 ) where x0 is the average composition, the anisotropy in the magnetic energy is proportional to (OJs/Ox) 2 where Js is the saturation magnetic polarization of the precipitated particles. The quantity (OJs/Ox) 2 is expected to vary rapidly with temperature and to be very large near the Curie temperature, To, so that thermomagnetic treatment will be most effective when the spinodal decomposition temperature T is at, or just below, the Curie temperature. If the alloy is cooled to lower temperatures the effectiveness of the field diminishes rapidly. The anisotropy in the elastic energy depends on two factors: (1) it is proportional to (d In a / d x ) 2 where 'a' is the stress-free lattice parameter, and (2) it is proportional to the variation in the elastic energy coefficient with crystallographic direction; the latter can be approximated by Ay = ]71100]- 71111][. Cahn
174
R.A. McCURRIE
(1963) estimated that the elastic energy is much greater than the magnetic energy except near the Curie temperature. Thus according to Cahn's (1963) theory a large ratio of Fm/F-r favours the elongation of the particles when they are heat treated in a magnetic field. The shape of the particles is established during the first stages of the decomposition and the magnetic shape anisotropy can be further increased only by a subsequent increase in their saturation magnetic polarization by diffusion of atoms between the two phases al and a2 without thereby changing their shape, though their wavelength is increased by this process.
17.3. Discussion of the Ndel-Zijlstra and Cahn theories Electron micrographs of alnico 8 (De Vos 1966, 1969) which had been given an isothermal heat treatment in a magnetic field show that even in the initial stages of the spinodal decomposition the three (100) decomposition waves are developed which have practically the same wavelength, a result which disagrees with Cahn (1963) who suggested that the (100) decomposition waves perpendicular to the magnetic field direction are suppressed from the beginning of the spinodal decomposition. De Vos's (1966, 1969) electron micrographs of alnico 8 also show that elongated Fe-Co rich particles with their axes of elongation parallel to the (100} directions develop even in the absence of an applied field; this result is also in disagreement with Cahn's (1963) theoretical predictions. According to the discussion in section 7.2 of the relationship between the field direction and the preferred direction of magnetization Heidenreich and Nesbitt (1952) and Nesbitt and Heidenreich (1952a, b) found that when the field direction was parallel to a principal crystallographic direction, i.e., [100], [110] or [111], the easy or preferred direction of magnetization is parallel to the field direction. However, Heidenreich and Nesbitt (1952), Nesbitt and Heidenreich (1952a, b), Hoselitz and McCaig (1951), McCaig (1953) and Yermolenko et al. (1964) showed that when the thermomagnetic field is applied at an angle to a (100) direction, the direction of easy magnetization lies between the field direction and the chosen (100) direction. The above authors also found that the magnetic anisotropy (at room temperature) has a maximum value when the field is parallel to a (100) direction. Thus from the results presented in section 7.2 and the short summary of these given above there is strong evidence that in addition to the magnetic and interracial energies the anisotropy of elastic energy has some effect in determining the orientation of the elongated Fe-Co rich particles during thermomagnetic treatment. This conclusion is also supported by the microstructural observations made by De Vos (1966, 1969). Although Cahn's (1963) suggestion that the anisotropy of the elastic energy is important in determining the nature of the spinodal decomposition waves does not agree with the electron microscopic observations of De Vos (1966, 1969) it is clear that the orientation of the particles is affected by the anisotropy of the elastic energy. The experiments performed by Zijlstra (1960-1962) and De Vos (1966, 1969) show that the Ndel-Zijlstra theory of thermomagnetic treatment or magnetic annealing is in better agreement with the experimental results than that
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
175
proposed by Cahn (1963). Strong support for this conclusion is provided by the following three experiments carried out by Zijlstra (1960-1962): (1) A specimen of alnico 5 (51% Fe, 24% Co, 14% Ni, 8% A1 and 3% Cu by weight) was heat treated in a magnetic field of 128 kAm -1 parallel to the [100] direction for 7 h at 748°C and subsequently a part of the same specimen was annealed for 24h at the same temperature with the field parallel to the [010] direction. A part of this specimen was then annealed for a further 24 h at 748°C. Electron micrographs of each of the three thermomagnetic treatments (actually thermal magnetic anneals) are shown in figs. 40(a), (b) and (c) from which it can be seen that when the alloy is annealed in a field perpendicular to the initial field direction, the particles become elongated in the new field direction thus reducing their magnetic free energy, in agreement with the N6el-Zijlstra theory. The electron micrographs shown in figs. 41(a) and (b) also confirm that in the initial stages of the phase separation the Fe-Co rich particles are spherical (fig. 41(a)) and that they are elongated by heat treatment in the magnetic field-the direction of elongation being parallel to the field direction as shown in fig. 41(b). (2) A polycrystalline specimen (disk) of alnico 5 with the same composition as that given above was heat treated in a non-inductively wound furnace for 7 h at
i~
a
b t
i~ i~
C ....!
Fig. 40. Microscopical demonstration of crossed-field annealing of a single crystal: (a) after heat treatment for 7 hours at 748°C with field along the [100] direction; (b) after subsequent heat treatment for 24 hours at 748°C with field along the [010] direction; (c) after final heat treatment for 24 hours at 748°C with field along the [010] direction. All three micrographs are made of the (001) plane (after Zijlstra 1960).
176
R.A. McCURRIE
a
I
b
2pm Fig. 41. (a) Electron micrograph of an alnico showing that in the initial stages of the phase separation the Fe-Co rich particles are spherical. (b) Electron micrograph after heat treatment in a magnetic field. The direction of elongation of the Fe-Co rich particles is parallel to the direction of the field (after Zijlstra 1962).
755°C in the absence of an applied field. After this treatment the specimen was shown to be isotropic but when it was subsequently heat treated in a magnetic field of 6 4 0 k A m -t at the same t e m p e r a t u r e it became anisotropic with an anisotropy energy approximately equal to that of a polycrystalline alnico 5 specimen which had been given a m o r e conventional thermomagnetic heat treatment, i.e., Ku ~ 8 x 104 Jm -3. (3) A specimen of polycrystalline Mishima alloy, Fe2NiA1, which is not usually considered to respond to thermomagnetic treatment was heat treated in a field of 640 k A m -1 for 2 weeks at 725°C after which it became magnetically anisotropic with an anisotropy energy K ~ 6 × 104 Jm73 which is comparable to that of alnico 5. After this treatment, however, the particles are too large to be single domains so that the coercivity is correspondingly low ~10 k A m -1 parallel to the preferred direction, i.e., the field direction. None of the above three results is to be expected according to the theory proposed by Cahn (1963). However, it should be emphasized that Zijlstra's (1960-1962) results were obtained by heat treatment times much longer than those used in commercial practice so that it seems likely for shorter thermomagnetic heat treatments (e.g. in cooling of alnico 5) that the orientation of the axes of
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS
177
elongation are partly determined by the anisotropy in the elastic energy but there now seems to be little doubt that the N6el-Zijlstra theory of the thermomagnetic treatment of the alnicos is in good general agreement with the experimental results.
18. Rotational hysteresis The rotational hysteresis energy W~(H) in a field is defined as the energy required to rotate the specimen through 360 °, i.e., Wr(H)
= f~'~ F(O) dO.
It can also be conveniently obtained by measuring the area enclosed by the 360 ° clockwise torque curve and the 360 ° anticlockwise torque curve (McCurrie and Jackson 1980); the rotational hysteresis energy W~(H) is equal to half this area, i.e.,
W~CH)= ½
Fc(O) dO +
/'Ac(O) dO , JO
where Fc(0) and FAt(0) are the torque curves in a given field for clockwise and anticlockwise rotation in the applied field. The clockwise and anticlockwise torque curves corresponding to the maximum value of Wr(H) for single crystal alnico 9 are shown in fig. 42. McCurrie and Jackson (1980) have measured the rotational hysteresis energies of alnico 9 and single crystal alnico 9 as a function of the applied field and their results are shown in fig. 43. Note the very rapid variation in W~(H) for applied fields close to the coercivity. From the value of the rotational hysteresis integrals, defined by
j~ where Wr(H) is the rotational hysteresis energy observed in a field H, R can therefore be obtained from the area under the Wr(H)/Js vs 1/H curve (Bean and Meiklejohn 1956, Jacobs and Luborsky 1957, Luborsky 1961, Luborsky and Morelock 1964). McCurrie and Jackson (1980) have concluded that magnetization reversal in alnico 9 and ticonal 900 occurs by curling. This conclusion is also supported by their measurements of the angular variation of the coercivity discussed in section 10. The rotational hysteresis energy of single crystal alnico 8 as a function of the applied field has also been measured by Livshitz et al. (1970c). They also observed a very sharp peak in the rotational hysteresis energy but in contrast to the results obtained by McCurrie and Jackson (1980) they observed a smaller peak in a higher applied f i e l d - about 2.5 times the field corresponding to the first sharp peak.
178
R.A. M c C U R R I E
1"00 I Ha= 188 kAm -1
0'751-
H c = 138 kAm -1
0"50 I
E 0.25
.-j
Acw w
0
90
270
12( Angle 0 °
0
~0.25
~0-50
Ticonal 9 0 0 (100) plane
- 0-75
-1.00 uFig. 42. Torque curves showing rotational hysteresis in a single crystal of alnico 9 (ticonal 900) in an applied field of 188 k A m -1 (McCurrie and Jackson 1980). T h e rotational hysteresis energy Wr(H)can be determined by halving the area enclosed between the two curves: C W - c l o c k w i s e rotation; A C W anticlockwise rotation.
2"0
E
1.5 • Ticonal 9 0 0
1.0
0-5
0 .P~ 0
2
I , ~--..-.-~ 4 6 8 H ~'105Am -1)
I 10
Fig. 43. Variation of rotational hysteresis energy of columnar alnico 9 and single crystal alnico 9 (ticonal 900) with applied field (McCurrie and Jackson 1980).
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 179
19. Anhysteretic magnetization The anhysteretic magnetization of a ferromagnetic material is the magnetization which results from the application of a static field H and a superimposed alternating field Ha > H which is gradually reduced to zero while the static field H is still on. The anhysteretic magnetization c u r v e - s o m e t i m e s referred to as the ideal magnetization c u r v e - r i s e s much more steeply than the conventional curve and if the specimen has a low or zero external demagnetization factor the initial slope of the anhysteretic magnetization curve is known as the anhysteretic susceptibility Ka. A simple general theory of anhysteretic magnetization curves has been presented by Ndel (1943) and N6el et al. (1943) but for a short review the reader is referred to Kneller (1969). The reciprocal K21 is known as the internal demagnetization factor. Dussler (1927) has shown that the geometrical demagnetization factor Dg of open magnetic circuits also depends on the structural details of the material. The demagnetizing field HD for a uniformly magnetized ellipsoid is given by HD = D g M ,
but for non-uniformly magnetized particles such as occur in the alnicos it has been found by experiment that Ka 1 = D,
where
D > Og.
The difference D i = AD = D - D g has been attributed to internal interaction effects arising from the structure of the materials. Unfortunately, Di is not a constant, characteristic of the material, but also depends on Dg as one would expect since the shape and structural effects are due fundamentally to magnetostatic interactions. Bulgakov (1950) found that for alnico 5 that the values of Di parallel and perpendicular to the preferred axis of magnetization were respectively 0.02 and 0.4. Similar measurements were also made by Gould and McCaig (1954) on alnico 5 who obtained values of 0.01 and 0.5 for D~. They suggested that the precipitated particles were oriented parallel to the thermomagnetic field and separated by a non-ferromagnetic matrix, but they stressed that their measurements of D~ did not enable them to make any really firm conclusions.
20. Magnetic viscosity In all the above discussions of coercivity theory it has been assumed that after saturation of a ferromagnetic material in the forward direction the demagnetization curve represents instantaneous and stable values of B or M as a function of the reverse applied field H. However, if a steady reverse field less than the coercivity is applied after
180
R.A. M c C U R R I E
saturation, the magnetization decreases with time t after the application of the field H. This time dependent change of the magnetization in an applied field is known as magnetic viscosity. The magnetic viscosity of cast alnico 2 (54% Fe, 18% Ni, 12% Co, 10% A1, 6% Cu) as measured by Street and Woolley (1949) is shown in fig. 44. Measurements on the same alloy which had been heat treated at 1250°C for 20 minutes and then allowed to cool at about 2°C per second gave similar results to the cast alloy. According to Street and Woolley (1949) the magnetic polarization at time t is given by the empirical relation
J=C-Slnt, where C is a constant and S is a parameter which depends on the temperature T and the applied field H. Since a similar effect also occurs when the applied field is positive, the phenomenon of magnetic viscosity is a general property of all ferromagnetic materials, though its presence is not always readily observable. The above equation suggests that the magnetization reversal by the field H involves the thermally activated surmounting of energy barriers in the material. For further details on the magnetic viscosity in the alnicos the reader is referred to the papers by Bulgakov and Kondorsky (1949), Street and Woolley (1949, 1950, 1956), Street et al. (1952a, b), Phillips et al. (1954) and Barbier (1954).
0"20 _
Alnico
2
~
523°K
0-15
-ff <~ 0.10
0"0,'
--
-I
30
~
86°K
60
120
300
Time
600
1200
I
t in s e c
Fig. 44. C h a n g e in net magnetic polarization as a function of time at various temperatures for alnico 2 (after Street and Woolley 1949) 54% Fe - 18% Ni - 12% C o - 10% Al - 6% Co. Cast alloy cooled from 1250°C held at this temperature for 20 rain and then cooled at 2°Cs -1, followed by 2 h at 600°C. Not in o p t i m u m p e r m a n e n t magnet state. However, the fully heat treated alloy gave similar magnetic viscosity results.
STRUCTURE AND PROPERTIES OF ALNICOPERMANENTMAGNETALLOYS 181
21. Temperature dependence of magnetic properties The effects of temperature on the magnetic properties of the alnicos are complicated and depend on the previous heat treatment of the alloys. Clegg and McCaig (1957) investigated the temperature dependence of the saturation magnetic polarization, the coercivity BHc and the remanence of alnico 5 after various heat treatments. The temperature dependence of the coercivity for various specimens is shown in fig. 9. Curves (c) and (g) represent specimens with optimum permanent magnet properties and may therefore be regarded as typical. The temperature dependence of the magnetic properties of alnicos has also been investigated by McCaig (1968), Dietrich (1966a, b, 1967), Clegg and McCaig (1958), Roberts (1958), Clegg (1955), Pawlek and Reichel (1955), Bulgakov (1949) and Jellinghaus (1943).The effects of low temperatures on alnico 5 and alnico 5-7 alloys have been studied by Clegg (1955). In a different type of investigation Bates and Simpson (1955) measured the heat changes which occur when the alnicos are cycled through a hysteresis loop. For general discussions of the temperature dependence and stability of the magnetic properties of permanent magnets the reader is referred to Gould (1958, 1962), Parker and Studders (1962), Schiller and Brinkmann (1970), Heck (1974), Joksch (1975) and McCaig (1977), Gould and McCaig (1954).
22. Dynamic excitation (AC magnetization) Very few studies have been made on the effects of applying alternating fields to alnico magnets. The response of the magnets is complex due to the effects of magnetic viscosity and eddy currents and therefore depends on the frequency and magnitude of the applied fields. Sabir and Shepherd (1974) have studied the behaviour of alnico 5 in sinusoidal fields in the frequency range 50-350 Hz. The energy loss per unit volume was obtained by measuring the areas under the dynamic B - H loops and agreed with direct wattmeter measurements and also with theoretical calculations. Eddy current losses were found to be negligible at 50 Hz and even at 350 Hz were only about 10% of the total loss. The total loss at a fixed field was found to be almost a linear function of the frequency. The dynamic excitation of alnico 5 has also been studied by Shepherd et al. (1974).
23. Prospects for improvement in the magnetic properties Since the observed coercivities are only ~0.3HA (the anisotropy field H A = (Dz- Dx)Ms) even in the most favourable cases there is certainly some room for improvement in He. This could be achieved by reducing the particle thickness to avoid curling and to make the particles more regular in shape to prevent parasitic nucleation of magnetization reversal. However, the attainment of these objectives is likely to present considerable metallurgical difficulties.
182
R.A. McCURRIE
Since the coercivity depends on the difference in the demagnetization factors Dz and Dx it can readily be appreciated from fig. 38 that when the length to diameter ratio (m) of the particles is greater than about 10, the coercivity is about 94% of the theoretical m a x i m u m for a given Ms and p so that there is little to be gained by any further increase in rn resulting from more elaborate thermomagnetic treatment. No way has yet been found to increase Ms of the Fe-Co-rich particles significantly so it appears that there is little prospect for any further i m p r o v e m e n t in the coercivities of the best alnicos, 8 and 9. The p e r m a n e n t magnet properties of single crystal alnico 8 and 9 are of course significantly better than those of the fully columnar alnico 9 owing to the higher degree of particle alignment but any prospective i m p r o v e m e n t in their properties is similarly limited by the factors already discussed. From table 3 it can be seen that in a highly oriented columnar magnet, remanences Jr ~ 1.43 T can be achieved so that the m a x i m u m possible energy product (BH)ma× is (BH)max = B~/4tXo = J~/41Xo = 400 kJm
3,
provided of course that the intrinsic coercivity Hc satisfies the condition: Hc > Jd2/z0, i.e., Hc > 570 k A m -~ . However, in view of the requirements mentioned above there seems to be little prospect of increasing the coercivity Hc much beyond about 180 k A m 1 without reducing the remanence. The best laboratory properties of alnico p e r m a n e n t magnets have been obtained by Naastepad (1966) for a single crystal of an alloy containing 35 wt % Fe, 34.8% Co, 14.9% Ni, 7.5% A1, 5.4% Ti and 2.4% Cu which had a coercivity of 122 k A m 1 and an energy product (BH)max of 107 kJm -3. Unfortunately these exceptionally high values of the m a x i m u m energy product cannot be obtained on a commercial scale, but it is possible to obtain a commercial alnico 9 with BHc = 120 k A m -1 and a (BH)max of 75 kJm -3. It appears that the alnicos, which have been available since 1931, have now reached the zenith of their development and there is little prospect that any further substantial i m p r o v e m e n t in their magnetic properties can be made.
24.
Summary
The relatively high coercivities of the alnicos are due to the shape anisotropy of Fe or F e - C o rich single domain particles which are precipitated in a weakly ferromagnetic or non-ferromagnetic N i - A I rich matrix. After cooling from about 1200°C at a controlled rate ~30°Cs -I the isotropic
S T R U C T U R E AND PROPERTIES OF ALNICO P E R M A N E N T M A G N E T ALLOYS
183
alnicos 1-4 are subsequently tempered for several hours at about 600-650°C. The anisotropic alnicos 5, 6, 7 and the grain oriented alnico 5DG are produced by controlled cooling from 1250°C in a saturating magnetic field ~200-300 kAm 1 and then tempered for several hours at about 600°C. The high coercivity alnicos 8 and 9 are also cooled from about 1250°C and then annealed isothermally in a saturating magnetic field ~200-300 kAm 1 for a few minutes at about 820°C after which they are given a two-stage tempering treatment usually for several hours at about 650°C and then at 550°C. The phase separation takes place by spinodal decomposition at 800-850°C as the alloys are cooled. The final shapes and sizes of the particles are determined in the very early stages of the spinodal decomposition and microstructural investigations have shown that the Fe or F e - C o rich particles are elongated parallel to the (100) directions in the matrix. In the isotropic Fe2NiA1 and Fe-Ni-Al-low cobalt containing alloys the particles often have mixed rod-like and plate-like shapes which form a complex three-dimensional interconnected structure in which preference for particle axis alignment with the (100) directions is not well defined. Microstructural studies of the anisotropic field treated alnicos 5-9 show that the precipitated F e - C o rich particles are rod-like, and preferentially aligned parallel to the field direction during thermomagnetic treatment. In these alloys the higher coercivities can be attributed to an increase in the shape anisotropy of the precipitated particles though there is evidence to show that the magnetization reversal occurs by the incoherent mechanism known as curling, rather than coherent rotation of the magnetization vector. In the crystal oriented alnicos 5-7 and 9, the direction of the applied field during the thermomagnetic treatment should be as close as possible to a particular (100) columnar axis in order to maximize the remanence, coercivity and energy product. In order for the thermomagnetic treatment to be effective the Curie temperature must be above the spinodal decomposition temperature. Furthermore the ratio of (2xJ)2/-/ (where AJ is the difference between the saturation magnetic polarizations of the cq and c~2 phases and 3' is the interracial energy) between the F e - C o rich particles and the matrix should be as high as possible so that the particles can be elongated (by minimization of their magnetic free energy) in the field direction. All of the above requirements can be satisfied if the cobalt content is in the range 24-42 wt %. This high cobalt content also has the beneficial effects of increasing the remanence and the coercivity (He ~ Js). The addition of Ti to alnicos 8 and 9 lowers the saturation magnetic polarization and Curie temperature of the matrix, but increases the perfection and elongation of the particles. Titanium also increases the time required for the thermomagnetic treatment to be effective and it is for this reason that alnicos 8 and 9 are given an isothermal heat treatment in a magnetic field at about 820°C for a few minutes. The principal effect of the tempering heat treatment is to increase the difference •J in the saturation magnetic polarization between the F e - C o rich particles and the Ni-A1 rich matrix. This increases the shape anisotropy field of the precipitated particles which is proportional to AJ and hence increases the coercivity. The shapes and the sizes of the particles do not change significantly during this heat treatment. The optimum volume fraction of the particles p ~ 0.6-0.7.
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References Aharoni, A., 1959, J. Appl. Phys. Suppl. 30, 70 S. Aharoni, A. and S. Shtrikman, 1958, Phys. Rev., 109, 1522. Albanese, G., G. Asti and R. Criscuoli, 1970, IEEE Trans. Magn., MAG-6, 161. Allec, G., 1971, Cobalt, No. 52, 156. Andrfi, W., 1956, Ann. Phys. (Leipzig) 19, 10. Arbuzov, M.P. and A.A. Pavlyukov, 1965, Fiz. Met. Metalloved. 20, No. 5, 724 (Engl. Transl., Phys. Met. Metallog. 20, No. 5, 83). Baran, W., 1959, Tech. Mitt. Krupp, 17, 150. Barbier, J.C., 1954, Ann. Phys. (Paris) 9, 84. Bate, G., 1961, J. Appl. Phys., Suppl. 32, 239 S. Bates, L.F., 1955, Research, 8, 462. Bates, L.F. and D.H. Martin, 1955, Proc. Phys. Soc. Lond. B68, 537. Bates, L.F. and A.W. Simpson, 1955, Proc. Phys. Soc. Lond. B68, 849. Bates, L.F., D.J. Craik and E.D. Isaac, 1962, Proc. Phys. Soc. Lond. 79, 970. Bean, C.P. and W.H. Meiklejohn, 1956, Bull. Amer. Phys. Soc., Set. II, 1, 148. Belova, V.M., V.I. Nikolaev, S.Yu. Stephanovich and S.S. Yakimov, 1969, Fiz. Tverd. Tela, 11, 3662. Belozersky, G.N., Yu.N. Grinblat and A.I. Shapiro, 1971, Fiz. Met. Metalloved. 32, No. 2, 301. (Engl. Transl., Phys. Met. MetaIlog. 32, No. 2, p. 75). Berkowitz, A.E., 1969, Constitution of Multiphase Alloys, ch. VII of 'Magnetism and Metallurgy', A.E. Berkowitz and E. Kneller, eds. (Academic Press, New York, London) Vol. 1, p. 331. Betteridge, W., 1938, J. Iron and Steel Inst. 139, 187. Bradley, A.J., 1949a, J. Iron and Steel Inst. 163, 19. Bradley, A.J., 1949b, Physica, 15, 175. Bradley, A.J., 1951, J. Iron and Steel Inst. 168, 233. Bradley, A.J., 1952, J. Iron and Steel Inst. 171, 41. Bradley, A.J. and A. Taylor, 1938a, Proc. Roy. Soc. Lond. A166, 353. Bradley, A.J. and A. Taylor, 1938b, Magnetism (Institute of Physics, London) 89. Bronner, C., 1970 IEEE, Trans. Magn. MAG-6, 301. Bronner, C., E. Planchard and J. Sauze, 1966a, Cobalt, No. 31, 63; 1966b, Cobalt, No. 32, 124.
Bronner, C., J. Sauze, E. Planchard, J.M. Drapier, D. Coutsouradis and L. Habraken, 1967, Cobalt, No. 36, 123. Bronner, C., J.-P. Haberer, E. Planchard, J. Sauze, J.M. Drapier, D. Coutsouradis and L. Habraken, 1968, Cobalt, No. 40, 131. Bronner, C., J.-P. Haberer, E. Planchard, J. Sauze, J.M. Drapier, D. Coutsouradis and L. Habraken, 1969, Cobalt, No. 42, 14. Bronner, C., J.-P. Haberer, E. Planchard, J. Sauze, J.M. Drapier, D. Coutsouradis and L. Habraken, 1970, Cobalt, No. 48, 111. Bronner, C., J.-P. Haberer, E. Planchard and J. Sauze, 1970a, Cobalt, No. 46, 15. Bronner, C., J.-P. Haberer, E. Planchard and J. Sauze, 1970b, Cobalt, No. 49, 187. Brown, Jr., W.F., 1957, Phys. Rev. 105, 1479. Brown, Jr., W.F. 1962, Magnetostatic Principles in Ferromagnetism (North-Holland, Amsterdam) p. 117. Brown, Jr., W.F., 1963, Micromagnetics (Interscience/Wiley, New York) p. 79. Brown, Jr., W.F., 1969, Ann. New York Acad. Sci. 147, 461. Bulgakov, N.V., 1949, Dokl. Akad. Nauk (SSSR) 69, 627. Bulgakov, N.V., 1950, Dokl. Akad. Nauk, (SSSR) 70, 205. Bulgakov, N.V. and E. Kondorsky, 1949, Dokl. Akad. Nauk. (SSSR) 69, 325. Bulygina, T.I. and V.V. Sergeyev, 1969, Fiz. Met. Metalloved. 27, No. 4, 703. (Engl. Transl., Phys. Met. Metallog. 27, No. 4, 132). Burgers, W.G. and J.L. Snoek, 1935, Physica, 2, 1064. Cahn, J.W., 1961, Acta Met. 9, 795. Cahn, J.W., 1962, Acta Met. 10, 179. Cahn, J.W., 1963, J. Appl. Phys. 34, 3581. Cahn, J.W., 1968, Trans. Met. Soc. AIME, 242, 166. Cahn, J.W. and J.E. Hilliard, 1958, J. Chem. Phys. 28, 258. Cahn, J.W. and J.E. Hilliard, 1959, J. Chem. Phys. 31,688. Clegg, A.G., 1955, Brit. J. Appl. Phys. 6, 120. Clegg, A.G., 1966, Z. Angew. Phys. 21, 77. Clegg, A.G., 1970, IEEE, Trans. Magn. MAG-6, 201. Ciegg, A.G. and M. McCaig, 1957, Proc. Phys. Soc. Lond. B70, 817. Clegg, A.G. and M. McCaig, 1958, Brit. J. Appl. Phys. 9, 194. Compaan, K. and H. Zijlstra, 1962, Phys. Rev. 126, 1722.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS Craik, D.J. and E.D. Isaac, 1960, Proc. Phys. Soc. 76, 160. Craik, D.J. and R. Lane, 1967, Brit. J. Appl. Phys. 18, 1269. Craik, D.J. and R. Lane, 1969, Brit. J. Appl. Phys. (J. Phys. D. Appl. Phys.) Ser. 2, Vol. 2, 33. Cronk, E.R., 1966, J. Appl. Phys. 37, 1097. Dean, A.V. and J.J. Mason, 1969, Cobalt, No. 43, p. 73. Dehler, H., 1942, Stahl u Eisen, 47, 983. De Jong, J.J., J.M.G. Smeets and H.B. Haanstra, 1958, J. Appl. Phys. 29, 297. De Vos, K.J., 1966, Doctoral Thesis, Technical High School (Eindhoven, The Netherlands). De Vos, K.J., 1969, 'Alnico Permanent Magnet Alloys', ch. 9 in: Magnetism and Metallurgy, A.E. Berkowitz and E. Kneller, eds. (Academic Press, New York, London) p. 473. Dietrich, H., 1966a, Cobalt, No. 30, 3. Dietrich, H., 1966b, A. Angew. Phys. 21, 125. Dietrich, H., 1967, Cobalt, No. 35, 78. Durand-Charre, M., C. Bronner and J.-P. Lagarde, 1978, IEEE: Trans. Magn. MAG-14, 797. Dussler, E., 1927, Z. Phys. 44, 286. Ebeling, D.G. and A.A. Burr, 1953, J. Metals, 5, 537. Edwards, A., 1957, Elect. Energy, 1, 146, 178. Edwards, A., 1962, Magnet Design and Selection of Material, ch. 6 of Permanent Magnets and Magnetism, D. Hadfield, ed. (Iliffe Books Ltd., London; Wiley, New York) p. 191. Fahlenbrach, H., 1954, Tech. Mitt. Krupp, 12, 177. Fahlenbrach, H., 1955, Naturwissenschaften, 42, 64. Fahlenbrach, H., 1956, Tech. Mitt. Krupp, 14, 2. Fahlenbrach, H. and H. Stfiblein, 1964, Proc. Intern. Conf. Magnetism (Inst. Phys., Nottingham, UK) p. 767. Frei, E.H., S. Shtrikman and D. Treves, 1957, Phys. Rev. 106, 445. Fujiwara, T. and T. Kato, 1960, J. Japan. Inst. Metals, 24, 526. Gould, J.E., 1958, Instrum. Practice, 12, 1083. Gould, J.E., 1962, Magnetic Stability, ch. 10 of Permanent Magnets and Magnetism, D. Hadfield, ed. (Iliffe Books Ltd, London; Wiley, New York). p. 443. Gould, J.E., 1964, Cobalt, No. 23, 82.
185
Gould, J.E., 1971, Cobalt Alloy Permanent Magnets (Centre d'Information du Cobalt, Brussels). Gould, J.E. and M. McCaig, 1954, Proc. Phys. Soc. Lond. B67, 584. Granovsky, B., P.P. Pashkov, V.V. Sergeyev and A.A. Fridman, 1967, Fiz. Met. Metalloved. 23, No. 3, 444 (Engl. Transl., Phys. Met. Metallog. 23, No. 3, 55). Guillaud, C., 1953, Rev. Mod. Phys. 25, 64. Haanstra, H.B., J.J. de Jong and J.M.G. Smeets, 1957, Philips Tech. Rev. 19, 11. Hansen, J.R., 1955, Proc. Conf. Magnetism and Magnetic Materials (Pittsburgh, Pa, USA) p. 198. Harrison, J., 1966, Z. Angew. Phys. 21, 101. Harrison, J. and W. Wright, 1967, Cobalt, No. 35, 63. Heck, C., 1974, Magnetic Materials and their Applications (Butterworths, London). Heidenreich, R.D. and E.A. Nesbitt, 1952, J. Appl. Phys. 23, 352. Heimke, G. and R. Kohlhaas, 1966, Z. Angew. Phys. 21, 73. Heimke, G., H. van Kempen and R. Kohlhaas, 1966, IEEE, Trans. Magn. MAG-2, 411. Higuchi, A., 1966, Z. Angew. Phys. 21, 80. Higuchi, A. and T. Miyamoto, 1970, IEEE, Trans. Magn. MAG-6, 218. Hillert, M., 1961, Acta Met. 9, 525. Hilliard, J.E., 1962, Trans. AIME, 224, 1201. Hilliard, J.E., 1967, Determination of Structural Anisotropy, Proc. 2nd Intern. Congress for Stereology, H. Elias, ed. (Springer, New York) p. 219. Hilliard, J.E., 1968, Measurement of Volume in Volume, ch. 3 of Quantitative Microscopy, R.T. DeHoff and F.N. Rhines, eds. (McGraw-Hill, New York, St. Louis, San Francisco, Toronto, London, Sydney) pp. 4576. Hilliard, J.E. and J.W. Cahn, 1961, Trans. Amer. Inst. Min. Engrs. 221, 344. Hoffmann, A. and H. St~blein, 1966, Tech. Mitt. Krupp, Forsch. Ber. 24, 113. Hoffmann, A. and H. St~iblein, 1967, Z. Angew. Phys. 23, 182. Hoffmann, A. and H. Stiiblein, 1970, IEEE, Trans. Magn. MAG-.6, 225. Hoffmann, A. and P. Pant, 1970, Tech. Mitt. Krupp, Forsch. Ber. 28, 117. Honda, K., 1934, Metallwirtschaft, 13, pp. 425427.
186
R.A. McCURRIE
Hoselitz, K. and M. McCaig, 1949a, Proc. Phys. Soc.. Lond. B62, 163. Hoselitz, K. and M. McCaig, 1949b, Nature (Lond.) 164, 581. Hoselitz, K. and M. McCaig, 1951, Proc. Phys. Soc. Lond. B64, 549. Hoselitz, K. and M. McCaig, 1952, Proc. Phys. Soc. Lond. B65, 229. Iwama, Y., 1968, Trans. Jap. Inst. Metals, 9, 273. Iwama, Y., M. Inagaki and T. Miyamoto, 1970, Trans. Jap. Inst. Metals, 11,268. Iwama, Y., M. Takeuchi and M. Iwata, 1976, Trans. Jap. Inst. Metals, 17, 481. Jacobs, I.S. and F.E. Luborsky, 1957, J. Appl. Phys. 28, 467. Jellinghaus, W., 1943, Arch. Eisenhfittenw. 16, 247. Joksch, C., 1975, Physica, 80B, 199. Jonas, B. and H.J. Meerkamp van Embden, 1941, Philips Tech. Rev. 6, 8. Julien, C.A. and E G . Jones, 1965a, J. Appl. Phys. Suppl. 36, 1173. Julien, C.A. and F.G. Jones, 1965b, Cobalt, No. 27, 73. Kittel, C., 1949, Rev. Mod. Phys. 21, 541. Kittel, C. and J.K. Galt, 1956, Solid State Physics, vol. 3, F. Seitz and D. Turnbull, eds. (Academic Press, New York, London) pp. 437-564. Kittel, C., E.A. Nesbitt and W. Shockley, 1950, Phys. Rev. 77, 839. Kneller, E., 1966, Handbueh der Physik, S. Fl/igge, ed., Ferromagnetism, vol. XVIII pt. 2, H.P.J. Wijn, ed. (Springer, Berlin, Heidelberg, New York) p. 512. Kneller, E., 1969, Fine Particle Theory, ch. VIII of Magnetism and Metallurgy, A.E. Berkowitz and E. Kneller, eds. (Academic Press, New York, London) vol. 1, p. 365. Koch, A.J.J., M.G. van der Steeg and K.J. de Vos, 1957, Proc. Conf. Magnetism and Magnetic Materials (Amer. I.E.E., Boston, Mass., USA) p. 173. Koch, A.J.J., M.G. van der Steeg and K.J. de Vos, 1959, Berichte der Arbeitsgemeinschaft Ferromagnetismus (Riederer, Stuttgart) p. 130. Kolbe, C.L. and D.L. Martin, 1960, J. Appl. Phys., Suppl. 31, 84 S. Kondorsky, E., 1952a, Izvest. Akad. Nauk SSSR, 16, 398. Kondorsky, E., 1952b, Dokl. Akad. Nauk SSSR, 82, 365.
Koshiba, S. and T. Nishinuma, 1957, J. Jap. Inst. Metals, 21, 166. Koshiba, S. and T. Nishinuma, 1960, J. Jap. Inst. Metals, 24, 433. Kronenberg, K.J., 1954, Z. Metallk. 45, 440. Kronenberg, K.J., 1960, J. Appl. Phys. 31, 80 S. Kronenberg, K.J., 1961, J. Appl. Phys. 32, 196 S. Kronenberg, K.J, and R.K. Tenzer, 1958, J. Appl. Phys. 29, 299. Kussmann, A. and J.H. WoIlenberger, 1956, Z. Angew. Phys. 8, 213. Kussman, A. and O. Yamada, 1956, Arch. Elektrotech. 42, 237. Lange, G., 1968, Deutsche Edelstahlwerke, Tech. Ber. 8, 209. Lindner, E., R. Wittig and K. Prissier, 1963, Neue Hfitte, 8, 557. Livshitz, B.G., B.A. Samarin and V.S. Shubakov, 1970a, IEEE, Trans. Magn., MAG-6, 242. Livshitz, B.G., E.G. Knizhnik, G.S. Kraposhin and Y.S. Linetsky, 1970b, IEEE, Trans. Magn., MAG-6, 237. Livshitz, B.G., V.I. Sumin and A.S. Lileev, 1970c, IEEE, Trans. Magn., MAG-6, 169. Luborsky, F.E., 1961, J. Appl. Phys. Suppl. 32, 171 S. Luborsky, F.E. and C.R. Morelock, 1964, J. Appl. Phys. 35, 2055. Luteijn, A.J. and K.J. de Vos, 1956, Philips Res. Repts. 11, 489. Makarov, E.F., V.A. Povitsky, E.B. Granovsky and A.A. Fridman, 1967, Phys. Status Solidi, 24, 45. Makarov, V.A., E.B. Granovsky, E.F. Makarov and V.A. Povitsky, 1972, Phys. Status Solidi, 14, (A) 331. Makino, N., 1962, Cobalt, No. 17, 3. Makino, N. and Y. Kimura, 1965, J. Appl. Phys. 36, 1185. Makino, N., Y. Kimura and I. Yamaki, 1963, J. Jap. Inst. Metals 27, 582. Marcon, G., C. Bronner and R. Peffen, 1971; Cobalt, No. 51, 99. Marcon, G., R. Peffen and H. Lemaire, 1978a, IEEE, Trans. Magn., MAG-14, 685. Marcon, G., R. Peffen and H. Lemaire, 1978b, IEEE, Trans. Magn., MAG-14, 688. Mason, J.J., D.W. Ashall and A.V. Dean, 1970, IEEE, Trans. Magn., MAG-6, 19l. McCaig, M., 1949, Proc. Phys. Soc. Lond. B62, 652. McCaig, M., 1953, J. Appl. Phys. 24, 366.
STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS McCaig, M., 1966, Z. Angew. Phys. 21, 66. McCaig, M., 1968, Cobalt, No. 41, 196. McCaig, M., 1977, Stability of Permanent Magnets, ch. 5 of Permanent Magnets in Theory and Practice (Pentech Press, London, Plymouth) p. 155. McCaig, M. and W. Wright, 1960, Brit. J. Appl. Phys. 11, 279. McCurrie, R.A., 1981, J. Appl. Phys. 52, 7344. McCurrie, R.A. and S. Jackson, 1980, IEEE Trans. Magn. MAG-16, 1310. Mishima, T., 1932, Ohm, 19, 353. Moon, J.R., 1974, J. Phys. D: Appl, Phys. 7, 1233. Naastepad, P.A., 1966, Z. Angew. Phys. 21, 104. N6el, L., 1943, Cahiers Phys. 17, 47. N6el, L., 1947a, Comptes Rendus Acad. Sci. (Paris) 224, 1550. N6el, L., 1947b, Comptes Rendus Acad. Sci. (Paris) 225, 109. N6el, L., R. Forrer, N. Janet and R. Battle, 1943, Cahiers Phys. 17, 51. Nesbitt, E.A., 1950, J. Appl. Phys. 21, 879. Nesbitt, E.A. and H.J. Williams, 1950, Phys. Rev. 80, 112. Nesbitt, E.A. and R.D. Heidenreich, 1952, J. Appl. Phys. 23, 366. Nesbitt, E.A. and H.J. Williams, 1955, J. Appl. Phys. 26, 1217. Nesbitt, E.A. and H.J. Williams, 1957, Proc. Conf. Magn. and Magn. Materials (Amer. I.E.E., Boston, Mass., USA) p. 184. Nesbitt, E.A., H.J. Williams and R.M. Bozorth, 1954, J. Appl. Phys. 25, 1014. Nicholson, R.B. and P.J. Tufton, 1966, Z. Angew. Phys. 21, 59. Oliver, D.A. and J.W. Shedden, 1938, Nature (Lond.) 142, 209. Paine, T.O. and F.E. Luborsky, 1960, J. Appl. Phys. Suppl. 31, 78 S. Palmer, D.J. and S.W.K. Shaw, 1969, Cobalt, No. 43, 63. Pant, P., 1974, Proc. 3rd Europ. Conf. on Hard Magnetic Materials (Amsterdam, 17-19 September, 1974) H. Zijlstra, ed. (Bond voor Material en Kennis, P.O. Box 9321, Den Haag, The Netherlands) p. 186. Parker, R.J. and R.J. Studders, 1962, Permanent Magnets and their Applications (Wiley, New York, London). Pashkov, P.P., A.A. Fridman, Ye.B. Granovsky, V.V. Sergeyev and R.Ya. Larichkina,
187
1969, J. Appl., Phys. Suppl. 40, 1308. Pashkov, P.P., A. Fridman and E. Granovsky, 1970, IEEE, Trans. Magn., MAG-6, 211. Pater, M., R. Bloch and E. Krainer, 1963, Z. Angew. Phys. 15, 261. Pawlek, F. and K. Reichel, 1955, Z. Metallk. 46, 308. Pfeiffer, I., 1969, Cobalt, No. 44, 115. Phillips, J.H., R. Street and J.C. Woolley, 1954, Phil. Mag. 45, 505. Planchard, E., R. Meyer and C. Bronner, 1964a, Z. Angew. Phys. 17, 174. Planchard, E., C. Bronner and J. Sauze, 1964b, Proceedings of the Journ6es Internationales des Applications du Cobalt (Brussels, 9-11th June, 1964)pp. 134-511. Planchard, E., C. Bronner and J. Sauze, 1965, Cobalt, No. 28, 132. Planchard, E., C. Bronner and J. Sauze, 1966a, Z. Angew. Phys. 21, 63. Planchard, E., C. Bronner and J. Sauze, 1966b, Z. Angew. Phys. 21, 95. Povitsky, V.A., E.B. Granovsky, A.A. Fridman, E.F. Makarov and P.P. Pashkov, 1970, IEEE, Trans. Magn., MAG-6, 215. Povolotskii, E.G., Ya.M. Dovgalevskii and V.K. Baitina, 1963, Metal Science and Heat Treatment, 11, 631. Ritzow, G., 1963, Neue Hiitte, 8, 282. Ritzow, G. and W. Ebert, 1957, Deutsche Elektrotechnik, 11, 527. Roberts, W.H., 1958, J. Appl. Phys. 29, 405. Sabir, S.A.Y. and W. Shepherd, 1974, Proc. IEE, 121, No. 8, 907. Saltykov, S.A., 1970, Stereometric Metallography (Metallurgizdat, Moscow) 3rd ed. Shepherd, W., H. Gaskell and P. Rashid, 1974, IEEE, Trans, Magn., MAG-10, 50. Schiller, K., 1968, Deutsche Edelstahlwerke, Tech. Ber. 8, 147. Schiller, K. and K. Brinkmann, 1970, Dauermagnete, Werkstoffe und Anwendungen (Springer, Berlin, Heidelberg, New York). Schulz, L.G., 1949, J. Appl. Phys. 20, 1030. Schulze, D., 1956, Exptl. Tech. Phys. 4, 193. Schwartz, L.H., 1976, Ferrous Alloy Phase Transformations, ch. 2 in: Applications of M6ssbauer Spectroscopy, R. Cohen, ed. (Academic Press, New York, San Francisco, London) vol. 1, pp. 58-61. Sergeyev, V. and T.Y. Bulygina, 1970, IEEE, Trans. Magn., MAG-6, 194. Shtrikman, S. and D. Treves, 1959, J. Phys., Radium, 20, 286.
188
R.A. McCURRIE
Shtrikman, S. and D. Treves, 1966, J. Appl. Phys. 37, 1103. Sixtus, K.J., Kronenberg, K.J. and R.K. Tenzer, 1956, J. Appl. Phys. 27, 1051. Snoek, J.L., 1938, Probleme der Technischen Magnetisierungskurve (Springer, Berlin) p. 73. Snoek, J.L., 1939, Physica, 6, 321. Stfiblein, H., 1963, Tech. Mitt. Krupp, Forsch. Ber. 21, 171. Stfiblein, H., 1968, Tech. Mitt. Krupp, Forsch. Ber. 26, 1. Steinort, E., E.R. Cronk, S.J. Garvin and H. Tiderman, 1962, J. Appl. Phys. Suppl. 33, 1310. Stoner, E.C. and E.P. Wohlfarth, 1947, Nature (Lond.) 160, 650. Stoner, E.C. and E.P. Wohlfarth, 1948, Phil. Trans. Roy. Soc. (Lond.) A240, 599. Street, R. and J.C. Woolley, 1949, Proc. Phys. Soc. Lond. A62, 562. Street, R. and J.C. Woolley, 1950, Proc. Phys. Soc. Lond. B63, 509. Street, R. and J.C. Woolley, 1956, Proc. Phys. Soc. Lond. B69, 1189. Street, R., J.C. Woolley and P.B. Smith, 1952a, Proc. Phys. Soc. Lond. B65, 461. Street, R., J.C. Woolley and P.B. Smith, 1952b, Proc. Phys. Soc. Lond. B65, 679. Sucksmith, W., 1939, Proc. Roy. Soc. Lond. A171, 525. Takeuchi, M. and Y. Iwama, 1976, Trans. Jap. Inst. Metals, 17, 489. Tenzer, R.K. and K.J. Kronenberg, 1958, J. Appl. Phys. 29, 302. Underwood, E.E., 1 9 7 0 , Quantitative Stereology (Addison-Wesley; Reading, Massachusetts, Menlo Park, California, London. Don Mills, Ontario). Underwood, E.E., 1973, Applications of Quantitative Metallography, in: Metals Handbook
(Amer. Soc. Metals, Metals Park, Ohio, USA, 1973) 8th ed., vol. 8, pp. 37-47. Vallier, G., C. Bronner and R. Peffen, 1967, Cobalt, No. 34, 10. Van der Steeg, M.G. and K.J. de Vos, 1964, Z. Angew. Phys. 17, 98. Van Wieringen, J.S. and J.G. Rensen, 1966, Z. Angew. Phys. 21, 69. Wittig, R., 1962, Z. Angew. Phys. 14, 248. Wittig, R., 1966, Z. Angew. Phys. 21, 98. Wohlfarth, E.P., 1955, Proc. Roy. Soc. Lond. A232, 208. Wright, W., 1970, Cobalt, No. 48, 115. Wright, W. and R. Ogden, 1964, Cobalt, No. 24, 140. Wyrwich, W., 1963, Z. Angew. Phys. 15, 263. Yamada, O., 1955, Z. Phys. 142, 225. Yermolenko, A.S. and Ya.S. Shur, 1964, Fiz. Met. Metalloved. 17, No. l, 31 (Engl. Transl., Phys. Met. Metallog. 17, No. 1, 31). Yermolenko, A.S., E.N. Melkisheva and Ya.S. Shur, 1964, Fiz. Met. Metalloved. 18, No. 4, 540 (Engl. Transl., Phys. Met. Metallog. 18, No. 4, 63). Yermolenko, A.S. and A.V. Korolyov, 1970, IEEE, Trans. Magn., MAG-6, 252. Zijlstra, H., 1956, J. Appl. Phys. 27, 1249. Zijlstra, H., 1960, Doctoral Thesis, University of Amsterdam, The Netherlands. Zijlstra, H., 1961, J. Appl. Phys. Suppl. 32, 194 S, Zijlstra, H., 1962, Z. Angew. Phys. 14, 251. Zijlstra, H., 1966, Z. Angew. Phys. 21, 6. Zingery, W.L., W.B. Whalley, E.B. Romberg and F.W. Wheeler, 1966, J. Appl. Phys. 37, 1101. Zumbusch, W., 1942a, Arch. Eisenhfittenw. 16, 101. Zumbusch, W., 1942b, Electrotechnik-Maschinenbau, 60, 522.
chapter 4 OXIDE SPINELS*
S. KRUPI(~KA AND P. NOVAK Institute of Physics Czechoslovak Academy of Sciences Prague Czechoslovakia
* For accounts of specifically non-microwave and microwave ferrites see chs. 3 and 4, Vol. 2, by P.I. Slick and J. Nicolas. For an account of garnets, see ch. 1 Vol. 2, by M.A. Gilleo.
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 189
CONTENTS 1. C r y s t a l s t r u c t u r e a n d c h e m i s t r y . . . . . . . . . . . . . . . . . . . 1.l. D e s c r i p t i o n of t h e c r y s t a l s t r u c t u r e . . . . . . . . . . . . . . . . 1.2. C a t i o n s e n t e r i n g t h e o x i d e spinels . . . . . . . . . . . . . . . . 1.3. T h e r m o d y n a m i c s t a b i l i t y . . . . . . . . . . . . . . . . . . . 1A. C r y s t a l field a n d c o v a l e n c y . . . . . . . . . . . . . . . . . . . 1.5. C r y s t a l e n e r g y , c a t i o n d i s t r i b u t i o n a n d site p r e f e r e n c e s . . . . . . . . . 1.6. O r d e r i n g a n d d i s t o r t i o n s . . . . . . . . . . . . . . . . . . . 2. M a g n e t i c o r d e r i n g . . . . . . . . . . . . . . . . . . . . . . . 2.1. E x c h a n g e i n t e r a c t i o n s in spinels . . . . . . . . . . . . . . . . . 2.2. M a g n e t i c o r d e r i n g : t h e o r y . . . . . . . . . . . . . . . . . . . 2.3. M a g n e t i c o r d e r i n g : e x p e r i m e n t . . . . . . . . . . . . . . . . . 2.3.1. Spinels w i t h o n e m a g n e t i c s u b l a t t i c e o n l y . . . . . . . . . . . 2.3.2. Spinels w i t h m a g n e t i c i o n s in b o t h s u b l a t t i c e s . . . . . . . . . . 2.3.3. T h e effect o f d i a m a g n e t i c s u b s t i t u t i o n s . . . . . . . . . . . . 2.3.4. T e m p e r a t u r e a n d field d e p e n d e n c e s . . . . . . . . . . . . . 2.4. S p i n w a v e s . . . . . . . . . . . . . . . . . . . . . . . . 3. M a g n e t i c p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . . . 3.1. A n i s o t r o p y a n d m a g n e t o s t r i c t i o n . . . . . . . . . . . . . . . . . 3.1.1. I n t r o d u c t o r y r e m a r k s . . . . . . . . . . . . . . . . . . 3.1.2. M i c r o s c o p i c origin: a n i s o t r o p y . . . . . . . . . . . . . . . 3.1.3. M i c r o s c o p i c origin: m a g n e t o s t r i c t i o n . . . . . . . . . . . . . 3.2. M a g n e t i c a n n e a l a n d r e l a t e d p h e n o m e n a . . . . . . . . . . . . . . 3.2.1. O r i g i n . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. E x a m p l e s o f local a n i s o t r o p i c c o n f i g u r a t i o n s . . . . . . . . . . 3.2.3. K i n e t i c s , m a g n e t i c a f t e r - e f f e c t s . . . . . . . . . . . . . . . 3.2.4. S u r v e y of e x p e r i m e n t a l r e s u l t s . . . . . . . . . . . . . . . 3.3. D y n a m i c s of m a g n e t i z a t i o n . . . . . . . . . . . . . . . . . . 4. O t h e r p h y s i c a l p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . 4.1. E l e c t r i c a l p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . 4.1.1. D C e l e c t r i c a l c o n d u c t i v i t y a n d S e e b e c k effect . . . . . . . . . . 4.1.2. D i e l e c t r i c c o n s t a n t . . . . . . . . . . . . . . . . . . . 4.1.3. O p t i c a l a n d m a g n e t o o p t i c a l s p e c t r a . . . . . . . . . . . . . 4.2. M e c h a n i c a l a n d t h e r m a l p r o p e r t i e s . . . . . . . . . . . . . . . . 4.2.1. I n f r a r e d s p e c t r a . . . . . . . . . . . . . . . . . . . . 4.2.2. E l a s t i c c o n s t a n t s . . . . . . . . . . . . . . . . . . . . 4.2.3. H e a t c a p a c i t y . . . . . . . . . . . . . . . . . . . . . 4.2.4. T h e r m a l c o n d u c t i v i t y . . . . . . . . . . . . . . . . . . 4.2.5. T h e r m a l e x p a n s i o n . . . . . . . . . . . . . . . . . . . Appendix: Intrinsic magnetic properties . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
190
191 191 194 196 202 206 211 216 217 221 224 224 226 227 229 231 233 233 233 235 238 245 245 247 249 251 256 260 26O 261 275 276 284 284 285 287 288 289 291 298
1. Crystal structure and chemistry The spinel structure is one of the most frequently encountered with the MM~X4 compounds. X represents oxygen or some Chalcogenic bivalent anion (S2-, Se 2 , Te ~ ) which may be partly substituted by proper monovalent anions (F , I-, Br-); M, M' are metallic ions (or a combination of them) whose valencies have to fulfil the electroneutrality requirements. Due to the large electronegativity of oxygen the ionic type of bonds prevails in almost all oxide spinels. As a consequence, the electrical resistivity is usually high and we are allowed to classify these compounds as insulators even though sometimes the term low-mobility semiconductors would apply. This is not the case with the other bivalent anions (S, Se, Te) possessing considerable lower electronegativities. They behave more like semiconductors or even metals and, therefore, they are treated separately (see Van Stapele, ch. 8).
1.1. Description of the crystal structure The spinel structure is called after the mineral spinel MgAI204. It is formed by a nearly close-packed fcc array of anions with holes partly filled by the cations. There are two kinds of holes differing in coordination: tetrahedral (or A) and octahedral (or B). From all these sites available in the elementary cube containing 32 anions, only 8 of the A-type and 16 of the B-type are occupied by cations. The geometry of the occupied interstices may be seen from fig. 1, where the primitive cell containing 2 formula units MM~X4 is shown. The symmetry is cubic and corresponds to the space group O7(Fd3m). A small displacement, defined by a single parameter u, of the anions from their ideal position is allowed along the corresponding body diagonal (fig. 2) which enables a better matching of the anion positions to the relative radii of A and B cations. The coordinates of ions in spinel are summarized in table 1. For the ideal close-packed anion lattice u equals 2. In real oxide spinels usually u ¢ ~ and in the model of hard spheres it should increase linearly with (rA-- rB)/a (fig. 3). The local symmetry of the cation sites is cubic in the A positions and trigonal in B, the trigonal axis being one of the body diagonals (fig. 1); note that the trigonal symmetry is due to both the configuration of neighbouring cations and the distortion of the anion octahedron if u ¢ ~. Each of the four body diagonals 191
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TABLE 1 Coordinates of ions in the elementary cell of spinel structure (in fractions of the lattice parameter ). i
8 ions in A-sites 16 i o n s in B - s i t e s
1
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O X I D E SPINELS
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belongs to just one of the B cations in the primitive cell in fig. 1. Hence, these cations are non-equivalent differing in their local symmetry axis and each of them may be taken as representing one fcc sublattice with the lattice constant a. On the other hand, the local symmetry of the A positions remains cubic even if u # 3, so that both sublattices represented by A sites in the primitive cell are mutually equivalent. When considering some aspects for which the local symmetry is irrelevant, all the B positions may be treated as belonging to only one sublattice (octahedral or B) in the same way as the A positions may be unified to form one tetrahedral sublattice (A). Both translational and local symmetries corresponding to the O 7 space group strictly apply only if each sublattice contains only one kind of cations, i.e., if all M ions in MM~X4 are in tetrahedral and all M' in octahedral positions. The spinel is then called normal. It was early established by X-ray diffraction (Barth and Posnjak 1932), and later by neutron diffraction (Hastings and Corliss 1953) as well, that besides this, another cation distribution exists in many spinels called inverse: here, one half of the cations M' are in A positions and the rest, together with the M ions are randomly distributed among the B positions. There are also many examples of intermediate cases between a normal and an inverse spinel (mixed spinels). Therefore, in order to characterize fully the spinel structure, a further parameter is needed describing the degree of inversion. The chemical
S. KRUPICKA AND P. NOVAK
194
formula may then be explicitly written as
(1)
MaM~-~[MI-~M~+a]X4,
where the cations on B sites are in brackets. Note that 6 = 1 means a normal spinel, 6 = 0 an inverse one. If there are different cations coexisting in equivalent interstices (partial or full inversion, solid solutions) the symmetry is perturbe~d. Nevertheless, new symmetry relations may appear when the different cations order regularly (section 1.6). The symmetry of the spinel structure may also be changed by a spontaneous distortion due to the cooperative Jahn-Teller effect (section 1.6). It has been pointed out on the basis of far infrared spectra and calorimetric measurements (Grimes 1972, 1974, Grimes et al. 1978) that in some spinels the octahedrally coordinated cations might be shifted a little out of their central positions ("off centre ions") which would also change the space group. The attempts to prove this conclusion by a direct diffraction study have given controversial results until now (Rouse et al. 1976, Hwang et al. 1973, Thompson and Grimes 1977). 1.2. Cations entering the oxide spinels
The,electroneutrality considerations lead to 3 basic spinel types, according to the cation valency combinations in MM~O4:M2+M~3+O4 2- (2-3 spinels), M4+M~2+O2(4-2 spinels) and M6+M~+O 2- (6-1 spinels). Other possible types may be deduced from these by formal substitutions (e.g. Nf+~½(M"> + M '3+ giving ~,,l+~,3+c~2Iv-to.5 -tvx2.5 '~.J4 , 3+ M2+~[]~/3 .± . .~.4 12/3 leading to so-called y - M ~ O 3 defect sesquioxide phase, etc.). The basic binary spinel types are listed in table 2a together with relevant cations and their ionic radii. Additional spinel types derived by substitutions of the basic ones are listed in table 2b. It is seen from tables 2a and 2b that practically any cation with radius within the limits 0.4 to = 1 ~ may be incorporated into the spinel structure and most of them can occur in both octahedral and tetrahedral positions. The smallest cations with valency />4, however, are found in the tetrahedral coordination only, while the large monovalent cations occurring mainly in 6-1 spinels are confined to the octahedral sites. Besides the geometrical factors, the distribution of cations among A and B positions is influenced by many others, as briefly discussed in section 1.5. The interstices available for cations in the spinel structure have radii RA = (u - ~)aX/5- r(O>);
R , = (~- u ) a - r(O2-).
(2)
In table 3, these are compared with corresponding ionic radii as listed in table 2, using the experimental values for a and u. The agreement is satisfactory though a small but rather systematic contraction of the ionic radii, up to a few percent, is observed. On the other hand, a comparison of experimental a and u values with the calculated ones based on the eq. (1) (table 4), where the ionic radii from table 2 are inserted for RA, RB, shows that this contraction concerns the lattice
195
O X I D E SP1NELS
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S. KRUPICKA AND P. NOV.~A~
196
TABLE 3 Radii of A and B interstices, R, and corresponding ionic radii RM (all in A). A Spinel ZnFezO4 NiFe204 MnFe204 Fe304 MnCrzO4 FeV204 CoFe204 Mg2TiO4 Na2WO4
B
R
RM
R
Rra
0.715 0.632 0.722 0.616 0.77 0.731 0.653 0.75 0.62
0.74 0.63 0.766 0.63 0.80 0.77 0.64 0.71 0.56
0.762 0.775 0.783 0.801 0.732 0.76 0.778 0.745 1.08
0.785 0.808 0.785 0.853 0.755 0.78 0.787 0.773 1.16
TABLE 4 Comparison of experimental values of a and u with those calculated using eqs. (2) and table 2. Lattice o parameter (A) Spinel ZnFe204 MnFe204 CoFe204 NiFe204 ZnCr204 MnCr204 Fe304 Co2GeO4 Mg2TiO4 Na2WO4
Distribution of ions ZnZ+[Fe3+] Mn2+ Fe3+ rMn3+ 1 0.82 oast 0.18Fe2+ 0.18Fe3+ a.641 3+ 2+ 2+ 3+ Fe0.ssCo0.12[Co0.88Fea.12] Fe3+[Ni2+Fe3+] Zn2+[Cr~+] Mn2+[Cr~+] Fe3+[Fe2+Fe3+] Ge4+[Co~+] Mg2+[Mg2+Ti4+] W6+[Na~]
u
exp.
calc.
exp.
calc.
8.433 8.50 8.38 8.33 8.321 8.437 8.394 8.3175 8.441 9.1297
8.533 8.611 8.384 8.423 8.453 8.545 8.543 8.223 8.453 9.255
0.3852 0.3848 0.3818 0.3822 0.3863 0.3889 0.379 0.375 0.3875 0.369
0.3853 0.3861 0.3808 0.380 0.3866 0.3892 0.3777 0.3757 0.3846 0.3635
p a r a m e t e r a a n d h e n c e the whole structure, leaving u u n c h a n g e d . A n overall view of the g e o m e t r i c a l relations in various types of spinels m a y be acquired from fig. 3; the e x p e r i m e n t a l u values follow quite well the linear d e p e n d e n c e on the r e d u c e d difference of ionic radii ( r ( B ) - r(A))/a.
1.3. Thermodynamic stability T h e oxide spinels m a y usually be p r e p a r e d at e l e v a t e d t e m p e r a t u r e s by a direct solid state r e a c t i o n b e t w e e n the simple oxides. T h e r e l e v a n t t e m p e r a t u r e r a n g e is a b o u t 800 to 1500°C, d e p e n d i n g o n the type of cations. T h e t h e r m o d y n a m i c stability of spinels c o m p a r e d to the simple oxides is given by the G i b b s free
OXIDE SPINELS
197
e n e r g y of f o r m a t i o n A G c o n n e c t e d with t h e r e a c t i o n M O + M~O3 ---)MM~O4.
(3)
B y c o m b i n i n g A G with t h e e n t h a l p y of f o r m a t i o n AH, t h e e n t r o p y c h a n g e A S c o r r e s p o n d i n g to r e a c t i o n (3) m a y b e e s t i m a t e d . I n s t e a d of A G , A H d a t a a r e s o m e t i m e s u s e d w h e n c o m p a r i n g t h e r m o d y n a m i c stability for v a r i o u s spinels. T h e values of A G , A H a n d A S for s o m e s e l e c t e d spinels a r e given in t a b l e 5 a n d t h e A H ' s for 2 - 3 spinels a r e d i s p l a y e d in fig. 4 as d e p e n d i n g on t h e t y p e of d i v a l e n t cation. T h e r e l a t i v e l y g r e a t stability of o x i d e spinels is c o n n e c t e d with t h e s t r o n g l y ionic c h a r a c t e r of t h e b o n d . T h e spinels with a n i o n s possessing s m a l l e r e l e c t r o n e g a t i v i t i e s t h a n o x y g e n (S, Se, T e ) a r e m o r e c o v a l e n t a n d b e c o m e also less stable. This m a n i f e s t s itself in a d e c r e a s e d n u m b e r of such spinels, t h e i r s m a l l e r m u t u a l solubility a n d m o r e r e s t r i c t e d n u m b e r of c a t i o n s e n t e r i n g t h e s t r u c t u r e . T h e r e is s t r o n g c o m p e t i t i o n b e t w e e n spinel and, e.g., n i c k e l a r s e n i d e s t r u c t u r e , a n d s o m e s u l p h o s p i n e l s can b e t r a n s f o r m e d i n t o t h e l a t t e r u n d e r high p r e s s u r e ( B o u c h a r d 1967). T h e o x i d e spinels, on t h e o t h e r h a n d , f o r m solid s o l u t i o n s a l m o s t w i t h o u t
TABLE 5 AG, AH and AS values for selected spinels; after Navrotsky and Kleppa (1968). Spinel
AG*
AH(970 K)t
AS:~
MgAI204
1273 K: -8.4 1673 K: -8.4
-8.72 ± 0.29
0
MgFe204
1273 K: -5.3
-4.93 - 0.24
+0.3
Fe304
1000 K: -7.5
1000 K: -5.1
+2.2
CoFe204
1273 K: -9.4 1473 K: -8.2
-5.89 + 0.21
+2.7
NiFe204
1273 K: -6.0
- 1.22 ± 0.22
+3.8
ZnFe204
1400 K: -6.5
-2.67 ± 0.23
+2.7
FezTiO4
1073 K: -7.2
Co2TiO4
1073 K: -6.7
-6.04 ± 0.19
+0.7
Co2GeO4
- 14.1 ± 0.4
* Equilibrium measurements. t Calorimetric measurements. :~High temperature values calculated at the temperature for which AG is taken.
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,
I ii I If
",t\1,~ ',,t I !,i'~ I,"",. I "\ ~,, , ~, , ,, \.
2
t I1
MAt20`
", ".~' ,'
+ MFe204
~ f'~t,
•
4
,/I
'l ~
A Mg 2+
MMn204 Mn 2+ Fe 2.
/
I \
~ Co 2+ Ni 2`
Cu 2+ ZD 2+
C 2+
Fig. 4. Enthalpy of formation AH for 2-3 spinels (Navrotsky and Kleppa 1968, Jacob and Walderraman 1977). restriction and the competing structures are of other t y p e s - i n the first place olivine and phenacite structures. They usually appear if one of the cations is very small (Si4+, Ge4+). The situation may be elucidated on the basis of the hypothetical phase diagram in fig. 5. We may infer from it that under normal conditions all germanates are spinels except Zn2GeO4 having the phenacite structure, while the silicates are olivines. Most of the latter ones can be transformed into spinels under high pressure and/or elevated temperatures. Both olivine and phenacite structures are less densely packed compared with spinels, the typical volume change being - 8 % and +19% for the olivine--> spinel and olivine-->phenacite transformation, respectively. The thermodynamic relations among olivine, spinel and phenacite structures in silicates and germanates are discussed by Navrotsky (1973a, b, 1974, 1975), Navrotsky and Hughes (1976) and Reinen (1968). The AG values for both groups of oxides are shown in fig. 6. With large cations, e.g., large divalent cations (Ca 2*, Ba 2+, etc.) in M2+M~>O4, the spinel structure becomes also unstable and other structures (hexagonal) appear. The mutual relations to spinel have not yet been established. Hitherto no attention was paid to the chemical stability of the oxide spinels against the oxidizing or reducing influence of the atmosphere. This may be justified if the incorporated cations have fixed valencies that cannot be changed
OXIDE SPINELS
F .
.
.
.
.
199
.
i~Geq [co~Geq jn2Geq I L
. . . . .
,Fe~SJO~ iI A+~'
•
'
. . . . . 1 ' N~S~Oj ' Z ISjO ; , , ylic%j ', ,In92vq ', l'J I'---~---~' ' , f ~ ~ ',n~2sJq', . . . . .
J
L
. . . . .
3
I
L. . . . F . . . . .
"
31
I
z~Geq! L . . . . .
A
Temperature Fig. 5. Phase relations between spinel, olivine and phenacite; after Navrotsky (1973). i
i
i
i
,
,
Hg 16
14
~9
~8
I
-I0
I
-8
-6
I
-4
I
I
-2
0
Germanates a G ~kcaL/moLJ Fig. 6. Gibbs free energy of transformation olivine-spinel in germanates and silicates; after Navrotsky and Hughes (1976).
200
S. KRUPICKA AND P. NOV/~d~ TABLE 6 Valencies and ground states of 3d" ions. Number of 3d electrons
Valency
0
1+ 2+ 3+ 4+ 5+ Ground term
1
2
3
4
5
6
7
8
9
10
Cr Mn Fe
Mn Fe Co
Fe Co
Co Ni
Cu
Cu Zn
Ti V
V Cr Mn
Ni
Sc Ti V
Ti V Cr
1S
2D
3F
4F
69
58
5D
4F
3F
2D
IS
within wide limits of the oxygen pressure. In the case of transition metal ions, however, this certainly is not a plausible approach, because these ions usually exist in several valency states (see tables 2a and 6). As a consequence the thermodynamic stability has then to be considered for both the crystal and gaseous phases in mutual contact. This leads to definite deviations from chemical stoichiometry of the ideal spinel depending on both the temperature T and the partial oxygen pressure Poz. If this deviation exceeds some critical value (depending on T and po~) the spinel structure may become unstable. The situation is illustrated in figs. 7 and 8. Note that in air the transition metal oxides with spinel structure melt often incongruently, which makes it difficult to prepare single crystals of an arbitrary composition from their own melt. Also the fact that at a given temperature the spinel of a definite composition is in thermodynamical
i
~~'~4~
600
hematite[I o.o 5 3
1400
1200
,pc]
1000
Fig. 7. Phase diagram for system Fe-O (Tretyakov 1967); projection into temperatureiequilibrium pressure of oxygen plane is shown. The heavy lines define the borders of the stability regions of the respective phases. The thin lines are the lines of constant 3' in the formula Fe304+~.
OXIDE
201
SP1NELS
•~
.~<~
'~
e-
•.
/,
i
~
'~t'-I
~
~ ~
/
<~ s
/ \
•~
÷
{~. ~
~
~
\
"~
~0~
~ - ~ .~
Z-
~,<~
,~ ~. ~
~'~o~ 0
0
<:)
~'~
i
(=3 (:~
o i::::)
(:b e~l
~ e',,l 0",1
i:::) ~ ¢',1
C) ~ .
.
(::) co
.
.
~ N'-
~ ¢M
.
.~ ~ ~ ' ~
<:) <::)
l::i
~
~
~
~
i,-i
<~L~ !
~
~
~ -
-
7
I
'" ~
/
i
/
" i " ~ --~ , --"P-~
,
/111
!
'
~-+---~<..'~.,~.,.--C7~o~ '< ~, ,
o~ o~
o°O~
\ i ~ .#. ,' " , ~
.__
21)
:A<<~-~"~, . , , "
i.~
-
~
"~.
'~
'
#
~L_L_
~1
"Ill
o:~:'~"~ - i ' o ' i
"-/o~ , ~." *\ , ; ~*
' ~ ,
•
~
~
I
i
i ~ LiP ' ~.~b.¢',/9
~
I
11# ''~ , '
l i V ~,:'~.~,"r.
' ,', ,' ,' ~
A.
~1o,...>
">~z / o~ " * _
°O~
•
"~
"
?
~
';
i
\: I
, ,.x , ~ ! ~ Z : / ' 7 '%
--
~--o
~
: - ~
,.s~ll
i
,\
,
ii
.
[
,
~\,
,\, ..+ "v-Gb% I - , . ; ; \ " "; PA' <::> ~ ' - < \ " " i . ~ ,\ ,~ c< ..,. "..~.~<..\, " < \ ~r,~ -<
~
ix.
~
,\,
,
~x
\ ~
0
%
%
©
0
~,\:\I\ "-l~'i
9--' 0 .-~
l.i..
il
Q:: ~..
J
[
• ~
£ o
~J_
ba
.
S. KRUPICKA AND P. NOV~d,~
202
equilibrium only if the partial oxygen pressure has a definite value, is very important for the production of these materials. On the other hand, when cooling the material rapidly or under equilibrium conditions in a controlled atmosphere to room temperature (or more precisely to temperatures at which the ionic diffusion is ineffective) we can preserve the original spinel structure even at this temperature under non-equilibrium condition, e.g. in air.
1.4. Crystal field and covalency With respect to the magnetic properties the interest is primarily in transition metal ions, particularly those of 3d" group (table 6). The outer d-electrons of these ions may be regarded as practically localized in almost all oxide spinels so that the crystal (or better ligand) field theory applies. From the energy spectra determined by this theory the low lying levels are decisive for the magnetic behaviour. Note that the origin of the ligand field splitting of levels is to be seen in both the electrostatic crystal field and the covalency between the cation and the surrounding anions (ligands). Both these effects also contribute to the stabilization of cations in the given surrounding (crystal or ligand field stabilization energy = lowering of the ground level with respect to the ground level of the free ion). Although the local symmetry is trigonal in octahedral sites (point group D3d) and cubic in tetrahedral ones (point group Td), the prevailing part of the ligand field in both cases is cubic (point group Oh and Td, respectively). As a rule, the cubic ligand field strength, which is characterized by the cubic field splitting parameter A = 10Dq, corresponds to the so-called intermediate ligand field: it is weaker than the correlation between equivalent d-electrons but definitely stronger than the spin orbit coupling, i.e., /~correl > A >
AL_ S .
The only exceptions exhibiting characteristics of the "strong" crystal field (low spin state) are Co 3+, possibly Ni 3+ and the ions from the 4d n group. The splittings of the ground state terms of ions d" in the intermediate octahedral cubic fields are shown in fig. 9; in the tetrahedral case the sequence of levels is reversed which corresponds to A < 0. In table 7 the experimental data on the splitting parameter A in both B and A positions for various ions and spinels are summarized; for comparison and/or completion the data of some other oxides are included. The trigonal field in the octahedral positions leaves the orbital doublet in fig. 9 unsplit while the triplets T are split into a doublet and singlet. It depends on the type of ion and possibly, on other circumstances which of them is lower. The singlet is usually lower for Fe 2+ and the doublet for Co 2+. Note that this does not automatically apply to other structures, e.g. garnets. The splitting by the trigonal component of the ligand field in spinels is about one order of magnitude smaller than that in cubic field. Unfortunately, there are only few experimental data available; the examples are given in table 8. Sometimes they have been estimated
OXIDE SPINELS
203
i 6Dq
' 4Dq 7"29(3) I
-4Dq k i d ~and d~
T2y(3)
-6Dq
*I
E9(2) d~and d 9
A~9(1)
/
12Oq ~ 2Dq 729(3) Ii -6Dq
*
d2and d 7
t-I
i 5Dq
t -I
I
T~9(3)
~9(3)
i - 12Dq v
~g(3) A2g(O
d 3 and d 8
Fig. 9. Splitting of the ground multiplets of 3d" ions in octahedral field. The orbital degeneracy is given in parenthesis.
in a more or less indirect way, e.g., using the temperature dependence of the nuclear quadrupole splitting which, for ions with L > 0 , reflects the spatial distribution of the electronic cloud (EibschLitz et al. 1966). In the presence of the Jahn-Teller ions (see section 1.6) the local symmetry may be tetragonal in both types of sites. This symmetry splits both the E doublets and T triplets. The latter is split similarly as in a trigonal field, i.e., into a doublet and a singlet. If the symmetry is orthorhombic, the T level is additionally split so that only singlets appear. Note that due to partial disorder (inverse spinels, solid solutions) the local fields often possess fluctuating components with lower symmetries. In early work on d-level splitting in insulators only the effect of electrostatic crystal field was considered. This leads among others to the conservation of the centre of gravity of the split d-levels which makes it easy to determine the crystal field stabilization in terms of 10 Dq (Dunitz and Orgel 1957, McClure 1957). This was frequently used in evaluating the relative preferences of cations for A and B positions in spinels (section 1.5). It appeared, however, that this simple picture is inadequate because it entirely neglects the covalency whose effect has been shown to be of comparable magnitude. Due to covalent mixing of states the centre of gravity of 3d levels is generally shifted upwards, while the energy of the (p, s) valency band is lowered (fig. 10). As a consequence, a contribution to the stabilization energy appears which is difficult to estimate (Goodenough 1963, Blasse 1964).
204
S. KRUPICKA A N D P. NOV/kK
e-,
..,.d ©
~
cq
t.-,
.t::l
II
II
~D
° ° ~', t"q ¢q
¢q
I
I
[
II
II
,...,
t'q
-'T I
E
I
I
I
I
I
I
©
v~
.% +
©.--,
+
+
+
O
~D
% re)
o
I
0"5
~
+
OXIDE SPINELS
205
[~ ~
~.~
t"q
r.i
dd
Z ~5 ~
t"¢3
r¢3
.~
,~
~5
206
S. KRUPICKA AND P. NOV~J( TABLE 8 Trigonal field splitting of energy levels of Cr 3+ and Fe 2+ ions. Parameters v, v' are defined in the usual way: v = (t2gA] Vtrigltzga) - (t2gE[Vtriglt2gE); I)' = (t2gE] VtriglegE). The splitting of the ground state triplet T2g of Fe 2+ is ~v, while for Cr3+ the splitting of 4T 1 is ~'~'I/9+ /)t and that of 47"2is -~v/2 (excited states). Ion Cr3+ Cr 3+ Cr3+ Fe z+
Spinel MgA1204 ZnGa204 Li0.sGazsO4 GeFezO4
o (cm-1)
v' (crn 1)
Ref.
- 200 -650 -400 - 1145
- 1700 -1100 2400
1 2 3 4
1. Wood, D.L. et al., 1968, J. Chem. Phys. 48, 5255. 2. Kahan, M.H. and R.M. Macfarlane, 1971, J. Chem. Phys. 54, 5197. 3. Szymczak, H. et al., 1975, J. Phys. C8, 3937. 4. Eibsch/itz, H. et al., 1966, Phys. Rev. 151, 245.
2p 2s
without covaLency
~¢ith covatenoy
Fig. 10. Effect of the covalency on the energy levels of transition metal oxide (schematically). A p r o m i s i n g d i r e c t m e t h o d f o r d e t e r m i n i n g t h e r e l a t i v e p o s i t i o n s of t h e d l e v e l s in A a n d B sites of f e r r i m a g n e t i c spinels s e e m s to b e t h e p h o t o e m i s s i o n m e t h o d c o m b i n e d w i t h t h e m e a s u r e m e n t of e l e c t r o n spin p o l a r i z a t i o n ( A l v a r a d o et al. 1975, 1977).
1.5. C r y s t a l energy, c a t i o n distribution a n d site p r e f e r e n c e s T h e far l a r g e s t c o n t r i b u t i o n to t h e crystal e n e r g y in o x i d e spinels is t h e C o u l o m b e n e r g y of t h e c h a r g e d i o n s ( M a d e l u n g e n e r g y ) :
OXIDE SP1NELS
207 (4)
Ec = -(e2/a)AM,
where e is the charge of electron, a the lattice p a r a m e t e r and AM the Madelung constant. AM m a y be expressed as a function of the mean electric charge qA of the cations in A positions and of the oxygen p a r a m e t e r u. It was calculated by several authors (De Boer et al. 1950, Gorter 1954, D e l o r m e 1958, T h o m p s o n and Grimes 1977b) with slightly differing results. H e r e we give the formula based on the generalized Ewald method used by T h o m p s o n and Grimes (1977b): AM = AM(qA, U) = 139.8 + 1186A, -- 648332, --(10.82 + 412.2A, - 1903A ])qA + 2.609q~,
(5)
where au = u - 0 . 3 7 5 . The dependence of AM on qA for different values of the oxygen p a r a m e t e r u is given in fig. 11. With increasing AM the stability of the spinel increases. Therefore, owing to its dependence on qA, the Coulomb energy will generally play an important role in the equilibrium distribution of cations among A and B positions, even though in some cases other energy contributions may become important. The Born repulsion energy is difficult to estimate in a direct way and it is usually deduced from the simple oxide data (Miller 1959). The polarization energy appears as a consequence of the deformation of the spherical electron cloud of ions in the local electric field in the crystal. A t t e m p t s to calculate it in the classical way lead apparently to an overestimation (Smit et al. 1962, Smit 1968), so that only qualitative conclusions are usually used (Goodenough 1963). In the quantum mechanical picture it is difficult to distinguish this effect f r o m
o~
138LL
o
\pS \
i
0.3F5 0.3F8 0.381
134
- "
0,384 0.38F 0,390
130 -
2 % Fig. 11. Dependence of Madelung constant on the average ionic charge qA of A-site ions for several values of the parameter u.
208
S. KRUPICKA AND P. NOV.Ad(
covalency. The last relevant contribution is the ligand field energy treated in the preceding paragraph. As already mentioned in section 1.2, the spinels may have various degrees of inversion, according to the formula MaM~-a [M>aM~+a]04. If the energy difference for two limiting cases 6 = 0, 8 = 1 is not very large, we expect the distribution of cations to be random at high temperatures (i.e. 6 = ½) due to the prevailing influence of the entropy term - T S in the free energy. When the temperature is lowered, the spinel tends to be more or less normal or inverse depending on the sign and amount of energy connected with the interchange of cations M, M' in different sublattices. The equilibrium distribution is determined by the minimum of the Gibbs free energy, i.e., dG dH d6 - d ~
dS T~=0.
(6)
If we restrict ourselves to the configurational entropy of cations and supposing total randomization in both sublattices, S may be approximated by S = Nk[-8
In 8 + 2 ( 6 - 1) l n ( 1 - 8 ) - (8 + 1) 1n(6 + 1)].
(7)
Defining further AP = d H / d 6 we find
8(1 +
6) _ exp(-AP/RT)
(l - 8) 2
(8)
which determines the equilibrium value 6 at the temperature T. Generally, Ap depends on 8 and frequently a linear expression A p = 14o + 1-116
(9)
is being used to describe the experimental results (fig. 12). Here, H0 and H0 +/-/1 may be interpreted as energies connected with the interchange of ions M, M' from different sublattices in the case of completely inverse and normal distribution, respectively. It may be shown that the linear dependence (9) is obtained when the short-range interactions between pairs of ions are considered (Driesens 1968). Sometimes, an entropy term - T S o is added to the exponent in eq. (8) (Driesens 1968, Reznickiy 1977). The representative values of /-/0, H1 are given in table 9. When Ap ~< 5 kcal/mol, a mixed type spinel is usually observed; otherwise the energy difference between normal and inverse structure is sufficient to attain the one o r the other in practically pure form. The achievement of the equilibrium depends on the rate of cation migration. As this is a thermally activated process, the time constant changes exponentially with temperature and if T ~< 500 K, the
OXIDE SPINEI~
209
o.J +8
o
Ng Fe20~
o
0
0.2
I
FO0
J
f
~
I
900
~
o
1100
13~00 r ~
Fig. 12. Dependence of the degree of inversion 6 on temperature. Data for MgFeaO4 are taken from Pauthenet and Bochirol (1951) (A), Kriessman and Harrison (1956) (rT), Mozzi and Paladino (1963) (©) and Faller and Birchenall (1970) (+), those for MnFe204 are from Jirfik and Vratislav (1974). The full lines correspond to formulae (8) and (9) with Ho, H1 given in table 9. For MnFe204 also the time t, necessary for establishing the equilibrium distribution of ions at given temperature, is shown.
•m i g r a t i o n b e c o m e s t o o slow to allow any o b s e r v a b l e c h a n g e in cation d i s t r i b u t i o n . S o m e t i m e s , t h e t e m p e r a t u r e d e p e n d e n c e of t h e m i g r a t i o n r a t e is so s t e e p that, d u e to t e c h n i c a l r e a s o n s , t h e 6 v a l u e s can b e v a r i e d o n l y in n a r r o w limits. This is t h e case, e.g., of t h e M n - F e spinels (Simgovfi a n d Simga 1974). T h e ~ v a l u e s a r e usually d e t e r m i n e d by diffraction m e t h o d s ( B e r t a u t 1951, Jirfik a n d V r a t i s l a v 1974), m e a s u r e m e n t s of t h e s p o n t a n e o u s m a g n e t i z a t i o n ( P a u t h e n e t a n d B o c h i r o l 1951), o r by M 6 s s b a u e r effect ( S a w a t z k i et al. 1969). It is i m p o r t a n t to r e a l i z e t h a t t h e e n e r g y A P c o n c e r n s t h e crystal as a whole. T h e m a i n c o n t r i b u t i o n s to A P c o m e f r o m t h e M a d e l u n g e n e r g y (4), B o r n r e p u l s i o n e n e r g y ,
S. KRUPICKA AND P. NOV~K
210
TABLE 9 Values of H0 and H1 for some spinels. Spinel MgFe204 MnFe204 MgMn204 NiMn204
T (K) 573-1473 603-1443 T < 1050 298-1213
g 0.1 < 0.763< 0.78 < 0.74 <
6 < 0.28 6 < 0.94 6 < 0.99 6 < 0.93
/40 (kcal/mol)
/-/1 (kcal/mol)
3.83 0.4 10.3 3.64
-8.63 -8.1 - 18.4 -9.6
Ref. 1 2 3 4
1. Average value of /40, //1 taken from Pauthenet and Bochirol (1951), Kriessman and Harrison (1956), Mozzi and Palladino (1963). 2. Jirfik, Z. and S. Vratislav, 1974, Czech. J. Phys. B24, 642. 3. Manaila, R. and P. Pausescu, 1965, Phys. Status Solidi 9, 385. 4. Boucher, B., R. Buhl and M. Perrin, 1969, Acta Crystallogr., B25, 2326. and further, from polarization and ligand field effects. T h e attempts to explain the observed degree of inversion on the basis of only the M a d e l u n g energy have not been successful. T h e only conclusion we m a y draw on the basis of fig. 11 is a prediction that the stability of the normal structure increases with increasing u for 2-3 spinels and vice versa for 4 - 2 spinels. This m e a n s that the 2-3 spinels with largest bivalent cations (Mn 2+, Cd2+), as well as 4 - 2 spinels with smallest tetravalent cations (Si 4+, G e 4+) are expected to be normal in a g r e e m e n t with what has been f o u n d experimentally. In other (intermediate) cases such reasoning does not lead to satisfactory results which shows that other energy contributions b e c o m e important in controlling the equilibrium distribution of cations. T h e problem with all energies included is too involved to be solved without serious simplifications. O n the basis of systematic studies of cation distributions in various spinels it has been recognized early, however, that some regularities exist in them pointing to the possibility to connect the distribution to individual site preferences of cations. In such a case, the energy 2xP in eq. (8) could be expressed as a difference AP = P(M)- P(M')
(10)
of individual preference energies P of cations M and M'. O n c e P ( M ) was k n o w n for all relevant cations, the distribution of ions in arbitrary spinel could be predicted. T h e attempts were m a d e to determine P ( M ) s f r o m the ligand field stabilization (with or without covalency effects) (Dunitz and Orgel 1957, M c C l u r e 1957, Blasse 1964) and taking also M a d e l u n g and Born repulsive energies into account (Miller 1959, G o o d e n o u g h 1963). T h o u g h the latter p r o c e d u r e suffers from approximations that do not fully c o r r e s p o n d to the real situation, the results agree at least qualitatively with the experimental data. A n alternative a p p r o a c h was chosen by N a v r o t s k y and Kleppa (1967) based on empirical distribution data and t h e r m o d y n a m i c relations. T h e results of both procedures are c o m p a r e d in fig. 13. N o t e that the reliability of these data is better if they are applied to a definite class of spinels, e.g., the 2-3 type. T h e approximative character of the concept of
OXIDE SPINELS
211
/
3O P(H)
[k~at/~ot]
Phen0 mendo gioaL ~heory [26,21]/• /
•
+ Determined from / thermodynamic data [39] /
20
/
•
,
+
/
÷?~+~+--+ -10
/
/ \/\./jz
10
0
+ /
/
/
/
i
I
[
'
I
I
I :
I
Lri4t
E
:
',
,
:'Mn, 4 '
• GO 4* r--.~ 2, i
Fig. 13. Preference energies P. The cations are arranged according to increasing empirical octahedral site preferences (+). The approximate positions of several other ions within this sequence are indicated, as judged from the experimental distribution data.
individual preference energies may be seen among others from the fact that it requires /-/1 = 0 in eq. (9) in contradiction with experiment (table 9). Additional difficulties arise if the cations do not possess a fixed valency and/or in the presence of some short-range or long-range order. 1.6. O r d e r i n g a n d d i s t o r t i o n s
It follows from the preceding discussion that the spinels are often found with other than normal distribution of cations. When more than one kind of cations is present on an equivalent sublattice, a tendency generally exists to decrease the internal energy by ordering the cations. In most cases such ordering would be only short range, if any, but when the ratio between the numbers of different cations is suitable and if the corresponding energy gain is sufficiently large, a long-range order may develop. As a rule, some symmetry elements are lost and in most (but not all) cases the appearance of the superstructure destroys the overall cubic symmetry. The basic types of such ordering in spinels together with some of their characteristics are summarized in table 10. In all cases the main contribution to
212
S. KRUPI(~KA AND P. NOV~G( TABLE 10 Types of ordering in spinels.
Type
Sublattice
Characteristics
Symmetry* of ordered phase
1:1
A
Every ion M surrounded by four ions i~ and vice versa
F743m
Li0.sFe0.5[Cr2]O4
1: 1 a
B
P41 32
Zn[LiNb]O4
1: 1 fl
B
Immb
Zn[LiSb]O4
i :3
B
The rows of B-ions in [i10] and [110] have succession -M'-/('I'-M'- while those in [101] etc.-M'-M'-M'-M'Succession of (001) planes of B sublattice occupied alternatively by M' and l~I' ions In the [110] and [110] rows of B sites each fourth ion lVI', others M'
Example
(Fe304)
P43212
Fe[Li0.sFeLs]O4
* Symmetry of the ordered phase is taken from C. Haas, 1965, J. Phys. Chem. Solids 26, 1225.
t h e d r i v i n g f o r c e is b e l i e v e d to h a v e a M a d e l u n g c h a r a c t e r a n d t h e s t a b i l i z a t i o n of t h e s u p e r s t r u c t u r e s h o u l d t h u s i n c r e a s e with i n c r e a s i n g d i f f e r e n c e b e t w e e n t h e c h a r g e s of t h e i n e q u i v a l e n t c a t i o n s ( t a b l e 11). A n analysis, w h i c h is s i m i l a r to t h e o n e of e q u i l i b r i u m d i s t r i b u t i o n of c a t i o n s (section 1.5) c a n b e m a d e c o n c e r n i n g t h e t e m p e r a t u r e d e p e n d e n c e of o r d e r i n g . A t sufficiently high t e m p e r a t u r e s t h e e n t r o p y t e r m stabilizes t h e d i s o r d e r e d state. W h e n t h e s a m p l e s a r e q u i c k l y c o o l e d , this state m a y f r e e z e as t h e m i g r a t i o n of TABLE 11 Energy gained by ordering of cations (in units of eZ/a). The values which are taken from Blasse (1964), De Boer et al. (1950) and Gorter (1954) cannot be taken too literally. Being based on the point charge model they largely overestimate the real values. Type of ordering Difference of ion;s valencies
1:1; fl; B
1:3; B
I:I;A
1 2 3 4 5
1.0 4.0 9.0 16.0 25.0
0.7 2.8 6.3 11.2
0.5 2.0 4.5
OXIDE SPINELS
213
ions (which is necessary for the superstructure to appear) is negligible below 400°C. Consequently the spinels with the same composition may have profoundly different properties depending on their thermal history. A similar situation to that described above exists in magnetite Fe3+[Fe2+Fe3+]O4. H e r e the superstructure arises due to the ordering of the d-electrons of Fe 2+ and Fe 3÷ ions located at B sublattice. The activation energy is much lower compared to the case of ordering of different ions, the phase transition is sharp and appears at ~120 K. This transition attracted much attention during the last years (Evans 1975, Buckwald et al. 1975, Iida et al. 1977) and it turned out that it is much more complicated than originally proposed by Verwey and Haaijman (1941). In the oxide-spinels another type of ordering, called the cooperative J a h n Teller effect, is relatively frequently encountered. The necessary condition for this effect to appear is the presence of transition metal ions which have an orbitally degenerate electronic ground state (for the orbital degeneracy of electronic states see fig. 9). The interaction between the degenerate states and the lattice vibrations leads to an effective coupling between electronic states on different cations. When this coupling is sufficiently strong and the concentration of active cations exceeds a certain critical value, the electronic states order and simultaneously a structural phase transition from cubic to lower symmetry appears. The phase with lower symmetry is stable only below a critical t e m p e r a t u r e Tc. In most cases the system undergoes a first order transition at To, though a second order transition was also observed. The dependence of the order p a r a m e t e r c / a on the reduced tern-
,0
o -
o"-~ o
ok
E
L
.3
2. o5
0.15
2.85
;4
,5 o.2s
I
o
o.2s
I
o',s
/%
Ozs
Fig. 14. Temperature dependence of the ordering parameter se in some spinels exhibiting the cooperative Jahn-Teller effect. ~: is defined as the ratio (c/a - 1)r/(c/a - 1)0. The data are taken from McMurdie et al. (1950) (Fe0.15Mnz8504), Ohnishi et al. (1959) (CuFe204, CuFel.7Cro.304)and Pollert and Jirfik (1976) (CrMn204).
214
S. KRUPIOKA AND P. NOVAK
perature for some spinels is shown in fig. 14. A typical dependence of the lattice parameters c and a on the concentration of active cations is displayed in fig. 15. In the past much experimental and theoretical effort has been exerted in order to understand various aspects of the cooperative Jahn-Teller effect in spinels. For a review see Englman (1972), Gehring and Gehring (1975). In the B site, there are two ions (namely Mn > and Cu 2+) both having doubly degenerate ground state of Eg type, which exhibit the Jahn-Teller effect. The corresponding distortion is always tetragonal with c/a > 1. With the active cations in the A sublattice the situation is more varied. The cations with the triplet ground state TI(Ni>), Tz(CU 2+) as well as those with the doublet state E (Fe > ) give rise to the Jahn-Teller ordering, though in the latter case the effect need not be very much pronounced. Tetragonal symmetry with both c/a > 1 and c/a < 1 may occur and in mixed spinels Fe3-xCrxO4 and NiFexCr2 ~O4 an orthorhombic deformation was
I
I
0
9.4
0
9.3 0 2+
9.2
3+
3+
o
9.1 9 8.9 8.8
~.
Ucu h
+
Cltetray
o
C
o
u VI/3
o o
8.7
o o
8.6
o o
o
8.5
z~mo A
[]
[] D ° r l
z~
++ + +
8.4f
+ -I- .t-
8.3 82
+ + +
0
0:2
'
'
0:0
'
018
'
;
X
Fig. 15. Room temperature values of the lattice parameters in the spinel system (Holba et al. 1975).
~VInl+2xCr2_2xO 4
OXIDE SPINELS
215
observed. Data concerning the cooperative Jahn-Teller are summarized
effect in the binary spinels
in t a b l e 12, w h i l e t h e v a l u e s of t h e c r i t i c a l c o n c e n t r a t i o n
of active
c a t i o n s i n s o m e m i x e d s p i n e l s a r e g i v e n in t a b l e 13. W h e n t h e c o n c e n t r a t i o n o f t h e a c t i v e c a t i o n s is less t h a n t h e c r i t i c a l , t h e m a c r o s c o p i c s y m m e t r y is c u b i c , b u t still the local deformations connected with the Jahn-Teller effect persist (Krupi~ka et
TABLE 12 Cooperative Jahn-Teller effect in binary spinels.
Spinel Mn304 CdMn204 ZnMn204 MgMn204 CoMn204 FeMn/O4 CrMn204 7-Mn203 CuFe204* CuCr204 CuRh204 NiCr204 NiRh204 FeCrzO4 FeV204
Distribution of ions
Active ion
c/a
Tc (K)
Ref.
normal normal normal 0.78 < 6 < 0.79 normal 8 - 0.15 inverse uncertain 0.06 < 6 < 0.24 normal normal normal normal normal normal
Mn 3+ 03) Mn 3+ 03) Mn 3+ 03) Mn 3+ 03) Mn 3+ 03) Mn 3+ 03) Mn 3+ 03) Mn3+03) Cu 2+ 03) Cu 2+ (A) Cu2+(A) Ni 2+(A) Ni 2+ (A) Fe 2+(A) Fe 2+ (A)
1.162 1.191 1.142 1.15 1.15 1.045-1.064 1.049 1.16 1.06 0.913 0.91 1.04 1.04 0.986 1.014
1443 670 1298 1200 1173 470 569
1-5 2, 6, 7 1, 2, 8 3, 9 2, 3, 4 2, 10 11 12 14-16 13, 14 12 17 18, 19 20 21
633 903 833 275 360 135 127
* Samples rapidly quenched from high temperatures are cubic. 1. Romein, F.C., 1953, Philips Res. Rep. 8, 304, 321. 2. Sinha, A.P.B., N.R. Sinjana and A.B. Biswas, 1957, Acta Crystallogr. 10, 439. 3. Miyahara, S. and K. Muramori, 1960, J. Phys. Soc. Jap. 15, 1906. 4. Wickham, D.G. and W.J. Croft, 1958, J. Phys. Chem. Solids 7, 351. 5. Brabers, V.A.M., 1971,J. Phys. Chem. Solids 32, 2181. 6. Robbrecht, G.G. and C.M. Henriet-Iserentant, 1970, Phys. Status Solidi 41, K43. 7. Day, S.K. and J.C. Anderson, 1965, Philos. Mag. 12, 975. 8. Nogues, M. and P. Poix, 1972, Ann. China. 7, 308. 9. Irani, K.S. et al., 1962, J. Phys. Chem. Solids 23, 711. 10. Finch, G.I., A.P.B. Sinha and K.P. Sinha, 1957, Proc. Roy. Soc. A242, 28. 11. Holba, P., M. Nevfiva and E. Pollert, 1975, Mater. Res. Bull. 10, 853.
12. Sinha, K.P. and A.P.B. Sinha, 1957, J. Phys. Chem. 61, 758. 13. Bertaut, E.F. and C. Delorme, 1954, Compt. Rend. 239, 504. 14. Ohnishi, H. and T. Teranishi, 1961, J. Phys. Soc. Jap. 16, 35. 15. Bertaut, E.F., 1951, J. Phys. Rad. 12, 252. 16. Prince, E. and R.G. Treuting, 1956, Acta Crystallogr. 9, 1025. 17. Tsushima, T., 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 189. 18. Miyahara, S. and S. Horiuti, 1964, Proc. Int. Conf. Magnetism, Nottingham, p. 550. 19. Horiuti, S. and S. Miyahara, 1964, J. Phys. Soc. Jap. 19, 423. 20. Whiple, E. and A. Wold, 1962, J. Inorg. Nucl. Chem. 25, 230. 21. Rogers, D.B. et al., 1963, J. Phys. Chem. Solids 24, 347.
216
S. KRUPI~KA AND P. NOV~,K TABLE 13 Critical concentration of the Jahn-Teller ions in some spinel systems.
Spinel
Active ion
c/a for x > xt
xt
Ref.
Mn3+(B) Mn3+(B) Mn3+(B) Mn3+(B) Mn3+ (B) Mn3÷(B) Mn3+(B) Mn3+(B) Cu2+(B) Cu2+(B)
>1 >1 >1 >1 >1 >1 >1 >1 >1 >1
0.40 0.48 0.6 0.59 0.6 0.57 0.55 0.65 0.32 0.37
1 2 3 3 3 5 4 4 3 3
Cu2x+M2-+x[Cr3÷]O4 M = Mg, Co, Zn, Cd
Cu2+ (A)
<1
0.5
3
Ni~+Zn~+~[Cr3+]O4 Fe~+Co~2x[Cr3+]O4
Ni2+(A) Fez+ (A)
>1 <1
0.6* 0.7¢
6 7
3+ 3+ Mn2+ [Mnz~Cr2-2x]O4 3+ 2+ 3+ 3+ Mny2+ Fel-y[Fel-yFea+y-zxMn2x]04
Co2+[Co~+-2xMn~+]04 Mg2÷[Al~-+2xMn~+]O4 Zn x2+Ge4+x[MnZ+zxMn~+]O4 Co2+[Crz3+zxMn23+]O4 ZnZ+[Cr3-+2xMn3x+]O4 Zn2+f[ Fe 23+ - 2 x Mn3+~¢-~ 2xP.J4 3+ 2+ 2+ ' 2 + 3+ Fel-sCu8 [Cu2xNli-2x 8Fe1+8104 3+ 2+ 3+ 2+ 2+ Fe1-~Cu~ [Fel+sM~-2x-sCu2x]O4 M = Mg, Co
* extrapolated to 0 K ?for T - 9 0 K 1. Holba, P., M. Nevf'iva and E. Pollert, 1975, Mater. Res. Bull. 10, 853. 2. Brabers, V.A.M., 1971, J. Phys. Chem. Solids 32, 2181. 3. Goodenough, J.B., 1963, Magnetism and the Chemical Bond (Wiley, New York, London). 4. Shet, S.G., 1969, Thesis, Univ. of Poona. 5. Mansour, B. et al., 1973, Compt. Rend. 277, 867. 6. Kino, Y., B. Liithi and M.E. Mullen, 1972, J. Phys. Soc. Jap. 33, 687. 7. Arnon, R.J. et al., 1964, J. Phys. Chem. Solids 25, 161. al. 1964, K u b o et al. 1969, K o z h u h a r et al. 1973). M o r e o v e r , the i n t e r a c t i o n b e t w e e n the J a h n - T e l l e r ions seems to lead to a clustering of these ions (Blasse 1965, K r u p i r k a et al. 1968, B r a b e r s 1971) at least in s o m e spinel systems.
2. Magnetic ordering Spinels r e p r e s e n t a classical e x a m p l e of a crystal structure allowing a special type of m a g n e t i c o r d e r called f e r r i m a g n e t i s m . Neglecting m i n o r differences we m a y consider all o c t a h e d r a l l y c o o r d i n a t e d cations to form o n e sublattice only (B) a n d similarly the t e t r a h e d r a l sites to c o m p o s e the o t h e r sublattice (A). T h e s e sublattices are crystallographically i n e q u i v a l e n t a n d if they b o t h c o n t a i n p a r a m a g n e t i c ions in sufficiently high c o n c e n t r a t i o n the f e r r i m a g n e t i s m (i.e. the antiparallel o r i e n t a t i o n of the two sublattice m a g n e t i z a t i o n s MA, M s ) m a y occur p r o v i d e d the i n t e r s u b l a t t i c e e x c h a n g e i n t e r a c t i o n s are a n t i f e r r o m a g n e t i c a n d some requirem e n t s c o n c e r n i n g signs a n d strengths of the i n t r a s u b l a t t i c e i n t e r a c t i o n s are
OXIDE SPINELS
217
fulfilled (see section 2.2). I n fact, spinels were the first materials where the existence of such magnetic ordering was recognized and for which the first molecular field theory was elaborated by N6el (1948). Until the discovery of ferrimagnetism the magnetic properties of the few magnetic spinels known, mainly those of magnetite, were classified as ferromagnetic. It was difficult, however, to understand the low magnetic moments and some other peculiarities of these materials, e.g., the deviations from the Curie-Weiss law (Serres 1932, Kopp 1919). The departures from a normal ferromagnetic behaviour were excellently explained by the N6el theory. If the magnetic cations occupy only one of the sublattices their magnetic moments usually order antiferromagnetically, though there are also some few cases of pure ferromagnetism.
2.1. Exchange interactions in spinels As already pointed out by N6el the cations in spinels are mutually separated by bigger anions (oxygen ions) which practically excludes a direct contact between the cation orbitals, making any direct exchange at least very weak. Instead of it, super exchange interactions appear, i.e., indirect exchange via anion p orbitals that may be strong enough to order the magnetic moments. It is well known that apart from the electronic structure of cations this type of interactions strongly depends on the geometry of arrangement of the two interacting cations and the intervening anion. Both the distance and the angles are relevant. A survey of the main super exchange interactions in spinels is given in fig. 16. Usually only the interactions within the first coordination sphere (both cations in contact with the anion) are supposed to be of importance and the others are often disregarded (see further). In the N6el theory of ferrimagnetism the interactions are taken as effective inter- and intra-sublattice interactions A-B, A - A and B-B. The type of magnetic order depends on their relative strength. The theory of super exchange interactions (Anderson 1959, 1963) and the semi-empirical rules of Goodenough (1958) and Kanamori (1959) yield some predictions concerning the sign and strength of the super exchange interactions. As they were originally formulated for the 180° and 90° configurations a direct application is possible only for the B-B interaction with the angle M-O-M' ~ 90° (table 14a). The case of the A-B interaction with the angle ~125 ° is more complicated. The usual way is to interpolate between the 180° and 90° case
6. AB(nn)
BB(nn)
AB(nnn) BB(nnn)
AA(nn)
Fig. 16. Main super exchange interactions in spinel structure.
218
S. K R U P I ( ~ K A A N D P. NOVi~d~[
T A B L E 14a Prediction of the exchange interaction for nn cation pairs in the B sublattice. d 3 - d3 d 5 - ds d 8_ d 8
tt or ]'$ * ]'~,weak
d ~- d 8 d 5 - d8 d 3- ds
~'~,w e a k I'1'or 1"$ ]'~weak
* Direct exchange between cations orbitals; it is of c o m p a r a b l e magnitude with the s u p e r exchange which is ferromagnetic here.
T A B L E 14b Prediction of the exchange interaction b e t w e e n cations in A and B sublattices. angle M - X - M ' A
B
180 °
90 °
d2 d5 d5 d5 d7 d7 d7
d3 d3 ds d8 d3 ds d8
i'J,weak ~t weak ]'~strong ]'J,strong T]'weak ~'~strong ~'~strong
]'$ or 1't w e a k t~,m e d i u m (weak) ]'~m e d i u m 1'$m e d i u m (weak) ]'$m e d i u m (weak) ~'~m e d i u m (weak) ]'~ or 1]'weak
125 °* uncertain I'$ (uncertain) ~'~ ]'$ T$(uncertain) ]'~, ]'~,
* Interpolation.
supposing that the change is smooth. This is indicated in table 14b for pairs of cations with the non-degenerate orbital ground state. If signs of the 180 ° and 90 ° interactions are opposite such interpolation does not give a definite result and the experiment is to be consulted. The A - A interactions are weak and do not influence the type of magnetic order as far as there is sufficient number of magnetic B ions. Quantitatively, the exchange interactions may be characterized by the appropriate exchange constants (integrals); usually the Heisenberg type isotropic exchange, ~ex = -- 2J~jS~Sj,
( 11)
between nearest neighbours is sufficient even though biquadratic exchange and sometimes anisotropic terms or exchange between more distant ions are also considered. The exchange integrals may be deduced from various experiments: directly from the paramagnetic resonance spectra and/or optical spectra of pairs of ions in diamagnetic host crystals; from the dispersion relations of magnons measured by inelastic neutron scattering; by analyzing the magnetic data, particularly the temperature dependence of the total magnetization and/or sublattice magnetizations. The most detailed results (obtained by EPR and optical investigations) have been published for Cr3+-Cr 3+ pairs in octahedral positions (fig. 17, tables 15(a) and (b)). The results obtained indirectly in magnetically concentrated systems have to be regarded with some caution because of the simplifications usually made (only nearest neighbour isotropic exchange, eq. (11), is considered, usually the molecular field approximation is used, often the collinear spin structure is assumed even when it is not fully justified etc.). Some of these results are listed in table 16.
OXIDE SPINELS
219
o Oxygen ions Bj
B2
Bo Fig. 17. Labelling of the B sites for table 15a.
TABLE 15a Bilinear exchange integrals for Cr3+ in ZnGa204 spinel according to Henning (1980). For labelling of the sites see fig. 17.
Pair
Distance (,~)
Exchange integral (cm-1)
Bo-B1 Bo-B2 Bo-B3 Bo-B4 Bo-B5 Bo-B6
2.947 5.104 5.894 5.894 6.589 8.335
-11.1 (5) -0.470 (5) -0.610 (5) -0.400 (5) -0.225 (5) -0.275 (5)
TABLE 15b Bilinear (J) and biquadratic (j) exchange integrals for nn Cr3+ pairs.
System Lio.sAlzsO4 MgA1204 Lio.sGaz.sO4 ZnGa204
Distance B0-B1 (A)
J (cm-1)
j (cm-1)
Ref.
2.79 2.86 2.90 2.95
-25 14.2 (10) -13.5 (5) 11.1 (3)
1.3 2.1 (7) -0.6 (13) -1.7 (4)
1 2 3 4
1, Szymczak, H. et al., 1973, Proc. Int. Conf. Magnetism, Moscow 1973, vol. 5, p. 425. 2. Henning, J.C.M. and H. van den Boom, 1977, Physica B + C 86-88, 1027. 3. Gutowski, M., 1978, Phys. Rev. B18, 5984. 4. Henning, J.C.M. et al., 1973, Phys. Rev. B7, 1825.
S. K R U P I C K A
220
AND
P. N O V A K
o I q
e'
b., O
,,-.¢
b,, 0a ui
~
b.,
=
~_o
~:~
I
<~.
o
<
< 0)
2 ~4,d ~D
.,=
t'-t"-
t--:
od
t'--
~. tq. c t",l t~
t-,¢-,: t ~
,4 '--~ r" ',1 ' ~
I
I I
I
e'.
t"- . ~
.=_. ~D
+
+
~+~+
~m+l t"-
ca
~.,
~+<
÷ ¢-i< m
O
O
(
cc la
~
(
C
© % ~+,4'
;:,..
¢~
~5
~t-.-
e,';
~5 ~e
.,I
,q
<
~=
..-
• 0a
OXIDE SPINELS
221
2.2. Magnetic ordering: theory
If both sublattices contain magnetic ions, the collinear ferrimagnetic arrangement (fig. 18(a)) occurs provided (i) the A - B interaction is antiferromagnetic and, (ii) each of the A - A and B-B interactions is either ferromagnetic, or antiferromagnetic but weak compared with the A - B interaction. This is a typical magnetic structure for many spinels, particularly inverted ferrospinels. The approximate behaviour of a ferrimagnetic spinel follows from the molecular field type theory given by N6el (1948). The molecular fields hA, hB acting on magnetic ions in A and B sublattices are sums of two molecular fields corresponding to inter-sublattice and intra-sublattice exchange, respectively:
hA = n(aMA -- MB), n> 0
(12)
hB = n(--MA + flMB), w h e r e MA, MB are the sublattice magnetizations and n, na, n/3 are the molecular field coefficients for A-B, A - A and B-B interactions respectively; they are related to the corresponding exchange integrals by,
n = NA 1 ~
--2Jo/(gAgBtz~),
j~A(i~B) na
= N A1
nfl = NB 1
(13)
E -- 2 J i j / ( g A l Z B ) 2 , jEA(i~j, iEA) E -j~B(i~j,i~B)
2Sij/(gBlzB)2 ,
where NA(NB) is the number of A(B) sites in the volume to which the magnetization is referred. For a description of the statistical behaviour of magnetic moments in both sublattices we have now two equations: IMAI = MAoBsA(gASAmBIH + hAI/kT),
IMBI= MBoBss(gBSB/~s]H + hsl/k T)
,
T a
b
c
d
Fig. 18. Basic types of the spin ordering in spinels: (a) Collinear ferrimagnetism (N6el configuration); (b) Canted ferrimagnetism (Yafet-Kittel configuration; (c) Antiferromagnetism; (d) Spiral structure.
222
s. KRUPICKA AND P. NOV,~K
that have to be simultaneously solved to obtain /]4fA, Ma and the total magnetization M = M A + MB as functions of temperature and magnetic field. Bs(x) is the Brillouin function. The main conclusions drawn from the solution are as follows: (i) In the paramagnetic region a hyperbolic dependence of 1/X on T,
1TX
O CA + Ca
;~ T- O"
(14)
is obtained instead of the Curie-Weiss law. In eq. (14)
0 = [CACB/(CA+ C B ) ] n ( - 2 + O~CAICB+/3CalCA), 0 '= [CACa/(CA+ Ca)]n(2 + a +/3), CA, Ca are Curie constants for the A and B sublattices respectively
CACa n2[Ca(1 + a ) - CB(1 +/3)12.
( - (CA + Ca) 3
(ii) The paramagnetic Curie temperature Tc following from eq. (13) for 1/X = 0, depends on all interactions present, viz. Tc = ½n{CAC~ + CB/3 + [(CAa -- CB/3)2 + 4CACB] 1/2} ;
(15)
(iii) For T < Tc, the temperature dependence of MA generally differs from
MB(T) which leads to a variety of possible types of temperature dependence M(T), depending on a and/3 (see fig. 19). Some of them are very different from the "normal" behaviour of ferromagnetics (non-monotonic curves, compensation point, etc.); (iv) At T = 0 the collinear ferrimagnetic arrangement (called often the Ndel configuration) with both sublattices magnetically saturated is predicted to be stable if c~ > --MB(O)/MA(O) and/3 > --MA(O)/MB(O). In other regions of the (c~/3) plane the simple theory predicts one or both sublattices to be unsaturated (partly or fully disordered). This conclusion has proved to be not correct due to the oversimplifications included in the model: (1) only two sublattices were considered instead of 6 (six cations in the primitive cell), and (2) the magnetic moments in each sublattice were a priori assumed to be parallel. The removal of the restriction (1) by Yafet and Kittel (1952) led to the so-called triangular arrangement (fig. 18(b)) in which the spins in one of the sublattices (say B) are canted and divided into two groups B1, B2 with opposite canting angles; the corresponding sublattice magnetization MB = MB1 + MB2 is then antiparallel to the spins in the other sublattice A. This configuration should have replaced the Ndel solution with one sublattice unsaturated. As shown by Kaplan (1960) and Kaplan
OXIDE SPINELS
223
/'4B
Ns
"K "~5
~g Of
c~p = i
/
~ y~///~/////////,, .
/
/
Paramagnetic region
Subtattice B unsaturated
Fig. 19. Division of (aft) plane into regions with different magnetic behaviour. For the ordered regions the type of the M ( T ) dependence is indicated. et al. (1961), h o w e v e r , it d o e s not r e p r e s e n t a state with m i n i m u m e x c h a n g e e n e r g y in cubic spinels, w h e r e o t h e r m o r e c o m p l e x c o n f i g u r a t i o n s of t h e spiral t y p e p o s s e s s i n g l o w e r e n e r g y exist (fig. 20). In t h e i r t h e o r e t i c a l study, which is u p to n o w t h e m o s t c o m p l e t e o n e c o n c e r n i n g t h e g r o u n d s t a t e m a g n e t i c c o n f i g u r a t i o n in spinels within t h e classical limit, e v e n r e s t r i c t i o n (2) was r e m o v e d . O n t h e o t h e r h a n d t h e A - A i n t e r a c t i o n s w e r e n e g l e c t e d a n d only n e a r e s t n e i g h b o u r inter-
U
8/9 2 o E
4
6
8
~I/E ' .......... I
10
12
14
,
EL Ua I
-20
K,TTEC
-60
-
80
LOWER BOUND
~
~
~
'
~
~
~
~
Fig. 20. Dependence of the normalized energy ~ = E / J ~ S A S B N of various spin configurations in spinel on the parameter u = 4JBBSB/3JABSA; after Kaplan et al. (1961).
224
S. KRUPICKA AND P. NOVfid(
actions were taken into account. They also found an improved criterion for the stability of the N6el configuration as expressed by the critical value uo = ~ of a single parameter u = 4JBBSB/3JABSA describing the relative strength of the B-B and A - B interactions. For u t> u0 the collinear structure is expected to change continuously into a ferrimagnetic spiral (fig. 18(d)). Nevertheless, the Yafet-Kittel type configurations may become stable in tetragonally deformed spinels (Mn304, CuCr204). Note that in this case 5 generally different exchange integrals between nearest neighbour cations have to be considered (including JAA which is usually taken ~0). Even the collinear ferrimagnet may become canted under the influence of a strong magnetic field whose torque is sufficient to compete with the exchange torques. The effect was theoretically studied in the molecular field approximation (Tyablikov 1956, Schl6mann 1960) and it was found that two critical fields Ha = n ( M B - MA), /-/2 = n(MB + MA) exist so that the overall magnetization M is constant and equal to ]MB- MA] for H < Ha and equals MA + M~3 for H > H2. In the intermediate region M linearly increases with H. As the molecular fields are rather high for most of the ferrimagnetic spinels, this effect is expected to become observable only in the region of the compensation point, i.e., when MA --~MB.
2.3. Magnetic ordering: experiment The results included in this section are mostly based on direct neutron diffraction determinations of the magnetic structure and completed by magnetic measurements.
2.3.1. Spinels with one magnetic sublattice only If only the A sublattice is occupied by magnetic ions, an antiferromagnetic arrangement appears in all known cases. As JAA is small, the corresponding N6el temperature, TN, is l o w (table 17). Two sublattices A1, A2 with mutually antiparallel spin alignment were found to be identical with the crystallographical ones (section 1.1) (Roth 1964). The situation for spinels with magnetic ions in the B sublattice only is more complex. As pointed out by Anderson (1956) the octahedral sublattice possesses a peculiar topology which prevents a long range order to be stabilized by nearest neighbour (n.n.) antiferromagnetic interactions only. Hence the interactions between more distant ions have to be considered. A number of different arrangements may then appear as discussed by Plumier (1969), Aiyama (1966), Akino and Motizuki (1971) and Akino (1974). The complexity may be somewhat reduced if the symmetry of the crystal structure is lowered either by the cooperative Jahn-Teller effect or due to the magnetic interactions. Note that large single ion anisotropy of some ions (Co >, Fe E+, Ni 2+) may strongly influence the resulting magnetic structure; this is believed to be the case, e.g., for normal 4-2 spinels G e 4+ [M2+]O42-, M = Fe, Co, Ni (Plumier 1969). In few cases the ferromagnetic ordering occurs. Only typical examples with magnetic ions in B sublattice together with the relevant data are listed in table 18.
O X I D E SPINELS
225
T A B L E 17 Spinels with magnetic ions in the A sublattice only. The A - A interactions seem to be enlarged by the presence of the transition metal ions Co 3+, Rh 3+ in the B sublattice even though their spin is zero. Spinel
Tr~ (K)
Mn2+Al~+O4 * Mn2+Rh~+O4 Fe2+A13+O4* . Co2+Al3+O4 * Co 2+Rh 32+O4 Co2+Coz3+O4 Ni2+Rh3+O4 CuZ+Rh~+O4
6 15 8 4 27 46 18 25
~ga(K)
-25
- 30 -50 -20 -70
Ref. 1 2 1 1 3 2 2, 3 2
* 5 to 15% inverse spinel. 1. W.L. Roth, 1964, J. Phys. Rad. 25, 507. 2. G. Blasse, 1963, Philips Res. Rep. 18, 383. 3. G. Blasse and D.J. Schipper, 1963, Phys. Lett. 5, 300.
T A B L E 18 Spinels with the magnetic ions in the B sublattice only.
Spinel Mg2+[Cr~+]O4
Crystallographic structure
cubic at 10 K, weakly tetragonal at 4.2 K cubic at 77 K, Mg2+ [ V 3 + ] 0 4 tetragonal at 4.2 K tetragonal Zn 2+[Mn 3+]O4 cubic Zn2+[Fe3+]O4 cubic Gen+[Fe~+]O4 Ge 4+[Ni2+]O4 cubic 4+ cubic C u + [NI•2+ 1/2Mn3/2]O4 Cu +rM~2+ cubic [ N 1/2Mn 4+ 3/2J10 4
Magnetic structure
TN or Tc (K)
Ref.
complex antiferromagnet
-350
14
1
antiferromagnet
-750
45
1
antiferromagnet complex antiferromagnet antiferromagnet antiferromagnet ferromagnett ferromagnet
-450 -50 - 15 -6 -20 -75
200* 9 10-11 15 150 57
2 3 4 4, 5 6 6
* Different N6el temperature TN = 50 K was reported in ref. (7). t Magnetic moments of Ni 2+ antiparallel to the Mn 4+ moments. 1. 2. 3. 4. 5. 6. 7.
~9a (K)
Plumier, R., Theses, Paris 1968. Aiyama, Y., 1966, J. Phys. Soc. Jap. 21, 1684. K6nig U. et al., 1970, Solid State Commun. 8, 759. Blasse, G. and J.F. Fast, 1963, Philips Res. Rep. 18, 393. Bertaut, E.F. et al., 1964, J. Phys. (France) 25, 516. Blasse, G., 1966, J. Phys. Chem. Solids 27, 383. Gerard, A. and M. Wautelet, 1973, Phys. Status Solidi a16, 395.
226
S. K R U P I C K A A N D P. N O V i ~ K
2.3.2. Spinels with magnetic ions in both subIattices The A - B interaction was always found to be antiferromagnetic. For many inverse or almost inverse ferrospinels this interaction is predicted to be strong (table 14b) and, accordingly, a collinear ferrimagnetism is expected to appear (section 2.2). This was confirmed experimentally-representative data are given in table 19. T A B L E 19 Examples of spinels with the collinear ferrimagnetic spin arrangement. riB(A) System
nB(B)
nB
theor,
neutrons
theor,
neutrons
theor,
neutrons
experiment
Fe3+ [Fe3+Fe2+]O4
5
5
9
9
4
4
4.03-4.2
Fe3+[Ni2+Fe3+]O4
5
5
7
5 (Fe 2.3 (Ni3+) 2÷)
2
2.3
2.22-2.40
Fe3+ [Li~.sFe~]O4
5
-
7.5
-
2.5
-
2.6
Mn0.98Fez0204*
5
4.99
9.74
9.72
4.74
4.73
4.52-4.84
* Partially inverse spinel with 6 = 0.13 (see Jir~ik, Z. and J. Zajf~ek, 1978, Czech. J. Phys. B28, 1315). A s s u m e d ionic distribution M n 2+ 3+ [Mn o. 3+13Fe3+ 2+13] 04. 0.85Feo.z5 1.74Feo.
When the A - B interaction becomes comparable with one (or both) of the intra-sublattice interactions the collinear structure is destabilized and complicated structures with canted spins are observed. Spiral structures were reported in several chromites and Yafet-Kittel-like structures in manganites, vanadates and some chromites (see table 20). In some of these compounds transitions between various spin arrangements have been observed. Note that the non-collinear structures may be also very sensitive to substitutions (Vratislav et al. 1977). T A B L E 20 Examples of spinels with the non-collinear spin structure. nB exp.
Low temperature magnetic structure
2.54
-1.88
Y-K-like structure in the B sublattice
1
2.52 (B1) 2.8 (B2)
1.02
-2.28
spiral in both A and B sublattices
2
2.44
5.88
3.44
0.2
spiral in the B sublattice
3
4.24
2.2
Y - K structure in the 13 sublattice
3
System
riB(A)
nB(B)
Mn304
4.34
3.64 (B1) 3.25 (Bz)
MnCr204
4.3
CoCr204
MnV204
nB N6el
-2.04
-2.74
1. Jensen, G.B. and O.V. Nielsen, 1974, J. Phys. C7, 409. 2. Vratislav, S. et al., 1977, J. Mag. Magn. Mat. 5, 41. 3. Plumier, R., 1968, Thesis, Paris.
Ref.
OXIDE SPINELS
227
A special group is formed by the inverse 4-2 spinels, examples being the titanates M2+[Ti4+M2+]O2 or stannates M2+[Sn4+M2+]O2- (for summary of experimental data see Landolt-B6rnstein 1970). In these compounds the spin moments are compensated at 0 K as far as the arrangement is strictly collinear. Nevertheless, finite magnetic moments may appear due to the unequal orbital contribution of the M 2+ ions in A and B positions. The measurements on ulv6spinel Fe2TiO4 indicate further a possibility of a weak ferromagnetic moment to appear due to a small canting of spins (Ishikawa et al. 1971).
2.3.3. The effect of diamagnetic substitutions In principle, diamagnetic ions may enter either one of the sublattices only, or both, depending on the relative site preferences of the ions present. The diamagnetic substitutions in A sublattice probably represent the most clear-cut case, the Zn substituted ferrites being a well known example. Because of JAA = 0 only the A - B interactions are effectively weakened. If the number of substituted ions is not too high, however, (usually up to 30 or 40%) the overall ferrimagnetic arrangement is not destroyed for T ~ 0 K even though some loosely bound spins may become locally canted or disordered at higher temperatures T < Tc. For larger substitutions the A - B interactions may become comparable to, or even weaker than the B - B interactions. In this way the collinear ferrimagnets often change to canted ones. Both local canting and long-range non-collinear structures were reported (e.g. Piekoszewski et al. 1977, Zhilyiakov and Naiden 1977 and the references therein), the interpretation of experimental results being, however, often controversial. Finally, above a certain critical concentration of diamagnetic ions both sublattices are practically decoupled and only the B sublattice becomes magnetically ordered (usually antiferromagnetically). While the diamagnetic substitution as a rule lowers the ferrimagnetic Curie temperature, the saturated magnetic moment at 0 K may increase. This is shown for Zn substituted ferrites in fig. 21. If the ferrimagnetic order could be retained even when approaching ZnFe204 the magnetic moment at 0 K should increase steadily up to the limit 10/ZB per molecule; the breakdown in the vicinity of 50% substitution may be interpreted in terms of spin canting mentioned above. For a more detailed description the statistical methods (Gilleo 1958, 1960, Rosencwaig 1970) originally developed for diamagnetically substituted garnets, may be used. Diamagnetic substitution in the B sublattice weaken both A - B and B-B interactions simultaneously and hence the collinear ferrimagnetic structure need not be so strongly affected, only Tc is always decreased. The examples often quoted are the A1 substituted ferrites (for experimental data see Landolt-B6rnstein 1970). As the net magnetization in simple ferrites is parallel to the sublattice magnetization MB, the B substitutions lower the saturated magnetic moment and a compensation point (M = 0) may appear. Note that the change in JBB/JAB and MA/MB ratios generally modify the form of the M versus T curve (see section 2.3.4). The lowering of the sublattice magnetic moments found in some neutron diffraction experiments (e.g. K6nig et al. 1969) may be due to the local spin canting.
S. KRUPICKA AND P. N O V ~ K
228
, , / 10
na
..-i~~
..>?.~C';" .-'S:"~JS:"
M
8
o~'g""" ~ o
o~ ' ' ; ' "
o~ . ~ - ' ~ o
% , /o.:>~o/o..~/
°\
\o
co
6
%
",o.
%
Ni"
\
- -
ob
o
ot~
oi~
MFe204
2
o.8
~.o
x
ZnFe204
Fig. 21. Dependence of the saturated magnetic moments of ZnxMl-xFe204 ferrites on x. Data are taken from Gorter (1954) (©) and Sobotta and Voitl~inder (1963) (+).
~"'+'°'~.o.~. X = '0 50 ~ O's
o' experi'men~al + at 90° K o a~ RT
o.. u
%\
J
emulg I 40 i.
o~ %
0--'°-oooQ "O,o\ ° \
so ~ + ° - o . o 0.50
\
%
½
"13.0
0
I
\
,or-----+.. "%. \ ~o4 }I,_ U.O,~/ ,~o,~°--o0.60 % \ \1 ~ ~'0 + ~0~0..~ o
0~0 ~o. o
-----÷000.00.75
'~" 0.~.0 ~ ~
"o,.~
o-~.o.~ ~O_o~O.~
0~--O--o.._o~2oZll ~--+o-o-o-o-o.o_o_o_o:oO~Oo~-/[ + o-o-o-o-o-o~ ~'~'O~o -,0 ~__._~_ ,~ o..O>° / -~-o........... -/ I .._...~.
_
x =/.00
-20 ~ + ' ° ~ 0 ~ 0 ~ 0 " 0 ~ 0
0
0.2
0.4
~_...o/
I
~°~
0.6
0.8
%
1,0
Fig. 22. Temperature dependence of the saturated magnetization of NiFe2-xVxO4 sYstem, after Blasse and Gorter (1962).
OXIDE SPINELS
229
2.3.4. Temperature and field dependences The constraint of antiparallel orientation of the sublattice magnetizations reduces the freedom of the individual m o m e n t s in a collinear ferrimagnet which results in deviations from the normal statistical behaviour as expressed by the Brillouin type t e m p e r a t u r e dependences of MA and MB. The same is of course true for the overall magnetization M = MB -- MA for which the different characteristic types of M = M ( T ) curves were predicted by the N6el theory (see fig. 19). All of these types were found experimentally. In fig. 22 the curves for the system of V substituted nickel ferrites are shown; all 3 types of M ( T ) dependence appear when the V content is gradually increased. A lot of neutron diffraction, M6ssbauer and N M R data are available concerning also the t e m p e r a t u r e course of i
1.0
1.0
-o "-, ~'o
~"
-,.\
0.8
~ % o
MB/M8 (0) 0.8
\~ xo
,xo 0.6
0.6
0.4
0.4
0.2
0.2 i
I
i
o12 o,~ o'6 o.8
~0
't 012 o'.~ o'.6 o18 1.o
7.0
r/rc i
1.0
Msms(# 0.8
-° ~'~o~
",oN,° o\
0.6
k o~ ~\°~ o
0.4
"~"b~'o
0.2
~o
o'.2 o'.4 o16 o.'8
,.o r/re
Fig, 23. Comparison ot experimental and theoretical temperature dependencies of Ms, MA and MB for the Li ferrite (Prince 1965). Full curves were obtained by taking the biquadratic exchange into account. Dashed lines correspond to the simple N6el model with the zero intra-sublattice exchange. Good agreement of the N6el model with the experimental Ms(T) may be also achieved if appropriate intra-sublattice interactions are assumed. Then, however, calculated Ma(T) and MB(T) for 0.4~ T/Tc ~ 0.9 are considerably smaller than those determined directly by neutrons (Prince 1964).
230
S. KRUPICKA AND P. N O V ~ K
individual sublattice magnetization (K6nig et al. 1969, Sawatzki et al. 1969, Prince 1964, Yasuoka 1962). Note that their interpretation in terms of molecular field coefficients usually leads to an overestimation of JAA; this difficulty may be removed, however, when biquadratic exchange is taken into account (see fig. 23). In spinels with non-collinear magnetic structure the canting angle represents the necessary additional degree of freedom for the system of magnetic moments to make their statistical behaviour Brillouin-like (within the limits of molecular field theories). For this it is irrelevant whether the non-collinearity is due to competing exchange interactions or induced by a strong external magnetic field. It holds also for all canted structures that the canting angle depends on the applied magnetic field, even for T ~ 0 K. As a consequence the net magnetization increases with increasing magnetic field even when technical saturation has been reached. This behaviour was experimentally found for many ferrimagnetic spinels possessing non-collinear magnetic structures, such as manganites, chromites and others, including systems with diamagnetic substitutions. Examples are given in fig. 24. Jacobs (1959) analyzed the data assuming a triangular spin configuration. He found for this special case that the increase of saturation magnetization at low temperatures may be related to the molecular field coefficient n/3 for the B-B interaction by the simple equation
AM
=
HintS.
(16)
The behaviour in the paramagnetic region was found to be similar in all ferrimagnetic spinels, and corresponds to the predictions of the N6el theory (eq.
(]4)). 560
[
.
.
.
520 L/" ° ~ ° - - ° - ,~.
.
.
.
°-- °~°~°~°--°
Mn Fe2 0,;
,7F°K
24O 200
za
160 _~/,~.... ~ ~
Zx
~'
~
z~ . . . . - - z a
4.2OK
(Mnj/c,'Aq
120 -I 80
a
[]
o
u~d u~
4.2 K
2'0 ~'o ~'o 8'0 ~'oo ~o ~4o (koe)
Fig. 24. Dependence of the magnetization on an applied magnetic field for three spinel systems (Jacobs 1959, 1960). While there certainly exists a non-collinear spin arrangement in Mn[FeCr]O4 and Mn[Cr2]O4, the spin structure of MnFe204 is not yet unambiguously determined.
OXIDE SPINELS
231
2.4. S p i n w a v e s
The simplest quantum mechanical approach to the ferrimagnetism in spinels uses the two sublattice model (Kaplan and Kittel 1953). As a consequence two magnon b r a n c h e s - o n e acoustical and one o p t i c a l - a r e obtained. An important result of this model is that for small values of the wave vector k, the energy of the acoustical magnons is quadratic function of k, E = if0 + ~ k 2 ,
(17)
with _ 2JAAS 2 + 4JBBS~ - I I J A B S A S B a2 ' 16ISA - 2SB[ where a is the lattice constant, JAA, JBB and JAB are the exchange integrals. The dispersion relation (17) yields the well known r 3/2 dependence of magnetization and specific heat at low temperatures M(T)/M(O)
~- 1 - ~'(3/2)0 3/2 ,
(18)
C~ -~ ( 1 5 / 4 ) k B [ M (O)/ ge~p.B];',(5/2)O 3/2 ,
with 0 = [g~dM(O)]3/2kBr/(4~), M (O) = Nola.B(gASa -- 2gBSB), ge~ = ( g A S A - g B S B ) / I S A - SBI ,
kB is the Boltzmann's constant, gA, gB are the g factors of magnetic ions in A and B sublattices respectively, No is the number of A cations, and ~'(x) is the Riemann ~" function. More sophisticated spin wave calculations in spinels (Kaplan 1958, Kowalewski 1962, Glasser and Milford 1963) take into account that there are six sublattices of cations (section 1.1). Accordingly six magnon branches appear. The quadratic form (17) of the dispersion relation for acoustical magnons still applies and therefore both magnetization and the specific heat should follow the r 3/2 dependence at low temperatures. Experimentally most attention was directed towards magnetite Fe304 where magnon dispersion curves were determined by several authors (Watanabe and Brockhouse 1962, Torrie 1967, G r o u p e de diffussion des neutrons 1970) (fig. 25) using neutron scattering. Some experimental data are also available for M n - F e (Wegener et al. 1974, Scheerlinck et al. 1974), Co (Teh et al. 1974) and Li (Wanic 1972) ferrites. By fitting the spin wave theory to these experiments the exchange
232
S. KRUPICKA AND P. NOV~K 120
~
,
L
,
,
,
,
,
E
/~0v]
1o0 ~
90
* /-+~
50
/
40 %
20
o
-
o .+
o/+
30
10 4
(5)a.a(6)
0/4-
/
I
/ 0.2
&
o'6
o18
a__Eo[ool]
2IF
Fig. 25. Dispersion curves of spin waves in magnetite (six branches). Data taken from Groupe de diffusion des neutrons (1971) (+) and Watanabe and Brockhouse (1962) (©). integrals may be estimated. Both the sign and the magnitude of the inter-sublattice exchange integral obtained by such procedure agree with the expected ones (compare tables 14, 16). The same cannot be said about the intra-sublattice integrals-e.g, the ferromagnetic B-B coupling and rather large values of JAg were found in Fe304. Such contradictory results may be connected either with approximations made in the spin wave calculations (consideration of only isotropic bilinear exchange between nearest neighbours, introduction of effective exchange integrals etc.) or with insufficiency of the G o o d e n o u g h - K a n a m o r i rules. The T 3/2 dependence of the magnetization and specific heat predicted by the spin wave theory was observed in several ferrite systems (Kouvel 1956, Heeger and Houston 1964). An example of the results obtained is shown in fig. 26. Several authors reported the observation of spin wave resonance in single crystal (Ivanov et al. 1972, Baszynski and Frait 1976, Sim~ovfi et al. 1976) and polycrystalline (Gilbart and Suran 1975) spinel ferrite thin films. From the resonance fields the value of constant @ in eq. (17) may be determined. This procedure is somewhat obscured by the unclear way in which the spins are pinned at the surfaces.
OXIDE SP1NELS
233 T(K)
.~
50
(Mc/s) ~
o
100
158
200
'
'
'
800
1ooo
2400
250
3200
4000
r ½ (K3,~) Fig. 26. Temperature dependence of the Mn55 NMR frequency ~ in MnFe204 (Heeger and Houston 1964). ~, is propotional to the sublattice magnetization.
3. Magnetic properties 3.1. A n i s o t r o p y a n d magnetostriction 3.1.1. Introductory r e m a r k s The anisotropy constants are usually defined with respect to the free energy F of the system. For cubic symmetry,
(20)
F = Fo + K l s + K2p + K3s 2 + . • • ,
where 2 2 S = 0/la2-1-
2 2 2 2. 0/10/3"}- 0 / 2 0 : 3 ,
~2 2~2 p = tXl0/2~ 3 ,
a l , 0/2, 0/3 are the direction cosines of magnetization, and K1, K2, K 3 . . . are the familiar anisotropy constants. In addition, expressions corresponding to the tetragonal symmetry and sometimes-also to the orthorhombic one may be relevant to spinels,
F = Fo+ K l a n + K z a ~ + K3(a4+ 0 / 4 ) + . . .
(tetragonal),
(21) F = Fo + K l a ~ + K ~ ( a ~ - 0/~) + . • •
(orthorhombic).
There are several complications connected with such definitions of anisotropy constants. First, as a rule, the anisotropy is determined from measurements at constant temperature and external stress so that the experimentally determined K 1 , / £ 2 . . . refer to the Gibbs potential and not to the Helmholtz free energy. The difference between the two sets of constants is due to the magnetostriction. The
234
S. K R U P I O K A
AND
P. N O V / i d ~
detailed analysis as well as the formulae connecting Ki and /£~ are given, e.g., by Carr (1966). For cubic crystals, /£1 =
K1
+ h2(Cll - -
C12) - - 2 h 2 c 4 4 - 3hoh3(C~l + 2 c 1 2 ) -}- " • " ,
(22)
g 2 = K 2 - 3 h l h 4 ( C l l - c12) - 1 2 h 2 h s c 4 4 + • • • ,
where Cll, c12, c44 are the elastic constants and coefficients hi characterize the magnetoelastic coupling. To define hi the Gibbs free energy G is to be expanded in powers of the stress tensor 0-,
(23)
G=Go-A~-½~g~,
g being the elastic compliance tensor. The components of the tensor A are further written as series in powers of m , Ai~ = h0 + hl(O~ 2
- -
1) +
h3s +
h4(o¢ 4 +
2s/3
- 13) + "
",
(24) A i j = h2ofio~j + hsoqce].
The last two formulae yield the definition of the hi. The magnetostriction e in a direction specified by the direction cosines /31, /32, /33 is related to the tensor A through the relation e = ~'~ Aij/3i/3j.
(25)
/,j
Combining eqs. (24) and (25) the connection between the parameters hi, the commonly used magnetostriction constants A100, Aln is established, 3-100= 2 h i 3 ;
/~111= 2h2/3 .
h2
and
(26)
One point to note in eq. (22) is the t e r m - 3 h o h 3 ( c n + 2 c 1 2 ) which corresponds to the contribution of the isotropic strain. This correction depends upon the choice of the unstrained volume, in particular it vanishes if the state of zero volume stress is defined by setting h0 = 0. Some authors take as unstrained volume the volume of a hypothetical crystal with magnetic interactions switched off. Isotropic strain term may then contribute substantially to anisotropy, e.g., for synthetic magnetite Birss (1964) estimated this contribution to be - 2 8 % . The disadvantages of such an approach are: (i) constant h0 may be estimated only indirectly; (ii) it is difficult to determine h 3 with sufficient precision. It seems therefore more convenient to refer the free energy to the volume of the real (magnetized) crystal, in which case the contribution of the isotropic strain vanishes identically. The contribution of the anisotropic strain to magnetocrystalline anisotropy of spinels is, with few exceptions, small. The relevant data for several spinels are given in table 21.
OXIDE SPINELS
235
TABLE 21 Magnetostrictive contribution AK~ to the first anisotropy constant. Temperature (K)
K1 x 10-5 (erg/cm3)
Fe304
300
- 1.1
Li0.sFe2.504
300
-0.9
0.004
300 77
-0.7 5.8
0.053 52
System
(disordered) NiFe204 TiFe204
AK1x 10 s (erg/cm3) - 0.24
The second complication in defining the anisotropy constants is connected with the possible dependence of the magnitude of magnetization on its direction with respect to the crystallographic axes (anisotropic magnetization). Effectively it leads to the dependence of anisotropy constants on external magnetic f i e l d - for a corresponding analysis see, e.g., Aubert (1968). Up to now the experimental results in spinels were analyzed without taking this contribution into account. Finally, note that in the presence of the relaxation effects (section 3.3) the anisotropy measured by static methods generally differs from the one determined by FMR. In the following two subsections the microscopic origin of the anisotropy and magnetostriction will be discussed. A survey of the experimental data will be given in the Appendix.
3.1.2. Microscopic origin: anisotropy The dominant source of the magnetocrystalline anisotropy in spinels is to be sought in the interplay of the ligand field, spin-orbit coupling and the exchange interaction of the magnetic ions. The magnetic dipole-dipole energy may also contribute in tetragonal or orthorhombic spinels. In most cases the single ion model (Yosida and Tachiki 1957, Wolf 1957) is sufficient to describe semiquantitatively the magnitude and temperature dependences of the anisotropy constants K1, K2. In this model the magnetic ions contribute additively to the macroscopic anisotropy effects; their interactions are approximated by effective fields (ligand and exchange) and the anisotropy appears as a result of the dependence o f their individual energy levels on the direction of magnetization. T o deduce the low lying levels (i.e. those which may be thermally populated) the properly chosen effective Hamiltonian is usually used. For ions with orbitally non-degenerate ground states this reduces to the familiar form of the spin Hamiltonian (S ~<~): 1 4 4 1 = IXBHexgS+D[S}-½S(S+ 1)] +~a[S~ S z4 - ~S(S + S,+ + 1)(3S 2 + 3 S - 1)]
+ ~6F[7S~- 6S(S + 1)S~ + 5 S ~ - 6S(S + 1) + 3S2(S + 1)2].
(27)
This Hamiltonian applies to a cubic crystal field (axes x, y, z) with an axial (e.g.
236
S. KRUPI(~KA AND P. NOV/~G(
trigonal or tetragonal) component along axis (. It may be used, for the 6S ions Fe 3+ and Mn 2+ (S = I) and also for Mn a+ and Fe z+ (S = 2) in octahedral coordination supposing that the splitting by the crystal field of lower symmetry results in an orbital singlet ground state. For S ~<-~the quartic terms with constants a and F can be dropped out of the spin Hamiltonian. The possible anisotropy of the g tensor corresponds to the anisotropic exchange interactions. For ions with orbitally degenerate ground state the effective Hamiltonian contains the terms depending on the orbital momentum and in general its form is more complicated compared with eq. (27). The ions, which in cubic symmetry have the orbital triplet lowest, were treated, e.g., by Slonczewsk! (1958), Baltzer (1962) and Novfik (1972). As an example we quote the effective Hamiltonian corresponding to Co 2+ ion situated at the B site of the spinel structure (only the most important terms are retained): E{ =
oqA6Sz + a±A(lxSx + lySy) + DI~
+
(28)
g~BtIexS.
Here ! = - a L is the pseudoangular momentum (1 = 1), z is the trigonal axis, the term Dl 2 reflects the presence of the trigonal crystal field. For Co 2÷ ion D is negative; this corresponds to a situation where the trigonal field splits the ground orbital triplet into lower doublet and higher singlet. The orbital moment is not quenched but it is confined to lie along the local trigonal axis. Due to the spin-orbit interaction the spin is then also coupled to the trigonal axis (see fig. 27), which is the source of the large single ion anisotropy. To obtain the single ion contribution ki(T) (i = 1, 2 . . . . ) to the cubic anisotropy constants Ki the free energy per ion is to be evaluated using the partition function relevant to the energy spectra of the effective Hamiltonian (Wolf 1957, Yosida and Tachiki 1957, Slonczewski 1958). For microscopic theory to be compatible
~rig
%
g
fl
•¢.__.~t xx/
Exci~ed sfa~e
~xGround ,
0 a
:El2
0
YC
b
Fig. 27. Origin of the anisotropy due to the B site Co2÷ ion. (a) Coupling of the spin of Co 2+ to the local trigonal axis. Co) Dependence of the lowest two levels of Co2+ on the angle between magnetization and the trigonal axis (assuming /zBH~x>>spin--orbit coupling). The effect of higher order terms is indicated by weak lines.
OXIDE SPINELS
237
with the macroscopic description put forward in section 3.1.1 (i.e. with /(i corresponding to the Gibbs free energy) the terms depending on strains must be added to the Hamiltonian (see section 3.1.3, eq. (30)). Note that averaging over inequivalent sites must be performed when calculating ki(T). In the cases where the Hamiltonian (27) applies the contribution to the cubic first anisotropy constant is (with the F term neglected): kI(T) = at(y) + 7[DE/(kT)]t(y),
(29)
where y = exp[-glzBHex/(kT)], r(y) and t(y) are functions depending on S (Wolf 1957), and 3/ is a constant which equals 4 for ~"--- [111] (four non-equivalent axes) and - ~ for ~--- [100] (three non-equivalent axes). The latter may be, e.g., the case in the presence of the local Jahn-Teller distortions. For T ~ 0
k~(O) = -½S(S - 1)(S - 1)(S - ~)a + 23,S(S - ½)(S - ~)D2/(glXBHex), so that for ions with $ 4 3 the a term does not contribute to anisotropy. The temperature dependence (29) may be fitted to the experimental curve KI(T) to evaluate the constants a, D, gHex (see figs. 28(a) and (b)). On the other hand these values may be compared with those deduced from an independent experiment (most often E P R in doped diamagnetic crystals) or estimated on the basis of the ligand field theory. In many ferrimagnetic spinels, in particular ferrites, the first term in eq. (29) was found to predominate (Yosida and Tachiki 1957, Wolf 1957). The second term becomes important if either S ~<3 or the ratio D2/gtZBHex is of the same order of magnitude as a. The representative values of the parameters D, a and F are given in table 22. The one ion character of corresponding contributions to the anisotropy is illustrated in figs. 29(a) and (b). The anisotropy contribution of ions with the orbitally degenerate ground state is considerably greater as a rule. The most often encountered example is that of Co 2+ in octahedral positions mentioned above. It is well known that even very small concentration of Co in magnetite or in other ferrites substantially influences their anisotropic behaviour (figs. 30(a) and (b)). The analogous model is believed to apply also to V 3+ ion in the B sublattice. For Fe 2+ ion the trigonal field in the B site usually splits the ground triplet into lower singlet and higher doublet, so that the conventional spin Hamiltonian (27) may be used. The ions Mn 3+ and Cu E+ which possess doubly degenerate ground state Eg in octahedral symmetry exhibit a strong Jahn-Teller effect (section 1.6). This, combined with presence of the local strains, leads to lowering of local symmetry and to splitting of the ground doublet so that eq. (27) applies as well. From ions in tetrahedral sublattices which have an orbitally degenerate ground state the case of Ni 2÷ ion was discussed in detail (Novfik 1972, Pointon and Wetton 1973). The single ion anisotropy is strong here though the spin-orbit coupling contributes to it only through the second order terms of perturbation theory.
238
S. KRUPIOKA AND P. NOV~d4 I
i
i
I
i
I
I
I
I
a
o.oO/°~°~
-s~
-I0~
-
:< ::;;i;:'o,:
150 [
0
100
I
I
200
I
I
300
I
I
400
I
500
T(K)
oo -to
too 3~/
T(K) 20o 3oo___ x~(Fe3+)
I// ~ -30t~ °
-5o~
o o o Experiment x = 1.55
b
Fig. 28. Two examples of the determination of the spin Hamiltonian parameters by fitting the theoretical Ka(T) dependence to the experimental data. (a) Li0.55Fe2.4504 (Follen 1960). S is the order parameter, i.e., S = 1 (0.1) corresponds to ordered (almost disordered) Li ferrite. Resulting spin Hamiltonian parameters are a(Fe~+) = 0.024 cm 1, a(Fe~+)= -0.012 em 1. (b) MnL55Fel.4504 (Krupi6ka and Novfik 1964). Parameters a(Fe3+) = 0.012cm -I, tzBHex(Mn~+)=28cm a, D(Mn3+)= _1.77cm-1. The D value is to be taken as the effective one due to the non-collinear spin structure; the corrected value is D = -2.8 cm 1.
3.1.3. Microscopic origin: magnetostriction In p r i n c i p l e t h e m a g n e t o s t r i c t i o n m a y b e u n d e r s t o o d u s i n g H a m i l t o n i a n s a n a l o g o u s t o eqs. (27) a n d (28), t o w h i c h t h e e l a s t i c e n e r g y of t h e c r y s t a l is a d d e d . T h e p a r a m e t e r s of t h e e f f e c t i v e H a m i l t o n i a n s a r e t a k e n to b e f u n c t i o n s o f strain, b u t u s u a l l y o n l y c o n s t a n t t e r m s a n d t e r m s l i n e a r in strain a r e r e t a i n e d . F o r i o n s w i t h
239
O X I D E SPINELS
0.1
-5
0.15
0.2
6"
• 4.2K • 77K
-10 K,
-15
i
i
°/°/°/
"-E" 0.1 o
E ,
0.05
0
i
\o ~ _ . 1
0.3
0.2
,~
0'.4-
-0.05 Mn3+
-0.
o
b
\
Fig. 29. Additive character of the single ion contributions to anisotropy. (a) Dependence of KI on the inversion degree 6 in MgFe204 (Arai 1973). (b) MgxMn0.6Fez.4-xO4 (Gerber and Elbinger 1970). 2+ 3+ Anisotropy contributions AK~(FeB ) and AKI(MnB ) are shown as functions of concentration A~ in the molecule of Fe2+ and Mn3+ at temperature T ~ 0.
an orbital singlet g r o u n d state the r e l e v a n t effective H a m i l t o n i a n m a y b e w r i t t e n in t h e form (Callen 1968):
011) Se, ix,] Y~ = Y((e = O) + ~,~' ~_, [ S ~ O (gH¢x)eix,., + S aeix~, + fourth o r d e r terms + 1 ~ cm,e 2gix .
(30)
tx
H e r e YC(e = 0) is the spin H a m i l t o n i a n (27). T h e q u a n t i t i e s OD/Oe,,, form a fourth r a n k tensor, which in cubic (trigonal) local s y m m e t r y has 9 (18) i n d e p e n d e n t components.
240
S. KRUPI(~KA AND P. NOV,~K
25 -ff-~
-
co .,j °
M~
15 _ 10
~NiZn
~~MgFe,
\
FeNiZn
5 0
50
100
150
200
250 300 T(K)
~0
,,,,
(~m-,)
5O 40, 30
~izn ',, .... \
Ni ~. X',
\ \
20 10 s~
16o
I~o
eoo
2so
so0 T (K)
Fig. 30. Co 2÷ contribution to Kl(a) and K2(b) for various ferrites of composition Mel-xCoxFe204 (Broese van Groenou et al. 1968). The symbols indicate the host ferrite as follows: Fe: Fe304, Mn: MnFe204, MnTi: MnTio.1sCoo.15Fei.704, MgMn: (Mgo.TsMno.25)Mno.29Fel.7104,MgFe: (Mgo.9~Feo.09)Coo.olFel.9904,Ni: NiFe204, NiZn: Nio.67Zno.33Fe204, NiZnFe: (Nio.46Zno.29Feo.25)Fe204, Co: CoFe204.
OXIDE SPINELS
241
g-.
0
=8~dZ~o_' o ,,0.001
g--,
-40
~7
-80
'
2x
0.003 3 -0.005
•~ -120
-
160
C Fig. 30c. Dependence of AK1 and AK2 on cobalt content in ordered samples of Lio.5-xl2Fezs-xlzCOx04 (Seleznev et al. 1970) (1) 4.2 K; (2) 77 K; (3) 300 K.
There is an important distinction when calculating magnetostriction in comparison with the determination of a n i s o t r o p y - namely in cubic systems the terms bilinear in spin ( - - O D / O e ~ K ) contribute to magnetostriction constants already in the first order of the perturbation theory. The same holds for the dipole-dipole interactions, which consequently must also be considered. On the other hand the bilinear terms are as a rule much larger than the fourth order terms, and the latter may therefore be neglected. Given the form of the spin Hamiltonian (30) the calculation of the magnetostriction proceeds similarly as the one of anisotropy. Broadly speaking two types of contributions may be distinguished: (i) the single ion terms, (ii) two ion terms. To the second category belongs the contribution of the dipole-dipole interaction (table 23); this may be determined without difficulty once the lattice geometry, magnitude of the magnetic moments and the elastic constants are known. Much more complicated is the reliable calculation of the single ion contribution. Here the main obstacle is the determination of the derivatives OD/Oe~,,. In principle relevant information may be obtained from E P R under pressure; however, no such experiments have been yet performed in spinels. Moreover, an assumption must be made that the local elastic properties are the same as the macroscopic ones. An empirical way of determining the single ion contributions to magnetostriction in spinels was worked out by Arai and Tsuya (Arai and Tsuya 1973-1975, Arai 1973). These authors used the measurements of magnetostriction
S. K R U P I C K A A N D P. N O V f i d (
242
T A B L E 22 Values of the spin Hamiltonian parameters.
System
Ion
ZnGa204 ZnAl204 MgA1204 Li0.sAlz504 ZnAI204 ZnGa204 ZnAI204
Fe~÷ Fe 3+ Fe 3+ Fe~+ M n ~+ Cr 3+ Cr 3+
MgxMn0.6Fez4-x O4
Fe~+ Mn 3+ Fe~+
( a - F ) x 102 (cm -I)
a × 102 (cm -1)
3.53 4.71 4.58 _+1.66 -
4.44 5.75 4.77 1.0" 0.075 -
D (cm -~) -0.2442 -0.3402 -0.2467 0.104 0.524 0.891
2.0
Ref.
Method
1 2 3 4 5 6 7
EPR
8 3 (3.5,-4.0)
Anisotropy
MgFe204
Fe 3+ Fe~+
2.9 - 1.8
9
Li0.sFe2.504
Fe~+ Fe 3+
2.4 - 1.2
10
* Preliminary result. 6. Kahan, H.M. and R.M. Macfarlane, 1971, J. Chem. Phys. 54, 5197. 7. Drumheller, T.E. and K. Locher, 1964, Helv. Phys. Acta 37, 626. 8. Gerber, R. and G. Elbinger, 1970, J. Phys. C3, 1363. 9. Arai, K.I., 1973, Rep. Res. Inst. Electr. C o m m u n . T o h o k u Univ. 25, 79. 10. Folen, V.J., 1960, J. Appl. Phys. 31, 166S.
1. Krebs, J.J. et al., 1979, Phys. Rev. B20, 2586. 2. Gerber, P. and F. Waldner, 1971, Helv. Phys. Acta 44, 401. 3. Brun, E. et al., 1961, C.R. Colloque A M P E R E 10, 167. 4. Folen, V.J., in Paramagnetic Resonance, vol. 1, ed. W. Low (Academic Press, New York, 1963), p. 68. 5. Soulie, E. et al., 1973, Solid State C o m m u n . 12, 345.
T A B L E 23 3 3 Magnetoelastic coupling constants L = -gA~00(cll - ca2) and M = -gAulC44; the calculated dipole~zlipole contribution is to be subtracted from the experimental value to obtain a contribution due to other mechanisms (single ion). L (cm-I/molecule)
System MnFe204 Fe304 CoFe204 NiFe204
Calculated dipole~tipole coupling -
14 12 l1 10
M (cm-1/molecule)
Measured coupling
Calculated dipole-dipole coupling
Measured coupling
15 12 300 27
6.5 8 7.5 7
-4 -69 - 150 19
OXIDE SPINELS
243
on Mg ferrites with different degree of inversion to determine the single ion contributions of Fe 3~ ion in both A and B sublattices (the dipole-dipole interaction was taken into account by subtracting its contribution f r o m the experimental results). Supposing that the Fe 3+ contribution is the same in various spinels the single ion contributions of Cu 2+ (Arai and Tsuya 1974) and Ni 2÷ (Arai and Tsuya 1975) ions were d e t e r m i n e d from m e a s u r e m e n t s on CuFe204 and Nil-xZnxFe204 spinels respectively. These results are s u m m a r i z e d in table 24. Ions with an orbitally d e g e n e r a t e g r o u n d state have a m o r e direct coupling between the lattice and magnetic m o m e n t s and the corresponding contribution to magnetostriction is large. Similarly, as with anisotropy, most attention was d e v o t e d to the octahedral C o 2÷ ion (Slonczewski 1960, G r e e n o u g h and Lee 1970). T o calculate the contribution of Co 2÷ ion to magnetostriction the elastic energy and a term ~_~ V ~ , e ~ , , ix,t~,
which describes the change of the ligand field induced by strain is a d d e d to Hamiltonian (28). T h e r e are only a few i n d e p e n d e n t matrix elements of V,~,; using s y m m e t r y a r g u m e n t s and making some approximations in the calculation of the e n e r g y levels their n u m b e r is r e d u c e d to two. Leaving these two p a r a m e t e r s free and changing the o t h e r p a r a m e t e r s of the effective H a m i l t o n i a n (28) within reasonable limits a g o o d fit of experimentally observed t e m p e r a t u r e d e p e n d e n c e s of A100(r), }till(T) m a y be o b t a i n e d ( G r e e n o u g h and Lee 1970) (fig. 31). T h e Ni 2÷ in tetrahedral sublattice gives also a large contribution to magnetostriction and TABLE 24 Single ion contributions to the magnetostrictive constants (sublattice fully occupied by a given ion). Ion
Site
Temperature (K)
hi00×
10 6
AlllX 106
A
4.2 77 300
71.1 50 8.6
--15.1 - 13.2 12.6
B
4.2 77 300
-79 -61 -21.4
24.9 2.3 -2.5
B
4.2 77 290
-36 -36 -33.5
-19.6 - 19.6 - 18
A
4.2
B
4.2
Fe3+
Ni2+
-1690
-370
Cu2+ 350
100
244
S. K R U P I C K A A N D P. N O V t ~ ( T(K) 0
100 ,
200
300
i
,
400 rO-e
, - 5ol
'
25
_,oo
20
E N - 150
15
&
% -200
I0
-250 x 10-e -30C
a i
i
i
ibo
2bo
3bo T(K)
Fig. 31. Contributions Aha, Ah2 of Co 2+ ions to the magnetostriction constants hi, h2 in CoxMnl-xFe204 ferrites (Greenough and Lee 1970) for x = 0.038 (A) and x = 0.078 (B). Full curves were calculated using the single ion model Ahl is given for x = 0.038 only.
may be treated similarly as the octahedral C o 2+ ion (Lioliossis and Pointon 1977). Anomalously large magnetostriction was observed in the spinels Fe3-xTixO4 when x is close to 1 (ulv6spinels) (Isbikawa and Syono 1971a, b, Ishikawa et al. 1971, Klerk et al. 1977). For almost stoichiometric (x = 0.95) ulv6spinel A100= 4.8 × 10-3 at 77 K, which is almost an order of magnitude larger than A100 of Co ferrite. The explanation is based on the presence of Fe z+ ions in the tetrahedral sites. These ions would produce a cooperative Jahn-Teller distortion at temperature T~ lying slightly below the Curie temperature. Long-range magnetic order seems to suppress the cooperative Jahn-Teller effects; nevertheless a softening of the crystal as T~ is approached is observed (fig. 32). Due to the small value of c n - c~2 the magnetostriction of Fe z+ in octahedral sites is then enhanced. The dependences of A100 and Alll for the system Fe3_xTixO4 on the content of Ti are shown in fig. 33. The distortion of the crystal is due to the exchange striction. In the discussion of the origin of magnetostriction we have disregarded the term in Hamiltonian (30) corresponding to the dependence of the exchange on strain (exchange striction). Though it generally gives a non-zero contribution to the magnetostriction constants, it is believed that in spinels with the collinear spin structure it plays only a minor role. In systems with the non-collinear arrangement, however, its presence is of importance as it often leads to a change of the crystal symmetry below the ordering temperature. The possibility of a symmetry lowering always exists when the system of spins has a symmetry lower than the crystal lattice. Experimentally the tetragonal deformation of the cubic lattice
OXIDE SPINELS 6
i
i
o
-o'--~o~...oOo.
@
5
x
4
3 .£
i
-o8~ D
245 i
i
o
o"~-.o.~ o
C,,+,+
o.~.
°~o°
~AttenuatJon(c11_
• BaLsam
012
•
o Norlaq
o
iiI
LU
E o
)
Cli -- Ct2
\o
.2
80
60
•
.g,o-~-'-° •
.%-'~~.~
40
I°
. ,,,"
o~
20 i
I
i
i
200 Temperature (K)
0
300
Fig. 32. Softening of Fe2TiO4 as T~ is approached (Ishikawa and Syono 1971a).
o~ x
A '<10e
/ x
AIO0
• A.;,
/
1000
I
05
~o.+ * / . i..~.......--~,/_......
0
05
0.8
x
Fig. 33. Al00and Am vs Ti content x for Fe3-xTixO4 system (Klerk et al. 1977) for the values of indicated in the figure.
T/Tc
below the ordering temperature was observed, e.g., in MnV204 (c/a = 0.99), MgCr204 (c/a = 0.998) and MgV204 (c/a = 0.994) (Plumier 1969).
3.2. Magnetic anneal and related phenomena 3.2.1.
Origin
Magnetic annealing effects appear as the result of some directional ordering of defects or local anisotropic configurations in the crystal. In spinels, these usually
246
S. KRUPICKA AND P. NOVAdK
are cation vacancies, substituted ions (impurities), anisotropic short-range order configurations (pairs or groups of ions) or local Jahn-Teller distortions. A typical example (even though not the simplest one) is an inverted spinel having cations of two kinds in crystallographically equivalent octahedral positions. In order to achieve some kind of directional order of the imperfections with respect to the direction of magnetization two conditions must be fulfilled, however: (i) an anisotropic coupling exists between the magnetization vector and the local configurations (defects), and (ii) in some range of T < Tc these imperfections are allowed to move or to transform into other ones with a lower energy of their coupling to magnetization. In such a way the magnetic anneal reflects the ability of the crystal to adapt itself by an inner rearrangement in the lattice to the given magnetic state and to stabilize this state by lowering its free energy. If the magnetization is homogeneous a macroscopic anisotropy results (induced anisotropy). For cubic crystals it is described by (N6el 1954, Penoyer and Bickford 1957): ;K, = - F
+-..,
o i
(31)
i,~j
where direction cosines/3i and c~i refer to the orientation of magnetization during the annealing process and anisotropy measurement respectively. For polycrystals we obtain by averaging FKI = K , cos 2 0,
(32)
with
0 being measured from the direction of the annealing field. The anisotropic coupling responsible for local directional order is of the same origin as that leading to the magnetocrystalline anisotropy: dipole-dipole interactions, single ion anisotropies and anisotropic exchange (and perhaps further interactions) in pairs or clusters. Special types of the induced anisotropy may occur in systems with a noncollinear spin arrangement. In such systems there exist as a rule several distinct configurations of spins possessing the same exchange energy. For a given direction of magnetization the configuration with the lowest anisotropy energy is stable. When the magnetization is rotated, the energy of another configuration may become lower. Nevertheless, if the relaxation time of the spin system is sufficiently long the initial configuration is temporarily retained and an induced anisotropy is observed. Besides the usual terms (31), it may also possess a unidirectional part. Krupi6ka et al. (1977), (1980) reported such anisotropy in manganese chromites MnxCr3 xO4 (x I> 1). It may be noted that the relaxation of this anisotropy is realized by the rearrangement of the spin system itself.
OXIDE SPINELS
247
3.2.2. Examples of local anisotropic configurations Cation vacancies
Many spinels, particularly those nominally containing Fe 2+, often exhibit deviations from the oxygen stoichiometry (oxygen excess) which leads to the presence of cation vacancies. If their concentration on B sites with the [111] local trigonal axis differs from those in other octahedral positions the dipole-dipole interactions contribute an axial anisotropic term of the form (Yanase 1962):
E dip = AdipNu (/x -
(33)
~..L' ) ( ~ 1 0 £ 2 -~- ~20L3 -~ ~'30£1) ,
with/x', Ix denoting the average magnetic moments sites, respectively. N is the number of B sites 4 x 10 -18 erg/cm 3 as estimated on the basis of the leads to the induced anisotropy of a G type (i.e. F
in the [111] sites and the other per unit volume and Adip--~ geometrical parameters. This = 0) with
G ( T., T) = ND(16A2dip/k T)(gS)4[M (T)/M(O)]2[M (Ta)/M (O)I2 ,
(34)
N[] is the number of vacancies per unit volume, Ta and T are the temperatures of annealing and measurement, respectively, and gS the average magnetic moment in /xu. In principle, a similar anisotropy might be introduced by an unequal distribution of non-magnetic substitutional impurities among four types of the B positions. Note that such an anisotropic distribution of vacancies and/or nonmagnetic ions also causes the distribution of magnetic ions (i.e. Fe 3+, Fe 2+ etc.) to be non-uniform which results in an active contribution of these ions to the induced anisotropy via the mechanism of single ion anisotropy or anisotropic exchange (Krupi~ka and Zfiv6ta 1968). Co 2+ in B positions
In the range of low concentrations the Co 2+ ions may be viewed as isolated. In the presence of exchange their low lying levels corresponding to the spin Hamiltonian (28) are anisotropic and hence their equilibrium distribution among the four types of B positions will depend on the direction of magnetization. The resulting induced single ion anisotropy is again of a G type with (Slonczewski 1958): a = nN[(X/3] o~A[/2) tanh(V'3laA ]/2kT) - (ah)2/4/XBH~x], n = (Nm + Nm - Nm- Niil)/N,
(35)
where T is the temperature of measurement, N the total number of Co 2+ in the B sites, N1~1 their equilibrium number in positions with local axis in [111] etc., A the parameter of spin-orbit coupling and a a numerical factor, 1 < a <3. In the special case of Co substituted magnetite laA] = 132cm -1 and IXBH~x--320cm -1
S. KRUPICKA AND P. NOV_rid(
248
were estimated (Slonczewski 1958). Equation (35) applies also to other ions for which eq. (28) may be used. Single ion contributions to the induced anisotropy arising from the preferential distribution in the B sites are also expected from ions with a singlet orbital ground state, via the D term in the spin Hamiltonian (27). These anisotropies are usually weak but in special cases (Fe 2+) they may achieve a considerable strength (Watanabe et al. 1978). If the concentration of Co 2+ (or other active ions) is increased these ions cannot be considered as isolated and contributions of more complicated local configurations including pairs and eventually larger groups of active ions become important (Iida and Inoue 1962, Iida and Miwa 1966). As an example a cluster containing an isolated Co2+-Co 2+ pair is shown in fig. 34; note that there are 6 inequivalent orientations of this pair corresponding to 6 face diagonals (110). If the occurrence of differently oriented pairs is unequal, an induced anisotropy appears depending quadratically on the Co 2+ concentration. Experimentally this was found to be almost a pure F - t y p e anisotropy ( G = 0) (fig. 35). The source of the anisotropy
Fig. 34. The simplest configuration necessary for the description of the Co2+-Co2+ pair contribution to induced anisotropy (Iida and Inoue 1962, Iida and Miwa 1966). 15 x 105
i
i
10
i
o
o
~E
Oe) x
F (.9
u~
5
o ~°~.
,.~'" 0.05
o~ ,
,
0.10
0.15
x
'.20
Fig. 35. Induced anisotropy constants F and O for Co-substituted magnetite CoxFe3-xO4,measured at room temperature after annealing in a magnetic field at 375 K (Penoyer and Bickford 1957).
OXIDE SPINELS
249
may be sought in both the anisotropic exchange and a local modification of the ligand field changing the single ion contributions of each ion within the pair (Tachiki 1960).
Mn3+-distorted octahedra If a small part of octahedral positions is occupied by Mn 3+ ions the overall symmetry of the crystal remains cubic, but local Jahn-Teller distortions may appear (section 1.6). Assuming these to be static (or quasistatic) the local ligand field of Mn 3+ lowers its symmetry which usually becomes tetragonal. The D term in eq. (27) then yields uniaxial anisotropy of F~type (G = 0) provided a preferential distribution of the distortion axes may be created by magnetic anneal (Nov~k 1966). Let us note that due to local stresses and other defects often only a small part of the distortions is expected to be free to move and to take part in the process (No%k 1966, Krupi~ka et al. 1980).
3.2.3. Kinetics, magnetic after-effects In order to achieve thermodynamic equilibrium in the magnetic annealing process (by establishing a local directional order) some rearrangements in the lattice are necessary. Hence any change of the imposed conditions (change in the direction of magnetization and/or its spatial distribution in the magnetic specimen) will be followed by a relaxation process leading to accommodation of the magnetic system to the new situation. This manifests itself in relaxation of the induced anisotropy and in various so-called after-effects summarized, e.g., by Krupi6ka and Z~v6ta (1968). The microscopic mechanism underlying the relaxation processes mentioned above usuallly possesses the character of a diffusion process (migration of ions and/or vacancies, electron hopping) and it is thermally activated. The relevant relaxation times then depend exponentially on temperature according to the Arrhenius relation ~- = a e x p ( - O / k T ) ;
(36)
the constant A depends on the type of the diffusion process and O is the activation energy. Except for a few simple cases when isolated ions or vacancies rearrange, two or more relaxation times usually exist. The distribution of relaxation times is often continuous due to some disorder in the lattice. In practice, the so-called logarithmic distribution of r (i.e. log r uniformly distributed between limits log rl, log ~'2) is considered as a good approximation. Large dispersion of relaxation times has been found in processes involving electron hopping and/or reorientation of Jahn-Teller distortions. The diffusion may be usually described as a selfdiffusion process, i.e., without taking into account the driving forces due to magnetization; this is illustrated in fig. 36. Then [Ei - Ejl = Io,j - oj l
o0
o,
from which eq. (36) follows provided [Ei -Ei[ ~ kT.
S. KRUPICKA AND P. NOVd~¢
250
-- ~l ~
:/ I
-U-]OjI
Ei
_ _
i
i
Fig. 36. Dependence of the particle energy on the position r relevant to the relaxation process. If the diffusion in question concerns the ions, the activation energies Q are typically between 0.7 and 2.5 eV depending on the type of ions and type of the process. Generally, the presence of cation vacancies makes the diffusion process faster, the factor Q is lowered and the preexponential factor A in eq. (36) becomes inversely proportional to the vacancy concentration within certain limits. A detailed analysis of the vacancy assisted diffusion of Co 2+ ions in Co substituted magnetite was made by Iida and lnoue (1962) and by Iida and Miwa (1966). In particular, one relaxation time should exist for isolated Co 2+ ions (the G term) and two different times for reorientation of Co2+-Co 2+ pairs (the F term). The effect of the size of the migrating ion on the diffusion rate and the activation energy was calculated by G e r b e r (1968) on the basis of a simple model. When the local anisotropic configurations refer to anisotropic distribution of electronic charge (e.g. the distribution of Fe z+ and Fe 3+ valency states) a migration of electrons is sufficient for the rearrangement process. The activation energy is then 4 0 . 7 eV and it is often very low (<0.1 eV). The mechanism of the electron motion is similar to electrical conductivity (hopping). The spinels with coexisting Fe 2+ and Fe 3+, or Co 2+ and Co 3+ ions are examples of materials possessing this type of relaxation. A special case is represented by the local Jahn-Teller distortions. They are connected with the ordering of partly filled orbitals and their reorientation does not need any diffusion even though some thermal activation is necessary in order to overcome an energy barrier. A p a r t from this process the distortions are usually stabilized by some defects and the mechanical stresses connected with them; they reorient only if these defects move. This seems to be the case of low t e m p e r a t u r e magnetic anneal in Mn-rich Mn ferrites where the distortions of Mn 3+ octahedra may be stabilized by some extra electrons placed at the neighbouring ions (Krupi6ka and Zfiv6ta 1968). Apart from thermal activation an optical process may take place in some particular cases of electronic processes. Effects similar to photomagnetic anneal
O X I D E SPINELS
251
originally discovered in Si doped Y I G (Teale and Temple 1967) were observed in Mg, Li, Li-Mn and other spinel ferrites (Holtwijk et al. 1970, Marais and Merceron 1974, Hisatake and Ohta 1977, Bernstein and Merceron 1977).
3.2.4. Survey of experimental results Most of the information on induced anisotropy effects comes from torque measurements. In some cases additional knowledge may be obtained from the study of disaccommodation and other relaxation effects (see, e.g., Braginski 1965, Krupi'~ka and Zfiv6ta 1968). C o 2+
containing spinels
As the anisotropic effect of Co 2+ is strong it usually outweighs other possible contributions to the induced anisotropy. The magnetic annealing effect of Co 2+ ions was first observed in CoxFe3_xO4 by Kato and Takei (1933) and later on frequently studied in this system by several authors (Penoyer and Bickford 1957, Slonczewski 1958, Iida 1960, Iida and Inoue 1962, Iida and Miwa 1966, Palmer 1960, Iizuka and Iida 1966). For low cobalt concentration x the results may be interpreted in terms of local ordering of both isolated Co 2+ ions and Co2+-Co 2+ pairs in octahedral sublattice (figs. 34 and 35). The presence of vacancies does not change the magnitude of the induced anisotropy but the rate of ordering ~.-1 was found to be proportional to the vacancy concentration provided this is >~10 5. For lower concentrations of cation vacancies the activation energy is increased from the usual value ~1 eV to ~ 2 eV indicating a more difficult diffusion mechanism. In Ni-Co (Perthel 1962, Glaz et al. 1980), N i - F e - C o ferrites (Michalk 1968) and N i - Z n - C o ferrites (Michalowski 1965) similar effects appear. The induced anisotropy is usually lowered due to fluctuations in the local symmetry which primarily concerns the G term. In table 25 the room temperature values of G and F found for the system CoxNi0.46_xZn0.29Fe22504+ 7 after magnetic anneal at 350°C are compared with those reported for CoxFe3-xO4. Let us note that the coexistence of more kinds of ions yields possibilities for new anisotropic configurations to appear. In Co substituted Li0.sFe2.504 a substantial reduction of the induced anisotropy was observed when the B sublattice becomes ordered (lvanova et al. 1979). In spinels containing both Co 2+ and Co 3+ ions in octahedral sites a preferential T A B L E 25 Constants of induced anisotropy in Co containing ferrites. System CoxFe3-xO4 CoxNi0.a6-xZn0.29Fez2504+~
F (105 erg/cm 3)
G(105 erg/cm 3)
Ref.
101 x 2 0.06 + 100 x 2
92.5 x 7x
1 2
1. Penoyer, R.F. and L.R. Bickford Jr., 1957, Phys. Rev. 108, 271. 2. Michalowsky, L., 1965, Phys. Status Solidi 8, 543.
252
S. KRUPII)KA AND P. N O V ~
occupation of certain positions by Co 2+ may be achieved by the electron transfer between Co 2+ and Co 3+ ions. If the concentration of Co ions on equivalent sites is sufficient for a direct electron exchange Co2+ ~,~-Co3+, the activation energy is low ~ 0 . t e V . This is, e.g., case of cobalt rich C o - F e and C o - F e - N i spinels investigated by Iizuka and Iida (1966)- see figs. 37(a) and ( b ) - or Co 3+ containing Co ferrite (Marais et al. 1970). Low temperature torque m e a s u r e m e n t s would be necessary here to get the full frozen-in induced anisotropy. More often the spinels with low concentration of both Co 2+ and Co 3+ are quoted in the literature (Sixtus 1960, Marais and Merceron 1959, Mizushima 1965). The Co ions are then separated by many other ions, e.g. Fe 3+, so that the electron transfer involves also these ions as intermediary. This results in rather high activation energy up to ~0.6 eV. r
,
,
,
,
J
i
,
i
-o-o- be¢ore rec~ucUon -×-x- al~er ~ o
20
°d,, \°i
15
x
10
~
.\ ,,
'
!
~Z
×
o /
0
~ttl,~.,,.
0.'2
0.'4
O.6
0.8
1.0 X
Fig. 37. The dependence of induced anisotropy on the composition in the system CoxFe3-xO4(Iizuka and Iida 1966). The reduction decreases the concentration of Co3+ ions.
N i - F e and other iron rich spinels
Induced anisotropy and various after-effects were studied in several systems containing Fe 2+ ions usually simultaneously with cation vacancies. Typical examples are iron rich Ni and Mg ferrites including magnetite (Motzke 1962, 1964, G e r b e r and Elbinger 1964, Wagner 1961). In pure magnetite with a slight oxygen excess an induced anisotropy of G type was observed (Knowles 1964) possessing a relaxation time ~ 2 0 s at room t e m p e r a t u r e . This is compatible with the preferential occupation of certain octahedral positions by vacancies. The magnitude and temperature dependence of G may be brought into reasonable agreement with the mechanism of a vacancy dipole-dipole contribution (eq. 34). In a m o r e recent study (Kronm/iller et al. 1974) the corresponding after-effect was shown to be composed of two processes which were attributed to different distributions of Fe 2+ and Fe 3+ around the vacancy. Only recently Brtining and Semmelhack (1979) have also reported F ¢ 0 and directly proportional to the cation vacancy concen-
OXIDE SPINELS
253
tration in their magnetite single crystal. The ratio F / G was practically independent of vacancy concentration ( F / G = ½). In mixed spinels, particularly Ni-Fe and Mg-Fe ferrites, the relaxation spectrum corresponds to two distinct magnetic annealing processes (fig. 38). One of them (observable around room temperature) is similar to that discussed above; in addition to the G term it possesses also an F term proportional to p x ( 2 - x ) , x and p denoting the concentration of Ni 2+ (or Mg 2+) ions and vacancies, respectively. This indicates the active role of vacancy-Ni 2+ pair ordering. The other process with the annealing temperature -300°C was usually found to be of pure F type with F proportional to x2(2- x) 2. It does not depend on p. This points to an ion pair ordering while the role of vacancies is believed to be similar as previously discussed for Co 2+ substituted magnetite, i.e., they increase the diffusion rate and lower the annealing temperature. For historical reasons these processes are usually denoted as III (lower temperature process) and I in the literature. An additional effect (II) lying in the region between I and III and reported in some papers was shown to be due to cobalt impurities. The magnetic annealing spectra of Mn-Fe spinels are a little more complicated (fig. 39) and were discussed, e.g., by Krupi~ka and Vilim (1957), Krupi~ka (1962), Marais and Merceron (1965) and Braginski and Merceron (1962). In particular, an additional effect labeled as IV with lower activation energy was observed below room temperature. It was ascribed to vacancies forming some complexes, e.g., with Mn 3+ and Fe 2+ ions. A similarly positioned induced anisotropy effect was observed in Ti or Sn substituted magnetite and ferrites (Knowles and Rankin 1971, Knowles 1974) where formation of some Me 4+ containing complexes (e.g. Ti4+-Fe 2+ pairs) may influence both the vacancy migration rate and the resulting induced anisotropy. For Ti substituted magnetite the corresponding anisotropy was found to be of G type (Knowles 1974). Let us note that by properly adjusting the concentration of Ti 4÷, Fe 2+ and cation vacancies the effect III may be suppressed so that practically only IV remains (fig. 40); this is important for the ferrite materials design.
1000
f
"~ 800
i
/
~<- 600
o
/
400 o o. . . . .
200
~-o-o-
/o /
...~o/
o
0
100
200
300
400 T(°C)
Fig. 38. The dependence of induced anisotropy in Ni0.4Fe2.604 on the annealing temperature Ta. Measurements were performed at -75°C after 10 minutes anneal at 7". (Motzke 1962 and 1964).
254
S. KRUPI(~KA AND P. NOVAK i
~,o"
,
,
0.4
i
i
i
,,, r~o
0.3
4,
Pf \
0.2
I',°,x
,vii>: \/7!,o
0.1
o-o-~-n,0 ',,,100 200,°'W,300 400 .,: '~
-200 -100
T(K) i
/o,,oo-O-'E
. . . .
i
5000 0
0~00 ~ 0 _ 0 . 0 #"
I
o
3000
[ 0
! 1000
oO.oop ~ 0~
-200 -100
I
I
0
I00
200 300
400 T (K)
Fig. 39. Comparison of the disaccommodation spectrum and the induced anisotropy for M n 0 . 2 F e 2 . 8 0 4 . 0 i (Marais and Merceron 1965).
~l~Ip(°lo)
/
III O.6 -
~
0.4
J
0.2 -50
4
~
~
/
~
iis/II
\k N 0
+50
+I00 Temperature °C
Fig. 40. Disaccommodation spectra for two Ti substituted MnZn ferrites; (A) Mno.68Zno.32+ " 3+ . Fe0.11Tlo.09Fe18204, (B) Mn0.64Zn0.3Fe~lTio.osFe3~O4;after Knowles and Rankin (1971). The DA maximum for MnZn ferrites without Ti is indicated by a dashed line.
OXIDE SPINELS
255
A further process was reported to appear at higher temperatures (350°C ~< T, ~< 450°C) in Mn and Zn substituted magnetite and was ascribed to reorientations involving also the ions in tetrahedral sites, i.e., Mn 2+ and Zn 2+ (Maxim 1969). The activation energies are rather high here, approximately 2 to 2.5 eV. In all processes mentioned above the presence of Fe 2+ ions is important because they may considerably enhance the induced anisotropy by their own contribution. As they coexist with Fe 3÷ ions in iron rich spinels they may also give rise to induced anisotropy and after-effects of electronic origin via the redistribution of valencies Fe2+ ~--Fe 3÷. A C magnetic losses are usually used for study of this effect (e.g. Kienlin 1957, K6hler 1959). Unless the concentration of Fe 2+ is too low, the activation energy is rather small, of the order of 10 -2 to 10 1 e V , and the kinetics is interpreted in terms of the electron hopping mechanism. Spinels containing M n 3+ and
C u 2+
Besides valency redistribution these ions may contribute to the magnetic annealing process by reorientations of local Jahn-Teller distortions (section 1.6). The most detailed study was p e r f o r m e d on the MnxFe3 xO4 system (Krupi6ka and Vilim 1957, Merceron 1965, Zfiv6ta et al. 1966, G e r b e r et al. 1966, Broese van G r o e n a u 1967, Broese van G r o e n a u and Pearson 1967, Marais and Merceron 1967, Krupi~ka and Zfiv6ta 1968, Y a m a d a and Iida 1968, Iida et al. 1968). The induced anisotropy measured on two series of samples given as a function of Mn content (fig. 41) demonstrates convincingly the effect of Mn 3+. The same effect is reflected in the part denoted as C of the magnetic loss factor spectra (see fig. 42). The corresponding activation energies lie between ~0.3 eV and 0.5 eV, close to the activation energy deduced from the electrical conductivity which supports the interpretation based on reorientation process correlated with the electron motion (Krupi6ka and Zfiv6ta 1968). The peaks B and A in fig. 42 may be attributed to
1000
,
800
200
, '
, ~
x
Ij
1.0
i
1.2
i
14
l
1.6
1.8 X
Fig. 41. Dependence of the induced anisotropy of MnxFe3-xO4+~, on the manganese content (Gerber et al. 1966). Samples were annealed at 1200°C at 760 mm Hg (a) and 10-2 mm Hg (b).
256
S. KRUPI(~KA AND P. NOV/~'(
0.4
~
B
.8~.
C
I
III I~
'
Ill/
',
lltt
A~
~
I
o
I s+
0.81
I
\1
X ebo
I \
/
/
lbo
I
\
\1 '1
ado
r (K)
Fig. 42. Magnetic losses vs T for MnxFe3 xO4+7 system. Figures show manganese concentration x; 1+ and 1- correspond to x = 1 with 3' positive and negative respectively (Z~v~ta et al. 1966, 1968).
Fe 2+~--Fe 3+ valency redistribution and to reorientation of free Mn 3+ distortions (i.e. not stabilized by electrons or other defects) respectively. The coexistence of peaks B and C in certain compositional range points to the coexistence of Fe > and Mn 3+ ions. Relaxation peaks similar to C were also found in other Mn and/or Cu containing spinels: M n - Z n (Okada and Akashi 1965, Giesecke 1959), Mn-Mg (Krupi6ka 1960), M n - C u (Krupi~.ka and Z/w6ta 1968). In Mn substituted Li ferrite (Marais et al. 1972) the magnetic annealing effect of Mn 3+ ions was found to be enhanced by clustering of these ions. 3.3. D y n a m i c s o f magnetization
Many ferrimagnetic spinels may be treated as collinear two sublatice ferrimagnets. In such systems the theory of ferrimagnetic resonance (e.g. Keffer 1966) predicts two resonance frequencies to+, w to occur. Neglecting the effects of anisotropy and demagnetization field, the lower one is given by (37)
to+ = y e f f H ,
with Ye~ = ( M , - M2)/(M~/y,
Mz/y2),
where MI, M2 are the sublattice magnetizations, and yl, 3/2 are respective gyromagnetic ratios. It is analogous to the simple ferromagnetic mode, except that the effective value Yen has to be substituted for the gyromagnetic ratio 3/. The higher resonance frequency to_ is related to the so-called exchange resonance frequency toex = n (72M1 - yIM2) ,
where n is the intersublattice molecular field coefficient.
(38)
OXIDE SPINELS
257
For H ~ AHex = n(M1 - M2), w_ = Wex-- y2~H,
(39)
with "Year= [T2(M1/3'1)- y1(M2/'Y2)]/(M1/yl- M2/T2), which demonstrates the dependence of both we× and o) on the strength of the inter-sublattice exchange. As this is rather strong in most of spinel ferrites ~Oexis expected to fall into the infrared rather than microwave region. This is presumably one of the reasons why the exchange resonance was not yet unambiguously detected in spinel ferrites. M o r e o v e r the exchange resonance may be excited only if Y~ ~ Y2 (Schl6man 1957). The effective gyromagnetic factor ")/eftin eq. (37) is connected with the effective spectroscopic splitting factor gen through the relation Yen = e/(2mc)ge~r = e / ( 2 m c ) ( M l - M 2 ) l ( M 1 / g l - M21g2).
(4o)
For S-state ions (Mn 2+, Fe 3+) g is close to its free electron value 2.0023. In other cases the spin-orbit coupling modifies the value of g. Effective g factors as obtained from F M R in several spinels are given in table 26. The width A H of the resonance line is in most ferrites of the order of several tens Oe. Nevertheless in very pure Li, Mg and Ni ferrites AH--~ 1 - 2 0 e was observed (Yakovlev et al. 1971). On the other hand, values of A H up to 1000 Oe may occur in ferrites containing Fe 2+ in the B sublattice. The values of A H in ferrimagnetic spinels are summarized in table 27. T h e r e are several relaxation processes which are responsible for the linewidth in spinel ferrites (for detailed discussion see Sparks 1964, Patton 1975). In materials containing magnetic inhomogeneities such as surface roughness, grain boundaries or atomic disorder the two-magnon scattering is important. In many ferrites, however, the effect of so-called slowly relaxing impurities dominates. This is supposed to be the case, e.g., for systems containing Fe 2+, Co 2+ or Mn 3+ in the B sublattice or Ni 2+ ion in the A sublattice. Relevant mechanism requires the presence of two or more low lying anisotropic levels. The magnetization precession then modulates the energy separation between the levels. As a consequence, the thermal equilibrium population for each level changes with a period of precession. The induced transitions between the anisotropic levels then give rise to the relaxation effect. Note that a similar mechanism applies to the valence exchange Fe 2+ ~--Fe 3+ (Clogston 1955, Teale 1967). In this case the energy levels are connected with the hopping of a Fe 2+ ion between the B sites having different orientation of the local trigonal axis. The linewidth corresponding to the slowly relaxing impurities is strongly t e m p e r a t u r e dependent exhibiting one or two maxima (fig. 43).
S. KRUPICKA AND P. N O V ~ K
258
TABLE 26 Values of the g factor from FMR studies. System Fe304
T (K)
A (cm)
130 293
g
Ref.
3.35 1.25 3.35
2.08 2.09 2.17
1
1.25
2.13
3.2 3.2 3.2
2.060 2.019 (3) 2.004 (2)
2
2.00
3
2.6 (2) 2.7 (3) 2.27
4 5
MnFe204
4.2 77 300
(Mn, Zn)Fe204
4.2-300
1.25-10
295-310 363 473
0.37-0.64 1.25 1.25
CoFe204
NiFe204
293
1.25
2.19
6
Nio.95Fe2.os04
4.2-290
1.25
2.2
7
Nio.75Fe2.2504
4.2 85 290
1.25 1.25 1.25
2.16 2.19 2.13
7
CuFe204
77 300
1.25 1.25
2.44 2,09
8
MgFe204
77 473
1.25 1.25
2.04 2.005
9
Lio.sFezsO4
300
1.25
2.005
10
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Bickford, L.R., 1949, Phys. Rev. 76, 137. Dillon, J.E. et al., 1955, Phys. Rev. 100, 750. Schl6mann, E., Conf. Magnetism Magn. Materials, Boston, 1956. Assadourian, L. and L. Silber, 1976, AIP Conf. Proc. 29, 684. Tannenwald, P.E., 1955, Phys. Rev. 99, 463. Yager, W.A. et al., 1950, Phys. Rev. 80, 744. Yager, W.A. et al., 1955, Phys. Rev. 99, 1203. Miyadai, T. et al., 1965, J. Phys. Soc. Jap. 20, 980. Kriessman, C.S. and H.S. Belson, 1959, J. Appl. Phys. 30, 170. Schnitzler, A.D. et al., 1962, J. Appl. Phys. 33, 1293.
OXIDE SPINELS
259
TABLE 27 Values of AH in spinel ferrites. System
T (K)
h (cm)
AH (Oe)
Ref.
Lio.sFe2.504
134 300
6 6
0.88 1.68
1
Mno.4zMgo.61Fel.9504
290
6.1
2.5
2
MnFe204
20 300
1.25 1.25
Mnl.03Fel.9704
15 290
3.2 3.2
Mno.asZno.55Fe204
290
CuFe204
20 80
3
173 38
4
1.25
35
5
290 300
1,25 1,25
120 60
6
NiFe204
290 290
1,25 3,2
35 2
7 8
Ni0.95Fe20504
4.2 85 290
1.25 1.25 1.25
30 55 50
9
Nio,vsFe2.2504
4.2 85 290
1.25 1.25 1.25
40 120 140
9
MgFe204
290
6.1
Fe304
290
1.25
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
2.3
4300
Remark Ordered state
Direction [111]
8
Inversion = 0.89
10
Direction [100]
Remeika, J.P. and R.L. Comstock, 1964, J. Appl. Phys. 35, 3320. Lyukshin, V.V. et al., 1976, Izv. Akad. Nauk SSSR Neorg. Mater. 11,285. Heeger, A.J. et al., 1964, Phys. Rev. 134A, 399. Watanabe, Y., 1974, J. Phys. Soc. Jpn. 37, 637. Gait, J.K. et al., 1951, Phys. Rev. 81, 470. Miydai, T. et al., 1965, J. Phys. Soc. Jap. 20, 980. Yager, W.A. et al., 1950, Phys. Rev. 80, 744. Yakovlev, Y.M. et al., 1971, Fiz. Tver. Tel. 13, 1151. Yager, W.A. et al., 1955, Phys. Rev. 99, 1203. Bickford, L.R. Jr., 1950, Phys. Rev. 78, 449.
S. KRUPICKA AND P. NOV./d{
260 aH
(Oe)
i
o DI,)
800
600
\
•
Doo]
20O
5'o
1~o
1~o
260
2~o
T(X)
~bo
Fig. 43. Temperature dependence of the FMR linewidth for MsI1.46Fel.5404system (Zfiv6ta and Novfik
197a).
4. Other physical properties 4.1. Electrical properties 4.1.1. D C electrical conductivity and Seebeck effect Most of the oxide spinels not containing transition metal ions are very good insulators at room temperature. The A13+ spinels MgA1204, ZnA1204 and others may be mentioned as examples possessing electrical conductivity of the order of 10-6O-~cm -1 even at temperatures ~900°C (Bradburn and Rigby 1953). This behaviour may be understood as due to a large energy gap (often of several eV) between the occupied valence band primarily formed by the oxygen 2p states and the empty conduction band. The actual values of electrical conductivity and the activation energies are then usually controlled by impurity levels within the gap. With the presence of the transition metal ions additional energy levels and/or narrow bands are introduced usually also lying in the gap. This need not necessarily change the picture of the electronic charge transport very much provided that transport within the partly occupied d levels (bands) themselves does not d o m i n a t e . In particular, many oxide spinels with 3d n ions in the A positions only possess a very low conductivity (fig. 44). The same is true for pure stoichiometric spinels having only one kind of ions on equivalent crystallographic sites such as the normal spinels ZnFe204 and CdFe204, or ordered Lio.sFezsO4. A considerable increase of the electrical conductivity is usually connected with the combined effect of disorder and the presence of cations able to change easily their valency states or actually coexisting with different valencies in the material.
OXIDE SPINELS
600
700
261 T °C 900 1000
800
'//!
,
/
104.5
(bV ×
R(#)
%/.o/
105.0
/
105.5
./
I×
.n~ . ~ ° I !,'o x
/o. /
106.0
/ /
// /
106.5
tOzo
x
17
lh
•
./ /
I
~%'b
./'.k_~Y"
f/
Zv
D
b
I 0 7 T ( K "1)
Fig. 44. Temperature dependence of the resistance for some Al spinels (Bradburn and Rigby 1953).
Typical examples are bivalent and trivalent Fe or Co ions in the B positions. The charge transfer may then be effectuated by hopping of electrons or holes between equivalent ions (valency exchange) which is a rather easy process (see, e.g., Verwey i951). The sign of the Seebeck coefficient (thermopower) is often helpful in clarifying the nature of the dominating charge carriers and the mechanism of their motion. A special case seems to be the vanadium spinels where besides hopping a nearly band-like conductivity may occur characterized by a drop of both resistivity and activation energy when the distance between neighbouring vanadium ions in B sites approaches (or decreases below) certain critical value (table 28, Rogers et al. 1963). A metallic conductivity was found in LiVzO4 ( V - V separation ~2.91 A, Rogers 1967). The most relevant for the scope of this book and perhaps the most often studied are the electrical transport properties of Fe spinels (ferrites) and their solid solutions. We shall start with magnetite Fe3+[Fe3+Fe2+]O] - which represents a rather singular case due to its high R T value of the DC conductivity (~250 fV~cm -1) and the peculiar character of the conductivity versus temperature dependence. Other ferrites may be regarded as belonging to systems of solid solutions MxFe3-xO4 where M stands for (usually bivalent) cations substituting Fe 2+ in magnetite or for combinations of such ions. Some of the substituting cations may also exist in higher valency states, e.g., Mn 3+ or Co3+; the relevant systems are then to be extended to include the mixed spinels with x > 1. In spite of a large amount of existing experimental data only few of them which have been obtained on well defined single crystals may be used to draw quan-
262
S. KRUPI(~KA AND P. NOVfid~
TABLE 28 Crystallograplaic and electrical conductivity data for vanadium spinels (after Rogers 1967 and Rogers et al. 1967).
Formula Mn[V2]O4 Fe[V2]O4
Mg[V2]O4 Zn[V2]O4 Li[V;]04
Lattice constant (A)
V-V separation (A)
Activation energy of electrical conductivity (eV)
8.522 8.454 8.418 8.410 -
3.014 2.990 2.974 2.973 2.91
0.37 0.25 0.18" 0.16 metallic*
* single crystal. titative conclusions about the n u m b e r of carriers, their mobility, activation energies etc. The other ones, particularly those related to polycrystalline samples, are to be taken with caution and may be explored mainly in a qualitative way. The discussion of the electronic transfer will be limited to conductivity and Seebeck effect. The evaluation of the Hall mobility is usually difficult due to a large contribution of the spontaneous magnetization for which no reliable theory seems to be available. Moreover, it has been argued that in the case of small polaron hopping which probably is the predominant transport mechanism in ferrites and related spinels no simple relation exists between Hall and drift mobilities (Adler 1968). It is usually admitted that the drift mobility is rather low, ~0.1 to 1 c m W - l s -1 for magnetite and much lower (10 -4 to 10-Scm2V-Is 1) for compositions approaching the stoichiometric ferrites (Klinger and Samochvalov 1977). As a rule, these values are deduced from conductivity or Seebeck effect measurements on the basis of some model, and no reliable independent method has been used for their determination. Even the magnetoresistance experiments though occasionally reported in the literature have not been interpreted from the point of view of electrical transport mechanisms (for a review see, e.g., Svirina 1970). M a g n e t i t e a n d substituted magnetite
The log o- versus T -1 plots for magnetite covering a broad t e m p e r a t u r e region are shown in figs. 45a and 45b. The Hall coefficient and mobility are displayed in fig. 46. At elevated temperatures (1500 K > T ~> Tc = 858 K) magnetite exhibits a semiconductive behaviour with thermally activated conductivity, which may be fitted (Parker and Tinsley 1976) by the formula: ~r = A T -~ e x p ( - q / k T ) ,
(41)
with A = 490 f~-lcm-lK and q = (99-+3)× 10 3eV. Note that eq. (41) can also explain the m a x i m u m in cr versus T observed at ~1100 K. In the vicinity of Tc (usually somewhat below) o- begins to depart from eq. (41); in a certain tem-
OXIDE SPINELS 103
.
.
.
.
102 ooooo-O--o~ o~ o~. 10~
263
250 ~ - p ~
.
"-O~ojO
~ 200
0.0~ 0
~(858K)
. . . . . .
I ~ 1oo~5°r o
O,lS eVJ" X
I0-'
I
. 50
i Lo~/ ternperef;ure transition
10-2
o
°"~t
' 4o0 . .800 ...
12oo (K)00',6
10-3 o
104
\o
10 -5
°~o
10-6 10-7 0
,
,
i2
14
f.o3e~,~o.. /6
18
20 loao/r
22
24
(K-')
Fig. 45a. Conductivity vs temperature for a single crystal of Fe304 (Miles et al. 1957).
-200 I
-205
"-•-210
~o
\2
o...-
o
-215
~o o
-220 o
-225
[! \ '%/ ?
-230
/
'°
o
-235
NO
~°,,o 4 i
r~
2
- ~ o - o - o . ~
3
4
-240
1ooo/T (K-~) Fig. 45b. Resistivity vs temperature for several specimens of magnetite (Parker and Tinsley 1976); (1) Stoichiometric single crystal, (2) oxygen defficient polycrystalline specimen Fe300.3988, (3) stoichiometric polycrystalline specimen, (4) single crystal according to Smith (1952).
264
S. KRUPICKA AND P. NOV/~K
10~ & i0 ~ (cmalc)
///
10 1
o~
bo
rv
1o-1 lo-2 10-3 O_ o
104 0.50
--0 I
t
I
I
I
i
i
i
E
~u 0.20
(cm2/VS)o 1o o~ 0.05
["
0-. 4 I
0.02 2
I
[
I
IO00/T (K 4) Fig. 46. Ordinary Hall coefficient R0 and Hall mobility/zH vs temperature (Siemons 1970).
perature interval it behaves metal-like with negative temperature coefficient and in the vicinity of room temperature it passes a new maximum. At Tv = 119 K magnetite undergoes a phase transition (the Verwey transition ) accompanied by a sudden decrease of conductivity of about two orders of magnitude. Below this it behaves like a semiconductor with a temperature dependent activation energy, at least down to ~10 K. Attempts have been made (fig. 47) to fit the or versus T dependence in this region to Mott's formula; o" = A e x p ( - B / T W 4 ) ,
(42)
derived for variable range hopping (Mott 1969). It was early recognized (Verwey and Haayman 1941) that the transition in magnetite at 119 K is connected with some kind of electronic charge ordering and a model was proposed for it based on regular arrangement of Fe 2+ and Fe > ions in rows parallel to [110] and [110] directions, respectively (Verwey ordering). The more recent models, partly based on new neutron diffraction, NMR and M6ssbauer data either abandon the presumption of definite ionic valencies (Cullen and Callen 1973) or correspond to more sophisticated ordering schemes of Fe 2+
OXIDE
265
SPINELS
~
T(K) n
2
n
I
I
n
I
o0%0
0
%%
o
.t%o
-2
"to
%
E
o
,o, %
t~ -6
'oo
c3
oI
-8
q
-10
o
-12 %
-14
~o
\%%o OoooO
O.2
Oi3
0 .'4
0'e 05 T@ (K)@
Fig. 47. log cr as a function of T -1/4 for Fe304 single crystal, after Drabble et al. (1971).
and Fe 3+ (Hargrove and Kfindig 1970, Fujii et al. 1975, Shirane et al. 1975, Iida et al. 1976-1978, Umemura and Iida 1979). These models assign the low temperature phase rather as monoclinic than orthorhombic. It is clear that any model explaining the electronic conductivity in magnetite also has to explain (or at least to be compatible with) the Verwey transition and vice versa. It must also account for the anisotropy of o- below this transition (Chikazumi 1975, Mizushima et al. 1978). The common feature of recent models of conduction in magnetite is the splitting of electronic 3d 6 levels of Fe2+(B) in the ordered phase by an energy gap of ~0.1 eV; only states below this gap are populated at 0 K because the number of Fe 2+ is half the number of the octahedral sites. The electronic charge transport is then effectuated by carriers either created by thermal activation across the gap or introduced by impurity atoms or oxygen non-stoichiometry. The separated levels are usually supposed to form some kind of narrow subbands that overlap above the Verwey transition. In the simplest case a tight-binding scheme combined with Coulomb repulsion was used which leads to a Hubbard-type Hamiltonian for description of the situation (Cullen and Callen 1970, 1973, Fazekas 1972). More refined theories include also polaronic effects (electron-phonon interaction) and other short-range energy contributions, included spin correlation and exchange effects (Haubenreisser 1961, Klinger 1975, Klinger and Samochvalov 1977 and ref. therein, Buchenau 1975).
266
S. K R U P I C K A A N D P. N O V A K
Due to the polarization effect upon their surroundings the electrons are usually supposed to be not entirely free to move below the transition and their transfer is described as a polaron hopping process, perhaps except at the lowest temperatures (<10 K) where polaron coherent tunelling might dominate the conduction. Above the Verwey transition the long-range order disappears and the energy gap between both subbands collapses accompanied by a sudden increase of the carrier number. The complicated temperature course of cr is then believed to result from a combination of narrow band conduction, short-range correlation of polarons and scattering processes connected with spatial charge and spin fluctuations. The loss of magnetic order at Tc seems to modify also the electronic structure (Parker 1975). The recent M6ssbauer study (Lu-San Pan and Evans 1978) indicates that at T > Tc the Fe z+ valency states may appear also in the A sublattice which may play a role in changing the character of the conduction process. The effect of small substitution or oxygen non-stoichiometry is twofold: The ordered phase becomes imperfect which lowers the temperature of the Verwey transition and makes it disappear for a certain critical impurity concentration. Besides, the ratio [Fe2+]/[Fe3+] is changed which introduces carriers into one of the split subbands (holes into the lower filled band or electrons into the empty higher one depending on the kind of impurity). In fig. 48 the thermopower versus temperature is plotted for single crystals with various degrees of oxidation. The
"~l
40
-40g
~"
-oi ~/,~ l
•
•
I
...
-
Ill
I,IIII
~-~,~
•
"
C
_,of \O.o/ o/ -200
/
'
"o
eo
s2o
1so
200
2~o
80
I2o
T(K)
Fig. 48. Absolute thermoelectric power vs temperature; after Kuipers (1978). (a) Experimental data for various magnetite single crystals. T h e lines are only meant as a guide to the eye. T h e vacancy concentration decreases from A to E. (b) Calculated values according the model of Kuipers and Brabers (1976), T denotes the cation vacancy concentration per formula unit.
OXIDE SPINELS t
,
i
267
,
,~ x : 8 . 1 0 -3 x x=3xlO v
-3
×=O
+ x' = 10 -4
0
~: : 1 0
"a
o x : 4 x l O -4 ,,?
\;:<:\ 0,% *,-o,
-2
,%\\
-3
-4
a i
i
I0
L
i
I°x
12
14
16
103/T (K -') 60 (lJ V. g -~ 2~ 0 )
-20
:~
t
-60
o Q.
£ co
- I00 ox:O
. x = l O -4
~,~. '~ ~. ~L PA
F..
,~ x = 4 . 1 0 -4 • x= 10 -3 x x : 3 ~ 10 -3
j - 180
/ 4.
b -22o
+ x = 8~10 -3
~o
1~o
1~o
I
2bo
240 T(K)
Fig. 49. Electrical properties of Ti-substituted magnetite Fe3-xTixO4 (Kuipers 1978). (a) Conductivity vs temperature relation. (b) Absolute thermoelectric power vs temperature.
268
S. KRUPICKA AND P. NOV,~K
tendency of the Seebeck coefficient to become positive toward low temperatures is in agreement with the presence of positive charge carriers (holes) introduced into filled Fe 2+ subband by increasing the oxygen content and with possible temperature variations of their mobility. This also demonstrates the sensitivity of the ordered phase upon the oxygen non-stoichiometry; above the transition, on the other hand, the influence is poor because both subbands overlap and the relative change in the carrier number is very small. The impurity ions have similar effect as the cation vacancies: cations with valencies 1 or 2 diminish the number of Fe 2÷ and introduce holes; cations with higher valencies act as donors. But in both cases the effect is again small above the transition temperature. As an example of the higher valency substitutions the behaviour for Ti substituted magnetite is given in fig. 49. The lowering of the transition temperature introduced by various dopants is demonstrated in fig. 50. The critical concentration for the disappearance of the Verwey transition is usually about 0.1 per formula unit.
o\! 8
o
Ni
~, Co • AL • Cr
z~T
-5
-5
-10
-I0
-15
-15
o.b7
doe
0.03
Oa
M9
•
Zn
"'"
(K)
(K)
•
o
\ o
0.01
?.02
X
0.'03
Fig. 50. Lowering of the transition temperature Tv by various dopants (Miyahara 1972).
Stoichiometric and iron rich ferrites If the concentration of ions substituted in magnetite increases the resultant fluctuations of the electrostatic potential make the free motion of electronic carriers more and more difficult. With certain critical concentrations practically all carriers, i.e. the Fe 2+ valency states, are localized in local potential minima for T ~ 0 K. This is called the Anderson localization (Anderson 1958, 1970, Klinger and Samochvalov 1977). At finite temperatures, however, they may be thermally
O X I D E SPINELS
269
activated to hop to other places (ions) and contribute in this way to the electrical transport. The existence of hopping in the Fe2+-Fe 3÷ pairs in condition of a fluctuating local potential was demonstrated in M6ssbauer spectra of Ti substituted Zn ferrites (Van Diepen and Lotgering 1977). The o- versus T dependence may usually be fitted by the exponential law o-= A T -~ e x p ( - q / k T )
/3 = 0, 1
or
_3 2~
(43)
in a fairly broad temperature region. For bivalent substitutions the activation energy q varies from several hundredths of eV for Fe 2+ content to ~0.2 to 0.6 eV for compositions close to stoichiometric ferrites MFe204 (fig. 51). As was shown by Miyata (1961) the preexponential factor A is almost fully determined by the Fe 2+ content and practically does not depend on the kind and concentration of the other cations present. At low temperatures an application of eq. (43) to the experimental dependences would lead to gradually diminishing the effective activation energy which in the low temperature limit can be approximated by the Mott formula ( 4 2 ) - s e e , e.g., Simga and Schneeweiss (1972), Kuipers (1978). Representative room temperature values of electrical conductivity are given in table 29. According to the small T A B L E 29 Representative room temperature electrical data of spinel ferrites. Composition Fe304 (") Lio.sFe2.504 (a) Mno.5Fe2.504 (a) Mnl.0Fe2.oO4 (a) Mn12Fe1.804(~) Ni0.67Fe2.2304(a) Ni0.96Fe2.0404(a) CoFea.94Ti0.0304 (a) Co0.99Fez0104 (b) Cot.01Fel.9904 (b) Cu0.97Fe2.03O4(b) MgMn204 c°)
(r (~-1 cm a) 250 3.6 39.8 0.45 1.6 × 10-4 6.65 0.016 0.13 1.4 x 10-3 8.0 x 10-8 0.01 2.5 × 10-5
q (eV) nearly metallic 0.17 0.06 0.08 0.35 0.08 0.28 0.14 0.22 0.56 0.15 0.36
a (~VK l) -48
1
-500 - 118 -350 - 1000 - 328 -210 - 558 -460 +800 -- 40 +97
2 3 3 3 4 2 5 6 6 7 8
(~)single crystals (b) polycrystals 1. 2. 3. 4. 5. 6. 7. 8.
Ref.
Kuipers, A.J.M., Thesis, Technical Univ. Eindhoven (1978). Austin, I.G. and D. Elwell, 1970, Contempt. Phys. 11, 455. Simga, Z. et al., 1972, Proc. 11th ICPS Warsaw, p. 1294. Yamada, T., 1975, J. Phys. Soc. Jap. 38, 1378. Yamada, T., 1973, J. Phys. Soc. Jap. 35, 130. Jonker, G.H., 1959, J. Phys. Chem. Solids 9, 165. Rosenherg, M. et al., 1966, Phys. Status Solidi 15, 521. Rosenberg, M. and P. Nicolau, 1964, Phys. Status Solidi 6, 101.
270
S. KRUPI(~KA AND P. NOV/MK b-
0 "a
x. x x o xx x
o
o
= ;.=
q
~~
0,-
["-:" ]
-,% °\°,,.
"
\o 0%
xu ~'o
--o
Xx
\
0 ~
o,.,
qb~ O ~
E
0
x
h
~\
h \
&
-0\,%, °
'q
>~
4-
xx
o,
¢.~
~ 0
,q
-,,
~X °\
%
~
h\
\
"°\ °
~o
h h
N×
h h
\ X
[]
i
i
i
i
""
~'
,'7
,'?
i
i
i
i
~i
i
.
'
-4i
i
i
'
%1
o
~?1
z:Z~
A
•=
~"
~
t"-
i
Oo/, I,/
ob
,.~
+~
o
~E
~N.. ~ ~ 0 0
!I
~' o/
~
l---.B II
o
o
~;
/.Oo
o.O°o'~
II
oqo
I
oo / .
~
/ i
o--i
*o
Io, - / o l . o / t
'
~ o, ,o/iA,o~/,~ / o io,/o~,%.,o~ ~1
/
d°
,6
i,%o.O /
i
,po
i
~
P /
P
o
,o
/o 7, ??b%" :o -o'~
o ,d
%
,
/
/
l o / ¢ / /.o~ z
Io
~o ~,
.7V.
o
op
~ 1 ~ '-~
_o
io .,~.
/
/
oo/iO _o.O.O "-~" o ---°°°~ -
oo~.Oi~
~
i
I
I
~,
+ +
+o ~o
,--4 ~ . ~
~
~ZN
,-
OXIDE SPINELS
271
polaron hopping model which is believed to be relevant for the conduction mechanism of ferrites, the activation energy q is the sum of the energy qn needed for removing the electron from an Fe 2+ (i.e. the binding energy of the polaron) and of the mobility activation energy q~ connected with transferring an electron between Fe 2+ and Fe 3+ ions. q. may be directly deduced from the Seebeck coefficient versus T -1 dependence; examples of these dependences are given in fig. 52. ].0
i
~Oo
E
a
b.6
ox~o
0.4
-o
\
io
~
o~o-o ........
O. 2 ~-,,~o..~o.-e..o _o.
[~7 r
4 ~ ° '''~"
0~°~0
o.o_o.o-o--o--
&
O,
o--O--°
L
100
3
o~ o - o - - o _ o _ c-.- 4
~
300
I
500
700
900 T(K)
4
o CoFe~.9~Tioo30~ x Nio.e~.Fe2.330,~ ~' Mn°~Fezs04 o MnFe2q
.o"
Ioc
2.3
)
/ °'°
°°
/o 3
o
/
/°
o
a
/e ~
x~O X /
a
a
X
X
X
X
2 ~ -×I" / x~ ~.i
z&
z~
z~
x
z~
b o
'
~
'
;
'
~
'
8
'
1'o ' 1~ lOa/T (K -1) Fig. 52. Seebeck coefficients vs temperature relation for ferrites with various Fe 2+ content. (a) Polycrystalline samples (after Klinger and Samochvalov 1977): (1) Ll0.sFe0.0olFezsO4, " 2+ 3+ . (5) N"10.sFe0.2Fe2 2+ 3+04; (2) (N10.3Zn0.7)o.99Fe0.mFe2" 2+ 3+04 ,. (6) Ni0.6Fe0Z74Fe~+O4; (3) (N10.3Zn0.7)0.964Fe0.036Fe2" 2+ 3+O4," (7) Zn0.4Fe02+6Fe~+O4; (4) (N10.3Zn07)0.89Fe0.nFe2' 2+ 3+O4,. (8) Fe~+Fe3+O4. (b) Single crystals, measurements by Y a m a d a (1973) (©), Y a m a d a (1975) (x), Simga et al. (1972) (A), (Eli).
272
S. KRUPICKA AND P. NOV~d( 12
tog ~ 10
O-
9
O~D,...,,~ - D - -
8
6
/ a
I
I
0.02
o.o~
0.'o6
o.b8
o.'1
E,
Fe2 +
f,.,,/r~2 + 6o 2+ Ni 2÷
b Fig. 53. (a) Influence of Mn and Co additions on the resistivity of Mg and Ni ferrites (Van Uitert 1956a, b, 1957): (1) MgFel.aMnxO4; (2) NiFel.gMnxO4z; (3) NiFel.gCoxO4_*. (b) The relevant level diagram (Elwell et al. 1963).
O X I D E SPINELS
273
When approaching stoichiometric ferrites MFe204 (M bivalent) both resistivity and activation energy are increased due to the lack of Fe 2+. This is because the energy levels of M 2+ ions are usually situated below those of Fe z+. From experiment we have the following sequence of levels: N i 2+ < C o 2+ < M n 2+ ~ F e 2+ ,
which at least at low temperatures prevents the occupation of an Fe 2+ state unless lower lying levels of M 2÷ are filled up (Lord and Parker 1960, Parker and Smith 1961, Elwell et al. 1963, 1966). This has been exploited in preparation of high resistivity ferrites using small additions of Co or Mn to, e.g., Mg or Ni ferrites (see fig. 53; Van Uitert 1956a, b, 1957). MnxFe3-x04 and CoxFe3-x04 systems
Some transition metal ions, e.g. Mn or Co, may exist in spinels like iron with various valency states. This enables us to extend the MxFe3-~O4 systems (M = Mn, Co) into their iron deficient regions. The relevant dependences are given in figs. 54-56. In CoxFe3-xO4 the Seebeck coefficient changes its sign at x = 1 where the valency exchange Fe2+~--Fe 3+ is replaced by Co2+~-~--Co3+; while the first corresponds to the electron (n-type) transport in the second one the Co 3+ holes hop from one Co 2+ to another. In MnxFe3 ~O4 the situation is more complicated because together with x the degree of inversion also changes (see section 1.5). F e 3 0 4 is an inverse spinel but MnFe204 is an almost normal one. It follows that there are still enough Fe ions in the B sublattice for 1 < x ~< 2 to play an active role in the conduction mechanism; it is only necessary to create carriers by exciting some electrons to Fe 2+ levels. This is the reason why the Seebeck coefficient does not change its sign at x = 1.
I0 8 6
(kT) 4 2 0 -2 -,~ -6 -8 -10 -12 -14 It) °Co
5
0
S
lO %Fog
Fig. 54. Thermopower e~-= e0T for COl-xFe2+xO4; 0.1 > x > - 0 . 1 (Parker 1975). Measurements of Jonker (1959) taken near 370 K. The full line was calculated by Parker.
274
S. KRUPICKA AND P. N O V ~ 8
i
~
i
z
t
i
~...x.°l i..>o
In R
o"
o.z
oO }
qCov)
6
0.6 _o.-~
5
__._....-..'"
~o~'~i ~1
0,5
/I
e
"~" ~'O~'o_
oe
1
0
o.1 L
I
I
I
1.10
~05
1.00
0.95
I
0.90 x
Fig. 55. Room temperature resistivity p and activation energy q for
i
0.5
" o x
q (ed
z~
CoxFe3-x04 (Jonker
1959).
I
Miyata
/
Lof:gering
Sim[a
o
1961 1964
/
1972
0.4
/ /o 0.3
z~
t°
0.2
0.1
05
10
15 x in Mn, Fea_~O~
Fig. 56. Activation energy of conductivity for MnxFe3-xO4 (Lotgering 1964, Simga et al. 1972).
OXIDE SPINELS
275
4.1.2. Dielectric constant
There are not many reliable data on dielectric constant E of ferrites and related spinels measured on the single crystals. The intrinsic E values were usually found to lie between 8 and 20. The very high dielectric constants often observed at low frequencies (fig. 57) have been ascribed to the effect of heterogeneity of the samples, i.e., pores and/or surface layers on grains, causing poor electrical contact between them (Koops 1951, Heikes and Johnston 1957, Krausse 1969). Sometimes some electronic polarization effect is supposed to be connected with the conduction hopping mechanism itself (and with some microscopic inhomogeneities related to it) which also could contribute to the low frequency dispersion of E (Rabkin and Novikova 1960, Rezlescu and Rezlescu 1974). For a general outline see Bosman and Van Daal (1970). At higher frequencies (cm wavelengths) the measured values may be regarded as insensitive to both of these contributions and they are usually taken as actual intrinsic dielectric constants corresponding to normal ionic and electronic polarizations. Some typical E values are given in table 30. In the frequency region of the lattice vibrations the ionic polarization becomes slow and damps out (infrared absorption) while the electronic polarization is fast enough to persist to the region of electronic excitations in near infrared and visible parts of the spectrum (crystal field and charge transfer transitions). To estimate the relative contribution of ionic and electronic polarizations, E measured in the near infrared and at microwave frequencies have to be compared. For NiFe204 the near infrared value is e ' = 7.0-+ 0.5 at A ~ 5 ~m (Miles et al. 1957). Taking E ~ 10 for the microwave region (see table 30) the contribution of ionic polarization would be ~3. As far as the temperature dependence is concerned, E usually increases with increasing temperature together with the electrical conductivity (Ioffe et al. 1957). Some Cu containing spinels were reported to show anomalies, however, in both temperature and frequency
i
1o5
!
.104
i
i
2
103
3
102 -
I0
6 1
10 2
103
1
104
1
105
t
10 6
1
10 z
108
Fr'equeney in els
Fig. 57. Dielectric constant e for various polycrystal]ine ferrites measured as a function of frequency (Van Uitert 1956b): (1) M n - Z n , (2) Cu-Zn, (3) N i - Z n , (4) NM1350, (5) N1250, (6) NM1250.
276
S. KRUPI(~KA AND P. N O V ~ TABLE 30 Microwave values of complex dielectric constant for some ferrites. Formula
Frequency (GHz)
E'
E"
Ref.
4.5
13.40
3.520
1
4.5
8.88
0.155
1
10 9.2 4.5
15 12.17 9.30
1 1.38 × 10-4 0.475
2 3 1
NiFe204 quenched NiFe204 slowly cooled Ni0,sZn0.sFe204 Ni0.gZn0.tMn0.02Fe204_+ MnFe204
1. Okamura, T., T. Fujimura and M. Date, 1952, Sci. Repts. Res. Inst. Tohoku Univ. A4, 191. 2. Miles, P.A., W.B. Westphal and A. von Hippel, 1957, Rev. Mod. Phys. 29, 279. 3. Kankowski, E.F. (unpublished)-after Von Aulock, Handbook of Microwave Ferrite Materials (Academic Press, New York, 1965).
dependences (Rezlescu and Rezlescu 1974). Note that relaxation maxima were observed in the temperature and frequency courses of the dielectric loss factor in the kHz r e g i o n - s e e fig. 58 (Kamiyoshi 1951). The interpretation is not entirely clear, however. The correlation of the relaxation maxima to the Fe z+ content and to the relevant electron hopping is demonstrated in fig. 59 (Samochvalov et al. 1967, see also Mizushima and Iida 1967, Mizushima et al. 1978). Z5
~ rj
Q) o
o" '
tab
~o '
I
- 50
0
100
50
r (°C) Fig. 58. tan 6 vs temperature at various frequencies f o r a slowly cooled CoFe204 (Kamiyoshi ]95]).
4.1.3. Optical and magnetooptical spectra The difference between the dielectric constant measured at microwaves and the one determined from the refractive index in the near infrared is typically ~ 3 to 10. It primarily corresponds to dispersion due to the phonon excitations w h o s e
O X I D E SPINELS 40 30
E', E'"
I
/,°
oO oo°
ooo°°°
15
30
C'
277
.°°e/ o
oT
U 2.o
/
o
o/
¢. 2 6 I oo°1 o ° 50 I00 T(K)
2.' o~'~ olo
c
o/ d
/o
2o
~o o-'1
o'
/o/~
"re/
/
Z,/' ..oy,o I -2" \o 10
~
__ol
o.o~ -o-
_"o°-- o- °~~ °o'-°o
"o,., ~ o~ /o / o o x
i..~o- io-c,-
~C~c - / / o
c,*
13
3"o
o_o=OL.oJ 0 ~°o9.~8°--#-°6"~cr°, 200
-
, ZOO
,
600
r(K) Fig. 59. Temperature dependence of the complex dielectric constant of magnetite (in the insert) and ferrites (Ni0.3Zn0.7)>xFe{+Fe204; (1) x = 0.085; (2) x = 0.049; (3) x = 0.01 (Samochvalov et al. 1967).
frequencies are lying in the far infrared. As we are dealing here with electronic excitations we postpone the discussion of the phonon spectra to the next paragraph and discuss first the near infrared and visible regions. The absorptions due to optical phonons are situated mostly below 0.1 eV. At photon energies above this limit a region of relative transparency occurs in most oxide spinels that are electrical insulators. This optical "window" is particularly broad and clear if the crystal contains no paramagnetic cations. The presence of transition metal ions (3d"), especially in magnetically ordered state, makes possible various electronic transitions that involve the crystal field split levels of these ions. These transitions modify the absorption edge, usually defined by the onset of interband transitions, by extending it towards the lower energies and adding several more or less distinct peaks. The situation is similar to that one in garnets, particularly Y3FesO12 (YIG), that is perhaps the most thoroughly investigated ferrimagnetic oxide as far as the optical properties are concerned (see e.g. Scott 1978). The possible types of transitions in YIG are schematically indicated in fig. 60. The Y3FesO12 garnet contains two Fe 3+ sublattices with octahedral and tetrahedral coordinations, respectively, and with mutually antiparallel magnetizations. Hence the inverse spinel ferrites not containing other transition metal ions except Fe 3÷ are expected to exhibit optical properties analogous to YIG. The examples are Li0.sFe2.sO4 and MgFe204; their absorption spectra in the near infrared are given in fig. 61 together with NiFe204. It seems that the presence of Ni 2+ brings no qualitative changes in this spectral region. Between 1 and 2 eV there do not exist enough reliable data due to the poor transparency of the
278
S. KRUPICKA AND P. NOVekK
,p
~p (FO
4s (Fe)
aa (Fe 2,) "t
4 r, ~
2p (0 2-) tetrahearat
oclaheolral
Fig. 60. Schematic density-of-states plot for Y3FesO12 showing examples of various types of the optical transitions: (A) crystal field, (B) intersublattice Fe 3+ pair transitions, (C) 2p-+ 3d charge transfer, (D) 2p ~ 4s charge transfer, (E) 3d ~ 4d charge transfer; after Scott (1978).
samples. But the similarity to YIG may again be followed above 2 eV in fig. 62 where the diagonal elements of the dielectric function are plotted for both Li ferrite and YIG. Region 0.1 to i e V
The "window" between ~0.15 and 0.4 eV in fig. 61 is clearly indicated though it is not so deep and broad as in YIG. This may be at least partly due to imperfections (chemical non-stoichiometry, impurity ions, crystallographic defects). In particular, the optical absorption seems to be strongly influenced by the presence of octahedral Fe 2+ forming electronic charge carriers (see section 4.1.1). A good piece of evidence has been obtained by Sim~a et al. (1979, 1980) who studied the optical constants of MnxFe3_xO4 single crystals by reflectance and ellipsometric methods down to 0.5 eV and extended the spectra further to lower energies by Kramers-Kronig analysis. Figure 63 shows the spectral behaviour of the real and imaginary parts of the dielectric function. The peak in the vicinity of 0.5 eV which is very strong in magnetite (x = 0) diminishes with decreasing Fe 2÷ concentration (increasing x) and finally disappears for x ~> 1.1 where practically no Fe z+ is expected. The comparison with theoretical predictions points to the small polaron model which is adequate for describing this effect (Sim~a 1979). Similar low energy peaks were observed in magnetite also by other a u t h o r s - B u c h e n a u and Mfiller (1972) and Schlegel et al. (1979); the interpretation in the latter case was different, however, being based on the analogy with photoemission spectra.
OXIDE SPINELS
279
200 ! Log oc
(cmt)
2.0 \~. A
100 80
ii°sF°25
60
.__MgFe204
40 20 10 8 6 I I
I I
o.'12 o.~s
05
o'.~ o.'5 O.L6 0.1?0!8
05
E
(w)
Fig. 61. Near infrared absorption spectra of several spinel ferrites as compared with YIG (after Zanmarchi and Bongers 1969).
5
E,;'
,
",-,,
co'
~o
2
1
/
,/
....
YSo, o,~
-'--.
~Fe2.504
zo
i
a'o
i
42o
/~;
2
" ' ' ' Q i
51o
i
8.o
~o(eV) Fig. 62. Comparison of diagonal elements of the dielectric functions of Li ferrite and YIG (after Vigfiovsk!) et al. 1979b).
S. KRUPI(2KA AND P. NOVAK
280
14 12
l I t
I | I
10
I
8 6 4 2 I
i
I
i
I
I
~
I
I
"rT
__~~/~_ i
i
i
i
[
i
i
i
i
t
E;
7
",
/
~
.
Hn,,Fe.~G
Mno,~ Fe2,q
~
i
6 5 4 \
3
%
2 E(eV) i
i - -
E(eV) i
i
14, -r,
12-; ",
Fe~O,
Mno.5 Fe 2 5 O~
10 8
6
i
i
i
i
i
i
r
J
i
i
i
i
i
i
i
i
i
i
i
i
i
i
I
i
2
3
1
E (eV)
2
3
4-
E (~V)
Fig. 63. Real and imaginary parts of the dielectric function vs energy for Mn=Fe3-xO4spinels (Sim~a et al. 1979).
O X I D E SPINELS
281
Region 1 to 2 eV The transitions observed in this spectral range are usually identified as transitions between 3d levels split by the crystal field. For example, the steep increase of the absorption in NiFe204 in the vicinity of l e V (fig. 61) was ascribed to the Ni 2+ crystal field transition 3A2~3T2. This peak can be observed in the spectrum of NiO ()~ = 1.15 Ixm) and manifests itself also in a Faraday rotation dispersion of NiFe204 (Zanmarchi and Bongers 1969); its energy should be equal to the crystal-field splitting parameter zl = lODq. This transition, like all crystal field transitions in octahedrally coordinated ions, is parity-forbidden but may be allowed due to statical or dynamical violation of the local inversion symmetry. The parity restriction is not valid for tetrahedral cations (symmetry Td). On the other hand, the crystal field transitions in many cations including the important case of Fe 3+ are also spin-forbidden. The fact that in spite of the selection rules many of these transitions appear in the spectra can be understood when allowing a simultaneous excitation of a magnon so that AStot = 0 remains valid (see, e.g., Scott 1978). Another model uses the admixture of higher states via spin--orbit coupling (Clogston 1959); the spin is no longer a good quantum number and the spin constraint is automatically removed. But in most cases this fails to account for the observed oscillator strengths and some other effects (Scott et al. 1974, Dillon 1971). For assignment of various crystal field transitions the diagrams of crystal field levels for transition metal ions are being used (Sugano et al. 1970). The possible Fe 3+ crystal field transitions in YIG that should also occur in inverse spinel ferrites are listed in table 31. Note that the oscillator strengths are larger for tetrahedral coordination where the parity constraint is absent. T A B L E 31 Crystal field transitions in YIG at 77 K (after Scott 1978). Transition energy (eV) 1.372 1.804 2.000 ~ 2.100 2.445 2.568 2.652
2.792 2.994
Assignment 6Alg(65) --~4Tlg(4G) 6Alg(6S) ---->4T2g(4G) 6A1(6S) ~ *ra(4G) 6A 1(6S) ~ *r2(4G) 6A1(65)---)4E, 4Al(4G ) 6Alg(68) ~ 4Eg, 4Alg(4G) 6Alg(6S)-~ 4T2g(4D) 6A1(65) --~4T2(4D)
Site B B A A m B B A
Oscillator strength 2× 2× 8x 1.6 x 3.2 × 2x 1x 6x
10-5 10-5 10-5 10-4 10-s 10-s 10 -4 10-s
Region above 2 e V The spectra in this region are ascribed to charge transfer transitions, the most probable mechanism being the intersublattice transfer (Blazey 1974, Scott et al. 1975, Wittkoek et al. 1975), e.g.,
282
S. KRUPICKA AND P. NOVSd~ (Fe 3+) + [Fe 3+] + hu -+ (Fe 4+) 5~ [Fe2+]
(see fig. 60). Other possibilities are biexciton transitions, i.e., simultaneous crystal field transitions in both sublattices with AStor= 0 (Blazey 1974, Krinchik et al. 1977) or charge transfer between 02- and Fe 3+ (fig. 60). But the oscillator strengths depending on Fe 3+ concentration and the fact that the diamagnetic dilution in any sublattice influences all absorptions (Krinchik et al. 1979) indicate the first model involving [Fe3+]-(Fe 3+) pairs is correct. At still higher energies (above 3-4 eV) also orbital promotion ( 3 d ~ 4s) or interband (2p ~ 4s) transitions become important.
Magnetooptical effects Unfortunately there are only scarce experimental data on spinels which can be directly compared with the above conclusions. One of them is the Li ferrite, studied by Malakhovsky et al. (1974) and Vigfiovsk~ et al. (1979, 1980a, b). The other ones are Mn-Fe spinels including magnetite, systematically investigated by Simga et al. (1979, 1980), and Ni and Co ferrites studied, e.g., by Kahn et al. (1969), Westwood and Sadler (1971), Krinchik et al. (1977, 1979) and Khrebtov et al. (1978). On the other hand, the assignment of various transitions can be often supported and completed on the basis of the magnetooptical data. They include the Faraday rotation - mainly in the near infrared (up to 1 eV) and both polar and transversal Kerr rotations above l e V . Actually, many of the references given above are partly or fully devoted to the magnetooptical studies. Sometimes also the reflectance circular dichroism has been examined from which both Faraday and Kerr rotations may be calculated (see, e.g., Ahrenkiel et al. 1974a, 1975). All magnetooptical effects are intimately related to the off-diagonal elements of the dielectric tensor function; both diagonal and off-diagonal elements are complex so that besides the index of refraction and absorption coefficient two additional independent measurements are necessary for determining the whole dielectric function (e.g. Kerr rotation and Kerr elipticity). Examples of the magnetooptical spectra of Li0.sFe2.504 and some other simple ferrites as compared with those of YIG are given in figs. 64(a) and (b). The spectral dependences are similar but the sign of rotation in spinel ferrites opposes that in YIG due to the opposite mutual orientation of sublattice and total magnetizations in both types of materials. As the magnetooptical effects depend on both diagonal and off-diagonal elements of the dielectric tensor function their strengths (magnetooptical activity) generally does not simply correspond to the oscillator strengths of the underlying optical transition. In order to obtain large magnetooptic effects the transition has also to be highly circularly polarized. An example of strong magnetooptical activity are spinels containing Co 2+ in A positions (Ahrenkiel et al. 1974b). This has been ascribed to the crystal field transitions 4A2(F)--+ 4T2(F ) and 4A2(F)--+ 4TI(P ) of CO2+(A). In fig. 65 the spectral dependence of the reflectance circular dichroism for some of such spinels measured on polycrystalline layers are shown.
OXIDE SPINELS
283
200 Io/°
.o.o.t_e.o-m-- o----re.
,,:,~.~"
~gFe, o~
,%0
E
-200
-400 c_
,,'/
iJ "o/ /
T = 300°K • o experimenf.a~
--
calculated
~- - 6 0 0
,i -800 a
~
- 100~
,~
~-
~
'
~,avel.eng~.h X (~m)
i
i
O.04
i r.,~,
b
i •" i ; ',,. i ' "',,o~..~,,'-. ,
:d !
~
....":":: '~
i
i
\~ .~ / . , . / - E; L F "~.J ~.-- :,, y/:. ~:/~ ~' /
i
~;
"£
~'J
.
"
..
,. ...... ...... f"
•
..~ ,' /
C; Y / G ~ '
" ' iI
2
.
',.0....'!, \ :, : ,,'I ',, ,. "../'"..... \ "~" ,' / ' , ~'x ." -~;z_~_J;( ;.~- \ :'.-.Z.g '- .>q
-0.04
b
.
: "
i
y". .
-I'
r.
•-~
i
~-
"/ ,.
4
....
-
' Ie
~ phol;on energy (eV)
Fig. 64. Comparison of magnetooptical behaviour of Fe spinels and YIG. (a) Faraday rotation in near infrared (Zanmarchi and Bonders 1969). (b) Spectral dependence of the complex off-diagonal element for YIG and Li ferrite (Vi~fiovsk~) et al. 1979b).
S. KRUPI(~KA AND P. NOV/~d,~
284
~
~
T - - T - - T - - r - -
4
20
~
ReD (%)
Rco(o/o)
_ _ Co Rh, 5 Feo 50,; j ' .
12
2 ,,
,,
0
0 l
-4
-e ,,,,
\
ll~l
0.6
- 12
0.8
~
[0
1.2
~
1.4
~
¢.6
~
1.8
-20
Fig. 65. Reflectance circular dichroism of CoRhl.sFe0.sO4 and CoCr204 at 80 K (Ahrenkie] and Coburn
1975).
4.2. Mechanical and thermal properties 4.2.1. Infrared spectra The first important paper on the infrared spectra of spinels was published by Waldron (1955). To explain the experimental data obtained for seven ferrite spinels Waldron refers to a rhombohedral unit cell containing only 14 ions (for a normal spinel MFe204 it consists of two MO4 tetrahedra and one Fen tetrahedron). Four modes were found to be infrared active. Two of them, having the higher frequency, were supposed to arise from the motion of the oxygen ions, the remaining two were assigned to the motions of the cations only. Group theory, taking the full cubic crystallographic unit cell into account, was applied to the vibrational problem by White and De Angelis (1967) and by Lutz (1969). Waldron's conclusion that only four modes are infrared active in an ideal normal spinel was proved to be right, the origin of modes was, however, found to be more complex. Very thorough experimental investigation of infrared spectra of normal spinels, performed by Preudhomme and Tarte (1971a, b, 1972) confirmed the complexity of the problem. Typical infrared patterns for normal 2-3 spinels are shown in fig. 66, the observed frequencies are summarized in table 32. It is to be mentioned that Grimes (1972b) suggested an entirely different explanation of infrared spectra of spinels based on the two-phonon processes. The calculation of the force constants of thiospinels was performed by Brtiesch and D'Ambrogio (1972), Lutz and Haueuseler (1975) and Lauwers and Herman (1980). The last authors made corresponding analysis also for MgA1204 and ZnGa204 spinels. When the symmetry of the spinel structure is lower than cubic or/and supplementary ordering of cations exists, more infrared bands may appear (White and De Angelis 1967). A splitting of one infrared band is observed in some spinels containing octahedraUy coordinated Jahn-Teller ions Mn 3+ and Cu 2+ (table 33). It is to be noted that the bands may be split also due to the presence of two different kinds
OXIDE SP1NELS i
i
i
i
i
285 i
i
~
i
80 60 o~ 40 20 4° #_
_
i
__
8O 60 40 20
80 60 40
Zn Fe2 04
20 800
'
600
4bo
Cm-1
' 2bo
Fig. 66. Typical infrared patterns for three normal 2-3 spinels (Preudhomme and Tarte 1971b). of ions in the same sublattice. Such a splitting exists, e.g., in the system ZnAlxCr2-xO4 ( P r e u d h o m m e and Tarte 1971b). 4 . 2 . 2 . JUlastic c o n s t a n t s
There are only few spinels for which all the elastic constants are known. Corresponding values at room temperature together with the anisotropy factor A = 2 c 4 4 / ( c l l - cl2) are summarized in table 34 (for an isotropic material A = 1). It is seen that NiCr204 and to some extent TiFe204 differ markedly from other spinel systems as far as the elastic constants are concerned. This anomaly is connected with the cooperative Jahn-Teller effect (section 1 . 6 ) - f o r NiCr204 the corresponding critical t e m p e r a t u r e TjT is close to room temperature. In the vicinity of Trr the elastic response of the system is sensitive to the t e m p e r a t u r e - t h e crystal softens (at least to some extent) as TIT is approached. For the system NixZnl_xCr204 this softening is demonstrated in fig. 67. A similar situation exists also in TiFezO4 (see section 3.1.3) and FeCrzO4, the corresponding temperatures TjT are low, h o w e v e r , compared to NiCr204. For spinels which do not contain Jahn-Teller ~ions the elastic constants depend only weakly on the t e m p e r a t u r e (e.g. Kapitonov and Smokotin 1976).
S. KRUPIOKA AND P. NOV~6d~2
286
TABLE 32 Infrared absorption bands of several spinels.
System
Absorption bands (cm-1) /21 v2 /23 iv4
Fe304 NiFe204 CoFe204 MnFe204 ZnFe204 CdFe204 CoCr204 MgAI204 Fe2GeO4 NizGeO4
570 593 575 545 552 548 630 688 688 690
390 404 374 390 425 412 530 522 402 453
268 330 320 335 336 319 402 580 319 335
178 196 181
Ref. 1 1 2 3 4 4 4 4 5 5
166 197 309 178 199
1. Grimes, N.W. and A.J. Collet, 1971, Nature (Phys. Sci.) 230, 158. 2. Waldron, R.D., 1955, Phys. Rev. 99, 1727. Mitsuishi, A. et al., 1958, J. Phys. Soc. Jap. 13, 1236. 3. Brabers, V.A.M. and J. Klerk, 1974, Solid State Commun. 14, 613. 4. Preudhomme, J. and P. Tarte, 1971, Spectrochim. Acta 27A, 1817. 5. Preudhomme, J. and P. Tarte, 1972, Spectrochim. Acta 28A, 69.
TABLE 33 Splitting of the /24 band in three spinels exhibiting the cooperative Jahn-Teller effect (after Siratori 1967). Compound ZnMn204 Mn304 CuCr204
/2~ ,
/22 t
/24 $
c/a
265 cm-1 247 135
167 cm -1 165 194
232 cm -1 220 155
1.14 1.16 0.91
* Stronger line of the split v4. + Weaker line of the split /24' $ Weighted mean of the two lines.
I n t a b l e 35 t h e d a t a o n t h e e l a s t i c m o d u l i a n d t h e c o m p r e s s i b i l i t y m e a s u r e d o n polycrystalline ferrites at r o o m t e m p e r a t u r e are given. W e n o t e t h a t in a n a l o g y t o t h e m a g n e t i c r e l a x a t i o n , a n e l a s t i c r e l a x a t i o n w a s o b s e r v e d in s o m e s p i n e l f e r r i t e s ( G i b b o n s 1957, I i d a 1967) c o n n e c t e d w i t h d i f f u s i o n a n d r e a r r a n g e m e n t p r o c e s s e s in t h e l a t t i c e .
OXIDE SP1NELS
287
TABLE 34 Elastic constants of several spinels (in units of 10-11 dyn/cm) at room temperature. A is the anisotropy factor (see text). System
cx
MgA1204 Fe304 NiFe204 Lio.sFez504 ZnCr204 FeCr204 NiCr204 TiFe204
c~2
27.9 15.3 27.5 10.4 21.99 10.94 24.07 13.41 25.57 14.23 32.2 14.4 17.5 17.1 cu cm = 2.65
c44
A
Ref.
15.3 9.55 8.12 9.29 8.46 11.7 5.86 3.96
2.43 1.12 1.47 1.74 1.49 1.31 24.1 2.99
1 2 3 4 5 6 5 7
1. 2. 3. 4.
Lewis, M.F., 1966, J. Acoust. Soc. Am. 40, 728. Doraiswami, M.S., 1947, Proc. Indian Acad. Sci. A25, 413. Gibbons, D.F., 1957, J. Appl. Phys. 28, 810. Kapitonov, A . M . and E.M. Smokotin, 1976, Phys. Status Solidi a34, K47. 5. Kino, Y. et al., 1972, J. Phys. Soc. Jap. 33, 687. 6. Hearmon, R.F.S., 1956, Adv. Phys. 5, 323. 7. Ishikawa, Y. and Y. Syono, 1971, J. Phys. Soc. Jap. 31, 461.
vt3 f x=O
(krns")
2
?
o.~"
x : 0.37
TN oo• °
J
f
•
x = 0.73
."
e •
F
r.
(X) Fig. 67. Soft mode sound velocity Vt=[(Cll--Cl2)/2p] lj2 as a function of temperature in a NixZnl-xCr204 system. Ta, TN are the critical temperatures for cooperative Jahn-Teller transition and the N6el transition respectively (Kino et al. 1972).
4.2.3. H e a t capacity In f e r r i m a g n e t i c s p i n e l s t h e specific h e a t at l o w t e m p e r a t u r e s ( T < Tc, OD) is d o m i n a t e d by t h e m a g n e t i c c o n t r i b u t i o n . T h e t e m p e r a t u r e d e p e n d e n c e of Cp is t h e n w e l l d e s c r i b e d by t h e spin w a v e t h e o r y , w h i c h p r e d i c t s Cp ~ T a/2 ( s e c t i o n 2.4). A t h i g h e r t e m p e r a t u r e s t h e l a t t i c e c o n t r i b u t i o n ( p r o p o r t i o n a l t o T s f o r
S. KRUPI(~KA A N D P. NOV_,~d(
288
T A B L E 35 Elastic moduli of several polycrystalline ferrites; after Seshagiri Rao et al. (1971).
System
X-ray density (g/cm 3)
MgFe204 CoFe204 NiFe204 ZnFe204
Elastic moduli (1011 dyn/cm 2) E n k
4.52 5.29 5.38 5.33
19.73 17.34 15.59 18.64
7.34 6.54 5.89, 7.27
21.17 16.62 14.69 14.27
/3 × 1013 (cm2/dyn)
Poisson ratio
4.72 ,6.02 6.81 7.01
0.34 0.33 0.32 0.28
T < OD) prevails. An example of the temperature dependence of Cp is shown in fig. 68. In table 36 the values of C. at room temperature are summarized together with the values of Debye temperatures OD deduced from the low temperature measurements. Venero and Westrum (1975) noted that at elevated temperatures the lattice part of Cp for spinels may be well described by Kopp's rule based on the component oxides. For example for normal 2-3 spinels: Cp(AB204) = Cp(AO) + Cp(B203). T(K) 100
200
300
400
40
.-.
i....-- ............
,-"
"-'20
•
_~°~ /
//
/
t
~
,
,~
0
03
I
o"°
: / 0 L-'-'~°
600
mm.m.m"m "ww~m" mrm m m'm''m'm'am~
-~ 30
,o
500
~
10
/"
dO, "~
./ o/°/-Io,I ~o k
,
20
,
3'0
,
T(K)
I
40
Fig. 68. Heat capacity vs temperature for Li0.sFe2.504(O) and Lio.sAlzsO4 (O) (Venero and Westrum 1975).
4.2.4. Thermal conductivity Thermal conductivity is a composite e f f e c t - i n magnetic spinels besides phonons, both electrons and magnons may participate in the transfer of heat. It was shown,
OXIDE SPINELS
289
TABLE 36 Thermal properties of several spinels. Cp
K
ff x 10 6
(K-1)
(cal/K moo
Fe304 NiFe204
36.18 34.81
660 625(7)*
0.015 0.009
CoFe204 MnFe204 CuFe204 ZnFe204 MgFe204 Li0.sFe2.504
36.53
584 (10)*
0.015 0.017 0.015 0.015
MgAI204
Oo (K)
(cal/s cm K)
System
33.22 34.43 27.79
762 (15)* 512(5)
0.015 0.036
8
12 7.5 12 4.61t 5.905
Ref. 1, 5, 6 3, 4, 7, 12 3, 4, 9 8, 12 9 1, 6, 11 4 2, 4, 9, 14 3, 10, 13
* Nonstoichiometric samples. ~ Natural spinel. Synthetic spinel. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Bartel, J.J. and E.F. Westrum, Jr., 1975, J. Chem. Thermodyn. 7, 706. Venero, A.F. and E.F. Westrum, Jr., 1975, J. Chem. Thermodyn. 7, 693. King, E.G., 1956, J. Phys. Chem. 60, 410; 1955, Ibid 59, 218. Kouvel, J.S., 1956, Phys. Rev. 102, 1489. Polack, S.R. and K.R. Atkins, 1962, Phys. Rev. 125, 1248. Smit, J. and H.P. Wijn, 1959, in: Ferrites (Wiley, New York) p. 225. Kamilov, I.K., 1963, Sov. Phys-Solid State 4, 1693. Suemune, Y., 1966, Jap. J. Appl. Phys. 5, 455. Smit, J. and H.P. Wijn, 1954, Physical Properties of Ferrites, in: Advances in Electronic and Electron Physics (Acad. Press, New York) vol. 6, 83. Slack, G.A., 1964, Phys. Rev. 134A, 1268. Weil, L., 1950, Compt. Rend. 231, 122. Bekker, Y.M., 1967, Izv. Akad. Nauk SSSR Neorg. Mater. 3, 196. Singh, H.P. et al., 1975, Acta Crystallogr. A3I, 820. Brunel, M. and F. de Bergevin, 1964, Compt. Rend. 258, 5628.
however, that in spinels the role of m a g n o n s is n e g a t i v e ( D o u t h e t a n d F r i e d b e r g 1 9 6 1 ) - they cause a scattering of p h o n o n s thus r e d u c i n g the t h e r m a l conductivity. T h e c o n t r i b u t i o n of electrons to the heat transfer is b e l i e v e d to be small in spinels (Slack 1962). T h e c o n d u c t i v i t y is very sensitive to the i m p u r i t i e s particularly to the t r a n s i t i o n m e t a l ions with an orbitally d e g e n e r a t e g r o u n d level (fig. 69). I n table 36 the t h e r m a l c o n d u c t i v i t y at r o o m t e m p e r a t u r e for several spinels is given.
4.2.5. T h e r m a l expansion F o r most spinels the t e m p e r a t u r e d e p e n d e n c e of the lattice p a r a m e t e r a m a y b e well a p p r o x i m a t e d by a = ao+ b o T + b~T 2.
290
S. KRUPIOKA AND p. NOVzid<
,'I / J
"d
,o'°""o,.
o
\
°\ \
~o.2°o '~ /
•
\
o
-6 E
/
24×I0-
'.0
o
30
~oo 300 ¢ooo T(K)
Fig. 69. Temperature dependence of the thermal conductivity for Mg~_xFe~A/204system (Slack 1964). Substitution of Fe 2+ ions into the A sublattice (orbital/y degenerate 2E ground state with a weak Jahn-Teller coupling) leads to pronounced reduction of the conductivity.
20
~'103
x =-
15
0.9 1.0 0.6
0.8 0.Tj,.Y~~
5
400
500
T (K) Fig. 70. Linear expansion coefficient ee vs temperature for Ni, Znl-xFe204 ferrites (after HenrietIserentant and Robbrecht 1972). The extrema of a appear at To
OXIDE SP1NELS
291
However, the onset of ithe magnetic order causes an anomaly in the temperature dependence of a connected with the volume magnetostriction-this is demonstrated for the example of the\NixZnl_xFe204 system in fig. 70. Values of the linear expansion coefficient a
Og
--
1 Oa a OT-
bo/a + (2bJa)T+...
are given in table 36.
Appendix: Intrinsic magnetic properties In this part some additional data mainly concerning the. intrinsic magnetic properties of the most important ferrimagnetic spinels are given. For more complete or detailed information the reader should consult the following literature: (a) Books and tables: Landolt-B6rnstein tables, New Series, ed., K.H. Hellwege and A.M. Hellwege (Springer Verlag 1970) vol. 4, part b. J. Smit and H.P.J. Wijn: Ferrites (Wiley, New York, 1959). S. Krupi6ka: Physik der Ferrite und der verwandten magnetischen Oxide (Academia Praha-Vieweg, Braunschweig, 1973). Handbook of Microwave Ferrite Materials, ed., W.H. von Aulock (Academic Press, New York and London, 1965). A. Oleg et al.: Tables of Magnetic Structures determined by Neutron Diffraction (Inst. of Nuclear Techniques, Krakow, 1970). (b) Papers: E.W. Gorter: Philips Res. Rep. 9 (1954), 295, 321, 403 (crystal chemistry and ferrimagnetism). 120
'i
~
~
'
100
8o
co/ ~
-273-200-100
~
0
ZOO 200
300
400 500 600 T(°C)
700
Fig. 71, Temperature dependence of magnetization of several ferrites (Smit and Wijn 1959), the measurements were made by Pauthenet (1950), (1952).
292
S. KRUPI~KA AND P. NOVI~K
26L' ......... i o o o o'o : OOOOooo ~-
°OOoo
~
a
4I 1
co
~, ,~~-
.%b
Kb o O ooo o°°
81
~,,
=
Kbb
2~oo8888o'~ ................ OI eKCIG °°°o °O Ooo
Ku°°o °°°°
-
f 20
40
60
80
I00 120
T(K) Fig. 72. Temperature dependence of the anisotropy constants of magnetite below the Verwey transitions (Chikazumi 1975). The free energy is expressed as: F = Fo + Kaoe~ + Kba 2 -guog211 q- gaaOd4 + KbbOL4 + KabOg2aOL2 where aa, oq,, oem are the direction cosines of the magnetization with respect to the monoclinic a, b axes and [111] respectively.
15
x~x
.KI .iO 4
×
\
./;./ I°!2,,s F%04
°-,~,.k."~-~,a04
4 0/25
_1~i ! -155~' :I." -185 °C I 0,'50
0/75
NiOFe203
Fig. 73. NixFe3-xO4 system. First anisotropy constant K1 plotted for several temperatures as a function of Ni-content x (Elbinger 1962).
OXIDE SPINELS
293
n
i
n -
~o
%
.~ -40
O. ~ o ~
o ~
o--
O.z~ ° " - " e ~
o - - - o ~
o--o
o...___.. °
,N--O
0 o ~ £ O ~
O~
J"'~ 0 ~ 8
O'O-- O - - O - -
O ~ O ~
O_O
-2o ~
O~
I ' ~
O ...........~ O ......~ O ~
0
E 0
3bo T(K) i
i
80
0 " "
/./,.-"0"-""
x
/ 60
/
/"
,o n~
0.2
. /
.....
-::
,,.z%.-........ o;
E
,0
0
,~'0
0.8
o--o--O--O--
-20
.o--o
1~o
~bo
, o--o--o
e'5o
' ebo
abo r(K)
Fig. 74. NixFe3-xO4 system. Magnetostrictions A]00 and An1 plotted against temperature for several Ni-concentrations x (Brabers et al. 1980). 0.5
-0.5
~
,
,
,
,
~ / / / i " :~~ ' ~ ' , o ~
~/////
? _,,o
~--.o ~,/ -e.s
,
\\i
,
o
,
,
~ o~ ~
\llx/o~
,
.
.x
'°°
\~o/ o.t11"
o.'2 o'.~ o:e o:e /o I.? I.? 7.'6 ~.'o X
Fig. 75. MnxFe3-,O4 system. First anisotropy constant Kx plotted for several temperatures as a function of Mn-content x (Penoyer and Shafer 1959).
S. K R U P I C K A A N D P. N O V A K
294
tO0 80
°'~°~°'°°'o
120 x
E
60
/°/°
~'%~Du
+
-A ~oo" I0 ~
& ..< 40
°I
/i
~ ,
o oo_o.o~o,o
20
o¢~''\o
.~,~ I.F
100 •...a. o
1.0
A!oo
1.9
oo
80
0
-20
- - % - co-o- 0-°--% "o ~ o _ .o~ 2o ~. °. . .
-40
, ~ ' ' ' - ~- ' ~ o ' ~ . ,.........,..-~
~o /
x o
-60
e
0.85
0.40
*
0.95
-150 -lO0
"~ 0 . ¥ 5
•
1.05
o tt
60
,, e , i ,, i -I..,.+,~, x ~ - X . x . I ..~l
-50 T (°C)
b
t
,t sI
20
-5'0
/:{
40
a
\
I
x
O. tO
•
o,
x
"\ %-
\
'~a
X~x~
+"4-
I
\.
~
~4-
•
\
'A'~'a ×,~.
o.o.o-
L
i
02
0;4
i
de
i
018 r/rc
Fig. 76. MnxFe3 xO4 system. Temperature dependence of magnetostrictions ,~100, Zlklll- (a) x ~< 1.05 (Miyata and Funatogawa 1962); (b) 1.9~> x i> 1 (Brabers et al. 1977); Am is small and negative ( - 5 x 10-6~
1.
G. Blasse: Philips Res. Rep. (1964), Suppl. no. 3 (crystal chemistry and ferrimagnetism). A. Broese van Groenou, P.F. Bongers and A.L. Stuyts: Mater. Sci. Eng. 3 (1968/69), 317 (review paper).
/4
I
\
CO,:Fe3_xO4
\
~3 f... cb
2
% x=O.04
\÷ o
\+
~x=oofo~ "%+
+-
0%0 °~Oo 4"°~°'~"oo °~°e°°'°°
o. . . . . . . . . .
i~,OCLo_o..____%_o
x=O
%0
i
200
5o0 T(K)
Fig. 77. Temperature dependence of K1 for Co-substituted magnetite (Bickford et al. 1957).
OXIDE SPINELS
100 K,.lO-~rg/cm3 I 50!
295
':N'°'o-%\ R@, \4,
0
i
o
50
,A
" "o.
-50
t
"o\o% ~ 150 Q~
o..%~ %
~" ~ ' > ' ~ - o - o _ ~ ; . . . . . .Q,,o-O ~ z ~ / ~ t k . ~~a'~:-.~.~'°--~o ~" o ~ o
-150
~
i
i
250
300
...o.o°
r/~/~ [~ .
i X = 02
l e t ~'-~
~... ~ /o
-I00
,
200
~/~o.~
_ o ~ . x:o.8 b~=o.o
~2~.~o~_o-/o
~= 0.2
~o o..o- ~-o.1 \'o~--o-°"°'...K~ *"~-a~,~ ~,~ I r ~ ' ~ - ¢ /(= 005 "
Fig. 78. Temperature dependence of K1 for MgxFe3 xO4 system (Brabers et al. 1980).
10
4t0.1
0.15
0.2 * 4.2K • 77K
-IO A
,o -20
~
~
~
~
A 300K
~-
" ; i
×
-30 L
t
Fig. 79. Dependence of magnetostrictions Am0, /~111 for MgFe204 on the degree of inversion 8 (after Arai 1973).
296
S. K R U P I C K A A N D P. N O V / k K
•
t"- q'3
r',- oo
oq
t"q t"q
d
),(
~5
z
oq. q3
t"q ,,.~
I
oo'~,
O e'~
I
o
o'3 ~,~
I
~D
I
I
I
I
I
I
X
/'q
u'3 t",,I ~-.a ee3
er~ eel
I
I
I
I
',,O P,-
I
X
q3
P'-
~,o
~
oq
eq I
I
,-.t
_=
o0
;>
I
e,,
.'= E O
?
,-...
¢e3
x~
I
t"'- t"q
~rq.
~5
"O
I
.,o e¢3 e-.
7
02
I
×~ (,.q
c5 I
t",- G', tt~
I
I
I
I
I
]
I
I
r~
o. t"q
I
I
I
I
,...-~ , ~
t'e3 e¢3
¢¢3 ee)
02
o (",,I
'~" 0 ~ e¢3 0'3
O 02 P-,- o o
~ ) tt3 q3 tr3 ~1~
1"-,-
17-,-
tt3 p--
oo
G'~ ©
E
q eq
o .¢)
eq
¢)
2
e~
r)
OXIDE
o
~
SPINELS
u
297
~
0
b
o
0
0
r~
©
u:
x
= -=
oo
r~
d 'E
©
.= :0 0 "O
~
M
~.,~ •
©
'.~
,
~~ ~ ~~ ~:~
~'~
~ ~=~
&
N
eg~e
~e~g
a
~
t---
~
...-k
0
© e.
~ ' - ~ ..~ . ~
..
~
~,o 0
a
~mN
,~
©
<
.~
= .~ .~ .~
~.~ ~-~ ~.~ --
a) ; ~ ' ~
~
~oo~, Nco~
,._;
~.~
N
~g
- ~ 2~
,. •~ .r.
..o r.,4 ~ ~ >: •
~ i ~ ~ ~~ ~ '~
S. KRUPI(~KA AND P. NOVAK
298
TABLE 38 Hyperfine magnetic fields in kOe at an A-site Fe 57 nucleus, a B-site iron nucleus with six nearest neighbor A-site iron ions, and the average field at the B-site iron nuclei in various ferrimagnetic spinels (van der Woude and Savatzky 1971). Ferrite MgFe204(sc) MgFe204(q) MnFe204 NiFe204 CoFezO4(sc) CoFe204(q) Li0.sFez.sO4 ZnFe204
Hhpf(A)
Hhpf(B,6nn Fe)
Hhpf(B)
-500 - 509 - 512 - 515 - 511 - 511 -518 -
-537 - 540 - 550 - 555 - 545 550 -545 - 557 (a)
-530 - 525 - 520 - 555 - 541 - 536 -545 - 485
(a) Obtained by adding supertransferred hyperfine field to Hhpf, sc and q indicate slowly cooled and quenched samples respectively.
Acknowledgement The authors acknowledge valuable discussions and the help of Dr. Simga when p r e p a r i n g t h i s c h a p t e r . G r a t i t u d e is a l s o e x p r e s s e d t o D r . Z f i v 6 t a f o r his c r i t i c a l r e a d i n g of t h e m a n u s c r i p t .
References Adler, D., 1968, Insulating and Metallic States in Transition Metal Oxides, in: Solid State Physics, eds., Seitz, F., D. Turnbull and H. Ehrenreich (Academic Press, New York, London) vol. 21, pp. 1-113. Ahrenkiel, R.K. and T.J. Coburn, 1975, IEEE Trans. Magn., MAG-11, 1103. Ahrenkiel, R.K., T.J. Coburn and E. Carnall, Jr., 1974a, IEEE Trans. Magn. MAG-10, 2. Ahrenkiel, R.K., T.J. Coburn, D. Pearlman, E. Carnall, Jr., T.W. Martin and S.L. Lyu, 1974b, AIP Conf. Proc. 24, 186. Ahrenkiel, R.K., S.L. Lyu and T.J. Coburn, 1975, J. Appl. Phys. 46, 894. Aiyama, Y., 1966, J. Phys. Soc. Jap. 31, 1684. Akino, T., 1974, J. Phys. Soc. Jap. 36, 84.
Akino, T. and K. Motizuki, 1971, J. Phys. Soc. Jap. 31, 691. Alvarado, S.F., W. Eib, F. Meier, D.T. Pierce, K. Sattler, H.C. Siegmann and J.P. Remeika, 1975, Phys. Rev. Lett. 34, 319. Alvarado, S.F., M. Erbudak and P. Munz, 1977, Physica 86--88B + C, 1188. Anderson, P.W., 1956, Phys. Rev. 102, 1008. Anderson, P.W., 1958, Phys. Rev. 109, 1492. Anderson, P.W., 1959, Phys. Rev. 115, 2. Anderson, P.W., 1963, Exchange in Insulators, in: Magnetism, eds., Rado, G.T. and H. Suhl (Academic Press, New York, London) vol. 1, pp. 25-86. Anderson, P.W., 1970, Comments Solid State Phys. 11, 193.
OXIDE SPINELS Arai, K.I., 1.973, Rep. Res. Inst. Electr. Commun. Tohoku Univ. 25, 79. Arai, K.I. and N. Tsuya, 1973, J. Phys. Chem. Solids 34, 431. Arai, K.I. and N. Tsuya, 1974, Phys. Status Solidi b66, 547. Arai, K.I. and N. Tsuya, 1975, J. Phys. Chem. Solids 36, 463. Aubert, G., 1968, J. Appl. Phys. 39, 504. Baltzer, P.K., 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 192. Barth, T.F.W. and E. Posnjak, 1932, Z. Kristallogr. 82, 325. Baszyfiski, J. and Z. Frait, 1976, Phys. Status Solidi b73, K85. Bernstein, P. and T. Merceron, 1977, J. Phys. (France) 38, C1-211. Bertaut, F., 1951, J. Phys. Rad. 12, 252. Bickford, L.R., J.M. Brownlow and R.F. Penoyer, 1957, Proc. Inst. Electr. Eng. 104B, 238. Birss, R.R., 1964, Symmetry and Magnetism (North-Holland, Amsterdam) ch. 5, §3. Blasse, G., 1964, Philips Res. Rep. Suppl. no. 3. Blasse, G., 1965, Philips Res. Rep. 20, 528. Blasse, G. and E.W. Goner, 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 176. Blazey, K.W., 1974, J. Appl. Phys. 45, 2273. Boshaan, A.J. and H.J. van Daal, 1970, Adv. Phys. 19, 1. Bouchard, R.J., 1967, Mater. Res. Bull. 2, 459. Brabers, V.A.M., 1971, J. Phys. Chem. Solids 32, 2181. Brabers, V.A.M., J. Klerk and Z. Simga, 1977, Physica 86--88B + C, 1461. Brabers, V.A.M., T. Merceron, M. Porte and R. Krishnan, 1980a, J. Mag. Mag. Mater. 15-18, 545. Brabers, V.A.M., J.C.J.M. Terhell and J.H. Hendriks, 1980b, J. Mag. Mag. Mater. 15-18, 599. Bradburn, T.E. and G.R. Rigby, 1953, Trans. Br. Ceram. Soc. 52, 417. Bragiflski, A., 1965, Phys. Status Solidi 11, 603. Bragiflski, A. and T. Merceron, 1962, J. Phys. Soc. Jap. 17, 1611. Broese van Groenou, A., 1967, J. Phys. Chem. Solids 28, 325. Broese van Groenou, A. and R.F. Pearson, 1967, J. Phys. Chem. Solids 28, 1027. Broese van Groenou, A., P.F. Bongers and .A.L. Stuyts, 1968, Mater. Sci. Eng. 3, 317. BriJesch, P. and F. D'Ambrogio, 1972, Phys. Status Solidi 50, 513.
299
Briining, S. and H.Ch. Semrnelhack, 1979, Conference on Physics of Magnetic Materials COMECON, Dresden, unpublished. Buchenau, M., 1975, Phys. Status Solidi b70, 181. Buchenau, U. and I. Mfiller, 1972, Solid State Commun. 11, 1291. Buckwald, R.A., A.A. Hirsch, D. Cabib and E. CaUen, 1975, Phys. Rev. Lett. 35, 878. Callen, E., 1968, J. Appl. Phys. 39, 519. Carr Jr., W.J., 1966, Secondary Effects in Ferromagnetism, in: Handbuch der Physik, ed., Fliigge, S. (Springer Verlag, Heidelberg, Berlin, New York) vol. 18/2. Chikazumi, S., 1975, Technical Report ISSP ser. A, no. 737. Clogston, A.M., 1955, Bell Syst. Tech. J. 34, 739. Clogston, A.M., 1959, J. Phys. Rad. 20, 151. Cullen, J.R. and E. Callen, 1970, J. Appl. Phys. 41, 879. Cullen, J.R. and E. Callen, 1973, Phys, Rev. B7, 397. De Boer, F., J.H. van Santen and E.J.W. Verwey, 1950, J. Chem. Phys. 18, 1032. Delorme, C., 1958, Bull. Soc. Fr. Mineral. Crystallogr. 81, 79. / Dillon Jr., J.F., 1971, Magneto-Optical Properties of Magnetic Crystals, in: Magnetic Properties of Materials, ed., Smit, J. (McGrawHill, New York) p. 149-204. Drabble, J.R., T.D. White and R.M. Hooper, 1971, Solid State Commun. 9, 275. Driessens, F.C.M., 1968, Ber. Bunsenges. Phys. Chem. 72, 1123. Dunitz, J.D. and L.E. Orgel, 1957, J. Phys. Chem. Solids 3, 20, 318. Eibschiitz, M., V. Ganiel and S. Strikman, 1966, Phys. Rev. 151, 245. Elbinger, G., 1962, Z. Angew. Phys. 4, 274. Elwell, D., R. Parker and A. Sharkey, 1963, J. Phys. Chem. Solids 24, 1325. Elwell, D., B.A. Griffiths and R. Parker, 1966, Br. J. Appl. Phys. 17, 587. Englman, R., 1972, The Jahn-Teller Effect in Molecules and Crystals (Wiley, New York). Evans, B.J., 1975, AIP Conf. Proc. 24, 73. Faller, J.G. and C.E. Birchenall, 1970, J. Appl. Crystallogr. 3, 496. Fazekas, P., 1972, Solid State Commun. 10, 175. Folen, V.J., 1960, J. Appl. Phys. 31, 166S. Fujii, Y., G. Shirane and Y. Yamada, 1975, Phys. Rev. Bll, 2036.
300
S. KRUPI~2KA AND P. NOV.~d(
Gehring, G.A. and K.A. Gehring, 1975, Rep. Progr. Phys. 38/1, 5. Gerber, R., 1968, Czech. J. Phys. B18, 1204. Gerber, R. and G. Elbinger, 1964, Phys. Status Solidi 4, 103. Gerber, R. and G. Elbinger, 1970, J. Phys. C3, 1363. Gerber, R., L. Michalowsky, K. Motzke and E. Steinbeiss, 1966, Phys. Status Solidi 16, 793. Gibart, P. and G. Suran, 1975, Internat. Coll. Mag. Thin Films, Regensburg. Gibbons, D.F., 1957, J. Appl. Phys. 28, 810. Giesecke, W., 1959, Z. Angew. Phys. 11, 91. Gilleo, M,A., 1958, Phys. Rev. 109, 777. Gilleo, M.A., 1960, J. Phys. Chem. Solids 13, 33. Glasser, M.L. and F.J. Milford, 1963, Phys. Rev. 130, 1783. Glaz, W., H. Szydlowski and S. Pachocka, 1980, Acta phys. polonica A58, 263. Goodenough, J.B., 1958, J. Phys. Chem. Solids 6, 287. Goodenough, J.B., 1963, Magnetism and Crystal Structure in Nonmetals, in: Magnetism, vol. 3, eds., Rado, G.T. and H. Suhl (Academic Press, New York and London), pp. 1~63. Goodenough, J.B., 1963, Magnetism and Chemical Bond (Wiley, New York). Gorter, E.W., 1954, Philips Res. Rep. 9, 295. Gorter, E.W., 1955, Proc. IRE 43, 1945. Greenough, R.D. and E.W. Lee, 1970, J. Phys. D3, 1595. Grimes, N.W., 1972a, Philos. Mag. 26, 1217. Grimes, N.W., 1972b, Spectr. Acta 28A, 2217. Grimes, N.W., 1974, Proc. Roy. Soc. A338, 223. Grimes, N.W., T.J. O'Connor and P. Thompson, 1978, J. Phys. C l l , L505. Groupe de diffusion in61astique des neutrons, 1971, J. Phys. (France) 32, C1-118. Gutowski, M., 1978, Phys. Rev. B18, 5984. Hargrove, R.S. and W. Kiindig, 1970, Solid State Commun. 8, 303. Hastings, J.M. and L.M. Corliss, 1953, Rev. Mod. Phys. 25, 114. /-Iaubenreisser, W., 1961, Phys. Status Solidi 1, 6t9. Heeger, A.J. and T. Houston, 1964, J. Appl. Phys. 35, 836. Heikes, R.R. and W.B. Johnston, 1957, J. Chem. Phys. 26, 582. Henning, J.C.M., 1980, Phys. Rev. B21, 4983. Henning, J.C.M., J.H. den Boef and G.G.P. van Gorkom, 1973, Phys. Rev. B7, 1825.
Henning, J.C.M. and H. van den Boom, 1977, Physica B + C86--88, 1027. Henriet-Iserentant, Ch. and G. Robbrecht, 1972, C.R. Hebd. Seances Acad. Sci. B275, 323. Hisatake, K. and K. Ohta, 1977, J. Phys. (France) 38, C1-219. Holba, P., M. Nevfiva and E. Pollert, 1975, Mater. Res. Bull. 10, 853. Holtwijk, T., W. Lems, A.G.H. Verhulst and U. Enz, 1970, IEEE Trans. Mag. MAG-6, 853. Hwang, L., A.H. Heuer and T.F. Mitchell, 1973, Philos Mag. 28, 249. Iida, S., 1960, J. Appl. Phys. 31,251S. Iida, S., 1967, J. Phys. Soc. Jap. 22, 1233. Iida, S. and T. Inoue, 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 281. Iida, S. and H. Miwa, 1966, J. Phys. Soc. Jap. 21, 2505. Iida, S., K. Mizushima, N. Yamada and T. Iizuka, 1968, J. Appl. Phys. 39, 818. Iida, S., K. Mizushima, M. Mizoguchi, J. Mada, S. Umemura, K. Nakao and J. Yoshida, 1976, AIP Conf. Proc. 29, 388. Iida, S., K. Mizushima, M. Mizoguchi, J. Mada, S. Umemura, K. Nakao and J. Yoshida, 1977, J. Phys. (France) 38, C1-73. Iida, S., K. Mizushima, M. Mizoguchi, S. Umemura and J. Yoshida, 1978, J. Appl. Phys. 49, 1455. Iizuka, S. and S. Iida, 1966, J. Phys. Soc. Jap. 21, 222. Ioffe, V.A., G.I. Khvostenko and Z.N. Zonn, 1957, Soviet. Phys.-J. Tech. Phys. 27, 1985. Ishikawa, Y. and Y. Syono, 1971a, Phys. Rev. Lett. 26, 1335. Ishikawa, Y. and Y. Syono, 1971b, J. Phys. Soc. Jap. 31, 461. Ishikawa, Y., S. Sato and Y. Syono, 1971, J. Phys. Soc. Jap. 31, 452. Ivanov, B.D., B.A. Kalinikos, O.A. Rybinskij and D.N. Czartorizskij, 1972, Fiz. Tverd. Tela 14, 653. Ivanova, A.V., V.N. Seleznev and A.I. Drokin, 1979, Zhurnal tekhn, fiziki 49, 2493. Jacob, K.T. and J. Walderraman, 1977, J. Solid State Chem. 22, 291. Jacobs, I.S., 1959, J. Phys. Chem. Solids 11, 1. Jacobs, I.S., 1960, J. Phys. Chem. Solids 15, 54. Jirfik, Z. and S. Vratislav, 1974, Czech. J. Phys. B24, 642. Jonker, G.H., 1959, J. Phys. Chem. Solids 9, 165.
OXIDE SPINELS Kahn, F.J., P.S. Pershan and J.P. Remeika, 1969, Phys. Rev. 186, 891. Kamiyoshi, K., 1951, Sci. Rep. Res. Inst. Tohoku Univ. A3, 716. Kanamori, J., 1959, J. Phys. Chem. Solids 10, 67. Kaplan, J. and C. Kittel, 1953, J. Chem. Phys. 21, 760. Kaplan, T.A., 1958, Phys. Rev. 109, 782. Kaplan, T.A., 1960, Phys. Rev. 116, 888. Kaplan, T.A., K. Dwight, D.H. Lyons and N. Menyuk, 1961, J. Appl. Phys. 32, 13S. Kato, Y. and T. Takei, 1933, J. Inst. Electr. Eng. Jap. 53, 408. Keffer, F., 1966, Spin Waves, in: Handbuch der Physik, vol. 18/2, ed., Fliigge, S. (Springer Verlag, Berlin, Heidelberg, New York) pp. 1-273. Khrebtov, A.P., A.A. Askochensky and J.M. Speranskaya, 1978, Izv. Akad. Nauk SSSR Ser. Fiz. 42, 1652. Kienlin, A.v., 1957, Z. Angew. Phys. 9, 245. Kino, Y., B. Lfithi and M.E. Mullen, 1972, J. Phys. Soc. Jap. 33, 687. Klerk, J., V.A.M. Brabers and A.J.M. Kuipers, 1977, J. Phys. (France) 38, C1-187. Klinger, M.I., 1975, J. Phys. C8, 3595. Klinger, M.I. and A.A. Samochvalov, 1977, Phys. Status Solidi, h79, 9. Knowles, J.E., 1964, Proc. Int. Conf. Magnetism, Nottingham, p. 619. Knowles, J.E., 1974, Philips Res. Rep. 29, 93. Knowles, J.E. and J. Rankin, 1971, J. Phys. (France) 32, C1-845. K6hler, D., 1959, Z. Angew. Phys. 11, 103. K6nig, U., Y. Gross and G. Chol, 1969, Phys. Status Solidi 33, 811. Koops, C.G., 1951, Phys. Rev. 83, 121. Kopp, W., 1919, Dissertation (Zurich). Kouvel, J.S., 1956, Phys. Rev. 102, 1489. Kowalewski, L., 1962, Acta Phys. Pol. 21, 121. Kozhuhar, A.Y., G.A. Tsinadze, V.A. Shapovalov and V.N. Seleznev, 1973, Phys. Lett. 42A, 377. Krause, J., 1969, J. Angew. Phys. 27, 251. Kriessman, C.J. and S.E. Harrison, 1956, Phys. Rev. 103, 857. Krinchik, G.S., A.P. Khrebtov, A.A. Askochensky, E.M. Speranskaya and S.A. Belyaev, 1977, Zh. Eksp. Teor. Fiz. 72, 699. Krinchik, G.S., K.M. Muchimov, Sh.M. Sharipov, A.P. Khrebtov and M. Speranskaya, 1979, Zh. Eksp. Teor. Fiz. 76, 2126. Krupi6ka, S., 1960, Czech. J. Phys. B10, 782.
301
Krupi~ka, S., 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 304. Krupi6ka, S. and P. Novfik, 1964, Phys. Status Solidi 4, Kl17. Krupi~ka, S. and F. Vilfm, 1957, Czech. J. Phys. 7, 723. Krupi~ka, S. and F. Vilfm, 1961, Czech. J. Phys. Bll, 10. Krupi6ka, S. and K. Zfiv6ta, 1968, J. Appl. Phys. 39, 930. Krupi6ka, S., L. Cervinka, P. Novfik and K. Zfiv6ta, 1964, Proc. Int. Conf. Magnetism, Nottingham, p. 650. Krupi~ka, S., Z. Sim~a and Z. Smetana, 1968, Czech. J. Phys. B18, 1016. Krupi~ka, S., Z. Jir~k, P. Nov~k, V. Roskovec and F. Zounovfi, 1977, Physica 86-88B+ C, 1459. Krupi~ka, S., Z. Jirfik, P. Novfik, F. Zounovfi and V. Roskovec, 1980, Acta Physica Slovaca 30, 251. Kubo, T., A. Hirai and H. Abe, 1969, J. Phys. Soc. Jap. 26, 1094. Kuipers, A.J.M., 1978, Thesis, Technical University Eindhoven. Kuipers, AJ.M. and V.A.M. Brabers, 1976, Phys. Rev. B14, 1401. Lauwers, H.A. and M.A. Herman, 1980, J. Phys. Chem. Solids 41, 223. Liolioussis, K.T. and A.J. Pointon, 1977, J. Phys. (France) 38, C1-191. Lord, H. and R. Parker, 1960, Nature 188, 929. Lotgering, F.K., 1964, J. Phys. Chem. Solids 25, 95. Lu-San Pan and B.J. Evans, 1978, J. Appl. Phys. 49, 1458. Lutz, H.D., 1969, Z. Naturforsch. 24a, 1417. Lutz, H.D. and H. Haeuseler, 1975, Bet. Bunsenges. Phys. Chem. 79, 604. Malakhovsky, A.V., I.S. Edelman, V.P. Gavrilin, G.I. Barinov, 1974, Sov. Phys. Solid State, 16, 266. Marais, A. and T. Merceron, 1959, C.R. Hebd. Seanees Acad. Sci. 248, 2976. Marais, A. and T. Merceron, 1965, C.R. Hebd. Seances Acad. Sci. 261, 2188. Marais, A. and T. Merceron, 1967, Phys. Status Solidi, 24, 635. Marais, A. and T. Merceron, 1974, Phys. Status Solidi, a22, K209. Marais, A., T. Merceron and M. Porte, 1969, C.R. Hebd. Seances Acad. Sei. B268, 730. Marais, A., T. Merceron, G. Maxim and M. Porte, 1972, Phys. Status Solidi, 52, 631.
302
S. KRUPICKA AND P. NOV~iJ(
Maxim, G., 1969, Phys. Status Solidi, 35, 211. McClure, D.S., 1957, J. Phys. Chem. Solids, 3, 311. McMurdie, H.P., B.M. Sullivan and F.A. Mauer, 1950, J. Res. Nat. Bur. Stand. 45, 35. Merceron, T., 1965, Ann. Phys. 10, 121. Michalk, C., 1968, Phys. Status Solidi, 27, K51. Michalowsky, L., 1965, Phys. Status Solidi, 8, 543. Miles, P.A., W.B. Westphal and A. yon Hippel, 1957, Rev. Mod. Phys. 29, 279. Miller, A., 1959, J. Appl. Phys. 30, 24S. Miyahara, Y., 1972, J. Phys. Soc. Jap. 32, 629. Miyata, N., 1961, J. Phys. Soc. Jap. 16, 206. Miyata, N. and Z. Funatogawa, 1962, J. Phys. Soc. Jap. 17, Suppl. B-l, 279. Mizoguchi, M., 1978a, J. Phys. Soc. Jap. 44, 150~1. Mizoguchi, M., 1978b, J. Phys. Soc. Jap. 44, 1512. Mizushima, M., 1963, J. Phys. Soc. Jap. 18, 1441. Mizushima, K. and S. Iida, 1967, J. Phys. Soc. Jap. 22, 1300. Mizushima, K., K. Nakao, S. Tanaka and S. Iida, 1978, J. Phys. Soc. Jap. 44, 1831. Mott, N.F., 1969, Philos. Mag. 19, 835. Motzke, K., 1962, Phys. Status Solidi, 2, K52, K307. Motzke, K., 1964, Phys. Status Solidi, 4, K13. Mozzi, R.L. and A.E. Paladino, 1963, J. Chem. Phys. 39, 435. Navrotsky, A., 1973a, J. Solid State Chem. 6, 21. Navrotsky, A., 1973b, Earth Planet. Sci. Lett. 19, 471. Navrotsky, A., 1974, J. Solid State Chem. 11, 10. Navrotsky, A., 1975, J. Solid State Chem. 12, 12. Navrotsky, A. and L. Hughes, Jr., 1976, J. Solid State Chem. 16, 185. Navrotsky, A. and O.J. Kleppa, 1967, J. Inorg. Nucl. Chem. 29, 2701. Navrotsky, A. and O.J. Kleppa, 1968, J. Inorg. Nucl. Chem. 30, 479. N6el, L., 1948, Ann. Phys. (France) 3, 137. N~el, L., 1954, J. Phys. Rad. 15, 225. Novfik, P., 1966, Czech. J. Phys. B16, 723. Novfik, P., 1972, Czech. J. Phys. B22, 1134. Ohnishi, H., T. Teranishi and S. Miyahara, 1959, J. Phys. Soc. Jap. 14, 106. Okada, T. and T. Akashi, 1965, J. Phys. Soc. Jap. 20, 639.
Palmer, W., 1960, Phys. Rev. 120, 342. Parker, R., 1975, Electrical Transport Properties, in: Magnetic Oxides, ed., Craik, D.J. (Wiley, New York) pp. 421-482. Parker, R. and M.S. Smith, 1961, J. Phys. Chem. Solids, 21, 76. Parker, R. and C.J. Tinsley, 1976, Phys. Status Solidi, a33, 189. Pauthenet, R., 1950, C.R. Hebd. Seances Acad. Sci. 230, 1842. Pauthenet, R., 1952, Ann. Phys. (France) 7, 7i0. Pauthenet, R. and L. Bochirol, 1951, J. Phys. Rad. 12, 249. Patton, C.E., 1975, Microwave Resonance and Relaxation, in: Magnetic Oxides, ed. Craik, D.J. (Wiley, New York) pp. 575-649. Penoyer, R.F. and L.R. Bickford, Jr., 1957, Phys. Rev. 108, 271. Penoyer, R.F. and M.W. Shafer, 1959, J. Appl. Phys. 30, 315S. Perthel, R., 1962, J. Phys. Soc. Jap. 17, Suppl. B-I, 288. Philips, B., S. Somiya and A. Muan, 1961, J. Am. Ceram, Soc. 16, 167. Piekoszewski, J., J. Suwalski and L. Dabrowski, 1977, Aeta Phys. Pol. A51, 179. Platz, W. and J. Heber, 1976, Z. Phys. B24, 333. Plumier, R., 1969, Theses, Paris. Pointon, A.J. and G.A. Wetton, 1973, AIP Conf. Proc. 10, 1573. Pollert, E. and Z. Jirfik, 1976, Czech. J. Phys. B26, 481. Preudhomme, J. and P. Tarte, 1971a, Spectrochim Acta 27A, 961. Preudhomme, J. and P. Tarte, 1971b, Spectrochim Acta 27A, 1817. Preudhomme, J. and P. Tarte, 1972, Spectrochim. Acta 28A, 69. Prince, E., 1964, J. Phys. Rad. 25, 503. Prince, E., 1965, J. Appl. Phys. 36, 161. Rabkin, L.I. and Z.I. Novikova, 1960, Ferrites (Minsk) p. 146. Rado, G.T. and J.M. Ferrari, 1975, Phys. Rev. B12, 5166. Rado, G.T. and J.M. Ferrari, 1977, Phys. Rev. B15, 290. Reinen, D., 1968, Z. Anorg. Allg. Chem. 356, 182. Rezlescu, N. and E. Rezlescu, 1974, Phys. Status Solidi a23, 575. Reznickiy, L.A., 1977, Izv. Akad. Nauk SSSR, Neorg. Mat. 13, 1669. Rogers, D.B., 1967, Cs. 6as. fyz. A17, 398.
OXIDE SPINELS Rogers, D.B., R.J. Arnott, A. Wold and J.B. Goodenough, 1963, J. Phys. Chem. Solids 24, 347. Rogers, D.B., J.L. Gilson and T.E. Gier, 1967, Solid State Commun. 5, 143. Rosencwaig, A., 1970, Can. J. Phys. 48, 2857. Roth, W.L., 1964, J. Phys. Rad. 25, 507. Rouse, K.D., M.V. Thomas and B.T.M. Willis, 1976, J. Phys. C9, L231. Samochvalov, A.A., S.A. Ismailov and A.A. Obuchov, 1967, Fiz. Tverd. Tela, 9, 884. Sawatzki, G.A., F. van der Woude and A.A. Morish, 1969, Phys. Rev. 187, 747. Scheerlinck, D., W. Wegener, S. Hautecler and V.A.M. Brabers, 1974, Solid State Commun. 15, 1529. Schlegel, A., S.F. Alvarado and P. Wachter, 1979, J. Phys. C12, 1157. Schl6mann, E., 1957, J. Phys. Chem. Solids, 2, 214. Schl6mann, E., 1960, Solid State Physics in Electronics and Telecommunication vol. 3 (Academic Press, New York) p. 322. Scott, G.B., 1978, The Optical Absorption and Magneto-Optic Spectra of Y3FesO12, in: Proc. International School on Physics "Enrico Fermi," ed., Paoletti, A. (North-Holland, Amsterdam) pp. 445-466. Scott, G.B., D.E. Lacklison and J.L. Page, 1974, Phys. Rev. B10, 971. Scott, G.B., D.E. Lacklison, H.I. Ralph and J.L. Page, 1975, Phys. Rev. B12, 2562. Seleznev, V.N., I.K. Pukhov, A.I. Drokin and V.A. Shapovalov, 1970, Fiz. Tver. Tela 12, 885. Seshagiri Rao, T., B. Revathi and M. Purnanandam, 1971, Indian J. Pure Appl. Phys. 9, 797. Serres, A., 1932, Ann. Phys. (France) 10, 32. Shannon, R.D., 1976, Acta Crystallogr. A32, 751. Shindo, I. and K. Kohn, 1979, J. Phys. Soc. Jap. 47, 1779. Shirane, G., S. Chikazumi, J. Akimitsu, K. Chiba, M. Matsui and Y. Fujii, 1975, J. Phys. Soc. Jap. 39, 949. Siemons, W.J., 1970, IBM J. Res. Dev. 14, 245. Simga, Z., 1979, Phys. Status Solidi b96, 581. Simga, Z. and O. Schneeweiss, 1972, Czech. J. Phys. B22, 1331. Simga, Z., J. ~imgovfi and V.A.M. Brabers, 1972, Proc. llth ICPS, vol. 2 (Polish Sci. Publishers, Warsaw) p. 1294.
303
Simga, Z., P. Sirok~, F. Lukeg and E. Schmidt, 1979, Phys. Status Solidi, b96, 137. Simga, Z., P. Sirok~, J. Kolfi~ek and V.A.M. Brabers, 1980, J. Mag. Mag. Mater. 15-18, 775. Simgovfi, J. and Z. Simga, 1974, Czech. J. Phys. B24, 449. Simgovfi, J., M. Marygko and K. Suk, 1976, Phys. Status Solidi, a38, K163. Siratori, K., 1967, J. Phys. Soc. Jap. 23, 948. Siratori, K., E. Kito, G. Kaji, A. Tasaki, S. Kimura, I. Shindo and K. Kohn, 1979, J. Phys. Soc. Jap. 47, 1779. Sixtus, K.J., 1960, Solid State Physics in Electronics and Telecommunication, vol. 3 (Academic Press, New York) p. 91. Slack, G.A., 1964, Phys. Rev. A134, 1268. Slonczewski, J.C., 1958, Phys. Rev. 110, 1341. Slonczewski, J.C., 1960, J. Phys. Chem. Solids, 15, 335. Smit, J., 1968, Solid State Commun. 6, 745. Stair, J. and H.P.J. Wijn, 1959, Ferrites (Wiley, New York). Smit, J., F.K. Lotgering and R.P. van Stapele, 1962, J. Phys. Soc. Jap. 17B-l, 268. Smith, D.O., 1952, Prog. Rep. Lab. Insul. Res. MIT, 11, 53. Sobotta, E.A. and J. Voitlfinder, 1963, Z. Phys. Chem., Frankfurt, 39, 54. Sparks, M., 1964, Ferromagnetic Relaxation Theory (McGraw-Hill, New York). Sugano, S., Y. Tanabe and M. Kamimura, 1970, Multiplets of Transition Metal Ions in Crystals (Academic Press, New York). Svirina, E.P., 1970, Izv. Akad. Nauk USSR, Ser. Fiz. 34, 1162. Szymczak, H., R. Wadas, W. Wardzynski and W. Zbieranowski, 1973, Proc. Int. Conf. Mag. ICM-73 (Moscow) p. 425. Tachiki, M., 1960, Progr. Theor. Phys. 23, 1055. Teale, R.W., 1967, Proc. Phys. Soc. 92, 411. Teale, R.W. and D.W. Temple, 1967, Phys. Rev. Lett. 19, 904. Teh, H.C., M.F. Collins and A.H. Mook, 1974, Can. J. Phys. 52, 396. Thompson, P. and N.W. Grimes, 1972a, J. Appl. Crystallogr. 10, 369. Thompson, P. and N.W. Grimes, 1972b, Philos. Mag. 36, 501. Torrie, B.H., 1967, Solid State Commun. 5, 715. Tretyakov, Yu., 1967, Termodinamika Ferritov (Chimija, Leningrad) p. 41. Tyablikov, S.V., 1956, Fiz. Met. Metalloved. 3, 3.
304
S. KRUPI~KA AND P. NOV_.~K
Umemura, S. and S. Iida, 1979, J. Phys. Soc. Jap. 47, 458. Van der Woude, F. and G.A. Sawatzky, 1971, Phys. Rev. B4, 3159. Van Diepen, A.M. and F.K. Lotgering, 1977, Physica 86.-88B + C, 981. Van Uitert, L.G., 1956a, J. Chem. Phys. 24, 306. Van Uitert, L.G., 1956b, Proc. IRE 44, 1294. Van Uitert, L.G., 1957, J. Appl. Phys. 28, 320. Venero, A.F. and E.F. Westrum, 1975, J. Chem. Thermodynamics 7, 693. Verwey, E.J.W., 1 9 5 1 , Semiconducting Materials (Butterworth Sci. Publications, London) p. 151. Verwey, E.J.W. and P.W. Haaijman, 1941, Physica 8, 979. Vi~fiovsk~, S., R. Krishnan, V. Prosser, N.P. Thuy and I. St[eda, 1979a, Appl. Phys. 18, 243. Vi~fiovsk3), S., N.P. Thuy, J. St6p~inek, R. Krishnan and V. Prosser, 1979b, J. Appl. Phys. 50, 7466. Vi~fiovsk~), S., R. Krishnan, N.P, Thuy, J. St6p~inek, V. Pa[izek and V. Prosser, 1980, J. Mag. Mag. Mater. 15--18, 831. Vratislav, S., J. Zaj/6ek, Z. Jir~ik and A.F. Andresen, 1977, J. Mag. Mag. Mater. 5, 41. Wagner, R., 1961, Ann. Phys. 7, 302. Waldron, R.D., 1955, Phys. Rev. 99, 1727. Wanic, A., 1972, Int. J. Mag. 3, 349. Watanabe, H. and B.N. Brockhouse, 1962, Phys. Lett. 1, 189. Watanabe, Y., K. Urade and S. Saito, 1978, Phys. Status Solidi, b90, 697. Wegener, W., D. Scheerlinck, E. Legrand, S. Hautecler and V.A.M. Brabers, 1974, Solid State Commun. 15, 345.
Westwood, W.D. and A.G. Sadler, 1971, Can. J. Phys. 49, 1103. White, W.B. and B.A. De Angelis, 1967, Spectrochim. Acta, 23A, 985. Willshee, J.C. and J. White, 1967, Trans. Br. Ceram. Soc. 66, 548, 551. Wittekoek, S., T.J.A. Popma, J.M. Robertson and P.F. Bongers, 1975, Phys. Rev. B12, 2777. Wolf, W.P., 1957, Phys. Rev. 108, 1152. Yafet, Y. and C. Kittel, 1952, Phys. Rev. 87, 290. Yakovlev, Y.M., E.V. Rubalskaya, L.G. Godes, B.L. Lapovok and T.N. Bushueva, 1971, Fiz. Tver. Tela 13, 1151. Yamada, T., 1973, J. Phys. Soc. Jap. 35, 130. Yamada, T., 1975, J. Phys. Soc. Jap. 38, 1378. Yamada, N. and S. Iida, 1968, J. Phys. Soc. Jap. 24, 952. Yanase, A., 1962, J. Phys. Soc. Jap., 17, 1005. Yasuoka, H., A. Hirai, M. Matsumura and T. Hashi, 1962, J. Phys. Soc. Jap. 17, 1071. Yosida, K. and M. Tachiki, 1957, Prog. Theor. Phys. 17, 331. Yshikawa, Y., S. Sato and Y. Syono, 1971, J. Phys. Soc. Jap. 31, 453. Zanmarchi, G. and P.F. Bongers, 1969, J. Appl. Phys. 40, 1230. Z~iv6ta, K. and P. Nov~k, 1971, J. Phys. (France) 32, C1-64. Zftv6ta, K., E.I. Trinkler and F. Zounov~, 1966, Phys. Status Solidi 14, K9. Z~iv6ta, K., F. Zounov~i and E.I. Trinkler, 1968, Czech. J. Phys. B18, 1314. Zhilyakov S.M. and E.P. Naiden, 1977, Izv. V.U.Z. Fiz no. 1, 56.
chapter 5 FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES WITH MAGNETOPLUMBITE STRUCTURE
H. KOJIMA Research Institute for Scientific Measurements Tohoku University, 2-1-1 Katahira, Sendai JAPAN
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 305
CONTENTS 1. G e r e r a l . . . . . . . 1.1. C h e m i c a l c o m p o s i t i o n
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1.2. P h a s e d i a g r a m . . . . . . . . . . . . . . . . . . . . . . 1.2.1. B a O - F e 2 0 3 s y s t e m s . . . . . . . . . . . . . . . . . . 1.2.2. S r O - F e 2 0 3 s y s t e m s . . . . . . . . . . . . . . . . . . 1.2.3. P b O - F e 2 0 3 s } s t c m s . . . . . . . . . . . . . . . . . . 1.3. P r e p m a t i o n . . . . . . . . . . . . . . . . . . . . . . . 2. M c o m p o u n d . . . . . . . . . . . . . . . . . . . . . . . . 2.1. BaFe1:.O19, SrFe12019 ~ n d Pb Fe1=O19 . . . 2.1.1. Crystal s t r u c t u r e . . . . . . . . 2.1.2. M a g n e t i c ~,t~ u c t u r e . . . . . . 2.1.3. S a t m atic n me gnet!2 a t i c n . . . . 2.1.4. M a g n e t o c r ~ stalline a n i s o t r c py . . 2.1.5. C o e r c i v e f o l c e 2.1.6. 2.1.7. 2.1.8. 2.1.9. 2.1.10. 2.1.11. 2.1.12. 2.1.13.
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F a r a m ~ g n e l i c proloert~e s . . . . . . . . . . . . . . . . Magnetic aftereffect . . . . . . . . . . . . . . . . . . FMR . . . . . . . . . . . . . . . . . . . . . . . NMR . . . . . . . . . . . . . . . . . . . . . . . M 6 s s b a u e r effe~ t Domain observation Optical pioperties M a g n e l ostriction
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2.1.15. H e a t c a p a c i t y . . . . . . . . . . . . . . . . . . . . 2.1.16. q h m m a l e x p a n s i c n . . . . . . . . . . . . . . . . . . . 2.1.17. E l e c t r i c a n d dielectric IZrOl:erties . . . . . . . . . . . . . . 2.2. Substitute d M c o m p o u n d . . . . . . . . . . . . . . . . . . . 2.2.1. B a O - S r O - F b O - F e 2 0 3 s y s t e m s . . . . . . . . . . . . . . . 2.2.2. G t h e r substitutions c f Ba:+ ions . . . . . . . . . . . . . . . 2.2.3. Substitt t i c n c f Fe3+ l'ons . . . . . . . . . . . . . . . . . Sub~,titution with A l>, Ga3+ a n d C r3+ icn . . . . . . . . . . . Sub,~ tilution with Sc3+ a n d In 3+ . . . . . . . . . . . . . . Substitution of Fe3+ with p a i r e d ions; C o - T i s y s t e m . . . . . . . C t h e r c c m b i n a t i o n s with I I - I V pairs . . . . . . . . . . . . 2.2.4. Effect of substitutions on t h e t e m p e r a t u r e d e p e n d e n c e of m a g n e t i z a t i o n 2.2.5. Substitution with a n i c n s . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1. General
A group of ferrimagnetic oxides with hexagonal structures will be described in this section'S. Most of these compounds have been developed over the past two decades and it can be said that the first fundamental step of the investigations on the properties of hexagonal ferrites, now seems to be nearly completed. Smit and Wijn (1959) and Wijn (1970) collected comprehensive data on the compounds, and moreover, many authors - such as Schieber (1967), Tebble and Craik (1969), Galasso (1970), Standley (1972), and others-spent a few chapters to treat the magnetic properties or crystal structures of the hexagonal iron oxides in their books.
1.1. Chemical composition ~fhe chemical compositions of the hexagonal compounds are shown in fig. 1" as part of a ternary phase diagram and in table 1 for the BaO-MeO-Fe203 system. Here, Me represents a divalent ion among the first transition elements, Zn, Mg, or a combination of ions whose valency is two. S denotes a cubic spinel MeO.Fe203 and will be explained in detail in ch. 3 of this handbook by Krupi6ka, in vol. 2, ch. 3 by Slick (1979) and in vol. 2, ch. 4 by Nicolas (1979). However, we refer to it here as to one of the major constituent blocks of the hexagonal compounds. M compounds, which have the chemical formulae of BaO.6Fe203 (BaM), SrO.6Fe203 (SrM) and PbO.6Fe203 (PbM) etc., were developed in the initial stage by Went et al. (1952) and Fahlenbrach and Heister (1953) as a typical hexagonal ferrimagnetic oxide for permanent magnet materials. They are isomorphous with the mineral magnetoplumbite, the chemical composition of which is approximately PbzFe15Mny(A1Ti)O38. Other interesting hexagonal compounds are potential industrial magnetic materials in the systems: 2MeO-BaO.8Fe203 (Ba-Me-W), 2MeO-2BaO.6Fe203 (Ba-Me-Y), 2MeO.3BaO.12Fe203 (Ba-Me-Z), 2MeO.2BaO.14Fe203 (Ba-MeX), and 2MeO.4BaO.18Fe203 (Ba-Me-U); they have more complicated crystal structures than BaM, and were originally investigated by Jonker et al. (1954) for ? CGS unit are used in this section. SI units are shown in brackets. * More detailed diagrams of B a O - Z n O - F e 2 0 3 and SrO-ZnO--Fe203 systems were recently reported by Slokar and Lucchini (1978a, b). 307
308
H. KOJIMA
/
°,°%\/\ \~
/ \\\/
\
%
E}00
Fig. 1. BaO-MeO-Fe203 system, showing the relationships of chemical compositions among ferrimagnetic hexagonal compounds (see table 1). use at very high frequencies. They will be described in ch. 6 by Sugimoto, and in vol. 2, ch. 3 (Slick 1979) and in vol. 2, ch. 4 of this handbook (Nicolas 1979). While BaO.Fe203 (B) was reported as an antiferromagnetic hexagonal compound by Okazaki et al. (1961a, b), here, it is rather important as an intermediate phase, when BaM is prepared from Fe203 and BaO (Beretka and Ridge 1958, St~iblein and May 1969, and Wullkopf 1975). In the BaO-Fe203 system, BaO-2Fe203 (T) does not exist as a stable phase at room temperature (Okazaki et al. 1961a) but it is an essential constituent block of Y, Z and U compounds. The constitutions and phase relationships of each compound will be evident from fig. 1 and table 1.
1.2. Phase diagram 1.2.1. BaO-Fe203 systems Numerous compounds have been found in the BaO-Fe203 system, for example, 7BaO.2Fe203 (Batti 1960), 5BaO-Fe203 (Bye and Howard 1971), 3BaO.Fe203 (Okazaki et al. 1961a, Bye and Howard 1971), 2BaO.Fe203 (Erchark et al. 1946), BaO.Fe203 (Okazaki et al. 1955), 2BaO.3Fe203 (Okazaki et al. 1961a, Appendino and Montorsi 1973), 5BaO-7Fe203 (Appendino and Montorsi 1973), BaO-2Fe203 (Okamoto et al. 1975), BaO-6Fe203 (Adelsk61d 1938, Went et al. 1952), 3BaO-4FeO-14Fe203 (Brady 1973), and in an oxidizing atmosphere BaFeO3-x (Mori, 1970), and further in a reducing atmosphere, BaO-FeO.3Fe203 (Braun 1957), BaO.FeO.7Fe203 (Braun 1957) and BaO.2FeO.8Fe203 (Wijn 1952, Neumann and Wijn 1968). Figure 2 is the phase diagram determined by Goto and Takada (1960) under the oxygen partial pressure of Po2 = ~ arm [0.02 MPa] in the solid phase region and
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES
t~ tt3
,,D
tt~
¢¢3 ¢¢5 tt~
~o ~=~. ~ = ~
e~ 0
I
I
tt3
d
d o©
e--
m
m
o ©
o66
<
d66666 ~66666 ©
©
©
©
©
Nmm 0
0 0
co
e-
i
ee"
0
*
309
310
H. K O J I M A
0.5
1,0
Fez03 / BoO 1.5 2.0 4.0 6.0 I
I
I
1600
"',~
/
L
1400 o0 1370
I
1565.
/
370 1330
O912oo El. E
(I)
O9
I
(2)
{3)
I000
800
I ~' 40
2BoO'Fe203
i
[
60
8o
~
Ioo
BoO'Fe203 BoO-6Fe203 Fee03 Mole %
Fig. 2. Phase diagram of a BaO-Fe203 system (Goto and Takada 1960). Poz = { atm [0.02 MPa] in the solid phase region and Po2= 1 atm [0.1 MPa] in the liquid phase region. (1) 2BaO.Fe203 + BaO.Fe203; (2) BaO-Fe203 + BaO.6Fe203; (3) BaO-6Fe203 + Fe203.
Po2 = 1 atm [0.1 MPa] above the eutectic temperature. Batti (1960) and Van H o o k (1964) obtained somewhat different phase relations for the same system at Po2 = ½atm [0.02 MPa] and Po2 = 1 arm [0.1 MPa], respectively, which are given in fig. 3 and fig. 4. The main differences among these diagrams around the corn-
/
/
1500
/
/
/ 1474
L 1420
p 1400
1380 / ~
O9
(3)
E I. . . .
1300
BaO
,2,
20):2 2!, 40
,!, 60
Weight
8o,!6
Fe203
%
Fig. 3. Phase diagram of a BaO-Fe203 system (Batti 1960). Po2 = ½atm [0.02 MPa]. (1) 2BaO.Fe203 + BaO.Fe203, (2) BaO.Fe203 + BaO-6Fe203, (3) BaO.6Fe203 + Fe203.
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES
1600
311
.--%U Liq
,9,
1500 //" /
1400
/(I)
Q..
E
"'*,% \
i5 (6)1(7) 1495
¢
v
1330
1300
(5) !
%
(I) x
C2)
i /
1315
13) 80
6O
BoO 4 0
(4)
Fe203
Mole %
Fig. 4. Phase diagram of BaO-Fe203 (Van Hook 1964). Po2 = 1 atm [0.1 MPa]: (1) BaO-Fe203+ liq., (2) BaO-6Fe203 + liq., (3) BaO-6Fe203 + BaO-Fe203, (4) BaO-6Fe203 + Fe203, (5) BaO-6Fe203 + Fe304, (6) 2FeO-2BaO-14Fe203 + liq., (7) 2FeO-2BaO-14Fe203 + Fe304, (8) 2FeO.BaO-8Fe2Oa + liq., (9) 2FeO-BaO.8Fe203 + Fe304, (10) Fe304 + liq.
1500 ,~]) [
102
Temperature 1400 II
(°C) 1500 I !
I0 13_ /
0 X
E
io-I ('4
io-Z
i, Io-3 0.54
I
-~BaW (3] 1.58
0.62
I/T
(10 -3 K-~ )
il
0.66
Fig. 5. P - T diagram of Fe304, BaO-6Fe203 (Van Hook 1964), 2FeO-BaO-8Fe~O3 (Neumann and Wijn 1968) and 2FeO.SrO.8Fe203 (Goto et al. 1974).
312
H. K O J I M A
position of BaO.6Fe203 are the solubility limit into the B phase and the existence of a phase transition at high temperatures. Though there is still some ambiguity, the solid solution range is considered to be practically narrower than Fe203/BaO = 5.0-6.0 as shown in fig. 2. According to Batti (1960) and Van Hook (1964) it is within 5.%6.0, and 5.8--6.0 according to Stfiblein and May (1969). Moreover, almost no solubility range is claimed by Reed and Fulrath (1973). As for the liquidus line, it seems to be most probable that BaM dissociates into a liquid phase and 2FeO-2BaO.14Fe203 (Ba-Fe-X) as shown in fig. 4, even when it is heated in air (/°o2 = ½arm [0.02 MPa]). In fact, an incongruent melting will occur in the composition. Figure 5 is the equilibrium diagram of (1) BaO.6Fe203 (BaM) ~- FeO.BaO-7Fe203 (Ba-Fe-X) + liquid + 02 and (2) Fe203 ~- Fe304+x + 02 (Van Hook 1964), and also (3) the stable region of 2FeO.BaO.8Fe203 (Neumann and Wijn, 1968). The latter authors obtained B a - F e - W under the condition of /9o2 = 0.05-0.1atm [5-10x 103pa] at 1400°C as a single phase. But Van Hook (1964) found that BaM is congruently melted in Po2 = 40 atm [4 MPa] as shown in fig. 6. Figure 7 is the phase diagram by Sloccari (1973), which shows the existence of the peritectoid reaction, BaO.Fe203 (B)+ BaO.6Fe203 (BaM)~-2BaO-3Fe203, at 11500-+ 10°C.
1.2.2. SrO-Fe203 systems The phase relations are quite similar to that of the BaO-Fe203 system. Figure 8 is the equilibrium diagram in Po2 = ½atm [0.02MPa] given by Goto et al. (1971,
//
1600,
//
Liq
,j / /
z/
/
/
/
(5)
1 /
/ f/
P
(I)
1400
.......
',
,_2
,/"
.........
(3)
I1)
E I1)
I-
(2)
(1)
(4)
1200
I BaO
6o
8o
Fe203
Mole % Fig. 6. Phase diagram of a BaO-Fe203 system (Van Hook 1964). P o 2 = 4 0 a t m [4MPa]: (1) BaO'Fe203 + liq., (2) BaO.Fe203 + BaO.6Fe203, (3) BaO.6Fe203 + liq., (4) BaO.6Fe203 + Fe203, (5) Fe203 + liq.
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES
50 1200 ;
o
D
000, i
0
D
0000
D °
a) r~
(3)
0
/
0-00~.
0
0000
O.
I
iooo
F: 1-
Mole % Fe=O 3 60 70 80 85.71 I[I 1 o,oo~ ?
I100=
313
•
oooe
o
9O0
(2)
i (I) I
80C
I
Ili
//\\
I
ol m
B(:]O/Fe203 Fig. 7. Phase diagram of a BaO-Fe203 system (Sloccari 1973). (1) BaO-Fe203+ 2BaO.3Fe203, (2) 2BaO.3Fe203 + BaO.6Fe203, (3) BaO-Fe203 + BaO-6Fe203, (0) one phase, ((3) two phase.
1974). They insisted from the results of ditterential thermal analysis that there might exist some solubility range of SrM in 3SrO.2Fe203, as indicated with the broken line in fig. 8. SrM is decomposed at 1435°C to SrFe]sOz7 (Sr-Fe-W)+ liquid, and at 1465°C, they change into Fe304 + liquid in air. The stable region of Sr-Fe-W is also indicated by the region (4) in fig. 5 from the results of Goto et al. (1974). Furthermore, they obtained Sr-Fe-X by heat treatment at 1420°C for two hours, but it is decomposed by prolonged heating to a mixed phase containing Sr-Fe-W in air
1.2.3. PbO-Fe203 systems The phase relations obtained by Mountvala and Ravitz (1962) and Berger and Pawlek (1957) are considered as reasonable representations under normally attainable equilibrium conditions. Figure 9 is the diagram by Mountvala and Ravitz (1962). PbM is incongruently melted to Fe203 + liquid at 1315°C (1255°C) *, and below 760°C (810°C) * it is decomposed to FezO3+ PbO.2Fe203. Mountvala * Data by Berger and Powlek (1957).
314
H. KOJIMA
1500 ,,1480 \',,,
Liq
~
,
/
(2) X
1300
o
,,./ ~ " (I0) 1465 (8)
/
,~5 (7)11395(9)
I/
/
(5)
,, (/
(3) ~ 1195
"\
09
~- I 1 0 0 ( I)
(4)
(6)
900
40 SrFeO3-x
60 Mole %
80
I00 Fe203
Fig. 8. Phase diagram of a SrO-Fe203 system (Ooto et al. 1971, 1974). Poz=½atm [0.02MPa]: (1) SrFeO3_x + 3SrO.2Fe203, (2) SrFeO3-x + liq., (3) 3SrO'2Fe203 + liq., (4) 3SrO'2Fe203 + SrO:6Fe203, (5) SrO'6Fe203 + liq., (6) SrO'6Fe203 + Fe203, (7) SrO.6Fe203 + 2FeO-SrO-8Fe203 + (2FeO-2SrO. 14Fe203), (8) 2FeO.SrO.8Fe203 + liq., (9) 2FeO.SrO.8Fe203 + Fe304, (10) Fe304 + liq. 2:1
14oo
1:2
/
2:5
1:5 1:6
/ 1315
13oo /
12oo S o II00
/
/
/
/
1 I I I I I I
/iq (9)
I
I
~
I
i 945
9oo ~-
! ,,/---I 9,ol
(8) (4)
800
(2)
\\\2 /
7ooF.... 7~oq I600 "
0 PbO
!" '
20
1/ I I L_~
(H)
i i i
I000
5
(61
, " 760
750
i (3)
/
(io)
650
60
40 Mole %
80
I00 Fe203
Fig. 9. Phase diagram of a PbO-Fe203 system (Mountvala and Ravitz 1962). (1) PbO + 2PbO.FezO3, (2) PbO + liq., (3) 2PbO.Fe203 + Fe203, (4) 2PbO.Fe203 + PbO-2Fe203, (5) PbO.2Fe203, (6) PbO-2Fe203 + PbO.6Fe203, (7) PbO-6Fe203, (8) PbO.2Fe203 + liq., (9) PbO.6Fe203 + liq., (10) PbO-2Fe203 + Fe203, (11) PbO.6Fe203 + Fe203, (12) Fe203 + liq.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
315
and Ravitz (1962) also claimed that there is a rather wide solid solution range of Fe203/PbO = 5.0-6.0 between 800°-945°C and proposed a crystal structure for the end member of the solid solution, PbO.5Fe203. It would be reasonable to explain the fact that the lattice parameters were found to be independent of composition in this solid solution range, but the saturation magnetization of PbO.5Fe203 is higher than that of PbO'6Fe203. There seems to be no investigation about the hexagonal phase of P b - M e - W , P b - M e - X etc. in this system.
1.3. Preparation The most typical way to obtain the ferrimagnetic hexagonal oxides as powder or in a sintered polycrystalline state is the solid state reaction of heating the mixtures of constituent oxides or of compounds which are easily changed to oxides by heating. BaCO3, SrCO3, PbO and c~-Fe203 etc. are generally used as starting materials, but oxalates, sulfates, chlorides, nitrates or hydroxides are also used for specific purposes. Proper reaction temperature, atmosphere and cooling conditions should, of course, be chosen according to the phase diagrams. However, single phase M type compounds, for example, can be usually obtained by heating in air (PQ = ~ atm [0.02 MPa]) between 800 ° and 1200°C, and just removing from the furnace. The formation processes of the reactions have been reported by many authors from various points of view. Erchak Jr, et al. (1946), and Erchak Jr. and Ward (1946) investigated the reaction between ferric oxide and barium carbonate and found the formation of BaO.2Fe203 above 550°C and BaO.6Fe203 above 750°C by X-ray diffraction. Sadler (1965) studied the reaction kinetics of BaM, and obtained the activation energy of 73.2 kcal/mol [3.06× 105 J/mol] above 735°C. Wullkopf (1972, 1975) observed the variations of the amount of reaction products, length, weight and grain size for the mixed compact of BaCO3 and 5.5Fe203 during the sintering process and collected the data, as shown in fig. 10. Similar results were also reported by Haberey et al. (1973). Furthermore, Haberey and Kockel (1976) found that SrM is formed from a mixture of SrCO3 and 6Fe203 through the following two endothermal reactions: SrCO3 + 6c~-Fe203 + (0.5 - x) × 102 --~ SrFeO3-x + 5.5a-Fe202 + CO2 SrFeO3-x + 5.5ol-Fe203---> SrO-6Fe203 + (0.5 - x) × ½02. Bowman et al. (1969) investigated the formation mechanism of PbM in the PbO-Fe203 system and concluded that PbM is formed through the intermediate compounds of 2PbO-Fe203 or PbO'2Fe203, depending upon the mixing method, the time and temperature of heating. They used two kinds of co-precipitation methods for mixing, in which the aqueous solution of ammonium bicarbonate was added to the solutions containing lead nitrate and ferric nitrate, or lead nitrate and ferric oxide. The co-precipitation method was also used to obtain a high coercivity BaM or
316
H. KOJIMA
1.0 0.8
(b)
\\k\\\\\ M/
' ~
0.6 .o
\/,/,, \/-
0.4
\/
\
\
/
! !
0
! I
/ 'l
1.0
(0) •~ 0.8 (D
>, 0.6
P "
\
/
0.2
\
0.4
z
//. w
"~ 0.2 rr 0
0
400
800
1200
i./411600
Temperoture (°C) Fig. 10. Changes of BaO-5.5Fe203 compact during heating (Wullkopf 1972, 1975): (a) variation of reaction products, F: Fe203, Bc: BaCO3, B: BaO.Fe203, M: BaO.6Fe203, Y: 2FeO.2BaO.6FezO3, W: 2FeO-BaO-8Fe203, Z: 2FeO-3BaO.12Fe203; (b) variation of length L, weight G, grain size D and saturation magnetization M.
SrM by Mee and Jeschke (1963), Haneda et al. (1974a), Roos et al. (1977) and Oh et al. (1978). Furthermore, Shirk and Buessem (1970) obtained a high coercivity BaM from a glass with the composition 0.265BzO3-0.405BaO-0.33Fe203 in mole ratio. They reported that single domain particles can be crystallized in the fast-quenched glass with this composition by the heat treatment under the appropriate condition (see also table 10). A molten salt synthesis utilizing NaC1KC1 for BaM and "SrM submicron crystals with high magnetic quality was proposed by Arendt (1973). Moreover, Okamoto et al. (1975) applied hydrothermal synthesis with ol-Fe203 suspension in barium hydroxide aqueous solution and obtained BaO.2Fe203 crystals, whose space group was reported as P63/m with the lattice parameter of a = 5.160 A and c = 13.811 A. Kiyama (1976) obtained BaO.6Fe203, BaO.4.5Fe203 and BaO.2Fe203 with Fe(OH)3 or FeOOH and Ba(OH)2 under the similar conditions in an autoclave and studied magnetic properties. Single crystals of M compounds were obtained by cooling a nearly eutectic melt (Kooy 1958); under the high oxygen pressure (Van Hook 1964, Menashi et al. 1973); using various kinds of flux (Mones and Banks 1958, Brixner 1959, Linares
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
317
1962, Suemune 1972, Aidelberg et al. 1974); or discontinuous grain growth (Lacour and Paulus 1968, 1975). B a - Z n - Y , B a - Z n - W , B a - Z n - Z , B a - C o - Z n - W and B a - C o - Z n - Z etc. were also grown by the flux method (Tauber et al. 1962, 1964, Savage and Tauber 1964, AuCoin et al. 1966, Suemune 1972). BaC12, BaO-B203, BaO-B2Og-PbO, Na2CO3 and NaFeO2 were recommended as a flux for these compounds. Takada et al. (1971) found that topotactic reactions among a - F e O O H or ~-Fe203 and BaCO3 or SrCO3 are effective to obtain a grain oriented specimen. The crystallographic relationships of the materials are ( 100 )~-F~OOH//(0001)~,_F~203//(0001)S~O.6Fe203, [010],,-F~OOH//[11,201a -Fe203//[1010]SrO.6F~203 • Hot press or hot forging processes are also useful to prepare a dense oriented sintered body (St~iblein 1973, Haneda et al. 1974a).
2. M compound A Ba 2+ ion in the M compound, BaO-6Fe203 (BaM), can be replaced partly or completely by Sr 2+, Pb 2+ and a combination of, for instance, Agl++ La 3÷ or Nal++ La 3+, without changing its crystal structure. Substitutions of Fe 3÷ and 02ion in the compound are also possible. In all cases, substituted ions would be chosen to keep electrical neutrality and to have similar ionic radii with the original ions (see table 2; a more comprehensive table of ionic radii can be seen, for example, in the book of Galasso (1970)). BaM was at first the only main constituent of M-type oxide magnet, produced on an industrial scale but TABLE 2 Ionic radii of several related ions (Pauling 1960). Element
valence
r (A)
Element
valence
r (A)
Element
valence
r (4)
Ag AI As
+1 +3 +3 +5 +2 +3 +2 - 1 +2 +3 +2 - 1 +2 +3
1.26 0.50 0.58? 0.46t 1.35 0.96? 0.99 1.88 0.72? 0.63? 0.72? 1.36 0.74t 0.64t
Ga Ge In Ir La Li Mg Mn
+3 +4 +3 +4 +3 +1 +2 +2 +3 +4 +1 +5 +2 - 1
0.62 0.53? 0.81 0.68? 1.15 0.60 0.65 0.80? 0.66t 0.60? 0;95 0.70 0.69? 1.40
P
+3 +5 +2 +3 +5 +3 +4 +2 +5 +4 +3 +5 +2 +4
0.44t 0.35t 1.207 0.76? 0.62? 0.81 0.71 1.13 0.68t 0.68 0.95 0.59 0.74 0.80
Ba Bi Ca C1 Co Cr Cu F Fe
? Ahrens (1952).
Na Nb Ni O
Pb Sb Sc Sn Sr Ta Ti T1 V Zn Zr
318
H. K O J I M A
SrO-6Fe203 (SrM) has more recently taken over some part of BaM. PbO.6Fe203 (PbM) is used only as an additional material for oxide magnet purposes at present (see ch. 7 by Stfiblein for the applications). In the following section the fundamental properties of BaM, SrM and PbM are described. The properties of solid solutions among BaM, SrM and PbM, and substituted M compounds are treated separately in this chapter.
2.1. BaFele019, SrFe12019 and PbFea2019 2.1. i. Crystal struclure Adelsk61d (1938) determined the crystal structures of BaM, SrM and PbM, prepared by heating co-precipitated mixtures from the solutions of nitrates. Figure 11 is a perspective drawing of BaM. The 02 ions form a hexagonal close packed lattice, so that its layer sequence perpendicular to the [001] direction is A B A B . . . or A C A C . . . as is shown in the figure. Every five oxygen layers, one O 2 ion is replaced with Ba 2+, Sr 2+ or Pb 2+ in BaM, SrM or PbM respectively and this occurs due to the similarity of their ionic radii as given in table 2. Five oxygen layers
(15) (12)
(11)
A
(10)
C
(9)
A
(8)
C
(7) (6)
B
{5)
(4)
(3) (2)
Fig. 11. Perspective illustration of BaO.6Fe203.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
319
make one molecule and two molecules make one unit cell. Each molecule shows 180° rotational symmetry around the hexagonal c-axis against the lower or upper molecule. The O z- layer containing Ba 2+ is a mirror plane, being perpendicular to the c-axis. Fe 3+ ions occupy the interstitial positions of the oxygen lattice. The space group of the compound is denoted as P63/mmc (D4h) using H e r m a n n Mauguin's (Sch6nflies') symbols. Figure 12 illustrates more clearly the layer structure of BaM, where z means the layer height along the [001] direction and the layer numbers are the same as in fig. 11. Explanation of the symbols used in the figures are also given here. Wyckoff's notations are adopted for every site in the crystal (Henry and Lonsdal 1952). The positions of each atom are tabulated in table 3 (Galasso 1970). Figure
~ (6) 0.45
C~) 0 -2 {12) 0,95
ion
(~) Be2+ ion
Fe3+(4f2)IOctahedral site (5) 0.35
(11) 0,85
(~ Fe3+(2o)J
T
141 0.25
clot 0.75
~
(~ Fe3+ under the layer Lt~ Fe3+ above the layer T relative orientation of magnetic moment
(5) 0.15
(9) 0.65
(2) 0.05
(8) 0.55
(I) Z=O
(7) 0.50
(13) 1.00
Fig. 12. The layer sequence of BaO.6Fe203.
320
H. KOJIMA TABLE 3 Atomic positions of BaFe120~9 (see fig. 12) (Galasso 1970).
Ion 2Ba 2+
24Fe 3+
3802-
Site
Coordinate
x
z
-
0.028 0.189 -0.108
2d 2a 2b 4fl 4f/ 12k
I, 2, 2; 2, ½, ¼ 0,0,0;0,0,1 0,0,¼;0,0, 3 )l I ±(½, 2, Z; 2, 5,Z ~q_ 1 ___(1, 2, z ; 2, 3,1 ~+z) +(x, 2x, z; 2x, x, Y.; x, 2, z; x, 2x, l - z; 2x, x, ½+ z; £, x, ½+ z)
0.167
4e
+(0, 0, z; 0, 0, 1+ z) 1 2 2 ±(3, 3, z; ~, ½, ½+ z) ±(x, 2x, ¼; 2x, x, 3; x, g, ¼) --+(x, 2x, z ; 2x, x, 2 ; x, 2, z; x, 2x, ~1- z; 2x, x, ~+z; £, x, 1+z) 1 1 1 ±(x, 2x, z ; 2 x , x, 2;x, 2, z ; x , 2 x , ~ - z ; 2 x , x , ~ + z ; x , x , ~ )
0.186 0.167 0.500
4f 6h 12k
-
--
0.150 -0.050 0.050 0.150
13, t h e (110) s e c t i o n of B a M , is a n o t h e r e x p r e s s i o n o f t h e c r y s t a l s t r u c t u r e , s h o w i n g a t o m s a n d s y m m e t r y e l e m e n t s in a m i r r o r p l a n e c o n t a i n i n g t h e c - a x i s ( B r a u n 1957). S a n d R a r e t h e b u i l d i n g b l o c k s of t h e crystal, a n d S* a n d R * i n d i c a t e t h e b l o c k s , o b t a i n e d by r o t a t i n g S a n d R t h r o u g h 180 ° a r o u n d t h e c-axis, as p r e v i o u s l y i l l u s t r a t e d . It can b e said, t h e r e f o r e , t h a t t h e u n i t cell of B a M is 21
63
6 C 6
63
++3++2,
R~
ooz
~'~hz ~U/~z iIz [JTo]
Fig. 13. The (110) cross section of BaO-6Fe203.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
321
expressed as RSR*S*. Moreover, Townes et al. (1967) refined the crystal structure of BaM by X-ray investigation. They stated two points: o(i) The Fe 3÷ ion in the trigonal bipyramidal site, 2b, is split into half atoms 0.156 A away from the mirror plane, 4e. (ii) Some iron octahedra occur in pairs which share a common face to form Fe209 coordination groups. The former is supported by some M6ssbauer investigators (see ch. 2 section 4.2.1 M6ssbauer effect). Atomic coordinates, interatomic distances and structure factors are tabulated in their paper which gives more accurate results. Figure 14 shows perspective drawing of the R (BaFe6Oll), S (Fe6Os) and T (Ba2FesO14) blocks separately. The T block is related only with the Y, Z and U I-
0
(
Fig. 14. Perspective drawings of building blocks in the hexagonal compounds, T(Ba2Fe8014), S(Fe6Os) and R(BaFe6On).
322
H. KOJIMA j
Qlf
2
j ~ J
Fig. 15. Unit cell of BaO.6Fe20), showing the crystal structure composed of spinel blocks and Ba layers (Gorter I954). TABLE 4 Lattice constants, molecular weights and X-ray densities of M-type compounds. Lattice constant Compound
Molecular weight (g/mol)
a (,~)
c (,~)
c/a
X-ray density (g/cm ~)
Ref.
23.i94 23.20 23.182 23.17
3.936 3.94 3.936 3.943
5.29 5.29 5.30 5.33
(a) (b) (c) (d)
BaFe12019
1111.49
5.893 5.89 5.889 5.876
SrFe12019
1061.77
5.885 5.876 5.864
23.047 23.08 23.031
3.916 3.92s 3.928
5.10 5.11 5.14
(e) (c) (d)
PbFe12019
1181.35
5.877 5.889
23.02 23.07
3.917 3.917
5.70 5.66
(d) (c)
(a) Tauber et al. (1963) (b) Smit and Wijn (1959) (c) Bertaut et al. (1959) (d) Adelsk61d (1938) (e) Routil and Barham (1974)
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
323
c o m p o u n d s but is shown here to illustrate the relationship a m o n g the blocks (see ch. 2 sections 4.l and 4.3). S has the cubic spinel structure with the [ l l l ] axis vertical. In other words, M is synthesized by piling up a Ba layer and a spinel block, whose layer sequence is A B C A . . . . alternatively (see fig. 11). G o r t e r (1954) showed this simply by fig. 15, where spinel block contains four oxygen layers. Molecular weight, X-ray density and lattice constants reported by various investigators are tabulated in table 4.
2. 1.2. Magnetic structure M-type c o m p o u n d s have a typical ferrimagnetic structure, that is, the orientation of the magnetic m o m e n t s of the ferric ions in the crystal are generally aligned along the c-axis in antiparallel with each other. Ndel (1948) and A n d e r s o n (1950) first considered from the theoretical view point that these alignments of magnetic ions can be realized by superexchange interaction through oxygen ions and such a structure has been proved from the experimental results of saturation magnetization, neutron diffraction, M6ssbauer effect and nuclear magnetic resonance etc. Grill and H a b e r e y (1974) calculated the exchange parameters of Fe > ions in BaM, as shown in table 5. H e r e it can be clearly seen that the closer the angle of the F e - O - F e b o n d approaches 18(t°, the larger the exchange p a r a m e t e r b e c o m e s
TABLE 5 Distances and angles of the Fe-O-Fe bonds and calculated exchange parameters in BaFe12Ot,~ (Grill and Haberey 1974). Distance (A)
Angle (degree)
Exchange parameter
Calculated value (K//z~)
'~ Fe(b')-OR2Fe(f2) { ]' Fe(b')-OR2-Fe(f:) ,~
1.886 + 2.060 1.886 + 2.060
142.41 132.95
Jbf2
35.96
{ Fe(f0-Os~-Fe(k) I" ,~Fe(f~)-Os2-Fe(k) ~"
1.897 + 2.092 1.907+ 2.107
126.55 121.00
Jkf~
19.63
]"Fe(a)-Osz-Fe(f~) +
1.997 + 1.907
124.93
Jaf~
18.15
{ Fe(f2)-OR3-Fe(k) ]"
1.975 + 1.928
127.88
Jf2k
4.08
]"Fe(b')-OR,-Fe(k) '[' '["Fe(b")-OR~-Fe(k) 1'
2.162+ 1.976 2.472 + 1.976
119.38 119.38
Jbk
3.69
]"Fe(k)-OR,-Fe(k) 1" ~"Fe(k)-Os,-Fe(k) ~" I"Fe(k)-Os2-Fe(k) ~ '["Fe(k)-OR~-Fe(k) ~"
1.976 + 1.976 2.092 + 2.092 2.107+ 2.107 1.928 + 1.928
97.99 88.17 90.08 98.05
J~k
<0. I
"["Fe(a)-Os2-Fe(k) 1"
1.995 + 2.107
95.84
J~k
<0.1
{ Fe(f2~OR2-Fe(f2) $
2.060 + 2.060
84.64
Jf2f2
<0.1
Bond
324
H. K O J I M A
and when the angle is closer to 90 ° , the p a r a m e t e r becomes negligible small. Thus, arrows in figs. 11 and 13 etc. are the orientation of the magnetic m o m e n t s of each ferric ion as a result of superexchange interaction. One can see in these figures that the S block contains four Fe 3+ of up-spin in octahedral sites and two Fe 3+ of down-spin in tetrahedral sites. In the R block, there exist three Fe 3+ of up-spin in octahedral sites, two Fe 3÷ of down-spin in octahedral sites and one Fe 3+ of up-spin in a trigonal bipyramidal site. Considering the magnetization values of B a M with the Andersons (1950) indirect exchange theory, the exchange scheme of the compound is illustrated in fig. 16, proposed by Gorter (1957), and these relations are tabulated in table 6. Notations of the sublattices commonly used for M6ssbauer or N M R investigations are also shown in the last column of the table.
[20 =l14f, ~ J4f2~ 2
14f2~ b[ [4f2//~12k [[[
I 14f2,2kHt t20--lt4', Fig. 16. Exchange interaction scheme in the unit cell of the magnetoplumbite structure. Each arrow represents the magnetic moment of a Fe 3+ ion (Gorter 1957). TABLE 6 Coordination number and direction of magnetic moment of Fe 3÷ ions in the unit cell of the magnetoplumbite type crystal.
Coordination number
Number of positions
Wyckof's notation
Direction of magnetic moment per mole
Remarks
6 (Octahedral site)
12 4
k f2
I" I" I" I' '~ 1' ~ ~,
I (a) III (d)
2
a
t
v (b)
4 (Tetrahedral site)
4
fl
$ ,~
II (c)
5 (Trigonal bipyramidal site)
2
b
I"
IV (e)
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
325
The total magnetization at temperature T, therefore, is expressed as Ms(T) = 6O-k(T) -- 2o-f~(T) - 2o-~2(T) + O'b(T) + O'a(T),
(1)
where, Ok, O-fl, O'f2, O'b and O'a denote the magnetization of one Fe 3+ ion in each sublattice. Because Fe 3+ has the magnetic moment of 5/~B at 0 K, eq. (1) is calculated as Md0 K) = 5 x (6 - 2 - 2 + 1 + 1) = 20/~B.
(2)
This value agrees well with the experimental result of BaM as described in the next section. The large magnetocrystalline anisotropy of compounds was explained by Smit (1959) from the effect of Fe 3+ in the trigonal bipyramidal site, where a ferric ion is surrounded by five oxygen ions. Fuchikami (1965) also showed theoretically the contribution of Fe B+ in the trigonal site as principally responsible for the uniaxial anisotropy. On the other hand, Van Wieringen (1967) stressed from the M6ssbauer investigations that the contributions to the anisotropy from all of five sublattices should be more or less equally considered.
2.1.3. Saturation magnetization The saturation magnetization per unit volume, Ms, per gram o-s, the number of Bohr magnetons per mole Ns at room temperature or 0 K and the ferromagnetic Curie temperature 0c for BaM, SrM and PbM reported by various authors are collected in table 7. Values of NS at 0 K for these three compounds are about 20/-tB and agree well with the theoretically expected values from their magnetic structures as given by eq. (1) or (2). The temperature dependences of the saturation magnetization Ms near the Curie points are shown for BaM and SrM by Shirk and Buessem (1969) in fig. 17. Figure 18 illustrates the compariso n of Ms for BaM (Rathenau et al. 1952), SrM (Jahn and Mfiller 1969) and PbM (Pauthenet and Rimet 1959a) in a wider temperature range. In addition, fig. 19 and fig. 20 are other reported o-~T relations for BaM and SrM (Shirk and Buessem 1969) and BaM (Tauber et al. 1963, Casimir et al. 1959) respectively. Belov et al. (1965) pointed out that the spontaneous magnetization of BaM along the c-axis is somewhat greater than that in the perpendicular direction to it, and found the difference of 0c between both directions to be as shown in table 8. Similar facts are reported on the paramagnetic Curie points, as described later. Though the reported results are slightly different from author to author, the magnetic characteristics of M-type compounds may be summarized as follows: (i) The saturation magnetization becomes smaller according to the order to SrM, BaM and PbM; (ii) The Curie temperatures also become smaller in the same order; (iii) Saturation magnetization versus temperature curves are almost straight or rather concave with a steep slope in the temperature range of 200 and 600 K.
326
H. KOJIMA
©
÷
k~
s,
d °
(-q d
o.
0
+1 o';
I
+J
['---
8 +~
I
+1 t-,-
t'--
8 o'3 ~
0
tt3
or-e0
I
+1 t~
tt3
t'q
,4~d
p-- ,,o
5
'4~ eq
z
o
r~
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
327
120
80
--(
,
•
'o_ ×
6O
4 0
20
.
700
.
.
.
.
•
.
I
o
680
.
I T
720 740 760 Temperature (K)
780
Fig. 17. Saturation magnetization versus temperature near the Curie points of BaO.hFc_-(% and SrO.6Fe203 (Shirk and Buessem 1969): (1) BaM, (2) SrM. -200
600
-I00
TemperQture (°C) IO0 200
0
300
400
500
(I)
~.
400
x
300
,,¢
x
I
'-" 2 0 0
~
ioo
-
.
-
I'
0 0
200
.
.
.
+
----
.
~
i
\
i
400 Temperafure
600
-
__ 800
(K)
Fig. 18. Saturation magnetization of BaO.6Fe203, SrO.6Fe203 and PbO.6Fe203 as a function of temperature: (1) BaM (Rathenau et al. 1952), (2) SrM (Jahn and Mfiller 1969), (3) PbM (Pauthenet and Rimer 1959a).
TABLE 8 Differences of ferromagnetic Curie temperature 0¢ of BaFe12Ot9 along and perpendicular to the c-axis (Belov et al. 1965). Sample
0c//(°C)
00~ (°C)
0c/j-0ci
Single crystal
440.3
436.5
3.8 °
Polycrystal (oriented)
459.4
453.3
6.1 °
328
H. K O J I M A
I \,
100
~g < E, 80
b x 60 k x 40 03
2O
0
0
200 400 600 Temperature (K)
800
Fig. 19. Plot of saturation magnetization per gram versus temperature for BaO-6Fe203 and SrO.6Fe203 (Shirk and Buessem 1969): (1) BaM, (2) SrM. Temperature (°C) 2O0
0
200
400
I
I
I
100
,E
\
80
b-
'O
x 60 b & 4O ID
C 20
0
400 600 200 800 Temperature (K) Fig. 20. Plot of saturation magnetization per gram versus temperature for BaO.6Fe203: (1) Tauber et al. (1963), (2) Casimir et al. (1959).
0
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
329
2.1.4. Magnetocrystalline anisotropy Villers (1959a) measured the specific magnetization of a PbM single crystal as a function of the applied field. From his results along various measured directions against the c-axis, as shown in fig. 21, a fairly large uniaxial anisotropy can be estimated for the crystal. In fig. 22, magnetizing curves of B a M (Casimir et al. 1959) and P b M (Pauthenet and Rimet 1959a) perpendicular to the c-axis are c o m p a r e d at various temperatures. Magnetocrystalline anisotropy constants K~ as a function of t e m p e r a t u r e are plotted for B a M (Rathenau et al. 1952, Shirk and Buessem 1969), SrM (Jahn and Mfiller 1969, Shirk and Buessem 1969) and PbM (Pauthenet and Rimet 1959a, Villers 1959b) in figs. 23, 24 and 25 respectively. When the direction of the spontaneous magnetization in a hexagonal crystal is expressed by polar coordinates, 0 and ~b with respect to the crystal axis, assuming the z-axis is the c hexagonal axis, then the magnetocrystalline energy E is given by E = K~ sin 2 0 + / ( 2 sin 4 0 + K3 sin 6 0 + / ( 4 sin 6 0 COS 6 (D q-
.
.
.
.
(3)
For M-type compounds,/£2,/(3 . . . . are negligible in comparison with K1 and their 70
I
0=0
otOj,.e_e-e- -
60
/ - T
r
~
Fy
) 5o
/
y,
b 4o ×
H ,x 3 0
vl
,
__.t/#
I
20
/
)
v
b
,o/ 0
0
5
I0
15
20
H (kOe) [ x l O 6 / ( 4 n -) A / m ]
Fig. 21. Magnetization per gram of PbO.6Fe203 single crystal as a function of the magnetic field applied at various angles with respect to the c-axis (Villers 1959a).
330
H. K O J I M A
600 20.4 0 ~ C ' 0 4 2 ~ " 0 " .7 - - - ~ - - - 0 - 0
500
;.~,.
--0-
.
.77.4
K -
K
,~ 2.3-4.2-9,5-15-20.4 K 400
b //
~,l
,~ 300 ×
/
eoo
7SI
~
• JI
tOO
'
'
~
567 K
:4 t
~
:
0
[
!
!
,-----r - ° - 5
0
; I0
I 15
I 20
H (kOe) E x l O e / ( 4 r r )
i 25
G-
30
A/m]
Fig. 22. Magnetization of BaO.6FezO3 and PbO.6Fe203 single crystals at various temperatures as a function of the magnetic field applied perpendicular to the c-axis: ([]) B a M (Casimir et al. 1959), (O) PbM (Pauthenet and Rimer 1959a).
-200
%
4
L
I
Temperofure (°C) 0 I00 200 500
-I00 I
!
r
F
!
r
400
L !
500
i
I L .........
x
~J5
! L
ro
E
/
o
~L × v
~-o
I
T
-
i i
0
200
400 Temperafure
600
800
(K)
Fig. 23. Magnetocrystalline anisotropy constant K~ of BaO-6Fe203 as a function of temperature: (C)) R a t h e n a u et al. (1952), (Q) Shirk and Buessem (1969).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
331
~ 5 tO -3
4
% ,x, 3
.,
t,3
E 0
"" 2
--
[
X
"-- o
0
200
:
400
Temperafure
600
%800
(K)
Fig. 24. Magnetocrystalline anisotropy constant K~ of SrO.6Fe203 as a function of temperature: (O) Jahn and Miiller (1969), (z~) Shirk and Buessem (1969).
t¢3
E4
4
J
E
s%
%s
X t...a
,<
.-,%.
0
(2) K 2
2 ,n E O
\°Xo ~'~.~
ID
%
O
0
x 0 0
200
400
Temperature
600
x
800
(K)
Fig. 25. Magnetocrystalline anisotropy constant KI and K2 of PbO.6Fe203 as a function of temperature: (O), (O), Kj K2, Pauthenet and Rimet (1959a); (A) K~ Villers (1959b).
values were reported only for PbM, as shown in fig. 25 and table 9. The order of the values of Kj among the three compounds is again, the same as M~, i.e., SrM > BaM > PbM, though the difference between SrM and BaM is not clear in s o m e cases. Now, because HA defines the maximum coercivity as described in the next section, we shall briefly compare HA values among these compounds. Since the magnetocrystalline anisotropy field HA for uniaxial materials is given by Ha = 2KI/Ms,
(4)
we can easily estimate the value of HA from the data of K1 and Ms, described here. Figures 26 and 27 give curves of HA against temperature for BaM (Rathenau et al. 1952, Shirk and Buessem 1969) and SrM (Jahn and M/iller 1969, Shirk and
332
H. KOJIMA
X
x~ ~+~
0
o
~+
©
II
dddd e.
II
×
dd
e-
e.
~
~
e-
¢=
-ff
d +l
~
+1
tt~
t--
~.
x
+1
+i
Ca
e.
¢e)
xa
eqeq
¢q.
Me4
m
+1 t'q
m. +1
+1
ff
o ~7
m
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
-200 ,
20
T e m p e r e f u r e (°C) 0 I00 200 300 i I! I i
-I00 ~
400
333
500
I
i
"..4 < i 5 - -
'~ o
I0
x
o
5
31
i!
0
0
260
i
400 Temper0ture
600
l
800
(K)
Fig. 26. Magnetocrystalline anisotropy field HA versus temperature for BaO.6Fe203: (C)) Rathenau et al. (1952), (A) Shirk and Buessem (1969).
25
20
\
< 15 .........
o
(3)
" - . . ~
""\ \
×
10 o '1-
5
0 0
200
400 Temperature
600
800
(K)
Fig. 27. Magnetocrystalline anisotropy field HA versus temperature for SrO.6Fe203 and PbO'6Fe203. SrM: (1) Jahn and M/iller (1969), (2) Shirk and Buessem (1969). PbM: (3) calculated from the data of Pauthenet and Rimet (1959a).
334
H. KOJIMA
Buessem 1969) respectively. The broken line in fig. 27 shows HA of PbM calculated from the results of Pauthenet and Rimet (1959a). There are broad maxima between 400 and 600 K, except Rathenau's results. Beside the data in figs. 23-27, the reported values of the magnetocrystalline anisotropy constant K~ and anisotropy field Ha are tabulated in table 9. Above all, from these points of view, SrM eventually shows the best properties as the permanent magnet material among the three compounds. 2.1.5.
())ercive force
It can be generally said that the coercive force of ferrite magnets such as sintered or bonded compacts of BaM, SrM or PbM powders, originates in the magnetic behaviour of single domain particles with uniaxial magnetocrystalline anisotropy. Now we shall briefly describe general considerations regarding the coercive force of such materials. The critical diameter of a particle, where a single domain state can be energetically realized, was obtained by Kittel (1946) and Ndel (1947) as D = (9/2¢r)(O-w/m~),
(5)
cr,~ in the equation denotes the domain wall energy per unit area and approximately written by O-w= 4(AK) '/2 .
(6)
Here, A expresses the exchange constant. In table I{L the values of D~, ow and MHc are listed for M compounds.
Since only rotation of magnetization can be expected in a particle of smaller diameter than D~, assuming its demagnetizing factor as N. we can write the coercive force as MHc = 2 K / M ~ - N M ~ .
(7)
For the magnetizing process of a powder assembly, Stoner and Wohlfarth (1948) assumed the coherent rotation mode without any interaction effect, and concluded that the coercivity factor obtained was 0.48 for the randomly oriented powders; then MHc is given by MHc
=
0.48(2K/Ms - NMs) .
(8)
For M compounds, crystals are usually easy to grow along the c plane, so that N affects MHc more unfavourably than spherical particles. However, we still cannot attain the MHc value of eq. (8) experimentally for practical hexagonal ferrite powders. To explain this, various magnetization reversal mechanisms of incoherent type have been proposed. For example, by considering the interaction field of surrounding magnetic dipoles, Eldridge (1961) simply estimated the effect of mutual interaction. Hence, we can
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
335
e~
0
8
©
io<
,=
$
!c ,
t¢3
I
;o II
[,q
X kD kD
5
I
II
II
a O
O
.o
0 ,,=
O
'i
N O
"a
a
!
ff
)
N
1
e~
I
D.
e~ o
6 L)
6 L)
)
~d
8
11
© e~
©
© 0
0
~.~
¢..)
#
&-a
m.
o
uq
~
6
trl
x
~'~
m
O~ ,4
o
o.
~D tt3
t~q
X
d ©
o. O0
e~ ¢-
E
+1 t'4
¢×
O
4
e. o o
o,
~ E
g =N
336
H. K O J I M A
generally express MHc using his results: MHc = MHc(0)- CpMs, with C = 1.7.
(9)
Here MHc(0) and p express the coercive force of ideal coherent rotation and the volumetric packing factor of the powder assembly. Bottoni et al. (1972) deduced the partial existence of chains of spheres with fanning mode from the rotational hysteresis measurements for dry-milled BaM powders. Many researchers, for example, Hoselitz and Nolan (1969), Ratnum and Buessem (1972), Haneda and Kojima (1973a, 1974) besides others mentioned below, have been discussing the causes for the reduction of domain nucleation field and they concluded that domain wall movement should be also considered for the magnetizing process of M compound powders, even though they are sufficiently small compared to Dc in table 10. For instance, lattice defects (Heimke 1962, 1963), different phases (Richter and Dietrich 1968), stacking faults or deformation twins (Rantnam and Buessem 1970), local changes in anisotropy (Aharoni 1962), inhomogeneity of magnetic field in the edge of plate like crystals (Holtz 1970) etc. can be given as factors to be considered as possible causes. Experimental results of packing effects on MHc are illustrated in fig. 28 for BaM (1), (2) by Shimizu and Fukami (1972), BaM (3) by Luborsky (1966) and SrM (4) by Hagner and Heinecke (1974). We can say from these results that the constant C is rather smaller than the value of eq. (9) for BaM or SrM, and this may be caused by their larger Ks and lower Ms values. The last authors especially stressed the importance of the agglomeration effect to verify the dependence of MHc on the packing density. To prevent the agglomeration, they used a soft ferrite to dilute SrM powders and measured MHc above the Curie temperature of the soft
4000
<
3000
g (4)
_o 2 0 0 0 x
o o "1"
I000
0
0
0.2
0.4 Packing
0.6 factor
0.8
1.0
P
Fig. 28. Effect of the packing factor on the coercive force of BaO.6Fe203 and SrO'6Fe203. (1), (2) BaM (Shimizu and Fukami 1972), (3) BaM (Luborsky 1966), (4) SrM (Hagner and Heinecke 1974).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
337
ferrite. But Tfmfisoiu et al. (1976) reported a very high MHc value of 6500 Oe [5.17x 105A/m], obtained for SrM by the ordinary dispersion method in zirconium oxide powder or an epoxy resin, if the packing factor p ranges from 0.1 to 0.01. Curve (1) in fig. 29 is an example of the change in MHc during the milling process (after Haneda and Kojima (1974)). Though the shape of the curve depends on the grinding conditions, MHc generally increases at first and then decreases with milling time. The first rise is presumably caused by the approach to the single domain behaviour and the following decrease may be explained b y various causes introduced by the prolonged milling process, as mentioned before. Curve (2) in the figure shows MHc obtained by annealing the specimenS of curve (1) at 1000°C for an hour. The remarkable increase may be mainly due to the recovery of various defects. The MHc versus particle diameter relations of BaM are compared in fig. 30. Shirk and Buessem (1971) determined the particle size by X-ray (1) and electron microscope (2), while Sixtus et al. (1956) measured MHc against thickness (3) and diameter (4) of the platelets. Powders larger than 10 .4 c m seem to behave as multidomain particles and below 2 x 10 6cm by X-ray or 6 x 10-6cm by electron microscope, superparamagnetic effects are likely to be predominant. Since superparamagnetic powders do not show a hysteresis loop, MHc abruptly tends to zero in this region. If the particle has volume V and Sc denotes the superparamagnetic critical size, the coercivity factor against V/Sc can be expressed as in fig. 31, according to the calculated results of Shirk and Buessem (1971) for the case of BaM. Hence, one can say the Stoner-Wohlfarth model is valid only under the condition of V ~ 100So, that is roughly larger than 4 x 10-6 cm in diameter for a BaM particle; the agreement of this estimation with the results in fig. 30 is reasonably good.
k
II 1
0
/
~'
--e~e'--
•
O
I
0
0
50
100 Milling time (hr)
150
200
Fig. 29. Milling and annealing effect on the coercive force of BaO.6Fe203 (Haneda and Kojima 1974), (1) as milled powder, (2) after annealing at 1000°C for 1 h.
338
H. KOJIMA 104
<
I
I
I
I
I
I
I
I
I i I
I
I
I
I
I
I
I
I
o
i0 3
O x
I)
(2)
x\
O i0 2
I0
I
I
10-6
I I
I
I
II
I
10-5
I
I I
iO-4
Porficle
I
I
[ I
IO-3
diomefer
I fO-Z
(cm)
Fig, 30. Relation of coercive force and particle size in BaO.6Fe203: (1) diameter as spheres determined by X-ray, (2) by electron microscope (Shirk and Buessem 1971), (3) thickness of platelets determined by optical microscope, (4) diameter (Sixtus et al. 1956).
Figure 32 shows the changes of MHc with temperature; i.e., for SrM (1) and BaM (2) by Mee and Jeschke (1963), BaM (3) by Sixtus et al. (1956), BaM (4) by Rathenau (1953) and SrM (5) by Jahn and Mdller (1969). All results show maxima between 200 ° and 300°C. Rathenau tried to explain the maximum of MHc by assuming a single domain state around 300°C and a multidomain state at room 0.6
i
i
E
~
i
i
i
E
E
i
I
I
i
i
i
I
I
I
0.5
0.4
8 0.3
$ o.2
3
0.1
0
I
I0
10 2
I
03
V/Sc Fig, 31. Coercivity factor against particle size for isotropic powder assemblies (Shirk and Buessem 1971). V: volume of a particle, So: super-paramagnetic critical size; dotted line: Stoner-Wohlfarth model.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
6
o~
.---o
°'~
''°
.-
339
l
?< 5~
~"
£
!
i
-200
i
0
200 Temperature
I
400
(°C)
Fig. 32. Temperature dependence of the coercive force for BaO-6Fe2Os and SrO-6Fe203. (1) BaM, (2) SrM (Mee and Jeschke 1963), (3) BaM (Sixtus et al. 1956), (4) BaM (Rathenau 1953), (5) SrM (Jahn and M/iller 1969).
9 8
I i i
r
i
i
6
s
j
J 5
-200
0
200 Temperature (*C)
400
Fig. 33. Temperature dependence of ",/~/Ms, which is proportional to the critical diameter of single domain particle (Rathenau 1953).
340
H. K O J I M A
temperature. He reported the temperature dependence of (KO1/2/Msas in fig. 33, to which the critical particle diameter Do would be proportional. His explanation is based on the increase of this quantity with temperature. However, this might only be one reason, because many authors reported maxima of HA in the same temperature range as MHc (see figs. 26 and 27). Craik and Hill (1977) pointed out that the strong domain wall pinning could be expected at grain boundaries of BaM powders without supposing any imperfections and so the role of grain boundaries is important in relation to the coercivity mechanisms. Thus, the magnetization reversal process in hexagonal oxide powders are still open to investigation for some details, even for the particles of critical size. But we may now conclude that all the factors described here should be considered, though the dominant magnetizing mechanism depends perhaps on the preparation method. When the magnetization reversal is achieved by the nucleation and growth of reverse domain, the angular variation of coercive force, plotted as MHc versus 1/cos 0, shows a linear relation. Here, 0 expresses the angle between the applied field and the easy axis of the oriented powder assembly. Ratnam and Buessem (1972) obtained this relation with BaM particles of 100-200 Ixm as shown in fig. 34. However, if particles perfectly follow the Stoner-Wohlfarth model then MHc can be drawn as the curve S-W in fig. 35; here the value of the effective anisotropy field HA is assumed to be 12000 Oe [9.5 × 105 A/m], considering the demagnetizing factor. For practical powders, magnetizing process takes place by both of these mechanisms and thus curve (2) is observed as the angular dependence of ordinary ball-milled BaM powders. For the sample prepared under relatively defect-free conditions, for instance by the chemical co-precipitation 240 o
E 200 <
/
F-
~O -×
160
,¢ ×
120
/
O IO × v
u "r
40
/
/
f
o .
o
0.2
0,4
0,6
0,8
1.0
cos 8 Fig. 34. A n g u l a r dependence of the coercive force for oriented BaO.6Fe203 powders (Ratnam and B u e s s e m /972).
F U N D A M E N T A L PROPERTIES OF H E X A G O N A L FERRITES 12
I
341
/I
~lo \
i
/ K//
tt
I
S-W
2
, ~ Q
/
O ~ Q ~ O
---''-tD'-''~"
~
~ ,
(2) 0 0
0
40 0 (degree}
60
80
Fig. 35. Analysis of magnetizing process in BaO.6Fe;O; powders from the angular variation of coercivity (Haneda and Kojima 1973a): (1) co-precipitated powders, (2) ball-milled powders, (S-W) calculated curve by the coherent rotation model, (K) calculated curve by the magnetizing process with wall motion.
method, they may be magnetized mostly by coherent rotation, as proved by curve (1) in fig. 35, where it completely agrees with curve S - W in the range 4 0 ° < 0 < 90 ° . To see the difference more clearly, magnetizing curves are compared with the theoretical S - W curve in fig. 36. Demagnetizing curves of defect-less powders of BaM (1) and SrM (3) agree well with the calculated curves for coherent rotation, S-W, but ball-milled BaM powders (2) behave rather differently from the S - W model (Haneda and Kojima 1973a, Tfinfisoiu et al. 1976). Ratnam and Buessem
i//
I
f
id " /'"'1
.g ,"
I
I
5
--
,/i~
Fig. 36. Demagnetizing curves of unoriented powder assemblies: (1) co-precipitated BaM, (2) ballmilled BaM (Haneda and Kojima 1973a), (3) wet-milled and annealed SrM (Tfinfisoiu et al. 1976).
342
H. KOJIMA
(1972) and Haneda and Kojima (1973a) proposed methods to estimate the ratio of the two magnetizing mechanisms in a powder assembly from the angular variation of MHc. The highest MHc values obtained hitherto by special preparation methods are listed, together with other experimental conditions, in table 10.
2.1.6. Paramagnetic properties Borovik and Mamaluy (1963) measured the temperature dependence of the susceptibility per gram above the Curie point for M compounds. Figure 37 shows the 1/xg-r relations of BaM (1) (Gorter 1954), SrM (2) and PbM (3) (Borovik and Mamaluy 1963). They also determined N6el's constants for the susceptibility per atom XA; ~r, CA and X0,A in eq. (10) (N6el 1948) by a graphical method from the results of fig. 37. Here, 1 1 T ~ XA Xo,A CA
oT-0'
(10)
and 0 can be given by o = nCAA~
(2 + o~+/?),
(11)
where CA is the atomic Curie constant for Fe3+; A,/x are the numbers of the Fe 3+ ions in the A and B sublattice; n, a and /3 are the molecular field constants connected with the exchange interactions of the AB, A A and BB types. If the T (°C) 600 8
I
I
I
800 iI
IO00 i ] ~ t , ~I I
1
,~.
.o/e
{,9
~.
I 6
[/I/
..
l
~s x 4 3
~o x- 2
1
/ I
1
I
0
II00 1300 T{K) Fig, 37. Temperature dependence of the specific susceptibility above the Curie temperature: (1) BaM (Gorter 1954), (2) SrM, (3) PbM (Borovik and Mamaluy 1963). 700
900
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
343
m o l a r susceptibility XM is used i n s t e a d of XA in eq. (10), t h e n CM can b e o b t a i n e d i n s t e a d of CA. T h e c o n s t a n t s are t a b u l a t e d in t a b l e 11. B o r o v i k a n d M a m a l u y c o n c l u d e d that the c o n s t a n t s X0,A, Cr, CA, a n d t h e r e f o r e the m o l e c u l a r field c o n s t a n t s are r o u g h l y the s a m e for h e x a g o n a l a n d cubic ferrites. A l d o n a r d et al. (1966) m e a s u r e d XM of P b M a n d f o u n d different values for AiM with a p p l i e d m a g n e t i c field parallel a n d p e r p e n d i c u l a r to the c-axis, as s h o w n in fig. 38. T h e y also d e r i v e d t h e following f o r m u l a from the precise m e a s u r e m e n t of the t e m p e r a t u r e c h a n g e in XM in cgs u n i t b e t w e e n 800 a n d 1200 K along the c-axis: 1 XM
1 T 38.21 + 6 5
4367 T-655"
(12)
10 9
I C aXiS
o
H II
•
H .L c oxis /
~7
2
I
.,//
fd-
J/"
!
Az
-~5
~3 "2_ I ///1 0 ////
710
720
7:30 T(K)
740
750
Fig. 38. Temperature dependence of the molar susceptibility of PbM along parallel and perpendicular directions to the c-axis (Al6onard et al. 1966).
TABLE 11 N6el constants of M compounds according to eq. (10) (Borovik and Mamaluy 1963).
Compound
CA cm3K/atom
CM cm3K/mol
BaM SrM PbM
0.0515 0.0475 0.0526
58 51 61
CA: atomic Curie constant of Fe3+ ions, CM: Curie constant obtained from molar susceptibility.
104 (emu/atom) [1/(4zr) × 10 4 S I / a t o m ]
o- x 105 K atom/cm3
5.1 5.8 6.8
26 27 31
l/X0, A X
344
H. K O J I M A
2.1.7. Magnetic aftereffect Diilken et al. (1969) investigated the relaxation phenomena of polycrystal BaM. They measured the complex permeability between 77 and 743 K in the frequency range from 500 Hz to 100 kHz. The real p a r t / x ' and the imaginary part/x" of the initial permeability as a function of temperature T, measured at i kHz for Fe 2+ free BaM, show linear relations with T, as shown in fig. 39(a). However, /x" of BaM with 0.24wt% Fe 2+ measured at 10kHz shows three maxima at - 1 8 5 °, - 1 4 5 ° and +60°C, as shown in fig. 39(b). If k and Q denote Boltzmann's constant and the appropriate activation energy, then the relaxation time ~- is expressed as,
r
=
"r=
exp(O/kT).
(13)
Diilken et al. (1969) determined O for the three maxima as (I) 0.1 eV, (II) 0.2 eV and (III) 0.6 eV, and the relaxation frequency f = 1/2~-~-= as (I), (II) - 101° Hz and ( I I I ) ~ 1 0 1 3 Hz. These relaxation phenomena can be explained by the diffusion process between Fe 2+ and Fe 3+, which is often observed in cubic ferrites.
5
t h.
I
I
--o-c~-c. -o-o-oc - o - o F'
10°5
Io-) l
5
=._o_oj F"
°-% I
t0 -2
(b) I
!.c-.o--~ ~
"ov---o-c-~-.o~
I 1°°5
F'
510-1l
(a) lo-'
lo-2
5 o'o--c-~ -200
~c.o.o~5 -I00
0 Temperature
I00 (°C)
Fig. 39. Temperature variation of the complex permeabi|ity for polycrystal BaO.6Fe203 (Dtinke] ¢t al. 1969): (a) Fe z+ free B a M at i kHz, (b) B a M with 0.24 w t % Fe 2+ at 10 kHz.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
345
2.1.8. F M R Numerous experiments of ferromagnetic resonance absorption in BaM or SrM have been reported, most of which aim to determine the anisotropy field H A and the effective spectroscopic splitting factor gen against temperature. Several authors also especially investigated the effects by the shape, size or surface roughness of the samples, the existence of domain walls, or the angle between the applied d.c. field and the easy axis, etc. Figure 40 shows the resonance absorption in BaM at various temperatures. Smit and Beliers (1955) showed with a thin single crystal that only the absorption peak excited by a parallel a.c. field is observed at lower temperature, but the perpendicular field peak appears above room temperature and splits into two at 200°C (fig. 40(a)). Grosser (1970) investigated the resonance absorption of an isotropic polycrystal between 21°C (fres= 22.22 GHz) and 465°C @es = 22.03 GHz) as shown in fig. 40(b), where the resonance field at room temperature moves to lower fields with increasing temperature near the Curie
2.5
\ \\ \ \
A t3 (3 03 ..Q
2.0
1.5
b) \ \
I 450*
\
420*
\
1.0 Q.
o J~
4ti~ .-
0.5
0o
4
8 H
50
~/
(kOe)
12
16
I
(a)
200"C
a~ o
40
IP
to
II
..a
30 g "..7-¢.~ 0 o~ t~
<
20
[xlOS/(4~-) A/m]
11
,/i I
I
I/
20
I
'
IJ
I0 0
I
13 15 17 H (kOe) [x106/(4~) A/m]
19
Fig. 40. Ferromagnetic resonance absorption in BaO.6Fe203 versus applied d.c. field at various temperatures: (a) single crystal (Smit and Beljers 1955), (b) isotropic polycrystal (Grosser 1970).
346
H. KOJIMA
points. The ordinate of the figure is illustrated in arbitrary scale but it is proportional to/x". Figure 41 is the relation of resonance frequency and applied d.c. field for a BaM single-crystal, by Silber et al. (1967). The solid lines in the figure express the calculated results for various angles 00 between the c-axis and the applied field, using the following resonance conditions: (o~/y)2 = [Ha(1 - 2 sin 2 0) + Hext cos(0o - 0)]Hext(sin 0o/sin 0),
(14)
sin 0 cos 0/sin(00- 0) = HexdHa.
(15)
and
Here, ~o, y and 0 represent the resonance frequency, gyromagnetic ratio and angle between the c-axis and the magnetization vector, respectively. The effective anisotropy field is generally given by Ha = HA--(NIl- N±)M~. Thus, Silber et al. determined y from the slope and HA from the intersection with the frequency axis of the zero-degree curve in fig. 41. The "knees" in the experimental data
0o
44*
59*
ID
°.o
.........---
. i'
rv
46
42
0
4
Applied
8
field
2
(k0e)
16
20
"xl06/(4=) A/m]
Fig. 41. Relation of resonance frequency and magnetic field applied at various angles to the c-axis of BaO.6Fe203 single crystal (Silber et al. 1967).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
347
represent the change from the single domain state at higher fields to the multidomain state at lower fields. The resonance frequencies and absorption intensities in BaM specimens with cylindrical domain structure have been calculated by Sigal (1977) and compared with the experimental results, changing the direction of magnetic field with the easy axis. Typical experimental results are summarized in table 12. When the d.c. field is cycled between _-_25kOe [+_1.99 x 106A/m] for BaM milled powder, Hempel and Kmitta (1971) found a microwave absorption peak at about 2 kOe [1.59 x 105 A/m] with f - - 9.4 GHz, which shows a pronounced hysteresis apart from the F M R occurring at about 15 kOe [1.19 x 106 A/m]. They also observed that the low field losses and the line width of the F M R decrease with increasing annealing temperature of the sample. While Roos et al. (1977) found microwave absorption of chemically co-precipitated, polycrystalline BaM at H --HAl2, when the sample was previously saturated; however, no absorption peak in negative fields was found for the conventionally prepared BaM. They obtained three peaks at H = -6.6 kOe [-5.25 x 105 A/m], -8.8 kOe [-7.00 x 105 A/m] and -15.3 kOe [-1.22 × 106 A/m] with f = 11.9 GHz, and concluded from these results that the magnetization in most particles of the chemically precipitated sample is reversed by coherent rotation. Besides such basic investigations, several studies relevant to the applications to microwave devices have been reported. For example, Dixon Jr. and Weiner (1970) obtained H a = 17-5 kOe [13.5-4.0 x 105 A/m] over the frequency range of f = 23.2-37.6 GHz with BaZnxTixFe12 2xO19. De Bitetto (1964) also investigated the F M R of BaO.x(TiCoO3)-(6-x)Fe203 and SrO-xA1203.(6-x)Fe203 systems and determined HA as 17.5-6.6 kOe and 19.3--53.4 kOe [15.442.5 x 105 A/m] respectively. 2.1.9. N M R Streever (1969) obtained the NMR line shapes of Fe 57 in single-crystal powders at 4.2K and resintered single-domain powder at 77 K for BaM, by plotting the spin-echo amplitudes versus frequency as shown in figs. 42(a) and (b). Each line can be assigned on the basis of the changes in relative intensities and shift in external magnetic fields. M6ssbauer data are also useful to analyze the signals and the reverse is naturally also true. The relations of the sublattices and the notations in the figure are identical to those used in table 5. L/itgemeier et al. (1977) measured relaxation rates of Fe 57 nuclei in BaM between 1.2 and 4.2K and proved that the relaxation time is much shorter for the wall signals than for the domain signals due to the influence of the wall excitations. The temperature dependence of NMR frequencies is summarized in fig. 43, after the results of Streever and Hareyama et al. (1970). Though the temperature changes of signal III (sublattice d) and V (b) show some differences between the two papers, the frequency changes of each signal are almost continuous over the whole temperature range. The temperature dependence of signal I (a) from Fe 3+ in octahedral a sites is more remarkable than those of signal II (c), III (d), IV (e) and V (b), while signal IV (e) appears at a lower frequency than the others. These results
348
H. K O J I M A
T A B L E 12 Summarized results of F M R experiments for M-type compounds.
Compound
BaM
BaM
BaM
Experimental condition
fr~s(GHz)
T(°C)
single cryst, disc, d = 1 m m , t = 40 tzm; disc _1_c-axis, Hr~s and ha in basal plane, angle between Hres and ha is 45 °
23.93 23.98 ' 23.98 23.98 23.98
-196 20 112 155 200
2.00 (assumed) 1.98 2.00 2.01 2.02
single cryst, disc, d = 0.083 cm, t = 0.030 cm; Hr~s//disc,
58.2 58.4 58.6 58.8 59.0
R.T.
1.87
25
1.96
R.T.
1.91 1.91
20
2.05
Hre~//c-axis, hr~A_H ~
single cryst, sphere, d = 0.4 m m
53.0-55.3
ge~
Hresffc-axis, h~//c-axis BaM SrM BaM
BaM BaM
oriented polycrist, slab single cryst, disc, d = 2.60 cm, t = 0.01 cm single cryst, sphere, d = 0.036 cm
51-65
single cryst, sphere, d = 0.05 cm
66.6, 120 66.6, 120
R.T.
2.02 ± 0.01
4.2 (K) 20 (°C)
1.99 - 0.03
single cryst, sphere, d = 0.038~.05 cm,
BaM
Hre~~~c-axis
I>52.0 22
BaM
* Spin wave line width (a) Smit and Beliers (1955) (b) W a n g et al. (1961) (c) Mita (1963) (d) D e Bitetto (1964) (e) Burlier (1962)
(f) (g) (h) (i)
Silber et al. (1967) Kurtin (1969) Dixon and Weiner (1970) Grosser (1970)
R.T. 21 200 300 35O 40O
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
349
T A B L E 12 (continued) Hr~ (kOe) [x 106/(4~-)A/ml hrr//'Hres 14.3 15.05 15.40 15.40 15.35
hrr-l-Hres -10 17.15 17.55 17.15 16.85 3.844 3.886 3.964 4.042 4.140 18.7-28.2
HA (kOe) [X 106/(47r)A/m]
A H (Oe) [x llY/(4~)A/m]
16.2 17.0 17.3 17.3 17.3 18.4
0-13
Ref.
47rMs = 6.67 (kG) 4.80 3.90 3.50 3.12
(a)
p = 5.13 (g/cm3) 3'4 = 2.62 (MHz/G)
(b)
17.55
<12
(c)
17.5 19.3
1600 1600
(d)
17.0 2.0-7.0
Remarks
3' = 2.87 (MHz/G)
16.2 16.1 17.1
(e)
(f) ~<10 46
4~'M~ = 5.2 (kO) AHk* = 2 ± 1.5 (Oe)
(g)
17.0
4~'Ms = 4.8 (kG)
(h)
17.0 17.0 15.1 13.1 10.5
Ms = 375 (G) 248 177 142 106
(i)
350
H. KOJIMA I0
(b)
l I I
/,
4 i
=
2
m o_
E
0 I0
:>
(a)
~
8 6
III lI
2 0 58
/
/% 62
66 Frequency
70
74
78
(MHz)
Fig. 42. Plot of the spin-echo amplitudes versus resonance frequency for BaO.6Fe203 (Streever 1969): (a) single-crystal powders at 4.2 K, (b) resintered single-domain powder at 77 K.
78 .........
~ _ ~ i__~__ .~
74 O. . . . . . .
I 70 2;
I I°
66
"7
'~ ~.,~
g62
r
b_
58
~
]7
54 0
I I00
200 Temperofure ( K )
°""°~' 500
Fig. 43. Temperature dependence of NMR frequency: (O) Streever (1969); (O) Hareyama et al. (1970).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
351
can be understood from the differences of F e - O - F e bonds for each Fe 3+ ions (see table 5).
2.1.10. M6ssbauer effect Van Loef and Van Groenou (1964) investigated the M6ssbauer effect with BaM single crystals and oriented crystallites enriched in Fe 57. Changing the y-ray direction parallel or perpendicular to the c-axis and with or without the magnetic field of 13 kOe [10.3 x 105 A/m], they observed spectra of I + V (sublattice a + b), II (c), III (d) and IV (e); (note that different labelling methods are used by other investigators). The temperature dependence of the sublattice magnetization, anisotropy and dipole fields, and the exchange constant of the Bloch wall as a function of relative magnetization are discussed in relation with the experimental results. Furthermore, in contrast to other authors, an especially high hyperfine field of the sublattice e was reported by Van Loef et al. (1964). Zinn et al. (1964) also observed M6ssbauer spectra in BaM and explained the temperature dependence of the saturation magnetization by the temperature changes of internal fields for each sublattice, although they considered only two kinds of sublattices as a whole. Kreber et al. (1975) did further M6ssbauer study with BaM, an oriented and enriched polycrystal between 4.2 and 200 K, and nonenriched fine powder at 300 and 870 K. They resolved the spectra as I (sublattice a), II + I I I + V (c + d + b) and IV (e) at low temperature, and I (a), I I I + V (d + b), II (c) and IV (e) above 200 K, respectively. Based on the observed large quadrupole splitting of sublattice e and its distinct change near 80 K, they proposed a model in which Fe 3+ occupies randomly one of the two equivalent sites of Wyckhoff's notation 4e instead of 2b at low temperature. Here, 4e sites are located on the trigonal axis and 0.156A away from 2b site on the mirror plane (see also section 2.1.1 on crystal structure). Using their model, they showed that the temperature dependence of the splitting values, which they had observed, and also the anisotropy behaviour obtained by the M6ssbauer data of Rensen and van Wieringen (1969) can be understood by the molecular orbital calculation after Trautwein et al. (1975). As for SrM, Van Wieringen and Rensen (1966) observed spectra for powders, enriched in Fe 57 at room temperature. Four subspectra are assigned as I (sublattice a), II + V (c + b), III (d) and IV (e). Internal field Hi, quadrupole splitting and isomer shift 6 of four subspectra as a function of temperature are illustrated in figs. 44(a), (b), (c) and 45. Van Wieringen (1967) reviewed M6ssbauer data of M compounds and derived the temperature dependence of saturation magnetization from the values of Hi in fig. 44(a). Figure 44(d) shows the result together with directly measured values, expressed with the open circles, which fit quite satisfactorily with the deduced curve. Comparing the results of BaM by Zinn et al. (1964) or Van Loef and Franssen (1963) with the results by Van Wieringen and Rensen (1966) it can be concluded that the M6ssbauer data of SrM are qualitatively the same as those of BaM, but the main quantitative difference concern rather lower values of Hi and e in SrM. M6ssbauer effect measurements of PbM single and polycrystals between 15 and 780 K were reported by Zinn et al. (1964). Differing from BaM, an intense spectral line at v -- 0, arising from the paramag-
352
H. KOJIMA 120 E '
"'---o
;'
I
iI
(d)
l
90
II
'~o 6 0 - -
~.~. 3o o
I (n
E E
0
60
-I
(b)
-j E E
!
uo
6OO
(o) ,---1
500
400
....... ~---~r-- - - ~
.. "~"
0
3OO o
200
z
I00
0 0
200
400
600
800
T (K) Fig. 44. Variations of the internal field (a), quadrupole splitting (b), isomer shift (c) and saturation magnetization (d) of SrO.6Fe203 against temperature (Van Wieringen and Rensen 1966, Van Wieringen 1967).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
353
f'
6 . 0 x 10 5
5.0 J
I
I
I
I[(c) I
E(d)
IV(e)
I
I I
-I0
4
I
V(b) J
I
I
I
0
-5
v
I
I
I
5
I
I
i
I
I0
( mm/sec
Fig. 45. Assignment of the M6ssbauer spectrum of SrO.6Fe203 at room temperature (Van Wieringen and Rensen 1966, Van Wieringen 1967).
netic phase was observed in PbO.xFe203 (x = 4-6) near the Curie temperature. A signal corresponding to the paramagnetic phase of 30% was obtained at 700 K, though further investigation regarding the effect of the PbO.2Fe203 paramagnetic phase in the sample seems to be necessary to explain these phenomena. As described hitherto, two kinds of labelling for the M/Sssbauer absorption peaks of M compounds seem to be used. That is, Kreber and Gonser (1973) considered one of the lines V (b) with III (d) as an unresolved one, while Van Wieringen and Rensen (1966) recognized peak V (b) overlapped with peak II (c). Since the N M R data at low temperature by Streever (1969) and at higher temperature by Hareyama et al. (1970) proved that the hyperfine fields and their temperature dependence of III (d) and V (b) are almost the same as shown in fig. 43, the assignment of Kreber and Gonser is suggested to be reasonable. However, when we compare the results of N M R and M6ssbauer measurements, we should, of course, realize that the spectra observed by these two experimental procedures are based on different physical origins. In conclusion, Van Wieringen (1967) summarized the results of M6ssbauer studies with M compounds as follows: (1) The iron ions are trivalent in all sublattices; (2) All five sublattices may be expected to contribute to the crystal anisotropy; (3) The rapid drop in the magnetization with increasing temperature is entirely due to Fe 3+ in sublattice a (signal I). The interest regarding the M6ssbauer studies with M compounds also concerns the determination of ion distributions in the substituted compounds as discussed in detail below. For example, Rensen et al. (1971) investigated A1, Cr, ZnTi,
354
H KOJIMA
ZnGe, ZnSn, ZnZr, CuTi, CoTi, CoCr and NiTi substituted M compounds and found that AI firstly enters the 2a site (sublattice b) and then the 12k site (a); Cr also starts by entering the 2a site. In addition, they concluded that there is no indication of Fe 3+ ions in an asymmetric 4e site at low temperature, contrary to the results of Towns et al. (1967) or Kreber et al. (1975). Kreber and Gonser (1973, 1976) reported that As ions occupy preferentially the 2b site (sublattice e), while Ti 4+ + Co 2+ firstly occupy 4fl (c) o r 4f 2 (d) sites and then randomly the 2a (b), 12k (a), and lastly 2b site (e). If Ba 2+ ion in BaM is replaced with a trivalent ion, Fe 3+ may partly change its valency t o Fe z+ to keep the neutrality. LaFe12Oa9 was investigated from this point of view by Drofenik et al. (1973) and also by Van Diepen and Lotgering (1974). In both papers the authors described the difficulty in observing the Fe z+ sublattice, but the latter authors discussed the preference of Fe z+ ion from the intensity ratio of subspectra. Moreover, Drofenik et al. (1973) determined the Curie point as 697 K from the appearance of the paramagnetic Mrssbauer absorption peak. The hyperfine field at Fe 57 nuclei in different sublattices in LaFe12019 as a function of temperature are similar to BaM or SrM but the change in the 12K sublattice (I) is found to be more convex than that of SrM as in fig. 46. This agrees with the more convex o-s-T curve of LaM as compared to that of SrM. 600
<
"~ 4 0 0 0
\\,,,
×
O
-~
200
\\ g \\ g \\ g
"7-
It
II
0
0
200
',
400 600 800 T (K) F i g 46 Temperature dependence of hyperfine field in LaO 6Fe203 (Drofenik et al. 1973)
2.1.11. D o m a i n observation In the earlier days, domain structures were mainly discussed qualitatively in connection with the magnetic properties of the materials, magnetic anisotropy, magnetizing process and so forth. However, as the sophistication of techniques in domain observation and sample preparation improved, more quantitative investigations were attempted. Further, some of the results acquired in this research
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L FERR1TES
355
field have led to the development of the industrial application of bubble domains. Kooy and Enz (1960), for example, observed the plate-like domains in thin layers of BaM, which were peeled off from the surface of single crystals. They discussed the results of the experimental domain period under the influence of magnetic field and compared them with theoretically calculated results. Specific wall energy and critical diameter of cylindrical domain were also reported in the paper as ~rw= 2.7erg/cm 2 [2.7x 10-3j/m 2] at 50°C and Dc = 0.3 Ixm for a 3 Ixm platlet. Figure 47 illustrates the domain period versus the magnetic field applied parallel to the easy axis for (a) BaM (Kooy and Enz 1960), (b) SrO-4.5Fe203-1.5A1203 and (c) SrO-4.2Fe203.1.8A1203 (Rosenberg et al. 1967). The curve for BaM is the
300
(c) 250
o
~o 150 x
c~ I 0 0 .4-
c~
1
I
_jl
200
E
]
(b)
ii
J I
250 '~ 2 0 0
L 2
~5o
+
I00 ~
c:T
5O 0
50
0
0.5
1.0
0
1.5
H (kOe) [xlOS/(4"rr) A / m ]
0
200
400
H (Oe) [xlO3/(4rr) A/m]
12 I0 '-' 8 10 x
+
cE
6
4
0
0
J
J
1__
I
2
3
4
H (kOe) [x106/(4"n") A/m] Fig. 47. Domain period as a function of the applied field: (a) BaM, thickness: 3 x 10 .4 cm (Kooy and Enz 1960); (b) SrO'4.5Fe203'l.SA1203; (c) SrO-4.2Fe203.1.8A1203 (Rosenberg et al. 1967). D1 + D2: width of antiparallel two domains.
356
H. KOJIMA
result of t h e t h e o r e t i c a l curve fitting. ( U n f o r t u n a t e l y , t h e crystal t h i c k n e s s is not c l e a r for (b) o r (c), b u t t h e s a m e a u t h o r s (1966) r e p o r t e d s e p a r a t e l y t h e D - t r e l a t i o n s of t h e s a m e c o m p o u n d s ; as d e s c r i b e d later.) F i g u r e 48 shows t h e c h a n g e s of d o m a i n structures on t h e b a s a l p l a n e of B a M p l a t e l e t b y t h e F a r a d a y effect ( K o j i m a a n d GotO 1965). C y l i n d r i c a l d o m a i n s a r e c l e a r l y seen in t h e h i g h e r field, just b e f o r e t h e s a t u r a t e d state, as s h o w n in (d) a n d (e).
Fig. 48. Changes of domain structures observed by Faraday effect on the basal plane of BaO-6Fe203 (Kojima and Got6 1965): (a) demagnetized state, (b), (c) H = 3600 Oe [2.86 × 105 A/m] parallel to the c-axis, (d), (e) H = 3900 Oe [3.09 x 105 A/m] parallel to the c-axis. 0: set angle of the analyzer from the crossed nicosol state.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
357
Moreover, it was proved that maze, parallel or honeycomb domains can be realized as a remanent structure for B a M (Kojima and G o t 6 1965) and for P b M (Kacz6r and G e m p e r l e 1961, Palatnik et al. 1975) and for BaM, SrM and P b M (Kojima and G o t 0 1970). H e n c e a specified domain structure among these three can be brought into existence at will by choosing certain angle ranges of applied magnetizing field direction against the c-axis before the remanent state is produced in the crystal. Utilizing these facts, HA and K1 were determined for small single platelets by Kojima and G o t 6 (1964) as shown in table 9(d). The effects of various kinds of defects on the domain nucleation process were discussed by Kojima and G o t 0 (1965), Wells and R a t n a m (1971) for BaM, and Tfinfisoiu (1972) for A1 substituted SrM, Sr(Fe7.2A14.8)O19. Kojima and G o t 6 found that the h o n e y c o m b domains are m o r e likely to appear in a defect-less crystal which can easily be changed to a crystal showing maze remanent domains by water quenching or pricking with a needle. M o r e quantitative relations have been obtained on the variation of domain width D with crystal thickness t. For simple slab domains, the relevant theoretical equation is given by Kittel (1946) as, D = (O-w/1.7Ms)l/2t m •
(16)
For the domains with reverse spikes near the surface, Kaczdr (1964) modified the relation as: D = [0.3751/Ms)(O'wtX/Tr)l/212/3t2/3,
(17)
where [,, = 1 + 8 r r 2 M d K 1 .
G o t 5 (1966) obtained an experimental formulae D = 0.392t °665 for B a M and D = 0.441t °64° for SrM in the thickness range 2 t x m < t < 2 0 txm. On the other hand, Kacz6r and G e m p e r l e (1960) reported D oc t 1/2 for t < 10 txm and D o c t 2/3 for t > 10 Ixm on the domains of PbM. Rosenberg et al. (1966), moreover, obtained the relations for S r O - ( 6 - x)Fe2OyxA1203; D oc t 0.586 at x = 0, D oc t 0-616 at x = 1.0, D oct 0-665 at x = 1.5, D oct °.418 at x = 1.8, D oct 0.ass at x = 1.9 and D o c t 0.431 at x ~ 2.0. For thinner crystals observed by G o t 6 (1966), the results can be rewritten as D = [0.386(t- 1.460)] 1/2 for B a M and D = [0.432(t- 1.1260)] 1/2 for SrM respectively. H e n c e the one half Power law may be valid in this case, though the physical meanings of the constants are not clear. However, if we consider the existence of a surface layer where the Kittel model might b e c o m e unstable, giving a kind of lattice distorted layer, and also the resolution limit in m e a s u r e m e n t s with an optical microscope, the numerical values in these formulae seem to be reasonable. For thicker crystals, the two third power law related to spike domains seems to be valid. Some deviation from the law could be understood by the complicated domain structures and the resulting ambiguity in the measured values of domain widths.
358
H. KOJIMA
The temperature variation of the domain width D in BaM was studied by Kojima and Goff) (1962). They obtained the temperature coefficient of D as 8.9× 10-4/°C and that of O'w as - 2 . 3 × 10 3/°C. Gemperle et al. (1963) also performed similar experiment with PbM and found the thermal hysteresis of the domain width, as Shimada et al. (1973) observed with honeycomb domains. Kacz6r (1972) discussed these results from a theoretical point of view and showed the free energy decreases linearly to zero as T/Oc changes from 0.2 to 1.0, and the domain width almost doubles in the same temperature range. Furthermore, undulating Bloch walls, for which Goodenough (1956) first gave a theoretical explanation, can be seen on the surface of crystals with medium thickness, for instance, 10 fxm < t < 50 txm for BaM. Szymczak (1971) reported the temperature dependence of domain width, wave amplitude and wave length in these domains. The stability with temperature for honeycomb domains was investigated by Gemperle et al. (1963) with PbM and by Shimada et al. (1973) with BaM. The latter authors observed the increase of the nearest neighbour distance among the cylindrical domains during the temperature rise. The honeycomb domains reversibly change to a mixture of honeycomb and stripe domains by the heat treatment from 600 K to room temperature. It was pointed out that the equilibrium distance theoretically predicted by Kaczdr and Gemperie (1961) would be realized only in such a mixed domain structure. Regarding the same phenomenon, Kozlowski and Zietek (1965) showed from a theoretical consideration that the deviation from Kacz6r and Gemperle's equation in these experiments would rapidly increase for thinner specimens. Grundy (1965) observed Kittel type slab domains in PbM of 1000-2000 thickness by Lorentz microscopy and determined the Bloch wall thickness as 250 _+150 A. Grundy and Herd (1973) used the same technique and applied it in an investigation of the nucleation mode of bubble domains. They gave the material length l = Crw/(4~-M2) as 0.03-0.04 Ixm for BaM and PbM. Wall mobility constant ,1 of 0.7× 102cm/s/Oe for BaFe12019 and 1.6× 102cm/s/Oe for BaFeu.aA10.7019 were reported by Asti et al. (1968).
2.1.12. Optical properties The absorption coefficient a (=2~-K/nA) and Faraday rotation &F of BaM measured at 300 K as a function of wavelength from 1 ~m to 8 p~m by Zanmarchi and Bongers (1969) are shown in fig. 49. It is seen that &V changes sign between 2 ~m and 3 ~m. Drews and Jaumann (1969) measured the absorption coefficient K, refractive index n, Faraday rotation &F, Faraday ellipticity ~/v and Kerr rotation against air ~bw and against glass &KC for the same material in the shorter wavelength region of 0.4 ~m-1.7 ~m. The results are illustrated in fig. 50. Kahn et al. (1969) also added the data of the polar Kerr spectra for PbM, showing° a negative peak at 4.43eV (2799,~) and a positive peak at 5.5 eV (2254A). According to their conclusion, charge transfer transitions occurring at about 4 eV (3100 A) and 5 eV (2480 A), associated with Feoct and Fetet complexes, respectively, are responsible for the principal magnetooptical spectra. Blazey (1974) reported on the wavelength-modulated reflectivity spectra of BaM with the minima at 2.2eV (5636A) and 2.6eV (4769 A) corresponding to the internal
150
I00 'E
300
13
200
¢j
E rj
50 I00
0
"o
v
LL
-g. 0 0 2
0
4
6
X
8
'-I00 I0
(Fm)
Fig. 49. Absorption coefficient a(=2~'K/nA) and Faraday rotation ~bF of BaO.6Fe203 in infrared region at room temperature (Zanmarchi and Bongers 1969). xlO 2 I0.0
7.5
1~F
o o~
5.0
-
-
I--
xlO 2
"F]F
-2.0
LL 2.5
--I.0
o E
o
2
g,
~,,
o -
2.5
1.0
-8-
6
-5.0
2.0 I
3
m
r-
i o- 2
2
-
L
10.4
I
0
0.5
1.0
1.5
2.0
X (/~m) Fig. 50. Optical properties of BaO-6Fe~O3 as a function of wavelength. K: absorption coefficient, n: refractive index, OF: Faraday rotation, rTF: Faraday ellipticity, CbKL:Kerr rotation against air, ~bKo: Kerr rotation against glass, t: 4.5 p~m, / 4 : 1 5 kOe [1.19 x 106 A/m]. 359
360
H. K O J I M A
transition of Fetet and at 3.9 eV (3179 A), 4.3 eV (2883 A) and 4.8 eV (2583 A), these being assumed to be charge transfers to Feoct.
2.1.13. Magnetostriction The saturation magnetostriction in a hexagonal crystal is given by Mason (1954) in the form, a = /~A[(OZI~I q- a2~2) 2 -- (O/1]~ 1 q- O~2][~2)@3~3]q- ~.B[(I -- O~2)
x ( I - fl~) ~ - ( o ~ # , + o~=/?~)=] + a d o
- o d ) B 1 - (o~/3, + o~fl=),~,8~]
(18)
+ 4AD(alB1 + o12f12)a3B3,
where al, a2, O~3 and ill, fi2, r3 are the direction cosines of the magnetization vector and measuring direction. Here, the direction cosines are taken with respect to the Crystal axes, the z-axis coinciding the c-axis. Kuntsevich et al. (1968) determined the constants AA, As, Ac and AD in eq. (18) for BaM in measurements with the following geometry: •A:O/1 =/31: 1, AB:OZl= /3== 1, Ac:OZl = J~3= 1, h D : a l = / 3 1 = a 3 = / 3 3 = l/X/2. Thus, they found the constants at room temperature as AA = -- (15 --+0.5) X 10-6, AB = + (16 + 0.5) X 10-6, Ac = + (11 -+ 0.5) X 10-6 and AD = -- (13 --+0.5) X 10-6. For polycrystals, they also obtained the longitudinal and transverse magnetostrictions, hi! = -(9-+ 0.5)x 10 6 and h~ = + (4.5 -+ 0.5) x 10-6. However, these values do not coincide with the values derived by the simple averaging of the formula for a single crystal. The authors explained these results from the effects of the defects in the crystals and the interference of grains during deformation.
K
E
I
8.6
6
E
6.4
15.0
6.3
8.4
6.2 14.5 8.2
6.1
Z
6.0
/ 8.0
"14.0'
I00
200 T (K)
300
5.9
Fig. 51. Temperature dependence of Young's modulus E, rigidity modulus G and bulk modulus K (x 1011 dyn/cm 2) [× 101° N/m 2] (B.P.N. Reddy and P.J. Reddy 1974a).
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
361
2.1.14. Mechanical properties Fundamental studies of the mechanical properties of hexagonal ferrites are quite few. Clark et al. (1976) referred to the following mechanical data for their BaM specimen at room temperature. Density: 5g/cm 3, porosity: 5%, Young's modulus: l a x 106kg/cm2 [1.38x 1011N/m2], Poisson's ratio: 0.28, compressive strength: 4.5 x 103kg/cm2 [4.41x 108N/m2], tensile strength: 5.6x 102kg/cm2 [5.52x 107 N/m2]. Reddy and Reddy (1974a) measured the elastic modulus of sintered BaM with a density of 4.8910 g/cm3. Figure 51 shows the relations of Young's modulus E, rigidity modulus G and bulk modulus K versus temperature. These moduli decrease with temperature, in contrast with those of Ni-Zn or Mn-Zn cubic ferrites. Hodge et al. (1973) investigated the compressive deformation of sintered BaM with 18% porosity in creep and press forging modes in the temperature range 1000° to 1200°C. Figure 52 is the true strain rate against l I T plot for an isotropic compact at 5% true strain. The activation energy for creep was estimated from the experiments as 123-+6kcal/mol [(5.15-+0.25)x 105 J/moll.
-2 (x 13
--<.. ..3
,
~
"
~
-6 6.8
7.0
7.2 I/T
7.4
7.6
7.8
( K -I x l O -4)
Fig. 52. Arrhenius plot of creep by compressive deformation of isotropic BaO.6Fe203 (Hodge et al. 1973). (1) 421.8 kg/cm 2 [4.14 x 104 N/m2], (2) 281.2 kg/cm 2 [2.76 × 104 N/m2], (3) 140.6 kg/cm 2 [1.38 x 104 N/mZ].
2.1.15. Heat capacity Reddy and Reddy (1974b) determined the heat capacity of a BaM sintered rod in the temperature range 80 to 303 K. Cp is plotted versus temperature in fig. 53, giving values of 52.42 cal/mol deg [2.194 x 102 J/mol deg] and 107.56 cal/mol deg [4.502× 102J/mol deg] at 80 and 303K, respectively. Furthermore, the Debye temperature was estimated from the calorimetric measurements at 166 K and from the elastic measurements as 158 K, both of which are rather low compared with the temperatures of Ni-Zn or Mn-Zn ferrites.
362
H. K O J I M A 10
O0
-8 E '-"a
90
Cp
"-S 8 0 .x.
I0
/
8
"e 6
%
70
"o "5
60
-6 u
50
°
:,.,"
2
0
0
I O0
200
300
T(K)
Fig. 53. Heat capacity and thermal expansion coefficient of sintered BaO-6Fe203. Cp: heat capacity (Reddy and Reddy 1974b), (1) o~(Reddy and Reddy 1973), (2) a parallel to the magnetized direction, (3) a perpendicular to the magnetized direction (Clark et al. 1976).
2.1.16. Thermal expansion Reddy and Reddy (1973) also measured the thermal expansion coefficient o~ of sintered B a M by a two terminal capacitance dilatometer. The result is illustrated by curve (1) in fig. 53. They derived the following experimental equation in the t e m p e r a t u r e range of 80 to 300 K: a = 0.572
x 10 7 T -
1.437 x 101° T 2 + 0.175 x 1012 T 3 .
(19)
Clark et al. (1976) gave the values c~ of B a M parallel and perpendicular to the magnetized direction, which are shown as curves (2) and (3) in fig. 53. They also reported the thermal conductivity of their specimen having 5% porosity as 4 W / m deg at r o o m temperature. A b o v e r o o m temperature, Davis (1965) observed the change of lattice constants in B a M up to 1000°C by X-ray diffraction, but the value is fairly high and no noticeable change was found around the Curie point. K 6 m o t o and Kojima (1976) showed the t e m p e r a t u r e variations of the a and c-axis in B a M in fig. 54, where the sharp kinks can be seen at 450°C for both axes, but the value is rather low. In table 13, the expansion coefficients of B a M by several authors are compared. The cause of the discrepancy in the list may be explained by the difference of porosity, grain size, degree of crystal orientation, chemical composition in the specimens, or accuracy of measuring methods.
FUNDAMENTAL
P R O P E R T I E S OF H E X A G O N A L
FERRITES
363
7
A5
7
o X
--4 O
O 3 1D
0
0
200 Temperature
400 (°C)
600
Fig. 54. Variations of the lattice constants in BaO.6Fe203 with temperature (K6moto and Kojima 1976).
T A B L E 13 T h e r m a l e x p a n s i o n c o e f f i c i e n t o f B a M (x 10-6/deg). T (°C)
R.T.
a
0°
27 °
R.T.
8.5 (a)
8.4 c°)
8.8 ~)
11.1 (d)
T (°C)
25-150
150-250
25-250
25-640
~(e)
9.5
T(°C) an (f) ao (f)
10
-
10.5
100
5.7 10.8
6.8 11.0
200
9.8
-
250
8.2 12.1
10.5 13.8
10.2
300
18.6 17.2
350
-
450
20.7 17.2
* By X-ray diffraction (a) H a b e r e y et al. (1973) Co)R e d d y a n d R e d d y (1973) (c>C l a r k et al. (1976)
(d/Davis* (1965) (e) B u e s s e m a n d D o f f (1957) If) K 6 m o t o * a n d K o j i m a (1976).
11.5 7.3
550
364
•
H. KOJIMA
2.1.17. Electric and dielectric properties
Zfiv&a (1963) observed the electrical conductivity of BaM and PbM single crystals and found that the relations among the conductivities are approximately expressed by 100"BaM ~" OrpbM and 10or//~ o-1 for both compounds. Here, o-B~ and O-pbM mean the values of the conductivities with each ferrite, and o-//and o-~ denote the values measured along and perpendicular to the c-axis, respectively. Figure 55(a) and (b) show the conductivities of BaM and PbM, rewritten from these results by Wijn (1970). Z~veta also estimated the activation energy for the temperature dependence of the conductivity and, moreover, reported on the thermoelectric force for the same specimens. He finally concluded that an electron hopping mechanism between Fe ions might reasonably be assumed and so the conductivity
A
TIE I0-I T
b id z
io-3
/o)
A
TE
10-3
",,,.\
T
b 164 II C
id 5
I 2
3
4
5
I/T
(xlO-3/deg K)
6
7
Fig. 55. Temperature dependence of the electrical d.c. conductivity of the single crystals: (a) BaFe12019, (b) PbFe12019. The different marks indicate the measuring points of different crystals (Zfiveta 1963).
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
365
10-2
Ld ~
10-4 IE 0-5
b
10-6
to-T
io-e
j0-9 2
5
4 I/T
5 6 7 (xlO-3/deg K)
8
9
Fig. 56. Temperature dependence of the conductivity of BaFe12019 polycrystal containing 0.022% Fe 2+ by weight. The figures stand for the used frequency in Hz (Haberey and Wijn 1968). 104'
'
I
'
I0
.c,-''~"
I !
IOM
'
---
i!
///
o
1 ,o
-150
-I00
-50
0
50
I00
150
T (°C) Fig. 57. Temperature dependence of the real part of the dielectric constant for the same specimens in fig. 56 (Haberey and Wijn 1968).
366
H. KOJIMA
is related to the presence of Fe 2+. D u l l e n k o p f and Wijn (1969) r e p o r t e d similar experiments in the frequency range of 1 to 8 G H z and b e t w e e n - 5 5 ° and 100°C. T h e specimens were polycrystals containing Fe z+ up to 0.5% by weight. T h e m o d e l of a thermally activated h o p p i n g process again received support in this work. Figure 56 shows the t e m p e r a t u r e d e p e n d e n c e of the conductivity for the p r o p o s e d composition of BaFe12.59019.39 3+ polycrystal, d e t e r m i n e d by chemical analysis, at various frequencies r e p o r t e d by H a b e r e y and Wijn (1968). T h e y also described the t e m p e r a t u r e d e p e n d e n c e of dielectric constants E' for the same specimen, as shown in fig. 57.
TABLE 14 Properties of the magnetoplumbite type compounds substituted Ba ion. Compound
a (A)
c (A,)
o's (Gcm3/g) [x 4zr x 10-7 Wbm/kg]
NB (/xB/mol)
LaFe2÷Fe3+nOig*
-
65 (R.T.)
19.5 (0 K) 13 (300 K)
Na0.5La0.sFe12019
-
69 (R.T.) 113 (0 K)
21.5 (0 K)
Ca0.88La0.i4Fe12019*
5.877
22.91
Ag0.sLa0.sFe12Oi9
5.85
22.85
LaFea2019*
52 (R.T.) 73.4 (77 K)
-
96.2 (0 K)
19.2 (0 K)
LaFei2019* LaFe12019*
Tl0.sLa0.sFea2019 (a) (b) (c) (d)
Aharoni and Schiber (1961) Summergrad and Banks (1957) Ichinose and Kurihara (1963) Laroria and Shinha (1963)
(e) Lotgering (1974) (f) Van Diepen and Lotgering (1974) (g) Drofenik et al, (1973)
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S
367
2.2. Substituted M compound 2.2.1. BaO-SrO-PbO-Fe203 systems As already discussed, replacement of Ba 2+ ion with Sr 2+, Pb 2+ or both of them is possible with any mixing ratio without changing the crystal structure. For example, Ba0.75Sr0.zsFea2019 (Borovik a n d Yakovleva 1962a, 1962b) and Sr0.7sPb0.25Fe12019 (Borovik and Yakovleva 1963) attracted special interest owing to the improved properties as permanent magnet materials. Hunty (1963) however, found no improvement of these mixed ferrites. Kojima and Miyakawa (1965)
T A B L E 14 (continued)
KI (erg/cm 3) [x 10 ~J/m 3] 2,5
x
10 6
/(2 (erg/cm 3) [x 10-1J/m 3] --
0c (K)
Composition
695
3.0 x 106
-
713 _+ 10
-
-
718
-
CaO 13.70 Fe203 82.78 La203 2.00 FeO 1.52 (mol %)
708
(10-13) x l0 s (0 K)
0 (293 K) (5-10) x l0 s (77 K)
LaM 86.2 Fe304 10.3 LaFeO3 3.4 (wt %)
NB-T
G-La205
Ref.
(a)
o--T o-j/, o - l - H o-s-La203
(c)
Br = 1600 G MHc = 2450 Oe BHc = 1100 Oe
(d)
o-//,o-±-H o--T
(e)
K1-T
M6ssbauer spect. Hhf-T
(f)
Fe304
M6ssbauer spect.
(g)
removed by 10% H2804
e-T 8-T Hi-T
Fe304 10
(wt %) 697 -+ 2
Other data in the paper
M6ssbauer spect.
(g)
368
H. KOJIMA
investigated the changes of lattice constants, saturation magnetization and Curie points for the Ba-Sr, B a - P b and Sr-Pb binary hexaferrites systems and found that there are no sharp kinks on the curves relating the properties and the composition. These facts suggested that those systems form complete solid solutions between both end m e m b e r s and no special c o m p o u n d can exist at any mixing ratio. Therefore, it is m o r e plausible that the i m p r o v e m e n t s due to the substitutions in the Borovik's papers might be due to the acceleration of the solid state reaction or sintering process etc., and not to the intrinsic properties of a specific compound. Though such non-intrinsic but practically useful effects in the p e r m a n e n t magnet properties of hard ferrites introduced by many kinds of additives were once actively studied the results will n o t be mentioned further, since the details will be discussed in ch. 7 by Stfiblein. 2.2.2. Other substitutions of B a 2+ ions Ferrimagnetic properties of the magnetoplumbite type compounds are naturally based on the superexchange interaction of F e - O - F e , so that no remarkable effect on the magnetic properties would be expected by the replacement of a Ba ion. However, the properties could be influenced to some extent by the changes in the distance or the angle between F e - O - F e arising from the substitution, leading to differences among BaM, SrM and PbM. Table 14 shows the properties of several examples for Ba 2+ substituted ferrites. In some cases m a r k e d * in the table, the partial coexistence of Fe 2+ may be unavoidable in order to keep electrical neutrality?. The examples are so few that no general tendency can be deduced from the table. As described before, when discussing the M6ssbauer effect, Drofenik et al. (1973) concluded from the t e m p e r a t u r e dependence of the hyperfine fields for L a M that a m o r e convex magnetization against t e m p e r a t u r e curve than SrM comes from the difference of the behaviour of the 12k sublattices. It is also pointed out in this p a p e r that in LaFet2019 and T10.sLa0.sFe12019 no Fe 2+ sublattice was observed in the M6ssbauer experiment and the averaged hyperfine fields could originate from a fast electron exchange between Fe 2+ and Fe 3+, or in the process of electron sharing by the six ions in the 12k sites of these compounds. Van Diepen and Lotgering (1974) insisted from a similar study that the substitution of Ba 2+ with La 3+ causes a valency change of Fe 3+ to Fe 2+ at the 2a or 4f2 site, although they also found no subspectrum of Fe 2+. 2.2.3. Substitution of Fe 3+ ions Substitution with A13+, Ga 3+ and Cr 3+ ion. T h e replacement of Fe 3+ in B a M or SrM with AP +, G a 3+ or Cr 3+ has been intensively investigated. Because of the resemblance of their ionic radii with Fe 3+ (shown in table 2) especially the former two ions are easily replaced at any substitution ratio without changing the crystal structure. Figure 58(a) and (b) show the variations of the lattice constants a and c
t Replacements with combinations of a few ions are also cited in the next section.
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
369
23.2
22.8 o,=I
22.6 (j,
22.4
(b 22.2
i 22.0
i
A
o
0
2
4
6 X
8
I0
12
Fig. 58. (a) Lattice parameter a, and (b) c as a function of substituted ratio. (1) BaAlxFe12-,Om, (2) BaGaxFe12-xOm,(3) BaCr, Fe12-xO19,(4) SrCrxFem-xO19(Bertaut et al. 1959), (5) SrAlxFe12-xOt9(Goto and Takahashi 1973). for (1) BaAlxFe12_x019, (2) BaGaxFe12-xO19, (3) BaCrxFe12-xO19, (4) SrCrxFelz-xO19 (Bertaut et al. 1959) and (5) SrAlxFem_xO19 (Goto and Takahashi 1973). Almost the same results as given on line (1) for the Ba-A1-M system by Vinnik and Zvereva (1969) and also on line (5) for SrAlxFe12-~O19 were reported by Florescu et al. (1973). The parameters decrease linearly with the substitution ratio in all cases. Numerical values for the end members were given by Adelsk61d (1938) and Bertaut et al. (1959) as in table 15. This table also contains the results for Ca/Sk112019 by Wisnyi (1967); Ca(AlFe)12019 by MacChesny et al. (1971); BaGaa2019, SrGa~2Oa9 and LaMgGanO19 by Verstegen (1973).
370
H. KOJIMA TABLE 15 Lattice parameters of some substituted M-type compounds with A1, Ga or Gr. Formula
a (4)
c (4)
Ref.
BaA112019
5.577 5.66
22.67 22.285
Adelsk61d (1938) Bertaut et al. (1959)
SrAl12019
5.557
21.945
Adelsk61d (1938)
CaA1~2OI9
5.566
22.010
Wisnyi (1967)
Ca(A1Fe)12019 5.792-+0.004
22.56_+0.04
MacChesneyet al. (1971)
BaGa12019
5.818 5.850 -+0.004
23.00 23.77 _+0.02
Bertaut et al. (1959) Verstegen (1973)
SrGa12Oa9
5.796 -+0.004
23.77 _+0.02
Verstegen (1973)
LaMgGa11019 5.799-+0.003
22.71 -+0.01
Verstegen (1973)
BaCrsFe4Oa9 SrCr6Fe6019
22.82 22.77
Bertaut et al. (1959) Bertaut et al. (1959)
5.844 5.844
Van Uitert (1957), and Van Uitert and Swanekamp (1957) reported 4¢rMs of BaAl~Fe12_xO19, (1) fired below 1400°C and (2) fired above 1400°C, and (3) SrAlxFe12_xOi9 after Rodrigue (1963) as shown in fig. 59(a). Figure 59(b) illustrates (1) BaAlxFe12_xO19; (2) BaGa~Fe12_~O~9 (Mones and Banks 1958); (3) SrAlxFe,2_xO~9 (Rodrigue 1963) and (4) ditto (Gotto and Takahashi 1973). Lines (3) and (4) agree quite well. In figs. 60(a) and (b), Bertaut et al. (1959) summarized NB at 0 K per mole in Bohr magneton and 0c for (1) BaAl~Fe~2_xO~9, (2) BaGa~Fe12_xO19, (3) BaCrxFe~2_xO~9; the m a r k A in (a) relates to SrCrxFe12-~O19. Albanese et al. (1974) estimated 0c for BaAlxFe~2 xO,9 and SrAlxFe~2-xO19 from the M6ssbauer experiments, as shown in table 16. The lines D~ and D2 in fig. 60(a) were drawn on the hypotheses that AP + ions enter the 2a and 12k sites, or G a 3+ the 4fl and 12k sites, respectively (after Bertaut et al. (1959)). With these results, and in addition referring to the X-ray investigations, they came to the conclusion that AI 3÷ and Cr 3+ first occupy 2a sites and then 12k sites, while G a 3+ enters first 4fl and then 12k sites. These assumptions are thoroughly supported by Rensen et al. (1971) by M6ssbauer studies, but in contrast with these results, Suchet (1971) expressed a strong preference of AI 3÷ to the 4f~ and 2a sites. Glasser et al. (1972) observed M6ssbauer and E S R spectra for CaAl12-xFe~O~9 with x <~ 4.8, i.e., mainly on the A1 rich side. They recognized a m a r k e d preference of Fe 3÷ for the tetrahedral 4fl sites from M6ssbauer investigations and interpreted the majority of E S R resonances by supposing Fe 3÷ ions in an axially distorted site. T h e relations of a, Ms, 0c, K, MHc and the critical radius for a single-domain
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
800 1 .(3)
r...<-.,
60 O l ~ ' ~
I
[ i
371
I
i
Ib)
A
,.i
o
400 qb
(.3
200 121
5000
I
(0) 3)
4000
! I i
~', ,,,
~o 3 0 0 0
x.
2000
I==
1000
0
0
2
4
6
I 8
10 12 X Fig. 59. (a) Saturation 4~rM~, and (b) Curie temperature 0c as a function of substituted ratio. (a) 4~-Ms: (1) BaAlxFe12-xO19 fired below 1400°C, (2) ditto fired above 1400°C (Van Uitert and Swanekamp 1957), (3) SrAlxFelz-xO19 (Rodrigue 1963); (b) 0c: (1) BaAlxFelz-xO19, (2) BaGa~Fet2 xO19 (Mones and Banks 1958), (3) SrAlxFel2-xOl9 (Rodrigue 1963), (4) ditto (Goto and Takahashi 1973).
particle Rc etc. versus x for BaCrxFel2 xO19; and BaAlxFel2-xOi9, BaGaxFe12-xO19 and BaCrxFe12_xOx9 were given by Haneda and Kojima (1971 and 1973b). In fig. 61, curves (3), (4) and (5) indicate H A for BaAlxFe12-xO19, BaGaxFei2-xO19 and BaCrxFei2 xO19 (Haneda and Kojima 1973b) besides the marks • and A illustrating HA for SrAlxFe~2_xO19, as obtained by De Bitetto (1964) and Rodrigue (1963). Curves (1) and (2) are drawn with the calculated values of eqs. (20) and (21) by De Bitetto who gave the experimental formulae:
372
H. K O J I M A
800
I
(b) 700 A
•v" 6 0 0 0
500 --
400
300
25
I
(a) 20'~
\2a
D2
\\
D,,\ \ 0
2
,
)--'~,X~L 6
4
8
I0
12
X Fig. 60. (a) Saturation at 0 K and, (b) Curie temperature versus substitution ratio (Bertaut et al. 1959): (1) BaAlxFe12-xO19, (2) BaGaxFeu-xO19, (3) BaCrxFeu-xO19, (A) SrCrxFelz-xO19, D1, D2: calculated values.
T A B L E 16 Curie temperature for the compounds BaAlxFe12-xO19 and SrAlxFelz_xOl9 (AIbanese et al. 1974). BaAlxFei2-xO19
SrAlxFe12-xO19
x
Tc (K)
x
T~ (K)
0 2.5 4
723 -+ 5 595 ---5 518---5
0 1 2
723 -+ 5 658 -+ 5 590---5
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES
7O
,
373
I (2)
I
6O
I
I
// °/(I)
,/
5O
/ z~
-g
/ •/ //~e'~
40
131
I// /
~D
o X
0
"1-
~
(51
I0
0 0
I
2
3
4
x
Fig. 61. Anisotropy field HA as a function of substitution ratio: (1) and (2) see text, (0) SrAlxFe12-xO19 (De Bitetto 1964), (A) ditto (Rodrigue 1963), (3) BaAlxFe12-xOxg, (4) BaGaxFex2-xO19, (5) BaCrxFe~z_xO19 (Haneda and Kojima 1973b).
HA(x)/H(o) = (12 - x)/612 - x/2 + (x/6)zss],
(20)
HA(x)/H(o) =
(21)
or (12 - x ) / ( 1 2 - 3 x ) .
Since D e B i t e t t o e x p e r i m e n t a l l y o b t a i n e d a r e l a t i o n for K as a f u n c t i o n of x for SrAlxFe~z-xO19 in t h e f o r m ,
K(x~/K(o) = 1 - x / 1 2 ,
(22)
w e can say that t h e m a g n e t o c r y s t a l l i n e e n e r g y m a y b e r o u g h l y a s s u m e d to h a v e a b o u t t h e s a m e s t r e n g t h for all t h e five sublattices. A s s u m m a r i z e d in fig. 62, t h e M s - x d e p e n d e n c e is r e l a t e d to t h e v a l i d i t y of eq. (20) o r eq. (21). D e B i t e t t o c l a i m e d t h a t an e m p i r i c a l fitting f o r m u l a ,
374
H. KOJIMA 1.0
0.8
1~ O.6
0,4
0.2
0
I
2
3
4
5
6
x
Fig. 62. Variations of normalized saturation magnetization with composition in MAlxFe12-xO19(De Bitetto 1964): (0) Ba (Bertaut et al. 1959), (A) Ba (Mones and Banks 1958), (V) Ba (Van Uitert and Swanekamp 1957), (V) Pb (Bozorth and Kramer t959), (D) Ba, (C)) Sr (Du Pr6 et al. 1958), (&) Ba (Vinnik and Zvereva 1970).
M(x)/M(o) = ~[2 - x/2 + (x/6)zss],
(23)
which is shown by curve (2) in fig. 62, is m o r e plausible than most other authors' results given by curve (1), i.e. by
M(x)/M(o) = 1 - (x/4).
(24)
D a t a by Vinnik and Z v e r e v a (1970) for the B a - A 1 - M system m e a s u r e d at 4.2 K were a d d e d to fig. 62. T h e y concluded that the preference of A13+ seems to agree with the results of Bertaut et al. (1959) and the deviation at x = 3.3 m a y be due to the differences of applied field. H o w e v e r , we would like to point out here that the occupied site with a substituted ion might be different according to the preparation conditions, starting materials and various other factors, although the substitution ratio m a y be perfectly identical. HA was d e t e r m i n e d by D e Bitetto using F M R m e a s u r e m e n t s and the line width A H was also given for the S r - A I - M system between x = 0-1.7. A l b a n e s e et al. (1974) reported H i - T and Hi(T)/I-L(o)--T/Oc relations by M6ssbauer investigations for A1 or G a substituted B a M and SrM. H e i n e c k e and Jahn (1972) studied the angular variation of the nucleation field Hn for single d o m a i n particles of SrA13.sFes.2019 and c o m p a r e d the Hn-O relation with the 1/cos 0 law or the c o h e r e n t rotation model. Interesting investigations of the f o r m a t i o n m o d e of the domain structures on the c-plane of PbA1Fel~O19 were r e p o r t e d by Williams and S h e r w o o d (1958) using a motion picture technique. Tanasoiu (1972) o b s e r v e d r e m a n e n t domain structures on the c-plane of SrAI4.8FeT.2OI9, the main magnetic properties of which were previously d e t e r m i n e d as 4~rMs = 315 G [315 × 10 -4 T], To= 5 1 8 K and Crw= 5 . 8 e r g / c m 2 [5.8× 10-3j/m2]. H e f o u n d that the r e m a n e n t
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
375
structure after thermal demagnetization consists of a great number of domains with irregular shape and are very unstable, while the remanent state by a.c. demagnetization consists of only a few domains. MacChesney et al. (1971) studied the ferrimagnetic phase of the CaO-A1203Fe203 system and, as for the hexagonal magnetic phase, they found the composition range extends from CaAI~20~4 to at least CaA14.2FetsOls.6. The lattice constants of an idealized composition Ca(A1Fe)12019 were already referred to in table 15. The magnetic moment at room temperature for the group varies from 1 to 10 emu/g [12.56 to 125.6 x 10-~ Wbm/kg] according to the Fe content, but they show rather high anisotropy fields of about 60 kOe [4.78 x 10 6 A/m] regardless of the composition. 1 / x - T relations up to 1000 K were determined by Florescu et al. (1973) for SrAlxFe~2-xO19 from x = 2.0 to 9.0 and they estimated N6el's parameters by the graphical method (N6el 1948) from these results. The photoluminescence of BaGa~2019, SrGa120~9 and LaMgGauO~9 with and without Mn 2+ phosphors was reported by Verstegen (1973) who found that the emission strongly resembles that of Mn 2+ in MgGa204. Substitution with Sc 3+ and In 3+. The partial replacement of Fe 3+ with Sc3+ or In 3+ ions in M-type compounds were investigated mainly by research groups in the U S S R with an interest in their specific magnetic ordering. Perekalina and Cheparin (1967) measured the relations of a, c-x, ~rs-T and K ~ - T for BaScxFe~2 xO19 single crystals with x = 1.2-1.8, as shown in table 17 and figs. 63 and 64. Maxima
80 7O •
.~,^
"" o
"~ 6o r
'~~4-O0~5_xS~=~~~ 0~2,03~" 0~ ×
C31
10 0
r 0
200
400 Temperature
I,o 600
(K)
Fig. 63. Temperature dependence of the specific magnetization BaScxFe12-xOa9single crystals (Perekalina and Cheparin 1967): (1) x = 1.2, (2) x = 1.4, (3) x = 1.8.
376
H. KOJIMA
o<
+1
o<
+1
tt3
x
t'¢3 t'e'j
"~"
'~" ¢xl t'xl ('xl ~:7~ t'~ , ~ ,.~j . . . . . . ~.,
tt3 0~ trq
tt3 "~" ,,..~ "
X
uS,.-~o~ ~ u E e 6
b, © X
X
,,~
~
.
.
t¢3 t ~
t'q
e¢3
r~
.= .
.
.
.
.
.
¢¢3 ~D v
.= ~mmmm~m~
e~
FUNDAMENTAL
PROPERTIES
9
OF HEXAGONAL
FERRITES
377
r
(I). 8
/,
I \_
7 6 E 5 o X
4 tO
E
-2 3 03
%2 X
0
-I
-2
I 0
I 200
400
Temperature
600 (K)
Fig. 64. T e m p e r a t u r e d e p e n d e n c e of t h e a n i s o t r o p y c o n s t a n t K1 for BaScxFelz-xO19 ( P e r e k a l i n a a n d C h e p a r i n 1967): x = 1.2, x = 1.4, x = 1.8.
in the O-s-T relations, which shift towards higher temperatures with increasing Sc content, and the change of K1 for BaScl.sFe10.2019 to negative values between 125 and 355 K are in contrast with pure M-type compounds. It was suggested that the t e m p e r a t u r e dependences of ~rs can be explained by N6el'S theory (N6el 1948). Aleshko-Ozhevkii et al. (1968, 1969) determined the magnetic structure by neutron diffraction studies at 77 K in magnetic fields up to 5 k O e [3.89 x 105 A/m] for BaScxFe12-xO19 with x = 1.2-1.8. They showed conclusively that Sc 3+ ions occupy 4fl and 2b sites, so that antiphase conical helixes were formed in certain blocks of the crystal unit cell. In a later p a p e r these authors estimated (i) the periods along the c-axis; (ii) the cone vertex half angle; and (iii) the phase angle of the projection of theo total magnetic m o m e n t s in the basal plane which were, o respectively: (i) 141A, (ii) 30 °, (iii) 150 ° for x = 1.8; (i) 91 A, (ii) 20 °, (iii) 135 ° for x = 1.4; and (i) 70 A, (ii) 12 °, (iii) 120 ° for x = 1.2. Alesko-Ozhevskii and Yamzin (1969) added a detailed explanation of the intensity anomalies of the satellites in the neutron diffraction patterns of BaScxFe12-xO19 on the basis of the superposition of ferro- and antiferromagnetic reflections. Koroleva and Mitian (1971)
378
H. KOJIMA
suggested the possibility of the appearance of these magnetic antiphase helical structure based on Moriya's rule (Moriya 1960). The same behaviour of o-s-T and K1-T plots for single crystals of BaInxFe12_xO19 for x > 1.9 and PbInl.gFemO~9 were observed by Perekalina et al. (1970). Their main data are added to table 17, which can also be understood by the model of two magnetic sublattices with a weak exchange interaction. Bashkirov et al. (1975) carried out M6ssbauer studies for BaIn3FegO19 and showed the presence of an angular magnetic structure, which was presumably caused by the almost full occupation of 2b and 4fi sites with In 3+. Magnetic order-disorder transition of the compound was observed between 300 and 250 K with an external field of H = 16 k O e [1.28 x 10 6 A / m ] and below 100 K in the absence of an external field. The difficulty of realizing the saturated state even in 50 k O e [3.98 x 106 A/m] for BaInz4Fe9.6Oa9 was reported by Perekalina et al. (1970). These anomalous magnetic properties are due to the fact that collinear structures are not realized even at helium temperatures.
Substitution of Fe 3+ with paired ions; Co-Ti system Smit et al. (1960) measured the torque curves of BaCox/zTix/2Felz-x019 for x = 0.9, 1.0 and 1.5 at T = 90 K and H = 32 k O e [2.55 x 10 6 A/m] after thermal demagnetization and suggested from the results that the characteristic details of these curves were due to the effects of incomplete alignment, both on a microscopic and an atomic scale. Rodrigue (1963) pointed out that the effective internal anisotropy fields of B a M could be varied from virtually zero to 17.5 k O e [1.39 × 106 A/m] by substituting with Co-Ti, and this is quite advantageous for applications to microwave devices. In fig. 65, the data in this p a p e r were cited in (a), (b) and (d). De Bitetto (1964) determined the relation of H A with x by r o o m t e m p e r a t u r e microwave ferrimagnetic resonance measurements. The line widths A H of these oriented polycrystalline compounds were all about 2 k O e [1.6× 105A/m]. His results are also plotted in figs. 65 (a), (b) and (c). Lines (1) and (2) in (a) are drawn based on G o r t e r ' s assumption (Casimir et al. 1959): (i) a random distribution of both Co and Ti ions among only the nine octahedral sites (12k, 2a and 4f2), or (ii) both ions are substituted preferentially for some Fe 3+ ions with only the eight favourably oriented moments (12k, 2a, 2b). It seems that D e Bitetto's data are situated on line (1), G o r t e r ' s results on line (2), but that Smit and Wijn's and Rodrigue's data are just between the two lines. The microscopic structure of C o - T i substituted samples were reported by Bonnenberg and Wijn (1968) using an electron microprobe analyser. They found, for instance, that in the composition BaComTimFe~2019, the concentration of Fe, Co and Ba, Ti showed the same distribution tendency in pairs but the opposite tendency in the sintered grains. Investigations of the cation distribution on an atomic scale were reported by K r e b e r and Gonser (1976). They compared the electric quadrupole splitting E and the area of the M6ssbauer spectra for BaCox/2Tix/2Fe12-xO19 sublattices from x = 0 up to x = 11 at temperatures above the corresponding Curie points of each compositions. Their conclusions are as follows: The Fe 3+ ions in 4fl and 4f2 sites are replaced for x ~<4 and the remaining octahedral 2a and 12k sites are substituted randomly for 4 < x < 8. Finally, for x > 8, a weak substitution in the
F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S 800
I
, _,
I
% x
400"
L
379
i
Idl
I
i (c)
~,0<
E
.2 z.0 %
-×
1.0
~g 18~
(b) 12
E
0 X
o I
r.o~ ~ ~ _
§
o.8
x
0.6
(a)
- ...... --~
0
I
2 x
Fig. 65. Normalized magnetic saturation at room temperature, anisotropy field, anisotropy constant and Curie temperature against composition in Ba(TiCo)xFe12-xO19. (a) M(x)/M(01: (©) De Bitetto (1964) at room temperature, (11) Gorter (Casimir et al. 1959) at 77 K, (A) Smit and Wijn (1959 at 20 K, (3) Rodrigue (1963) at room temperature, (1) and (2) calculated values (see text); (b) Ha: ((2)) De Bitetto (1964), ( 0 ) Rodrigue (1963); (c) KI: De Bitetto (1964); (d) 0o: Rodrigue (1963).
2b site occurs. When comparing these conclusions with the above mentioned results in fig. 65, it should be noticed that the latter observations correspond to the paramagnetic region.
Other combinations with H-IVpairs. D u e to the interest in the effect of substituting ions on the magnetic properties of M compounds, attempts to replace Fe 3+ by non-magnetic ions are still being reported occasionally. Since equal amounts of
380
H. KOJIMA
M2++ M 4+ are simplest for electrical neutrality in these substituted compounds, a number of papers has been published regarding such a substitution. For instance, Tauber et al. (1963) investigated BaZnx/2Irx/zFe~2 xOi9 single crystals with x = 0-0.6 and found that the lattice constant a increased from 5.893-+0.001 A to 5.920-+ 0.001A but that c remained constant at 23.194_+0.002A with increasing I r content. The o-~-T relations for x = 0, 0.32, 1.04 and 1.2, determined by the chemical analysis of total Ir, were given in their paper. Other main results obtained using FMR are summarized in table 18. They showed that the substitution of Ir 4+ causes the spin system in the compound to be pulled down toward the basal plane. Similar FMR measurements have been done by Dixon et al. (1971) with single crystals of BaZnx/zTix/zFelz-x019 for nominal compositions, x = 2.0-5.0. They succeeded in decreasing the resonance line width A H to 36 Oe [2865 A/m] with x = 3.0. The variation of A H versus x at 37.6 G H z was illustrated in their paper. A summary of their results is given in table 18. Rensen et al. (1971) discussed ZnTi, ZnGe, ZnSn, ZnZr, CuTi, CoZr or NiTi substitution pairs. They referred briefly to the cation distributions for each compound from M6ssbauer effect results. Magnetization, anisotropy field and M6ssbauer spectra of BaZnxTiyMnzFe12_x_y_z019 were investigated between 4.2 and 300 K by Mahoney et al. (1972). The o-~-T curves for various nominal x values, H~-x and e - x diagrams and tables of magnetic moments at 0 K and cation distributions were given in their paper. They concluded that Ti 4+ mainly, and Mn 3+ completely occupied 12k and 2a sites, and Z n 2+ w a s primarily assigned to 4fi sites on crystal chemical grounds, but partly distributed on to 12k or 2a sites to fit with the observed magnetic moment. Haneda and Kojima (1973b) measured HA, MHc and Rc as a function of x for BaZnx/zGex/zFe12-x019 and BaZnzx/3Vx/3Felz-x019, BaZn2x/3Tax/3Fe12-~019 and BaZn2x/3Nbx/3Fe12-~O19, also involving M2++ M 5+ pairs. The main problem concerned the changes of MHc with x for these compounds and this was also considered in connection with the changes of H A and also Rc for sintered specimens. o
o
2.2.4. Effect of substitutions on the temperature dependence of magnetization An attempt to improve the temperature dependence of the magnetization of the magnetoplumbite structure, which is inferior by one order than for Alnico magnets, was perhaps reported f o r the first time by Heimke (1960). H e showed that the Ms-T relation could be changed for the M-type compound BaTiO3"5Fe203+ 1.5% CaSiO3, that is, its magnetization varies almost parallel relative to the temperature axis below 0°C, as illustrated by line (1) in fig. 66(a) (using the scale of the right-hand axis). For an explanation of this result, he proposed two kinds of exchange schemes other than the one reported by Gorter (1957). Esper and Kaiser (1972) continued this analysis and obtained interesting results on the changes in the temperature dependence of O-s for M compounds. Their o-s- T relations are shown in fig. 66(b) as curves (2) and (3), with (1) as the normal relation of BaM. Their typical substituted compound has the composition Ba(Sb203)0.25(Fe203)5.75 and the sample of curve (2), having almost the same temperature coefficient a(o-s)= 0.2% per degree and about ~O-s of BaM, was
FUNDAMENTAL
PROPERTIES
OF HEXAGONAL
FERRITES
-g T X
o X ~
X
rO
{IN]{[{
{{
O
8 © r eq
tt3
÷1 k~) tt~ ~
ee)
tt3
0J
~2 t--
e~
¢e5
,<1
© e'~
¢o
t~, ,,o
O r.¢) X ©
cq ¢¢~ ,~1- tt3
.+
+
¢-
N +
+ ¢
~z
rqrd ©
i--.
381
382
H. K O J I M A I00
..L,~
i
(c)
80
60
40
i 20 0 E
I ..Q b--
I0
I00
I
--.
X
b~
(b )
-4) 1
Bo
--.<\-..~ ~.
20
5000
I00
N
8O
i~)-~ I ~_,p~.~,-~-~-~. (5) _
60
(0 ) -
4000
~ . ,
5000
E
~o ×
2000
4O
\
2O
i I
0 0
200
400 Temperature
600
I000
i
o
800
(K)
Fig. 66. Temperature dependence of the saturation magnetization o's for some substituted M compounds. (a): (1) 4~rMs of BaTiO3'5Fe203 with the scale of the right ordinate (Heimke 1960), (2) "4+ 2+ 3+ 5+ 2+ 3+ BaTlo.6Feo.6Felo.8Ol9, (3) BaSbo.sFel.oFelo.5019 (Lotgering 1974); (b): (1) BaM, (2) and (3) Sb-substituted BaM (Esper and Kaiser 1972); (c): (1) SrM, (2) As-substituted SrM (Esper and Kaiser 1972).
FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES
383
p r e p a r e d through the heat treatment in air and below 1300°C. The sample of curve (3) received a secondary heat treatment above 1200 ° in N2 or above 1300°C in air, after the normal solid state reaction. Sb205, i.e., Sb 5+ was used as a starting material in both cases. It was claimed that the anomalous t e m p e r a t u r e dependence of curve (3) was caused by the partial replacement of Fe 3÷ in 4f2 sites with non-magnetic trivalent ions having ionic radius smaller than Fe 3÷. In this case, the crystal structure or the magnetic coupling scheme gradually turns to the Wstructure from M-type, though the sample of curve (2) still has a distorted M structure. In conclusion As and P were r e c o m m e n d e d as the most suitable replacing ions to realize a low t e m p e r a t u r e coefficient around room temperature. A valve c~(o-s)= 0.1% per degree was obtained with As substituted SrM as illustrated with curve (2) in fig. 66(c), in contrast to curve (1) for the normal SrM. On the other hand, Kreber and Gonser (1973) concluded from the M6ssbauer experiments at r o o m t e m p e r a t u r e and 77 K for the same composition, that As ions occupy preferentially 2b sites, although they did not describe the preparation conditions. Lotgering (1974) showed in curve (2) in fig. 66(a) the saturation magnetization measured parallel to the easy direction, o-//, of oriented polycrystalline BaFe2+0.6Ti4+0.6Fe10.8019 and curve (3) for or// of BaFe2+1.0SbS+0.sFe10.sO19, both of which behave very similarly with t e m p e r a t u r e as curve (1) obtained by H e i m k e (1960). Lotgering reported Ti 4+ and Sb s+ to occupy 4f2 sites, which was supported by the X-ray and neutron diffraction investigations. H e stressed the effect of Fe 2+ on a 4f2 site on the t e m p e r a t u r e dependence of the magnetic anisotropy for the substituted compounds, which would be caused by the effect of an Fe 3+, Ti 4+ or Sb 5+ ion on the neighbouring 4f2 site. As described before, Grill and H a b e r y (1974) calculated the exchange parameters of BaM (see table 5) and mentioned that the t e m p e r a t u r e coefficient of the magnetization at room temperature cannot be decreased without decreasing the magnetization, and moreover, the saturation magnetization would only be increased with a diamagnetic substitution on 4f2 sites, measuring the magnetic properties of Bal-xDxPxFe12-x019 with D = K ~+, Bi 3÷ and P = Cu 2+, Ni 2+, Mn 4+ between 180 and 770 K, Grill (1974) practically proved that all the compounds have lower ~r~, 0c and almost the same c~(o-s) values as those of pure BaM. On the other hand, H a n e d a et al. (1974b) studied the effect of replacements of Fe 3+ in M type compounds with (Cu 2+ + Ge4+), (Cu 2+ + Si4+) and moreover with (Cu 2+ + Vs+), (Cu 2+ + Nb 5+) or (Cu 2+ + TaS+). They obtained ~(Br) = 0.1% per degree without reducing other p e r m a n e n t magnetic properties and insisted that ce(Br) can be improved by changing the temperature coefficient a(MHc) or C~(BHC) by such substitutions, instead of improving or(O-s), as proposed by most other investigators. Esper and Kaiser (1975) found that the anisotropy field HA, and accordingly MHc, and also their temperature coefficients can be varied with Sb-substituted BaM by different heat treatments. HA can be changed from 6.3 to 12.6kOe [5001000 kA/m] by varying the preparation conditions, and c~(MHC) was determined to be negative for HA = 6 . 3 k O e [500kA/m] and positive for HA = 12.6kOe [1000 kA/m]?. The results of the studies on the mechanisms of the i m p r o v e m e n t t o~(MHc)=+ 0.28%/°C and o~(BHc)- -0.09%/°C near room temperature for the normal BaM were estimated by Haneda et al. (1974b).
384
H. KOJIMA
of these t e m p e r a t u r e coefficients are fairly confused, but Lotgering's consideration (Lotgering 1974) seems to be most reasonable. H e proposed that the effects of partially existing reduced Fe 2+ ions could be considered to contribute to the temperature change of the anisotropy with any combinations of substituted ions.
2.2.5. Substitution with anions Q u i t e a few researches have been published on the substitution with anions in Mtype compounds. It is presumably more difficult to obtain the specimens with definite concentration of substituted anions than in the case of cations. Moreover, if it is possible to replace O 2- with only anions, this will dilute the ferromagnetic ions, so that the magnetic properties would be unfavourable for most industrial purposes. H e n c e some examples described here concern the substitution of 02with F 1- and some other kinds of cations for the purpose of valency compensation. Because of the resemblance in their ionic radii, F 1- seems to be the only suitable anion (see table 2). Frei et al. (1960) obtained an M-type c o m p o u n d BaFz.2FeO-5Fe203, showing specific gravity p = 5.25 g/cm 3 and saturation magnetization at r o o m temperature o-s = 72 emu/g [9 x 10 -3 Wbm/kg] in comparison with p = 5.25 g/cm 3 and O-s= 67 emu/g [8.4 x 10 -3 Wbm/kg] for BaM. F r o m these experiments, they suggested that the Fe e+ ions are on 4f2 sites and F 1- ions near Ba 2+ ions. C o m p o u n d s intended to give the formula BaCoxFe12-xO19-xFx with x = 0, 0.3, 0.4, 0.45, 0.47, 0.5, 1.0 and 2.0 were prepared by Robbins and Banks (1963) and recognized as single phase magnetoplumbite type by X-ray diffraction for the compositions x <~ 0.47. The estimated magnetization values for randomly oriented powders at 0 K and H = 6 k O e [4.8 x 105 A/m] were: 76, 76.5, 85, 95.2 and 100 emu/g [9.55, 9.61, 10.68, 11.96, 12.57 x 10 -5 Wbm/kg] for x = 0, 0.3, 0.4, 0.45, 0.47 respectively. They also confirmed from torque m e a s u r e m e n t s that the cone angle of the easy magnetization was 10 ° at 77 K for x = 0.3; and 40 ° at r o o m t e m p e r a t u r e and 58 ° between 200 and 77 K for x = 0.47. Robbins (1962) investigated the preferential site of Co 2+, Ni 2+ and Cu 2+ in the hexagonal compounds BaAla2019, BaGa12Oa9 and BaFe12019. Ba 2+ was replaced by La 3+ or O 2- by F ~-, for the charge compensation in these compounds. Referring to the results of Banks et al. (1962) regarding the same compounds we can deduce the following tendency for the preference of bivalent ions: In the BaMZ+Al12_xO~9_xFx system, the order of the tetrahedral preference is Co2+> Zn2+> Ni 2+, while in the BaM2+Galz_xO19_xFx system, it is Co2+> G a 3+ > N i 2+. These results were derived from X-ray investigations and diffuse reflectance measurements for powder compacts. Tables 19 and 20 give lists of the lattice parameters after Robbins (1962) for the BaA112019 and BaFe12019 systems, respectively. Examples of reflectance measurements are illustrated in fig. 67, with curve (1) for BaNi0sGa1150185F0s, curve (2) for BaCo0.sGalLsO18sF05 and curve (3) for BaNi1.sAl10.50175Fls. Assignments of the absorption peaks shown as T or O in the figure have been obtained from the literature values. As for BaM2+xFe~2_,O~9_~F~, Robbins obtained M phase single crystals with a flux of a Fe203 and NazCO3 mixture for the composition x ~< 0.5 for Ni 2+ and Co 2+, and the concentration x = 0-2 for Cu 2+. The bivalent cations in these substituted systems
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES T A B L E 19 Lattice parameters of substituted Bamll2019 with M 2+ and F 1- (Robbins 1962). Formula BaAl12019
BaNixAla2-xO19-xFx
B aNio.sZn2A19.sO16.sF2.5
BaCox Al12- x O19-xF x
BaCoZnAlloO17F2 BaCoo.sZn2A19.5Ox6.~F2.5
x
a (A)
c (A)
-
5.577
22.66
0.1 0.4 0.6
5.585 5.597 5.607
22.64 22.64 22.64
0.8
5.610
22.64
-
5.617
22.76
0.1 0.4 1.0 2.0 2.5
5.586 5.598 5.603 5.616 5.622
22.63 22.63 22.63 22.70 22.81
-
5.613 5.616
22.63 22.70
T A B L E 20 Lattice constants of M 2+ and F 1" substituted M compounds (Robbins 1962). Formula
x
a (,~)
c (A)
0.5 0.6 1.0 2.0
5.888 5.892 5.891 5.896
23.15 23.14 23.19 23.21
-
5.882
32.83
BaCuxFe12-xO19-xFx
0.35 0.63 1.14
5.883 5.884 5.885
23.15 23.16 23.19
BaCoxFe12-xO19-xFx
0.3 0.4 0.45 0.47
5.883 5.886 5.886 5.887
23.12 23.12 23.13 23.15
BaNixFe12-xO19-xFx
BaFe22+Nio.ssFels.4201s.42Fo.ss
385
386
H. K O J I M A 8O
7o
/s)
6O
r~i_
/ /~IT~-
(21
50
t j...
I//
t
/
iX
. . . .
1~
.//," (_./
200
.
.
.
.
g I
/i
i~ V1,
,~ ' Io
r,J
+%,.,d;
400
600 .X. ( m,u.m )
800
I000
Fig. 67. Examples of the reflectance spectra for the pellets with some anion substituted M compounds (Robbins 1962). (1) BaNi0.sGall.5Ois.sF0.5, (2) BaCo0.sGall.sO1s.sF0.5, (3) BaNii.sAl10.5017.sF1.5. T and O
are absorption peaks from relevant ions in tetrahedral or octahedral site.
also exhibited a preference for 4fl sites, as was confirmed from the results of magnetic measurements. The magnetic properties at 0 K are listed in table 21, where the saturation values were estimated from the o-s-T relations in a rather higher temperature range compared with the literature value o f BaFei2019 as a standard. Though the Curie temperatures seem to be higher than the other reported values by about 50°C, the increase of O-s and the decrease of 0¢ with increasing substitution ratio are clearly seen. For the higher substitution ratio of Co 2+, x > 0 . 5 , the compound changes to a mixture of M and W phases, then rapidly becomes single W phase with increasing x values, which was confirmed by X-ray and magnetic torque measurements in this paper. T A B L E 21
Magnetic properties of M 2+ and F 1- substituted M compounds (Robbins 1962). KI at R.T. (x 10 6 erg/cm 3) [x 105 J / m 3]
0% at 0 K (emu/g) [x 4~- x 10-7 Wbm/kg]
NB at 0 K (/xB)
0c (°C)
-
100
20
500
3.3
BaNixFe12-xOm-xFx
0.6
113
22.50
475
2.4
BaCuxFe~2-xO19-xFx
0.35 0.63 1.14
108.0 113.5 118.0
21.66 22.72 23.72
460 450 418
3.1 2.9 -
0.3 0.4
105 108.5
21.0 21.7
470 470-
-
Formula BaFez2019
BaCoxFel2-xOx9-xFx
x
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES
387
References Adelsk61d, V., 1938, Arkiv Kemi. Mineral. Geol. 12A, 1. Aharoni, A., 1962, Rev. Mod. Phys. 34, 227. Aharoni, A. and M. Schieber, 1961, Phys. Rev. 123, 807. Ahrens, L.H., 1952, Geochim. et Cosmochim. Acta, 2, 155. Aidelberg, J., J. Flicstein and M. Schieber, 1974, J. Cryst. Growth, 21, 195. Albanese, G., M. Carbucicchio and A. Deriu, 1974, Phys. Status Solidi A23, 351. A16onard, R., D. Bloch and P. Boutron, 1966, Compt. rend. B263, 951. Aleshke-Ozhevskii, O.P., R.A. Sizev, V.P. Cheparin and I.I. Yamzin, 1968, Zh. ETF Pis'ma, 7, 202. Aleshke-Ozhevskii, O.P. and I.I. Yamzin, 1969, Zh. Eksp. Teor. Fiz. 59, 1490. Anderson, P.W., 1950, Phys. Rev. 79, 350. Appendino, P. and M. Montorsi, 1973, Ann. Chim. (Rome) 63, 449. Arendt, R.H., 1973, J. Solid State Chem. 8, 339. Asti, G., F. Conti and C.M. Maggi, 1968, J. Appl. Phys. 39, 2039. AuCoin, T.R., R.O. Savage and A. Tauber, 1966, J. Appl. Phys. 37, 2908. Banks, E., M. Robbins and A. Tauber, 1962, J. Phys. Soc. Japan, 17, Supplement B-I, 196. Bashkirov, Sh.Sh., A.B. Liberman and V.I. Sinyavskii, 1975, Zh. Eksp. Teor. Fiz. 59, 1490. Batti, P., 1960, Ann. Chim. (Rome) 50, 1461. Belov, K.P., L.I. Koroleva, R.Z. Levitin, Yu.V. Jergin and A.V. Pedko, 1965, Phys. Status Solidi, 12, 219. Beretka, J., and M.J. Ridge, 1958, J. Chem. Soc. A10, 2463. Berger, W. and F. Pawlek, 1957, Arch. Eisenhiittenwesen, 28, 101. Bertaut, E.F., A. Deschamps and R. Pauthenet, 1959, J. Phys. et Rad. 20, 404. Blazey, K.W., 1974, J. Appl. Phys. 45, 2273. Bonnenberg, D. and H.P.J. Wijn, 1968, Z. angew. Phys. 24, 125. Borovik, E.S. and Yu.A. Mamaluy, 1963, Fiz. Metal. Metalloved. 15, 300. Borovik, E.S. and N.G. Yakovleva, 1962a, Fiz. Metal. Metalloved. 13, 470. Borovik, E.S. and N.G. Yakovleva, 1962b, Fiz. Metal. Metalloved. 14, 927. Borovik, E.S. and N.G. Yakovleva, 1963, Fiz. Metal. Metalloved. 15, 511.
Bottoni, G., D. Candolfo, A. Cecchetti, L. Giarda and F. Masoli, 1972, Phys. Status Solidi A32, K47. Bowman, W.S., Saturno, F.H. Norman and J.H, Horwood, 1969, J. Can. Ceram. Soc. 38, 1. Bozorth, R.M. and V. Kramer, I959, J. Phys. et Rad. 20, 393. Brady, L.J., 1973, J. Material Sci. 8, 993. Braun, P.B., 1957, Philips Res. Rep. 12, 491. Brixner, L,H., 1959, J, Amer. Chem. Soc. 81, 3841. Buessem, W.R. and A. Doff, 1957, The Thermal expansion of ferrites at temperatures near the Curie point, Proc. 13 Ann. Meeting, Met. Powd. Ass., Chicago, Ill., USA, II, 196. Burlier, C.R., 1962, J. Appl. Phys. 33, 1360. Bye, G.C. and C.R. Howard, 1971, J. Appl. Chem. Biotechnol. 21, 319. Casimir, H.B.G., J. Smit, U. Enz, J.F. Fast, H.P.J. Wijn, E.W. Gorter, A.J.W. Duyvesteyn, J.D. Fast and J.J. deJong, 1959, J. Phys. et Rad. 20, 360. Clark, A.F., W.M. Haynes, V.A. Deason and R.J. Trapani, 1976, Cryogenics, May, 267. Cochardt, A., 1967, J. Appl. Phys. 38, 1904. Craik, D J . and E.H. Hill, 1977, J. Phys. Colloque, 38, C1-39. Davis, R.T., 1965, Thesis, Thermal expansion anisotropy in BaFe120~9, The Penn. State Univ. College of Mineral Ind. De Bitetto, D.J., 1964, J. Appl. Phys. 35, 3482. Dixon, S. Jr. and M. Weiner, 1970, J. Appl. Phys. 41, 1375. Dixon, S. Jr., T.R. AuCoin and R.O. Savage, 1971, J. Appl. Phys. 42, 1732. Drews, U. and J. Jaumann, 1969, Z. angew, Phys. 26, 48. Drofenik, M., D. Hanzel and A. Moljik, 1973, J. Mater. Sci. 8, 924. Dtilken, H., F. Haberey and H.P.J. Wijn, 1969, Z, angew. Phys. 26, 29. Dullenkopf, P. and H.P.J. Wijn, 1969, Z. angew. Phys. 26, 22. Du Pr6, F.K., D.J. De Bitetto and F.G. Brockman, 1958, J. Appl. Phys. 29, 1127. Eldridge, D.F., 1961, J. Appl. Phys. 32, 247 S. Erchak, M. Jr., I. Fankuchen and R. Ward, 1946, J. Amer. Chem. Soc. 68, 2085. Erchak, M. Jr. and R. Ward, 1946, J. Amer. Chem. Soc. 68, 2093. Esper, F.J. and G. Kaiser, 1972, Int. J. Magnetism, 3, 189.
388
H. KOJIMA
Esper, F.J. and G. Kaiser, 1975, Physica, 80B, 116. Fahlenbrach, H. and W. Heister, 1953, Arch. Eisenhtittenw. 29, 523. Florrescu, V., M. Popescu and C. Ghizdeanu, 1973, Int. J. Magnetism, 5, 257. Frei, E.H., M. Schieber and S. Strikman, 1960, Phys. Rev. 118, 657. Fuchikami, N., 1965, J. Phys. Soc. Japan, 20, 760. Galasso, F.S., 1970, Structure and Properties of Inorganic Solids (Pergamon Press, Oxford) p. 226-234. Gemperle, R., E.V. Shtoltz and M. Zeleny, 1963, Phys. Status Solidi, 3, 2015. Glasser, F.P., F.W.D. Woodhams, R.E. Meads and W.G. Parker, 1972, J. Solid State Chem. 5, 255. Goodenough, J.B., 1956, Phys. Rev. 102, 356. Gorter, E.W., 1954, Philips Res. Rep. 9, 295 and 403. Gorter, E.W., 1957, Proc. IEE, 104B, 255 S. Got& K., 1966, Japan. J. Appl. Phys. 5, 117. Goto, Y. and T. Takada, 1960, J. Amer. Ceram. Soc. 43, 150. Goto, Y. and K. Takahashi, 1971, J. Japan Soc. Powder and Powder Metallurgy, 17, 193 (in Japanese). Goto, Y. and K. Takahashi, 1973, Japan. J. Appl. Phys. 12, 948. Goto, Y., M. Higashimoto and K. Takahashi, 1974, J. Japan Soc. Powder and Powder Metallurgy, 21, 21 (in Japanese). Grill, A., 1974, Int. J. Magnetism, 6, 173. Grill, A. and F. Haberey, 1974, Appl. Phys. 3, 131. Grosser, P., 1970, Z. angew. Phys. 30, 133. Grundy, P. J., 1965, Brit. J. Appl. Phys. 16, 409. Grundy, P.J. and S. Herd, 1973, Phys. Status Solidi A20, 295. Haberey, F. and A. Kockel, 1976, IEEE Trans. Mag. MAG-12, 983. Haberey, F. and H.P.J. Wijn, 1968, Phys. Status Solidi, 26, 231. Haberey, F., M. Velicescu and A. Kockel, 1973, Int. J. Mag. 5, 161. Hagner, J. and U. Heinecke, 1974, Phys. Status Solidi A22, K187. Haneda, K. and H. Kojima, 1971, Phys. Status Solidi A6, 259. Haneda, K. and H. Kojima, 1973a, J. Appl. Phys. 44, 3760. Haneda, K. and H. Kojima, 1973b, Japan. J. Appl. Phys. 12, 355.
Haneda, K. and H. Kojima, 1974, J. Amer. Ceram. Soc. 57, 68. Haneda, K., C. Miyakawa and H. Kojima, 1974a, J. Amer. Ceram. Soc. 57, 354. Haneda, K., C. Miyakawa and H. Kojima, 1974b, Improvement of temperature dependence of remanence in ferrite permanent magnets, AIP Conf. Proc. 24, 770. Hareyama, K., K. Kohn and K. Uematsu, 1970, J. Phys. Soc. Japan, 29, 791. Heimke, G., 1960, J. Appl. Phys. 31, 271 S. Heimke, G., 1962, Bet. Deut. Keram. Ges. 39, 326. Heimke, G., 1963, Z. angew. Phys. 15, 217. Heinecke, U. and L. Jahn, 1972, Phys. Status Solidi hl0, K93. Hempel, K.A. and H. Kmitta, 1971, J. Phys. Colloque, 32, C1-159. Henry, N.F.M. and K. Lonsdal, 1952, International Tables for X-ray Crystallography (Kynoch Press, Birmingham) p. 304. Hodge, M.H., W.R. Bitler and R.C. Bradt, 1973, J. Amer. Ceram. Soc. 56, 497. Holz, A., 1970, J. Appl. Phys. 41, 1095. Hoselitz, K. and R.D. Nolan, 1969, J. Phys. D, Ser. 2, 2, 1625. Hunty, P., 1963, Fiz. Metal. Metalloved. 16, 132. Ichinose, N. and K. Kurihara, 1963, J. Phys. Soc. Japan, 18, 1700. Jahn, L. and H.G. Mfiller, 1969, Phys. Status Solidi, 35, 723. Jonker, G.W., H.P.J. Wijn and P.B. Braun, 1954, Philips Techn. Rev. 18, 145. Kacz6r, C., 1964, Zh. Eksperim, Teor. Fiz. 46, 1787. Kacz6r, J., 1972, Phys. Lett., 41A, '461. Kacz6r, J. and R. Gemperle, 1960, Czech. J. Phys. BIO, 505. Kacz6r, K. and R. Gemperle, 1961, Czech. J. Phys. Bll, 510. Kahn, F.J., P.S. Pershan and J.P. Remeika, 1969, J. Appl. Phys. 40, 1508. Kittel, C., 1946, Phys. Rev. 70, 965. Kiyama, M., 1976, Bull. Chem. Soc. Japan, 49, 1855. Kojima, H. and K. Got& 1962, J. Phys. Soc. Japan, 17, Supplement B-l, 201. Kojima, H. and K. Got& 1964, Determination of critical field for magnetoplumbite type oxides by domain observation, Proc. Int. Conf. Magn. Nottingham, p. 727. Kojima, H. and K. Got& 1965, J. Appl. Phys. 36, 538. Kojima, H. and K. Got& 1970, Bulletin. Res. Inst.
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES Sci. Meas., Tohoku University, 19, 67 (in Japanese). Kojima, H. and C. Miyakawa, 1965, Bulletin, Res. Inst. Sci. Meas., Tohoku University, 13, 105 (in Japanese). K6moto, O. and H. Kojima, 1976, Hard Magnetic Materials, ed., S. Iida et al. (Maruzen, Tokyo) Voi. 3, p. 110 (in Japanese). Kooy, C., 1958, Philips Techn. Rev. 19, 286. Kooy, C. and U. Enz, 1960, Philips Res. Rep. 15, 7. Koroleva, L.I. and L.P. Mitina, 1971, Phys. Status Solidi AS, K55. Kozlowski, G. and W. Zietek, 1965, J. Appl. Phys. 36, 2162. Kreber, E. and U. Gonser, 1973, Appl. Phys. 1, 339. Kreber, E. and U. Gonser, 1976, Appl. Phys. 10, 175. Kreber, E., U. Gonser and A. Trautwen, 1975, J. Phys. Chem. Solids, 36, 263. Kuntsevich, S.P., Yu.A. Mamaluy and A.S. Miln6r, 1968, Fiz. Metal. Metalloved. 26, 610. Kurtin, S., S. Foner and B. Lax, 1969, J. Appl. Phys. 40, 818. Lacour, C. and M. Paulus, 1968, J. Cryst. Growth, 3, 814. Lacour, C. and M. Paulus, 1975, Phys. Status Solidi A27, 441. Laroria, K.K. and A.P.B. Shinha, 1963, J. Pure and Appl. Phys. 1, 215. Linares, R.C., 1962, J. Amer. Ceram. Soc. 45, 307. Lotgering, F.K., 1974, J. Phys. Chem. Solids, 35, 1633. Luborsky, F.E., 1966, J. Appl. Phys. 37, 1091. Ltitgemeier, M., A.V. Gonzales, W. Zietek and W. Zinn, 1977, Physica, 86--88B, 1363. MacChesney, J.B., R.C. Sherwood, E.T. Keve, P.B. O'Connor and L.D. Blitzer, 1971, New room temperature ferrimagnetic phases in the system CaO-AI203-Fe203, Ferrites, Proc. Int. Conf. Japan, p. 158. Mahoney, J.P., A. Tauber and R.O. Savage, 1972, Low temperature magnetic properties in BaFe12-x-y-zZnxTiyMnzO19, AIP Conf. Proc. no. 10, part 1, p. 159. Mason, W.P., 1954, Phys. Rev. 96, 302. Mee, C,D. and J.C. Jeschke, 1963, J. Appl. Phys. 34, 1271. Menashi, W.P., T.R. AuCoin, J.R. Shappirio and D.W. Eckart, 1973, J. Cryst. Growth, 20, 68. Mita, M., 1963, J. Phys. Soc. Japan, 18, 155.
389
Mones, A.H. and E. Banks, 1958, J. Phys. Chem. Solids, 4, 217. Mori, S., 1970, J. Phys. Soc. Japan, 28, 44. Moriya, T., 1960, Phys. Rev. 120, 91. Mountvala, A.J. and S.F. Ravitz, 1962, J. Amer. Ceram. Soc. 45, 285. N6el, L., 1947, Compt. rend. 224, 1488. N6el, L., 1948, Ann. Phys. (Paris) 3, 137. Neumann, H. and H.P.J. Wijn, 1968, J. Amer. Ceram. Soc. 51, 536. Oh, H.J., T. Nishikawa and M. Satou, 1978, J. Chem. Soc. Japan, 1, 42, (in Japanese). Okamoto, S., H. Sekizawa and S.I. Okamoto, 1975, J. Phys. Chem. Solids, 36, 591. Okazaki, C., B. Kubota and S. Mori, 1955, National Techn. Rep. 1, 23 (in Japanese). Okazaki, C., S. Mori and F. Kanamaru, 1961a, National Techn. Rep. 7, 21 (in Japanese). Okazaki, C., T. Kubota and S. Mori, 1961b, J. Phys. Soc. Japan, 16, 119. Palatnik, L.S., L.I. Lukashenko, L.Z. Lubyanyy, V.I. Lukashenko and Yu.A. Mamaluy, 1975, Fiz. Metal. Metalloved. 40, 61. Pauling, L., 1960, The Nature of the Chemical Bond, 3rd ed. (Cornell Univ. Press, Ithaca, N.Y.) p. 514. Paulus, M., 1960, Compt. rend. 250, 2332. Pauthenet, R. and G. Rimet, 1959a, Compt. rend. 249, 1875. Pauthenet, R. and G. Rimet, 1959b, Compt. rend. 249, 656. Perekalina, T.M. and V.P. Cheparin, 1967, Fiz. Tverd. Tela. 9, 217. Perekalina, T.M., M.A. Vinnik, R.I. Zevereva and A.P. Schurova, 1970, Zh. Eksp. Teor. Fiz. 59, 1490. Rathenau, G.W., 1953, Rev. Mod. Phys. 25, 297. Rathenau, G.W., J. Smit and A.L. Stuyts, 1952, Z. Phys. 133, 250. Ratnam, D.V. and W.R. Buessem, 1970, IEEE Trans. Magn. MAG-6, 610. Ratnam, D.V. and W.R. Buessem, 1972, J. Appl. Phys. 43, 1291. Reddy, B.P.N. and P.J. Reddy, 1973, Phys. Status Solidi A17, 589. Reddy, B.P.N. and P.J. Reddy, 1974a, Phil. Mag. 30, 557. Reddy, B.P.N. and P.J. Reddy, 1974b, Phys. Status Solidi A22, 219. Reed, J.S. and R.M. Fulrath, 1973, J. Amer. Ceram. Soc. 56, 207. Rensen, I.G. and I.S. van Wieringen, 1969, Solid State Commun. 1, 1139.
390
H. KOJIMA
Rensen, J.G., J.A. Schulkes and J.S. van Wieringen, 1971, J. Phys. Colloque, 32, C1-924. Richter, H.G. and H.E. Dietrich, 1968, IEEE Trans. Magn. MAG-4, 263. Robbins, M., 1962, Thesis, Fluoride-compensated cation substitution in oxides, Polytechnic Inst. Brooklyn, New York. Robbins, M. and E. Banks, 1963, J. Appl. Phys. 34, 1260. Rodrigue, G.P., 1963, IEEE Trans. Microwave Theory and Techniques, September, 351. Roos, W., H. Haak, C. Voigt and K.A. Hempel, 1977, J. Phys. Colloque, 38, C1-35. Rosenberg, M., C. Tfinfisoiu and V. Florescu, 1966, J. Appl. Phys. 37, 3826. Rosenberg, M., C. Tanasoiu and V. Florescu, 1967, Phys. Status Solidi, 21, 197. Routil, R.J. and D. Barham, 1974, Can. J. Chem. 52, 3235. Sadler, A.G., 1965, J. Can Ceram. Soc. 34, 155. Savage, R.O. and A. Tauber, 1964, J. Amer. Ceram. Soc. 47, 13. Schieber, M.M., 1967, Experimental Magnetochemistry in Series of Monographs on Selected Topics in Solid State Physics, ed. E.P. Wohlfarth (North-Holland, Amsterdam) v01. 8, p. 198-217. Shimada, Y., K. Got6 and H. Kojima, 1973, Phys. Status Solidi A18, K1. Shimizu, S. and K. Fukami, 1972, J. Japan Soc. Powder and Powder Metallurgy, 18, 259 (in Japanese). Shirk, B.T. and W.R. Buessem, 1969, J. Appl. Phys. 40, 1294. Shirk, B.T. and W.R. Buessem, 1970, J. Amer. Ceram. Soc. 53, 192. Shirk, B. and W.R. Buessem, 1971, IEEE Trans. Magn. MAG-7, 659. Sigal, M.A., 1977, Phys. Status Solidi A42, 775. Silber, L.M., E. Tsantes and P. Angelo, 1967, J. Appl. Phys. 38, 5315. Sixtus, K.J., K.J. Kronenberg and R.K. Tenzer, 1956, J. Appl. Phys. 27, 1051. Sloccari, G., 1973, J. Amer. Ceram. Soc. 56, 489. Slokar, G. and E. Lucchini, 1978a, J. Mag. and Mag. Mat. 8, 232. Slokar, G. and E. Lucchini, 1978b, J. Mag. and Mag. Mat. 8, 237. Smit, J., 1959, J. Phys. et Rad. 20, 370 (see Casimir et al. 1959).
Smit, J. and H.G. Beljers, 1955, Philips Res. Rep. 10, 113. Smit, J. and H.P.J. Wijn, 1959, Ferrites (Philips Technical Library, Eindhoven) p. 177-210. Smit, J., F.K. Lotgering and U. Enz, 1960, J. Appl. Phys. Supplement, 31, 137 S. St~iblein, H., 1973, Z. Werkstofftechnik, 4, 133. St~iblein, H. and W. May, 1969, Ber. Deut. Keram. Geselschaft, 46, 69. Standley, K.J., 1972, Oxide Magnetic Materials (Clarendon Press, Oxford) p. 149-160. Stoner, E.C. and E.P. Wohlfarth, 1948, Phil. Trans. A240, 599. Streever, R.S., 1969, Phys. Rev. 186, 285. Suchet, J.P., 1971, Compt. rend. S6ri C, 271, 895. Suemune, Y., 1972, J. Phys. Soc. Japan, 33, 279. Summergrad, R.N. and E. Banks, 1957, J. Phys. Chem. Solids 2, 312. Szymczak, R., 1971, J. Phys, Colloque, 32, C1-263. Takada, T., Y. Ikeda and Y. Bando, 1971, A new preparation method of the oriented ferrite magnets, Ferrites, Proc. Int. Conf. (Univ. Tokyo Press, Tokyo) p. 275. Tfinfisoiu, C., 1972, IEEE Trans. Magn. MAG8, 348. Tfinfisoiu, C., P. Nicolau and C. Micea, 1976, IEEE Trans. Magn. MAG-12, 980. Tauber, A., R.O. Savage, R.J. Gambino and C.G. Whinfrey, 1962, J. Appl. Phys. 33, 1381. Tauber, A., J.A. Kohn and I. Bandy, 1963, J. Appl. Phys. 34, 1265. Tauber, A., S. Dixon, Jr. and R.O. Savage, Jr., 1964, J. Appl. Phys. 35, 1008. Tebble, R.S. and D.J. Craik, 1969, Magnetic Materials (Wiley-Interscience, London) p. 359-368. Townes, W.D., J.H. Fang and A.J. Perrotta, 1967, Z. Kristallogr. 125, 437. Trautwein, A., E. Kreber, U. Gonser and F.E. Harris, 1975, J. Phys. Chem. Solids, 36, 325. Van Diepen, A.M. and F.K. Lotgering, 1974, J. Phys. Chem. Solids, 35, 1641. Van Hook, H.J., 1964, J. Amer. Ceram. Soc. 47, 579. Van Loef, J.J. and P.J.M. Franssen, 1963, Phys. Lett. 7, 225. Van Loef, J.J. and A.B. van Groenou, 1964, On the sub-lattice magnetization of BaFe12019, Proc. Int. Conf. Magn. Nottingham, p. 646. Van Uitert, L.G., 1957, J. Appl. Phys. 28, 317.
FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES Van Uitert, L.G. and F.W. Swanekamp, 1957, J. Appl. Phys. 28, 482. Van Wieringen, J.S., 1967, Philips Tech. Rev. 28, 33. Van Wieringen, J.S. and J.G. Rensen, 1966, Z. angew. Phys. 21, 69. Verstegen, J.M.P.J., 1973, J. Solid State Chemistry, 7, 468. Villers, G., 1959a, Compt. rend. 248, 2973. Villers, G., 1959b, Compt. rend. 249, 1337. Vinnik, M.A. and R.I. Zvereva, 1969, Kristallografiya, 14, 697. Wang, F.F.Y., K. Ishii and B.Y. Tsui, 1961, J. Appl. Phys. 32, 1621. Wells, R.G. and D.V. Ratnum, 1971, IEEE Trans. Magn. MAG-7, 651. Went, J.J., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/1952, Philips Techn. Rev. 13, 194.
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Wijn, H.P.J., 1952, Nature, 170, 707. Wijn, H.P.J., 1970, Landolt-B6rnstein Numerical Data and Functional Relationships in Science and Technology. New Series, III/4b. ed. K.-H. Hellwege (Springer, Berlin) p. 552681. Williams, H.J. and R.C. Sherwood, 1958, J. Appl. Phys. 29, 296. Wisnyi, L.G., 1967, Powder Diffraction File, 7-85. Wullkopf, H., 1972, International J. Magnetism, 3, 179. Wullkopf, H., 1975, Physica, 80B, 129. Zanmarchi, G. and P.F. Bongers, 1969, J. Appl. Phys. 40, 1230. Zfiveta, K., 1963, Phys. Status Solidi, 3, 2111. Zinn, W., S. Hfifner, M. Kalvius, P. Kienle and W. Wiedemann, 1964, Z. angew. Phys. 17, 147.
chapter 6 PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES
M. SUGIMOTO Saitama University, Faculty of Engineering 225 Shimo-ohkubo, Urawa 338 Japan
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-HollandPublishing Company, 1982 393
CONTENTS
1. C h e m i c a l c o m p o s i t i o n s , crystal s t r u c t u r e a n d spin o r i e n t a t i o n 1.1. BaMezFe16Oz7 ( W - t y p e ) . . . . . . . . . . . . 1.2. BaeMeeFel~Oz2 ( Y - t y p e ) 1.3. Ba3MeeFe24041 ( Z - t y p e )
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1.4. BazMe2Fe28046 ( X - t y p e ) . . . . . . . . . 1.5. Ba4MezFe36060 ( U - t y p e ) . . . . . . . . . 1.6. O t h e r c o m p o u n d s . . . . . . . . . . . 2. P r e p a r a t i o n ~nd f o r m a t i o n kinetics . . . . . . 3. SatuJ atic n r~ a g n e | i z a t i o n . . . . . : . . . . 4. M a g n e t o c r ~ stalline a n i s o t r o p y a n d r e l a l e d p h e n c m e n a
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5. M6ssb~ u e r effect . . . . . . . . . . . . . . . . . . 6. M a g n e l ostriction a n d N M R . . . . . . . . . . . . . . 6.1. M a g n e t o s l r i c t i o n . . . . . . . . . . . . . . . .
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6.2. N M R . . . . . . . . . 7. H i g h f r e q u e n c y m a g n e t i c lzrol:crties 8. E l e c t r i c p r o r erties a n d o l h e r effects
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8.1. Cc n d u c l i v i l y . . . . 8.2. E ieleclric c c n s t a n t . 8.3. J a h r - T e l l e r effect . . 8.4. M a g n e t o - o p t k al effect 8.5. E ' o m a ! n c bse r v a l i o n a n d References . . . . . . .
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1. Chemical compositions, crystal structures and spin orientation A group of compounds consisting of isotropic materials with spinel structure and higher anisotropic materials with hexagonal structure has been developed by Jonker et al. (1956/57). They are generically referred to as the ferroxplana-type compounds. The general chemical formula of these compounds is denoted by m(Ba2++ Me2+)-nFe203, where Me 2+ represents the divalent metal ions Mn, Fe, Co, Ni, Cu, Mg and Zn. In the triangle of fig. 1 in ch. 5 the symbols W, Y, Z, X and U represent the compounds with chemical composition BaMezFe16027, Ba2MezFe12022, Ba3Me2Fe24041, BazMezFe28046 and Ba4Me2Fe36060, respectively. If Me 2+ ions in the W-structure, as an example, are substituted by Zn 2+ ions, the composition may be conveniently indicated by the short notation of Zn2W. In the case of substitution of both Zn 2+ and Fe 2+ ions for Me 2+ ions it may be represented by ZnFeW.
1.1. BaMe2Fe16027 (W-type) The unit cell of the W-type compound is built up by superposition of four spinel blocks (S-block) and two blocks containing Ba ions (R-block) as shown in table 1 of ch. 5. Figure 1 shows a cross section of the W-structure having a hexagonal packing, which is closely related to the M-structure (Albanes e et al. 1976b). The only difference is that the successive R-blocks are interspaced by two S-blocks instead of one, as is the case in the M-structure. The crystal structure of R-blocks with chemical composition BaFe6Oll as well as that of S-blocks with chemical composition Me2Fe408 are represented in fig. 14 of ch. 5. In table 1 the number of ions and the coordination of the different cation sublattices in the W-structure are shown (Albanese et al. 1976b). The cations occupy seven different sublattices of 12K, 4e, 4fw, 4fw, 6g, 4f and 2d, in the nomenclature used by Braun (1957). The spin orientation according to the generally accepted collinear model is also indicated. This magnetic classification has been justified by the assumption that the magnetic behaviour of the nearest neighbour cations is determined by superexchange interaction.
395
396
M. S U G I M O T O
W- type Structure 4fly ® 4e © 4f e6g e 12K 4fv I • 2d
R
©o 20
I S*
Ba 2+
I S* R*
Fig. 1. Unit cell of the BaMe2Fe16027, Me2W, compound. T h e anions of O 2 , the divalent barium cation Ba 2÷, the metallic ions in the sublattices 4fw, 4e, 4f, 6g, 12K, 4fvi and 2d are indicated. T h e coordination figures of the metallic ions in the different lattice sites are shown (Albanese et al. 1976b).
TABLE 1 N u m b e r of ions, coordination and spin orientation for the various cations of a W-type c o m p o u n d (Albanese et al. 1976b).
Magnetic sublattice K fw
fvI a b
Sublattice
Coordination
N u m b e r of ions per formula unit
12K 4e 4fry 4fvi 6g 4f 2d
octahedral tetrahedral tetrahedral octahedral octahedral octahedral hexahedral
6 2 2 2 3 2 1
Block
Spin
R-S S S R S-S S R
up down down down up up up
PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES
397
1.2. Ba=Me2Fe12022(Y-type) T h e u n i t cell of t h e Y - t y p e c o m p o u n d is b u i l t u p b y t h e s u p e r p o s i t i o n of t h r e e S - b l o c k s a n d t h e so c a l l e d t h r e e T - b l o c k s as s h o w n in fig. 2, in w h i c h t h e d i f f e r e n t
Y - type Structure S
T
3 oVl (I) 6cvl 3 bvi o 1Bhvt o 6Civ
® 6clv O 0 2-
•
BCl 2+
S
T
S
T
Fig. 2. Unit cell of the Ba2Me2Fe12Oz~, Me2Y, compound. The anions of O 2-, the divalent barium cation Ba 2÷, the metallic ions in the sublattices 3avi, 6cvl, 3bvl, 18hw, 6cw and 6c~v are indicated. The coordination figures of the metallic ions in the different lattice sites, together with their spin orientation, are shown (Albanese et al. 1975b).
398
M. S U G I M O T O
lattice sites are distinguished by different symbols (Albanese et al. 1975). The Y-structure has the crystal symmetry characterized by the space group R3m. As shown in fig. 14 of ch. 5, the T-block with Ba2Fe8014 composition is formed by four oxygen layers having hexagonal packing and plays an unique role in the , TABLE 2 Number of ions, coordination and spin orientation for the various metallic sublattices of Y-structure? (Albanese et al. 1975b).
Sublattice
Coordination
Block
Number of ions per unit cell
tetrahedral octahedral octahedral octahedral tetrahedral octahedral
S S S-T T T T
6 3 18 6 6 3
6cw 3aw 18hvi 6cw 6c•v 3by1
Spin down up up down down up
t Sublattices having the same crystalline symmetry but belonging to different blocks are marked by an asterisk. TABLE 3 Strength of the superexchange interactions between Fe 3+ ions in the Y-structure (Albanese et al. 1975b). Interacts with n Fe 3+ ions Each Fe 3+ ion in lattice position 3avi 6Civ
18hvl
0Cvi
6C}'v
3bvl
n 6 6 3 3 9 1 3 2 1 4 6 3 1 3 3 3 6 2
lattice position 6cw 18hvl 6cIv 3avi 18hw 3avr 6clv 6Cvi 6C~v 18hvi 18hvl 6CTv 3bvi 6cw 18hvl 3bvI 6c•v 6Cvi
Strength of the superexchange interaction1 25 0(+) 0(+) 25 26 0(+) 26 30 25 0(+) 30 9(+) 1.7 9(+) 25 77 77 1.7
t The cross indicates interactions between sublattices with parallel spins.
PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES
399
Y - s t r u c t u r e . In fig. 2, t h e c o m m o n faces of t h e o c t a h e d r a inside t h e T - b l o c k a r e h a t c h e d . T h e p r e s e n c e of a n i o n o c t a h e d r a with c o m m o n faces is g e n e r a l l y r e s p o n s i b l e for t h e l o w e r stability of t h e s t r u c t u r e , d u e to t h e h i g h e r p o t e n t i a l e n e r g y of t h e s y s t e m as c o m p a r e d with s i t u a t i o n s w h e r e o n l y c o r n e r s a r e s h a r e d a n d t h e c a t i o n s a r e thus f u r t h e r a p a r t . This fact f a v o u r s t h e M e 2+ ions having a m a r k e d p r e f e r e n c e for t h e o c t a h e d r a l c o o r d i n a t i o n of t h e 6Cvi a n d 3bw lattice sites. T a b l e 2 shows t h e spin o r i e n t a t i o n for v a r i o u s s u b l a t t i c e s t o g e t h e r with t h e i r c o o r d i n a t i o n in t h e Y - s t r u c t u r e . A l b a n e s e et al. (1975b) c a l c u l a t e d t h e s t r e n g t h of t h e v a r i o u s s u p e r e x c h a n g e i n t e r a c t i o n s b e t w e e n F e 3+ ions in t h e Y - s t r u c t u r e . T a b l e 3 shows t h e results o b t a i n e d on t h e basis of t h e a s s u m p t i o n t h a t t h e i n t e r a c t i o n e n e r g y follows an e x p o n e n t i a l d e p e n d e n c e on t h e a n i o n - c a t i o n dist a n c e s a n d a c o s 2 0 law for t h e a n g u l a r d e p e n d e n c e . F r o m this t a b l e it a p p e a r s t h a t t h e s t r o n g e s t s u p e r e x c h a n g e i n t e r a c t i o n is t h e o n e b e t w e e n t h e t e t r a h e d r a l ions 6Cfv a n d t h e o c t a h e d r a l ions 3bvi inside t h e T - b l o c k , a n d t h e o n l y a p p r e c i a b l e p e r t u r b i n g i n t e r a c t i o n a p p e a r s to b e t h e o n e b e t w e e n t h e 6C?v a n d 6Cvr ions, b o t h b e l o n g i n g to t h e T - b l o c k .
1..3. Ba3Me2Fe24041 (Z-type) T h e c r y s t a l l i n e s t r u c t u r e of t h e Z - t y p e c o m p o u n d s is s h o w n in fig. 3 ( A l b a n e s e et al. 1976a). T h e unit cell is f o r m e d by the s u p e r p o s i t i o n of f o u r S-blocks, two T-blocks and one R-block, and the divalent and trivalent cations are distributed a m o n g ten different lattice sites. T a b l e 4 shows t h e n u m b e r of ions r e l a t i v e to t h e v a r i o u s c a t i o n sublattices t o g e t h e r with t h e i r spin o r i e n t a t i o n . TABLE 4 Number of ions, coordination and spin orientation of the various metallic sublattices of Z-structuret (Albanese et al. 1976a).
Sublattice 12kv~ 2dv 4fw 4f-}i 4etv 4fiv 12k~}i 2avl 4evl 4f]~v
Coordination octahedral five-fold octahedral octahedral tetrahedral tetrahedral octahedral octahedral octahedral tetrahedral
Block R-S R R S S S T-S T T T
Number of ions per unit cell
Spin
12 2 4 4 4 4 12 2 4 4
up up down up down down up up down down
t Sublattices having the same crystalline symmetry but belonging to different blocks are marked by an asterisk.
400
M. SUGIMOTO
Z - type S t r u c t u r e
R
S
© 12Kvx ® 2dv 4f-Vl ® 4f~ 1 @ 4elv ~ 4fly 12K~,I I) 2clvl • 4evl
T
© 4fly
© 0 zBCI 2÷
R.
T* I S* Fig. 3. Unit cell of Ba3Co2Fe24041, Co2Z, compound. The coordination figures of the metallic ions in the main lattice sites are shown (Albanese et al. 1976a).
1.4. Ba2Me2Fez8046 (X-type) T h e u n i t cell of the X-type c o m p o u n d s consists of f o u r a l t e r n a t e layers of the M - s t r u c t u r e a n d W - s t r u c t u r e , b e l o n g i n g to the space s y m m e t r y g r o u p R3m. F i g u r e 4 shows a cross section of the Zn2X structure, in which the spin o r i e n t a t i o n
PROPERTIES OF FERROXPLANA-TYPE HE XAGONAL FERRITES
401
X - type S t r u c t u r e f~
W
Y3~_
(
A
Q O
-- 0 2 -
Oct.
@ •
/X
A
ZX
-- BQ2÷ -
Tet.
[]
-
Tri.
Fig. 4. A collinear spin model for Zn~X (Tauber et al. 1970).
as well as the coordination figures of all cations are represented (Tauber et al. 1970).
1.5. Ba4Me2Fe3606o (U-type) The unit--cell of the U-type c o m p o u n d is a rhombohedral structure belonging to space group R3m, and is formed by three molecules. The structure is built up by the superposition of two M-blocks and one Y-block along the c-axis. Figure 5 shows a cross section of the Zn2U structure and the spin orientation of all cations (Kerecman etoal. 1968). Referring to hexagonal structure, its lattice p a r a m e t e r s are c = 113.2 A, a = 5.88 A and the X-ray density is 5.36.
1.6. Other compounds Kohn et al. (1964a,b) reported a new hexagonal ferrite with Ba4Zn2Fes2Os4 composition. T h e new structure is made up by the sequence of composite TS- and RS-block. Interleaving the TS- and RS-block at various ratios leads to a structure with unit cells ranging from 18 to 138 oxygen layers; these give rise to hexagonal unit cells with c parameters ranging up to about 1600 A. The expected empirical formulae for this group of compounds are listed in table 5. Kohn and Eckart (1971) discovered a new c o m p o u n d w~th composition, BasZn2Ti3Fe12031, which is a hexagonal structure with a = 5.844 A and c =-43.020 A and contains 18 oxygen layers, indicated by the symbol Zn2-18H.
402
M. SUGIMOTO
U type Structure -
(
)
i
A
0
_
0 2-
-
Oct.
•
M
A
_
Be2*
-
Tet.
[]-
Tri.
Fig. 5. A collinear spin model for Zn2U (Kerecman et al. 1968).
TABLE 5 Chemical compositions and crystallographic properties for new ferroxplana-type compounds (Robert et al. 1964).
Chemical composition
Structural unit (blocks)
Bal0ZnaFes60102 Ba12ZnmFe680124 Ba14Zni2Fes00146
[(TS)4T]3 [(TS)sT]3 (TS)6T
Ba16Zn14Fe920168 Ba4Zn2Fe52084
[(TS)TT]3 [RS2(RS)3]3
2. Preparation
and formation
Number of oxygen layers
Lattice parameter c (A)
Primitive symmetry
Space group
28 x 3 34 x 3 40 46 x 3 22 × 3
203 247 97 334 154
Rhombohedral Rhombohedral Hexagonal Rhombohedral Rhombohedral
P63/mmc P63/mmc R3m
kinetics
The processes for producing the ferroxplana-type compounds are very similar to those for M-type compounds. However, more accurate procedures based on the phase equilibrium are necessary to obtain the ferroxplana-type compounds,
PROPERTIES
OF FERROXPLANA-TYPE
HEXAGONAL
FERRITES
403
.. because their chemical compositions are"very complex. In particular, it is very difficult to produce a crystallographicall'y pure compound containing various amounts of ferrous iron. Neuman and Wijn (1968) shed light on the chemical equilibrium between the oxygen partial pressure o f gas atmosphere and the formation of Fe2W phase. In order to obtain a homogeneous W-compound, the samples must be sintered at 1250° to 1400°C in an atmosphere with a partial oxygen pressure between 2 x 10 .4 and 2 x 10-1 atm. Figure 6 shows the formation temperature and stability range of the phases for the W, Y and Z compounds. The spinel phase appeared as the first major reaction product of the raw oxides at about 555°C. The M phase was detected next by X-ray analysis and followed by the formation of a Y, Z, W phase in turn. Castelliz et al. (1969) also studied the kinetics of phase formation as well as the stability of the phases. Lotgering (1959) evolved a new method for making a sintered crystal-oriented ferroxplana compound. The advantage of crystal orientation is evident from the fact that the permeability of its compounds can be about 3 times larger than that of non-oriented compounds. This method differs essentially in the formation mechanism from that for the M-type compound. A paste or thick suspension consisting of BaFe12019 powder and raw oxides such as ZnO or CoO is poured into a die and then introduced into a static magnetic field. The crystal orientation is made topotactically by compressing the suspension into a pellet. The orientation preserved through the firing at 1100° to 1300°C. Licci and Asti (1979) tried to produce topotactically the crystal-oriented CoZnY compound. The hot-pressing method was performed to obtain a crystal-oriented Co2W compound by Okazaki and Igarashi (1970). A large and nearly perfect single crystal of the ferroxplana-type compounds, t
i
[
I
F
i
[
i
r
0.8
.=-
J
Z
o.z,
\/
/
\
0.2
Co
rr
4
~;oo
600
Boo
~ooo
~2oo
~oo
T('C) Fig. 6. F o r m a t i o n
temperature
a n d s t a b i l i t y r a n g e o f W - , Y-, Z - a n d M - p h a s e s 1964).
(Neckenbiirger
et al.
404
M. SUGIMOTO
which is useful for microwave devices, can be grown relatively easily by the flux method. Tauber et al. (1962, 1964) investigated many kinds of flux materials useful for growing single crystals of ferroxplana compounds. It was found that BaOB203 flUX must be less volatile and less viscous than the NaFeO2 flux to obtain a single crystal with lower ferromagnetic resonance linewidth. In general, the Wand Y-type compounds are easily melted at a lower temperature. The difficulty in growing the crystals of Z-, X-, and U-type compounds may be attributable to the high-melting composition necessitated by the large concentration of Fe203. Stearns et al. (1975) and Glass et al. (1980) have grown single crystal films of ZnzY or Zn2W by the isothermal dipping method of liquid phase epitaxy using a PbO-BaO-B203 flux. Many investigations on microstructures of sintered samples have been presented: Huijser-Gerits and Rieck (1970, 1974, 1976) studied thoroughly the influence of sintering conditions on microstructure; Drobek et al. (1961) observed the microstructures by the Use of electron microscope; both Cook (1967) as well as Landuyt and Amelinckx (1974) observed the stacking sequence by electron microscope.
3. Saturation magnetization Many attempts have been made to improve the saturation magnetization by the substitutions of various kinds of metal ions for cations occupying the octahedral and tetrahedral sites in the oxygen framework structure of the ferroxplana-type compounds. This may be attributed to their unique crystallographical structure as well as their importance as promising materials for technological application in the field of permanent magnets and microwave devices. Smit and Wijn (1959) proposed a formula on the basis of the over-simplification that the number of Bohr magnetons at saturation for the W-type compound is simply equal to the sum of the corresponding number for M- and S-structures, i.e.: (ns)w = (nB)M+ 2(nn)s.
(1)
This concept implies that we treat as different the two S-blocks which are perfectly equivalent. This drastic consequence frequently leads to a discrepancy with the experimental values. For example, the formula gives the value of (ns)w = 20/XB for the ZnzW compound, while Albanese et al. (1976a) and Savage and Tauber (1965) determined it experimentally as 35/x8 and 38.2/XB at 0 K (= 123 G cm3/g and 134 G cm3/g, respectively). The assumption of Smit and Wijn is applicable to the Y-type and Z-type compounds, but problems slightly analogous to that for the W-type compound still remain. The W-structure is characterized by the presence of two additional spinel blocks instead of one, as in the M-structure. Such a structure creates the possibility of changing the magnetic properties by a suitable substitution of the cation. Uitert and Swanekamp (1957) attempted to improve the saturation magnetization of W-type compounds by the substitution of non-magnetic ions for cations in
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES
405
tetrahedral and octahedral sites, and showed that the saturation magnetization is generally apt to decrease with increasing amount of substitution. In fig. 7, zinc ions seem likely to occupy the tetrahedral sites in BaMe2Fe16027 and a much greater fraction of A1, G a and In ions appears to occupy the octahedral sites. An anomalous behaviour of curve (1) at around zero saturation can be attributed to a lack of homogeneity in the samples. Albanese et al. (1977) reported that the saturation magnetization of BaZn2AlxFe16_xO27 is reduced when the amount of substitution of AP + for Fe 3+ in a-sites is increased, and a compensation point of superexchange interaction results at x = 4. In fig. 8 the saturation magnetization, o-s, for a number of simple and mixed W-type compounds is plotted as a function of temperature. It appears from the figure that almost straight lines are found over a large temperature range, and that zinc ions give higher saturation magnetization at low temperatures. In Zn2W compounds, the Z n 2+ ions may occupy two tetrahedral sublattices 4e and 4f~v (Albanese et al. 1976b), and in Mg2W compounds 90% of the Mg 2+ ions may
4000
E 3000 -x
7 \ ,~ \ \
g "~
2000
w
\ i1
I/1
3" .~
I000
I I
-
E
1000 2
6
B
Fig. 7. Effect of various substitutions on room-temperature saturation magnetization for BaNi2Fe16OzT. X denotes the number of metal ions replaced per formula unit. (1) AI for Fe, (2) Ga for Fe, (3) In or Cr for Fe, (4) Zn for Ni, (5) BaZn2GaFelsOz7, (6) BaZn2Ga3Fe13027 and (7) BaZn2AI3Fe13027 (Van Uitert and Swanekamp 1957).
406
M. S U G I M O T O 120
I
i
I
I
t
I
'
100 ~ ' ~ "
,
~'
ao
"'-Lx,. ~
Me2= ZnFe~
Me 2 W
0Yg
.
N o "k I.-~ 60 '4"
F
LO
Ni
F'
"""'/-c~'~'-.XX~D"'~IL~_
2o
0
l
J
1
-273 -200
I
r
0
,
,a,~
200
~a,z
400
600
T(°C) Fig. 8. Saturation magnetization as a function of temperature for a n u m b e r of c o m p o u n d s with W-structure, m e a s u r e d on polycrystalline specimens at a field of 6600 Oe (Smit and Wijn 1959).
,Zn
60
E
I
i
I
MeY
40 x
/Mg
E 20
0
-273
.d
Ni
I
-200
I
I
I
0
200
400
T [°0)
Fig. 9. Saturation magnetization as a function of temperature for a n u m b e r of c o m p o u n d s with Y-structure measured on polycrystalline specimens at a field of 11000 Oe (Smit and Wijn 1959).
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES
407
occupy the octahedral sites, and 10% of Mg the tetrahedral sites (Smit and Wijn 1959). Many other reports on the saturation magnetization of W-type compounds have been presented. A study on Fe2W substituted by Ni 2+ and F- (Banks et al. 1962), Fe2W substituted by Co 2+ and F- (Robbins et al. 1963), (NiZn)W and (Nil.6Co0.4)W (Hodges et al. 1964) and (Co165Fe0.35)W (Yamzin et al. 1966). An expected improvement in magnetic moment in the Y-type compounds was proposed by Albanese et al. (1975b). If all cations occupying 3by1 sites in a T-block can be substituted by non-magnetic ions, the magnetic moment might be markedly improved. This is due to the fact that 3bvi sites alone link the upper and lower parts of the unit cell through the strong interaction with six ions 6cw. Furthermore, the inversion symmetry around 3bvi sites might be broken by the partial substitution of iron ions in 6Cvi sites. However, such a drastic change in the magnetic order, has so far not been reported. Figure 9 shows the saturation magnetization of a number of simple Y-type compounds as a function of temperature. In the case of Y-type compounds, zinc ions also give the highest saturation magnetization. Albanese et al. (1975b) reported that in Ba2Mg2Fe~2022(Mg2Y), Mg2+ ions mainly occupy 3bvi and 6Cw sublattices of the tetragonal sites inside the T-block, and this occupation leads to the weakening effect of the superexchange interaction caused by a critical competition of the two exchange interaction 3bvr-6CTv and 6Cvr-6C•v. The temperature dependence of the saturation magnetization parallel and perpendicular to the c-axis of (Ba0.05Sr0.95Zn)Y single crystals is shown in fig. 10 (Enz 1961). We can see from these curves that this compound has a preferential plane. According to Albanese et al. (1975b), since the Co 2+ ions in Ba2Co2Fe12022(Co2Y) have a marked preference for octahedral coordination, 0.9 Co 2+ ions may occupy only the spin-down octahedral sublattice 6Cw, while the residual 1.1 Co 2+ ions probably distribute themselves among the 3avl, 18hvb 3by1 sublattices. In Ba2Zn2-2xCu2xF12022,(Zn2-2xCU2x)Y, the substitution of Zn by Cu resulted in a linear decrease of the saturation magnetization, o-~, as well as a flattening of the o-~ vs. T curve (Albanese et al. 1978). This suggests that for all the compositions nearly 28% of Cu ions enter the spin-down sublattices and the residual 72% occupy the spin-up sites. Among the spin-up sublattices, the 3bvi sites at the centre of the T-block play an important role for the equilibrium of the superexchange interactions in this compound, as already described. In addition, other experiments on Zn2Y by Savage and Tauber (1964), Mn2Y and (MnZn)Y by both Tauber et al. (1964) and Dixon et al. (1965) have been performed. In fig. 11 the saturation magnetization is plotted as a function of temperature for polycrystalline specimens of Z-type compounds. Zn2Z shows the highest saturation magnetization. The distribution of Co 2+ ions in Co2Z was deduced by Albanese et al. (1976a) such that 1.08 Co 2+ ions per unit formula occupy the spin-up sublattice, while the residual 0.92 enter the 4fvi and 4ev~ sublattices which are the only spin-down octahedral lattice sites. The Curie temperatures as seen in fig. 11 are in agreement with their values obtained from M6ssbauer measurements. Petrova (1967) measured the saturation magnetization and Curie temperature of (Co2-xZnx)Z.
408
M. SUGIMOTO BO
( Boo.05 Sr o.g5 Zn)Y 40 H.Lc
~
c
-
(a)
o - - - ' _ ~ T~290 ~K
0
80
I
I
i
F:
% -4"
(b)
40 0
BO
40 t
~
(c)
E
0~
-
80
0
Hllc i
0
5
-r
T=I2OO°K r
10
15
20
H ( k Oe ) [ x 106/(z./T) A / rn ] Fig. 10. Magnetization curves of single crystal of (Ba0.0sSr0.95Zn)Y(Enz 1961).
80 \
E
C o " ~
i
Me=Zn
Me2Z
60
x
/.0
~
2o
0
-273
-200
-100
0
100
200
300
/+00
500
T(*C)
Fig. 11. Saturation magnetization as a function of temperature for compounds with Z-structure, measured on polycrystalline specimens at a field of 11000 Oe for Co2Z and Zn2Z and 18000 Oe for Cu2Z (Smit and Wijn 1959).
PROPERTIES OF FERROXPLANA-TYPE
HEXAGONAL
FERRITES
409
Figure 12 shows the temperature dependence of the saturation magnetization for Ba2Zn2Fe~O46(Zn2X), Ba2Co2Fe2sO46(Co2X) and BaeZn2Fe36060(Zn2U) single crystals (Tauber et al. 1970 and Kerecman et al. 1968). If we assume that the Zn 2+ ions in Zn2X are equally distributed over the sublattices (spin-up and spin-down), the magnetic moment can be calculated as n u = 50.0/XB ( H = % T = 0 ) by reference to the collinear Gorter-type spin model of fig. 4. This calculated value is in excellent agreement with the experimental value 50.4/xB ( H = w, T = 0). However, crystal chemistry would require most of the Zn 2+ ions to be on tetrahedral site, leading to: 20 x 5 - 8 x 5
= 60/x B .
Tauber et al. (1970) explained that this roughly 18% difference between experimental and calculated result in ZnzX may arise because of the spin system is not colinear or because of non-stoichiometry of the crystals. In the case of Co2X, the calculated value 47#B ( H = ~, T = 0) is in good agreement with the experimental value 46/XB. As pointed out by Tauber et al. (1970), the agreement may be fortuitously given by the stoichiometry. The Curie temperatures of 705-+ 3 K for Zn2X and 740_+ 4 K for CozX are the highest values among the ferroxplana-type compounds containing Zn 2+ ions. The magnetic moment of Zn2U was calculated as 60.5/xB from O-s ( H = o0, T = 0 K). The value of the magnetic moment obtained from the sum of those for M- and Y-blocks, 58.4 (Gorter 1957) and 59.2 (Vinnik 1966), is in good agreement with the experimental value. However, a simple Gorter-type model (where all
100
_•
I
l
I
'
r
'
500
4OO 13r}
.x
80 .a
300
~
(:3
~:
6O C)
×
=
x
200
d~ (Co~X)
40
-.t x c9
v
E 100
2O
:~
0 0
200
/-.00
600
T (K) Fig. 12. Saturation magnetization as a function of temperature for Zn2X, Co2X and Zn2U (Tauber et al. 1970, K e r e c m a n et al. 1968).
410
M. S U G I M O T O
Z n 2+ ions are tetrahedral in the layers of Y and M but not all in spinel blocks) gives 60tXa, seemingly in better agreement. The magnetic m o m e n t s in spinels containing large amounts of Zn are lowered by the formation of angles between the m o m e n t s of octahedral ions. T a u b e r et al. described that since this effect is more pronounced in Zn2W than in Zn2Y, the experimental m o m e n t for Zn2U is still less than the value predicted from theory. The Curie t e m p e r a t u r e of Zn2U was given as 673 + 2 K. Figure 13 shows the saturation magnetization of BasZn2Ti3Fe12031(Zn2-18H) and BasMg2Ti3FeI2031(Mg2-18H) as a function of temperature. Zn2-18H could be saturated in 7 k O e fields below 15 K in the easy plane and followed a o's = o-0 + x H law. A magnetic m o m e n t nB ( H = ~, T = 0) = 14.1 ¥ 0.6/XB and Curie t e m p e r a t u r e Tc = 310~-5 K were extracted from the magnetization data. Mg2-18H crystals could not be saturated in 15.5 k O e field applied parallel to either the (0001) plane or [0001] axis below 120 K. A b o v e 120 K the magnetization followed a o%= cro+ x H law. At 300 K, Tc was measured as 391-7-3 K and nB ( H = ~, T = 0 ) = 7 . 8 * 5tXa was obtained by extrapolation from 120 K. Tauber et al. (1971) discussed the magnetic m o m e n t of these compounds as follows: A ferrimagnetic resultant according to the following site arrangement per formula unit, 9°~--~--4tet~--4 °~t was predicted. When this alignment was used to compute the
40
~30 E
B
% ×
~ 20 X
I O0
200
300
~00
T(K) Fig. 13. Saturation magnetization as a function of temperature for Znz-18H and Mg2-18H (Tauber et al. 1971).
P R O P E R T I E S OF F E R R O X P L A N A - T Y P E H E X A G O N A L F E R R I T E S
411
moment for Zn2-18H assuming the following cation distribution, ( 7 . 4 1 F e 3+, l T i 4+, 0 . 5 9 Z n 2+) ~
<-- ( 1 . 4 1 Z n 2+, 2 . 5 9 F e 3+) ~-- ( 2 F e 3+, 2.0Ti4+),
the resultant magnetic moment came to: (37.05/-tB)--~ - ~-- (12.95/xB) - ~-- (10/xB) = (14.1/.t~).
Zn 2+ ions occupation in octahedral sites in Y-blocks was discussed by Townes a n d Fang (1970). For Mg2-18H, one of many possible distributions giving the magnetic moment is: (6.78Fe 3+, 1.22Ti 4+, 2Mg)---~ ~--(4Fe 3+) ~--(1.22Fe 3+, 1.78Ti 4+, 1Mg) × (33.9/xB)2-~- ~ ( 2 0 / x B ) - *--(6.1/.tB) = (7.8/.tB).
In table 6 the saturation magnetizations and Curie temperatures of the ferroxplana-type compounds are shown.
TABLE 6
The saturation magnetization of ferroxplana-type compounds at absolute zero and at 20°C, and Curie point. o-0 (gauss)
0-20 (gauss)
47rMs
T¢
(cm3/g)
(cm3/g)
(gauss)
(°C)
97 98 79 108
59 78 52 73
3900 5220 3450 4800
415 455 520 430
Mn~Y CoaY Ni2Y Zn2Y Mg2Y
42 39 25 72 29
31 34 24 42 23
2100 2300 1600 2850 1500
290 340 390 130 280
Smit and Wijin (1959)
Co2Z CuzZ Zn2Z
69 60 55
50 46 58
3350 3100 3900
410 440 360
Smit and Wijin (1959)
Zn2X Cu2X
107 95
-
4700 3900
432 467
Tauber et al. (1970) Silber and Tsantes (1969)
Zn2U
-
-
3700
400
Kerecman et al. (1968)
37 20 _+2
-
-
37 291
Savage et al. (1974)
Compounds symbol MnzW Fe2W NiFeW ZnFeW
Znz-18H CuNi-18H
Ref.
Smit and Wijin (1959)
412
M. SUGIMOTO
4. Magnetocrystalline anisotropy and related phenomena One of the reasons for the great scientific and technical interest in the ferroxplana-type compounds is their large crystalline anisotropy. In addition, this anisotropy can be modified over a large range of values by the substitution of the transition metal ions for other divalent ions. A simplified description of the crystalline anisotropy energy density, applicable to most ferroxplana-type compounds, is given in ch. 5. The anisotropy constant, K1 = HAMs~2, and the anisotropy field, HA, as a function of temperature for BaZn2Fe16027(Zn2W) are shown fig. 14 (Albanese et al. 1976b). The value of the anisotropy field was deduced from the saturation magnetization. Although Ks of Zn2W is lower than that of BaFea20~9, the saturation magnetization of Zn2W at room temperature is substantially higher than that of any other hexagonal compounds. For this reason, Zn2W has been of interest for special applications as permanent magnet materials (Lotgering et al. 1980). According to Albanese et al. (1977), /{-1 of Zn2W decreases linearly with increasing substitution of AI for Fe in its structure. The experimental values of/{1,
~o.3 X
%U
2
%
i
(a)
X
0
100
200
300
/*00
500
600
T(K)
_<.~15
HA
I
I
x
(b) s
3=
0
~.
~00
200
300
zoo
soo
600
T(K)
Fig. 14. Temperature dependence of the first anisotropy constant KI and of magnetic anisotropy field HA for Zn2W (Albanese et al. 1976b).
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES
413
/£2 and K3 are shown in fig. 15 as a function of temperature for a BaZnl.38Co0.62Fea6027, (ZnCo)W, single crystal. In addition, there were studies on the crystalline anisotropy of (CoxFe2-x)W by Bickford (1960b), by Lotgering et al. (1961) and Perekalina (1964); on the crystalline anisotropy field of Zn2W, Ni2W, NiZnW, (ZnxNi2-x)W, (Nil.sCo0.4)W and (Nil.26Co0.74)W by Hodges and Harrison (1964), (Ni2_xCo~)W by Rodrique et al. (1962). The dependence of the anisotropy on the Cu content and on temperature for Ba2Zn2-2xCu2,Fe12022, (Zn2-2xCu2x)Y, polycrystalline samples was evaluated by Albanese et al. (1978) assuming the Stoner and Wohlfarth model (1948) using a p a r a m e t e r H A defined as the field at which the magnetization reaches 95.4% of its saturation value in the planar phase or, 91.3% for the axial configuration. The temperature dependence of HA for (Zn2-2xCu2~)Y is shown in fig. 16. The introduction of the Cu ions strongly influenced the magnetocrystalline anisotropy. Smirnovskaya et al. (1978) measured the magnetic anisotropy of Ba2COl.ysZn0.2sFe12022, (Col.75Zn0.25)Y, single crystals in the temperature range 78-290 K. The measurements carried out in various magnetic fields up to 20 kOe for three crystallographic planes; the basal plane, the plane (0110) and (1210). Figure 17 shows the torque curves of (Col.75Zn0.25)Yin the (0110) plane and the basal plane. The torque curve measured in the basal plane at 78 K in a field of 20 kOe is shown in fig. 17(a). It follows from this curve that the easy magnetization directions in the basal plane meet at angles of 60° and that they lie along the crystallographic direction [1010], [1100] and [0110]. Figure 17(b) gives the torque curves obtained at 78, 140 and 175 K in magnetic fields of 5, 10 and 20 kOe in the (0110) plane. Furthermore, there are many experiments on the torque anisotropy measurements for Co2Y and Co2Z by
K;...___ f
E
g o
0
I
gE o
to
o
.,e"
-1
-2
-3
/ 200
40O
6O0
T (K)
Fig. 15. Temperature dependence of anisotropy constants K~, K 2 a n d K3for (ZnCo)W(Asti et al. 1978).
414
M. SUGIMOTO 25
(Z
2-2X C u 2 x ) Y
, X=l
20 \
15
X=7
x
"10 ×=0 1-
0 0
ioo
20o
3o0
T(K)
Fig. 16. Temperature dependence of anisotropy field HA for various x values (Albanese et al. 1978).
Bickford (1960a) as well as the crystalline anisotropy field for Zn2Y, C02Y, Mg2Y and Ni2Y by Smit and Wijn (1959). The temperature dependence of the first-order anisotropy constant/£1 and the second-order constant K: for Ba3Co2Fe24041, CozZ compound is shown in fig. 18. According to Rinaldi and Asti (1976), a positive cubic first-order anisotropy due to Co 2+ ions in octahedral sites probably gives a negative contribution to K1 and a positive contribution to K2. It seems reasonable to assume that K2 is essentially due to cobalt ions, because K2 is nearly zero for all the hexagonal ferrites not containing cobalt. The transition from planar to axial configurations can be interpreted by taking into account the various sublattices whose magnetizations have different temperature dependences for K~, At low temperatures the prevailing contribution to K1 is probably from Co 2+ ions occupying the 2dv sublattice. Figure 19 shows the complete magnetization loop and a section of it with some inner curves of polycrystalline Ba3Co~.75Zn0.2sFe24041, (CoxZn2_x)Z measured at a temperature of 4.2 K. The measurements were carried out in several cycles with increasing field amplitude in the positive field range. The recurrent curves show that irreversible processes occur when the sample is magnetized up to above 13'. Moreover, fig. 20 gives magnetization curves of a grain-oriented sample of the same composition. This constricted Perminvar-type hysteresis loop may be interpreted by a reversible rectifier characteristic induced in single domain particles with conar anisotropy. 13a2Zn2Fe28046(Zn2X) exhibits a uniaxial anisotropy at all temperature and
P R O P E R T I E S OF F E R R O X P L A N A - T Y P E H E X A G O N A L F E R R I T E S
[10~01 I
I
111201 [01101 ]
I
L
]
I
[1210l
I
I
]
415
111001
I
]
(a)
I
0 10 20 30 /.0 50 60 70 80 90100110120 ~P ( d e g r e e )
~
0 -¢.0
~-
-
-ao
o
120 80
J
E
D
, , ~
/.,0 0 -40 -80 -120
t
8090100110
I
L
I
80 90100110 -0" (degree)
\.F I
I
(b)
I
8090 100110
Fig. 17. Torque curves in the (0iI0) plane for Col.75Y. (A) 20 kOe, (B) 10 kOe, (C) 5 kOe, all at T = 78 K, (D) 140 K, (E) 160 K, (F) 175 K, all in H = 20 kOe (Smirnovskaya et al. 1978).
%
3
0
-1 200
z,O0
600
T (K) Fig. 18. Temperature dependence of crystalline anisotropy constants K1 and K2 for Co2Z (Albanese et al. 1976a).
416
M. S U G I M O T O
revemib
,4-"
~
" 250
-
o ";
/
/
/"
<
/
/ /
T=4.2 K
PB'/'~
. ~eversible ~
.
.
/
.
%3 S ~21-
200
150
0
1 H (kOe [,,t061(z, TT) Alrn]
20
Fig. 19. Magnetization curve of isotropic polycrystalline sample (Col.75Zn0.25)Y, T = 4.2 K (Oerling 1970).
Ea=K~sin20. Figure 21 shows the temperature dependence of the magnetocrystalline anisotropy constant K~ for Zn2X or C02X which was obtained by evaluating HAMs~2 (Tauber et al. 1970). At room temperature the c-axis of Ba2Co2Fe28046(Co2X) is the hard direction and (0001) the easy. The anisotropy energy is given as follows: EA = K~ sin 2 0 + K2 s i n 4 0
+
K~ s i n 3 0
c o s 0 c o s 3q~ 2 .
(2)
At about 416 K, however, E A = K 1 sin20 and the c-axis becomes the easy direction and [0001] the hard. Silber and Tsantes (1969) made measurement of the magnetocrystalline anisotropy of single crystals of BazZn2Fe2,O46(ZnzX) and BazCo2FezsO46(CozX) by the ferromagnetic resonance method at room temperature. At room temperature, the one-ion Slonczewski theory (1958) accounted rather well for the change in anisotropy on substitution of cobalt for zinc in X-type compounds. The higher order anisotropy constants observed in the cobalt-bearing samples can be unambiguously attributed to the cobalt ions. In fig. 22 the dependence of the anisotropy constants on temperature for CoZnX is shown. The temperature dependence of the crystalline anisotropy constant/£1 and the anisotropy field HA for Ba4Zn2Fe36Or0(Zn2U) crystal is shown in fig. 23. KI was calculated from H A and Ms at different temperature. A rapid variation of/£1 with increasing temperature is seen. The constancy of H A for a wide range of
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES
o
417
2
X
(a) L
t
i
[
~
-1
I
2'0
H (kOe) H//c
~
3
~
2
%
IE 1
-26
(b) I
-,'o
I
10 15 20 -1
-2
'~ 3 % 2
H (kOe)
HLc
S
:E I I
-20 -1~5
(c)
I
- 1'0
1(3 15
- 5 -I
-2
J
20
H (kOe)
HAc
-3
Fig. 20. Magnetization curves of grain oriented (Co1.75Zn0.25)Y, T = 4.2 K. (a) a = 0°, (b) a = 45 °, (c) a = 90°. a is the angle between the c-axis and the direction of applied field (Gerling 1970).
418
M. SUGIMOTO 100
~
I
'
I
'
r
r
25
20
8O 1 (C02X)
o
<
~ 6o i.I
2 ~0 o
5
~ 20
o
0 0
400
200
600
T (K)
Fig. 21. Temperature dependence of crystalline anisotropy constant K1 and anisotropy field HA of Zn2X and Coax (Tauber et al. 1970).
1.2
~E 1.0 ~n~
0.2
K1
0.6
:~"
"~ 0.1
0.0 "200
300 T(K)
~
o . o = ~
I
100
2 -0.4
L00
100
200
S00
T (K)
~ L00
-o.6F 100
200
300
,'-00
T (K)
Fig. 22. Temperature dependence of crystalline anisotropy constants for CoZnX (Silber and Tsantes 1970).
P R O P E R T I E S OF F E R R O X P L A N A - T Y P E H E X A G O N A L
FERRITES
2
2 E
419
-g
u~ O ×
-.i"
E
%
oi
x
% O
HA
x
v I
200
400 T
600
(K)
Fig. 23. Temperature dependence of crystalline anisotropy constant K1 and anisotropy field HA for Zn2U (Kerecman et al. 1968).
i
I
i
I
I
4
12 K2
E
0
10
u
E
~o -0.5
z~
8
~
-~.0
\
- 1.5
-~
-zo
HA
6
"~
z,
o
2
:Z" i
0
I
l
100
200 T
L
300
K)
Fig. 24. Temperature dependence of crystalline amsotropy constants K1 and/<2, and anisotropy field HA for Zn2-18H (Tauber et al. 1971).
420
M. SUGIMOTO
temperatures may be due to the proportional change in K1 and Ms. BasZn2Ti3FelzO31(Znz-18H), B asMg2Ti3Fe12031(Mg2-18H), B aSll(Nil.lCUo.4)Ti2.7Fe]z3Mn0.4031(NiCu-18H) and Bas.a(Mgl.3Zn0.7)Ti2.9Fen.7031(MgZn-18H) exhibit an easy plane of magnetization at all temperatures except for N i C u - 1 8 H and their anisotropy energy is EA = K1 sin 2 0 + K2 sin 4 0. T h e anisotropy constants K1 i
i
I
r
i
4
2
,10
K~ "-.
f
go_
7 \ <
8~
x
~-2
6
o
x -4
/-.
o
-'r
,x-," - 6
2
I
r
I
100
i
I
200
300
400
T(K)
Fig. 25. Temperature dependence of crystalline anisotropy constants K1 and/(2, and anisotropy field HA for Mg2-18H Tauber et al. 1971).
r
1 -
I
I
[]
i
I
K2
6
o
s
-
g
g<
y...
-1
~ ~o~
\
-2
3
"~
-/,
1
I
0
1
I
100
I
200 T
I
I
o
0
300
(K)
Fig. 26. Temperature dependence of crystalline anisotropy constants K1 and K2, and anisotropy field HA for MgZn-18H (Savage et al. 1974).
PROPERTIES
OF
FERROXPLANA-TYPE
HEXAGONAL
FERRITES
421
and K2 for Zn2-18H, Mg2-18H, M g Z n - 1 8 H and CuNi-18H, respectively, are shown in figs. 24-27. The crystalline anisotropy constants KI and K2 were extracted from the following equation:
I--I~/I = (-2K1 + 4K2)/Ies + (4K212/I4),
(3)
where Hi is the internal field, Is is the spontaneous magnetization. The anisotropy field HA was computed from HA = -- 2(K1 + 2K2/Is).
(4)
The magnetization was invariant to rotation about [0001] for all temperatures at which the basal plane is the easy plane of magnetization.
3
i
I
J
I
i
I
~
r
1
6 <
0
5--
E u ""
8
¢,1 .e
.ac
-3
2 ~
-4
1
-5
~
100
1 200
i
I
300
i
I
4,00
,
I
0
500
T(K)
Fig. 27. Temperature dependence of crystalline anisotropy constants K 1 and K2, and anisotropy field H A for CuNi-18H (Savage et al. 1974).
5. Miissbauer effect Many studies on the M6ssbauer measurements for both single crystals and polycrystalline samples have been carried out to determine the magnetic behaviour of the cations in various lattice sites. Figures 28 (a) and (b) show the spectra of the polycrystalline Mg2W measured at 85 and 300 K, respectively. The spectra have been resolved into different Z e e m a n sextets due to the Fe 57 nuclei in the various sublattices. In discussing the connection between the sextets and the sublattices, it is possible to use the analogy with M-type compounds, because the
422
M. S U G 1 M O T O i
l
I
l
I
r
[
l
1
[
1
1.00 O.98 0.96 •,
0.9 L
0 ~-
0.92 I
I
II III
c-
,
I
I
,
,
II
I ,
,
L.i . . . . . . L. . . . . L . . . . . l . . . . . . . . . . .
J
t-
tOO o
u
0.99
~, > .-
0.98
0.97 0.96
O
n..
0.95
I II
L
III IV V
E
e
J
I
-6
J
L
,
,
j
,
,
r
,
I
,
L-L . . . . . t . -
-I0 -8
I
,
_t . . . .
,
l l ........
1
I
I
r
I
I
I
I
_L.
-2
0
2
~.
6
10
Velocity
(mmlsec)
Fig. 28. MOssbauer s p e c t r u m for polycrystalline MgzW c o m p o u n d : (a) T = 85 K. I - sublattices a, fw, fvl, I I - sublattice K, I I I - s u b l a n i c e b; (b) T = 300 K. I - s u b l a t t i c e K, I I - sublattice ftv, I I I - s u b l a t t i c e a, I V - sublattice fvi, V - sublattice b ( A l b a n e s e and Asti 1970).
W-type structure is closely related to that of the M-type compound. For example, the sextets attributed to Fe in the trigonal position b (fivefold coordination) are denoted in fig. 28 by a dotted line for 1 site out of 18 in the unitary cell. In fig. 29, the temperature dependence of the hyperfine magnetic fields for the observed sextets is shown. Albanese et al. (1976a) also measured the M6ssbauer absorption in Zn2W to determine its spin orientation. Kimich et al. (1970) studied the Fe2W compound. The preferred sites of Fe 2+ in the lattice of Fe2W were determined by Fayek et al. (1980) from a M6ssbauer study. The M6ssbauer absorption spectra of Fe 57 14.4keV gamma rays for polycrystalline samples of Co2Y at different temperatures a r e shown in fig. 30. The spectrum measured at 78 K shows only one Zeeman sextet with a mean hyperfine magnetic field of 508kOe. With increasing temperature the spectra can be interpreted as the superposition of three different sextets. Albanese et al. (1975b) established the correspondence between the three observed sextets and the iron sublattices of CozY structure as follows: Sextet II, being the only one which is contracted in the presence of the external field, is due to all the Fe 3+ ions with spin up, i.e., the sublattices 18Hvi, 3avl, 3bvi. Sextet III, the one having the highest hyperfine field, can be assigned to the sublattice 6C~v on the grounds of the
PROPERTIES OF FERROXPLANA-TYPE I
I
]
HEXAGONAL
I
I
I
FERRITES
423
I
600
--
E
K
-.~--&-.-&.-~.::...
500
__ -
-
-
-
b
L,oo
\L.IX x
300
200
-r
I00
I
I
I
I
1
100
200
300
t-O0
500
I
600
I
I
700
800
T(~) Fig. 29. Hyperfine magnetic fields at iron nuclei of various sublattices ol Mg2W c o m p o u n d as a function of temperature (Albanese and Asti 1970).
0,l 909B ~ 0,:4' 9, ~:""0.. 9i ..... 6 1 ;. 0.;: 0 . 2,.. /. ..
.A~
0.90 100
':~,,:
.~.
~
~
~",,.
=
.;s'~c
0.98 0
036
.E 0.94 E 21 O U
~.
I
L
II
k
I
,
I
I
,
i
b)
I
__,
1.00
0.98
-~ 0.96 er 0.9z,
c) Ill
~
,
,
_
i
,
1.00 0.9B 0.96 0.94 092
(d)
090 i
I
i
I
-10-8-6-4-2
I
A_
I
I
0
2
4
I
i
i
6 8 10
Velocity ( m m / s e c ) Fig. 30. Mbssbauer spectra for CozY compound: (a) T = 78 K, (b) T = 296K, (c) T = 403 K, (d) T = 673 K (Albanese and Asti 1970).
424
M. S U G I M O T O I
I
I
¢
I
I
i
1
I
I
I
I
I
I
h
I
I
I
P
r
i
i
1.00 ¢-
0.98
¢-
~ 0.96 ]
i
[[
III
I
I
-10
J
I
[
I
I
J
i
I
J l
i
I
-4
L
i
~
I
-6
--
i
,
u_
-8
I
i
I
I
-2
I
I
2
Velocity
J
~
,
I
!
L
i
6
8
)
10
(mm/sec)
Fig. 31. M6ssbauer spectrum for CozZ polycrystalline compound at room temperature (Albanese and Asti 1970).
[
0.980.961'00~
~
I
~
~
I
I
~
I
'
.
t
r
I
.
f
I
, ., . .
I
O~
it
.~'~
]
ou
,
J
--
I
1.00 4:.......... i"~
I
~ [
]
i
r
.
I
i
I
I
I
i
,
0
i
I
i
.
[
.:~:~-•~F
I l
P
E
2 ~
I
I
I
i
-10 -B -6 -/, -2
>
I
I
I I
i
{
i
z, 6 ~
P '
i
~
I
,
]
8 10 ~ i
i
.
I ,.""'"
.~ ".
0.98
0.96 0.9/., l
I
[ I
I I
I I I
i l I
I I I
-10 -8 -6 -4 -2 0 2 4 6 Velocity (mm/sec)
I
B
Fig. 32. M6ssbauer spectra for Co2Z single-crystal compound at room temperature: (a) Hext = 0, (b) /-/~×t = 25 kOe (Albanese and Asti 1970).
PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES
425
spectrum taken in an external field. Finally, sextet I must be assigned to the remaining spin-down sublattices, i.e., to 6Cry and to the fraction of 6CvI sublattice occupied by iron ions. M6ssbauer measurements on the Mg2Y compound (A1banese et al. 1975b), on (Znl-xCux)2Y (Albanese et al. 1978), on Zn2Y and (Mn0.625Zn)2Y (Albanese et al. 1968) have been reported. Figure 31 shows the M6ssbauer spectra for a polycrystalline sample of CozZ at room temperature. T h e spectra can be interpreted as the superposition of at least four sextets. In order to determine the spin orientation of the various iron sublattices, one often uses the M6ssbauer spectrum for a single crystal measured in an external magnetic field perpendicular to the c-axis and to the gamma ray direction. The spectra for a CozZ single crystal in the absence and in the presence of the external magnetic field of 25 kOe, respectively, are shown in fig. 32. In the presence of the external field sextets II and III collapse into a single sextet with broad lines proving that sextet III is due to iron sublattices with spin-up and sextet II to iron sublattices with spin-down. In a similar way, by comparing the Hhf values both in the presence and in the absence of external field, sextet IV is assigned to be the spin-down sublattice. As regards sextet I, from the spectrum in an external field, it may b e deduced that part of the contributing sublattices has spin-up, and part has spin-down.
6. Magnetostriction and NMR
6.1. Magnetostriction The anisotropic part of the magnetostriction of the ferroxplana-type compounds is expressed by a phenomenological formula with four constants, which is the same formula as that of W-type compounds described in ch. 5. The constants AA, AB, Ac and AD are also determined experimentally in the same way. The values of these constants for FeeW single crystals were determined as AA = 13× 10-6, As = 3 × 10-6, Ac = - 2 3 × 10-6 and AD = 3 × 10-6 using wire strain gauges (Fonton and Zalesskii 1965). In these measurements, two samples in the form of disks having different cuts were used: parallel to the basal plane and parallel to the plane with the c-axis. Figure 33 shows the magnetostriction of a single crystal of Fe2W cut parallel to the basal plane. In fig. 33(a), c u r v e s /~A and AB illustrate, respectively, the dependence of the longitudinal and transverse magnetostriction in the basal plane on the external field. The magnetostriction A, reaches saturation in fields of about 18000 Oe, corresponding to the saturation magnetization of the sample at fight angles to the c-axis. Curve C represents the change in the magnetostriction in the basal plane when the sample is magnetized along the c-axis (at right angles to the plane of the disk). Figure 33(b) shows the dependence of the magnetostriction in t h e basal plane on the angle q~, obtained by rotating the crystal in a magnetic field of 21000 Oe. Here ~ is the angle between the direction of an external magnetic field and the
426
M, S U G I M O T O 18
18
16
(a)
16
XA
1/,
"~
%
I~
12
12
10
10
8
8
6 4
6 /.
2
2
0
18
-2 -4
21
r 30
2427
q 60
r 90
I r f 120150180
~ 2
e)
-6
-4
(degree)
-6
-8
o
-10
-8 -10
Fig. 33. Magnetostriction of a disk, cut parallel to the basal plane of Fe=W single crystal: (a) dependence of the magnetostriction in the basal plane on the external intensity, (b) dependence of the magnetostriction along the direction x on the orientation of the magnetization vector in the basal plane (Fonton and Zalesskii 1965).
c-axis. The value of the magnetostriction for q~ = 0 represents the transverse effect in the basal plane and the longitudinal effect is given by ~0 = 90 °. Figure 34 shows the dependence of the magnetostriction on the external field intensity for a single crystal of Fe2W with disk shape cut parallel to the plane with 15
10
,-< ~o" O
-5
-10
-15 -20
Fig. 34. Dependence of the magnetostriction on the external field intensity for a disk, cut parallel to the plane with the c-axis of Fe2W single crystal (Fonton and Zalesskii 1965).
PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES
427
the c-axis. T h e ,hA curve in fig. 34 corresponds to the ,hA curve in fig. 33. The difference in the saturation magnetostriction in these two cases seems to be due to the different initial states of the samples. Since, as seen in the figure, the magnetostriction constants are opposite in sign and analogous to that o f a cobalt crystal, Fe2W exhibits first an elongation and then contraction of the linear dimensions. Kuntsevich and Palekhin (1978) measured the t e m p e r a t u r e dependences of the longitudinal (All) and transverse (hl) saturation magnetostrictions in the basal plane for BaCo1.sFe0.2Fe16027(Col.8Fe0.E)W, 2+ 3+ and observed their abrupt changes in the t e m p e r a t u r e range 430-460K. In addition, the t e m p e r a t u r e dependence of the longitudinal magnetostriction (`hn) for Cu2Y in the t e m p e r a t u r e range 200-350 K was measured by Belov et al. (1980).
6.2. N M R T h e nuclear magnetic resonance (NMR) of 55Mn has been studied in single crystals of Ba2Zn2_xFe12_yMnx+yO22(Zn2Y type) for values of (x + y) of about 0.5 by Streever et al. (1971). In fig. 35 (a) and (b), the zero field N M R spectra of Mn0.sZnl.sY single crystal measured at 4.2 K and 77 K are shown. The spectrum at 4.2 K was interpreted on the basis of the MnFeaO4 results that the broad line 1.0
i
i
i
I
0.8
I
4.2°K
0.6
(a)
0.4 ~. 0.2 E >
"~ 1.0
~
i
I
i
I
ct"
0.8
7 7*K
0.6 Cb) 0.t. 0.2
'1 300
340
380
420
460
500
5/.0
580
620
Frequency (MHz} Fig. 35. The zero field NMR spectrum of Mn0.sZnY measured at (a) 4.2 K, (b) 77 K (Streever et al. 1971).
428
M. SUGIMOTO
extending from about 300 to about 470 MHz is due to the Mn 3÷ ions (replacing iron) on the octahedral sites and two relatively narrow lines at 555 and 585 MHz are due to the Mn 2+ ions (replacing zinc) on the two types of tetrahedral sites with roughly the same degree of preference. Both Mn 2+ lines were observed to shift to higher frequency with externally applied fields which is consistent with this interpretation. The hyperfine fields and the temperature dependences of the resonance frequencies for the Mn 2÷ ions on the two types of tetragonal sites can be consistently explained in terms of the different electronic environments of the two sites.
7. High frequency magnetic properties Ferromagnetic resonance in the high frequency range is a well-known phenomenon. It involves the excitation of magnetic dipoles in a material under the driving force of a high frequency magnetic field. As a material for high frequency or microwave devices, considerable interest has previously been shown in the ferroxplana-type compounds having large magnetic anisotropy and lower dispersion frequency. In compounds with planar anisotropy, ferromagnetic resonance occurs at a frequency which depends on both the applied magnetic field HAl and the anisotropy field HA2 as illustrated in fig. 36. The resonance frequency is given by the relation (Bady 1961): (/"/7) 2 =
H&(HA, + HA2),
where F is the resonance frequency (GHz) and y is the gyromagnetic ratio (assumed to be 2.8). Since/-/12 usually can take very much higher values than HA1, the resonance frequency reaches higher values. Moreover, the static initial permeability is given by (Smit and Wijn 1959): #Zo- 1 = ~4~'o'JHA, ,
where/z0 is the static initial permeability and o-s is the saturation magnetization. As seen in this equation, it is possible to obtain a compound with higher initial permeability up to the high frequency range by controlling the value of HA1. Figure 37 shows the frequency dependence of the initial permeability for Co2Z. For comparison, this figure also gives the property of the spinel NiFe204. Although the permeability at low frequency is approximately equal for both compounds, the dispersion frequency of about 1000 MHz for Co2Z is substantially higher than that of about 200 MHz for the spinel. Such higher-frequency dispersion characteristics are found with many other planar compounds having large HA,. The dispersion may be due to the ferromagnetic resonance. The experiments on the ferromagnetic resonance linewidth can be roughly divided into three classes according to the measuring method: The low power
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES 14
429
I ! I
12 10
8 6
2 -0 10
]
4
2
5
100
2 Frequency
5
1000
2
5
(MHz)
Fig. 36. Dependence of ferromagnetic resonance frequency of a spherical sample of a ferroxplana compound on the applied magnetic field and the anisotropy field (Braden et al. 1966).
transverse pumping method, the higher power transverse pumping method and the high power parallel-pumping method. The theoretical discussion of Schl6mann et al. (1962, 1963) has led to the conclusion that a large planar anisotropy favours the excitation of spin waves and reduces the threshold for the onset of instability. Mita (1965) has analyzed the first and the second order non-linear behaviours observed in Zn2Y on the basis of this theory, and he also analyzed the linewidth induced by surface imperfections in Zn2Y on the basis of the two-magnon mechanism (1968). The theory of parallel pumping phenomenon has been worked out by Bady et al. (1962). Douthett et al. (1962) found that their phenomenological theory closely predicts the response in Zn2Y single crystal through frequency doubling experiments at low levels. Furthermore, Hwa and Silver (1977) have experimentally compared the two theoretical models of Gurevich (1969) and Rado (1972) for ferromagnetic resonance, and found that both models give good agreement with the experimental results of Mg2Y at 9.3 GHz. The microwave linewidth AH of Y- and Z-type compounds respectively are shown in figs. 38 (a) and (b) (Braden et al. 1966). In Y-type compounds, zXH varied between 100 Oe in (Cu0.7Ni0.3Znl.0)Y and 1430 Oe in Co2Y. In general, the Y-type compounds were found to have the most useful microwave properties compared with W- and Z-type compounds. The temperature dependence of the linewidth of Co2Y is shown in fig. 39. The linewidth increases linearly as the temperature is decreased to 220 K, and below 220 K it remains fairly constant down to 77 K. The linewidth of C o 2 Y behaves similarly to that of Zn2Y. The field for resonance (H0) decreases to a sharp minimum at 220 K, and then increases again as the temperature is lowered. Grant et al. (1974) observed the lowest resonance linewidth of 38 Oe for a single-crystal sphere of Zn2Z at 35 GHz at
430
M. SUGIMOTO 40
35
30
"~ 25 1-"
c 20 IJ" L.
m 15
10
5
0
2
~
6
8
10
12
HAl(kOe) ix106 /(47F)AIm] Fig. 37. Magnetic spectrum of a polycrystalline specimen of C o 2 Z . For comparison, the spectrum of NiFezOa with approximately the same low frequency permeability is given (Smit and Wijn 1959).
r o o m temperature, while Braden et al. (1960) obtained the linewidth of 1115 O e for polycrystalline Zn2Z. K e r e c m a n et al. (1969) measured the linewidths of ZnzU and Mn-substituted ZnzU and obtained the value of 120 and 1 8 . 5 0 e at 26.5 G H z and at 300 K. Savage et al. (1965) obtained a minimum linewidth of 3 . 8 0 e at 9.0 G H z at r o o m temperature for Mn-substituted ZnzY single crystal. Weiner and C02 Y
1260
655
1430
•
N i2
Y
300
Zn2 Y 29~0
870
"
655 -
1260
C02 Y
"
Cu
Y
87o
30o
Fig. 38(a). The microwave linewidtb of Y-type compounds (Braden et al. 1966).
Ni2 Y
PROPERTIES OF FERROXPLANA-TYPE
HEXAGONAL
FERRITES
Ni2 Z
Ni2
431 Z
(b)
Zn 2 V
Cu 2 7
Fig. 38(b). T h e microwave linewidth of Z-type compounds. T h e dotted line indicates the region of zero anisotropy (Braden et al. 1966).
,
,
,
i
,
,
1800
'- 4000
f =23 k M c o_
"-{ 1600 - 3000
<
,~
1~o0
<
~-
AH
d
G 1200
~, 2000
~. 1000
o
o
o 800
"~
1000
z~q
:~
600
~s
/.00 I
1oo
I
I
150
I
Y 200
r
I
250
I
I
300
0
A
3so
T(K) Fig. 39. Field f o r resonance, Hr, and l i n e w i d t h , / - / , of Co2Y as a function o f t e m p e r a t u r e ( B u f f l e [ ]962).
Dixon (1970) have theoretically and experimentally investigated subsidiaryresonance phenomena in an Mn-substituted ZneY single crystal and observed a linewidth of 5.0 Oe at 17.2 GHz. Investigations on the effect of surface finish on the linewidth were carried out by Dixon (1963) for Zn2Y and by Kerecman et al. (1969) for Mn substituted Zn2U. The variation of the magnetic susceptibility with microwave magnetic field for Zn2Y single crystal is shown in fig. 40. Measurements were made on an unpolished sample with a diameter of 0.02 inches. It should be noted that the susceptibility, the field required for resonance, and the shape of the resonance curve vary as a function of RF magnetic field intensity (Dixon 1962). Green and Healy (1963) measured the imaginary part of the parallel susceptibility for Zn2Y single crystal with spherical and flake shapes and calculated the spin wave linewidth of 8 . 0 0 e
432
M. S U G I M O T O I X
1.0
J
I
J
-
~~ I
I
I
(0.140e)
X
__>, 0.8 Q.
8
",/~~~(3650e)
0.6
.,$ iO'1
0.4
F N
E o z
0.2
0
1
400
r
600
I
?
o
800 1000 1200 1/.,00 HA[0e ) [ x 103/(/.,/'/1A/rn ]
i
I
1600
1800
Fig. 40. Variation of the normalized susceptibility and the field required for resonance with the incident rf power as a p a r a m e t e r for Zn2Y compound: frequency = 8957 Mlqz, A H = 85 O e (Dixon 1962),
for a sphere of Zn2Y and 9.24 Oe for flake Zn2Y, respectively, from the minimum RF critical field. Helszajn et al. (1969) measured the decrease of the mainresonance susceptibility at 17.03 GHz under second-order perpendicular pumping for Mn-Zn2Y. The anisotropy field for W-, Y- and Z-type compounds are shown in figs. 41 (a), (b) and (c). Table 7 shows the high frequency properties for some ferroxplanatype compounds.
Co2 W
Ni2W
Ni2W
(a)
Zn2 W
Cu2 W
Fig. 41(a). T h e approximate location of zero anisotropy for W-type compounds. T h e data show values of linewidth and anisotropy field for s o m e c o m p o u n d (Braden et al. 1966),
PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERR1TES Co2Y
Zn2Y
15
433
Co2Y
21
N; 2 ¥ Cu2¥ Ni2 ¥ Fig. 41(b). The anisotropy field (in kOe) of Y-type compounds which have plana anisotropy (Braden et
an. 1966).
Ni2 Z
-t9 ,
- 2.8 - 9.9 C02 Z_9.9 -2.8 -1.9
Ni2 Z
\/-l~\/I-,OSjr-jj/.~",/,~__~
(c)
Zn2 Z Cu2 Z Fig. 41(c). The anisotropy field (in kOe) of Z-type compounds. Planar anisotropy is indicated by a negative sign, and uniaxial anisotropy is indicated by a positive sign (Braden et al. 1966).
TABLE 7 The microwave linewidth, the measuring frequency and the anisotropy field for ferroxplana-type compounds at room temperature. Compounds symbol
AH (Oe)
f (GHz)
HA (kOe)
Zn2Y (Zno.9sFeo2~os)2Y Zn2Z Zn2X ZnzU
13 14 38 45 155
9 9 35 54 26-40
9.5 12.0 4.8 13.7 10.0
Ref. Verweel (1967b) Verweel (1967b) Smit and Wijn (1959) Silber and Tsantes (1969) Kerecman et al. (1969)
434
M. S U G I M O T O
8. Electric properties and other effects
8.1. Conductivity In high frequency applications, the low electrical conductivity of materials is very important. As was described in ch. 5 concerning W compounds, the ferroxplanatype compounds with hexagonal structure show a similar anisotropy of the electrical conductivity. The conductivity in the basal plane is higher than that along the hexagonal axis. Figure 42 shows the temperature dependence of the electrical conductivity, o-ii (parallel to the c-axis), and o-± (perpendicular to the c-axis) for single crystals of Fe2W and Co2W (Simga et al. 1966). As seen in this figure, the values of o71 are 2 to 3 orders higher than ~r±. The possible origin of the anisotropy in the Conductivity may be the alternating layers in the direction of the c-axis and thus the electrical resistance in this direction is greater than in the basal plane. In table 8, values of the activation energies for Fe2W and Co2W are given. Kasami et al. (1966) measured the temperature dependence of the electrical resistivity for Zn2Y at 77-500 K, and observed a strong anisotropy in the electrical 10
I
I
i
i
i
i
10
12
10- I
10-2
S E
10-3
U i
C~ 10-4 "t::,
10-5
lff 6
10-7
10 6 4
8
6
lIT
(xlO-3K
-1)
Fig. 42. Temperature dependence of the electrical conductivity, oql, (parallel to the c-axis) and o-±, (perpendicular to the c-axis) for single crystals of Fe2W, Co2W and Zn2Y (Sim~a et al. 1966, Kasami et al. 1966).
PROPERTIES OF IZlERROXPLANA-TYPE HEXAGONAL FERRITES
435
TABLE 8 Activation energies, q, in (eV) for the conductivity of the samples Fe2W and Co2W (Simga et al. 1966).
Crystal
Direction of current
7%100
11c-axis L c-axis IIc-axis 2 c-axis
0.025 0.029 0.059 0.064
Fe2W
Co~W
Temperature range (K) 100--170 1 7 0 - 3 0 0 0.029 0.033 0.079 0.075
0.041 0.039 0.095 0.083
300-670 0.095 0.083
resistivity as well as a l o w e r v a l u e of a.c. resistivity c o m p a r e d to that of t h e d.c. resistivity. B u n g e t a n d R o s e n b e r g (1967) m e a s u r e d t h e e l e c t r i c a l resistivity of Co2Z at 200-500 K. K a s a m i a n d K o i d e (1966) m e a s u r e d t h e electrical resistivity of Zn2U at room temperature.
8.2. Dielectric constant T h e d i e l e c t r i c c o n s t a n t s of p o l y c r y s t a l l i n e BaNi2AlxFe16_xO27, (NiA1) W , as a f u n c t i o n of a l u m i n i u m c o n c e n t r a t i o n , x, has b e e n m e a s u r e d at 9.5 G H z a n d at r o o m t e m p e r a t u r e (Taft 1964); See t a b l e 9.
TABLE 9 Dielectric constant, e of polycrystalline isotropic compounds of BaNi2AlxFe16_xO27 (Taft 1964). x
0.60 15.4
0,73 14.9
0.86 15.1
1.00 14.5
8.3. Jahn-Teller effect C u F e 2 0 4 is a w e l l - k n o w n f e r r i t e which exhibits t h e J a h n - T e l l e r p h e n o m e n o n d u e to C u 2+ ions l o c a t e d at o c t a h e d r a l sites. B e l o v et al. (1980) o b s e r v e d a s t e e p rise of p e r m e a b i l i t y at 300 K for Cu2Y as i l l u s t r a t e d in fig. 43. Cu2Y, which has Tc-650°C, e x h i b i t e d also a m a r k e d c h a n g e of t h e m a g n e t o s t r i c t i o n as well as of t h e m a g n e t o r e s i s t a n c e at t h e s a m e t e m p e r a t u r e . T h e m a g n e t i c a n i s o t r o p y c o n s t a n t was K1 < 0 b e l o w 300 K a n d K1 > 0 a b o v e this t e m p e r a t u r e . T h i s p h e n o m e n o n is i n t e r p r e t e d as t h e J a h n - T e l l e r effect d u e to C u 2+ ions l o c a t e d at o c t a h e d r a l sites in spinel blocks.
436
M. SUGIMOTO 20
15
~10
200
300
400
T(K)
Fig. 43. Temperature dependences of the permeability,/~, of Cu2Y (Belov 1980).
8.4. Magneto-optical effect Figures 44 (b), (c) and (d) give the spectral dependence of the transverse Kerr effect for Co2W, Co2Y and Co2Z single crystals, respectively. For comparison, the spectrum of the W compound (a) is also presented. As seen in figs. 44 (b), (c) and (d), all ferroxplana-type compounds exhibited a positive peak of rotation angle at energies of 1.9-2.3 eV, respectively. Such a marked peak, however, could not be seen in the W compound as shown in fig. 44(a). The peak at 2.5-5 eV was also observed in the W compound.
8.5. Domain observation and chemical analysis Verweel (1967a,b) reported that the Boch walls of the ferroxplana-type compounds can be displayed by the well-known Bitter technique. Fano and Licci (1975) reported an analytical method based on automatic potentiometric titration for the analysis of Zn2Y.
PROPERTIES OF F E R R O X P L A N A - T Y P E H E X A G O N A L FERRITES
437
LIJ
x© -I .= 0
=
o~
(PoJ£OLX)
Q'eI~UD
IJO!~.D)~OJ J l e ~ l
eSJ~)ASUDJL
0
E~ o~ 0 0
hi
~o ~
•
I
J
I
(PDJ£OLX) ~ el6Ub UO!;D~OJ JJa~l
I
r
esJa^suoJ/
L~
=
438
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0
-- 0
M
©
=
i
i
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I
(FoJcO|x)~)
' el BuD
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i
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I
)
~
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/ .~t
i
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PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES
439
References Acquarone, M., 1979, J. Phys. C. Solid State Phys. 12, 1373. Albanese, G. and G. Asti, 1970, IEEE Trans. MAG-6, 158. Albanese, G. and S. Rinaldi, 1974, J. Appl. Phys. 45, 3400. Albanese, G., G. Asti and C. Lamborizio, 1968, J. Appl. Phys. 39, 1198. Albanese, G., M. Carbucicchio and G. Asti, 1975a, Nuovo Cimento, 14, 207. Albanese, G., M. Carbucicchio and A. Deriu, 1975b, Appl. Phys. 7, 227. Albanese, G., A. Deriu and S. Rinaldi, 1976a, J. Phys. C. Solid State Phys. 9, 1313. Albanese, G., M. Carbucicchio and G. Asti, 1976b, Appl. Phys. 11, 81. Albanese, G., M. Carbucicchio, F. Bolzoni, S. Rinaldi, G. Sloccari and E. Lucchini, 1977, Physica, 86--88B, 941. Albanese, G., A. Deriu, F. Licci and S. Rinaldi, 1978, IEEE Trans. MAG-14, 710. Asti, G., F. Bolzoni, F. Licci and M. Canali, 1978, IEEE Trans. MAG-14, 883. Auld, B.A., R.E. Tokhein and D.K. Winslow, 1963, J. Appl. Phys. 34, 2281. Bady, I., 1961, IRE Trans. MTT-9, 60. Banks, E., M. Robbins and A. Tauber, 1962, J. Phys. Soc. Japan, 17, 196. Belov, K.P., A.N. Goryaga, L.G. Antoshina and M.M. Lukina, 1980, Sov. Phys. Solid State, 22, 2013. Bickford, L.R. Jr., 1960a, Phys. Rev. 119, 1000. Bickford, L.R. Jr., 1960b, J. Appl. Phys. 31, 259S. Blocker, T.G. and A.J. Heeger, 1967, J. Appl. Phys. 38, 1111. Braden, R.A., J. Gordon and R.L. Harvey, 1966, IEEE Trans. MAG-2, 43. Braun, P.B., 1957, Philips Res. Rept. 12, 491. Burlier, C.R., 1962, J. Appl. Phys. 33, 1360. Bunget, I. and M. Rosenberg, 1967, Phys. Status Solidi, 20, K163. Castelliz, L.M., K.M. Kim and P.S. Boucher, 1969, J. Canadian Ceram. Soc. 38, 57. Cook, C.F. Jr., 1967, J. Appl. Phys. 38, 2488. Dixon, S. Jr., 1962, J. Appl. Phys. 33, 1368. Dixon, S. Jr., 1963, J. Appl. Phys. 34, 3441. Dixon, S. Jr., A. Tauber and R.O. Savage Jr., 1965, J. Appl. Phys. 36, 1018. Douthett, D.D., I. Kaufman and A.S. Risley, 1962, J. Appl. Phys. 33, 1395. Drobek, J., W.C. Bigelow and R.G. Wells, 1961, J. Am. Ceram. Soc. 44, 262.
Enz, U., 1961, J. Appl. Phys. 32, 22S. Fagg, L.W. and S.S. Hanna, 1959, Rev. Mod. Phys. 31,711. Fano, V. and F. Licci, 1975, Analyst. 100, 507. Fayer, M.K. and A.A. Bahgat, 1980, Indian J. Pure Appl. Phys. 18, 945. Fonton, S.S. and A.V. Zalesskii, 1965, Soviet Phys. JETP, 20, 1138. Gerling, W.H., 1970, IEEE Trans. MAG-6, 737. Glass, H.L. and J.H.W. Liaw, 1978, J. Appl. Phys. 49, 1578. Gordon, J., R.L. Harvey and R.A. Braden, 1962, J. Am. Ceram. Soc. 45, 297. Grant, R.W., M.D. Lind, G.P. Espinosa and I.B. Goldberg, 1974, AIP Conf. Proc. 24, 493. Green, J.J. and B.J. Healy, 1963, J. Appl. Phys. 34, 1285. Gundlach, R., 1968, Electronics, 41, 104. Harvey, R.L., I. Gordon and R.A. Braden, 1961, RCA Review, 648. Helszojn, J. and J. Mestay, 1969, Electronics, 5, 525. Hodges, L.R. and G.R. Harrison, 1964, J. Am. Ceram. Soc. 47, 601. Huijser-Gerits, E.M.C. and G.D. Rieck, 1974, J. Appl. Cryst. 7, 474. Huijser-Gerits, E.M.C. and G.D. Rieck, 1976, J. Appl. Cryst. 9, 18. Huijser-Gerits, E.M.C., G.D. Rieck and D.L. Vogel, 1970, J. Appl. Cryst. 3, B243. Hwa, C. and L.M. Silber, 1977, Physica, 8688B, 1239. Jonker, G.H., H.P.J. Wijn and P.B. Braun, 1956/57, Philips Techn. Rev. 18, 145. Kasami, A. and S. Koide, 1966, J. Phys. Soc. Japan, 21, 552. Kasuya, T. and R.C. LeCraw, 1961, Phys. Rev. 6, 223. Kerecman, A.J., A. Tauber, T.R. AuCoin and R.O. Savage, 1968, J. Appl. Phys. 39, 726. Kerecman, A.J. and T.R. AuCoin, 1969, J. Appl. Phys. 40, 1416. Kimich, T.A., V.F. Belov, M.N. Shipko and E.V. Korneev, 1970, Soviet Phys. Solid State, 11, 1960. Kohn, J.A. and D.W. Eckart, 1964a, J. Appl. Phys. 35, 968. Kohn, J.A. and D.W. Eckart, 1964b, Z. Kristallogr. 119, 454. Kohn, J.A. and D.W. Eckart, 1971, Mat. Res. Bull, 6, 743.
440
M. SUGIMOTO
Kuntsevich, S.P. and V.P. Palekhin, 1978, Soviet Phys. Solid State, 20, 1661. Landuyt, van J., S. Amelinckx, J.A. Kohn and D.W. Eckart, 1974, J. Solid State Chem. 9, 103. Licci, F. and G. Asti, 1979, IEEE Trans. MAG15, 1867. Lotgering, F.K., 1958/59, Philips Tech. Rev. 20, 354. Lotgering, F.K., 1959, J. Inorg. Nucl. Chem. 9, 113. Lotgering, F.K., P.H.G.M. Vromans and M.A.H. Huyberts, 1980, J. Appl. Phys. 51, 5913. Mita, M., 1965, J. Phys. Soc. Japan, 20, 1599. Mita, M., 1968, J. Phys. Soc. Japan, 24, 725. Neckenbfirger, E., 1966, IEEE Trans. MAG-2, 473. Neckenbtirger, E., H. Severin, J.K. Vogel and G. Winkler, 1964, Z. Angew. Phys. 18, 65. Neumann, H. and H.P.J. Wijn, 1968, J. Am. Ceram. Soc. 51, 536. Okazaki, K. and H. Igarashi, 1970, Proceedings of ICF, 131. Perekalina, T.M., D.G. Sannikov and E.M. Smirmovskaya, 1979, Sov. Phys. Solid State, 21, 1579. Reisch, F.E., R.W. Grant, M.D. Lind, G.P. Espinosa and I.B. Goldberg, 1975, IEEE Trans. MAG-11, 1256. Robbins, M., S. Lerner and E. Banks, 1963, Phys. Chem. Solids, 24, 759. Savage, R.O. and A. Tauber, 1964, J. Am. Ceram. Soc. 47, 13. Savage, R.O. Jr., S. Dixon Jr. and A. Tauber, 1964, J. Appl. Phys. 36, 873. Savage~ R.O., A. Tauber and J.R. Shappirio, 1974, AIP Conf. Proc. 34, 491. Schl6mann, E., R.I. Joseph and I. Bady, 1963, J. Appl. Phys. 34, 672. Silber, L.M. and E. Tsantes, 1969, IEEE Trans. MAG-5, 6O0.
Silber, L.M: and E. Tsantes, 1970, Proceedings of ICF, 40. Simga, Z., A.V. Zalesskij and K. Zaveta, 1966, Phys. Status Solidi, 14, 485. Slonczewski, J.C., 1958, Phys. Rev. 110, 1341. Smirnovskaya, E.M., T.M. Perekalina and S.A. Cherkezyan, 1978, Soy. Phys. Solid State, 20, 1953. Smit, J. and H.P.J. Wijn, 1959, Ferrites (Philips Technical Library, Eindhoven). Stearns, F.S. and H.L. Glass, 1975, Mat. Res. Bull. 10, 1255. Streever, R.L., T.R. AuCoin and P.J. Caplan, 1971, J. Phys. Chem. Solids, 32, 519. Suemune, Y., 1972, J. Phys. Soc. Japan, 33, 279. Suhl, H., 1956, Proc. IRE. 44, 1270. Tauber, A., S. Dixon Jr. and R.O. Savage, Jr., 1964, J. Appl. Phys. 35, 1008. Tauber, A., J.S. Megill and J.R. Shappirio, 1970, J. Appl. Phys. 41, 1353. Tauber, A., R.O. Savage, Jr. and M.D. Grebenau, 1971, J. Appl. Phys. 42, 1738. Uitert, L.G. and F.W. Swanekamp, 1957, J. Appl. Phys. 28, 482. Verweel, J.,:1967a, Z. Angew Phys. 23, 200. Verweel, J., 1967b, J. Appl. Phys. 38, 1111. Vinnik, M.A., A.P. Erastova and Yu.G. Saksonov, 1968, Fiz. Tverd. Tela, 8, 269; 1966, Sov. Phys. Solid State, 8, 219. Voekov, D.V. and A.A. Zheltukhin, 1980, Izv. Akad. Nauk. SSSR, 44, 1480. Wijn, H.P.J., 1952, Nature, 170, 707. Weiner, M. and S. Dixon, Jr., 1970, IEEE Trans. MAG-6, 397. Yamzin, 1.I., R.A. Sizov, I.S. Zheludov, T.M. Perekalina and A.V. Zalesskii, 1966, Ah. Eksperim. i Teor. Fiz. 50, 595; 1966, Sov. Phys. JETP, 23, 395. Zalesskii, A.V. and T.M. Perekalina, 1965, Zh. Eksperim, i Teor. Fiz. 48, 48; 1965, Soy. Phys. JETP, 21, 64.
chapter 7 HARD FERRITES AND PLASTOFERRITES
H. STABLEIN Fried. Krupp GmbH Krupp WlDIA Krupp Forschungsinstitut D 4300 Essen F.R.G.
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 441
CONTENTS 1. G e n e r a l . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. H i s t o r i c a l d e v e l o p m e n t . . . . . . . . . . . . . . . . . . . . 1.2. A s p e c t s for a p p l i c a t i o n s as p e r m a n e n t m a g n e t m a t e r i a l . . . . . . . . . 1.3. C o m p o s i t i o n s a n d p h a s e d i a g r a m s . . . . . . . . . . . . . . . . 1.3.1. B a O - F e 2 0 3 s y s t e m . . . . . . . . . . . . . . . . . . . 1.3.2. B a O - F e 2 0 3 - b a s e d s y s t e m s . . . . . . . . . . . . . . . . . 1.3.3. S r O - F e 2 0 3 s y s t e m . . . . . . . . . . . . . . . . . . . 1.3.4. S r O - F e 2 0 3 - b a s e d s y s t e m s . . . . . . . . . . . . . . . . . 1.3.5. P b O - F e 2 0 3 s y s t e m . . . . . . . . . . . . . . . . . . . 1.3.6. B a O - S r O - P b O - F e 2 0 3 - m i x e d s y s t e m s . . . . . . . . . . . . . 1.3.7. C a O - F e 2 0 3 - b a s e d s y s t e m . . . . . . . . . . . . . . . . . 2. M a n u f a c t u r i n g t e c h n o l o g i e s of h a r d ferrites . . . . . . . . . . . . . . 2.1. U s u a l t e c h n o l o g y . . . . . . . . . . . . . . . . . . . . . . 2.1.1. R a w m a t e r i a l s ; m a i n c o m p o n e n t s a n d a d d i t i v e s . . . . . . . . . 2.1.2. M i x i n g ; g r a n u l a t i o n . . . . . . . . . . . . . . . . . . . 2.1.3. R e a c t i o n s i n t e r i n g ; i n t e r m e d i a t e p r o d u c t s . . . . . . . . . . . 2.1.4. P r e p a r a t i o n of m o u l d a b l e p o w d e r . . . . . . . . . . . . . . 2.1.5. D i e p r e s s i n g ; o r i e n t i n g field . . . . . . . . . . . . . . . . 2.1.6. Final s i n t e r i n g ; s h r i n k a g e ; grain g r o w t h . . . . . . . . . . . . 2.1.7. M a c h i n i n g (grinding etc.) . . . . . . . . . . . . . . . . . 2.1.8. M a g n e t i z i n g a n d d e m a g n e t i z i n g . . . . . . . . ~ . . . . . . 2.2. Special t e c h n o l o g i e s . . . . . . . . . . . . . . . . . . . . . 2.2.1. Single s i n t e r i n g t e c h n i q u e . . . . . . . . . . . . . . . . . 2.2.2. P r e c i p i t a t i o n t e c h n i q u e s . . . . . . . . . . . . . . . . . 2.2.3. M e l t i n g t e c h n i q u e s . . . . . . . . . . . . . . . . . . . 2.2.4. F l u i d b e d a n d s p r a y t e c h n i q u e s . . . . . . . . . . . . . . . 2.2.5. H o t p r e s s i n g a n d hot d e f o r m a t i o n t e c h n i q u e s . . . . . . . . . . 2.2.6. R o l l i n g a n d e x t r u s i o n t e c h n i q u e s . . . . . . . . . . . . . . 2.2.7. P r e p a r a t i o n of thin l a y e r s . . . . . . . . . . . . . . . . . 3. T e c h n i c a l p r o p e r t i e s of h a r d ferrites . . . . . . . . . . . . . . . . . 3.1. M a g n e t i c c h a r a c t e r i s t i c s at r o o m t e m p e r a t u r e ; s t a n d a r d i z a t i o n . . . . . . 3.2. I n f l u e n c e of t e m p e r a t u r e o n m a g n e t i c p r o p e r t i e s . . . . . . . . . . . 3.3. I n f l u e n c e of d e v i a t i o n from the p r e f e r r e d axis, of m e c h a n i c a l stress, a n d of n e u t r o n i r r a d i a t i o n on m a g n e t i c p r o p e r t i e s . . . . . . . . . . . . . . . . 3.4. V a r i o u s physical a n d c h e m i c a l p r o p e r t i e s . . . . . . . . . . . . . . 3.5. C o m p a r i s o n w i t h o t h e r p e r m a n e n t m a g n e t m a t e r i a l s ; a p p l i c a t i o n s . . . . . 4. B o n d e d h a r d ferrites, p l a s t o f e r r i t e s . . . . . . . . . . . . . . . . . 4.1. M a n u f a c t u r i n g t e c h n o l o g i e s for p l a s t o f e r r i t e s . . . . . . . . . . . . 4.2. T e c h n i c a l p r o p e r t i e s a n d a p p l i c a t i o n s of p l a s t o f e r r i t e s . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
443 443 444 449 451 454 457 458 459 461 462 462 462 464 468 472 480 489 497 508 510 513 514 517 519 525 526 527 535 535 535 550 561 567 577 582 583 585 592
1. General
' H a r d ferrites' are permanent magnet materials on the basis of the phases BaFe12019, SrFe12019 or PbFe12019 as well as their solid solutions, e.g. Bal-xSrxFe~zO~9. After appropriate treatment in production they possess considerable magnetic 'hardness', i.e., coercivity, in an order of magnitude of several 100 k A / m (several kOe)*. Being oxidic the materials are mechanically hard too, but this is not what is meant by the term 'hard ferrites'. Chemically and crystallographically the hard ferrites belong to the large group of hexagonal ferrites which all exhibit hexagonal crystal structures of considerable similarity and among which there are both hard as well as soft magnetic substances. Of these only the hard ferrites on the basis of BaFea2019 and SrFelzO19 are of considerable economic importance. Tonnage-wise they are the main permanent magnet materials in use today, see fig. 77. In contrast, hard ferrites on the basis of PbFe12019 are not in c o m m o n use for magnetic and, in particular, toxicological reasons. 'Plastoferrites' are composite materials composed of hard ferrite powder and plastics. The pulverized particles are embedded in the plastic and this makes it possible to use the advantageous forming methods known in plastics technology for hard ferrite materials as well. This chapter mainly covers the production processes for, and properties of, hard ferrites and plastoferrites and deals with them in detail in sections 2 to 4. Section 1 contains some remarks on their historical development and mentions compositional, crystallographic and magnetic aspects as far as this is necessary for a direct understanding of sections 2 to 4. The fundamentals are covered in detail in chs. 5 and 6 of Kojima and Sugimoto in this Volume.
1.1. Historical development As mentioned in the introduction, the phases BaFe12019, SrFe12019 and PbFe12019 form the basis of the hard ferrite magnets. These can also be written in the form *In this chapter SI units are used first, followed by CGS units, l kA]m ~ 12.57Oe~ 12.50e = 100/80e; 1 mT ~ 10 G; 1 kJ/rn3~-0.1257MGOe ~ 0.125 MGOe = 1/8 MGOe; 100 kA/m ~1.257 kOe ~ 1.25kOe = 10/8kOe; 1 T ~ 10 kG. 443
444
H. ST]kBLEIN
MO.6Fe203 with M = Ba, Sr, Pb. Adelsk61d (1938) was the first to correctly describe the composition and crystal structure of these phases. H e thus established a link with the results of earlier work on the mineral magnetoplumbite (Aminoff 1925, who also proposed the name; Blix 1937), the structure of which is isomorphous with those of the compounds mentioned above and whose composition was described by Berry (1951) as PbFeT.sMn3.sA10.sTi0.5019. Some of the Fe ions are substituted by manganese, aluminium and titanium. Aspects relating to the structure of these substances and their relation to similar lattice structures of the/3-A1203 type (Na20"llA1203) or the aluminates MO.6A1203 (M = Ca, St, Ba) were of particular interest at the time, while the magnetic properties hardly aroused attention. Only the high magnetizability of magnetoplumbite was mentioned (Aminoff 1925, Flink 1924) and this characteristic was utilized for separating magnetoplumbite from non-magnetic admixtures (Blix 1937). In this connection it should be mentioned that Hausknecht (1913) had already experimented with mixtures of iron oxides and barium oxide and discovered an abnormally high magnetism in annealed specimens roughly composed of BaO + 5Fe203 but did not look further into the question of structure. Further details on the manufacture of BaFe12019 from mixtures of Fe203 and BaCO3 were given by Erchak et al. (1946) to the effect that t h e compound forms during annealing at a temperature above around 750°C in an oxygen atmosphere. The occurrence of the compound was proven with atomic ratios Fe/Ba ~ 4 with emphasis on Fe/Ba ~ 12. Initially merely of an academic nature, interest in this compound changed rapidly when from about 1950 its magnetic properties were investigated more closely. At that time the soft magnetic (cubic) spinel ferrites developed at Philips were already known (Snoek 1947). In the further course of this work the considerable crystal anisotropy of BaFe~2Oi9 was discovered and a technology developed which permitted it to be utilized as a permanent magnet material (Went et al. 1952, Rathenau et al. 1952). Independently of this and almost at the same time, researchers at Krupp discovered the hard magnetic properties of this material and put them to use (Fahlenbrach 1953, Fahlenbrach et al. 1953). Since then hard ferrites have been increasingly used as permanent magnets throughout the world, not only in electrical engineering. They proved particularly suitable in the area of magnet mechanics where the forces set up by magnetic fields are utilized for adhesion, attraction, repulsion, clamping, rotating, etc. On the work done in parallel by researchers, manufacturers and users in the field of hard ferrites there is a vast amount of literature. Some of this is referred to in the pertinent sections below. Further information is found in chapters 5 and 6 by Kojima and Sugimoto in this Volume.
1.2. Aspects for applications as permanent magnet material The potential suitability and actual use of any material for a specific purpose depend on a number of physical and economic factors. For permanent magnet applications in particular the material is expected to exhibit the following properties:
HARD FERRITES AND PLASTOFERRITES
445
(a) Magnetic saturation polarization* Js should, at least up to r o o m t e m p e r a t u r e and preferably appreciably above r o o m temperature, be as large as possible. (b) Coercivity must be sufficient for the same t e m p e r a t u r e range. T o be able to achieve this, there must be preferred directions for the spins which correspond to a sufficiently large minimum of free energy so that the spins are coupled to these directions. (c) For the same t e m p e r a t u r e range the material should be stable both structurally and chemically. (d) T h e cost of the material and of production should be low in relation to the characteristics attainable. This means in particular that starting materials needed are available in adequate quantities, are of sufficient purity and easy to handle, that the composition of the material in terms of main and accompanying constituents and the individual stages of production in terms of level and variations of temperature, time, pressure and atmosphere, the required aids etc. are sufficiently inexpensive and non-critical and that suitable forming facilities are available. For none of these aspects is there a clear-cut, generally applicable limit governing suitability or non-suitability as a p e r m a n e n t magnet material. Which material is best suited to any particular application depends on how all the attendant circumstances are taken into account. The question that concerns us here is how hard ferrites m e e t requirements (a)
to (d). (a) Saturation polarization of the c o m p o u n d BaFe12019 at r o o m t e m p e r a t u r e is described by Stuijts et al. (1954) as Js = 0.475 T (4.75 kG). It is thus considerably below that of iron (2.15T) or that of AlNiCo alloys (up to about 1.4T). In commercial hard ferrites the value is up to about 10% lower owing to the porosity of the samples, the presence of non-magnetic phases and, perhaps, partial substitution of iron ions by, for instance, aluminium. T h e r e has thus been no lack of attempts at finding substitutes to increase the saturation polarization but as yet without appreciable success (Schieber 1967, Asti 1976). An exact comparison of the values given in literature as saturation polarization is often problematical, however, if the composition and homogeneity of the specimens are not exactly defined and an adequate field strength was not allowed for in measuring. In fig. 1 the saturation polarization of BaFe12019 is shown as a function of t e m p e r a t u r e (Smit et al. 1959). The Curie t e m p e r a t u r e of about 450°C is still relatively high but at about -0.2% /K the slope of the curve is unusually steep. The resultant change in the magnetic flux can be very undesirable in certain applications. Suitable substitutes were therefore tried to improve t e m p e r a t u r e variation (Heimke 1960, Esper et al. 1972, 1975, H a n e d a et al. 1975). This aim has * In this chapter the term "magnetic polarization" or, shortly, "polarization" J is used as defined by the International Electrotechnical Commission in IEC Publication 50(901), Advance edition of International Electrotechnical Vocabulary, 1st ed., 1973 (term no. 901-01-13), It is connected to "magnetization" M (term no. 901-01-07) and "magnetic flux density" B (= "magnetic induction"; term no. 901-01-03) by J =/x0M = B -/*oH, where magnetic constant/z0 = 4~- × 10 vH/m (term no. 901-0111),
446
H. ST~BLEIN 150 mT.crn3 g
4
7
--".,,.
5o
, -273-200
i
o
I
200
°C
\ ~oo
Fig. 1. Saturation polarization Yjsample density p of BaFe12019as a function of temperature (Smit et al. 1959). been essentially achieved but only by way of incurring other inevitable drawbacks that have so far prevented practical use. The magnitude and temperature variation in the saturation polarization of hard ferrites therefore do not compare very favourably with other permanent magnet materials. (b) The hard ferrites have a relatively high crystal anisotropy energy Ek which for these hexagonally crystallizing substances can be simply expressed as Ek = K sin 2 0. In the Weiss domain considered, 0 is the angle between c-axis and polarization Js (see fig. 39) and K is the anisotropy constant. According to Rathenau et al. (1952), at room temperature it has roughly the value K = + 3 × 1 0 5 J / m 3 ( + 3 × 106 erg/cm3), which means that the c-axis is the preferred direction for the spins and re-magnetization of a domain should take place at a reverse field (anisotropy field HA) of 2K/Ys = 1260 kA/m (15.8 kOe), provided that re-magnetization occurs in a single-domain particle by coherent rotation of the spins. Assuming the same conditions in a texture-free specimen, polarization should disappear wher~ there is a counter field of 0.96K/Js = 600 kA/m (7.6 kOe). Coercivities of up to 80% of this value have in fact been found; however, only in very fine particles of around 0.1 p~m (Mee et al. 1963, Haneda et al. 1973a, Gordes 1973). In commercial specimens the crystallites are present in sizes of around 1 ~m, and only smaller jHc values are attained. In fig. 2, K, and in fig. 3, 2K/Ys and 0.96K/Js are plotted as a function of temperature (Rathenau et al. 1952). From the latter the coercivity might be expected to be largely independent of temperature. In fig. 3, however, it can be seen from the jH~ curve of a specimen having crystallites of around 1 p~m that this is not the case, the temperature coefficient of this specimen being about
HARD FERRITES AND PLASTOFERRITES
447
3 m3
% i
-200
i
0
i
200
~ - -
°C400
T Fig. 2. Crystal anisotropy constant K of BaFe12019 as a function of temperature (Rathenau et al. 1952).
1600 k__~A m
20
I
kOe
H = 2___~K
1200
15
800
10
HA ~00
5
'o c
6000
T
Fig. 3. Anisotropy field HA = 2K/Js for anisotropic and HA = 0.96K/Js for isotropic BaFe12019 and coercivity jHc of fine-grained sintered specimens (~1 p,m) as a function of temperature (Rathenau et al. 1952).
+0.4% /K at room temperature and thus fairly high. The temperature dependence of jHc in specimens with crystallites of varying sizes was also measured by Sixtus et al. (1956). The deviation of the quantities 0.96K/Js and ]/arc from one another is explained by the formation and shift of domain walls during re-magnetization (Goto et al. 1980). Although the coercivity jHc of commercial hard ferrites is thus appreciably below the theoretical value, it is attractively high enough for a large number of
448
H. ST,~d3LEIN
applications. It was several times higher than that of the AlNiCo materials then commonly used. The resultant stability of the magnetic flux meant that the hard ferrites could be rapidly introduced into dynamic permanent magnet applications with very beneficial consequences. A more detailed description of Js and K of the various hexaferrites is given in sections 3.1 and 3.2. (c) A stable structure can by no means be taken for granted in permanent magnet materials. In a number of materials the structure at room temperature is in a 'frozen', metastable state which by diffusion or allotropic transformation can change towards equilibrium as a result of a temperature rise, for instance, this having an adverse effect on the magnetic values, especially the coercivity. This phenomenon is termed 'structural ageing' which in most materials occurs far below the Curie temperature and thus imposes restrictions on the actual use of the magnets. Hard ferrites are an exception in this respect. Their structure remains stable far beyond the Curie t e m p e r a t u r e - i n Ba- and Sr-based hard ferrites up to temperatures of more than 1400°C (in air) before oxygen is released and phase transformations occur; cf sections 1.3.1 and 1.3.3. Chemical stability prevails when the material does not react with the ambient medium. Naturally, the type of reaction and its extent depend on the medium. As the cations of the BaFe12Oi9 and SrFe120~9 lattices are in the highest state of oxidation, these materials are stable and not liable to oxidize which is an advantage over metallic materials. Data on the stability of the hard ferrites in different media are given in section 3.4. (d) With hard ferrites the costs of materials and production are lower than in other grades of permanent magnets if related to the same energy content. A number of favourable circumstances contributes to this, some of which may be briefly mentioned here. Detailed technological information is given in section 2.1. The raw materials required are inexpensive, abundantly available and easy to handle. Extreme purity is not necessary. As a rule the iron oxides used have 0.5 to 1% by weight of impurities, and natural hematite (a-Fe203) or iron oxides from wastes can also be used. Powder metallurgical treatment is effected by the time-tested methods used in the ceramics industry and, in the case of the plastoferrites, in the plastics industry. The temperatures necessary for the raw materials to react to form ferrite ('calcination') and for sintering are normally around 1200°C to 1300°C. Both processes take place in air, while with metal powders a protective atmosphere or vacuum is always required. For the highgrade ferrites a powder consisting of single-domain particles in sizes of 1 ~zm or less is needed, a fineness which can easily be adjusted by grinding in water. With metal powders, however, water would not be suitable as a grinding fluid so that as a rule organic liquids have to be used which, in view of pollution control requirements and for health reasons, are more difficult to handle. The powder is generally shaped by one-sided or two-sided pressing in a die and the plastoferrites by injection moulding, calendering, etc., i.e., by well-known processes. General information and special aspects of the requirements (a) to (d) are
HARD FERRITES AND PLASTOFERRITES
449
described, for example, in the books and papers of Von Aulock (1965), Becker (1962), Gmelin (1959), Heck (1967), Heimke (1976), Landolt-B6rnstein (1962, 1970, 1981) and Smit et al. (1959) as well as in the books mentioned at the end of section 3.5.
1.3. Compositionsandphasediagrams A number of relevant phase diagrams is discussed in this section. The information from the diagrams is, among other things, useful in the following questions and problems: (1) The diagrams furnish information on the existence ranges of the hexaferrite phases MO.6FezO3 (M, e.g. Ba, Sr, Pb) in terms of composition, temperature and oxygen partial pressure. (2) They furnish information on further phases MO.nFe203 (n = molar ratio of Fe203 and MO) which may form as intermediates ('precursor phases') in the reaction of the raw materials or which are present after the reaction in equilibrium with the hexaferrite phase. Some of these phases play an important role for production and properties. The emphasis is placed on the quasi-binary systems MO-Fe203 because these are relatively easy to discuss and represent good approximations even for more complex conditions. Such conditions obtain in practice because apart from the main constituents MO and Fe203 the magnet specimens contain further substances introduced intentionally or otherwise which are important and sometimes decisive for the production process and properties. The relevant quasi-ternary and
1600 oC
!N
'
Liq!id
~
l"°°,s .'-
l@"
..
1565 °
7
T 1200
l
I"e " i
1000 11 II 8°°2
'1 B2F
BF .BF"+,,M"
1' 60
'
BF
80
LI
PI
~
1o0 | %5
rnol % Fig. 4. Phase diagram of BaO-Fe203 (Ooto et al. 1960). Atmosphere: 02 above and air below
eutectic temperature.
450
H. STJid3LE1N
higher phase diagrams are therefore also mentioned. This section concentrates on the compositions that are significant for magnet engineering and magnet applications, i.e., on the side of the systems that is rich in Fe=O3. In connection with the phase diagrams there is of course the question as to the possible substitutes in the anion and cation sublattices of the hexaferrites. Here, too, only the most important are mentioned; more detailed information is given in chapters 5 and 6 of Kojima and Sugimoto in this Volume. The following abbreviations are used in the phase diagrams and in the text: B - = B a O ; S-= SrO; P - = P b O ; F-~Fe203; M--= (Ba, Sr, Pb)O.6Fe203 (magnetoplumbite), if need be by BaM, SrM and PbM; as to X and W see table 2. 1600 oC
,..¢'_
l~lot5 o
_7%50°
I /
I
I 1200
c~-B F+ M
I I
I I I
I1~5oz5o i
I~-BF .BF~
I000
Ip_BF+BE
'r--+:
800 _ _ ~ _ - B F * B ~ ~o
I B~
0•
IF _F
i
80
60
B5
too/%
100 M
~2o3
=
Fig. 5. Phase diagram of BaO-Fe203 (Batti 1960). Atmosphere: 02 for liquids, otherwise air. 1600
,2o,
~-
3 ,26o~
~BF-+L~
'
/
W-I
1338 °
M+j
'
,oo
me/ %
Fig. 6. Phase diagram of BaO--Fe203 (Ziolowski 1962). Atmosphere: air.
HARD FERRITES AND PLASTOFERRITES
451
Phase designations in inverted commas mean that owing to an appreciable homogeneity range the actual composition may deviate from the one indicated in the formula. 1.3.1. B a O - F e 2 0 3 system T h e systems and subsystems mentioned by G o t o et al. (1960), Batti (1960), Ziolowski (1962), Van H o o k (1964), Sloccari (1973) and A p p e n d i n o et al. (1973) are given in figs. 4-12. They do not correspond in all details. T h e following may be stated: H o m o g e n e i t y range. According to Van H o o k (1964) BaFe12019 is in terms of oxygen content and cation ratio stoichiometrically at least within 1600 oC
Liquid B2F
1495° / 14550/..
L+B~. .~.
--/L
1400 .....
9F÷L ~,Z/
t
..xl,.
l-x÷%q
+M 1315+..5°
BF+M
B2F+ BF 1200 40
20 B2F
60
II
ao
too
Mxw %03
BF
rnol % Fig. 7. Phase diagram of BaO-Fe203 (Van Hook 1964), isobaric projection with 02 atmosphere of i bar (the compounds Fe304, X and W also contain Fe2+).
1600
,
0C
BF+ L
Liquid L
~ """
. s . ~ ~''~
.~ "" ""
L+Fe304
I ~00 M÷Fe3q
sF÷w
iT -
w÷%£
8F÷ X
1200 - -
M'FsO~ M BF+ M
I000
60 BF
F ÷ 80
I00 MXW Fe203
tool %
Fig. 8. As fig. 7, but with COz/CO atmosphere
(1OO2 ~
0.01 bar).
452
H. ST]/d3LEIN
Baa+0.04Fe12019_+0.03 between room temperature and 1450°C at Po2 = i bar. Other authors who examined specimens made in air or oxygen arrived at the conclusion too that there is only a very small homogeneity range (Batti 1960, Ziolowski 1962, St~blein et al. 1969, Reed et al. 1973, Lacour et al. 1975a and Sloccari et al. 1977a). According to Goto et al. (1960) however, the homogeneity range extends from BaO-6Fe203 to BaO-4.5Fe203 (1350°C) and to BaO.5Fe203 (800°C) respectively. The cause of this discrepancy has not yet been reliably clarified. It is conceivable, however, that the specimens deviating from the stoichiometric composition were of the two-phase type and that the BaO.Fe203 phase was overlooked. This is possible because its presence, particularly in small amounts, is difficult to verify or not at all verifiable radiographically and because it easily dissolves in concentrated muriatic acid so that it cannot be detected microscopically in specimens thus prepared.
I
1600 oC
z/L +
, / Fe203
Liquid f~ I
1~O0
" F'~,~ I L+BF~ ~ .
//.L+M M BF+M
Fe203
1200 i
i
~0
80
60 BF
M
I00 Fe203
tool %
l°c{
Fig. 9. As fig. 7, but with 02 atmosphere of 40 bar. 103
riK]
1650
O.52
i ~6oo
0.5~
1550 0.56
M= X+L~
Q58
1500 E 1450 1400
(2.60 i
OOt
o7
i
7
lb
bar 76g
Oxygen pressure
Fig. 10. Decomposition of barium hexaferrite M as a function of oxygen pressure and temperature compared with that of Fe203 (Van Hook 1964).
H A R D FERRITES AND PLASTOFERRITES
453
,BF+ M ii150o+10o
1200 oC
tO00 BF
BF,M
+
55
2
800
dO
6,0
80
100
rnol % - - ~ Fig. 11. Phase diagram of BaO-Fe203 (Sloccari 1973). Atmosphere: air.
1200 oC
1000
800
'
1
j--'
11100 c~-BF+M
r - ! I
0- Fy3 i 0ol ~o I BF
~
I
80 z %5
M
I00 Fe 0 23
tool %
Fig. 12. Phase diagram of BaO--Fe203 (Appendino et al. 1973). Atmosphere: air.
Recently, the existence of a metastable compound BaO.nFezO3 with n = 4.0 to 5.8 at 600°C and n ~-- 16/3 at 900°C was reported (Durant et al. 1980, 1981), decomposing at 950°C and having nearly the same lattice parameters as BaO.6Fe203 (see table 31). BaFe12Oa9 is unstable at elevated temperatures. At a pressure of Po2 ~ 0.01 bar the hexaferrite, as can be seen in fig. 8, releases 02 and disintegrates into the phases BaFelsO23 ('X-phase'; BaO-FeO.7Fe203) and BaFe204; at Po2 = 1 bar there is, as can be seen in fig. 7, a peritectic reaction attended by the formation of the X-phase, and it is only at Po2 = 40 bar, as can be seen in fig. 9, that (almost) congruent melting takes place at about 1500°C (Van H o o k 1964, 1976)o This latter fact deserves attention in making BaFe12019 monocrystals from the melt, cf. Menashi et al. (1973). Figure 10 gives the decomposition temperature as a function of pressure Po2. In air it is around 1430°C, a somewhat smaller value than according to the phase diagrams in figs. 5 and 6. Towards lower temperatures the hexaferrite lattice is completely stable as all experience gathered so far has shown.
454
H. STJLBLEIN
Neighbouring phases. All phase diagrams correspond in that on the side richer in Fe203 no further B a - F e - o x i d e phases occur below 1250°C, i.e., the two-phase field (BaFe12019 + c~-Fe203) occurs there, cf. figs. 4, 5 and 7 to 9. Conditions on the side of BaFe12019 richer in B a O are not so clear, cf. table 1. BF, BzF3 and BF2 are mentioned as neighbouring phases. As can be seen from figs. 6 and 12, BF occurs in several modifications (Ziolowski 1962, Meriani 1972, Appendino et al. 1973, Haberey et al. 1974). BaFe12019 and BaFe204 (BF) form an eutecticum for which eutectic temperatures between 1315 and 1370°C are given. The two phases BzF3 and BF2 occur only up to 1150°C maximum and the adjustment to equilibrium proceeds very slowly (Ziolowski 1962, Sloccari 1973, Appendino et al. 1973) which perhaps explains why these phases were not found by other workers.
1.3.2. BaO-Fe20~-based systems As mentioned above, the hexaferrite decomposes at elevated temperatures and oxygen partial pressures that are not excessively high to form the 'X-phase' BaO.FeO.7Fe203, cf. figs. 7, 8 and 10, at which one of every 15 Fe ions is in a two-valued state. T o represent this compound in the quasi-binary system B a O Fe203 is therefore incorrect. Figure 13 shows the Fe203-rich portion of the B a O - F e 2 0 3 - M e O system, with Me meaning a divalent cation, e.g., a 3d-element, i.e., particularly Fe 2+. The letters correspond to certain stoichiometric compositions explained in detail in table 2. Compounds of the X-, W-, Z- and Y-type were described by Braun (1957), cf. Smit et al. (1959). Later, further compounds were found which range between M and X or between U and Y (Kohn et al. 1971). In total the structurally allied compounds lying on the straight lines M - W and M - Y are identical with the designation 'hexagonal ferrites'. Also stackings of mixed hexagonal ferrites are known and were investigated by means of high resolution electron microscopy and diffraction (Hirotsu et al. 1978, Van Tendeloo et al. 1979). Investigations into the B a O - F e 2 0 3 - F e O system were carried out by Batti (1961a). In the system BaO-FezO3-ZnO, Slokar et al. (1978a) found the corresponding X-, W-, U-, Z- and Y-phases at 1200°C in air. An outline of various systems is given by Batti (1976). A material with composition 3BaO-4FeO-14Fe203 was reported by Brady (1973) and Durant et al. (1981). G o t t o (1972) and Mansour et al. (1975) compiled further B a - F e - o x i d e compounds containing Fe 4+ or Fe 6+ in addition to Fe 3+. A comprehensive review on the BaO-Fe~O3-FeO system and on crystallographic and magnetic data of the compounds involved was given by Sch6ps (1979). Batti (1961b) carried out investigations into the BaO-FezO3-AI203 system at i bar 02 and 1300°C. It was found that iron can be substituted in the compound BaFea2019 up to the composition BaFe4.zA17.8019. Only a few investigations were made to find out whether Ba can be substituted by Ca. According to Van Uitert (1957) up to 70 at.% of Ba can be replaced without changing the lattice type. According to investigations by Sloccari et al. (1977a) into the B a O - F e 2 0 3 - C a O system, there is a solid solution between BaFe12019 and a hypothetical CaFesO13 at 1100°C in air up to a molar ratio of about 1.75 : 1. In a later paper the homogeneity range was defined more precisely
~2
tt~ tt~
I
I
I
I
v
III
0
© ~7
(.q c~
6
©
III 0
.r"0 ;>
0
t~
.r.
0 e'~ ,,..,
'=~
C,
A
A
.=Z
6
©
Z
0 e~ 0 t'~ 0
< 455
456
. H. ST~d3LEIN
I00~
9O
tool % BaO Fig. 13. Quasi-ternary system FezO3-BaO.Fe203 (BF)-MeI10-Fe203 (S). Symbols explained in table 2.
TABLE 2 Compounds of the quasi-ternary system BaO-Fe203-MeO, Me--Divalent cation, e.g., Fe z+, Zn 2+. Stoichiometric composition (mol %)
Compound Symbol
Formula
BaO
MeO
Fe203
S BF T (hypothetical)
2(MeO.Fe203) BaO-Fe203 BaO.2Fe203
50 33.3
50 -
50 50 66.7
M M6S M4S X (M2S) W (MS)
BaO.6FezO3 2(3BaO-MeO. 19F~O3) 2(2BaO.MeO. 13Fe203) 2(BaO.MeO.7Fe203) BaO.2MeO.8Fe~O3
14.3 13.04 12.50 11.1 9.1
4.35 6.25 11.1 18.2
85.7 82.61 81.25 77.8 72.7
U (M2Y) Z (MY) Y
2(2BaO.MeO.9Fe~O3) 3BaO.2MeO. 12Fe203 2(BaO.MeO.3Fe203)
16.7 17.6 20.0
8.3 11.8 20.0
75.0 70.6 60.0
HARD FERRITESAND PLASTOFERRITES
457
(Lucchini et al. 1980a) and established that the primary magnetic properties were not changed substantially by the Ca substitution (Asti et al. 1980). According to Kojima et al. (1980) (CaO)l_x(BaO)x'n(Fe203) has a solubility range of x = 1.0 to 0.6 and n = 5.0 to 5.6. Isotropic magnets with Br = 222mT, (BH)ma~= 10.2 kJ/m 3 (1.28MGOe), BHc = 121 kA/m (1.52 kOe) and 1He = 168 kA/m (2.12 kOe) were prepared. The subject is also dealt with in section 1.3.7. The BaO-Fe203-SiO2 system is of particular interest owing to the usual addition of SiO2 in the commercial manufacture of permanent magnets. Haberey (1978) and Haberey et al. (1980a) furnished a tentative diagram for air atmosphere. At 1250°C, up to 0.55% by weight of SiO2 dissolves in BaFe120~9. Any surplus forms a second glassy phase which is rich in SiO2, has a melting point of about 1050°C and promotes sintering while impeding grain growth, cf. section 2.1.6. St/iblein (1978) too, found a glassy phase of very similar composition. 1.3.3. SrO-Fe203 system This system was examined by Batti (1962a) in I bar 02 and by Goto et al. (1971) in air. Their findings are shown in figs. 14 and 15, respectively. Both diagrams agree very well. The homogeneity range is very narrow and in the eutectic range somewhat enlarged, at most towards the side rich in SrO (Routil et al. 1974). Towards higher temperatures incongruent melting occurs at 1448°C (1 bar 02) and 1390°C (air), with the W-phase SrFe18027 (=SrO.2FeO.8Fe203) being formed. Haberey et al. (1976) likewise observed the formation of the W-phase in annealing in air above 1300°C, while in vacuum annealing above ll00°C Fe304 and 87F5 (or $4F3)formed with the release of 02. In contrast to the behaviour of BaFe12019 (figs. 7, 8, 10), in 8rFe12019 the corresponding X-phase was only found as an intermediate product (Goto 1972). Towards lower temperatures SrFe12019 is stable according to experience hitherto gained.
1600 oC
L'+SF., ~~ 1600°t100 lSO0o
~ ~ > ,
Liquid 1520°'10° 1
J
1400
, s;
÷
1210o+_10° S F+M 75
1200 ,
M Fe203
L÷M
I
f
1448°?_10°
"55 :L i
0
20
60
80
I00
Fe203
rnol ~ = Fig. 14. Phase diagramof SrO-Fe203 (Batti 1962a). Atmosphere: 02.
458
H. STJ~d3LEIN
1600 oC
i
l~O0
SrFe(}-x'L---1225+-~ 1200
•
L÷M
55.L M 6"0203
I000
8O0
0 SrO
20 ZO SrFe03x 5 5 -
i
60 rnol %
'l
80
DO
M
Fe25
Fig. 15, Phase diagram of SrO-Fe203 (Goto et al. 1971). Atmosphere: air.
Towards the Fe203-richer side the two-phase region (SrFe12019+ o~-Fe203) follows analogous to the BaO-Fe203 system. On the SrO-richer side the phases S7F5 and $3F2 are given in figs. 14 and 15 as neighbouring phases, both of them being very close to the composition $4F3 mentioned by Kanamaru et al. (1972). The eutectic temperatures of 1210°C (1 bar 02) or 1195°C (air) as well as the eutectic contents of 53.8 or 55 mole % Fe203 are close to one another. An SF phase analogous to BF does not Seem to exist (Routil et al. 1974, Haberey et al. 1976, Vogel et al. 1979a).
1.3.4. SrO-Fe2OB-based systems Very little has become known on investigations into the SrO-Fe203-MeO system. As mentioned above, the occurrence of the X- or W-phase was observed especially for Me = Fe 2+. In the S r O - F e 2 0 3 - Z n O system Slokar et al. (1978b) found the corresponding X- and W-phases at ll00°C in air. In the Sr-Fe oxide compounds containing proportions of F e 4+ a r e found more frequently than in the B a - F e oxides (Brisi et al. 1969, Goto 1972). In fig. 16 the compounds known from literature are compiled (Haberey et al. 1976). A review was also given by Sch6ps (1979). Investigations into the SrO-FeaO3-A1203 system at 1 bar 0 2 and 1200°C were carried out by Batti et al. (1967); a complete solid solution between SrFe12019 and SrAl12019 was found. The SrO-FeRO3-CaO system was investigated by Lucchini et al. (1976). It was found that at 1100°C in air there is a solid solution with M-structure between
HARD FERRITES AND PLASTOFERRITES
459
SrO
sue°g x Sr. Fe 0
20
-
Sr Fe 0
SrFe03-~"/~'-"""~- / ,
t S.Ze. o~
'°2
h
J~
(SF)
Z/\/\ 2(FeO2 )
80
60
/\
/\
gO
20
Fe203
mol % 2(FeO2) Fig. 16. Compositionsof the Sr-Fem-FeTM oxides mentioned in literature (Haberey et al. 1976). SrFe120 m and a hypothetical CaFesO13 up to a molar ratio of about 2: 1. On re-examination the result was not confirmed completely (Lucchini et al. 1980b). The primary magnetic properties were not changed substantially by the Ca substitution (Asti et al. 1980). According to Kojima et al. (1980) (CaO)l-~(SrO)x.n(Fe203) has a solubility range of x = 1.0 to 0.6 and n = 5.0 to 5.6. Isotropic magnets with Br = 220 mT, (BH)max = 10.7 kJ/m 3 (1.34 MGOe), ~Hc = 153 kA/m (1.92 kOe) and jHc = 218 kA/m (2.74 kOe) were prepared. The subject is also dealt with in section 1.3.7. Investigations into the SrO-FeaO3-SiO2 system were carried out by Kools (1978a), Kools et al. (1980), Haberey (1978) and Haberey et al. (1980a). At 1250°C they found the maximum solubility of SiO2 in SrFe12Om to be 0.6 and 0.4% by weight. Any additional SiO2 leads to the occurrence of phases which at usual sintering temperatures are liquid and, similarly to barium hexaferrite (section 1.3.2), promote sintering and impede grain growth, cf. section 2.1.6. The occurring phases were also reviewed by Broese van G r o e n o u et al. (1979b). 1.3.5. P b O - F e 2 0 3 system
The phase diagrams in air given by Berger et al. (1957) and by Mountvala et al. (1962) are shown in figs. 17 and 18, respectively. Concerning the homogeneity range of the hexaferrite phase, there is only moderate agreement. While Berger et al. (1957) give no appreciable homogeneity range, Mountvala et al. (1962) have found such a range from PbO-5Fe203 to
H. ST,g~BLEIN
460
...:-"..J /I
/J .,'
1400 oc
/
r / ,, /
•/
,PJ
! ! ! !
t
/ ,"
~
I
/
/
, /
I
/
' --- ~ pl
I I A~ "--
/7 \ \\
Viscous or / Granular ,,,
/
\ \
,
\ \
- \\
f
x "
1/
\
~%03
I
solid
"P F+PF
/LL%~I..... z: z/" '°2 F÷ Fe203
20
P~o
/
/L÷MI
%F+W
¢../
i
PbO÷P2F
6000
/
/
/ ~
t
// / L"r?;÷%%
, ,~._
1200 Gelantineous
[
,'
iI
Liquid
/I
#
I P~°:%5
5~
~o
,
60
8ol
~%
mol %
lw
M
~-~o~
=
Fig. 17. Phase diagram of PbO-Fe203 (Berger et al. 1957). Atmosphere: air.
1~00 °C
! /.. - _,
L+Fe203
1
/ 1200
1315°
//
L +.NI'"
]1
/I
looo
-
"\\
i
o~,
/L÷%~-
,oo~I PbO+L ,,~ \ I[
o I
%~-.e% ,
I"C% .M'"
II1 " 7 6 0 °
750°
i ..... ,,j..;~_o__j] -;~÷~%% Pbo
;'o--:,%
'
%F tool %
I I
' "%"~~%%~oo
,o ,' P~
,'
M
~o£~
=
Fig. 18. Phase diagram of PbO-Fe203 (Mountvala et aI. 1962). A t m o s p h e r e : air.
HARD FERRITES AND PLASTOFERRITES
461
PbO.6Fe203. The results obtained by Cocco (1955) who found a solid solution between the boundaries PbO-2.5Fe203 and PbO-5Fe203 show an even greater variance. It should be taken into account, however, that according to Adelsk61d (1938) only the composition PbO.6Fe203 explains the measured radiographic data and density values, not, however, the composition PbO@Fe203, for instance. The existence of the PbO-rich side of the PbO.6Fe203 phase therefore cannot be regarded as being proven beyond doubt, especially since equilibrium adjustment proceeds very slowly and the structures of PbO.6Fe203 and of the neighbouring phase richer in PbO are very similar and so it is difficult to distinguish between them radiographically. The thermal stability of lead hexaferrite is rather small in comparison with that of the Ba or Sr compound, namely 1250°C (Berger et al. 1957) and 1315°C (Mountvala et al. 1962); one of the decomposition products is o~-Fe203. Nothing is known about the presence of FeO-bearing compounds such as X, W, Y etc. in the PbO-Fe203 system. The differences mentioned are probably attributable to the high vapour pressure of PbO (Berger et al. 1957, Bowman et al. 1969). Towards lower temperatures the phase diagrams shown give rise to confusion as they seem to indicate the decomposition of the compound PbO-6Fe203 below 820° and 760°C, respectively. However, even after prolonged anneals of up to 1000 h in the range from 650 to 850°C this could not be determined (Berger et al. 1957). The diagrams should therefore be interpreted to the effect that no formation of PbO.6Fe203 was observed from the starting materials at these low temperatures. All workers unanimously mention o~-Fe203 as neighbouring phase for the side poorer in PbO, but PzF and PF2 for the side richer in PbO, each forming low-melting peritectics with PbO-6Fe203 at about 900 and 950°C, respectively. This is of importance for the industrial manufacture of the Ba or Sr hard ferrites when small additions of PbO are added to the raw mix as a flux.
1.3.6. BaO-SrO-PbO-Fe203-mixed systems In view of the identical structure and the only slight difference between the lattice constants of the compounds MO.6Fe203 (M = Ba, St, Pb) (maximum deviation Ac/c = 6.5%~ after Adelsk61d (1938); see also table 31) it is obvious that complete miscibility exists in the entire region of stoichiometric composition, cf. Goto (1972). Special conditions may, however, occur on the side poorer in Fe203 when the composition is not stoichiometric because the structure and molar ratio FezO3/MO of the neighbouring phases differ depending on the type of oxide MO. Batti (1962b) examined the compounds of the BaO-SrO-Fe203 system produced at 1100°C and found that depending on the BaO/SrO ratio the phases BF (Ba can in part be substituted by Sr), BSF2 (a small portion of SrO can be substituted by additional BaO) and $7F5 o c c u r . Later on isothermal sections up to 1235°C were investigated by Batti et al. (1976). Batti et al. (1968) synthesized specimens of the BaO-SrO-FezO3-AI203 system at 1400°C in i bar O2 and found that iron can be largely substituted by aluminium in the entire Bal-xSrxFe12019 region. Equal solubility of CaO was found in the entire range of BaxSrl-xFe12019 (Sloccari et al. 1977b).
462
H. STJ~BLEIN
1.3. 7. CaO-Fe203-based system In spite of the close chemical affinity of calcium, strontium and barium no hexaferrite phase exists in the system CaO-Fe203 (Adelsk61d 1938), probably because of the smaller ionic radius of Ca. However, a magnetic Ca hexaferrite phase can be stabilized by the presence of at least 2 mol % La203 (Ichinose et al. 1963, Lotgering et al. 1980). From this material isotropic and anisotropic grades exhibiting useful magnetic properties can be prepared (Yamamoto et al. 1978a, 1979a) even if La203 containing some Nd203 is used (Yamamoto et al. 1980). The magnetic properties can be improved by substitution of Ca by Ba (Yamamoto et al. 1979b) or by Sr (Yamamoto et al. 1978b).
2. Manufacturing technologies of hard ferrites
2.1. Usual technology The principle underlying the usual manufacturing process is shown diagrammatically in fig. 19. The raw materials used are generally the barium and strontium carbonates as well as natural and synthetic iron oxide o~-Fe203 (rarely magnetite Fe304). In addition to these main constituents so-called additives such as SiO2, A1203 etc. are used individually or combined in amounts of about 0.5 to 2.5% by weight. They serve to control the reaction kinetics, shrinkage and grain growth (see section 2.1.6) but sometimes they also affect the primary magnetic properties of the hexaferrite phase (saturation polarization, crystal anisotropy energy). The raw materials are intimately mixed and, if required, granulated or briquetted, and annealed at temperatures of between about 1000 and 1300°C in air ('reaction sintering', 'calcination'). Hexaferrite is thus produced more or less completely as a reaction product. The reacted mass is crushed and ground to a powder of sufficient fineness. There are several possibilities for further treatment depending on which magnet grades are to be manufactured. (a) Being anisotropic, the highest grades are obtained by wet compression moulding in a magnetic field. For this purpose the aqueous suspension, whose ferrite particles are, in the ideal case, single crystals and consist of a magnetic domain, is poured into the mould cavity. A magnetic field is applied to align the ferrite particles, thus producing a 'preferred direction' in the suspension. Compression takes place in this state, removing most of the water. (b) Not quite such high anisotropic grades are obtained by dry compression moulding of ferrite powder in a magnetic field because with this process the particles cannot be as easily aligned. The ferrite powder is obtained by removing the water and drying the ground suspension. The resultant caking of the ferrite particles impairs the directional effect of the magnetic field, which is the reason why the dried mass has to be loosened. (c) For the lowest (i.e. isotropic) grade the powder does of course not have to be alignable in compression moulding. The dried powder is therefore turned into an easier-to-process granulate which is compacted in dry condition.
HARD FERRITES AND PLASTOFERRITES
463
Section
J (4 milling)
dry [ wet
2,1.2
Granulation or of ready-to-
hard powderferrite fromraw press
materials
_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I Reaction sintering I 4 .......
.............
I 2.1.3. ~ ............
',
I ,,r ,orushio
I
Wetm""ng
O-con'ent I' I
__/
Ioeogglomerotionl Gronu,ot,on with binder
/
PressureFiltrati°n] I magnetic Drypressingin I ~ Orypressing .......... field 4 in magnetic field ~ ................ I~
I
Production of shaped from powderParts
onisotropic magnets
. . . . . . .
-
-~
I~
l
anisotropic
I
I ~
mag,',ets I I
~-q2
- ~ - -
-..7--- ~
2.1.5.
isotropic | magnets I
--~J- -
I Final sintering I
. . . . . . . . . . .
2.1.6. ...........
.........
[
Gri!ding - i
Assemblage,
Magnetization
)-21~7.--
~ 2.1,8.
Fig. 19. Usual production technology of bulk isotropic and anisotropic hard ferrites.
Compression moulding provides a porous compact with a relative density of about 60% of the radiographic density and only little strength. Indirect shaping by machining the compact is therefore only possible to a very limited extent. In subsequent finish-sintering the relative density increases to about 90 to 98%. The attendant shrinkage (contraction) of the linear dimensions occurs parallel to the preferred direction 1.5 to 2 times as great as in the direction perpendicular to it. The compact is then much stronger but also brittle and can only be machined by grinding, cutting, etc. If necessary, the bulk magnet is completed to form a magnet system and magnetized. Under certain circumstances the sequence of these two latter operations can be reversed. This outline shows that the method usually employed in manufacturing hard ferrites consists of steps well known in powder metallurgy. Compaction under the
464
H. STJ~d3LEIN
action of a magnetic field is the only technological suitable and useful variant for magnetic powder which up to recently has frequently been improved process-wise. The manufacturing operation must be seen as the sum of a number of interdependent separate steps. Any change at one point affects the subsequent steps. The following provides details of the individual steps in manufacture and their interdependence.
2.I.1. Raw materials; main components and additives According to the molar formula MO.6Fe203 the main constituents are the oxides of iron, barium and strontium. It was found at an early stage that extreme purity is not required in production and is even undesirable if optimum magnetic values are to be achieved. This is one of the reasons why iron oxide, for instance, made in different ways and from different sources can, in principle, be used. However, undefined variations in the starting materials must be avoided owing to the interdependence of the individual steps (fig. 19). In production it is therefore of major importance that the physical and chemical parameters of the starting materials remain constant. Other important factors are a minimum price, storage capability and ease of handling. For these reasons synthetic and natural iron oxides of the a-Fe203 type (hematite) have mainly proved successful for production in long runs. Some pertinent data are compiled in table 3. With these data it must be borne in mind that purity, grain size, size distribution and shape, apparent powder and tap density of the iron oxide etc. are very much dependent on the manufacturing conditions (Gallagher et al. 1973, Stephens 1959, Balek 1970, Gadalla et al. 1973) and are controlled as much as possible by the manufacturers so that reactivity, apparent density and the content of impurities, for instance, are matched to production requirements (Erzberger 1975). Natural iron oxides have long been used in the manufacture of hard ferrites. Depending on source, the ores contain varying amounts of impurities ("gangue"), especially SiO2, which must be reduced to admissible values of less than 1% by weight. Further attendant oxides may be A1203, TiO2 etc. The particles of these iron oxides are generally angular with smooth cleavage surfaces, cf. fig. 20, and only become rounder after a long period of milling, cf. fig. 21. In this way the reactivity increases as a result of the, at first relatively large, oxide particles being reduced in size. Some of the iron oxides used are obtained by spray roasting HC1 pickling solutions from steel plants according to the formula (Eisenhuth 1968): 4FeCI2 + 4H20 + 02 ~ 2Fe203 + 8HC1. If the reaction is not fully completed some tenths percent by weight of chlorine usually remain in the iron oxide which can affect storage and processing owing to corrosion and its impact on the environment and must therefore be allowed for. The chlorine content can generally be reduced to below 0.1% by washing with water. The other impurities obviously depend on the type of steel pickled. Typical
HARD FERRITES AND PLASTOFERRITES
465
© ,.,d
'K
:Z
(2
e.
6
O
e'~
H"~
I
v..a
©
oq.
%
q3 oo
oq. cq..
c5 t-z.
cq..
06
,7
oo ¢¢)
e..,
.! ©
"7
I
tt3
e-,
oq.
c'q e-,
I
cA G~
o0 G~
i©
O o9
,o e~ ©
L) "~.=: Z
r,,t3
O
'0<
""
466
H. ST~/d3LEIN
Fig. 20. Scanning electron micrograph of natural c~-iron oxide (hematite) as supplied.
amounts are some tenths percent by weight of manganese oxide, for example, which i s of no significance in the manufacture of hard ferrites. A r o u n d 500°C roasted oxides from Ruthner process occur as 20-400 ~ m thick hollow spheres of relatively low apparent powder density, cf. fig. 22, which can be increased considerably by mechanical treatment so that the oxide is easier to process. The particles are not compact and very fine (about 0.1 i~m) and spherical, cf. fig. 23. Owing to their reactivity and low price these oxides have frequently been used for some years in manufacturing both hard and soft magnetic ferrites (Ruthner et al. 1970, Hiraga 1970, Ito et al. 1974, Ruthner 1980). In contrast, HC1 regeneration by the Lurgi process taking place at 850°C in a fluidized bed yields relatively coarse particles with a diameter range of some tenth of a m m up to some mm. The apparent density of ca. 3 g/cm 3 is relatively high. These oxides can also be used for hard ferrite production if milled sufficiently to increase reactivity for the hexaferrite formation process. An advantage c o m p a r e d with Ruthner oxide is their low C1 content in the order of a few hundredths %. Pickling with sulphuric acid has lost ground over pickling with hydrochloric acid since the recycling of these solutions created considerable pollution problems. The iron oxides obtained in this way therefore need not be discussed at length.
HARD FERRITES AND PLASTOFERRITES
467
Fig. 21. Hematite of fig. 20 after 16 h of wet milling. It is not u n c o m m o n to use mixtures of different iron oxides in production owing to their different physical and chemical properties. Two other processes mentioned in literature for manufacturing Fe203 are worth noting, namely from pyrite according to the formula (Otsuka et al. 1973): 2FeS2 + 1102 ~ Fe203 + 4SO2, and the oxidation of carbonyl iron ( O k a m u r a et al. 1952, 1955). Fagherazzi (1976) provides a review of different processes and also reports on iron oxide produced in the beneficiation of ilmenite (FeTiO3). Van den Broek (1974, 1977) reports on experience gained in manufacture using various iron oxides. Carbonates generally serve as a source of B a O and SrO because they are chemically stable, inexpensive to store and only have to separate CO2 during decomposition (Jfiger 1976, 1978, Ullmann 1974). Commercial materials may further contain impurities such as SiO2, C a O and other compounds. Moreover, barium carbonate generally contains some strontium carbonate and vice versa. In principle, other salts, e.g., the alkaline earth nitrates or chlorides, could be used but the separated gases are corrosive and present a health hazard. Experiments
468
H. ST~BLEIN
Fig. 22. Scanning electron micrograph showing hollow spherical agglomeration of ferric oxide particles made by spray roasting (courtesy M.J. Ruthner of Ruthner AG, A-1121 Wien).
by Granovskii et al. (1970) with barium acetate, formate, nitrate, hydroxide and peroxide showed no advantages c o m p a r e d with barium carbonate as raw material. In manufacturing hexaferrites an excess of BaO, SrO or P b O above the stoichiometric molar ratio of 1:6 is normally used, e.g., about 10tool% with barium hexaferrites. This corresponds to a mixture of about 97% by weight of BaO.6Fe203 + 3% by weight of BaO-Fe203. Such a composition is considerably easier to sinter than t h e stoichiometric one. However, it must be seen in connection with the above-mentioned additives which in both phases can b e c o m e enriched to varying degrees or even form new phases, thus altering the above ratio, cf. section 2.1.6. Therefore the weighed amount and the additives must be matched to optimize the manufacturing process.
2.1.2. Mixing; granulation The steps described below serve to prepare the raw materials so that the reaction to form hexaferrite can take place in subsequent annealing treatment. As this is a solid-state reaction there have to be sufficient short diffusion paths for the reactants. T o achieve this the raw materials must be fine enough (the finer they have to be, the smaller the proportion of the substance in the total mass is), well
HARD FERR1TES AND PLASTOFERRITES
469
Fig. 23. Scanning electron micrograph of spray roasted oxide particles (courtesy M.J. Ruthner of Ruthner AG, A-1121 Wien). mixed, compacted and in contact with one another. If the raw materials are not fine enough, they can be ground and mixed in the same step. The good mix thus achieved must be maintained until the reaction occurs, i.e., on the way from the mixer to the furnace there must be no segregation resulting in local changes in concentration when handling, charging and shaking the mixture. The equipment and processes used for this purpose vary and therefore only general aspects are discussed in the following. Mixing ('homogenizing') can take place either with a wet or dry process (Ries 1969a). In wet mixing (and grinding) generally using an aqueous suspension (slurry), vibration, drum or agitator mills (attritors) are used. This mixing method is extremely effective but requires energy for dewatering and drying (Sch6ps et al. 1976). For this purpose, the suspension can be dewatered either mechanically, e.g., in a filter press, and then dried or fed directly to an atomizer. T h e r e are two possibilities for dry mixing: (1) grinding and mixing, in drum or ball mills, (2) intensive mixing in an edge-runner mill or in a high-intensity counterflow mixer with swirler. The first method is used when the raw materials are not fine enough for the subsequent reaction. Using the second method (fig. 24) depends on whether the material is to be fed direct to the reaction furnace or as a granulate. In an edge-runner mill the grinding wheels rotate in a pan in such a way that there is relative motion between tread and pan bottom. The material is subjected to friction, comminution, mixing and kneading and is also compacted
470
H. ST~?~BLEIN
and agglomerated to a certain extent. The intensive mixer can only operate with dry material or convert the powder into a granulate through the addition of moisture or a binding agent; see further below. In a continuous or tunnel kiln the material can be m o v e d through the reaction chamber in boxes or on trays, in bulk or in tablet form. Through the rotary kiln, however, the material must m o v e without any boxes or trays, in which case, owing to the fineness of the particles, no uniform and loss-free passage is guaranteed. The mixture is generally turned into a granulate of pellets several m m in diameter (Ries 1970, 1971b, 1975a, b). One way of doing this is to use granulating pans having an inclined, rotating drum. The granulate is formed by spraying liquid, e.g. about 10%, onto the dry mixture so that a liquid film forms on the particles. The particles granulate when the material on top tumbles down like an avalanche, see fig. 25.
4 5
7
Fig. 24. Diagram of a feeding, mixing and granulating plant for ferrite mixtures with raw material bins (1), feeding and weighing station (2), edge-runner mill (3), vane feeder (4), belt weigher (5), granulator (6) and belt conveyor (7) (Ries 1969b, 1971a).
HARD FERRITES AND PLASTOFERRITES
471
Usually an organic binding agent is added to the water to make the granulate less sensitive to abrasion and disintegration. This must, of course, be expellable during annealing with a minimum of residue. Certain cellulose products, alcohols, waxes and alginates are proven binding agents. As a result of granulation the relative density of the mixture increases appreciably, e.g., to twice the apparent powder density, as the following example shows. This is a mixture of 47.5% by weight of natural iron oxide (ce-FezO3), 31.7% spray-roasted iron oxide from HC1 recycling, 17.8% BaCO3 and 3.0% PbO: Apparent powder density of mixture
1.33 g/cm 3 ~ 27% rel. density,
Tap density of mixture
1.78 g/cm 3 ~ 36% rel. density.
Density of a green pellet,
2.64 g/cm 3 ~ 53% rel. density,
Density of a pellet sintered at 1180°C
3.51 g/cm 3 -~ 66% rel. density.
The high compaction of the particles in the pellets promotes diffusion and reaction during annealing. A particularly smooth throughput is achieved with a granulate having a narrow particle-size range, this being produced by screening and separating the pellets which are too large or too small. Mixing and granulating can also be carried out in a single unit which first operates as a dry mixer and then, after the addition of a liquid, as a granulator. The processes and equipment
Fig. 25. Discharge area of a pelletizing pan with granulate (courtesy of Maschinenfabrik Gustav Eirich, D-6969 Hardheim i. Odenw.).
472
H. STJd3LEIN
for mixing and granulating, with particular reference to the ferrite industry, having been described in detail by Ries (1959, 1963, 1966, 1969b, 1971a, 1973). Schinkmann (1960) has also referred to the importance of thorough blending and shown what damage occurs as a result of local irregularities in the reaction: warpings, distortions, cracks, pores, formation of vitreous reaction mass and occurrence of fine, white, acicular precipitates. Discontinuous crystal growth is also promoted (Arendt 1973a), cf. section 2.1.6.
2.1.3. Reaction sintering ; intermediate products This production step serves to convert the raw materials into the hexaferrite phase in the form of sufficiently large crystals. Using suitable manufacturing processes even a densely sintered compact can be produced which merely needs to be ground and magnetized before use. This special method for producing magnets is described in detail in section 2.2.1. Normally, however, the reaction product should not be of such density so that less grinding work is required in subsequent crushing and milling. On the other hand, it is generally desired that the reaction takes plac e to as large a degree as possible. The reaction has been investigated by numerous workers. One characteristic of all hexaferrites is that these compounds are not obtained from the raw materials in one single step but that intermediate products ('precursor phases') with a more simple structure are formed first which subsequently react to form the hexaferrite phase. The type of intermediate product mainly depends on whether barium, strontium or lead hexaferrite is being formed. This is a consequence of the different phase diagrams (cf. section 1.3). The total reaction C to form the barium hexaferrite phase takes place according to Suchet (1956) in the two unit steps A and B: A: B:
BaCO3 + Fe203--~ BaO-Fe203 + C02 BaO.Fe203 + 5Fe203~ BaO-6Fe203
C:
BaCO3 + 6Fe203~ BaO.6Fe203 + CO2.
The intermediate product which occurs is the monoferrite BaO'Fe203. A number of later investigations has directly confirmed this reaction sequence (Winkler 1965, Beretka 1968, Beretka et al. 1968, St~iblein et al. 1969, Bye et al. 1971, Wullkopf 1972, 1973, 1974, Haberey et al. 1973b, K6nig 1974, Gadalla et al. 1975, Efremov et al. 1977), but others only indirectly because although the authors recorded comparable results they gave a different interpretation to them at the time (Sadler et al. 1964, Sadler 1965). Some authors do not exclude the possibility that intermediate products even richer in BaO than monoferrite may have formed in an early stage of the reaction without this having been proved beyond doubt. If BaCO3/Fe203 diffusion couples are used, layers of intermediate products richer in BaO are in fact found in addition to mono- and hexaferrite (Wilson et al. 1972). However, it is generally found that the BaCO3 decrease equals the BaO.Fe203 increase, as unit step A requires, and so, at the most, small amounts of such
HARD FERRITES AND PLASTOFERRITES
473
phases richer in B a O could be present. On the other hand, Gadalla et al. (1975) report that, in addition to the monoferrite, 2BaO.3Fe203 occurs as an intermediate product up to a maximum of 1200°C. In this connection it should be pointed out that the monoferrite was the first intermediate product to be f o u n d both in the synthesis of other hexagonal ferrites of the types Y, Z and U and also in the synthesis of 2BaO-Fe203 (Winkler 1965), i.e., in feeds corresponding to very different BaO/Fe203 molar ratios. The fact that the 1:1 molar compound BaO-Fe203 was always the intermediate phase to be found first in appreciable amounts, both in feeds with an excess of B a O and Fe203, points to the ease with which this compound can be formed. There are, however, no studies on the cause(s) of this. It is noteworthy, however, that no intermediate monoferrite was found when a co-precipitated raw mixture was reacted to produce hexaferrite (Roos 1979, 1980), see section 2.2.2. Information varies on the temperatures at which reactions A and B occur, depending on the prevailing conditions and state of the raw materials. Important factors are the provenance, manufacture, particle-shape, -size and -range, powder surface area, impurities, apparent density of the mixture, molar ratio Fe203/BaO etc. However, there is obviously no clear connection between the above factors and the reaction kinetics and in particular the reaction temperature. Furthermore, both reactions are affected in varying ways by these factors (Wullkopf 1974). Naturally the well-known laws applying to solid-state reactions apply here, too, especially as, apart from the reaction time the reaction temperature also plays a certain role. The above-mentioned studies on reactions A and B provide the following information on temperatures: The first, though very small, amounts of CO2 are released from about 400°C (start of reaction A). Decomposition of barium carbonate thus begins at a temperature around 350°C lower than when pure barium carbonate is heated (Bulzan et al. 1976). Radiographically detectable quantities of monoferrite are generally found only at about 600 to 650°C upwards, with very fine raw material particles at 100 to 200°C lower, and by 950°C all the barium carbonate has been converted and reaction A finished. The appearance of hexaferrite at 700 to 800°C marks the beginning of reaction B which ends with the disappearance of the iron oxide. Figures vary considerably on this point, ranging from 900 to 1200°C. This is plausible as the complete reaction is especially dependent on intimate mixing of the reactants and is affected particularly by the upper end of the FezO3 particlesize range (Bye et al. 1972). A comparison of the figures shows that the temperature ranges of both reactions overlap to a certain extent. The mechanism of reaction step B was studied in detail using diffusion couples of BaO'Fe203 and Fe203 pellets (Stfiblein et al. 1972, 1973a, 1973b). It was shown that the hexaferrite crystals in the reaction layers grow in a preferred direction. Layers with different orientation can be clearly distinguished, see fig. 26. A 0.1 to 0.2 mm thick reaction layer of hexaferrite crystals, whose basal plane is preferably parallel to the contact surface, i.e., which have a {0 0. l} fibre texture (stage I) forms on the contact surface of both reactants. The {0 0. l} texture is all the more
474
H. S T ~ B L E I N
Z,~c~ 3-.9 o
/
2
t.
j. c
I--3,
o~ 0.2
0.~
mm
Reaction interface
~. Fe203
BaO. Fe203 q 15 arb. units
f
I0 ,
7, C
• 3 (00.8)
H.O]
/
\ o0'2
0.2
0.,~
tom
Reac ion interface Distance
Fig. 26. X-ray intensity ratios and intensity values across the thickness of the hexaferrite layer in the couple Fe2Os-BaO.Fe203.
HARD FERRITES AND PLASTOFERRITES
475
p r o n o u n c e d the smoother the contact surface is. The texture forms regardless of whether the Fe203 contact surface has a random polycrystalline structure or consists of a single Fe203 crystal cut parallel or perpendicular to the basal plane. A topotactic mechanism can therefore be excluded as the cause of the {0 0. l} texture. This {0 0. l} orientation is retained as the thickness of the layer increases. With the increase in layer thickness the orientation becomes weaker on the side facing the BaO.Fe203 whereas the {0 0. l} texture facing the Fe;O3 side fades away. At the same time a {h k. 0} texture forms where the basal planes of the hexaferrite crystals lie perpendicular to the contact surface (stage II). The explanation for this may be found in the anisotropic growth rate of the hexaferrite crystals which is relatively low along the c-axis but relatively high perpendicular to it. It is assumed that in stage I a discrete random nucleation of the hexaferrite first occurs on the Fe203 contact surface and that the incubation period and growth rate are not dependent on orientation. After a certain growth the state shown diagrammatically in fig. 27 is reached where only the two possible extreme cases of orientation are illustrated. After the reaction of the uppermost iron oxide layer, i.e., at the end of stage I, the {0 0. l} crystallites constitute most of the surface area. In stage II the reaction can then only proceed perpendicular to the phase boundary. In this case the {h k. 0} orientated crystals have the best opportunity of growing. Therefore in both stages the direction of maximum growth of the hexaferrite crystals is parallel to the direction in which the reaction rate is highest. This explanation contradicts a paper by Takada et al. (1970b) in which a topotactic mechanism is presumed. These authors found that hexaferrite platelets had grown with their basal planes parallel to small platelet-shaped Fe:O3 crystals. This result corresponds exactly to the above-mentioned stage I of the diffusion experiments and can therefore be explained by the anisotropic growth rate of the hexaferrite. The latter explanation is also given by Kohatsu et al. (1968) from analogous diffusion experiments with CaO-6A1203, a material crystallographically similar to hexaferrite, where a topotactic mechanism could definitely be excluded.
SaO'Fe203 Nuclei
Reaction interface
aO6Fe25 (differently oriented)
Fig. 27. First stage reaction model for the formation of hexaferrite from monoferrite and hematite.
476
H. STPd3LEIN
A still atmosphere impairs ferrite formation after reaction C because the CO2 obtaining first impedes further decomposition (Mondin 1969, Bye et al. 1971). Therefore, it must always be ensured that there is an adequate supply of oxygen during the reaction. According to Heimke (1966) a certain amount of H20 has a positive effect on the reaction. Beretka (1968) found no change in the reaction sequence as in formulas A and B by adding 0.5% NaF, but a 150 to 200°C reduction in the formation temperatures. Bye et al. (1971) achieved similar results by adding 0.5% LiF which accelerates carbonate decomposition, the reaction as in formula B and the grain growth and causes the formation of a liquid phase. However, it was later established that the lithium ferrites LiFeO2 and LiFesO8 were the first products to form in the reaction (Wilson et al. 1972). According to Haberey et al. (1973b) monoferrite formation takes place endothermally and hexaferrite formation without any heat change. Bye et al. (1971) found an activation energy of 209 kJ/mol (50 kcal/mol) for the step determining the rate of carbonate decomposition. Sadler (1965) gives a similar value of 190.5kJ/mol (45.5kcal/mol) for reactions at temperatures below 735°C and a value of 306.5 kJ/mol (73.2 kcal/mol) for temperatures above 735°C. It was found that the reaction can be satisfactorily expressed by the formula derived by Jander (1927): [ 1 - ( 1 - p)i/312 = kt, expressing the relation between reacted portion p of ball-shaped particles, reaction rate constant k and reaction period t. According to Kojima et al. (1969) as well, Jander's formula is the one best suited to describe the reaction rate. However, between 850 and 900°C activation energies of 201 to 904 kJ/mol (48 to 216 kcal/mol) were found, depending on the type and treatment of the iron oxide used in the reaction. A very low value of 59-+42k J/tool (14 _+10 kcal/mol) for the subsequent reaction stage was given by Cho et al. (1975a). Literature data on the reaction mechanism and kinetics were compiled by Schrps (1979). The formation of the strontium hexaferrite phase was investigated by Beretka et al. (1971) and by Haberey et al. (1976). Beretka et al. (1971) describe the two unit steps D and E by the following formulas: D:
S r C O 3 + Fe203--~ (SrO'Fe203 + 2SrO.Fe203) + CO2,
E:
(...) + 5Fe203-~ SrO.6Fe203,
where, however, only SrO-Fe203 is claimed to appear after reaction in a vacuum. Apart from the fact that owing to the different molar ratios on both sides the equations can, at best, only describe the reaction qualitatively, there is considerable doubt about the existence of strontium monoferrite (see section 1.3). On the other hand, Haberey et al. (1976) and Vogel et al. (1979b) found the unit steps F and G: F:
SrCO3 + ~Fe203 + (0.5 - x)½02-~ SrFeO3-x + CO2,
G:
SrFeO3_x+ 5.5Fe203-~ SrO-6Fe203 + (0.5 - x).102,
HARD FERRITESAND PLASTOFERRITES
477
where the intermediate product strontium perovskite SrFeO3_x only occurs at the reaction temperature whereas 7SrO-5Fe203 (4SrO.3Fe203) was found after quenching. It may be that the 02 supply recorded in reaction F does not come from the atmosphere but from carbonate decomposition, i.e. that instead of the recorded CO2 a corresponding mixture of CO2 and CO is given off (Haberey et al. 1977a, cf. also Wullkopf 1978). The results of Beretka et al. (1971) can, at least partly, be interpreted by the explanation of Haberey et al. (1976). As far as the reaction temperatures are concerned, the picture is as follows: The initial traces of CO2 are found from 300°C upwards, once again appreciably lower than with the decomposition of pure carbonate (from about 650°C upwards). Considerable amounts of the intermediate product occur at 600 to 660°C and SrCO3 can be detected radiographically only below 800°C (end of reactions D and F respectively). The hexaferrite phase occurs from 800°C upwards and iron oxide up to about 11500C (start and end of reactions E and G). Owing to the small number of test results the temperature values should not be regarded as i00% accurate meaning that they correspond roughly to the reaction temperatures of barium hexaferrite. According to Haberey et al. (1976) reaction F is strongly endothermal, reaction G weakly endothermal. This corresponds qualitatively to the heat changes dffring the formation of barium compounds. Another reaction sequence than D-E and F-G was reported for co-precipitated ferric hydroxide and strontium laurate, see section 2.2.2 (Qian et al. 1981). The formation of lead hexaferrite has also been investigated by several authors (Berger et al. 1957, Mountvala et al. 1962, Bowman et al. 1969, Mahdy et al. 1976b) for which the reaction steps H, I and K are given: H: I: K:
2PbO + Fe203--~ 2PbO.Fe203, 2PbO.Fe203 + 3Fe203 ~ 2[PbO-2Fe203], 2[PbO.2Fe203] + 8Fe203~ 2[PbO-6Fe203].
However, both intermediate products are not always found during the reaction, for kinetic reasons according to Bowman et al. (1969). Some partial reactions can obviously proceed very slowly, see section 1.3.5. The following temperatures must not therefore be considered as homogeneity ranges for the state of equilibrium, but must be seen in the dynamic sense, i.e., longer periods displace the temperature ranges towards lower values and they depend on the reactivity of the raw materials: PbO is present up to a maximum temperature of 750°C, 2PbO.Fe203 was found between 670 and 850°C and PbO-2Fe203 between 600 and 825°C; PbO.6Fe203 can occur from 750°C upwards and Fe203 up to a maximum of 1000°C. The relatively high vapour pressure of PbO results in the renewed occurrence (precipitation) of Fe203 from 1150°C upwards (Bowman et al. 1969). According to Berger et al. (1957) appreciable losses in weight can occur from 950°C upwards owing to the evaporation of PbO. Reaction sintering in industrial plants mainly takes place nowadays in internallyfired rotary kilns with ceramic lining where temperatures of about 1200-1350°C
478
H. ST.~3LEIN
necessary for the barium and strontium hexaferrite reaction can be attained (Petzi 1974b). Cartoceti et al. (1976) have investigated the heat balance of such a kiln charged with a wet mix and found that less than 10% of the total combustion heat is utilized for the hexaferrite reaction. The balance is somewhat more favourable when a dry mixture is used. It must be fed as a granulate to permit uniform throughput (cf. section 2.1.2) and first passes through the reaction zone, undergoing no abrasion if possible, and then through the cooling pipe below the kiln shell, cf. fig. 28 (Petzi 1971). Owing to direct firing b y g a s or oil burners the oxygen partial pressure varies in the kiln chamber but is always lower than in the atmosphere and especially low in the burner zone, a s is shown in fig. 29 (Petzi 1971). Therefore direct contact between flame and material must be avoided for a perfect reaction. Temperature and annealing time depend on the reactivity and particle size of the raw materials used and also on the desired technological properties of the powder and on the magnetic properties of the magnet grade to be manufactured. Temperatures of 1000 to 1100°C are, under certain circumstances, sufficient for isotropic hard ferrites as unreacted constituents can form hexaferrite during the final sintering (cf. section 2.1.6) and a small crystallite size in hexaferrite is admissible and generally desirable and necessary. Anisotropic hard ferrites require higher reaction temperatures of the mix because the minimum size of all hexaferrite crystallites must be around 1 Ixm. Fine grinding down
Fig. 28. Rotary kiln for calcining hexaferrite obtained from raw materials showing below the cooling pipe for processed material (courtesy of Fa. Riedhammer, D-8500 Nfirnberg).
HARD FERRITES AND PLASTOFERRITES temperature-O2-curve
db
sintering_ 1400° c ternflerqture1200
..- ,...~"'"'"'~' .......................... "-,..-..
""""
T "''... furnace ",,...
1000
800 \ ' cooh'ng 600 ~ M , ' / , coo 2oo
~.
furnace length
__Pyr~2_~_-~ temperatureme(~surmg_
tube
,/r'~'~
/
1
21% 02 20 18 furnace atmosp.here -15 -14 12 10
86
O , j . J ~ ' " / ..,..,.,,i- . . . . . . .
0
2
3
,~
479
5
-2 6rn
charge__ vibrator
burner (gas-or oilheated)
Fig. 29. Temperature and atmosphere along the length of the rotary kiln of fig. 28. The atmosphere was measured in the lower half near the pellets (M1)and in the upper half (M2),where the 02 content is very low within the burner zone (Petzi 1971). to a size below 1 }xm (cf. section 2.1.4) produces particles which consist of one single crystallite and which can therefore be aligned in a magnetic field (cf. section 2.1.5). Accordirlg to Van den Broek (1974, 1977) a reaction temperature matched precisely to the raw materials used is therefore of major importance because deviations from it cannot be entirely corrected in subsequent manufacturing. T o produce plastoferrites (cf. section 4.1) the same considerations as with compact ferrites apply regarding the particle size to be produced, i.e., it depends on whether alignable powder particles are needed or not. Moreover, for magnetic and practical reasons, the powder should only consist of the hexaferrite phase. Of course, other kiln types can be used for reaction sintering, such as bogie, end-discharge pusher or batch furnaces as long as the temperature, reaction time and atmosphere requirements are met. In this case the powder is used, for example, in bulk or briquet form. Owing to the poor thermal conductivity of powders the innermost parts must be given sufficient time to react and recrystallize. Fagherazzi et al. (1972) have described a pot-grate kiln which permits exact temperature control with little crystal growth and caking. Iron hydroxide with acicular particles is said to be especially good as raw material. The reacted pellets are friable giving platelet-shaped single-domain crystals with coercivities HHc of up to 340 kA/m (4.26 kOe) with BaFe12019 and 455 kA/m (5.7 kOe) with SrFe12019, without tempering being necessary (cf. section 2.1.4). A recent further development of the rotary kiln type shown in fig. 28 is called the passage pendulum kiln, see fig. 30. The reaction tube no longer rotates continuously in the same sense, but oscillates around an equilibrium position. As a consequence there are constructional advantages with the energy supply, enabling a more efficient and compact setup.
480
H. ST,3d3LEIN
Fig. 30. Passage pendulum kiln for calcining of hexaferrites from raw materials at max. temperatures of 1350 to 1400°C, with adjustable temperature curve and controllable energy supply. Length 6 to 10 m (courtesy of Fa. Riedhammer, D-8500 Nfrnberg).
2.1.4. Preparation of mouldable powder The reaction-sintered mass is hard and often coarse-sized and therefore has to be turned into a mouldable and sinterable powder with crystallite and particle size fulfilling certain magneto-physical requirements. These requirements stem firstly from the fact that crystallite size is linked with coercivity. The critical size for single-domain behaviour is around 1 p~m. There is always grain growth and recrystallization during sintering and so before sintering the crystallite size has to be considerably smaller than 1 fxm, e.g., with most crystallites in the size range 0.1 to 0.5 txm. The coercivity of the magnetic material can therefore be influenced by the intensity and duration of milling. Secondly, the requirements depend on whether isotropic or anisotropic magnets are to be manufactured. For manufacturing isotropic magnets the powder particles can be polycrystalline, while for manufacturing anisotropic magnets preferably all of them have to be monocrystalline so that they can be aligned in the magnetic field (see section 2.1.5). As torque in a magnetic field is proportional to volume, for good alignment the particles should not be unnecessarily fine; this also facilitates the escape of air or milling fluid during pressing and reduces shrinkage during sintering. The reaction-sintered lumps are crushed and ground to produce the powder. Using jaw or roll crushers a granulate in particle sizes of one or several
HARD FERRITES AND PLASTOFERRITES
481
millimetres is produced which in the dry state can be reduced in ball or vibration mills, for instance, to particle sizes of, at the most, 100 or several 100 ixm. In certain circumstances this can suffice for the manufacture of isotropic magnets from polycrystalline particles. Particle sizes under 1 Ixm are obtained by batchwise wet milling, e.g., in roller or vibration mills, or continuously in attritors, for instance. Figures 31 to 33 show some common types. During milling additions can be introduced if the feed is to be corrected. S o m e economic aspects of various types of mill were examined by Maurer et al. (1966) and technical aspects described by John (1973). The advantage of the attritor and the vibration mill over roller mills is seen in the intensive grinding action which gives relatively short milling times (Heimke 1962, Richter 1968, Stanley et al. 1974) and is said to result in relatively little abrasion (Maurer et al. 1966). As grinding media steel balls of uniform size are normally used as long as differential wear during operation does not cause certain size variations. According to Kal3ner (1970) the use of grinding balls with different diameters gives no advantages. H e also found that the addition of interfacially active agents to the milling fluid showed no effects on the result, but failed to
Fig. 31. Ball mill (Fa. Dorst Keramikmaschinenbau, D-8113 Kochel am See) having a capacity of 5.3 m 3 (courtesy of Fried. K r u p p G m b H , Krupp W l D I A , D-4300 Essen).
482
H. STABLEIN
Fig. 32. Rotary vibrating mill with a total capacity of 12l (courtesy of Fa. Siebtechnik GmbH, D-4330 Mfilheim (Ruhr) 1).
mention the type of agents tested. The experiments carried out by Tul'chinskii et al. (1971) are, however, claimed to show that the milling time can be reduced to a third without affecting the ultimate magnetic values if ammonium carbonate is added to the grinding water. After fine milling the water content has to be adjusted or the water removed depending on subsequent treatment which is in turn dependent on the magnetic quality to be obtained, cf. section 2.1, fig. 19. For wet compaction water contents of 20 to 50% by weight are required, which can be obtained by decanting, partial evaporation or adding water. These water contents roughly correspond to 43 to 15% by volume of ferrite. The high ferrite contents cause the suspension's consistency to be paste-like, the low ones cause it to be fluid. By way of comparison, a packing density of about 15% by volume of ferrite is obtained when a milled suspension settles or the dry powder is poured. For optimal alignment in a magnetic field the packing density has to be sufficiently low. If the powder is to be subsequently treated in the dry state the water is either removed by means of spray driers, whereby the particles can form fine hollow spheres, e.g., a few 0.1 mm in diameter of correspondingly low apparent powder density (approx. 1.0-1.2g/cm3), or by filter pressing, evaporation, etc. In the drying process rather constant particle aggregates with poor magnetic field alignability are formed which can be broken up in suitable mills (pinned disc mill, jet mill, etc.) to obtain a powder with good alignability (Kools 1978b) which,
HARD FERRITES AND PLASTOFERRITES
483
Fig. 33. Attritor mill for hard ferrites (courtesy of Fa. Netzsch GmbH, D-8672 Selb).
however, due to its fineness does not flow well and is m o r e difficult to handle during pressing. If, on the other hand, isotropic hard ferrite is to be manufactured, the particles are granulated either after drying with the addition of binders and means to facilitate compaction (cf. section 2.1.2), e.g., by a vibrating screen that sizes the material at the same time, or by an atomizer with additions of dispersants, binders and lubricants. Dispersants lower the viscosity and the required minimum content of water already in amounts of a few hundredths to a few tenths of a percent. G u m arabic, a m m o n i u m citrate and polyethylenimine was successfully tried by Vogel (1979) in soft ferrite suspensions and found to be compatible with polyvinyl alcohol. Binders must give a certain strength to the
484
H. STJd~LEIN
granules to enable good flowability. Granulate with aggregate sizes of smaller than about 1 mm is easy to handle. The effect of polyvinyl alcohol (0.75 to 3%) and of polyamine sulfone (1.5%) as binders in soft ferrite powders were described by Harvey et al. (1980). The drying kinetics of single droplets of ferrite suspensions were investigated by Malakhovskij (1980). The phenomena deriving from the interaction of milling material, grinding media and grinding fluid are examined more closely in the following. Reducing the particle size is accompanied by two undesired effects: the grinding media undergo abrasion and the material and water react, with earth alkaline hydroxide being formed and part of the ferrite destroyed. Figure 34 shows different particle size ranges for powder milled with a feed size of <1 mm in a ball mill (Bungardt et al. 1968). Logarithmically the particle sizes largely reflect a normal distribution. Richter (1968) obtained the same results, establishing a closer reflection of the Gaussian curve than of the Rosin-Rammler distribution (1933). The deviations from the normal distribution in the fine and coarse range were greater after milling in the ball mill than after milling in the attritor. This is held as attributable to the different grinding mechanisms of the mills: abrasion grinding preferable for the attritor, impact grinding and chipping grinding preferable for the ball mill. Initially grinding progresses quickly but then the curves show only slight progress as a point is reachedwhere as many particles agglomerate as are ground. During ball milling the particle size variations
o
a:l "4
"6
)(i 2
2
~
6 a101
2
z
6 8100
z
~ pm
810 ~
Particle d i a m e t e r
Fig. 34. Particle size distributions of BaO.5.6Fe20~ after ball milling at different milling times (Bungardt et al. 1968).
HARD FERRITES AND PLASTOFERRITES
485
decrease somewhat. The authors found, however, that the variations are not related to the milling conditions and in particular that it is the same after ball milling as after attritor milling and is therefore related to the material. Nevertheless, the proportion of coarse or fine particles can be influenced by the milling conditions (mill type, grinding media geometry, quantity of grinding balls, etc.). The particle size distributions shown in fig. 34 were determined using an electron microscope. Special preparation is required because they are singledomain particles which cannot be demagnetized by magnetic fields and which therefore always attract each other magnetically and conglomerate. Horn et al. (1968) drew the particles magnetically onto a slightly sticky carrier, while Machintosh et al. (1976) electrostatically charged the powder at a temperature over Curie point and drew it onto a carrier. A g o o d dispersion was attained in both experiments. Heidel et al. (1977), however, only found a partially satisfactory dispersion of the powder in the magnetic field. In contrast, determining the size of the particles via air separation or changing the resistance of an electrolyte (Coulter counter) gives values which are too large by 1 to 2 powers of ten because an agglomerate particle size is measured (Bungardt et al. 1968). The problems encountered in determining the particle size of hexaferrite powders and the resultant difficulties in describing them have been referred to in particular by Bungardt et al. (1968) and Kools (1975). Hexaferrite particles preferably have the shape of platelets because they split relatively easily parallel to the basal phase of the hexagonal crystal lattice. They mostly lie with this plane on the carrier (St/iblein 1957) and so the electron microscope captures the largest surface of the particle. Although further splitting of the particles in the basal plane enlarges the surface area it does not seem to reduce the particle size. This is probably one of the reasons why the specific surface area grows noticeably with the duration of milling, but as seen under the microscope the particle size hardly decreases (Maurer et al. 1966, Richter 1968). A further reason for these deviations is that Ba-hexaferrite particles may be surrounded by a barium carbonate/barium hydroxide film, the formation of which will be dealt with later. Inner surfaces of these porous layers can give the false impression that the specific powder surface areas values are excessively high. Kools (1975) compared the particle sizes calculated from measurements of the surface area or of the permeability to gas (Fisher sub-sieve-sizer) with those determined with scanning microscopy. Particularly puzzling was the proportion of very fine particles, probably attributable mainly to abrasion and foreign phases of the commercial hexaferrite magnets. Indeed, the particle sizes determined by the various methods were more uniform when the finest particles had been removed by acid treatment. Nevertheless, the values obtained by the different methods only agreed qualitatively. The method of determining the permeability to gas proved itself relatively insensitive to the content of finest particles. With a magnetic powder such as hexaferrite powder magnetic quantities can also be used to examine the effect of milling, especially the coercivity of the magnetic polarization 1He and the specific saturation polarization Js/p (=47r~r in the CGS system). Figure 35 shows the she curve according to Heimke's experi-
486
H. ST.~?,LEIN
300 kA b"
m
250,~ 200 150
b
J"c ,°° L , t
.
, ....____
a
50
0
i
200 ~00 Millingtime
)
600rain
Fig. 35. Intrinsic coercivity]He vs. milling time of Ba-hexaferrite powder (Heimke 1962). Curve (a): calcined 4h 1370°C+milled; curve (a'): as curve (a)+ 0.5 h 1000°C;curve (b): calcined 0.5 h 1160°C+ milled; curve (b'): as curve (b) + 0.5 h 1000°C. ments (1962, 1963). As the milling time lengthens jHc drops, if a low calcined, i.e., fine crystalline, material is used. When a high calcined, i.e. coarse-crystalline, material is milled, however, jHc rises at first. Under further milling jH~ then drops, as numerous experiments have shown (Tenzer 1963, Bungardt et al. 1968, Richter 1968, Haneda et al. 1974a, Mackintosh et al. 1976). In most experiments the maximum jH~ value was between 103 and 143 kA/m [1.3-1.8 kOe], and in one case (Mackintosh et al. 1976) it was 190 kA/m [2.4 kOe] and is thus evidently dependent on the particular experimental conditions. This behaviour is at first surprising. It is expected that as the material is ground finer the number of multi-domain particles will decrease and that of single-domain particles increase and as a result coercivity will rise. This is evidently the case for the initially coarse material. The fall in jH~ must stem from another mechanism. Heimke (1962, 1963) and most of the authors mentioned attribute it to lattice defects which permit a relatively easy formation of remagnetization nuclei and therefore of domain boundaries. By heat treatment of the ground powder, e.g., ~h of annealing at 1000°C, coercivity can be noticeably increased, both for the initially coarse and the fine powder, cf. fig. 35. According to Heimke (1962, 1963) this is due to curing of the lattice defects. The coercivity is then mainly determined by the crystallite size and in addition by the material as was found by Richter (1968), which for barium or strontium hexaferrite powder obtained maximum jH~ values of 240 and 290 kA/m (3.0 and 3.6 kOe) respectively. Roughly ideal single-domain behaviour of ]/arc~600 kA/m (7.5 kOe) can be obtained after very long milling. Tanasoiu et al. (1976b) obtained a strontium hexaferrite powder with fl-/c = 520 kA/m (6.5 kOe)
HARD FERRITES AND PLASTOFERRITES
487
after 1700 hours of milling and annealing at 1000°C. Similar values are obtained when the crystallites are produced without plastic deformation, cf. sections 1.2 and 2.2.2. Annealing is of particular importance in the manufacture of powders for plastoferrites, cf. section 4.1, but after Fahlenbrach (1965), it is unnecessary or even harmful in the manufacture of compact hard ferrites. The influence of annealing on the magnetic characteristics of barium hexaferrite powder was also investigated by Sch6ps et al. (1977). Tenzer (1963, 1965) attributes the drop in coercivity during milling to the formation of superparamagnetic crystallites and the jHc rise during annealing to their being sintered and recrystallized. If superparamagnetic crystallites were the cause of the low coercivity, etching the powder in acid should produce a noticeable jHc rise owing to preferential decomposition of the very fine particles. In fact, however, Richter (1968) found that this only gave an increase of 5 to 15%, i.e., only a fraction of the rises of 50 to 300% attained through annealing for 0.5h at 900°C. Furthermore, X-ray measurements have shown that the line broadening in milled powders is largely caused by lattice distortions and to a lesser extent by ultrafine crystallites, and so lattice defects are regarded as the main cause of the 1He drop. The same conclusion is reached by Haneda et al. (1974a) on the basis of M6ssbauer experiments and the angular dependence of the coercivity, by Hoselitz et al. (1970) on the basis of remanent torque curves, Bottoni et al. (1972) on the basis of investigations into rotational hysteresis, and by Ratnam et al. (1970) on the basis of electron microscope studies and the angular dependence of coercivity. According to the latter stacking faults and deformation twins are the major lattice defects. Esper et al. (1978) have pointed out the significance of the annealing atmosphere in regenerating the coercivity. On tempering the milled powder in an N2 atmosphere the jHc rise is distinctly lower than annealing in air or does not occur at all. In partial contrast to Richter's (1968) experiments, however, it was found that jHc rises roughly in proportion to the percent by weight removed by etching and that at around 70% by weight powder loss a value approximately the same as after optimal annealing in air is attained. The authors interpret their results in a model in which the powder particles exhibit two types of lattice defect. Outside an undisturbed core covering ~ of the particle radius there are "mechanical" dislocations while the outermost layer covering 10% of the radius is additionally disturbed by oxygen vacancies. The second magnetic quantity, specific saturation polarization Js/p, decreases as milling time increases (Heimke 1964, Bottoni et al. 1972, Haneda et al. 1974, Mackintosh et al. 1976, Giarda 1976), in extreme cases to almost ~ of the initial value (Tanasoiu et al. 1976b). After annealing very different behaviour was established: a further, though only slight drop, a partial or almost complete restoration of the initial value. There are evidently a number of influences at play here. Firstly, there is the reaction of the hexaferrite with the water; H a n e d a et al, (1974a) were in fact able to prove that o~-Fe203 is released after sufficiently long milling. If there is a surplus of alkaline earth present and this reacts with the iron oxide released or with particles abraded from the steel balls there has to be a
488
H. STJid3LEIN
corresponding recovery back towards the initial value. The rise in the Fe 2+ content with the time of milling is, however, not connected with the fall in saturation polarization, but is due to abrasion of the grinding media (Heimke 1964). A drop in saturation polarization was, however, also found after strong, dry deformation of high-coercivity Ba-hexaferrite crystals (Ratnam et al. 1970) and during milling of Sr-hexaferrite powder in alcohol (Tanasoiu et al. 1976a and b). In these cases, too, the drop was completely or largely reversed by annealing. It is to be concluded from this that the superexchange interaction between the five magnetic sublattices of the hexaferrite is changed during deformation. Iwanow et al. (1966) and Richter et al. (1968a) gave an alternative explanation to the effect that a new soft-magnetic phase forms having a Curie point of about 150°C and disappearing during annealing. Apart from coercivity and saturation polarization, which can only be measured in the dried powder, the hysteresis loop of the suspension can be used for directly assessing the state of the particles (Kools 1975). From this loop the alignability of the particles in the suspension, which is important to know for the manufacture of oriented magnets, can be assessed from the ratio between remanence and saturation polarization. Within several hours of milling the ratio at first rises rapidly, this being due to the reduction of the crystal aggregates to single-crystal particles; during continued milling it reaches a maximum value and then starts to fall slowly. As already mentioned, during milling in water a reaction takes place between the barium hexaferrite and the milling fluid. Barium hydroxide is formed and as a result the pH value of the water may rise to 13 or 14. It was formerly supposed that this might be due to unreacted remnants from reaction sintering. This is contradicted by results obtained by Stfiblein et al. (1969) to the effect that BaO losses also occur after repeated milling and sintering and with sub- and suprastoichiometric compositions (Fe203/BaO<6 or >6). It was also found that BaO.Fe203 is particularly easily decomposed, see also Belyanina et al. (1977). After multiple milling and sintering a composition almost the same as BaO.6Fe203 was obtained. Analog milling tests in ethyl alcohol or acetone produced for both substances only a slight increase in the molar ratio, which can be explained by the material being milled picking up abraded particles. The relatively low resistance of the monoferrite to water can be see when boiling it in water, where BaO losses of over 50% were determined. In contrast, Ba-hexaferrite showed itself resistant to boiling water. The reaction between barium hexaferrite and water was also found by Bungardt et al. (1968), and after Tanasoiu et al. (1976a) there is an analogous phenomenon in the case of strontium hexaferrite. The hydroxide is the cause of a number of undesired effects, some of which have already been mentioned; barium carbonate/barium hydroxide films form on the powder particles during drying, giving the false impression that the specific surface area is too high and that adjacent particles are agglomerating which causes poor magnetic field alignability and hinders sintering (cf. section 2.1.6). If a dry powder of good alignability is required disaggregation has to be carried out.
HARD FERRITES AND PLASTOFERRITES
489
2.1.5. Die pressing; orienting field The treated powder is turned into a compact in two stages: (1) By applying pressure at room temperature (pressing) and (2) by annealing at temperatures above 1000°C at normal pressure (sintering; cf. section 2.1.6). Their relative shares in the total compaction process can be altered by varying the pressure, thereby producing different microstructures with the same final density. In principle, both steps can be carried out at the same time by what is known as hot compaction, cf. section 2.2.5, but technical difficulties prevent wide-spread application. In this section we will therefore only consider those phenomena which take place when hard ferrite powder is compacted at room temperature. For pressing, powder (or powder suspension) is subjected to pressure in a largely enclosed space. Normally a die is used which has a continuous opening ('die cavity') of (almost) constant cross-sectional area which is closed by movable upper and lower punches, cf. fig. 36. This process is called die pressing because, in addition to compaction, shaping to dimensions similar to those of the part to be produced also takes place. For very long production runs the walls of the die cavity are made of hard metal because of the abrasive action of the ferrite particles. Another possibility is isostatic compaction where pressure is exerted from all sides with the powder enclosed in a deformable container. Although a higher degree of compaction can be attained, which can have a positive effect on the strength of the compacts, the homogeneity of their density, their sintering behaviour and magnetic characteristics after sintering (Kools 1973, Stfiblein 1973), this process is too expensive for normal operating practice. Shaping is only possible to a limited extent, e.g., for cylinders, or in post-compacting parts which have already been die-pressed. , The degree of compaction attainable depends on the pressure, the state of the powder and on friction. Figure 37 shows the density of (almost) isotropic compacts of barium hexaferrite after die pressing (<5 kbar) and after quasi-isostatic postcompaction between 5 and 26 kbar (Stfiblein 1973). A relative density of about 85% was achieved with a maximum pressure of 26 kbar. This density could not be increased by stress-relieving at 400-600°C, by renewed application of pressure or by using pressing aids. The same density was also achieved when pressing anisotropic compacts. The compaction behaviour can be expressed, for example, a)
b) Upperpunch
(or
erpunch /
Fig. 36. Die pressing with relative movement of both punches (a), or of only the lower punch (b) with respect to the die during densification.
490
H. ST~d3LEIN
by the formula pp = 2.88 x pO.129,
(1)
with pp = green density in g/cm 3 and p = pressure in kbar; another formula is given in fig. 37. As the compact volume is V - 1/pp, eq. (1) can be re-written as
(2)
V x p0.129 = c o n s t ,
which has a certain similarity to the equation for an ideal gas with the exponent of p, however, indicating that compaction is much more difficult c o m p a r e d with gas. It should also be mentioned that SmCo5 powder was compacted to 82% at p = 20 kbar (Buschow et al. 1968) and hexaferrite raw mix to 80% relative density at p = 26 kbar (Stfiblein 1975), i.e., to similarly high values. ~.5 9/cm~
4O
3.5
./
J ~ experimental
t~
o I/op =0.35-0.091gp •
_,op =2.88.p °.7"~
30
2.50
'
I0
,
20
, kbar
30
Pressing p r e s s u r e p
Fig. 37. Green density pp of isotropic Ba-hexaferrite specimens vs. isostatic pressing pressure p.
Figure 38 shows the magnetic characteristics of the compacts mentioned in fig. 37 as a function of density (Stfiblein 1973). The remanence Br rises linearly and coercivity ]/-arc falls linearly with the density. The rise in r e m a n e n c e is understandable as the specimen m o m e n t is roughly proportional to the density. The coercivity decrease at first appears to be due to plastic deformation of the crystallites. However, the jHc difference remains qualitatively the same even after annealing at 1000°C so that density and interaction effects cannot be ruled out. Bungardt et al. (1968) and Maurer et al. (1972) studied the effect of grain fineness on density by crushing powder for different periods (up to 240 h) and in
HARD FERRITES AND PLASTOFERRITES
491
(BH)m
,i
o.3O.f 0
O--
0
f
l 0
I 20
t 4.0
9 /c rn s
i 5.0
Green density.gp
Fig. 38. Remanence Br, (BH)max,normal and intrinsic coercivities 8He and jHc, and fullness factor vs. green density of specimens from fig. 37.
pp
different mills and then compacting samples at constant pressure. Depending on the type of mill there was a more or less rapid decrease in apparent density from about 66 to 47% as fineness increased. Possible causes for this fall with increasing fineness are poor removal of air during pressing, a rather unfavourable particlesize range and the drop in density owing to the Ba-hydroxide/Ba-carbonate layers on the powder particles (cf. section 2.1.4). With the same pressure in the range p = 1 to 4 kbar isostatic compaction produces 5-8% higher density values than die pressing (Drofenik et al. 1970). In commercial manufacturing considerable importance must be attached to density throughout the compact in addition to the overall density achieved by compaction. However, die pressing produces non-uniform densities owing to friction between the powder and the die wall (Gasiorek 1980). As this is a surface effect, compacts with a high height-to-diameter ratio are particularly affected. Parts with a height-to-diameter ratio of considerably more than 2 are not normally manufactured. Sintering results in a largely uniform density, producing non-uniform shrinkage and thus, under certain circumstances, inadmissible deformation of the sintered parts. The uniformity can be influenced by controlled relative movement of both punches and the die to one another and by additions which facilitate pressing (cf. section 2.1.2). With two-sided pressing (fig. 36(a)) both punches execute a movement relative to the die during compaction, the lower punch generally being fixed. With the same relative movement of both punches the zone of lowest density ('neutral zone') is roughly halfway up the green; sintering then produces a cylinder slightly arched inward but deformation
uniform
492
H. ST~d3LEIN
as a whole is the least pronounced. With unequal relative movement of the punches the neutral zone can be shifted to any other point. Conversely, one-sided pressing (fig. 36(b)) results in relatively large deformation with the neutral zone located on the surface of the stationary punch. For pressing isotropic grades the granulate (cf. section 2.1.4) is fed from powder reservoirs into the die cavity whose volume determines the amount to be pressed. As the apparent density of the granulate may be up to about 100% higher than that of powder, a lower filling height in the die cavity and smaller punch movements during compacting are sufficient for a given mass of the part to be produced. However, the largest granulate particle must be appreciably smaller than the minimum wall thickness of the part to be pressed. With this volumetric feeding it is obviously important that the apparent density of the granulate remains constant in order to ensure as few size and weight variations of the parts as possible. With fairly small presses rates of 1 piece per second can be achieved, with rotary-table machines up to 3 pieces per second. The pressures applied range from 0.5 to 2 kbar, thus producing green densities of about 50 to 60%. The low plasticity of the particles and wall friction cause rejects due to spalling and "press cones" at higher pressures (Schiller 1968), which cannot be avoided even when lubricants are used. It should be pointed out that in die pressing as a result of the one-directional movement of the punches a slight orientation of the particles ('compaction anisotropy') occurs when they are single-crystalline and platelet shaped. The plane of the platelets is aligned preferably perpendicular to the direction of pressing. Thus the c-axis, being perpendicular to that plane, is preferably parallel to the pressing direction. The resulting anisotropy increases to a certain extent with increasing green density. However, no anisotropy is obtained with purely isostatic compaction even if the particles are single-crystalline and platelet shaped (Gordon 1956, Pawlek et al. 1957b, Stfiblein 1957, Drofenik et al. 1970). The possibility of aligning the crystallites in a magnetic field is of major importance for improving the quality of standard commercial hexaferrites. The basis for this is the relatively high crystal anisotropy energy Ek = K sin20 with K = 3 x 105 J/m 3 (3 × 106 erg/cm 3) (section 1.2). The diagram in fig. 39 shows that polarization Js is deflected through angle 0 from its normal position parallel to the c-axis of the hexagonal lattice when an external magnetic field H is applied at an c-AxLs
H rticle
Fig. 39. Orientational relationship of a fixed platelet-shaped hexaferrite particle showing hexagonal c-axis, the directions of magnetic field H (angle o~) and spontaneous polarization J~ (angle 0) (c-axis, H, and Js are parallel to the sheet).
HARD FERRITES AND PLASTOFERRITES
493
angle o~ to the c-axis; c-axis, J~ and H are on the same plane. The torque per unit volume which ties Js to the c-axis is Mc = K sin 20,
(3)
i.e., it disappears when 0 -- 0 ° and 90 ° and therefore has a m a x i m u m value K when 0 = 45 °. T h e torque per unit volume which turns Js in the direction of H is MI-I = H J s sin(a - 0),
(4)
and is therefore at a m a x i m u m when Js is perpendicular to H and disappears when both quantities are parallel. For the special case where a = 90 ° it is easy to quantify to what extent Js is tied to the c-axis. From the equilibriu m condition Mc = M n it follows that sin 0 = H J d 2 K = H / H A where HA = anisotropy field strength (cf. section 1.2) giving, for example, angles 0 = 18.5, 39 and 72 ° in fields of H = 400, 800 and 1200 k A / m (5, 10 and 15 kOe) respectively and finally 0 = 90 ° for H = HA = 1260 k A / m (15.8 kOe). When a < 9 0 °, with equal field strength values H, angles 0 are smaller than those mentioned and Js and H do not b e c o m e parallel until H ~ ~. If the crystallites were freely rotatable any small field H would be sufficient to m a k e all c-axes completely parallel in field direction. In fact this free movability is not present because mechanical and magnetic forces act even with monocrystalline single-domain particles of bulk material. According to Kools (1974, 1975) the monocrystalline particles in a suspension are present spontaneously in the form of curled, random-orientated chains representing magnetically largely self-contained and relatively stable entities. These break up somewhat abruptly in fields between 16 and 40 k A / m (0.2 to 0.5 kOe) and then align themselves in the field direction. According to W i p p e r m a n n (1968) the aligning of crystallites of dry loose bulk material starts from H = 30 k A / m (0.38 kOe) which even in this state suggests a similar chain formation of the crystallites. In compacting a further factor is the frictional forces due to contact between the particles. T h e possibilities of aligning polycrystalline particles with a r a n d o m arrangement of the c-axes are, of course, even worse. In manufacturing oriented magnet grades d.c. fields of about 400 to 800 k A / m (5-10 kOe) are used, as experience has shown that good crystal orientation can be achieved in this way and fields of higher strength are considerably m o r e expensive. Fields of higher strength would in fact be desirable to further improve alignment because if the crystallites are already aligned to a certain extent and angles a (fig. 39) are therefore correspondingly small (at least under 45 °) a m a x i m u m torque Mc is achieved when J~ is parallel to H, i.e., only when H ~ ~. According to W i p p e r m a n n (1968) pulse fields can also be used for aligning. H e found that m o s t of the aligning was completed when H = 100-150 k A / m (1.261.9 kOe) which was the case after 0.2 to 0.3 ms with the form of pulse used. To manufacture anisotropic grades either dry powder or a suspension', in most
494
H. STJ~BLEIN
cases aqueous, is used; we therefore distinguish between a dry and a wet compaction process. In both cases monocrystalline or quasi-monocrystalline particles are required. With dry pressing filling the die cavity is not without problems as the fine powder does not flow very well and volumetric filling can produce size and weight variations in the compacts. The powder can be successfully 'sucked in magnetically (fig. 40(a); Richter et al. 1968b). In this method the powder reservoir (5) is pushed over the die (1) and the die cavity closed by the lower punch (4). An inhomogeneous field is induced by coil (2) which, together with the effect of gravity and suction caused by the upward movement of the die, ensures that the cavity is filled, fig. 40(b). The powder fills the cavity fairly uniformly although under the action of the field it tends towards a radiated filamentary consistency. After the powder reservoir (fig. 40(c)) is removed, the upper punch (3) lowered, the orienting field (fig. 40(d)) switched on, and after compacting (fig. 40(e)) and demagnetization by a counter field, the compact is ejected and the die 'drawn off' (fig. 40(f)). This sequence of punch and die movements is therefore called the 'draw-off method' (Fischer 1962) and is also applied in wet pressing. In this case the suspension is usually injected into the closed die cavity through passages in the die or in a punch and aligned in a magnetic field, the material compacted, water expelled, the compact demagnetized and the die drawn off. During the compacting of oriented specimens slight disorientation occurs because the crystallites prevent one another from adopting the optimum magnetic position when being pressed against one another (Stuijts 1956, St/iblein 1973, Kools 1978b). The suspension can be pressed into the die cavity at a pressure of several bar. Recent machines operate at pressures of up to 300 bar (Fischer 1978). As the filling period is short and a certain amount of compaction and dewatering takes place in the filling phase shorter strokes and thus shorter cycles are possible. A particular advantage for segment magnets is the more radial field formation in the die cavity at the start of the punch movement. Figure 41 shows a hydraulic press with a maximum tonnage rating of 1 MN and a high-pressure filling device operating at a maximum pressure of 300bar. In order to further reduce the pressing time per piece, dies with several cavities can be used both with the wet and dry methods. With wet pressing the chamber filling method has proved successful. Here, the suspension is first poured into a central chamber from where all the die cavities are filled at the same time. This procedure facilitates uniform filling of all cavities and thus makes for~ uniform density of the compacts. Obviously such tools are expensive and only worth while for large production runs. Odor et al. (1977) suggested a process for manufacturing single segment magnets with magnetically different zones. A pasty ferrite/water mixture, exhibiting high coercivity after sintering, is fed into the die cavity either at one or both segment ends while for the other zones a mixture which, once sintered, exhibits high remanence is introduced into the other parts of the die cavity. A compact is thus produced which is particularly well suited to withstand the different magnetic stresses set up in motors. Strijbos (1974) investigated the dewatering stage in detail. With an anisotropic
HARD FERRITES AND PLASTOFERRITES
495
"• ~
O
8~ 09
0J
-
i
E ~ .-= e-,
~
A .k
t.f3
-4
©,----
z- .
.
.
. ©
496
H. STJ~d3LEIN
Fig. 41. Hydraulic press, tonnage rating i MN, with a high pressure slurry pump for filling pressures of up to 300 bar for pressing oriented hexaferrites by the wet method (courtesy of Fa. Dorst, D-8113 Kochel; see also Fischer 1978).
HARD FERRITES AND PLASTOFERRITES
497
filter cake the permeability for water is anisotropic and 2 to 2.5 times greater in the direction of the magnetic field than perpendicular to it. This is a consequence of the chain-like structure of the suspension which is retained at least during initial dewatering. To remove the water during pressing passages (holes) are incorporated in one or both punch faces which are covered with filters. 10 to 13% by weight of water remains in the compact which corresponds to the free space between the particles. This water must be carefully removed (dried off) as otherwise the compacts may crack. The compaction pressure of around 0.5 kbar usually is smaller than in the dry process. Both methods have their advantages and drawbacks. Wet pressing offers the advantage of better magnetic values due to improved crystal alignment, ease of preparation of a suspension rather than of a powder, lower compaction pressure and more uniform density of fairly large pieces. The advantages of dry pressing are simpler tooling, the possibility of making smaller parts, shorter cycle and finally dry compacts. Mechanical presses are generally used for dry pressing, hydraulic ones for the wet method. The spatial arrangement of the field for alignment must be adapted to the desired crystal orientation in the compact. Homogeneous magnets with equal pole strength values (fig. 42(a)) can only be obtained if a homogeneous field is induced for alignment. If the die cavity is in the diverging part of the field then the magnets become inhomogeneous (fig. 42(b)) which is reflected by unequal pole strength values (Steingroever 1966). With segment magnets radial (fig. 42(c)) or diametral preferred directions (fig. 42(d)) can be produced by an appropriate field. Principally, field and direction of pressing can either be parallel or perpendicular to one another. Under certain circumstances, the extremely inhomogeneous fields at the punch edges can impede uniform powder distribution. If necessary, these fields can be eliminated by a non-magnetic covering.
2.1.6. Final sintering; shrinkage; grain growth Final sintering, also referred to as sintering, completes the conversion, begun by the pressing operation, of the loose powder into a compact shape and produces a
..... y
I.t'I I#II#W
Fig. 42. Anisotropichexaferritecompactshavinghomogeneous(a), inhomogeneous(b), radial (c) and diametral (d) preferred directionsof magnetization.
498
H. STABLEIN
magnetically favourable microstructure with crystal sizes in the order of magnitude of 1 p,m. During sintering the relative density increases from about 55-65% to over 90%, and sometimes even to about 98%. Since the mass of the compact remains constant, disregarding side effects, such as evaporation of moisture and lubricants, release of CO2 from residual carbonates, oxidation of abraded metallic particles from the grinding media, etc., the volume therefore decreases to approximately two thirds of the initial value. The reduction in linear dimensions due to the extensive elimination of pores, i.e., shrinkage, amounts to about 16% with the isotropic piece and about 22 or 13% with the anisotropic piece in a direction parallel or perpendicular to the preferred direction, respectively. The crystal recovery, recrystallization and crystal growth (continuous and discontinuous (abnormal) crystal growth) taking place during sintering are desirable in one respect and undesirable in another. While at a relatively low temperature coercivity jHc increases with crystal recovery, as already mentioned in section 2.1.4, it falls again as a result of crystal growth when the temperature is set to the value needed for shrinkage. The driving force behind all this is the decrease in surface and grain boundary energy and the potential energy elastically stored in the lattice. At a sufficiently high temperature it causes the atoms to diffuse through lattice defects, e.g., vacant sites or grain boundaries, which of course play an important role as regards the extent and rate of sintering. As practice has shown, the presence of further solid or, at elevated temperatures, liquid phases is of particular significance. Samples of high-coercivity barium or strontium hexaferrite crystals, i.e., fine crystals with few defects, crystallized out of salt melts, for instance, do not undergo shrinkage even at temperatures of 1300°C, well above the temperatures normally used (Arendt 1973a). Only after the addition of 2 to 4% by weight of sintering aids, some of a vitreous nature with the composition Z1-Z2-A1203 (Z1 = PbO, BaO or SrO; Z2 = SiO2 and/or B203) were good sintering properties obtained. The author assumes that these materials form a liquid phase during sintering. The influence of the molar ratio n = Fe203/MO ( M = Ba, Sr, Pb) has been investigated repeatedly. Dealing with barium hexaferrite, Stuijts (1956) found that with stoichiometric composition shrinkage is relatively small and grain growth proceeds normally, whereas even a slight excess of BaO (n < 5.9) permits dense sintering owing to the formation of BaO-Fe203. In that case, if the temperature is sufficiently high, abnormal grain growth can occur. Similar results were recorded by Lacour et al. (1973a, b, 1975a, b) and St~iblein (1978) for barium hexaferrite, Krijtenburg (1974) for strontium hexaferrite and Pawlek et al. (1957a) and Mahdy et al. (1976a) for lead hexaferrite. According to Bungardt et al. (1968) the activation energies for sinter compaction in the range from 1120 to 1280°C amount to 770 +_ 12 or 5 5 6 + 12 kJ/mol (184--3 or 133-+ 3 kcal/mol) for samples of BaO.5.9Fe203 or BaO.5.3Fe203 milled for a relatively short time. From this and the time dependence of compaction it is concluded that volume diffusion is the main transport mechanism. With increasing fineness of the powder, values between 835 and 1256 kJ/mol (200 and 300 kcal/mol) were found which is due to a retardation of the diffusion by BaCO3
HARD FERRITES AND PLASTOFERRITES
499
layers deposited on the particle surfaces, cf. section 2.1.4. Cho et al. (1975b) give 544 + 84 kJ/mol (130 + 20 kcal/mol) as activation energy for the grain growth of barium hexaferrite sinter specimens, irrespective of whether the material is a pure or SiO2-bearing ferrite. Deviation from the stoichiometric composition and the presence of other materials (additives) must not be viewed separately. From all experience gained so far as it can be said that these conditions lead, in principle, to a reduction in the saturation polarization of the magnet material as a result of the formation of non-magnetic phases or a lowering of the saturation polarization of the hexaferrite phases. But since the saturation polarization of the hexaferrites is in any case already low compared with that of other permanent magnet materials, only relatively small quantities of these additives are normally permissible. Depending on the controls to be applied to the manufacturing process and on the properties specified for a certain magnet grade an optimal compromise must be made. The precise mechanism by which they act is not known in all cases. Some additives can be substituted in the hexaferrite lattice, such as A1, Cr and Ga in Fe sites (Bertaut et al. 1959) whereby the saturation polarization in particular as well as the anisotropy field and consequently the coercivity of the hexaferrite phase are affected. In this connection the effect of SiO2 additives was investigated in detail and it was found that they cause the formation of low-melting and, in some instances, vitreous eutectics with 50 to 60% mol SiO2 (Haberey 1978, Kools 1978a, Stfiblein 1978, Kools et al. 1980). In addition to Fe203 the eutectics contain a relatively large proportion of alkaline earth oxides. This overproportional alkaline earth consumption explains why the feed in industrial production must have a 10% excess of alkaline earth over the stoichiometric value. Because of the low melting temperatures, sintering of the magnet specimens takes place in the presence of a liquid phase. Kools (1978a) attributes the grain-growth-inhibiting effect to the formation of a solid phase which mainly exists on the most strongly reacting crystal surfaces parallel to the c-axis. Figure 43 shows which value combinations can be obtained for remanence Br and coercivity jHc with samples sintered to different densities if they contain no SiO2 (curve A) or 0.5% SiO2 (curve B) (Krijtenburg 1965, Stuijts 1968). Table 4 shows some of these additives. Additives of SiO2 and A1203 are therefore quite common in production. The effects of other materials such as B203 or sulphates are disputed because the specific conditions of each case probably determine whether the positive effects outweigh the negative ones or vice versa (Krijtenburg 1965, 1974). Some additives are already present as desired impurities in the main constituents, such as SiO2 in the iron oxide raw material, cf. table 3. Others are introduced in the form mentioned in table 4 or as a compound or combined additive, such as AI(Granovskii et al. 1970), Ca- (Miiller et al. 1959, Pingault 1974, H a m a m u r a 1977) or Pb-silicate (Ruthner et al. 1970), as borate (Arendt 1973a), boric acid+ SiO2 (Harada 1980) etc. Many other substances have been used as additives which were ineffective or worsened matters at least if present in proportions exceeding certain values. The latter include, e.g. TiO2, MgO, NiO, SnO2, V205 (Kojima 1955a, 1958, Chroust 1972, Gadalla et al. 1976). The sintering rate and density can also be influenced by the partial pressure of
500
H. ST~d3LEIN
N
~
O
O'~
~A
+
+
÷
+
m-
+
+ +
I
÷
+
.= +
+
'7 <
e~
<
+
HARD FERRITES AND PLASTOFERRITES
501
~,~0"~i. xx
mT
x
~
dO0
-
•
"~,-~''~ x
"--o-"Q~°° ° i °
•
o°
"\~.
o
%
\ x
01~
28 O0
i
200
i
300
Io I I • xl
kA/m
t
zOO
Fig. 43. Remanence Br vs. intrinsic coercivity jHc of Sr-hexaferrites sintered to various densities. Specimens along curve (A) contain no silica, those along curve (B) contain ca. 0.5% SiO2 (Krijtenburg 1965, Stuijts 1968).
oxygen in the sintering atmosphere. Tests with SrO.5.5Fe203 (Sutarno et al. 1971), SrO-5.9Fe203 (Reed et al. 1975, Klug et al. 1978) and PbO-5Fe203 (Mahdy et al. 1976a) have shown that amenability to sintering increases as the partial pressure decreases, which is attributable to the growing concentration of vacant sites. Intensive fine grinding prior to sintering is necessary not only because particle sizes around 1 ixm are a prerequisite for high coercivity jHc (section 2.1.4) but also because of the significance of surface energy as the motive force of compaction. The sinter density that c a n b e obtained increases at first as the fineness of the powder increases. According to Maurer et al. (1972) it reaches a maximum with barium hexaferrite powder with a specific surface area of 5 mZ/g. As the fineness increases further the density can fall again. This may be due to the increasing influence of the BaCO3 layers (cf. section 2.1.4) because they inhibit diffusion and disintegrate giving off CO2. If the latter occurs with closed pores then the C02 gas pressure can lead to local swelling and the surface can develop blisters (Bungardt et al. 1968). A cause for the stop of further densification is the start of discontinuous grain growth. Whereas with normal grain growth the pores are usually located at the crystal boundaries, cf. fig. 49, fast growth causes them to be enclosed within the crystals, cf. fig. 50. The further removal of pores within the crystals to achieve more densification must take place by means of volume diffusion of vacant sites, a much slower process than the grain boundary diffusion of the vacant sites. The following graphs are to show the influence of the sintering temperature on different physical properties of the sintered compact. Figure 44 shows shrinkage,
502
H. ST~/d3LEIN
© tO
preferred dLrection x~
tO
20
~
10'
1 2" "£
ll/,,"Slproferred {
tO
0
1--
#~
,50 %
o~ "o
J
9-.~---x~-'J~L' ,,.
t2o ~
tlO4 /O
/
6000 Nlmm 2
~
~ooo 2000
0
0
500
1000
°C
1500
Sintering tempereture
Fig. 44. Shrinkage, shrinkage ratio, apparent density, porosity and Vickers hardness vs. sintering temperature of anisotropic Ba-hexaferrite specimens (St/~blein 1968a).
density and hardness of anisotropic Ba-hexaferrite specimens, properties which begin to change from 800-900°C upwards (Stfiblein 1968a). The shrinkage S Ip parallel to the preferred direction is, in the case under consideration, about 1.6 times greater than the shrinkage S" perpendicular to it. This ratio is a consequence of the platelet-like growth of the crystallites. As the latter can be controlled by SiO2 additives (Stuijts 1968), the ratio of both shrinkages is, perforce, also affected. As the SiO2 content decreases, S"/S" increases sharply. In contrast to the above-mentioned properties the permanent magnet characteristics (fig. 45) change from a few 100°C upwards, particularly coercivity jHc, as already described in section 2.1.4 for the annealing of finely milled powder. The other characteristics also increase to a certain extent, especially those measured in the preferred direction. As a function of sintering temperature, all magnetic values attain, in both directions, peaks whose location and amount depend on the composition and manufacturing conditions. With increasing milling time, for example, the temperature of the curve peak falls but the peak itself rises (Sixtus et al. 1956). The fact that the peaks measured parallel to the preferred direction
H A R D FERRITES AND PLASTOFERRITES
503
measured II preferred direction /
,~00
-
'201
,~
xx~x ;
mT
c 13
300
,~o
200
,6o
1oo
so
[.I ~1
7--~-~/
.'
i
I I
/
E
g~
. . ~.~___+.____÷ - : V 7 " - - -~U I BHc (BH) I
/. , :
Lo'--
0
C
I .
0
_
../ . . . .
+-
, --
-1"-
+ . . . . .
b~ +.,.+-%. ~ I
500 1000 Sintering temperature
"+4"4
°C
1500
Fig. 45. Remanence Br, (BH)max, normal and intrinsic coercivity eH~ and jHc, resp., vs. sintering temperature of anisotropic Ba-hexaferrite specimens (Stfiblein 1968a).
occur at different temperatures (cf. also Harada 1970, Gershov 1971) is, in addition to the composition and preparation, the reason why there are anisotropic grades with high remanence Br and low coercivity jHc and vice versa. While with most grades the demagnetization curve exhibits a bulge in the preferred direction the demagnetization curve perpendicular to the preferred direction is a straight line. In this case the peaks of Br, (BH)ma× and BHc lie at the same sintering temperature. Similar conditions apply to isotropic grades although only higher values of the properties occur. Therefore with isotropic magnets there is practically only one grade, irrespective of provenance and manufacturer, with narrow ranges for Br, (BH)ma× and BHc, there being only a certain amount of latitude left for 1He. While density and magnetic characteristics normally exhibit a smooth curve in the temperature range from 1100 to 1250°C, Heimke (1958) observed with barium hexaferrites an abnormal trend around 1150°C, the c~-fi-transformation temperature of CaSiO3, after an amount of this material corresponding to 1% SiO2 had been added to facilitate sintering. The graph of the properties of anisotropic specimens above the sintering temperature shows that the temperature must be kept constant to within 10°C in order to retain uniform quality of the sintered pieces with a given condition of the compacts. However, the sintering period is also important. With isothermal
504
H. STJ~d3LEIN Range: : Sintering temp. :
T
j ,r_, i
:
1000
1100
I
I
1170 1200°C I
A mount of orientation
I
~-- 1,0 /
400 mT
I l l meesured porallel to I1 " perpendiculor tc kA/m ~ direction . tl(i) "/
I 300
~ 0,9
320
24,0
(a).
J
/
.0.8 O.7
" />
"
0.6
¢11
~ 200 .~ 160 E
iI
80
~-~..~_
i
0
2.6
3.0
4.0
........
g/cm 3
~--
0.2
i--
0.1
5.0
5.3
A p p a r e n t density
Fig. 46. Remanence Br and intrinsic coercivity ~Hc vs. apparent density of Ba-hexaferrite specimens pressed with (a) and without (i) orienting magnetic field (St~iblein 1968a).
sintering relatively coarse powders shrink according to a power law whereas very fine powders shrink according to a logarithmic law (Bungardt et al. 1968). The influence of the pressure decreases with increasing compaction (Sutarno et al. 1970c, St~iblein 1973). Considering the values as a function of density provides a more quantitative view of the phenomena during sintering. The remanence values, measured parallel and perpendicular to the preferred direction, and coercivity jHo, measured parallel to the preferred direction, are shown in this way in fig. 46. The values marked (a) relate to the same specimens as in figs. 44 and 45, whereas those marked (i) refer to specimens which were manufactured from the same powder as (a) but without the application of a magnetic orienting field. The degree of alignment is shown as a dotted line. ~: = 1.0 corresponds to the saturation polarization, numbers ~ < 1.0 to fractions of it. With the isotropic specimen the degree of alignment is sc = 0.5. There are three density ranges, I, II and III, which correspond roughly to temperature ranges up to 1000, 1000 to 1200
HARD FERRITES AND PLASTOFERRITES
505
and above 1200°C, respectively, and in each of which characteristic phenomena occur. The remanence values only increase in temperature range II almost linearly but not quite proportional to the density. There are two reasons for this: the shearing effect caused by porosity (Denes 1962) and the change in the crystal texture caused by crystal growth (Rathenau et al. 1952). If the shearing effect is considered mathematically the dot-dash curves obtains in fig. 46. For the (almost) isotropic specimen this gives degrees of alignment of sc = 0.55 and 0.464 measured parallel and perpendicular to the direction of pressing respectively, regardless of specimen density, as is reasonably expected. Conversely, the degree of alignment of the anisotropic specimen only rises slightly at first in range II and then considerably in range III (Reed et al. 1973). This sharpening can also be quantitatively verified radiographicaUy, as fig. 47 shows, and also with the angular dependence of the remanence (Stiiblein et al. 1966a). c~
8
50-
40.
"s 30-
20. J 10-
g. o
11100
I
12100
I
I
1300 oIc
t~O0
Sintering temperature
Fig. 47. Pole densities of the basal plane of barium ferrite parallel to the preferred direction (St~iblein et al. 1966a).
Figures 48--50 show the structure of the specimens sintered at 1000, 1225 and 1385-1395°C. It is easy to see the transition from the initial, very porous, state (fig. 48) to a rather dense microstructure with at first relatively slight, continuous crystal growth and intercrystalline pores (fig. 49). This is followed by the appearance of a discontinuous, pronounced laminar crystal growth with intracrystalline pores (fig. 50). The phenomena in ranges I to III (fig. 46) can therefore be summarized as follows: Range ! is characterized by the curing of lattice defects, which can be best seen in the substantial rise in coercivity and a smaller rise in remanence. Compaction of the specimens and a relatively slight grain growth take place in range II. Coercivity gradually drops and the crystal texture of anisotropic specimens becomes somewhat sharper. In range III exaggerated crystal growth is the cause of the sharp drop in coercivity and the noticeable sharpening in the texture of the
506
H. STABLEIN
Fig. 48. Micrographs of Ba-hexaferrite specimens sintered at 1000°C, not etched (Stfiblein 1968a): (a) anisotropic specimen cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen.
Fig. 49. Micrographs of Ba-hexaferrite specimens sintered at 1225°C, etched with 50% HCI at 80°C (Sti~blein 1968a): (a) anisotropic specimen cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen.
Fig. 50. Micrographs of Ba-hexaferrite specimens, etched with 50% HC1 at 80°C (Sti~blein 1968a): (a) anisotropic specimen, sintered at 1395°C, cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen, sintered at 1385°C.
HARD FERRITESAND PLASTOFERRITES
507
anisotropic specimen. That this sharpening is linked with an increase in remanence in spite of a sharp jHo drop, shows that the nucleation for remagnetization is made more difficult, i.e., it only begins with a negative field. On the other hand the local stray fields of the crystallites in the isotropic specimen promote the formation of remagnetization nuclei in positive fields (Rathenau et al. 1952) so that remanence becomes less than half of the saturation polarization. Further tests showed that the same magnetic values can be achieved in range II by using various temperature/time combinations, provided that sintering was adjusted to produce equal density values. It is therefore unimportant for the magnetic values whether a shorter annealing time is used at higher sintering temperature or vice versa and how high the heating and cooling rates are. Shrinkage and grain growth cannot therefore be influenced independently by varying the sintering temperature. This can be most simply interpreted by assuming a common elementary process for both phenomena (Stfiblein 1968a). Reference has already been made above to the anisotropic shrinkage of oriented specimens which is caused by the anisotropic growth rate of the hexaferrite crystals and which results in their platelet-like shape, cf. section 2.1.3 and figs. 49 and 50. Other properties, too, are more or less anisotropic, cf. sections 3.3 and 3.4, in particular thermal expansion, which amounts to about 14 or 10 x 10-6/K parallel or perpendicular to the c-axis. This results in particular difficulties in manufacturing toroidal magnets with a radial preferred direction (Kools 1973). Pieces which have been die pressed in the normal way break when heated owing to inhomogeneity of density and alignment. The inhomogeneities can be reduced by isostatic compaction and the compact strength increased so that the pieces can be heated without breaking. The stresses in the toroid which then occur with anisotropic shrinkage during sintering can balance each other out by creep; thus producing an unbroken piece at the end of the sintering cycle. During cooling, however, stresses occur as a result of the different coefficients of expansion. These stresses can result in radial cracks at the hole (maximum tangential stress) and in tangential cracks with an average diameter (maximum radial stress). They can be avoided if the ID/OD ratio of the toroid exceeds 0.80 to 0.85 because then the maximum stresses during cooling are below the ultimate strength. In large-scale commercial production sintering is usually carried out in electrically- or gas-heated continuous kilns (Petzi 1974a, 1975, 1980) where the compacts are stacked on plates and pushed through, see fig. 51. Because air is needed as sintering atmosphere these kilns are simpler than those for sintering soft magnetic ferrites which require a protective atmosphere. Barium and strontium hexaferrites are predominantly sintered at 1200 to 1250°C for several hours and the heating and cooling steps both require another 5 to 10 hours, with larger pieces even longer. Recently, however, also faster and more economic sintering techniques have been considered. Lead hexaferrites can and must be sintered at a temperature several hundred degrees lower even if only to minimize evaporation losses of PbO. Batch kilns are used for smaller quantities and in the laboratory. Fairly large batch kilns can also be used if special burners (jet burners) and rapid air circulation are employed (Remmey 1970, Bohning 1978).
508
H. ST~d3LEIN
Fig. 51. Electrically heated pusher type kiln for sintering of hard ferrites. Ceramic conveyor trays are automatically returned. Length of furnace 11 m, useful width and height 280 × 100 mm 2 (courtesy of Fa. Riedhammer, D-8500 N~rnberg).
2.1.7. Machining (grinding etc.) After sintering the magnet parts have dimensions which correspond only to a varying degree to the required dimensions. With good manufacturing methods they lie within a range below the limits listed in table 5. According to the German magnet standard D I N 17410 (May 1977) these limits are admissible for the supply of unground magnets unless manufacturer and purchaser agreed otherwise. Dimensional variations are the result of variations in the raw materials supplied and individual production steps, inhomogeneities in the material and processing conditions. This needs to be explained in more detail. With isotropic homogeneous shrinkage sintered pieces and compacts are exactly similar in the mathematical sense and dimensional variations from piece to piece only occur as a result of different degrees of shrinkage, e.g., owing to different green and/or sinter densities. The situation is similar with anisotropic, homogeneous shrinkage where there are merely different degrees of shrinkage for different spatial directions as is the case with oriented magnets. Additional dimensional variations occur with inhomogeneous shrinkage. A more or less deformed line stems from a straight edge, a more or less concave or convex surface from a plane, two parallel edges or surfaces are inclined towards one another or warped, concentric circles become
HARD FERRITES AND PLASTOFERRITES
509
TABLE 5
Permissible deviations in size of hard ferrite magnets (in mm) to D I N 17 410 (May 1977).
Isotropic hard ferrites
Rated size from to
4 6 8 10 13 16 20 25 30 35 40 45 50 55 60 70 80 90
4 6 8 10 13 16 20 25 30 35 40 45 50 55 60 70 80 90 100
perpendicular to pressing direction
in pressing direction
Anisotropic hard ferrites perpendict/lar in to pressing pressing direction direction*
___
±
-4-
0.25 0.25 0.25 0.30 0.30 0.30 0.30 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.75 0.90 1.10 1.25 1.40
0.30 0.30 0.30 0.40 0.40 0.40 0.40 0.40 0.45 0.50 0.55 0.60 0.80 0,90 1.00 1.10 1.35 1.55 1.70
0.25 0.25 0.25 0.30 0.30 0.35 0.45 0.55 0.70 0.80 0.95 1.10 1.20 1.30 1.45 1.65 1.90 2.15 2.40
0.30 0.30 0.30 0.40 0.40 0.45 0.55 0.70 0.90 1.00 1.20 1.35 -
* Wet pressed hard ferrites are machined on the pole faces.
non-concentric and deformed etc. The causes for this are inhomogeneities in the material and varying processing conditions. Further configurational deficiencies are burrs on the edges, undesired sintered-on loose particles etc. In all these cases where these geometric defects are intolerable the piece must be machined. This is especially advisable for the pole faces of the magnet when otherwise unnecessary air gaps occur in the magnetic path which absorb too much magnetic energy. Owing to the brittleness of the material only such machining methods can be considered which produce very fine chips, e.g., grinding, tumbling, lapping or polishing. Diamonds are predominantly used as grinding medium, owing to their hardness even compared with ceramics, and sometimes silicon carbide. Good cooling is always necessary. In recent years highly advanced processes for grinding segment magnets have been used where, for example, the magnets, lying behind one another on guideways, are pushed through a gap formed by 2 grinding wheels. Both inside and outside radii can be ground in one operation. A number of fundamental investigations were carried out on the very complicated mechanism of grinding ferrites (Broese van Groenou 1975, Veldkamp et al. 1976, Broese van Groenou et al. 1977). Zones of tensile and compressive stress
510
H. STJ~3LEIN
with plastic deformation, brittle fracture and crumbling occur. Scratching on the basal plane results in more crumbling than on the prism face; other factors such as power requirement, and specific grinding energy are anisotropic, too. One particular result was that the specific grinding energy does not depend very much on the circumferential speed of the grinding wheel. During high-speed grinding with speeds of up to roughly 100 m/s a faster removal rate is possible at constant shear force, i.e., grinding time saved, or less energy can be applied with the same rate of removal, thus producing less deformation in the piece. Reference should be made at this point to the manufacture of magnets by indirect shaping. Normally the sintered piece already has its final shape and size ("direct" shaping), apart from corrective grinding. It may, however, be advisable or necessary to produce smaller parts from larger, pressed or sintered stock, i.e., as semi-finished parts, e.g., because they have better magnetic properties or because a cylinder with diametral preferred direction is easier to manufacture in this way. Assuming the pieces are sintered, precision machining methods are used in this process, too, e.g., parting off by cut-off wheels of pieces less than 1 mm thick. With pressed pieces actual machining is relatively easy to carry out but owing to their low strength they require careful handling.
2.1.8. Magnetizing and demagnetizing In as-manufactured condition a permanent magnet is either totally non-magnetic or only incompletely magnetized. It is usually magnetized after being incorporated into the magnet system. The required amount of field strength effective in the permanent magnet is 2 to 3 times as great as its coercivity jHc (St/iblein 1963, Dietrich 1969). The direction and spatial directional distribution of the magnetizing field are brought into line with the desired polarized state of the permanent magnet. How well this must be done depends, among other things, on the material. With isotropic magnets the remanence accurately reflects the directional distribution and any inhomogeneities of the magnetizing field after it has been switched off. With anisotropic magnets, however, the preferred direction largely determines the remanent state. Figure 52 shows that remanence is independent of /3 where deviations/3 of the magnetizing field from the preferred direction are not too great. This is due to the fact that the polarization direction in every crystallite in the remanent state runs parallel to the local c-axis. With complete alignment of all crystallites remanence would be independent of angle/3 (apart from a certain small range around/3 ~ ~-/2). With actual specimens it depends on the degree of alignment. With the well-aligned 1350°C specimen in fig. 52 remanence only drops from/3 ~ 50 to 60 ° upwards, whereas with the less well-aligned 1100°C specimen it starts falling from/3 ~ 30 to 40 ° upwards. In many cases a permanent magnet is not used in the fully magnetized state. One reason for this may be that a certain magnetic flux is required of the magnet. However, in large production runs geometrical and magnetic variations occur from piece to piece. These are eliminated by defined, individual weakening ('calibration'). Another reason is the higher stability of the weakened condition (Gould 1962,
HARD FERRITES AND PLASTOFERRITES
511
Preferred axis Remanence~
kfagnetizing field
~
Remanence r2
Perfect alignment ~" 1.0
_
~ ~ 5 0 o c
/ _
1250°C~\ ,
E ~
si, feting mp t e\
\\
O~
Q~
IlO0°C -1250oC 1350°C i
i
i
i
i
30 ° 60° Deviation from preferred axis
~0 o
Fig. 52. Relative remanence values rl and r2 of oriented barium hexaferrite, measured parallel and perpendicular, respectively, to the preferred direction, after magnetizing at /3° from preferred axis (St~iblein et al. 1966a).
Dietrich 1968). This condition is achieved by partial demagnetization, generally using an alternating field of sufficient amplitude which diminishes slowly enough, and less frequently by means of an opposing field, rotating field or by thermal treatment. Defined weakening is not simple, particularly with anisotropic grades owing to their rectangular hysteresis loop, if the alternating field is applied parallel to the preferred direction as the dependence of the field amplitude is relatively large, cf. fig. 53. This disadvantage can be avoided when the position is perpendicular to the demagnetizing field and preferred direction. However, higher field strengths are required for the same degree of weakening. The abovementioned methods can, of course, be used for complete demagnetization ('neutralization') too. The various weakening or demagnetizing methods result in different domain structures (Tanasoiu 1972) even if the overall macroscopic condition is the same. This can be seen, for instance, in the shape of the magnetization curve, cf. fig. 54 (St/iblein 1970). Specimens demagnetized thermally or with an a.c. or d.c. field react completely differently to any applied field. Moreover, with a.c. demagnetizing field weakening the temperature and field direction with respect to the preferred direction are important. Magnetization and demagnetization techniques have been described in numerous papers and text books (Rademakers et al. 1957, Dambier et al. 1960, Underhill 1957, Parker et al. 1962, Knight 1962, Schiller et al. 1970).
~00 rn7
300
¢ 200
~ 2
I00
00
200
400 No
600 kA/rn
--
Fig. 53. Remanence Br of an anisotropic hexaferrite magnet with intrinsic coercivity 1He = 143 k A / m after full magnetization and subsequent demagnetization in a gradual diminishing a.c. field of initial amplitude H0. Curve (1): field parallel to preferred axis, curve (2): field perpendicular to preferred axis.
400mf
300L200.7
100.
s
O
kA/
Fig. 54. Magnetization curves and parts of the outer hysteresis loop (first quadrant) of an anisotropic barium hexaferrite specimen having Br = 364 mT (3.64 kG) and jHc = 240 k A / m (3.02 kOe), measured parallel to preferred axis, after different methods and conditions of demagnetization (St/iblein 1970). Curve (1): thermal; curve (2): a.c. at -196°C, ± preferred axis; curve (3): a.c. at -196°C, [[ preferred axis; curve (4): a.c. at 20°C,.A- preferred axis; curve (5): a.c. at 20°C, I] preferred axis; curve (6): a.c. at 300°C, ± preferred axis; curve (7): a.c. at 300°C, II preferred axis; curve (8): d.c., starting from outer loop, third quadrant. 512
HARD FERRITES AND PLASTOFERRITES
513
2.2. Special technologies In terms of the magnetic values attainable, the manufacturing process described in section 2.1 has proved to be highly economic but it is not the only one that can be employed. In the following further possibilities for the manufacture of hard ferrites are described. In table 6 they are compared diagrammatically with the TABLE 6 Technologies available for manufacturing magnets.
D~ hnique
0 "i"~ Manufacturing step
to
Mechanical m i x i n g P r e c i p i t a t i o n of the raw materials Reaction in furnace Reaction in fluidized bed Reaction in salt bath
Crushing,
grinding
Die p r e s s i n g at room temperature S h a p i n g by rblling,
extruding
i
Hot p r e s s i n g
Sintering
Further p r o c e s s i n g
514
H. ST]kBLEIN
conventional process. Some of these processes require fewer main operations, e.g., the sing!e-sintering technique where reaction and final sintering take place simultaneously, or hot pressing of the powder where shaping and sintering are carried out at the same time. In other processes one operation is replaced by another. This includes the precipitation techniques where mechanical mixing is at least partly replaced by a precipitation reaction, the fluidized bed processes where the reacting mass is suspended in the form of fine particles in a stream of gas, or plastic working (rolling, extruding) which, compared with the pressing of a powder or a suspension of powder particles, offers different possibilities. In the salt bath processes both mixing and reaction takes place together in a molten bath. Naturally, the processes can be combined, for instance, co-precipitation with hot pressing or single sintering with rolling. A review on non-conventional powder preparation techniques of ceramic powders was given by Johnson (1981). While offering some advantages, these special technologies generally entail major drawbacks. With further advances in technology, it may be that one or the other process will be employed to a greater extent than at present.
2.2.1. Single sintering technique The characteristic feature of this technique is that only one single sintering operation takes place, cf. table 6. This means that during sintering the raw materials must react to form hexaferrite (cf. section 2.1.3) and, at the same time, a dense, true-to-shape body must be produced (cf. section 2.1.6). Good mixing and high reactivity of the raw materials are, of course, particularly important in this process. This is facilitated or ensured by intensive mixing and milling of the mix and by the addition of substances (e.g. SiO2, PbO, B203) which promote sintering. Shrinkage on sintering is about 1.5 times that in double sintering as the raw mix which is shaped generally has a density on pressing of between 2.0 and 2.6 g/era~ at the usual pressures of around 0.5 kbar compared with a typical density of pressed ferrite powder of 2.7-3.3 g/cm3. This has to be taken into account in the sizing of the press-working tools. The sintering temperature is roughly equal to that applied in double sintering. Milling time and sintering temperature have to be adapted to one another, as is shown in fig. 55 (Stfiblein 1971), to ensure that a dense and, at the same time, high-coercivity body is produced. Single-sintered parts show a greater tendency to inhomogeneous shrinkage (distortion) than doubled-sintered parts. The extent, however, largely depends on the raw material used and the processing conditions. Isotropic or at the most weakly anisotopic magnets are normally obtained by means of single sintering. More detailed investigations have, however, shown that appreciably anisotropic parts can also be manufactured owing to the fact that the platelet-shaped hexaferrite crystals grow on plane Fe203 surfaces (section 2.1.3). It was found that sintering always produces an isotropic magnet if the raw mix contains iron oxides of isometric shape (spherical, cubical) regardless of other conditions under which manufacture takes place. Anisotropic magnets, however, are obtained when mixes are reacted where the iron oxide particles are anisometric (acicular, platelet-shaped) and if these were oriented during shaping
H A R D FERRITES AND PLASTOFERRITES
515
oc 1300
1250
2.2
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Fig. 55. (BH)m.x value in kJ/m 3 vs. milling time (vibration mill, wet) and sintering temperature. Material: mixture of synthetic a-Fe2Oa (Bayer 1660) and BaCO3.
and retained their configuration up to the hexaferrite reaction. Acicular iron oxides occur, for instance, when moisture is carefully withdrawn from the acicular a-FeOOH (goethite). However, the particle shape of the natural iron oxides (hematite) is as a rule isometric. Nevertheless, there are noteworthy exceptions probably connected with the formation of the iron ore deposits where the particles show a propensity for cleavage along the basal plane. Processing is basically the same as with the isotropic magnets. Owing to the shape of the particles only a few special requirements have to be met. Milling is not only important for increasing the activity during sintering but also because it permits the shape of the particles to be influenced. Depending on the oxide used, particulate aggregates, for instance, not capable of being aligned can be separated into single alignable particles or an existing anisometry of the particles can be destroyed so that these lose their alignability. In shaping the anisometric particles have to be aligned. In dry or wet pressing this occurs when the punch moves into the die; this is also the case with the platelet-shaped hexaferrite particles (press working anisotropy, cf. section 2.1.5). The particles can also be aligned by rolling or extruding a plasticized raw mix. Suitable plasticizing agents are soft waxes, for instance, with fusion points of around 45°C, which are easy to shape at room temperature and can be easily evaporated or drained after shaping. Figure 56 shows the influence of the sintering temperature on the demagnetization curve of a specimen which originally consisted of a mixture of SrCO3 and acicular a-Fe203. Within a narrow temperature range (a few multiples of 10 degrees) the transition takes place from the high coercivity to the low coercivity condition,_ the duration of annealing also making itself felt. This transition is due to abnormal grain growth. In the case described the growing crystallites were fairly well aligned so that growth at the expense of the small, poorly aligned crystallites led to an improvement in texture and thus to an increase in remanence. The remanence
516
H. STJifl3LEIN 400
rnT 300 200 tO0 1 6 l~J
-400
_._
~
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kA/rn -300 Field strength H -
tO0 ~-
- 200 -300 -
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-500 Fig. 56. Demagnetization curves of differently sintered specimens. Starting material: mixture of synthetic, needle-like c~-FeaO3 (Bayer) and SrCO3, wet pressed.
~00 mT
(BH)max=15.9 k J
j
300 200 100
Field strength H /
-30'9
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~00
~,I
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Fig. 57. Demagnetization curves of differently prepared specimens after sintering at 1230°C. Starting material: mixture of natural hematite with pronounced cleavability along basal plane and BaCO3, Curves (la) and (lb): anisotropic magnet due to wet milling and wet pressing of the mixture, measured parallel and perpendicular to pressing direction. Curve (2): isotropic magnet due to dry milling and dry pressing.
HARD FERRITES AND PLASTOFERRITES
517
values attainable correspond to those of double-sintered, anisotropic magnets. As, however, this high anisotropy occurs owing to crystal growth and thus at the expense of coercivity, the magnetic values of single-sintered anisotropic specimens are, as a rule, not as good as those of the double-sintered specimens. It should be pointed out that with poorly oriented specimens abnormal crystal growth does not lead to an improvement in remanence. This behaviour is analogous to that of double-sintered magnets (section 2.1.6). Figure 57 shows the demagnetization curves of a mix subjected to a different treatment. Natural iron oxides and barium carbonate were used. After 16 hours of wet milling in a vibration mill, wet die pressing and sintering at 1230°C an anisotropic magnet was obtained with a (BH)max value of 15.9 kJ/cm 3 (2.0 MGOe) in the preferred direction. After 22 hours of dry milling, dry die pressing and sintering at 1250°C, however, an isotropic body with a (BH)max value of 7.2 kJ/m 3 (0.9 MGOe) was obtained. Even better values can be achieved with synthetic iron oxides or hydroxides (Takada et al. 1970b, Esper et al. 1974). Brief mention may also be made of another manufacturing method which is similar to both single and double sintering. However, in this process anisometric iron oxide particles are also used and the mix die pressed. After reaction, pressing is repeated in the same die without prior milling, which is analogous to calibration, and sintering repeated. This process enables oriented magnets to be produced without using any magnetic field (DE-OS 2 110 489).
2.2.2. Precipitation techniques With these techniques at least one of the metal ions derives from a feed substance obtained by precipitation or hydrolysis from an aqueous solution. The term co-precipitation is used when all cations are derived from a common solution. The aim of these techniques is to obtain as intimate mixing of the feed materials as possible from the very start. This facilitates the formation of the compound in the subsequent reaction step owing to the short diffusion paths. The reaction can take place at relatively low temperatures and under optimum conditions a powder can be obtained containing single domain particles of correspondingly high coercivity. The next logical step would be to obtain the hexaferrite rather than the mix of feed substances from the aqueous phase. This appears to be possible but its practicability cannot yet be assessed for hexaferrites. The advantages offered by these techniques are the following: they can be used even with contaminated raw materials (self-cleaning effect), there is no carry-over of impurities by abrasion in milling and a narrow particle-size range is obtained. The large water requirements must be regarded as a disadvantage for commercial applications. In actual operating practice, an aqueous solution of one or several salts is used. As metal salts, especially chlorides (not with lead) nitrates, oxalates, and acetates can be considered. The hydroxides or carbonates of these metals, which are practically insoluble in water (exception: Ba(OH)2), can be recovered from the solution. This takes place either by precipitation by means of an alkaline solution (e.g. NaOH, NH4OH) and/or water-soluble carbonate (e.g. Na2CO3, ammonia
518
H. ST~kBLEIN
carbonate) or passing NH3 and C O 2 gas through the solution or by means of the thermal hydrolysis of the salts. Another technique is called freeze drying, because a thin stream of aqueous solution is squirted into a cold, immiscible liquid forming freezed granules there. The granules are separated from the liquid and the ice is sublimated, while the raw mixture is retained (Schnettler et al. 1968). The particle size of the precipitated product depends not only on the type of product but particularly on the conditions under which precipitation takes place and can range from about 0.01 to 10 txm. The temperature necessary in the subsequent hexaferrite reaction depends on the particle size. Hexaferrite single-domain particles of very high coercivity can only be obtained from very fine feed substances which react at temperatures of 800 to 900°C. Table 7 shows some of the results published in literature. The precipitation techniques can be subdivided into chemical co-precipitation, chemical partial precipitation, thermal hydrolysis, electrolytic co-precipitation and hydrothermal treatment. Most of the tests were carried out using chemical precipitation. In the tests carried out by Sutarno et al. (1967) the metal salts separated in very different particle sizes (table 7). While the iron hydroxide was amorphous, the carbonates of barium, strontium and lead were present in particle sizes of around 5 ~xm. As a result, segregation occurred with larger mixes and the formation of hexaferrites took place in the same temperature range as with mechanically mixed feeds. Obviously it is of no advantage if only one raw material is highly reactive. All raw materials must exhibit a sufficient degree of reactivity and steps must be taken to ensure that they are intimately mixed. The tests carried out by Haneda et al. (1973b, 1974b) led to amorphous pre~ cipitation products and the main quantity reacted to form hexaferrite after annealing at 800 to 850°C. After two hours of annealing at 925°C, a particle size of 0.15 ixm (BET-method), a specific saturation polarization of Js/p = 85.16 mT cm3/g (o-s = 67.8emu) and a c0ercivity jHc of 480 kA/m (6 kOe) were obtained with non-oriented specimens. The hysteresis loops measured and calculated according to Stoner-Wohlfarth (1948) compared favourably from which the conclusion can be drawn that there was coherent reversal of magnetization in these obviously almost ideal crystals. Further processing by pressing and sintering or by hot pressing (cf. section 2.2:5) produced partly oriented, high-coercivity specimens. Similar results were attained by Gordes (1973) and Roos et al. (1977) who, in addition, succeeded in increasing the coercivity of the particles to 1He = 510 kA/m (6.4 kOe) and the specific saturation polarization to JJp--88.8mTcm3/g (O's= 70.7 emu) by strong etching in hydrochloric acid with an attendant loss of material of about 70%. The hexaferrite formation of the co-precipitated mixture took place between 700 and 800°C possibly without BaFe204 as an intermediate phase and yielded a small grain size distribution (Roos 1979, 1980), see also section 2.1.3. Mee et al. (1963) used a chemical precipitation technique (not described in detail) for making platelet-shaped Ba- and Sr-hexaferrite particles with diameters from 80 to 150nm and coercivities of 425 and 456kA/m (5.35 and 5.75 kOe) respectively. Goldman et al. (1977) investigated the influence of different manufacturing parameters in chemical co-precipitation for magnetically soft ferrites. Qian et al. (1981) prepared Sr-hexaferrite by annealing a co-precipitated
HARD FERRITES AND PLASTOFERRITES
519
mixture of ferric hydroxide and strontium laurate for 70 days at 550°C. The mixture was prepared from iron nitrate, strontium nitrate, lauric acid and ammonium hydroxide. Intermediates are y-Fe203 and solid solutions of SrO in y-Fe203. No magnetic or grain size data were reported. While the above-mentioned co-precipitation method mainly served to produce magnetically ideal hexaferrite particles, tests for chemical partial precipitation were conducted with a view to establishing possible advantages in the industrial manufacture of hard ferrites. The iron oxide is not precipitated but exists from the very start as a solid phase. The alkaline earth component is either introduced in the form of a solution, e.g., St(NO3)2 (Sutarno et al. 1969) or Ba(OH)2 (Erickson 1962) or initially as a solid phase SrSO4 which is re-precipitated into SrCO3 by ion exchange (Cochardt 1966). In the latter process, the fact that SrCO3 is even more insoluble in water than SrSO4 is utilized so that the ion exchange takes place in the presence of Na2CO3 or (NH3)2CO3. The process has long been known for making SrCO3 from SrSO4 (Gallo 1936, Ullmanns Encyclopfidie 1965, Sutarno et al. 1970b) but was used by Cochardt (1969) for making strontium hexaferrite. In this H - C process (H for hematite, C for celestite = natural strontium sulphate) the raw materials iron oxide and celestite are ground as an aqueous suspension together with Na2CO3 in a mill, with size reduction, blending and chemical reaction taking place simultaneously (Steinort 1974). An analogous approach cannot be used for barium hexaferrite because BaSO4 is more insoluble in water than BaCO3. By thermal hydrolysis of a Ba- and Fe-acetate solution in contact with paraffin oil at a temperature of 300°C Metzer et al. (1974, 1975) produced amorphous precipitates with a specific surface area of more than 100 m2/g and particle sizes from 10 to 20 nm from which hexaferrite powder with a specific surface area of 5.7 m2/g, a particle size of 0.2 Ixm and a coercivity jHo of 420 kA/m (5.3 kOe) could be obtained by annealing. Beer et al. (1958) described a continuous electrolytic co-precipitation process for making powders for isotropic barium hexaferrites. This process uses metallic cathodes and an alkaline electrolyte; no detailed information, however, is given. By means of freeze drying Miller (1970) produced barium hexaferrites starting with a solution of iron oxalate and barium acetate. Other substance combinations turned out to be more disadvantageous. Specimens with different Fe203/BaO ratios having different additives of SiO2, A1203, PbO, Bi203, CaO or TiO2 were dry or hot pressed without application of a magnetic field. While all the processes described above furnish a raw mix which needs to be heat treated for the formation of hexaferrites, the hydrothermal process (Takada et al. 1970a, Van der Giessen 1970) furnishes barium hexaferrite particles directly as precipitate. No magnetic data, however, were given. With the DS process the techniques of co-precipitation and spray calcining are carried out simultaneously, see section 2.2.4.
2.2..3. Melting techniques As explained in section 1.3, it is not possible to directly separate Ba(Sr)Fe~:O19 crystals from a melt of alkaline earth and iron oxide with a cation ratio,
520
H. STABLEIN
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H A R D FERRITES A N D PLASTOFERRITES
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522
H. ST~A3LEIN
Ba(Sr):Fe = 1:12, at least not in air. This was confirmed in tests carried out by Bergmann (1958) who attempted to make BaFe12019 and found a lack of oxygen in the reaction product. With BaFea2019 and, presumably, also SrFelzO19, higher oxygen pressures are needed to avoid the formation of primary phases containing Fe 2+. From melts richer in B a O or SrO, however, hexaferrite can be separated as a primary phase (Kooy 1958, Goto et al. 1971). This process supplies monocrystals in sizes of up to several millimeters. Whether high-coercivity crystals in sizes from 0.1 to 1 ~ m can also be made is not known. Non-crystalline solid specimens of the systems BaO-Fe203 and PbO-Fe203 can be made in a larger range of compositions by splat-cooling the melt (Kantor et al. 1973). On heating a eutectic specimen (40mol % BaO, 60tool % Fe203) BaO.Fe203 crystallizes at 610°C and at 770°C BaO-6Fe203 also (Monteil et al. 1977). No detailed information was given on their magnetic properties, however. In an analogous way amorphous specimens of the system SrO-Fe203 can be prepared, too, in which SrO.6Fe203 crystals are formed at temperatures of at least 720°C (Monteil et al. 1978). Relatively large crystals can be crystallized out of molten fluxes, e.g., from melts containing NaFeO2 or PbO, Bi203, B203 or alkali halide/earth alkali halide (composition, for instance, as with Arendt 1973b). These processes are used to make crystals for scientific purposes, e.g., for studying domain configurations and wall movements. In the past few years a number of melting processes has become known in which technically interesting aspects play a role. They are compiled in table 8. According to Routil et al. (1969, 1971, 1974), Ba- and Sr-hexaferrites can be made directly using their sulphates, i.e., from the most important minerals of barium and strontium without it being first necessary to convert them into carbonates. In addition to the raw materials sulphate and iron oxide only NaCO3 or other suitable additives are required. Stoichiometric hexaferrite crystals crystallize from a large range of compositions; two possibilities are shown in table 8. Typical reaction conditions are 1 hour at 1200°C in air. The formation of strontium hexaferrite was investigated in detail and NazFe204 and 7SrO.5Fe203 were found as intermediate products. Depending on the composition of the raw mix and temperature, the process can be operated as a straight-forward solid state reaction or as a reaction in which a molten component is present. The iron oxide used need not be particularly fine and an excess of A1203 and SiO2 impurities is converted into water-soluble Na-compounds (self-cleaning). Phase separation of the reaction product is carried out by leaching and magnetic separation. Depending on reaction conditions, the hexaferrite particles can be in millimeter-sizes. Magnetic properties are not mentioned. The process of Wickham (1970) is based on the normal raw material mix of iron oxide and Ba- or Sr-carbonate which can react in a melt composed of 80 mol % Na2SO4 and 20 mol % K2S04 at 940°C. In this composition, the sulphate mixture has the lowest melting point of 845°C. Fine crystalline reaction products BaFe12019 or SrFe~20~9 can therefore presumably be made although no information is furnished on this.
H A R D FERRITES A N D PLASTOFERRITES
523
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524
H. STPd3LEIN
The same raw materials iron oxide and carbonates were used by Arendt (1973b), but preferably a salt melt consisting o f 50 mol % NaCI and 50 mol % KC1. The best magnetic properties were obtained under the reaction conditions ½h at 1000 to 1050°C in air, e.g., BaFe12019 powder with up to jHc = 340 kA/m (4.3 kOe) and theoretical saturation polarization. The quality of the iron oxides used is of special importance when high-coercivity hexaferrite crystals are to be produced because the Fe 2+ content must be kept sufficiently low. In this case, an aqueous FeC13 solution is used, precipitated with a solution of 50 mol % NaOH and 50 mo! % KOH, Ba- or Sr-carbonate is admixed followed by spray-drying which produces an intimate mixture of the reaction couples and of the melting agent. After further processing as described, hexaferrite powder was obtained with theoretical saturation polarization and coercivity up to 430 kA/m (5.4 kOe) for BaFea2019 or up to 475 kA/m (5.97 kOe) for SrFe12019. Rather than using a salt bath, Shirk et al. (1970) used a glass melt in making BaFe12019 crystals. They quenched a melt consisting of 26.5moi% BzO3, 40.5 mol % BaO and 33 mol % Fe203 between brass rollers as 100 ~xm thick strip so rapidly that the glassy state was retained from which the BaFe12019 crystals precipitated in the form of hexaferrite by heat treatment- maximum 45 % by weight- which corresponded to the total iron oxide charged. The particle size can be varied within wide limits by heat treatment and superparamagnetic, single, or multi-domain behaviour generated. After annealing at 660 o~--690°C, a coercivity jHc = 206 or 230 kA/m (2.6 or 2.9 kOe), being constant between 77 and 300 K, was attained; after annealing at 820°C, however, a maximum coercivity of 425 kA/m (5.35 kOe) was attained at 300 K which again, however, showed the usual temperature dependence (see section 3.2). From a similarly composed melt (21.24mo1% B203, 47.23mo1% BaO, 31.53 mol % Fe203) Laville et al. (1980) produced ca. 50 Ixm thick, amorphous ribbons by quenching between steel rollers. After annealing at 707°C the ribbons showed permanent magnetic characteristics a s B r = 45 mT (450 G), ~Hc = 31 kA/m (390 Oe), and jHc = 320 kA/m (4 kOe). A hexaferrite phase also crystallizes by annealing at least at 667°C amorphous specimens of 30 mol % NazO, 10 mol % BaO, and 60 mol % Fe203 (= eutectic composition of the quasibinary_ system Na20-BaFe12019) exhibiting jHc = 320 to 366 kA/m (4.0 to 4.6 kOe) (Laville et al. 1978). Other papers deal with the amorphous state only of specimens of the system B203-BaO(PbO)-FezO3-GeO2 (Ardelean et al. 1977, 1980, Burzo et al. 1980, Moon et al. 1975, Syono et al. 1979, Hayashi et al. 1980). Similar results were reported for Ba-Sr-hexaferrite crystals (Oda et al. 1982). 0.3 ixm crystals of Sr-hexaferrite were obtained by annealing a SrO-BzO3-SiOzFe203 glass at 800°C for 5 h (Kanamaru et al. 1981). To sum up it can be stated that some of the melting techniques exhibit a number of attractive aspects because the mixing and the reaction of the raw materials is greatly facilitated by a liquid phase present in a fairly large quantity, cf. table 6 in section 2.2. Technically, the possibilities are probably not yet fully exploited. A disadvantage is that by-products occur per force and that water consumption is relatively high.
HARD FERRITES AND PLASTOFERRITES
525
2.2.4. Fluid bed and spray techniques Using the conventional solid raw materials, the aim of these techniques is to control the hexaferrite reaction from the start so that only single crystals of single domain size are produced. This reduces milling requirements and the resultant risk of contamination by abraded particles and tempering to increase coercivity (cf. section 2.1.4) may perhaps also be dispensed with because the powder already has a high coercivity. Two processes are compiled in table 9. TABLE 9 Fluid-bed and spray techniques. Manufacturing method Fluid bed
Spray calcining
Procedure
Properties of the reaction products
Reference
40 to 500 txm (micro-) granulate from the raw materials reacts in an air stream, e.g. 2 to 3 h at 980 to 1050°C
Slight milling required. Sirone et al. 0.5 ~m size, platelet(1972), shaped Sr-hexaferrite Fagherazzi et al. particles with max. (1974), jHc = 445 kA/m (5.6 kOe) Giarda et al. and Js/p = 63 mTcm3/g (1977)
Milled aqueous suspension of the
Easy to separate 40-200 txm agglomer-
raw material, e.g. Fe203 and Bacarbonate, sprayed into hot fumace, Reaction conditions e.g. 5 s at 1050°C
ates from 0.5-1 Ixm sized, platelet-shaped crystallites with an apparent powder density of 1.0 to 1.6 g/cm3. No magnetic data.
Ruthner (1977)
The fluid bed process uses fine granulate which is made to react in a hot air stream. Granulation is necessary to avoid segregation of the raw material owing to the different behaviour of the particles if suspended individually in the air stream. In spray calcining, however, an aqueous suspension is sprayed into the hot reaction chamber giving a fine subdivision through the formation of droplets. Both processes can be operated continuously (Sironi et al. 1972, Ruthner 1977, 1979). According to Fagherazzi et al. (1974) and Giarda et al. (1977), particularly high coercivity strontium hexaferrite powders with jHc up to 445 kA/m (5.6 kOe) are obtained in the fluid bed process if a mix of SrCO3 and acicular a - F e O O H is used. The latter can be precipitated from a FeSO4.7H20 solution by an alkali. By a proper choice of the raw materials and of the reaction temperature powders are prepared which can be processed either to compact ferrites or to plastoferrites (Giarda et al. 1978). Spray calcining is possible, too, by using a proper solution, see also section 2.2.2. By feeding and spraying a solution of I mole Sr(NO3)2 and 12 mole FeC12 into a 900°C reactor a hard ferrite powder with jHc -- 400 to 430 kA/m (ca. 5.1 to 5.4 kOe) was obtained (DS process; Dornier 1979).
526
H. ST,XA3LEIN
2.2.5. Hot pressing and hot deformation techniques In hot pressing (also known as pressure sintering) a porous mass is compacted under the simultaneous action of pressure (>> 1 bar) and temperature (~ 800°C). In this way the microstructure can be influenced as desired to a much greater extent than is possible in a two-stage process of pressing at room temperature (section 2.1.5) followed by sintering (section 2.1.6). Owing to the effect of the pressure, the temperature can be 100 or even several 100°C lower than in normal sintering so that crystal growth is reduced. In many cases the process produces particles of very low porosity and/or particularly small crystallite size. Such a structure is also desired in hard ferrites in order to obtain at the same time higher remanence and high coercivity (Stuijts 1970, 1973, Jonker et al. 1971). Compaction is usually effected in a die with punches, similar to die pressing at room temperature (section 2.1.5). The hot isostatic method could, in principle, also be used but nothing is as yet known about its use in the manufacture of hexaferrites. Contrary to hot pressing, hot working ideally uses a dense body, the shape of which is changed in the plastic stage. Press forging (upsetting) is such a possibility in which the width is enlarged at the expense of the height of the part. An inverse change of shape is obtained in extruding which produces a thinner and longer part. While such forming is impossible with hexaferrites at room temperature, it can be carried out to a limited extent at elevated temperature. Table 10 and 11 give data from literature on hot pressing and hot forming. It should be taken into account that in some cases both operations took place more or less simultaneously. As the outlines show, very differently prepared starting specimens were used, namely from raw mixes, from reacted hexaferrite powder or from pre-oriented and pre-sintered specimens. The composition of the specimens also varies greatly and has not been defined in all cases. The following processing parameters are mentioned: pressing 5 seconds to 1 hour; temperature preferably 1000 to 1200°C; pressure 35 bar to 12 kbar; tool material A1203, graphite, ZrO2, SiC, Fe. It can be seen that the magnetic values attained vary within wide limits. This is attributable, on the one hand, to the different conditions of the specimens used and, on the other, to the different conditions in hot forming. For a given specimen density, the type and extent of crystal orientation is, of course, of decisive importance for the remanence. With the specimens previously subjected to orientation in a magnetic field a higher remanence is generally obtained than with non-pre-oriented specimens. Flow of the material and crystal growth during compaction play a considerable role in the formation of the texture. According to Von Basel (1981) oriented grain growth is the main reason for the increase of the degree of texture with increasing pressing time. Even die pressing of a raw mix gives anisotropic sintered bodies with a c-axes fibre texture. Such a fibre texture seems to be even more pronounced in press forging because the specimen is then not only shortened axially, but also widened radially. The opposite occurs in extrusion where the specimen is elongated axially and made smaller radially. The c-axes therefore orient themselves preferably perpendicularly to the direction of extrusion and a c-axes ring fibre texture is
HARD FERRITES AND PLASTOFERRITES
527
formed. With such a texture the remanence perpendicular to the direction of extrusion can at best only reach the 2/7r part (approximately 64%) of the saturation polarization, see fig. 70(b). The highest jHc values after hot forming are attained if high-coercivity ferrite powder is used which was obtained by co-precipitation (section 2.2.2). Haneda et al. (1974b) produced in this way dense specimens with iHc = 400 kA/m (5 kOe) which corresponds to about 83% of the initial value of jHc = 480 kA/m (6 kOe) of the powder used. The possible reaction between the hexaferrite and the die wall is a difficulty which these hot techniques entail. The presence of magnetite and other not identified phases impairs the saturation polarization and the permanent magnet characteristics and causes, particularly towards the abscissa, a buckled, e.g. concave, course of the demagnetization curve in the second quadrant so that the (BH)max value and the coercivities fl-/~ and jHc are adversely affected to a fairly great extent. In such cases, these characteristics can be substantially improved by an oxidizing annealing treatment in air, e.g. for two hours at 950°C (St~iblein 1974).
2.2.6. Rolling and extrusion techniques Ferrite powder is usually shaped by pressing using a die and punch as described in section 2.1.5. This technique enables practically all shapes of magnets required in various applications to be manufactured. The typical feature of this technique is that well defined components can thus be made. In contrast, rolling (calendering) or extrusion produces semi-finished products of any length or width which then has to be cut or stemmed to the desired dimensions in a further operation. While these techniques are frequently used for plastic-bonded hard ferrites (section 4.1) they are of a more limited importance for the compact ferrites. Ferrite powder alone is not amenable to rolling or extruding. A binding agent has therefore to be added to make the powder cohesive, to impart movability to the particles and plasticity to the mix and which can be removed on sintering without leaving any or few residuals. For this purpose, the same substances can be used as in granulation (cf. section 2.1.2), but in a much higher concentration, e.g. 50% by volume. Some possible combinations of binding and plasticising agents were mentioned by Schat et al. ~(1970). Strijbos (1973) investigated the mechanism of removing carbonaceous residuals of burnt binding agents. Table 12 gives some data from literature. A particularly important feature of these techniques is that they enable anisometrically-shaped powder particles (acicular or platelet shape) to be oriented by the shearing forces set up between the rolls or in the die and in this way to make the product anisotropic. Using this method, Carlow et al. (1968) oriented Si3N4 whiskers by extrusion with the whisker axes being arranged parallel to the direction of extrusion. With hexaferrites the platelet shape of the particles is utilized (cf. section 2.1.5). The hexaferrite powder used must consist of alignable crystallites. In the "Ferriroll" process (BH)m,x values of up to 28kJ/m 3 (3.5MGOe) are said to have been attained by rolling or calendering, with 0.25 mm thick foils having been stacked until the desired thickness of the part was reached (anonymous, 1967). For this purpose, lead hexaferrite powder with
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HARD FERRITES AND PLASTOFERRITES
535
particles of a pronounced platelet shape was obviously used. The planes of the platelets become preferably aligned parallel to the rolling plane as a result of the shearing forces. By a similar procedure radially oriented cylindrical magnets were prepared from Sr-ferrite and used in,stepper motors (Torii et al. 1979, 1980, Torii 1981, Saito et al. 1981). Much less anisotropy is achieved when barium ferrite powder is used. The manufacture of strips, tubes and segment magnets with a uniform, exactly radial, preferred direction was described by Schiller (1968) and Richter et al. (1968b). In segment magnets (BH)max = 10.5 kJ/m 3 (1.3 M G O e ) was reached in radial direction (Schiller et al. 1970). Not only hexaferrite powder but also a raw mix can be used. If anisometric iron oxide particles are employed, then anisotropic magnets are obtained under certain circumstances after single sintering for the reasons described in section 2.2.1. In this way, St~iblein (1974) attained (BH)max values of up to 16 kJ/m 3 (2 M G O e ) in Ba- and Sr-hexaferrites.
2.2. 7. Preparation of thin layers Layers with thicknesses of about 0.1 to 100 Ixm are of no importance at present in permanent magnet engineering. Investigations so far have been carried out with a view to their use as masking material in the manufacture of integrated semiconductor circuits (Taylor et al. 1972) or as material for microwave and millimeter wave applications (Glass et al. 1977, 1978), for bubble stores, and for studying the reaction mechanism of the formation of Ba-hexaferrite (St~iblein et al. 1972, 1973a, 1973b, cf. section 2.1.3). Some data are compiled in table 13. Permanent magnetic characteristics are not available. In this connection, it may be pointed out that hexaferrite materials were also studied as substrata for thin epitactical layers (Stearns et al. 1975, Glass et al. 1977, 1978). For this purpose the system (St, Ba) (Fe, A1, Ga)12019 was thoroughly measured by Haberey et al. (1977b). It was found that Sr(Fe, A1, Ga)12019 always crystallizes as a single phase with a magnetoplumbite lattice and furnishes wide latitude for independently adjusting the lattice constants and the magnetic saturation polarization. When barium and aluminium are present together, a miscibility gap occurs because instead of BaO-6A1203 the compounds BaO.4.6A1203 and BaO.6.6A1203 are present with a different structure. Later on Haberey et al. (1980b) prepared transparent magnetic SrFesALO19 foils, 3 to 10 p~m thick, on non-magnetic, transparent SrGaa2019 single crystals.
3. Technical properties of hard ferrites
3.1. Magnetic characteristics at room temperature; standardization The behaviour of the flux density B and the polarization J under the action of their own demagnetizing field - H (and possibly of an additional external opposing field) is a significant factor in the actual use of permanent magnets. It is usually assumed that these 3 quantities run parallel or antiparallel to one another although this is not always the case in real magnet systems. The relevant magnetic states of the permanent magnet are then shown in the 2nd (and 4th) quadrant of
536
H. STJ~d3LEIN
the hysteresis loop, the "demagnetization curve", in the two possible representations B(H) and J(H). The maximum demagnetization curve physically possible with the characteristics Br, (BH)m~, ~-/~, jH~, /Xrec and (BpH)m~* can be described by the saturation polarization J~ and the crystal anisotropy constant /£1 as well as the associated anisotropy field HA under the following conditions, cf. section 1.2: (1) The specimen consists of a pure hexaferrite phase, i.e., there are neither pores nor foreign phases. (2) There is no interaction between the crystallites and polarization is reversed by coherent spin rotation (Stoner-Wohlfarth model, Stoner et al. 1948). (3) The c-axes of all the crystallites are completely oriented in the anisotropic specimen and distributed at random in the isotropic specimen. Tables 14 to 16 contain references for the three above-mentioned quantities J~, /£1 and HA. SrM? presents the most favourable combination. The optimum limiting values listed in table 17 are based on the values given by Jahn (1968). The associated demagnetization curves are marked in figs. 58 and 59 with "S-W". For BaM and PbM specimens the optimum limiting values have to be modified in line with the respective values for J~ and/£1. The demagnetization curves of commercial magnet grades are also plotted in figs. 58 and 59. The relevant characteristics are listed in table 18. The demagnetization curves reach the limiting curves satisfactorily to a greater or lesser extent for the following reasons only: (1) The actual saturation polarization is not only correspondingly smaller owing to the presence of pores and non-magnetic phase constituents (cf. section 2.1.6). T A B L E 14 Saturation polarization Js of Ba-, Sr- and Pb-hexaferrites, m e a s u r e d with single crystals (S) and commercial specimens (C). Specimen used
Ba-M B a - M (S) B a - M (S) B a - M (C) B a - M (C) B a - M (C) S r - M (S) P b - M (S) P b - M (S)
0 (K)
660 716 -+ 50 704-+ 38 618
Js in mT* at r o o m temperature
475 480 460 _+ 12 427 422-448 433 472-+ 9 462-466 438---4
Reference ~Casimir et al. (1959) LStuijts et al. (1954, 1955) Smit et al. (1955) Jahn (1968), see also Jahn et al. (1969) Hempel et al. (1965) St~iblein et al. (1966a) Voigt et al. (1%9) Jahn (1968), see also Jahn et al. (1969) Voigt (1969) P a u t h e n e t et al. (1959) N6el et al. (1%0)
* I m T & 10 G * (BpH)max, the m a x i m u m " d y n a m i c " energy product, is defined as the m a x i m u m value of the product of Bp and H. Here, - H represents the abscissa of a point on the demagnetization curve and Bp the flux density, obtained with the disappearance of field strength - H . t For designation see section 1,3, page 450.
H A R D FERRITES AND PLASTOFERRITES
537
TABLE 15 Constants K1 and K2 of crystal anisotropy of Ba-, Sr- and Pb-hexaferrites. S = single crystal specimen. KI* in kJ/m 3 at Specimen used BaM BaM BaM BaM (S) SrM (S) PbM (S)
0(K) 440 ± 30 465 ---20 282
room temperature 310 300 270 313 _+9 346 ± 7 220
Kz/K1+ <5% <3% <3% <2%
Reference Went et al. (1952) Stuijts et al. (1955) Gerling et al. (1969) Giron et al. (1959) Jahn (1968), see also Jahn et al. (1969) Jahn (1968), see also Jahn et al. (1969) Pauthenet et al. (1959) N6el et al. (1960)
* i kJ/m 3 ~- 10 4 erg/cm 3. t Because of K1 >>K2 with hard ferrites it is sufficient in all practical cases to consider only the first term K1 = K and to neglect all higher ones, as was done in sections 1.2 and 2.1.5.
T h e s a t u r a t i o n p o l a r i z a t i o n o f t h e h e x a f e r r i t e p h a s e , t o o , c a n d e c r e a s e if, f o r example, aluminium or chromium ions are inserted on lattice sites of the iron. The s a t u r a t i o n p o l a r i z a t i o n o f c o m m e r c i a l s p e c i m e n s is t h e r e f o r e o n l y a b o u t 9 0 % o f t h a t o f t h e p u r e h e x a f e r r i t e p h a s e , cf. t a b l e 14. (2) A s r e g a r d s t h e c o e r c i v i t y j H c t h e r e a r e r e l a t i v e l y g r e a t e r d i f f e r e n c e s t o t h e above limiting values at least in commercially manufactured specimens, because t h e m a g n e t i z a t i o n is n o t r e v e r s e d b y c o h e r e n t r o t a t i o n o f t h e s p i n s b u t b y
TABLE 16 Anisotropy field HA of Ba-, Sr- and Pb-hexaferrites at room temperature, measured with single crystals (S) and commercial specimens (C). Specimen used
HA* (MA/m)
BaM (S) BaM (S) BaM (S) BaM (S) BaM (C) BaM (C) BaM SrM SrM (S) SrM
1.35 1.29 1.27-1.38 1.35 1.35 1.22-1.24 1.43 1.54 1.40-1.51 1.63
PbM (S) PbM (S) PbM
1.i0 1.11-1.15 1.31
* 1 MA/m --" 12.57 kOe
Reference Smit et al. (1955) Silber et al. (1967) Jahn (1968), see also Jahn et al. (1969) Dixon et al. (1970) Hempel et al. (1965) Voigt et al. (1969) Mamalui et al. (1975) De Bitetto (1964) Jahn (1968), see also Jahn et al. (1969) Mamalui et al. (1975) ~Pauthenet et al. (1959) tN6el et al. (1960) Voigt (1969) Mamalui et al. (1975)
538
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Fig. 58. Demagnetization curves J(H) of commercial hard ferrite grades (curves (la) to (4)) compared with ideal coherent rotation model (Stoner-Wohlfarth curves "S-W" fitted to Js = 472mT and /£1 = 346 k j/m3): (la) grade KOEROX 360 (anisotropic); (lb) grade K O E R O X 380 (anisotropic); (2) grade K O E R O X 300 K (anisotropic); (3a) grade KOEROX 300 (anisotropic); (3b) grade K O E R O X 330 (anisotropic); (3c) grade KOEROX 330 K (anisotropic); (4) grade KOEROX 100 (isotropic). (KOEROX is the registered trademark of Fried. Krupp GmbH, D-4300 Essen, for hard ferrites.)
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nucleation of domains magnetized in opposite directions and by Bloch wall displacement• These processes take place in sometimes considerably smaller opposing fields than the coherent rotation (Haneda et al. 1973a, Roos et al. 1980). (3) The c-axes of the anisotropic specimens are never completely aligned. This means a reduction in the above-mentioned limiting values of both Br and jHc. B r - c o s o~ decreases as the angle a between the c-axis and the magnetic field increases (fig. 39). The dependence HA(a), however, for coherent spin rotation is
540
H. ST~BLEIN TABLE 18 Remanence Br, maximum dynamic energy product (BvH)max, maximum static energy product (BH)max, coercivity eric, intrinsic coercivity jHc and relative recoil permeability/zrec of commercial hard ferrite grades*. Manufacturers' sales literature often gives the ranges of magnetic characteristics prevailing in mass production. The values given below were obtained from favourably sized specimens of the upper quality level. Minimum values of standardized grades are shown in tables 20 and 22. Nominally isotropic grades can exhibit slight anisotropy, see text on page 540. Grade Isotropic: KOEROX** 100 Anisotropic: KOEROX 360 KOEROX 300 KOEROX 300 K KOEROX 330 KOEROX 330 K KOEROX 380
B~ (mT)
(BpH)max (BH)max (kJ/m3) (kJ/m3)
BHo
JHc
(kA/m)
(kA/m)
]abrec
230
35
9.1
151
240
1.18
400 375 370 370 360 400
67 67 78 88 92 102
30.2 25.3 25.3 25.3 24.0 30.4
175 185 224 249 263 260
176 186 225 250 300 265
1.06 1.07 1.06 1.06 1.06 1.05
* 1 mT~ 10 G; I kJ/m3 --"0.1257 MGOe ~ 1/8 MGOe; i kA/m ~ 12.57 Oe ~ 100/80e. ** KOEROX is the registered trademark of Fried. Krupp GmbH, D-4300 Essen, for hard ferrites.
very strong, especially with small a, e.g., HA(10 °) ~ 0.67HA(0°), see curves " S W " in figs. 73 and 74. C o m m e r c i a l "isotropic" specimens often exhibit slight directional orientation which derives f r o m the anisometric particle shape and the theological p h e n o m e n a during m a n u f a c t u r e (cf. section 2.1.5). M e a s u r e d in the preferred direction, this influence can offset the disadvantages m e n t i o n e d u n d e r (1), page 536, cf. curves 4 in figs. 58 and 59. T h e r e m a n e n c e can be quantitatively calculated f r o m the orientation distribution of the crystallites, which is d e t e r m i n e d by radiography, assuming that after magnetization the spins in each crystallite lie parallel to the nearest c-axis and there is no interaction b e t w e e n adjacent domains. Slightly t o o high Br values were f o u n d in such a c o m p a r i s o n (Stfiblein et al. 1966a). T h e difference can be attributed to anisotropic internal shearing (Stfiblein 1968a). If the r e m a n e n c e is a s s u m e d as given, then u n d e r the action of an increasing opposing field changes in magnetic state first occur, as described by the S t o n e r - W o h l f a r t h theory. Deviations are o b s e r v e d with the grades f r o m H ~ - 1 4 0 k A / m (~--1.76 k O e ) shown in figs. 58 and 59, because i n h o m o g e n e o u s magnetization processes then occur. These set in so suddenly with the anisotropic grades that the polarity of a b o u t ~ of the m a g n e t v o l u m e is reversed within a field c h a n g e of s o m e k A / m (several 10 Oe). Quantitative calculations or predictions are no longer possible in this case. Figures 58 and 59 contain the demagnetization curves of only one isotropic but several anisotropic grades (No. 4 and l(a) to 3(c)). T h e isotropic grade is easy
HARD FERRITES AND PLASTOFERRITES
541
to manufacture and the course of its demagnetization curve largely corresponds to what is physically possible, at least between points Br and uric. This is the important region in actual applications and thus there is no need for further isotropic grades. The picture is different with the anisotropic grades. In principle, it is easy to manufacture grades of high remanence and low coercivity and vice versa (including transitions) either by appropriate selection of the manufacturing conditions (especially the sintering conditions, cf. section 2.1.6 and fig. 45) or by the type and amount of additives (cf. section 2.1.1). In order to obtain both properties with values near their upper limits, all parameters relating to composition and manufacturing technology must be matched precisely. For example, the highest-quality grades corresponding to the curves lb and 3c are manufactured by wet pressing (cf. section 2.1.5) using strontium hexaferrite. Higher manufacturing costs are, of course, reflected in the prices with the result that the necessary quality criteria will not be set higher than absolutely necessary in view of the geometric and magneto-physical circumstances and possibilities. This not only applies for use at room temperature but for the entire temperature range under consideration (cf. section 3.2) including all other influences (cf. sections 3.3 to 3.5). In order to obtain the optimum magnetic values the material must be completely magnetized. This requires field strengths at least double to treble the coercivity jHc (Stfiblein 1963). Here, the actual field strength in the material is meant, i.e., any existing demagnetizing field has to be applied additionally. If magnetization or remagnetization is incomplete, inner hysteresis loops with correspondingly lower characteristic values will be passed through, cf. figs. 60(a) to (d). It is worth noting that the innermost loops have only a narrow lancet-like shape, even with anisotropic grades. Here, predominantly reversible magnetization changes take place. The rectangular shape of the outermost loop is only reached gradually. Inner hysteresis loops of hard ferrites (and other permanent magnet materials) were measured by Dietrich (1969). It may be appropriate at this point to make a few remarks on national and international material designations and classifications. Every manufacturer has, of course, his own trademark(s), cf. table 19. The various qualities are designated by additional numbers or letters. This may be purely continuous numeration without any reference to magnetic values. In certain countries, however, the number has a direct relationship to the (BH)m,x value (so far always expressed in the CGS numerical value for the unit GOe) and a letter can represent the high-remanence grade with R, B etc. and the high-coercivity grade with K, H etc. For example, a ferrite grade "100" means a (practically) isotropic material with a (BH)max value of approximately 100 × 104 GOe (= 1 MGOe ~ 8 kj/m3). Analog designations for anisotropic materials with correspondingly higher (BH)m~x values are "250" to "430". Moskowitz (1976) has listed the tradenames of hard ferrites and other permanent magnet grades. In recent work on standards for permanent magnet materials a designation system is contemplated which is understandable internationally, is related to the most important permanent magnet characteristics and takes into account the ISO
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H A R D FERRITES AND PLASTOFERRITES -7
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TABLE 19 Standard designations and trademarks of sintered hard ferrites from various countries. Some trademarks are of historical interest only. Country Federal Rep. Germany
Standard designation Hartferrit
Trademarks Cekasyd DF Dralodur Ferram KOEROX Ox Oxidur Oxit Oxyd Roboxid SAF-Ferrit Unox
German Democ. Rep.
Maniperm
France
Oxonyte Spinal Spinalor
Great Britain
Caslox Feroba Magnadur
Italy
Oximag Sinterox
Japan
MPA MPB
FB Ferrinet FXD SSR YBM
Netherlands
Ferroxdure (FXD)
Spain
Ferdurite Ferribarita
CSSR USSR USA
Durox Bi; BA Ceramic
Arnox Ceramagnet Cromag Duramax F Ferbalite Ferrimag Genox Indox M Magnite Mi-T-Mag MO Moldite Westro KF
Korea (South) 544
HARD FERRITES AND PLASTOFERRITES
545
(International Standardization Organization) recommendation R 1000 on the introduction of the SI system (Syst6me Internationale d'Unit6s). As an example, table 20 shows the hard ferrite grades covered by D I N standard 17 410 of May 1977 in the Federal Republic of Germany. These are characterized by a pair of numbers. The first n u m b e r indicates the minimum (BH)max value in kJ/m 3, the second n u m b e r the minimum value of the coercivity ~Hc/lO in kA/m. The selection of these two values allows for the fact that the (BH)ma~ value is the most important characteristic for static applications where the state of the p e r m a n e n t magnet is constant in terms of space and time, whereas for dynamic applications the coercivity jHc represents a measure of and a reference to the stability and the load capacity of the magnet in alternating counter fields. Proceeding from this national work on standards the International Electrotechnical Commission (IEC) has recently started work on magnetic materials in its technical committee 68. Initially, a classification of all magnetic materials was drawn up (IEC publication 404-1, 1979) containing the typical values or value ranges of the characteristics of interest. Table 21 contains the values given for hard ferrites. T h e lower limits of the value ranges largely match the minimum values of D I N 17 410, table 20. The p e r m a n e n t magnet materials were specified in another I E C document (68 C O 24, 1980) and the values in table 20 largely adopted. Only the grade 26/18 was added, cf. table 22, thus showing that standards of quality are in good agreement worldwide*. T h e characteristic values for p e r m a n e n t magnets are usually determined by passing "slowly", quasi-statically through the demagnetization curve or h y s t e r e s i s loop. However, the polarization J obtained with a constant field strength is actually dependent on time and one therefore speaks of "thermal after-effect". In a n u m b e r of p e r m a n e n t magnet materials the polarization decreases according to the formula AJ = S log t + C where S is proportional to the absolute temperature, C is a constant and t the measuring period. With anisotropic specimens, J is highly dependent on the working point and the direction of m e a s u r e m e n t according to Dietrich (1970). A J is much smaller above the knee of the demagnetization curve than below it, i.e. on the steep gradient of the hysteresis loop, and much smaller a J values are observed in the jHc range if m e a s u r e m e n t s are m a d e perpendicular to the preferred direction. A difference must be made between the thermal after-effect and the natural stability, which means the change in the state of magnetization of a p e r m a n e n t magnet or p e r m a n e n t magnet system in its own demagnetizing magnetic field following prior magnetization (and, possibly, stabilization). The results obtained by various authors are compiled in table 23. As the specimens used were not * National standards or standard-like agreements on hard ferrites in other countries are: -Japanese Industrial Standard (JIS) C 2502 (1975) "Materials for Permanent Magnet"; -Magnetic Materials Producers Association (MMPA) Standard No. 0100-75, Evanston/Ill., USA, "Standard Specification for Permanent Magnet Materials"; -Fachbereichstandard TGL 16541/01 (1976), GDR, "Hartmagnetische Werkstoffe, Oxidische Sinterwerkstoffe". - GOST 24 063-80, USSR, "Magnetically hard ferrites" (contains only Ba-hexaferrites). /
546
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adequately characterized in all cases, it is not possible to make a quantitative comparison. Qualitatively, it can, however, be concluded that the natural stability increases as coercivity increases. Kronenberg et al. (1960) established a logarithmic dependence of the flux density on time. According to Dietrich (1970) the instability disappears if the working point is close to remanence or coercivity 8He and has its maximum value when the working point is close to the (BH)max point. The problem of natural stability was dealt with theoretically by N6el (1951). 3.2. Influence of temperature on magnetic properties The magnetic state and magnetic properties of a magnet below its Curie temperature Tc (~450°C for hard ferrites) are, for various reasons, dependent on its temperature history and the temperature at which they are measured. The temperature history includes the sintering treatment where the density and the grain size of the magnet and thus its remanence and coercivity, inter alia, are adjusted by control of the sintering temperature and period, cf. section 2.1.6. In contrast to metallic permanent magnets hexaferrites do not require any further heat treatment with the result that only the structure produced by sintering determines the magnetic properties at the service temperature. Irreversible changes in the structure and thus in the magnetic properties would only occur if the magnet were again reheated to sintering temperature, i.e., to around 1200°C. Hexaferrites are thus the permanent magnets with by far the most stable structure. The temperature history can also influence the directional distribution of the domains. After magnetization the polarizations of each crystallite should be oriented parallel to the direction of the adjacent local c-axis, i.e., 0 ° to a maximum of 90 ° to the magnetizing field. This occurs when the nucleation field strength is n o t exceeded anywhere. If, however, it is exceeded, polarization changes irreversibly to the opposite direction and angles exceeding 90 ° are observed. With commercial anisotropic magnet grades the nucleation field strength is practically identical to the coercivity jHc since the hysteresis loop is more or less rectangular, cf. figs. 58 and 60. Irreversible changes in the directional distribution of the spins and thus irreversible changes in the flux emitted from the permanent magnet therefore occur when the (local) coercivity is no longer greater than the (local) demagnetization field. With hexaferrites the coercivity drops as the temperature decreases, in this case with the danger of irreversible magnetization changes occurring. The term "irreversible" refers only to the instantaneous change which cannot be reversed by temperature changes but by re-magnetization only. With the reversible magnetization changes there is a clear relationship between the magnetic characteristic value o r magnetic state and temperature. For a not too large temperature range A T the change ABr in the remanence and AjHc in the coercivity can be regarded as linear and described by a temperature coefficient c~: 1 ABr a(Br) = Br AT '
and
1 AjH¢ a(sHc) = iHc A T '
H A R D FERRITES AND PLASTOFERRITES
551
where the initial values Br and ~Hc are usually related to room temperature. In the following the temperature dependences of Br and of jHc and then the temperature dependence of the entire demagnetization curve will be examined. Figure 61 shows the saturation polarizations Js of BaM, SrM and PbM as well as the remanences Br of anisotropic and isotropic commercial barium ferrites as a function of temperature. Further similar data are given by Rathenau et al. (1952) (BaM), Richter (1962) and Schiller (1965) (anisotropic Ba-ferrite) and Fahlenbrach (1963) (isotropic Ba-ferrite). All curves are straight-lined in a wide temperature range and with a gradient which corresponds to a temperature coefficient of about a(Js)= (B 0 = - 0 . 2 % / K near room temperature. Both temperature coefficients are equal when the polarization of the material is rigid, i.e., no polarization reversals take place. If and at what counter field H v this behaviour is present can be seen from the fact that the gradient of the demagnetization curve from the remanence up to this field Hp lies at or at least near the theoretical value of /~e~ (cf. table 17). The temperature dependences of B~ and Js are then determined by the same mechanism. In order to assess the jH~ temperature dependence it is useful, as in section 3.1, to first observe the behaviour with coherent magnetization reversal (StonerWohlfarth theory). The temperature dependence of the coercivity jH~ is then
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552
H. STPd3LEIN
given by the temperature dependence of the values H A = 2K/Js for ideally oriented specimens and HA = 0.48 (2K/J,) for isotropic ones. The values found by various authors for BaM and SrM are shown in fig. 62 (curve (a), (b) and (c) of A). Here, the possible influence of a demagnetizating field owing to the platelet-like shape of the ferrite particles (cf. section 2.1.6) has been disregarded. If this influence is taken into consideration, however, and if the crystallites are idealized as extended platelets (fig. 39), then the effective anisotropy field strength is given by the equation H A = 2K/Js-Js/I, Zo for oriented specimens and HA = 0.48 (2K/Js-Js/I, zo) for isotropic specimens which are shown in fig. 62 under B. Figures 63 and 64 contain measured temperature dependences of jHc for anisotropic and isotropic specimens, respectively. The anisotropic specimens fall considerably short of the theoretical values of fig. 62, the best attaining about 40%. With the isotropic specimens, on the other hand, agreement with the theoretical values is better. This applies especially to specimens which were manufactured by co-precipitation (section 2.2.2) and which are listed here for comparative purposes. The curve measured by Mee et al. (1963) on relatively loosely pressed powder largely corresponds to the one theoretically predicted for curve B(c) in fig. 62. Compact specimens, however, only tend to approach the theoretical values at elevated temperatures and then only to a poor degree. This is
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Fig. 64. Measured intrinsic coercivity ]Hc of isotropic hexaferrite specimens vs. temperature, compared to calculated anisotropy field HA. Curve (la) HA = 0.48 (2K/J~ - Js/P-0), same as curve (Bc, isotropic) of fig. 62. Curve (lb) HA = 0.96K/J~, same as curve (Ac, isotropic) of fig. 62. Curve (2a) 30% by v o l . - specimen SrM (Mee et al. 1963). Curve (2b) 30% by v o l . - specimen BaM (Mee et al. 1963). Curves (3) B a M (Sixtus et al. 1956). Curves (4) B a M (Went et al. 1952). Curve (5) BaM (Rathenau et al. 1952, Rathenau 1953). Curve (6) BaM (Fahlenbrach 1963). Curve (7) BaM (Hennig 1966). Curve (8) K O E R O X 100, see also fig. 65(a).
554
H. STABLEIN
attributable to the formation and displacement of Bloch walls. The ever increasing deviation towards lower temperatures is related to the fact that the critical particle size decreases with the temperature (Rathenau et al. 1952, Rathenau 1953, Sixtus et al. 1956), i.e., an increasingly larger proportion of the crystallites tends towards spontaneous Bloch wall formation. As can be seen from figs. 63 and 64, the curve gradients, e.g. in the range from 0 to 100°C, vary considerably, even with roughly the same jHc values at room temperature. For the commercial specimens listed there (jHc> 100kA/m), changes AIHdAT of 0.4 to 1.1 kA/m per K (5 to 1 3 . 8 0 e per K) are found without these values exhibiting a distinct variation with the coercivity. The temperature coefficients of these specimens lie in the range of a(jH~) = 0.15 to 0.50%/K where c~(jH~) tends to increase when jH~ drops, it must be assumed that the temperature variation of jHc depends on the precise constitution of the structure and thus on the details of the manufacturing process. However, this does not appear to have been studied in detail. The K O E R O X materials shown in fig. 62 exhibit in the range from - 4 5 to +85°C average AjHdAT values of 0.67kA/m per K (8.3Oe per K) for the isotropic specimen K O E R O X 100 and 0.79 to 0.94 kA/m per K (9.9 to 1 1 . 7 0 e per K) for the anisotropic grades, i.e., a change fairly independent of coercivity. The average temperature coefficients for the same temperature range are a(jHc)= 0.27%/K for the isotropic grade and 0.28 to 0.48%/K for the anisotropic grades where the approximation a(jH~)-1/jH~ applies. In general, the temperature coefficient for these materials can be approximated from t~(jHc)-- 86/jHc in % / K (jH~ in kA/m). Here, the factor 86 is 100 times the average of the abovementioned range from 0.79 to 0.94 kA/m per K. (In CGS units: a ( j H c ) = 1.08/jHc in % K with jHo in kOe and an average value of 1 0 . 8 0 e / K . ) In practice, a permanent magnet is usually neither in the Br nor jHc state, but in between. In order to evaluate its temperature behaviour the change of the demagnetization curve with temperature must therefore be studied. Figure 65 contains the demagnetization curves of some commercial hard ferrite grades - m e a s u r e d at temperatures of -45, +25 and +85°C. Described ideally, the demag/ n e t i z a t i o n curves always consist of two almost straight sections, a Br and a jHc section, which are linked by a transition section ("knee"). The gradients of both sections hardly depend on temperature. As regards the gradient of the Br sections /Xrec~ 1 is always found for anisotropic grades in accordance with table 17 and even for the isotropic grade there is only a change in gradient of about +2% or - 2 % for the temperatures - 4 5 and +85°C, respectively, compared with the value at room temperature. Therefore, approximation curves for other temperatures can be simply plotted from the demagnetization curve for a certain temperature and from the temperature behaviour of Br and jHc. The behaviour of the magnetic flux as a function of temperature can be described very simply in an idealized diagram (cf. Schwabe 1957). Figure 66(a) contains two idealized demagnetization curves B(H) of an anisotropic hard ferrite for the temperatures T = room temperature and T ' < T. All domains are uniformly oriented on the Br curve sections P4Br and P;B'r, as shown at F1. In the iHc
H A R D FERRITES AND PLASTOFERRITES
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556
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state the polarity of 50% by volume of the magnet is reversed, which is shown diagrammatically in F3. A continuous transition, e.g. represented by F2, takes place on the vertical jHc curve sections P4jgc and P~jH'c. The absence or occurrence of irreversible losses with a temperature cycle T ~ T ' ~ T obviously depends on whether the load line corresponding to the actual working point lies above or below $2. With a load line lying above $2, e.g. at S1, the changes in B and H of the magnet are completely reversible. As is shown in sections (b) and (c) of the diagram, the flux density changes from B I ~ B ~ B 1 and the associated field strength from H1 ~ H~ ~/-/1. With a load line lying below $2 but still above $4, e.g. at $3, the reactions during cooling are still reversible up to the intermediate temperature where the knee PK of the associated demagnetization curve lies on $3. At the intermediate temperature flux density and field strength in the magnet pass through extreme values BK and HK respectively. Further cooling results in the state P; with the values B ; and H ; owing to the irreversible change in polarity of some of the domains. On reheating to T there is no change in the domain distribution established in this way. By plotting the point D this is expressed graphically in such a way that the section ratios are P4D/P4 jHc = P;P;/P~ j H ' c and the transition from D to P~ lies on $3, where the gradient of DP~ (just like that of P4B,) is equal to # .... On heating, both B and H drop to B~ and H~ respectively. The total changes for T ~ T ' ~ T are thus characterized by B 3 ~ B K ~ B ~ B ' ~ (part b) and H 3 ~ H w ~ H ; ~ H ~ (part c).
558
H. STJi,B L E I N
B~ B, B, B,
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=/./It Fig. 66. Reversible and irreversible changes of flux density (b) and field strength (c) of an oriented hard ferrite, shown with idealized demagnetization curves (a) of fig. 65(d) for T = 25°C and T ' = -45°C. Load line examples $1, $3, $5 cause 3 different kinds of demagnetization behaviour of a fully magnetized specimen on temperature cycling T ~ T ' ~ T, divided by the limiting cases S: and $4. Inserts F1, F2, F3 show schematically fully magnetized, partially demagnetized, and completely demagnetized state, respectively.
At a load line below $4, e.g. at $5, domains with reversed magnetization are already present in the initial state P5 whose volume fraction is numerically equal to the section ratio P4Ps/2 P4jHc. By cooling down from T ~ T' this fraction increases irreversibly to P~P~/2 P~ jH" causing flux density and field strength in the magnet to drop to B~ and H~ respectively. After reverting to the initial temperature the state P~ is resumed with B~ and H~. Point P~ can be determined via point E with P4E/P4 jHc = P~P~/P~jHc analogue to point D. The total changes for T ~ T ' ~ T are thus given by B s ~ B ~ B ~ (part (b)) and H s ~ H ~ H ~ (part (c)). The position of point P~ can be found in the same way as that of P~ and Pg. However, the position of points P2, P~, P~ and P~ can also be determined by a different approach. As the respective initial states P~, P;, P; and P; had the same field strength and their associated flux densities dropped by almost the same extent on heating, the states after cooling must also have the same field strength.
HARD FERRITES AND PLASTOFERRITES
559
The position of P2 and thus the desired field Strength are derived directly from the load line $2 passing P~. The changes shown in parts (b) and (c) run reversibly proportional to a (Br) on the sections marked with double arrows whereas the changes on the sections marked with single arrows are irreversibly proportional to a(iHc). The ratios shown idealized and schematically in fig. 66 must be modified for the actual conditions. Firstly, the knee of the demagnetization curve is in practice curved, cf. fig. 65(a) to (e). As a result the curve at BK and HK (fig. 66(b) and (c)) runs into a flat peak. Secondly, the gradients of the 1He sections are finite and the associated field strengths do not therefore coincide exactly. Thirdly, the demagnetization conditions in terms of magnitude and direction are not generally constant throughout the entire magnet volume with the result that various shearings are assigned to the individual volume elements. For example, Schwabe (1957) found that the most unfavourable points of a particular hard ferrite loudspeaker system are subject to a demagnetization field which is twice as strong as the mean field strength. Finally, inhomogeneous material properties can be caused by inhomogeneous manufacturing conditions (e.g. in the degree of orientation and in the grain size distribution), i.e., in this case a family of demagnetization curves must be expected. If, as a result, inhomogeneous demagnetization conditions and/or inhomogeneous material properties occur, the temperature behaviour of a permanent magnet system can be qualitatively estimated satisfactorily only to a greater or lesser extent. Table 24 and fig. 67 show the influence of the working point, the coercivity jHc and the maximum cooling temperature on the extent of the irreversible losses with anisotropic hard ferrites. As expected, the irreversible losses increase as working point, coercivity and temperature decreases. In practice, the described temperature behaviour can thus be allowed for by the choice of material and design. According to the above, irreversible losses may only occur when cooling takes T A B L E 24 Irreversible loss of flux density of oriented hard ferrites with intrinsic coercivities of jHc = 170 to 1 9 0 k A / m (2.13 to 2.38kOe) and with different length to diameter ratios l/d after having been cycled between 20°C and various lower temperatures (Gershov 1963).
l/d 0.18 0.39 0.73 1.0 1.3
Irreversible loss, % -20°C -407C -77°C 19.1 13.3 10.1 0.0 0.0
29.0 24.0 18.5 0.0 0.0
39.7 35.8 28.8 1.7 0.9
560
H. ST~d3LEIN
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lid
place after magnetization but not during heating up to 400°C, the latter being true, independent of the working point (Tenzer 1957, Assayag 1963, Gershov 1963). Irreversible losses during cooling can be avoided or at least reduced by selecting a material with a sufficiently high coercivity jHc and/or by employing a configuration with a sufficiently long magnet so that at the minimum temperature even those unit volumes with the strongest demagnetization are not influenced irreversibly. If these measures are not possible or inadequate, the loss expected later in service can be anticipated. With ferrites it is sufficient to cool the magnet only once to the lowest expected temperature. In principle, it would also be possible to anticipate the losses by partial demagnetization in a magnetic field but no information is available in literature on this point. The irreversible temperature variation is determined by the material and cannot be anticipated but merely influenced by the design. As is usual in permanent magnet technology, the negative temperature variation of the useful flux can be reduced or made positive, also with hard ferrites, using a shunt placed parallel to the useful flux and made of a material with a highly temperature-dependent polarization. The latter is, for example, required with eddy-current systems (speedometers, brake systems for electricity meters) in order to compensate also for the temperature dependence of the electrical resistance of the eddy-current material, e.g., c~(A1)= +0.46%/K and c~(Cu)= +0.43%/K. Such materials ("compensation materials") have been known for some time (St~iblein 1934). Common compensation materials are, for instance, Fe-30%Ni alloys. Their status and development potential are described, inter alia, by Schiller (1965) and Fahlenbach (1972). Owing to the relatively high temperature coefficient a(Br) of the hard ferrites, however, the cross section of the shunt must be larger than with the metallic materials with their 10 times smaller a(Br) value. This means more
HARD FERRITESAND PLASTOFERRITES
561
compensation material as well as a lower useful flux level of the compensated system. In fact, hard ferrite magnets have hitherto scarcely been used for applications where the temperature coefficient of the useful flux has to disappear or be positive. In this connection it must be noted that the temperature variation of the air gap flux of a system is determined not only by the temperature variation of the permanent magnet but also by that of the iron conductors. Their (smaller) temperature coefficient plays an important role, especially with flux densities of above about 1T (Fahlenbach 1963). However, the useful flux is drastically reduced with this procedure so that it is not suitable for general use.
3.3. Influence of deviation from the preferred axis, of mechanical stress, and of neutron irradiation on magnetic properties Influence of deviation from the preferred axis In anisotropic specimens the magnetic characteristics are, owing to the alignment of the c-axes, generally more or less strongly dependent on angle a between the preferred direction of the specimen and the direction of measurement or use. The degree of this dependence is therefore significant for the application of the magnets. In addition, the angular dependence permits certain conclusions to be drawn on the magnetic state and the mechanism of polarization reversal. This dependence presupposes that the magnetizing field and the direction of measurement are parallel to each other. On the other hand, fig. 52 shows the case where the direction of measurement of the magnetic flux was held constantly parallel or vertical to the preferred direction and merely the direction of the magnetizing field changed. In exactly isotropic specimens, of course, the characteristics show no angular dependence. It should be pointed out, however, that nominally "isotropic" specimens may be somewhat anisotropic owing to the flow conditions in powder compaction, cf. section 2.1.5. Depending on the details of the manufacturing process, the magnetic fluxes of the products at present industrially manufactured can differ by up to 20% from each other parallel or perpendicular to the direction of pressing, cf. fig. 46. Differences also obtain in the manufacture of plastic- or rubber-bonded hard ferrites in extruding, calendering or die-pressing, cf. section 4. The angular dependences discussed in the following also apply, albeit to a lesser extent, for such "isotropic" specimens. Figure 68 shows the angular dependence of the remanence Br(a) for some specimens sintered at various temperatures (St~iblein et al. 1966a). The remanence of the pressed state, which largely corresponds to that of the 1100°C specimen, is not shown (Stfiblein 1965). With complete alignment remanence has to run B r - cos a. Although the alignment is incomplete, Br roughly follows this function for sufficiently small angles because cos a changes only slightly in this area. Incomplete alignment is most noticeable in the area of a--~ 90°. As more and more disoriented crystals disappear as the sintering temperature rises, the cos a curve is increasingly approached. Joksch (1964) recorded the same angular dependences for some commercial grades.
562
H. ST.Sd3LEIN
~
q250°C :1350oC
COS, 0 ~ ,
00o
10°
20 °
30 °
,~0°
50 °
60 °
70 °
80 °
90 °
Angle ct to preferred axis Fig. 68. Measured relative remanences B~ vs. angle c~ to preferred axis for anisotropic BaM specimens, sintered at various temperatures (St~iblein et al. 1966a). 1100 ° specimen: Br = 330mT; jH~ = 246 kA/m. 1250 °` specimen: Br = 395 mT; jH~ = 142 kA/m. 1350 ° specimen: B, = 405 mT; jH~ = 41 kA/m.
If the spatial orientation distribution of the c-axes is known, B,(a) can be calculated from it, assuming that the polarization of each crystallite lies parallel to the nearest c-axis after magnetization. The quantitative calculation of the three specimens in fig. 68 showed good agreement, cf. fig. 69. Slight deviations between calculation and experiment point to anisotropic internal shearing owing to nonspherical pores. The influence of the texture sharpness on the remanence was calculated for some model arrangements of the c-axes (St~iblein 1966). With a "normal fibre
- ~ LO ~
I
.
.
smtenng terr
i )erature
O~ (J ¢p •
.................
a,,gnment
1 ............... . . . . . .
. . . . . . . . . . . . . .
¢. OJ
Q:
>1100°C -1250oc 0..0;
-- a cu a i from (oo.aj ,o Deviation
30 ° 60 ° from preferred axis
>1350°6, 90 o
Fig. 69. Measured relative remanences Br vs. angle o~ to preferred axis for the same specimens as in fig. 68, compared to values calculated from c-axis densities.
HARD FERRITES AND PLASTOFERRITES
563
texture", as arises in normal powder pressing in the magnetic orienting field (section 2.1.5) the curves shown in fig. 70(a) are obtained. The frequency distribution f ( a ) of the c-axes is assumed as f ( a ) ~ cos 2i a. i = 0 means the isotropic state, rising i the growing degree of orientation. By analogy, Br can be calculated for the "ring fibre texture" in which the c-axes are preferably parallel to one plane, but within this plane arbitrarily arranged, cf. fig. 70(b). In this f ( a ) - sin 2i a was applied. The actual relationships can be described reasonably well by these model functions, but m o r e precise results are obtained by using a series development according to Legendre polynomials (St/iblein et al. 1966b). T h e r e are various methods of radiographically determining the function f ( a ) (St/iblein et al. 1966b, 1971, Stickforth 1975, Willbrand et al. 1975). Frei et al. (1959) and Shtrikman et al. (1960) described the determination of f ( a ) from Br measurements. T h e accuracy is unsatisfactory, however, as in well aligned specimens the r e m a n e n c e only reacts weakly to changes in the degree of alignment, cf. also fig. 70(a). The angular dependence of the ferromagnetic resonance, too, can be used to determine f ( a ) (Hempel et al. 1964). If the entire or the precise function
•
E O.5
00o
I0 o
20 °
•
30 °
40 °
50 °
60 °
70 °
80 °
90 °
A n g l e c~ to p r e f e r r e d axis
~.o
b
o
O5
:_-5 / o
0o
10o
20 °
30 °
40 °
50 °
60 °
70 o
80 °
90 °
A n g l e c~to p r e f e r r e d a x i s
Fig. 70. Relative r e m a n e n c e s Br vs. angle c~ to preferred axis calculated for two models (Stfiblein 1966): c-axis distributed preferentially along a preferred direction (a), or along a preferred plane (b). Increasing parameter i means increasing sharpness of orientation, see text.
564
H. ST]~BLEIN
f(a) is not required but a qualitative measure of the orientational order only, the value of f = ( p - p 0 ) / ( 1 - p 0 ) is used sometimes (Lotgering 1959). Here, p = I(OOl)/E I(hkl), i.e, p is the ratio of the sum of all (00/) X-ray intensities and the sum of all (hkl) intensities (including 001) of the specimen considered, and p0 is the analogous expression for a random (isotropic) specimen, f-values range from 0 (isotropic) to 1 (completely aligned). The angular dependence of the (BH)~, value of some commercial specimens is shown in fig. 71. In all specimens it is very well reflected by a cos 2 a curve. This is to be expected because of (BH)ma~ ~ B 2, as long as the demagnetization curve B(H) in the second quadrant shows a pronounced knee, /x0BH~ is greater than B~/2 and the relatively weak #~eja) dependence is neglected. Ioo %
r t~
so Q
0
0o
10°
20 °
30 °
40 °
50 °
A n g l e ct to p r e f e r r e d
60 °
70 o
80 °
90 °
axis
Fig. 71. Relative (BH)max value of commercial hard ferrite grades vs. angle c~ to preferred axis (Joksch 1964, Stfiblein 1965). Absolute (BH)m,×(0 °) values range from 17.3 to 26.5 kJ/m 3 (2.2 to 3.3 MGOe), cf. fig. 72.
As fig. 72 shows, the curves of the relative coercivity BHc vary to a large extent for the individual specimens of fig. 71 in contrast to the curves of the (BH)max values. With rigid magnetization in opposing fields up to at least BH~, approximately she ~ Br is expected. The magnet of curve (3) behaves roughly in this way. If ~ / c < Br/tXo#.... with increasing a firstly jHc(a) and then B r ( a ) determine the angular dependence of BHc(a). The curve of the relative intrinsic coercivity ]Hc(a) is shown in fig. 73 for some commercial hard ferrite specimens. By comparison, fig. 74 shows the dependences for powder specimens manufactured by various methods. In both cases the angular dependences of two extreme cases are also plotted: coherent magnetization reversal after Stoner-Wohlfarth (SW) and nucleation and growth of reverse domains (Kondorsky 1940). In the latter case the effective coercivity is given by the component of the field applied in the direction of the easy axis, i.e. ] H c - 1/cos a. Commercial hard ferrites show a curve between both extreme cases which is far from SW behaviour. The lower jHc is, the greater is the tendency to a better approximation of the cos -1 a curve. The findings of Ratnam et al. (1972), in
HARD FERRITES AND PLASTOFERRITES
565
5 ..~
\ 0o
10 o
20 °
30 °
gO o
50 °
60 °
A n g l e cc to p r e f e r r e d
70 °
80 °
\ 90 °
axis
Fig. 72. Relative coercivity sHe of commercial hard ferrite grades vs. angle c~ to preferred axis. Curves (1) to (3): Joksch (1964); curves (4) and (5): Stfiblein (1965). Same specimens as in fig. 71 having the following characteristics:
Curve
Br (mT)
(BH)max (kJ/m 3)
1 390 26.5 2 370 24.0 3 310 17.3 ......................................... 4 5
380 345
25.2 20.8
BSc (kA/m)
jgc (kA/m)
137 152 204
139 154 227
153 191
155 193
which the coercivity is described very precisely by jHc(a) = 3 COS - 1 0 g k A / m for 100 to 200 fxm B a M crystals, fit into this pattern. O n the o t h e r hand, high-coercivity p o w d e r s m a n u f a c t u r e d by precipitation processes show a certain t e n d e n c y towards the S W curve, cf. curves (5) and (6) of fig. 74. All in all, it is clear that the reversal of magnetization in the hard ferrites (as in all o t h e r p e r m a n e n t m a g n e t materials) occurs, at least in the main, t h r o u g h n o n - c o h e r e n t reversal processes, cf. B e c k e r (1967). T h e angular d e p e n d e n c e of the p e r m a n e n t permeability was m e a s u r e d by Joksch (1964), /~rec rising as o~ increases and, vertical to the preferred direction, being 20 to 30% higher than parallel to it. This agrees well with the calculation f r o m the m o d e l of c o h e r e n t reversal of magnetization, cf. Table 17. This m o d e l therefore correctly describes the actual b e h a v i o u r as long as no incoherent process has taken place.
Influence of mechanical stress Mechanical impacts, stresses and vibrations do not influence the magnetic state of hard ferrites. A s s a y a g (1963) f o u n d no effect b e y o n d the m e a s u r e m e n t accuracy of
566
H. ST.~J3LEIN
150
I
I00 - . - _ x _ _ ,
~
:
/
/4
r
×
~
3
\ \
8 ~o
50
oc 0
N
0o
~o
20 °
30 °
~0 o
50 °
60 °
70 °
80 °
90 °
A n g l e ct to p r e f e r r e d axis
Fig. 73. Relative intrinsic coercivity sHe of commercial hard ferrite grades vs. angle c~ to preferred axis. Curve designation as in fig. 72. Shown are also theoretical dependences according to K o n d o r s k y - ( 1 / c o s a ) or to Stoner-Wohlfarth (SW) model. SW(0 °) = 1470 kA/m for SrM, cf. table 17.
75o% cos ~ / I
50
0 0o
I0 o
20 °
30 °
40 °
50 °
60 °
70 °
80 °
x 90 °
Angle cL to p r e f e r r e d axis
Fig. 74. Relative intrinsic coercivity ~H~ of non-commercial powder specimens. (1) Pressed BaM specimen having Br = 199 roT, (BH)max = 6.5 kJ/m 3, nHc = 90 kA/m, sH0 = 96 kA/m; density = 3.0 g/cm 3 (St~iblein 1965). (2) BaM powder, ball-milled, oriented, she(0 °) = 253 kA/m (Ratnam et al. 1972). (3) Same as (2), but additionally anneaed at 950°C, ~Hc(0°) = 294 kA/m. (4) BaM powder, ball-milled, oriented, she(0 °) = 120 kA/m (Haneda et al. 1973a). (5) BaM powder, co-precipitated, oriented, annealed at 9 2 5 ° C , ~Hc(0°) = 490 kA/m (Haneda et al. 1973a). (6) BaM powder, crystallized from glassy borate phase at 820°C, leached in dilute acetic acid, oriented, jHc(0 °) = 534 kA/m (Ratnam et al. 1970). SW(0 °) = 1470 kA/m for SrM, cf. table 17.
HARD FERRITES AND PLASTOFERRITES
567
1% on isotropic and anisotropic hard ferrites caused by semi-sinusoidal impact with acceleration amplitudes of 150 to 500 g lasting 1 ms, uniform acceleration up to 25 g and vibrations of 10 to 5 000 H z with accelerations up to 20 g. For the m e c h a n i s m of such effects on magnetostriction and the m a x i m u m elastic change attained, see Lliboutry (1950).
Influence of neutron irradiation Irradiation of isotropic and anisotropic Ba-hexaferrite specimens with fast n e u t r o n s having energies of at least 1 M e V impaired all magnetic characteristics drastically (Chukalkin et al. 1979). Specimens irradiated by 1.2 x 1024 m 2 s h o w e d only B~ of ca. 38%, (BH)max of ca. 13% and BHc and 1He of ca. 30% of the respective starting values. Supposedly, irradiation causes Fe 3÷ cation vacancies in 2b lattice sites, which are most i m p o r t a n t for the spin order. This o r d e r is turned f r o m an originally collinear structure into a helical and then into a block angled one (Chukalkin et al. 1981).
3.4. Various physical and chemical properties T h e most i m p o r t a n t magnetic characteristics were discussed in sections 3.1 to 3.3. In the present section various physical and chemical properties and data are c o m p i l e d which are of interest for classifying the materials and evaluating their b e h a v i o u r and which are in part widely dispersed and difficult to find in literature. T h e physical relationships cannot be dealt with in detail here so that reference must be m a d e to the relevant literature.
Magnetostriction Values for a B a M single crystal were given by Kuntsevich et al. (1968), cf. table 25. In particular it can be seen that turning the polarization f r o m the z direction (= c-axis) into the x direction (= parallel basal plane) p r o d u c e s contraction in the x direction and dilatation in both the y and z directions. T h e same authors f o u n d in isotropic B a M specimens saturation magnetostrictions of hll = - (9 -- 0.5) × 1 0 -6 (direction of m e a s u r e m e n t parallel to the field) and h . = + ( 4 . 5 _ _ 0 . 5 ) × 10 -6 (direction of m e a s u r e m e n t perpendicular to the field). In contrast, R a t h e n a u (1953) gives h ~ 20 × 1 0 - 6 with magnetization in the basal plane. T h e d o m i n a n t TABLE 25 Saturation magnetostriction of a BaM single crystal magnetized and measured along various directions (Kuntsevich et al. 1968). x, y, z = rectangular coordinate system; z-axis parallel to hexagonal c-axis; x-axis parallel to one of the a-axis in the basal plane. Direction of magnetization f i e l d measurement •~A hB hc hD
x x x 45° to X and z
x y z 45° to x and z
Saturation magnetostriction - (15 _+0.5) + (16 _+0.5) +(11 _+0.5) -(13+0.5)
× 10 6
568
H. ST~d3LEIN
contribution to magnetostriction originates from the Fe 3+ ions on 2b lattice sites (Kuntsevich et al. 1980). The saturation magnetostriction of the single crystal can be derived from the values for AA... AD in table 25 for any direction of measurement and polarization, cf. Mason (1954). Resistivity The specific resistivity p (and the specific conductivity o- = 1/p) of hard ferrites are many orders of magnitude higher (and lower, respectively) than in metallic materials and show the temperature dependence known from semiconductor materials, cf. fig. 75, curve (a). Commercial ferrite specimens usually have a d.c. resistivity of at least 10 6 ~ c m at room temperature (Went et al. 1952, Stuijts et al. 1955). This is, however, subject to strong fluctuations depending on composition and manufacturing conditions, but generally this does not have an adverse effect on applications because there is obviously no connection with the permanent
1000 200 2,0 '500 ' 100 0 - 5 0
-I00-125
-150oC
I
T
1
i0~
mS
(7
,t,SGHz,~ • GHz
tO2
lO~ 1
~ I0kHz" 106 Hz ,200
x_-OHz 0
1
2
3
,~
5
6
I -.f
10___.. 3 8 K
~crn 9 I0~
,.
Fig. 75. Specific conductivity o- and specific resistivity p vs, reciprocal absolute temperature T (and vs. temperature in °C). Curve (a): D.C. values of a commercial, non-oriented BaM specimen of composition BaFe31~gzO17.38 (Went et al. 1952, Haberey et al. 1968). Curves (b): Effective values of a non-oriented BaM specimen of composition BaFe 3+ 12.59019.89 for various frequencies (Haberey et al. 1968).
HARD FERRITES AND PLASTOFERRITES
569
magnetic characteristics. Special agreements should only be made with the manufacturer in those (rare) cases where emphasis is placed on high insulating properties, for instance. It must also be noted that resistivity also depends on the frequency, cf. fig. 75, curves (b). In this example the effective resistivity drops at room temperature by about 3 powers of ten if a change is made from the d.c. measurement to the 1 GHz a.c. measurement. At lower temperatures the ratio is even greater, at higher temperatures smaller. According to measurements by Rupprecht et al. (1959) the resistivity of anisotropic BaM specimens is up to about one power of ten higher in the preferred direction than perpendicular to it, at least in the frequency range 105 to 107Hz. Less anisotropy was found by Dullenkopf (1968) in nominally isotropic specimens where the resistivity was up to 30% higher in the direction of pressing than perpendicular to it. This is possibly a result of the crystal orientation caused by die pressing, cf. section 2.1.5. In order to explain the resistivity behaviour let us take a model from a coated dielectric in which highly conductive hard ferrite crystals are surrounded by grain boundaries (barrier layers) of poor conductivity (Haberey et al. 1968, Dullenkopf et al. 1969). Conductivity is attributable to electrons transient between Fe 3+ and Fe 2+ ions. In the polycrystalline state the resistance to d.c. and low-frequency current is largely determined by the properties of the barrier layers and may be increased by post-annealing at 400-700°C in an oxidizing atmosphere or decreased in a reducing atmosphere. Here, no connection with the Fe 2+ content was observed (Dullenkopf 1968), but influencing this by substituting Ti, Mn and Co is claimed to be possible (Dtilken 1971). We have a better understanding of the resistance mechanism in the super-high frequency range, where the resistance is inversely proportional to the Fe 2+ content (Dullenkopf et al. 1968) and which, in extreme cases should equal the d.c. resistance (averaged over all spatial directions) of a single crystal owing to capacitive short-circuiting of the barrier layers. The d.c. resistance was measured by Zfiv6ta (1963) for BaM and PbM. In both cases the resistance parallel to the c-axis (P0 was roughly ten times that perpendicular to it (p±) in the range from -150 to 200°C. At room temperature Pll ~ 700 l~cm and p± --~70 l~cm were found for BaM, Ptl ~ 50 ~ c m and p± ~ 5 ~ c m for PbM. Studies on the dielectric behaviour (e.g. Rupprecht et al. 1959, Haberey 1967, Haberey et al. 1968, Dfilken 1971, Vollmerhaus et al. 1975), the thermo-electric behaviour (e.g. Zfiv6ta 1963, Bunget et al. 1967, Dullenkopf 1968, Dullenkopf et al. 1968, 1969) and the magnetic after-effects of hard ferrites (e.g. Haberey 1969, Dfilken et al. 1969, Dfilken 1971) were carried out, partly in connection with the electrical conductivity.
Linear thermal expansion The extent of linear thermal expansion is of great interest in practice, firstly owing to the relationship with crack formation as a result of thermal shock, and secondly owing to the necessity to combine various materials in magnet systems exposed to specific temperature ranges. With hexaferrites the conditions are more difficult owing to the considerable anisotropy of thermal expansion. One particular
570
H. ST~3LEIN
consequence of this anisotropy is that crack-free toroids with a radial preferred direction can be manufactured, if at all, then only with thin walls (Kools 1973, cf. section 2.1.6). When hard ferrite magnets are cemented to metal components it is recommended to use an elastic binding agent to compensate for the different amounts of thermal expansion (Hamamura 1973). The coefficients of thermal expansion are compiled with references in fig. 76 and table 26. a increases continuously from 0 K up to a maximum value at Curie temperature both parallel and perpendicular to the c-axis, and then drops slightly. Thermal expansion is appreciably greater along the c-axis than in the basal plane. This is observed not only with specimens pressed in a magnetic field, cf. curves (1) and (2) in fig. 76, but also with die-pressed, nominally "isotropic" specimens which became slightly anisotropic during die pressing, cf. curves (3) and (4) (cf. also section 2.1.5). Conversely, an anisotropy of only 1% was found in the specimen relating to curve (5) (Buessem et al. 1957). As the comparison with the thermal expansion of iron in fig. 76 shows, considerable expansion differences are liable to occur when the material is cemented to the pole faces of isotropic and anisotropic magnets. 0
500 i
~
i
K
!
15.'106
i
i
i
I
D
i
/ #
,.;,4
..
,'3/,
5
5
!'
•.,4
II
0
'
~
'
,
0
,
~
,~
,
500
,
I
°C
Temperature
Fig. 76. Linear thermal expansion coefficienta of commercialhexaferrite specimens vs. temperature, compared to a of iron. Curve (1) SrM fl preferred axis Curve (2) SrM ± preferred axis / (Van den Broek et al. 1977/78) Curve (3) BaM ]1pressing axis ~ / Curve (4)BaM _Lpressing axisJ (Clark et 1976) Curve (5) BaM, isotropic (Buessem et al. 1957) Curve (6) Iron. al.
H A R D FERRITES A N D PLASTOFERRITES
.~ ~ - ~
×
~
~
~
_~
©
~
~ ~
o
o t~
O
~
571
O
o
~~ ~~~
~
~.~ Z ©
e~.s o
o
o
~"
0
~
2s
r,
~
~.~
09
0
,--k
8
"-d
0
I
I l l l
I
°~
O e~ o
= ~0 e~
©
.= O
*
572
H. STJkBLEIN
Other thermal properties 4 W/(m • K) (Clark et al. 1976) and 5.5 W/(m • K) (Valvo 1978/79) were given for the thermal conductivity of B a M and 0.84 J/(gK) ( T D K 1978) and 0.714 J/(gK) (Torii et al. 1979) for the specific heat.
Elastic properties T h e characteristics of various moduli are compiled in table 27. At least the modulus of elasticity is anisotropic (Kools 1973, Iwasa et al. 1981). According to Cavalotti et al. (1979) this modulus depends to a relatively small extent on composition and manufacturing conditions. The t e m p e r a t u r e dependence of all three m0duli is very low according to R e d d y et al. (1974); at -193°C the values were only a few percent lower than at r o o m temperature. Iwasa et al. (1981) determined the temperature dependence of BaM specimens as - 2 8 . 9 (isotropic), - 3 7 . 7 (]]c) and - 5 2 . 2 N/mm2K (2c) between r o o m t e m p e r a t u r e and 900°C. Poisson's n u m b e r of an isotropic B a M specimen was given as 0.28 (Clark et al. 1976) and as 0.24 (Iwasa et al. 1981). TABLE 27 Elastic moduli in kN/mm2 of commercial BaM specimens at room temperature. Property
Specimen
Value
Young's modulus
isotropic anisotropic, IIpreferred axis anisotropic, ± preferred axis isotropic isotropic isotropic isotropic anisotropic, [[ preferred axis anisotropic, L preferred axis
198 ] 177 ~ 211 J 151.9 138 130-140 183 } 154 317
Reference Kools (1973) Reddy et al. (1974) Clark et al. (1976) Cavallotti et al. (1979) Iwasa et al. (1981)
Rigidity modulus
isotropic
63.5
Reddy et al. (1974)
Bulk modulus
isotropic
83.4
Reddy et al. (1974)
Mechanical strength The tensile and flexural strength values compiled in table 28 exhibit very large fluctuations both within the series of m e a s u r e m e n t s made by one author and between various authors. Most of these fluctuations are probably attributable to the ceramic, brittle nature of the materials and the particular difficulties encountered in measuring. The fluctuations almost completely cover up the effects of composition, manufacturing conditions and anisotropy. It can be stated with reasonable certainty that both the tensile and flexural strength values are less than 150 N/ram 2. According to Wills et al. (1976) strength increases with the quality of the surface finfsh.
H A R D FERRITES AND PLASTOFERRITES
573
TABLE 28 Strength values in N/mm 2 of commercial hard ferrites at room temperature. Property Tensile strength
Flexural strength
Compressive strength
Specimen
Value
anisotropic BaM; 11preferred axis anisotropic BaM; ± preferred axis isotropic BaM anisotropic BaM isotropic BaM isotropic, anisotropic M
36.3--+ 7.8 73.4 ± 10.8 / 4.9-7.8 11.8-18.6 J 55 19.6-49.0
isotropic BaM anisotropic BaM anisotropic BaM, SrM; I preferred axis isotropic BaM anisotropic BaM, SrM isotropic, anisotropic M isotropic BaM
6.8-9.8 2.5-8.0 l 86.3 _+7.8 77 ± 33 88-147 J 29.4-88.3 60-130
anisotropic BaM isotropic BaM isotropic, anisotropic M
735 ± 78 440 >686
Reference Kools (1973) IHamamura (1973) Clark et al. (1976) TDK (1978) Gershov (1963) Kools (1973) Hamamura (1973) TDK (1978) Cavallotti et al. (1979) Kools (1973) Clark et al. (1976) TDK (1978)
On the other hand, the compressive strength determined by various authors exhibits comparatively small variations. As expected, the values are considerably higher than the tensile and flexural strength values. For the impact strength (notched-bar impact test) Hamamura (1973) found values between 2.4 and 9.8 kgm/cm 2 without any distinct effect of anisotropy but proportional to the density. The critical stress-intensity factor K~c was determined in connection with studies on crack formation and the grindability of hexaferrites, cf. section 2.1.7. The values in table 29 clearly show an influence of anisotropy. Cleavage along the TABLE 29 Critical stress-intensity factor Krc in MN/m 3/2 of commercial hard ferrites at room temperature. Specimen Anisotropic SrM, fracture surface ]]preferred axis Anisotropic SrM, fracture surface ± preferred axis Anisotropic SrM, fracture surface II preferred axis Anisotropic SrM, fracture surface 2 preferred axis Anisotropic BaM, fracture surface II preferred axis Anis0tropic BaM, fracture surface ± preferred axis Isotropic BaM Isotropic BaM * Maximum values are obtained for molar ratio FeaO3/SrO ~ 5.5.
Value
Reference
2.12"8[)
Veldkamp et al. (1976)
2.1-2.5" 1.5-2.1"
Veldkamp et al. (1979)
2.83-+0.101 0.96±0.05~ Iwasa et al. (1981) 1.57 ± 0.04J 1.3-3.2 Cavallotti et al. (1979)
574
H. S T ~ 3 L E I N
basal plane is easier than perpendicular to it. According to Veldkamp et al. (1976) K~c depends on the molar ratio Fe2OjSrO = n with anisotropic SrM. It slowly increases from n = 4.4 to a maximum at n ~ 5.5 and drops even more quickly when n is higher. The figures in table 29 are averages; the related variations reached a maximum of about _ 1 g N / m 3/2. A dependence on the molar ratio was also found with isotropic BaM specimens, but the K,c maximum occurred at n ~ 4 . 5 or lower (Cavallotti et al. 1979). The same authors also observed an influence of the pressing process: with dry-pressed specimens K~c= 2.73 _+0.24 MN/m 3/2, with wet-pressed specimens K~ = 2.05 MN/m 3/2. According to Iwasa et al. (1981) KI~ of BaM specimens decreased between room temperature and 1000°C linearly and rather slightly and between 1000 and 1200°C drastically. In the first mentioned region the temperature dependence is 6.23--_ 0.03 (isotropic), 0.42 -- 0.03 ([]c) and (8.38 -+ 0.06) x 10 .4 MN/m 312K (±c), and for the second region in the order of 10 -a MN/m 3/2 K. No anomaly was found around the Curie temperature. Fracture surface energies of 6.35 + 0 . 3 2 (isotropic), 2.82-+0.30 (][c) and 11.92-+ 0.84 J/m 2 ( ± c ) w e r e deduced.
T A B L E 30 Hardness of commercial hard ferrites at room temperature. Hardness Vickers
Specimen Anisotropic SrM, II preferred axis Anisotropic SrM, L preferred axis SrM Anisotropic B a M SrM, single cryst, no. 33,
Value
Reference
8.6 k N / m m ; 5.6 k N / m m 2 6.5 k N / m m 2 ca. 6 k N / m m 2 10.3 ± 1.0 k N / m m 2
Veldkamp et al. (1976) Broese van Groenou et al. (1979a) see fig. 44
IIc-axis SrM, single cryst, no. 33, ± c-axis SrM, single cryst, no. 57,
7.5 ±0.5 k N / m m 2
Jahn (1968)
9.6 ± 1.0 k N / m m 2
II c-axis SrM, single cryst, no. 57, L c-axis PbM, single crystal Ritz
SrM
Rockwell, Scale A Rockwell, Scale N load 147 N
Isotropic B a M Anisotropic B a M Isotropic B a M
Mohs
M
8.3 ± 0.5 k N / m m 2 11.0 k N / m m 2
Courtel et al. (1962)
24 k N / m m z
Broese van Groenou et al. (1979a)
73-76 } 72-80, 80-90
6-7
Gershov (1963) Cavallotti et al. (1979)
Schiller et al. (1970)
HARD FERRITES AND PLASTOFERR1TES
575
Hardness Table 30 shows hardness values determined by various tests. Like most of the mechanical properties hardness is thus anisotropic. Figure 44 shows the hardness as a function of the sintering temperature and thus of the density.
Lattice constants, X-ray density Lattice constants of M-ferrites are compiled in table 31. There is only a slight difference for the Ba, Sr and Pb compounds so that the volumes of the unit cells only differ by a maximum of 1%, giving values for the theoretical densities of 5.3, 5.1 and 5.6 to 5.7g/cm 3 respectively. A density of 5.59g/cm 3 obtains for the mineral magnetoplumbite with the lattice constants given by Berry (1951) and the (idealized) composition given by Blix (1937) as PbFev.sMn3.sA10.sTi0.sO19. TABLE 31 Lattice constants of M-ferrites in nm (at room temperature). Specimen
a
c
c/ a
Reference
BaM BaM BaM Ba0.sSr0.2M Ba0.6Sr0.4M Ba0.4Sr0.6M Bao.zSr0.sM SrM SrM SrM SrM PbM PbM
0.5876 0.5893 0.5894 0.5887 0.5890 0.5882 0.5884 0.5884 0.5885 0.5887 0.5864 0.5877 0.5893
2.317 2.3194 2.321 2.318 2.316 2.311 2.308 2.308 2.303 2.305 2.303 2.302 2.308
3.943 3.936 3.938 3.937 3.932 3.929 3.923 3.923 3.914 3.915 3.927 3.917 3.916
Adelsk61d (1938) Townes et al. (1967) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Adelsk61d (1938) Adelsk61d (1938) Klingenberg et al. (1979)
Magnetoplumbite Magnetoplumbite
0.606 0.588
2.369 2.302
3.91 3.915
Aminoff (1925) Berry (1951)
Chemical stability Being oxides, hard ferrites are, by nature, particularly unstable in strong acids, but are subject to more or less rapid chemical attack even in weak acids, alkalis and in other chemicals. Qualitative information on this is contained in table 32 (Schiller et al. 1970, Valvo 1978/79). Quantitative data on corrosion behaviour in different media will be found in table 33 (Hirschfeld et al. 1963) in which the specific loss of weight after 14 days of treatment is given. These and other data point to a number of remarkable aspects: (1) Fluoric acid and hydrochloric acid are by far the most aggressive media. (2) An increase in the temperature of the medium of only 30°C can mean a dramatic increase in corrosion. (3) The rise in the corrosion rate with increasing temperature is not uniform for
576
H. ST~ilBLEIN TABLE 32 Chemical stability of BaM-ferrites. Rather stable in: Ammonia Acetic acid Benzol-trichloroethylene (50 : 50) Citric acid (5%) Citric acid (10%) Cresol Developer Fixing bath Hydrogen peroxide (15%) Hydrogen peroxide (30%) Petrol Phenol solution Potassium hydroxid solution Sodium chloride solution (30%) Sodium hydroxide solution Sodium sulphate solution
More or less unstable in: Hydrochloric acid Hydrofluoric acid Nitric acid Oxalic acid Phosphoric acid Sulfuric acid
various media, so that the consecutive order, in terms of aggressiveness, depends on temperature. (4) A comparison between periods of treatment of 1, 4 and 8 days shows that the specific loss of weight is not constant. For this reason the loss of material cannot be extrapolated quantitatively to other reaction periods. (5) The above comparison further indicates that in some media the specimen TABLE 33 Specific weight loss of non-oriented Ba-hexaferrite specimens after being treated for 14 days in different aqueous media (Hirschfeld et al. 1963). Concentration: 15 wt %.
Medium
Hydrofluoric acid Hydrochloric acid Sulfuric acid Phosphoric acid Potassium hydroxid solution Nitric acid Tartaric acid Acetic acid Ammonia Aqua destillata
Specific weight loss in g/m 2 at 20-25°C 50-55°C (a) (a) 57 25 11 8 4 4 1 2(c)
(a) (a) 300 650 9 610 60 4 (b) - 15(c)
(a) Specimen completely dissolved (b) not determined (c) means weight increase
HARD FERRITES AND PLASTOFERRITES
577
weight increases first and then decreases, Firmly adherent reaction products obviously form in the initial stage. These dissolve as the attack progresses. All in all the corrosion behaviour is very c o m p l e x and it depends to a considerable extent upon the test parameters. Quantitative predictions therefore require exactly defined test conditions.
3.5, Comparison with other permanent magnet materials; applications Since their discovery around 1950 hard ferrites have enjoyed a bigger upswing in sales than any other p e r m a n e n t magnet material. Figure 77 shows the rate of increase in output of various hard magnet grades as estimated by various authors. In spite of considerable fluctuations, a hard ferrite output in the order of 108 kg/a can be assumed for the beginning of the eighties in the western countries. Since the average price of hard ferrites is estimated at 10 DM/kg, this represents a value today of approximately 109DM/a. The value of the other p e r m a n e n t magnet materials can be expected to be in roughly the same order of magnitude because the comparably smaller tonnage output is set against a correspondingly higher average price. T h e main reason for this large proportion of hard ferrites in the total output of p e r m a n e n t magnets is their economy (see also section 1.2). The price per unit of magnetic energy ((BH)m~ value) is much lower for hard ferrites than for the other magnet materials (Steinort 1973, Rathenau 1974). A m a j o r advantage offered by hard ferrites is the low-cost and almost inexhaustible supply of raw materials which opens up excellent prospects for the use of this material in f u t u r e - in spite of the fact that the energy density values of hard ferrite grades are inferior to those of other materials as can be seen from figs. 78 and 79.
108 +/A/
5
f
2-
//.-
10z 5
/
/
/
/
.
.---"
t /' • t
2.
106
I
I
I
I
I
1930 1940 1950 1950 19F0 1980year
Fig. 77. Annual mass production of permanent magnets between 1940 and 1980 in the western world: ( ) hard ferrites (upper curve, Cartoceti et al. 1971, Steinort 1973, Andreotti 1973; lower curve, Van den Broek et al. 1977/78, Rathenau 1974); (0) hard ferrites (Schiller 1973); (---) all permanent magnets, (..... ) alloys only (Van den Broek et al. 1977/78, Rathenau 1974); (+) all permanent magnets (Schiller 1973).
578
H. ST~BLEIN /.5 T
2O II
/,
\
/.0
~,1~'°'~ 2 N
a5 ~
0,5
-750
kA/m
- 500
0
-250
Field s t r e n g t h
H
Fig. 78. Typical demagnetization curves of various permanent magnet materials: (1) hard ferrite; (2) AlNiCo, high B~ grade; (3) AlNiCo, high H~ grade; (4) Mn-AI-C alloy; (5) RECo5 alloy; (6) RE(Co, Cu, Fe)7 alloy.
QI I~
1 ~
I
I I !!II
tO
I,
~
I
I I III!I
kOe I
!
I I
: kh 25
'MGOe
kJ/m3 l
I00. /
J
xt6\ 14 ,~x~
24 xU/"
,,*_L3 _ 9 - "
×23 - - -7--" % :~o ×191"72"', .... , ", /
x I
," 3/ [× /
10.
x22
, 9 × ,17. 'L*×~2#21
q8
: ~ -x',
"--"
/x 6 ,'J~7,"
x 20
ix ', ',~ 10
',
', ', ', 1:',II lO0
',
', ', ' , ; I I ' , I 1000
', ', kA/m
jH c
Fig. 79. Permanent magnet materials compared by (BH)max (static energy) and intrinsic coercivity aHc (stability) (St~iblein 1972): (1) Co steel; (2) Cu-Ni-Fe, anisotropic; (3) Co-Fe-V-Cr, anisotropic, wire; (4) Co-Fe-V-Cr, anisotropic, strip; (5)-(7) AlNiCo, isotropic; (8)-(12) AlNiCo, anisotropie; (13)-(16) AlNiCo, columnar; (17) ESD (elongated single domain), anisotropic; (18) and (19) Cr-Fe-Co, anisotropic; (20) Hard ferrite, isotropic; (21) Hard ferrite, anisotropie, see table 18; (22) Mn-Bi, anisotropic; (23) Mn-AI-C, anisotropic; (24) Pt-Co, isotropic; (25) RE-Cos-type alloys, anisotropic; (26) RE-(Co, Cu, Fe, Mn)7-type alloys, anisotropic.
HARD FERRITES AND PLASTOFERRITES
579
Figure 78 shows the demagnetization curves of typical modern permanent magnet grades with their (BH)max points. Owing to their relatively low (B/-/')max values hard ferrites are not particularly suitable for those applications in which the most important requirement is to keep the volume of the (static) magnet system as small as possible. As soon as minimum possible mass is required conditions change, however, as can be seen from the comparison of the columns "volume efficiency" and "mass efficiency" in table 34. Owing to its low density hard ferrite is appreciably better in this case. The same applies to those cases where importance is attached to stability or reversible magnetic behaviour under alternating magnetic fields, i.e. to coercivity jHc. For a qualitative comparison of the materials in terms of their static as well as dynamic characteristics, it is advisable to use the (BI-I)max-jHcdiagram, cf. fig. 79. This brief description is also used in more recent standardization, cf. section 3.1. The hard ferrites are thus found to range in stability between the Alnico, C r - F e - C o and ESD magnets, on the one hand, and the intermetallic compounds MnBi, PtCo and R E (Co, Cu, Fe, Mn)y, on the other. The (BpH)max value* is a quantitative measure for the energy conversion capability with dynamic operation of the permanent magnet, cf. table 34. In these applications hard ferrites are at least equal to the AlNiCo alloys. In fig. 78 the ( B H ) m a x points are marked on the demagnetization curves. If flux density and field strength in the permanent magnet assume the values corresponding to the (BH)m~ point, a minimum volume of permanent magnet is required (with static applications). This can be achieved by an appropriate design of the magnet system. In this case B/txoH has to assume the values listed in table 34. The smaller this value is the more compact the permanent magnet has to be designed. Like the R E - C o alloys, hard ferrites therefore as a rule have compact shapes (small ratio between magnet length and magnet cross-sectional area) in contrast to AlNiCo alloys. Another important criterion for actual use is the temperature response of the magnetic properties, cf. section 3.2. Table 34 shows the temperature coefficients of the remanence a(Br) and of the intrinsic coercivity a(jHc) of some materials, as applying for a certain range around room temperature. Hard ferrites can be seen to exhibit the greatest temperature response of remanence, and this applies, of course, to the temperature response of the magnetic flux in the permanent magnet system. Hard ferrites are thus less suitable for applications where functioning must remain unaffected by temperature. Special mention has already been made in section 3.2 of the consequences of the large positive temperature coefficient of jHc of hard ferrites and in particular of the risk of irreversible losses on cooling below room temperature. Certain AlNiCo grades show a similar although less pronounced behaviour. Amenability to shaping and machining is an important criterion in actual * For the definition see section 3.1, footnote on p. 536. Some authors use half or one quarter of this value. References: D e s m o n d (1945), Schwabe (1958, 1959), Schiller (1967), St~iblein (1968b), Gould (1969), Zijlstra (1974).
580
H. S T ~ 3 3 L E I N
¢,q
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x
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× tt%
x
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H A R D FERRITES AND PLASTOFERRITES
581
(magnification I/4) Fig. 80. Assortment of hard ferrite permanent magnets (courtesy of Fried. Krupp GmbH, Krupp WIDIA, D-4300 Essen).
582
H. STJ~BLEIN
practice. Like AlNiCo* and the RE-Co materials, hard ferrites are produced by powder metallurgical methods. Being brittle they can only be machined by cutting processes producing minute chips?. Where the material has to be ductile, e.g., for making sheet or wire, permanent magnets of Co-Fe-V-Cr, Cr-Fe-Co or Cu-NiFe alloys have to be used (Zijlstra 1978). Table 34 further shows some comparative properties which occasionally have to be observed in the choice of material: the high specific electrical resistance of hard ferrites in comparison with metallic materials, their relatively low tensile strength and their relatively low linear thermal expansion. Hard ferrites are found in a variety of applications, the most important aspect being that of economy. Magnetically speaking it is the high coercivity and the resultant high stability and reversibility of the magnetic state ("rigid polarization") which led to their use especially in motors, generators, holding, attracting, repulsing, coupling and eddy current devices. It became apparent that they can be used to advantage in permanent magnet loudspeaker systems owing to their still adequate (BH)max values. General descriptions and special topics on the ap~ plication of hard ferrites can be found in text books of Hadfield (1962), Ireland (1968), McCaig (1967, 1977) Moskowitz (1976), Parker et al. (1962), Reichel (1980) and Schiller et al. (1970). A major disadvantage is the high temperature dependence which impairs their use in measuring instruments and at high or low temperatures. Hard ferrites for microwave applications were described by Akaiwa (1973) and by Nicolas (1979). Figure 80 shows a selection of hard ferrite magnets for various applications.
4. Bonded hard ferrites, plastoferrites In these composite materials hard ferrite powder is embedded in a non-magnetizable matrix. As with all composite materials, the different properties of two component materials can also be united here in one constructional element, producing new technological possibilities. Since the volume proportion of the magnetic phase is smaller than in the compact hard ferrites, reduced magnetic properties result. The bonded hard ferrites are therefore only used for those applications where this relatively low magnetic level is acceptable. If this is the case, then the advantages of the composite material, e.g., formability, low cost and improved non-magnetic properties, come to the fore. If synthetic or natural organic materials are used as matrix materials, their wide-ranging technological possibilities, e.g., in terms of elasticity, strength, resistance to fracture and impact, dimensional tolerance, lower density, shaping and further processing can be fully exploited for the magnetic composite materials. Nowadays, only organic materials are used for the matrix on a large scale. Common materials are rubber, poly* Manufacture by melting processes is feasible too and commonly used. t AlNiCo alloys after special treatment also by turning and drilling (Pant 1977, Pant et al. 1977).
HARD FERRITES AND PLASTOFERRITES
583
vinylchloride (PVC), polyamides (PA), polyolefins (e.g. polyethylene and polypropylene), polystyrene, phenol and polyester resins (Casper et al. 1965). Inorganic materials such as metal and glass have also been proposed but there seems to be no practical demand for them and their use would be more expensive. In this connection mention should be made of experiments by Passerone et al. (1975) on the wettability of hard ferrite with molten metals and tests by Cavallotti et al. (1976, 1977) and Asti et al. (1976) on the electrochemical and chemical manufacture of inorganically bonded hard ferrites. For glass-bonded hard ferrites, cf. section 2.2.3. The following sections will therefore only deal with the hard ferrites bonded with an organic matrix, which are also called plastic bonded hard ferrites or, simply, plastoferrites.
4. i. Manufacturing technologies for plastoferrites Figure 81 shows a diagrammatic representation of the process for manufacturing plastoferrites (Caspar et al. 1965, Richter et al. 1968b). In many cases raw material is used which is obtained in manufacturing compact magnets anyway, e.g., after reaction sintering or as waste material after final sintering or in indirect shaping, cf. fig. 19 and sections 2.1.1 to 2.1.4 and 2.1.7. This material is then processed further in order to meet the special requirements placed on the desired plastoferrite grade. These requirements relate in particular to high coercivity, alignability of the powder particles and the desired ferrite content of the powder. The top grade powders, however, require special manufacturing techniques tailor-made to meet the requirements of the plastoferrites. As far as coercivity is concerned, it should be high enough so that no irreversible polarization reversals occur along the B - H demagnetization curve, i.e., a rigid magnetization is maintained. This is ensured by using a crystallite size of roughly 1 txm. Depending on whether anisotropic or isotropic magnets are to be manufactured, the powder particles must be alignable or non-alignable. Alignability is achieved when the particles are either monocrystalline or made from compact material with preferred direction. If alignability is not wanted, however, in order that isotropic magnets are obtained, then the use of polycrystalline particles from isotropic material is appropriate since monocrystalline particles can be aligned during the shaping process owing to their platelet-like shape, cf. section 2.1.5. Asti et al. (1974) have referred to the significance of the particle shape as regards alignability and to the influence of special additions during the reaction process. Particle size and particle size distribution are major factors affecting the maximum attainable ferrite content as coarser powders can be more densely packed. The above-mentioned requirements imposed on the crystallite and particle size are largely fulfilled if suitable reaction and grinding conditions are selected. If intensive grinding is necessary, the resultant lattice defects must be eliminated by annealing prior to further processing, cf. section 2.1.4.
584
H. ST~13LEIN
Reacted hexaferrite from raw materials; or waste from sintered bulk material
Crushing, milling
Annealing
Mixing with matrix material: .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Thermoplastic .....
rigid . . . .
Injection moulding with or without magnetic field
~....
.
.
.
.
.
.
.
.
.
.
.
.
Rubber
~llsti; . . . . . . . . .
extrusion
.
.
.
.
.
.
Thermosetting
;lai:i~ . . . . . . . . .
;igid- . . . .
Die pressing with or without magnetic field
Rolling, calenderinfl
Annealing
Cutting, machining
I
AssembLing, magnetizing
Fig. 81. Manufacturing technology for plastic bonded hard ferrites (plastoferrites).
HARD FERRITES AND PLASTOFERRITES
585
Depending on the material used, the ferrite powder is mixed with the binding agent either in the cold or hot state in mixers, mixing extruders, kneaders or calenders. With increasing proportions of ferrite powder the viscosity of the paste-like mixture increases drastically in the loading range considered and also, as a consequence, the power needed for mixing and working. This is reflected in the form of wear on the machines and in the form of lowered jHc values in the magnets as a result of plastic deformation of the particles. The optimum percentage of ferrite for anisotropic magnets in order to obtain the desired magnetic properties lies between 50 and 65% by volume with injection moulding as otherwise the particles would interfere with one another when being aligned in the magnetic field. The corresponding figure for rolling is about 70% by volume. Slightly higher ferrite contents of about 70% by volume are also possible in injection moulding if no or nonintensive alignment is required. Ferrite contents of 80% by volume or even more can only be attained in die pressing. The subsequent shaping stage produces finished parts (injection moulding, die pressing) or semi-finished parts such as ribbons, strips etc. (extrusion, rolling) which are then punched or cut into their final shape. Special mention should be made of the dimensional accuracy and the cost-efficiency, especially of injection moulding, where further machining is generally not required. Mechanical and magnetic forces can be used to manufacture anisotropic magnets, the former mainly in extruding and rolling, with the platelet shape of the crystallites being exploited (cf. section 2.1.5), the latter mainly in injection moulding and die pressing comparable to the manufacture of compact anisotropic magnets (cf. section 2.1.5). If rubber is used as binding agent, vulcanization may be carried out after shaping, thus increasing the strength of the magnet. Thermosetting plastics, too, require heat treatment where the plastic is irreversibly cured. In injection moulding and die pressing the shaping of the actual magnetic material can be combined with the fitting of insert components (axles, pole sheets, etc.). Figure 82 shows an assortment of injection moulded magnets.
4.2. Technical properties and applications of plastoferrites Before discussing the magnetic characteristics let us deal with the question as to what values can be attained. Only an approximate answer can be given as it is not yet known how the demagnetization curves of a compact permanent magnetic material and a composite material using the same grade as magnetic component can be accurately transposed from one to the other. Approximate calculations are based on the conception that magnetic material and matrix, with the total volume remaining constant, are separate and concentrated in themselves. Here, a difference must be made between two extreme cases depending on whether permanent magnetic and matrix materials lie in parallel or in series with the magnetic flux (Edwards et al. 1975, Joksch 1976). In the former case, the magnetic flux, in comparison with the compact specimen, is diluted in proportion to the volume content of the magnetic material, whereas in the latter case shear is present as in a magnet system with air gap. Here the amount of shear is expressed by the volume
586
H. STi~d3LEIN
Fig. 82. Injection moulded plastoferrites (Ebeling et al. 1978). ratio between magnetic and matrix material. The demagnetization curves B(H) can be easily calculated for both extreme cases, assuming that there is no flux leakage a n d jHc is sufficiently high. The actual curve will lie between the two extreme cases. The model calculation is particularly simple if the magnetic material exhibits rigid magnetization with/£rec 1.0, i.e. with complete orientation of all crystallites, as the demagnetization curves B(H) are then identical for both extreme cases. This gives the values listed in table 35 for the anisotropic specimen. The corresponding demagnetization curves for bonded Sr hexaferrite magnets are shown in fig. 83 for various volume percentages xv of the magnetic material. The curve for Xv = 1.0 corresponds to the Stoner-Wohlfarth curve of the anisotropic magnet in fig. 59. When #rec exceeds 1.0 the r e m a n e n c e values for the two extreme cases differ, the difference increasing as /Xrec rises and the proportion of ferrite Xv falls. The series model provides slightly lower values than the parallel model. The m a x i m u m differences are, however, only 8% for /Xrec= 1.171 (isotropic specimen, cf. table 17) and for the technically interesting cases of Xv~> 0.5. Therefore, useful (somewhat too high) approximations result from the parallel model for the isotropic specimen, too. These are also listed in table 35. Figure 84 shows the respective demagnetization curves for various values of xv. The curve for Xv = 1.0 corresponds to the Stoner-Wohlfarth curve of the isotropic magnet shown in fig. 59. From studies on elastic bonded hard ferrites Besjasikowa et al. (1977) gave a =
H A R D FERRITES A N D PLASTOFERRITES
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588
H. ST.Sd3LEIN
-5
kOe
Field strength H -3 -2
-4 ,
,
Magnetic flux ~B densit~v_^ _ J .iX v
. -1
,
.
0¢6)
-400
kA/m
-300
300 |
-200
-100
0
Field strength H
Fig. 83. Demagnetization curves B(H) of anisotropic commercial plastoferrites (curves (1) to (3)) compared with ideal coherent rotation model (Stoner-Wohlfarth curve "S-W", 100% ; and fractions of that). (1) Injection moulded magnet (Drossel et al. 1969); (2) Rolled magnet (Blondot 1973); (3) Die pressed magnet (catalogue of Fa. Baermann, Bensberg near Cologne, F.R.G.). Magnetic flux ~B density ~ Xv
Field strength H ~ ^. -e.s
.Oe -2.0 I
-1.5
-1.0
~
t
,2so ! ....
~
-200
kA/m
-150
-100 Field strength H
-50
100
mT Io/o -: 2oo_l so
0
=
Fig. 84. As fig. 83 but for i s o t r o p i c plastoferrites: (1) Injection moulded magnet (Ebeling et al. 1978); (2) Rolled or extruded magnet (Blondot 1973); (3) Die pressed magnet (Ebeling et al. 1978). s o m e w h a t different d e p e n d e n c e of the characteristics on the ferrite c o n t e n t Xv: Br = 290x~ 4 m T ;
BHc = 135xv k A / m (1.7Xv k O e ) ;
(BH)max = 10.3x 24 kJ/m3(1.3x 24 M G O e ) . T h e s e s p e c i m e n s had possibly b e c o m e s o m e w h a t anisotropic. A s regards the coercivity jHc n o effect of t h e packing density is expected as
HARD FERRITES AND PLASTOFERRITES
589
there should be no or only slight interaction. In fact, Shimizu et al. (1972) found no influence in the range Xv = 0.5 to 0.7 with high-coercivity barium hexaferrite powders where j H c = 2 4 5 k A / m (3.1kOe). Somewhat different findings were reported by Hagner (1980) with SrM powders treated in various ways. A special preparation procedure assured microscopic deagglomeration of the particles. With increasing packing density xv the coercivity jHc first increased drastically, while no or only minor changes occurred above Xv-~ 0.5. This is explained by assuming a positive magnetostatic interaction between the SrM particles. With powder preparation the possible introduction of plastic deformation and its influence on coercivity has to be considered, see section 2.1.4. Wohlfarth (1959) provides a survey of a series of theoretical and experimental studies concerning the influence of the packing density on the coercivity of various materials. Figures 83 and 84 show the demagnetization curves of some high-quality commercial grades. Lower quality grades can be easily produced by reducing the ferrite content and are therefore not included. Isotropic magnets attain 70 to 75%, anisotropic magnets only 50 to 55% of what is theoretically possible. This different performance is due to the incomplete orientation of the crystallites in bulk material compared with monocrystal orientation and to the lower maximum ferrite content of the anisotropic grades. Similar viewpoints apply here as already described in section 3.1 for the compact magnets. Samow (1973) considers the manufacture of anisotropic magnets with Br = 270 mT (2.7 kG) and (BH)max = 14 kJ/m 3 (1.8 M G O e ) commercially feasible, for which a ferrite powder content of 70% by volume with an 80% degree of alignment would be necessary. The demagnetization curves of anisotropic magnets, measured perpendicular to the preferred direction, are, of course, lower than the curves of the isotropic grade, cf. fig. 85. Table 36 contains magnetic characteristics and densities of some internationally standardized bonded hard ferrite grades (IEC-Document 68 CO
Field strength H -3
kOe -2
-1
1
I
I
3OO
mT
-300
- 200
l
100
~
0 400 .~
-200
-300 Fig. 85. Demagnetization curves of isotropic (1) and anisotropic plastoferrites (2 and 3: measured parallel and perpendicular to preferred direction, resp.) (Ebeling et al. 1978).
590
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HARD FERRITES AND PLASTOFERRITES
591
TABLE 37 Standard designations and trademarks of plastoferrites from various countries. Some trademarks are of historical interest only. Some manufacturers use the same trademark (with different additional designation) for their sintered grades, see table 18, page 540. Country
Standard designation
Trademarks
Federal Rep. Germany
Hartferrit P
KOEROX P Oxidur P Oxilit Prox Sprox Tromaflex (TX) Tromalit (OP, OT)
German Democ. Rep.
Maniperm
Maniperm
France
Ferriflex Plastoferroxdnre Plastoferrite
Great Britain
Magnadur P, D, Sp
Italy
Ferriplast Plastomag
Netherlands
Ferroxdure P, D, Sp
Japan
Ferrogum KPM MBS RM RN YRM
USA
Koroseal Magnalox Magnyl Plastiform (PL)
24, 1980). T h e s e a r e b a s e d on t h e values in D I N 17 410 ( M a y 1977) of t h e F e d e r a l R e p u b l i c of G e r m a n y . T h e d e s i g n a t i o n s y s t e m i s t h e s a m e as that for c o m p a c t m a g n e t s , cf. section 3.1. In t h e G e r m a n D e m o c r a t i c R e p u b l i c t h e r e is a n o t h e r n a t i o n a l s t a n d a r d for i s o t r o p i c a n d a n i s o t r o p i c g r a d e s : T G L 16541/04 (1979). T a b l e 37 c o n t a i n s a s u m m a r y of t r a d e m a r k s of v a r i o u s countries. T h e t e m p e r a t u r e d e p e n d e n c e s of t h e m a g n e t i c c h a r a c t e r i s t i c s c o r r e s p o n d to t h o s e of c o m p a c t m a g n e t s , cf. t a b l e 22.
592
H. STJ~d3LEIN
Electrical, thermal, mechanical and chemical properties largely depend on the type of matrix material and the ferrite content. General statements can only be made to a limited extent and inquiries must be made at the manufacturer's in each individual case. The automobile industry places special requirements on the matrix material as regards its resistance to oil, petrol and solvents. The television industry demands a high degree of flame retardancy. Special grades have been developed for these purposes. Plastoferrites are used in a large number of applications, see fig. 82, where the main criterion, more so than with compact magnets, is the high economy of these material groups. The following applications deserve particular mention (Caspar et al. 1965, Hinderaker 1976, Samow 1973, Badner 1978): holding magnets, mainly for refrigerator catches but also for planning boards, toys etc., correction magnets for television tubes, fractional-horsepower motors and dynamos, actuating magnets for reed switches, electronic ignition systems and separators (filters) for cleaning fluids. The application as a magnetic information storage medium is discussed by Fayling (1979). According to Samow (1973) s o m e 106 kg of bonded hard ferrites are produced annually in Western Europe alone.
References Abrams, J.C. and M.G. McLaren, 1976, J. Amer. Ceram. Soc. 59, 347-350. AdelskGld, V., 1938, Arkiv fGr kemi, mineralogi och geologi 12A, No. 29, 1-9. See also: Zeitschr. Kristallographie, Erg. Bd. 6, 1941, Strukturbericht Vol. VI, 1938, 74-75. Akaiwa, Y., 1973, Jap. J. Appl. Phys. 12, No. i1, 1742-1747. Aminoff, G., 1925, Geol. FGren. FGrhandl. 47, No. 3, 283-289. Andreotti, R., 1973, 1. IOS-Kolloquium, Varese, Italien. Anonymous, 1967, Machine Design (16, 3, 1967) p. 12. Appendino, P. and M. Montorsi, 1973, Ann. di Chimica, 63, 449-456. Ardelean, I., E. Burzo and I. Pop, 1977, Solid State Commun. 23, 211-214. Ardelean, I. and E. Burzo, 1980, J. Magn. Magn. Mat. 15-18, 1369-1370. Arendt, R.H., 1973a, J. Appl. Phys. 44, 33003305. Arendt, R.H., 1973b, J. Solid State Chem. 8, 339-347. Assayag, P., 1963, Bull. Soc. Franc. Electr. 4, 5-23. Asti, G., 1976, Ceramurgia 6, No. 1, 3-10.
Asti, G. and S. Rinaldi, 1974, Proc. 3rd. Eur. Conf. on Hard Magn. Mat. Amsterdam, 9193. Asti, G., P. Cavallotti and R. Roberti, 1976, Proc. 3rd. Cimtec Rimini, paper 21; and 1977, Ceramurgia Internat. 3, no. 2, 70-77. Asti, G., M. Carbucicchio, A. Deriu, E. Lucchini and G. Slokar, 1980, J. Magn. Magn. Mat. 20, 44-46. Badner, JJ., 1978, J. Appl. Phys. 49 (3), 17881789. Balek, V., 1970, J. Mater. Sci. 5, 714-718. Barham, D. and A.E. Schwalm, 1974, J. Canad. Ceram. Soc. 43, 27-29. Batti, P., 1960, Ann. di Chimica, 50, 14611478. Batti, P., 1961a, Ann. di Chimica, 51, 13181339. Batti, P., 1961b, Univ. Trieste, Fac. Ingegneria No. 11. Batti, P., 1962a, Ann. di Chimica, 52, 941-961. Batti, P., 1962b, Ann. di Chimica, 52, 12271247. Batti, P., 1976, Ceramurgia, 6, 11-16. Batti, P. and G. Sloccari, 1967, Ann. di Chimica, 57, 777-804.
H A R D FERRITES AND PLASTOFERRITES Batti, P. and G. Sloccari, 1968, Ann. di Chimica, 58, 213-222. Batti, P. and G. Sloccari, 1976, Ceramurgia, 6, No. 3, 136-141. Bauer, I., 1976, Wahlarbeit W 146 der TH Aachen. Becker, J.J., 1962, Metallurg. Rev. 7, No. 28, 371-432. Becker, J.J., 1967, J. Appl. Phys. 38, 1015-1017. Beer, H.B. and G.V. Planer, 1958, Brit. Communications and Electronics, 5, 939-941. Belyanina, N.V., I.N. Ivanova, Yu.G. Saksonov and A.A. Shvarts, 1977, Russ. J. Inorg. Chem. 22 (11), 1718-1719. Beretka, J., 1968, Div. Build. Res. CSIRO, Report F2-1, Melbourne, Australia. Beretka, J. and M.J. Ridge, 1968, J. Chem. Soc. (A) 2463-2465. Beretka, J. and T. Brown, 1971, Aust. J. Chem. 24, 237-242. Berger, W. and F. Pawlek, 1957, Arch. Eisenhfittenwes. 28, 101-108. Bergmann, F., 1958, Ber. Arb. Gem. Ferromagn. (Dr. Riederer-Verlag, Stuttgart). Berry, L.G., 1951, Amer. Mineralogist, 36, 512514. Bertaut, E.F., A. Deschamps, R. Pauthenet and S. Pickart, 1959, J. Phys. Rad. 20, 404-408. Besjasikowa, T.G., B.W. Aisikowitsch, A.G. Alekseew, S.A. Kowatschewa and A.E. Kornew, 1977, Elektritschestvo (Moskow) No. 1, 81-83. Black, D.B., A.E. Schwalm and D. Barham, 1976, J. Canad. Ceram. Soc. 45, 4%52. Blix, R., 1937, Geol. F6ren. F6rhandl. 59, No. 3, 300-302. Blondot, 1973, Preprints Aimants 1973; Chambre syndicale des producteurs d'aciers fins & speciaux, 12, rue de Madrid, Paris 8°; paper Q. Bohning, R.G., 1978, Powd. Met. Internat. 10, 37. Bottoni, G., D. Candolfo, A. Cecchetti, L. Giarda and F. Masoli, 1972, Phys. Status Solidi A, 32, K47-K50. Bowman, W.S., Sutarno, N.F.H. Bright and J.L. Horwood, 1969, J. Canad. Ceram. Soc. 38, 1-8. Brady, L.J., 1973, J. Mat. Sci. 8, 993-999. Braun, P.B., 1957, Phil. Res. Rep. 12, 491548. Brisi, C. and P. Rolando, 1969, Ann. di Chimica, 59, 385-399.
593
Broese van Groenou, A., 1975, IEEE Trans. Magn. MAG-11, No. 5, 1446-1451. Broese Van Groenou, A. and J.D.B. Veldkamp, 1979a, Phil. Techn. Rdsch. Nr. 4/5, 109-123. Broese van Groenou, A. and P.E.C. Franken, 1979b, Proc. Brit. Ceram. Soc. No. 28, 243266. Broese van Groenou, A., J.D.B. Veldkamp and D. Snip, 1977, J. de Phys. 38, C1-285-289. Buessem, W.R. and A. Doff, 1957, Proc. 13. Annual Meeting, Metal Powder Association, Chicago/Ill., Vol. II: Ferrites and Electron. Core Session, 196-204. Bulzan, M. and E. Segal, 1976, Rev. Roumaine de Chim. 21, 651~53. Bungardt, K., P. Kagner and F. Th/immler, 1968, DEW-Techn. Ber. 8, 157-187. Bunget, I. and M. Rosenberg, 1967, Phys. Status Solidi, 21, K 131-K 133. Burzo, E., I. Ardelean and I. Ursu, 1980, J. Mat. Sci. 15, 581-593. Buschow, K.H.J., W. Luiten, P.A. Naastepad and F.F. Westendorp, 1968, Phil. Techn. Rev. 29, 336-337. Bye, G.C. and C.R. Howard, 1971, J. Appl. Chem. Biotechnol. 21, 319-323. Bye, G.C. and C.R. Howard, 1972, J. Appl. Chem. Biotechnol. 22, 1053-1064. Calow, C.A. and R.J. Wakelin, 1968, J. Inst. Met. 96, 147-154. Cartoceti, A. and E. Steinort, 1971, La metallurgia italiana-atti notizie No. 10, 291295. Cartoceti, A., F. Scansetti and E. Steinort, 1976, Ceramurgia 6, 39-46. Casimir, H.B.G., J. Smit, U. Enz, J.F. Fast, H.P.J. Wijn, E.W. Gorter, A.J.W. Duyvesteyn, J.D. Fast and J.J. de Jong, 1959, J. Phys. Rad. 20, 360-373. Caspar, H.J. and G. Samow, 1965, Valvo-Ber. 11, H. 5, 136-145. Cavallotti, P., U. Ducati and R. R0berti, 1976, Ceramurgia, 6, No. 1, 17-20. Cavallotti, P., R. Roberti, G. Caironi and G. Asti, 1977, J. de Phys. 38, Coll. C 1, suppl, au No. 4, C1-333-C1-336. Cavallotti, P., R. Roberti, A. Cartoceti and F. Scansetti, 1979, IEEE Trans. Magn. MAG15, No. 3, 1072-1074. Cho, K. and K. Kim, 1975a, J. Korean Ceram. Soc. 12, 71-75. Cho, K. and K. Kim, 1975b, J. Korean Ceram. Soc. 12, 76-81. Chroust, V., 1972, Fortschritte der Pulver-
594
H. STJ~d3LEIN
metallurgie (Forsch. Inst. in Sumperk, CSSR) No. 2, 3-38. Chukalkin, Yu.G., V.V. Petrov and B.N. Goshitskii, 1979, Izvest. Akad. Nauk SSSR, Neorg. Mater. 15, No. 7, 1307-1308. Chukalkin, Yu.G., V.V. Petrov and B.N. Goshchitskii, 1981, Phys. Status Solidi A, 67, 421-426. Clark, A.F., W.M. Haynes, V.A. Deason and R.J. Trapani, 1976, Cryogenics, May, 267270. Cocco, A., 1955, Ann. di Chimica, 45, 737-753. Cochardt, A., 1966, J. Appl. Phys. 37, No. 3, 1112-1115. Cochardt, A., 1969, DE-OS (Deutsche Offenlegungsschrift) 1 911 524. Courtel, R., H. Makram and G. Pigeat, 1962, Compt. Rend. 254, No. 26, 4447 4449. Curci, T.J., W.R. Bitler and R.C. Bradt, 1978, Mat. Sci. Res. 11, Proc. Cryst. Ceram. 359-368. Dambier, Th. and K. Ruschmeyer, 1960, AEGMitt. 50, 388-391. Davis, R.T., 1965, thesis Pennsylvania State University. DeBitetto, D.J., 1964, J. Appl. Phys. 35, 34823487. Denes, P.A., 1962, Amer. Ceram. Soc. Bull. 41, 509-512. DE-OS (= Deutsche Offenlegungsschrift) 2 110 489 (Priority: Japan, 2, 3, 70). Desmond, D.J., 1945, J. Instr. electr. Eng., P. 2. Power Engng. 92, No. 27, 229-244. Dietrich, H., 1968, Feinwerktechnik 72, 313. 322 and 425-433. Dietrich, H., 1969, Feinwerktechnik 73, 171180 and No. 5, 199-208. Dietrich, H., 1970, IEEE Trans. Magn. MAG6, No. 2, 272-275. Dixon, S., M. Weiner and T.R. AuCoin, 1970, J. Appl. Phys. 41, 135%1358. Dornier System GmbH, 1979, EP 0 011 265 A2 (Europ. Pat.). Drofenik, M. and D. Kolar, 1970, Ber. Dt. Keram. Ges. 47, 666~68. Drossel, E. and G. Samow, 1969, Valvo-Ber. 15, H. 2, 58--63. Dtilken, H., 1971, thesis Aachen. Dtilken, H., F. Haberey and H.P.J. Wijn, 1969, Z. Angew. Phys. 26, 29-31. Dullenkopf, P., 1968, thesis Aachen. Dullenkopf, P. and H.P.J. Wijn, 1968, Elektroanzeiger, 21, 472-473.
Dullenkopf, P. and H.P.J. Wijn, 1969, Z. Angew. Phys. 26, 22-29. Durant, B. and J.M. Pfiris, 1980, Ann. Chim. Fr. 5, 589-595. Durant, B. and J.M. P~ris, 1981, J. Mat. Sci. Lett. 16, 274-275. Ebeling, R. and H. Krause, 1978, VDI-Berichte, No. 309, Dfisseldorf. Edwards, A. and H.E. Gould, 1975, Report of Fa. IOS, Malgesso (Varese), Italy. Efremov, G.L. and I.I. Petrova, 1977 Iz. Akad. Nauk SSSR, Anorg. Mat. 13, 318-321. Eisenhuth, C., 1968, Stahl und Eisen, 88, 264. 269. Emberson, C.C., W.C.M. Leung and D. Barham, 1978, J. Canad. Ceram. Soc. 47, 1-5. Erchak Jr., M., I. Fankuchen and R. Ward, 1946, J. Amer. Chem. Soc. 68, 2085-2093. Erickson, R.H., 1962, US-Patent, 3 155 623. Erzberger, P., 1975, Firmenschrift der Fa. Bayer, Krefeld, Technische Eisenoxide zur HersteUung von Ferriten. Esper, FJ. and G. Kaiser, 1972, Int. J. Magn. 3, 189-195. Esper, F.J. and G. Kaiser, 1974, Bosch Techn. Ber. 4, 308-314, and Proc. 3rd Eur. Conf. on Hard Magn. Mat. (Amsterdam 1974) 106-108. Esper, F.J. and G. Kaiser, 1975, Ber. Dr. Keram. Ges. 52, 210213. Esper, FJ. and G. Kaiser, 1978, Ber. Dt. Keram. Ges. 55, 294-295. Fagherazzi, G., 1976, Ceramurgia, 6, 26-32. Fagherazzi, G. and L. Giarda, 1974, Proc. 3rd Europ. Conf. on Hard Magn. Mat. (Amsterdam) 79-82. Fagherazzi, G., C.M. Maggi and G. Sironi, 1972, Ceramurgia, 2, 181-189. Fahlenbrach, H., 1953, Elektrotechn. Zeitschr. A, 388--389. Fahlenbrach, H., 1963, Techn. Mitt. Krupp, Forsch.-Ber. 21, 113-119. Fahlenbrach, H., 1965, Techn. Mitt. Krupp, Forsch.-Ber. 23, 26-35. Fahlenbrach, H., 1972, Metall 26, 1230-1234. Fahlenbrach, H. and W. Heister, 1953, Arch. Eisenh/ittenwes. 24, 523-528, and 1954, Techn. Mitt. Krupp 12, 47-51. Fayling, R.E., 1979, IEEE Trans. Magn. MAG. 15, No. 6, 156%1569. Fischer, E., 1962, Angewandte Meg- und Regeltechnik 2, No. 24, a229-a233. Fischer, E., 1978, Powd. Met. Internat. 10, 3032 and Sprechsaal Nr. 2, 38-42.
HARD FERRITES AND PLASTOFERRITES Flink, G., 1924, Geol. F6ren. F6rhandl. 46, No. 6/7, 704-709. Foniok, F. and S. Makolagwa, 1977, J. Magn. Magn. Mat. 4, 95-104. Frei, E.H., S. Shtrikman and D. Treves, 1959, J. Appl. Phys. 30, 443. Gadalla, A.M. and H.W. Hennicke, 1973, Powd. Met. Internat. 5, 196-200. Gadalla, A.M. and H.W. Hennicke, 1975, J. Magn. Magn. Mat. 1, 144-152. Gadalla, A.M., H.E. Schfitz and H.W. Hennicke, 1976, J. Magn. Magn. Mat. 1, 241250. Gallagher, P.K., D.W. Johnson Jr., F. Schrey and D.J. Nitti, 1973, Ceram. Bull. 52, 8,42849. Gallo, G., 1936, Annali di Chimica, 109-115. Gasiorek, S., 1980, Sci. of Ceramics, 10, 311319. Gerling, W. and H.P.J. Wijn, 1969, Z. Angew. Phys. 27, 77-82. Gershov, LYu., 1963, Soviet Powd. Metallurgy and Metal Ceram. No. 3 (15), 22%234. Gershov, I.Yu., 1971, Soy. Powd. Met. 10, 388392. Giarda, L., 1976, Ceramurgia, 6, 33-38. Giarda, L., A. Cattalani and A. Franzosi, 1977, J. de Phys. 38, Coll. C 1, Suppl. au no. 4, C 1-325-328. Giarda, L., G. Bottoni, D. Candolfo, A. Cecchetti and F. Masoli, 1978, Ceramurgia Int. 4, No. 2, 79-81. Giron, V.S. and R. Pauthenet, 1959, Compt. Rend. 248, 943-946. Glass, H.L. and J.H.W. Liaw, 1978, J. Appl. Phys. 49, 1578-1581. Glass, H.L. and F.S. Stearns, 1977, IEEE Trans. Magn. MAG-13, No. 5, 1241-1243. Glazacheva, M.V. and L.S. Zevin, 1972, Izvestiya Akademii Nauk SSSR, Anorg. Mat. 8, No. 9, 1638-1640. Gmelin, 1959, 8th ed., system No. 59, Iron, Part D, Magnetische Werkstoffe Suppl. Vol. 2, p. 43d d41. Goldman, A. and A.M. Laing, 1977, J. de Phys. 38, (C1) 297-301. Gordes, F., 1973, Wahlarbeit W 138 des Instituts ffir Werkstotte der Elektrotechnik, TH Aachen. Gordon, I., 1956, Ceram. Bull. 35, 173-175. Goto, K., 1972, J. Jap. Soc. Powd. Met. 18, 209-216. Goto, Y., T. Takada, 1960, J. Amer. Ceram. Soc. 43, 150-153.
595
Goto, Y. and K. Takahashi, 1971, J. Jap. Soc. Powd. Met. 17, 193-197. Goto, K., M. Ito and T. Sakurai, 1980, Jap. J. Appl. Phys. 19, No. 7, 1339-1346. Gould, J.E., 1962, Magnetic Stability, in: Permanent Magnets and Magnetism, ed. D. Hadfield (Iliffe Books Ltd., London) p. 443472. Gould, J.E., 1969, IEEE Trans. Magn. MAG-5, No. 4, 812-821. Granovskii, I.V., Yu.D. Stepanova, D.Ya. Serebro,R.A. Lysyak and E.M. Krisan, 1970, Soy. Powd. Metallurgy and Met. Ceram. No. 6, 486-490 and No. 11,895-901. Gray, T J . and R.J. Routil, 1972, Sympos. Electr. Magn. Opt. Ceramics, London, 13-14 Dec. 1972, 91-103. Haag, R.M., 1969, Joint Fall Meeting, Electronics Div. and New England Section, Am Ceram. Soc. Boston. Haag, R.M., 1971, IEEE Trans. Magn. MAG-7, Sept., 609. Haberey, F., 1967, thesis Aachen. Haberey, F., 1969, J. Appl. Phys. 40, 28352837. Haberey, F., 1978, Ber. Dt. Keram. Ges. 55, 297-301. Haberey, F. and A. Kockel, 1976, IEEE Trans. Magn. MAG-12, No. 6, 983-985. Haberey, F. and F. Kools, 1980a, Ferrites, Proc. ICF 3, 356-361. Haberey, F. and H.P.J. Wijn, 1968, Phys. Status Solidi, 26, 231-240. Haberey, F. and H. Wullkopf, 1977a, private communication. Haberey, F., M. Velicescu and A. Kockel, 1973a, Int. J. Magnetism 5, 161-168. Haberey, F., M. Velicescu and A. Kockel, 1973b, Int. J. Magnetism 5, 161-168; F. Haberey, K. Kuncl, M. Velicescu; LinseisJournal 1/73, 6-10. Haberey, F., A. Kockel and K. Kuncl, 1974, Ber. Dt. Keram. Ges. 51, 131-134. Haberey, F., G. Oehlschlegel and K. Sahl, 1977b, Ber. Dt. Keram. Ges. 54, 373-378. Haberey, F., R. Leckebusch, M. Rosenberg and K. Sahl, 1980b, Mat. Res. Bull. lS, 493-500 and IEEE Trans. Magn. MAG-16, No. 5, 681-683. Hadfield, D. (ed.), 1962, Permanent Magnets and Magnetism (Iliffe Books, London, Wiley, New York). Hagner, J., 1980, Hermsdorfer Techn. Mitt. 20, No. 55, 1764-1771, 20, No. 56, 1810-1815, and 1981, 21, No. 57, 1819-1825.
596
H. STJ/G3LEIN
Hamamura, A., 1973, Sumitomo-Sondermetall Techn. Ber. 1, 37-46. Hamamura, A., 1977, Techn. Ber. der Fa. Sumitomo Sondermetalle 3, 29-35. Haneda, K. and H. Kojima, 1973a, J. Appl. Phys. 44, 3760-3762. Haneda, K. and H. Kojima, 1974a, J. Amer. Ceram. Soc. 57, No. 2, 68--71. Haneda, K., Ch. Miyakawa and H. Kojima, 1973b, Bull. Res. Inst. Sci. Meas. Tohoku Univ. 22, No. 1, 67-78. Haneda, H., Ch. Miyakawa and H. Kojima, 1974b, J. Amer. Ceram. Soc. 57, No. 8, 354357. Haneda, K., C. Miyakawa and H. Kojima, 1975, AIP Conf. Proc. No. 24, Magn. Magn. Mat. 1974, Amer. Inst. Phys. 770771. Harada, H., 1970, Ferrites, Proc. Int. Conf. Japan, 279-282. Harada, H., 1980, Ferrites, Proc. ICF 3, 354. 355. Harvey, J.W. and D.W. Johnson Jr., 1980, Ceramic Bull. 59, No. 6, 637~539, 645. Hausknecht, P., 1913, thesis, Strasbourg. Hayashi, N., Y. Syono, Y. Nakagawa, K. Okamura and S. Yajima, 1980, Sci. Rep. RITU, A, 28, No. 2, 164-171. Heck, C., 1967, Magnetische Werkstoffe und ihre technische Anwendung, (Dr. Alfred H/ithig Verlag, Heidelberg) and 1975, 2nd edition. Heidel, M. and W. Schneider, 1977, Hermsdorfer Techn. Mitt. 17, 1572-1574. Heimke, G., 1958, Naturwissenschaften, 45, 260-261. Heimke, G., 1960, Ber. Arb. Gem. Ferromagn. 1959, Stahleisen, 213.221. Heimke, G., 1962, Ber. Dt. Keram. Ges. 39, 326-33O. Heimke, G., 1963, Z. Angew. Phys. 15, 271-272. Heimke, G., 1964, Z. Angew. Phys. 17, 181183. Heimke, G., 1966, Ber. Dt. Keram. Ges. 43, 600.604. Heimke, G., 1976, Keramische Magnete, Appl. Mineralogy 10, (Springer, Wien). Hempel, K.-A., P. Grosser, 1964, Z. angew. Phys. 17, 153.157. Hempel, K.A. and C. Voigt, 1965, Z. angew, Phys. 19, 108-112. Hennig, G., 1966, thesis Berlin; see also IEEE Trans. Magn. MAG-2, No. 3, 165-166. Hinderaker, P.D., 1976, Machine Design (Febr. 12th) 94.98.
Hiraga, T., 1970, Ferrites, Proc. Intern. Conf. Japan, 179-182. Hirotsu, Y., H. Sato, 1978, J. Solid State Chem. 26, 1-16. Hirschfeld, D. and W. Fischer, 1963, unpublished. Hodge, M.H., W.R. Bitler and R.C. Bradt, 1973, J. Amer. Ceram. Soc. 56, 49%501. Hodge, M.H., W.R. Bitler and R.C. Bradt, 1975, in: Deformation of Ceramic Materials, ed., R.C. Bradt and U.R.E. Tressler (Plenum Press, New York) p. 483M96. Horn, E., P. KaBner and H. Dietrich, 1968, DEW-Techn. Ber. 8, 234-242. Hoselitz, K. and R.D. Nolan, 1970, IEEE Trans. Magn. MAG-6, No. 2, 302. Ichinose, N. and K. Kurihara, 1963, J. Phys. Soc. Jap. 18, 1700-1701. Ichinose,N. and Y. Tanno, 1975, Proc. USJapan Sem. Sci. Ceram., Hakone, Japan, 207-211. Ireland, J.R., 1959, Appl. Magnetics, Indiana Gen. Corp. 7. Ireland, J.R., 1968, Ceramic permanent-magnet motors (McGraw-Hill, New York). Ito, S., Y. Kajinaga, I. Imai and I. Endo, 1974, J. Jap. Soc. Powd. Met. 21, No. 5, 132-139. Iwanow, O.A., E.W. Shtolts and J.S. Shut, 1966, Fiz. Metal. i Metalloved. 22, 455458. Iwasa, M., E.C. Liang, R.C. Bradt and Y. Nakamura, 1981, J. Amer. Ceram. Soc. 64, No. 7, 390-393. Jfiger, P., 1976, Keram. Zeitschr. 28, Nr. 9, 454456; 1978, Keram. Zeitschr. 30, No. 5, 246-249. Jahn, L., 1968, thesis Halle; see also 1967, Phys. Status Solidi, 19, K 75-K 77. Jahn, L. and H.G. Miiller 1969, Phys. Status Solidi, 35, 723-730. Jander, W., 1927, Z. anorg, u. ailg. Chemie, 163, 1-30. Jaworski, J.M., G.A. Ingham, W.S. Bowman and G.E. Alexander, 1969, J. Canad. Ceram. Soc. 38, 171-175. John, W., 1973, Farbe + Lack, 79, 537-542. Johnson Jr., D.W., 1981, Ceram. Bull. 60, No. 2, 221-224, 243. Joksch, Ch., 1964, DEW-Techn. Ber. 4, 182188. Joksch, Chr., 1976, J. Magn. Magn. Mat. 2, 303--307. Jonker, G.H. and A.L. Stuijts, 1971, Phil. Techn. Rev. 32, 79-95.
H A R D FERRITES AND PLASTOFERRITES Kanamaru, F., M. Shimada and M. Koizumi, 1972, J. Phys. Chem. Sol. 33, 1169-1171. Kanamaru, F., K. Oda, T. Yoshio, M. Shimada and K. Takahashi, 1981, J. Jap. Soc. Powd. and Powd. Met. 28, 70-76. Kantor, P., A. Revcolevschi and R. Collongues, 1973, J. Mat. Sci. 8, 1359-1361. Kaf3ner, P., 1970, Chemie-Ing.-Technik, 42, 48. Klingenberg, R. and K. Sahl, 1979, Ber. Dt. Keram. Ges. 56, 75-78. Klug, F.J. and J.S. Reed, 1978, Ceramic Bull. 57, No. 12, 1109-1110, 1115. Knight, F., 1962, The Magnetizing, Testing and Demagnetizing of Permanent Magnets, in: Permanent Magnets and Magnetism, ed., D. Hadfield (Iliffe Books Ltd., London) p. 401442. Kockel, A., 1980, private communication. Kohatsu, I. and G.W. Brindley, 1968, Z. phys. Chemie, N.F. 60, 79-89. Kohn, J.A., D.W. Eckart and C.F. Cook Jr., 1971, Science, 172, 519-525. Kojima, H., 1955a, Sci. Rept. Res. Inst. Tohoku Univ. 7, Ser. A, No. 5, 502-506. Kojima, H., 1955b, Sci. Rept. Res. Inst. Tohoku Univ. 7, Ser. A, No. 5, 507-514. Kojima, H., 1956, Sci. Rept. Res. Inst. Tohoku Univ. 8, Ser. A, 540546. Kojima, H., 1958, Sci. Rept. Res. Inst. Tohoku Univ. 10, Ser. A, 175-182. Kojima, H., Ch. Miyakawa and N. Nakaigawa, 1969, Bull. Res. Inst. Sci. Meas. Tohoku Univ. 17, 1-12. Kojima, H., K. Goto and C. Miyakawa, 1980, Ferrites, Proc. ICF 3, 335-340. Kondorsky, E., 1940, J. Phys. USSR 2, 161-181. K6nig, U., 1974, Techn. Mitt. Krupp, Forsch.Ber. 32, 75-84. Kools, F., 1973, Sci. Ceramics, 7, 27-44. Kools, F., 1974, Proc. 3rd Eur. Conf. on Hard Magnetic Mat., Amsterdam, 98-101. Kools, F., 1975, Ber. Dt. Keram. Ges. 52, 213215. Kools, F., 1978a, Ber. Dt. Keram. Ges. 55, 301304. Kools, F., 1978b, Ber. Dt. Keram. Ges. 55, 296-297. Kools, F., M. Klerk, P. Franken and F. den Broeder, 1980, Sci. Ceramics, 10, 349-357. Kooy, C., 1958, Phil. Techn. Rev. 19, 286-289. Krijtenburg, G.S., 1965, Vortrag Nr. 2.13 auf der 1. Europ. Tagung fiber Magnetismus in Wien.
597
Krijtenburg, G.S., 1970, IEEE Trans. Magn. MAG-6, No. 2, 303. Krijtenburg, G.S., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam, 83-86. Kronenberg, K.J. and M.A. Bohlmann, 1960, J. Appl. Phys. Suppl. 31, 82 S-84 S. Krupi6ka, S., 1973, Physik der Ferrite und der verwandten magnetischen Oxide (Vieweg, Braunschweig). Kuntsevich, S.P., Yu.A. Mamalu i and A.S. Mil'ner, 1968, Fiz. metal, metalloved. 26, No. 4, 610-613. Kuntsevich, S.P., Yu. A. Mamaluj and V.P. Palekhin, 1980, Sov. Phys. Solid State, 22 (7), 1278-1279. Lacour, C. and M. Paulus, 1973a, Compt. Rend. Ser. C, 277, 1001-1004. Lacour, C. and M. Paulus, 1973b, Compt. Rend. Ser. C, 277, 1085-1088. Lacour, C. and M. Paulus, 1975a, Phys. Status Solidi A, 27, 441--456. Lacour, C. and M. Paulus, 1975b, Phys. Status Solidi A, 28, 71-80. Landolt-B6rnstein, 1962, Vol. 1I, Part 9, Magnetic properties I, Sect. 2924: Hexagonal Ferrites (Springer, Berlin) p. 2-222 to 2-236. Landolt-B6rnstein, 1963, 6th ed., Vol. 1V, Part. 2, p. 132. Landolt-B6rnstein, 1970, Vol. 4, Part b, Sect. 7: Hexagonal Ferrites (Springer, Berlin) p. 547583. Landolt-B6rnstein, 1981, Group III, Vol: 12c, in press. Laville, H. and J.C. Bernier, 1980, J. Mat. Sci. 15, 73-81. Laville, H., J.C. Bernier and J.P. Sanchez, 1978, Solid State Commun. 27, 259-262. Lliboutry, L., 1950, Thesis, Grenoble. Lotgering, F.K., 1959, J. Inorg. Nucl. Chem. 9, 113-123. Lotgering, F.K. and M.A.H. Huyberts, 1980, Solid State Commun. 34, 49-50. Lucchini, E. and G. Sloccari, 1976, Ceramurgia International, 2, 13-17. Lucchini, E. and G. Slokar, 1980a, J. Mat. Sci. 15, 2123-2125. Lucchini, E. and G. Slokar, 1980b, J. Magn. Magn. Mat. 21, 93-96. Mackintosh, G.H. and P.F. Messer, 1976, Science of Ceramics Vol. 8, Brit. Ceram. Soc., 403-414. Mahdy, A.N. and A.M. Gadalla, 1976a, J. Magn. Magn. Mat. 1, 326-329.
598
H. ST~d3LEIN
Mahdy, A.N. and A.M. Gadalla, 1976b, J. Magn. Magn. Mat. 1, 330-332. Malakhovskij, A.N., 1980, Soy. Powd. Metallurgy Met. Ceram. (SPMCAV) 19, No. 3, 201-203. Mamaluj, Yu.A., A.A. Murakhovskij and L.P. Ol'khovik, 1975, Inorg. Mater. 11, 1145-1146. Mansour, N.A., A.M. Gadalla and H.W. Hennicke, 1975, Ber. Dt. Keram. Ges. 52, 201204. Mason, W.P., 1954, Phys. Rev. 96, 302-310. Maurer, Th. and H.G. Richter, 1966, Powder Metallurgy 9, Nr. 18, 151-162, and 1966, Sprechsaal ffir Keramik, Glas, Email, Silikate, 99, Heft 24, 1084-1089. Maurer, Th. and H.G. Richter, 1972, Powd. Met. Int. 4, 78-8i. McCaig, M., 1967, Attraction and repulsion (Oliver and Boyd, Edinburgh). McCaig, M., 1977, Permanent magnets in theory and practice (Pentech Press, London). Mee, C.D. and J.C. Jeschke, 1963, J. Appl. Phys. 34, No. 4, part 2, 1271--1272. Menashi, W.P. and T.R. AuCoin, J.R. Shappirio, D.W. Eckart, 1973, J. Cryst. Growth, 20, 68-70. Meriani, S., 1972, Acta Cryst. B 28, 1241-1243. Metzer, A. and Ch. Gorin, 1975, Intermag. London, Report 34.6. Metzer, A., E. Basevi, A.M. Baniel and Ch. Gorin, 1974, US-Patent 3 796 793. Miller, R.J., 1970, thesis Ohio State University. Mondin, L.Ya., 1969, Poroshkovaya Metallurgya, 77, 99-103. Monteil, B., J.-C. Bernier and A. Revcolevschi, 1977, Mat. Res. Bull. 12, 235-240. Monteil, J.B., L. Padel and J.C. Bernier, 1978, J. Solid State Chem. 25, 1-8. Moon, D.W., J.M. Aitken, R.K. MacCrone and G.S. Cieloszyk, 1975, Phys. Chem. Glasses 16, 91-102. Mountvala, A.J. and s.F. Ravitz, 1962, J. Amer. Ceram. Soc. 45, 285-288. Moskowitz, L.R., 1976, Permanent Magnet Design and Application Handbook (Cahners Books International, Boston/Mass.) available from the Permanent Magnet Users Association of the Franklin Institute Research Laboratories, 20th & Parkway, Philadelphia, PA. 19103, USA. Miiller, H.G. and G. Heimke, 1959, Ber. Arb. Gem. Magnetismus 1958 (Dr. Riederer~Verlag, Stuttgart) 101-104. N6el, L., 1951, J. Phys. Radium, 12, 339.
N6el, L., R. Pauthenet, G. Rimet and V.S. Giron, 1960, J. Appl. Phys., Suppl. 31, 27 S-29 S. Nicolas, J., 1979, Rev. techn. Thomson c.s.f. 11, No. 2, 243-258. Nishikawa, T., T. Nishida, K. Inoue, H. Inoue and I. Uei, 1974, Yogyo Kyokai Shi, 82, No. 5, 241-247. Oda, K., T. Yoshio, K. Takahashi, 1982, J. Jap. Soc. Powd. Met. 29, No. 2, 39-44. Odor, F. and A. Mohr, 1977, IEEE Transl Magn. MAG-13, No. 5, 1161-1162. Okamura, T., H. Kojima and Y. Kamata, 1952, J. Appl. Phys. (Japan) 21, 9-12. Okamura, T., H. Kojima and S. Watanabe, 1955, Sci. Rept. Res. Inst. Tohoku Univ. 7, Ser. A, No. 4, 411-417 and 418-424. Okazaki, K. and H. Igarashi, 1970, Ferrites, Proc. Internat. Conf. Japan, 131-133. Oron, M. and P. Ramon, 1975, IEEE Trans. Magn. MAG-11, No. 5, 1452-1454. Otsuka, T., Y. Yamamichi, Y. Watanabe, K. Kanaya and T. Sasaki, 1973, J. Jap. Soc. Powder and Powd. Met. 20, No. 5, 126-132. Pant, P., 1977, Techn. Mitt. Krupp, Forsch.Ber. 35, No. i, 59-64. Pant, P. and H. Stfiblein, 1977, Proc. World Electrotechn. Congress, Moskow, Section 3B, Paper No. 10. Parker, R.S. and R.J. Studders, 1962, Permanent Magnets and Their Applications (Wiley, New York, London). Passerone, A., E. Biagini and V. Lorenzelli, 1975, Ceramurgia Int. 1, No. 1, 23-27. Pauthenet, R. and G. Rimet, 1959, Compt. Rend. 249, 1875-1877. Pawlek, F. and K. Reichel, 1957a, Arch. Eisenhfittenwes. 28, 241-244. Pawlek, F. and K. Reichel, 1957b, Naturwiss. 44, 390. Petrdlik, M., V. Rubes, I.D. Radomysel'skij, A.F. Zhornyak and I.S. Nikishov, 1971, Sov. Powd. Metallurgy and Met. Ceram. 10, 516520. Petzi, F., 1971, Powd. Met. Int. 3, No. 4, 199-202. Petzi, F., 1974a, Powd. Met. Int. 6, No. 3, 1-3. Petzi, F., 1974b, Keram. Zeitschrift, 26, No. 3, 1-10. Petzi, F., 1975, Ber. Dt. Keram. Ges. 52, No. 7, 249-251. Petzi, F., 1980, Powd. Met. Int. 12, No. 1, 32-37. Pingault, D., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam, 74-78.
H A R D FERRITES AND PLASTOFERRITES Qian, X. and B.J. Evans, 1981, J. Appl. Phys. 52 (3), 2523-2525. Rademakers, A. and H. van Suchtelen, 1957, Matronics, Nr. 12, 205-215. Rathenau, G.W., 1953, Rev. Mod. Phys. 25, 29%301. Rathenau, G.W., 1974, Proc. 3rd. Eur. Conf. on Hard Magn. Mat,, Amsterdam, %16 Rathenau, G.W., J. Smit and A.L. Stuyts, 1952, Z. Phys. 133, 250-260. Ratnam, D.V. and W.R. Buessem, 1970, IEEE Trans. Magn. MAG-6, No. 3, 610-614. Ratnam, D.V. and W.R. Buessem, 1972, J. Appl. Phys. 43, 1291-1293. Reddy, B.P.N. and P.J. Reddy, 1974, Phil. Mag. 30, No. 3, 8th series, 55%563. Reed, J.S. and R.M. Fulrath, 1973, J. Amer. Ceram. Soc. 56, 20%211. Reed, J.S. and F.J. Klug, 1975, Proc. US-Jap. Seminar Bas. Sci. Ceram., Hakone, Japan, 189-193. Reichel, K., 1980, Praktikum der Magnettechnik (Franzis-Verlag, M/inchen). Reinboth, H., 1970, Technologie und Anwendung magnetischer Werkstoffe, 3rd ed. (VEB Verlag Technik, Berlin). Remmey Jr., G.B., 1970, Powd. Met. Int. 2, 12%129. Richter, H., 1962, Diploma work, Clausthal. Richter, H.G., 1968, DEW-Techn. Bet. 8, 192208. Richter, H.G. and H.E. Dietrich, 1968a, IEEE Trans. Magn. MAG-4, 263-267. Richter, H. and H. V611er, 1968b, DEW-Techn. Ber. 8, 214-221. Ries, H.B., 1959, Ber. Dr. Keram. Ges. 36, 223-228. Ries, H.B., 1963, Angew. Mess- u. Regeltechnik, 3, No. 1, al-a15. Ries, H.B., 1966, Interceram. No. 1, 84-92 and No. 2, 177-179. Ries, H.B., 1969a, Aufbereitungstechnik No. 1. Ries, H.B., 1969b, Keram. Zeitschr. 21, No. 10., 664-666. Ries, H.B., 1970, Aufbereitungstechnik No. 3, 5, 10 and 12. Ries, H.B., 1971a, Keram. Zeitschr. 23, No. 9, 516-518, 520, 533-534 and No. 10, 591-597. Ries, H.B., 1971b, Aufbereitungstechnik No. 11. Ries, H.B., 1973, Interceram. No. 3, 207-210 and No. 4, 298-304. Ries, H.B., 1975a, Keramische Zeitschrift, 27, No. 1 and 2.
599
Ries, H.B., 1975b, Aufbereitungstechnik No. 12. Roos, W., 1979, Thesis, Aachen. Roos, W., 1980, J. Amer. Ceram. Soc. 63, No. 11-12, 601-603. Roos, W., H. Haak, C. Voigt and K.A. Hem pel, 1977, J. de Phys. Colloque C1, Suppl. No. 4, 38 (C1) 35.37. Roos, W., C. Voigt, H. Dederichs and K.A. Hempel, 1980, J. Magn. Magn. Mat. 15-18, 1455-1456. Rosin, P. and E. Rammler, 1933, Zement, 23, 427-433. Routil, R.J. and D. Barham, 1969, Canad. J. Chem. 47, 3919-3920. Routil, R.J. and D. Barham, 1971, J. Canad. Ceram. Soc. 40, 1-7. Routil, R.J. and D. Barham, 1974, Canad. J. Chem. 52, 3235-3246. Rupprecht, J. and C. Heck, 1959, Ber. Arb. Gem. Ferromagn. of 1958, 98-100. Ruthner, M.J., 1977, J. de Phys. 38, Coil, C 1, Suppl. au no. 4, C 1-311-315. Ruthner, M.J., 1979, Sci. of Sintering, 11, No. 3, 203-214. Ruthner, M.J., 1980, Ferrites, Proc. ICF 3, 6467. Ruthner, M.J., H.G. Richter and I.L. Steiner, 1970, Ferrites, Proc. Intern, Conf. Japan, 7578. Sadler, A.G., 1965, J. Canad. Ceram. Soc. 34, 155-162. Sadler, A.G., W.D. Westwood and D.C. Lewis, 1964, J. Canad. Ceram. Soc. 33, 12%137. Saito, K., F. Hashimoto, M. Okuda and M. Torii, 1981, IEEE Trans. Magn. MAG-17, No. 6, 2656-2658. Samow, G., 1973, Elektroanzeiger, 26, No. 22, 453455. Schat, B.R. and H.J. Engel, 1970, Proc. Brit. Ceram. Soc., No. 18, 281-292. Schieber, M., 1967, Experimental Magnetochemistry ed., E.P. Wohlfarth (North-Holland, Amsterdam) p. 202. Schinkmann, A., 1960, Hermsdorfer Technische Mitteilungen, 1, 42-49. Schnettler, F.J., F.R. Montforte and W.H. Rhodes 1968, Sci. Ceramics 4, 79-90. Sch6ps, W., 1979, Silikattechnik, 30, No. 7, 195-201. Sch/Sps, W. and H. Beer, 1977, Silikattechnik 28, No. 7, 208-210. Sch6ps, W., H. Beer and H. Gottwald, 1976, Silikattechnik, 235-239.
600
H. STJ~BLEIN
Schiller, K., 1965, DEW-Techn. Ber. 5, 64-73. Schiller, K., 1967, Z. Angew. Phys. 22, 481-484. Schiller, K., 1968, DEW-Techn. Ber. 8, 147-156. Schiller, K., 1973, Int. J. Magnetism, 5, 249250. Schiller, K. and K. Brinkmann, 1970, Dauermagnete, Werkstoffe und Anwendungen (Springer, Berlin). Schtitz, H.E. and H.W. Hennicke, 1978, Ber. Dt. Keram. Ges. 55, 308--311. Schwabe, E., 1957, Z. Angew. Phys. 9, 183-187. Schwabe, E., 1958, Feinwerktechn. 62, 1-8. Schwabe, E., 1959, in: Ber. Arbeitsgem. Ferromagn. 1958, Stuttgart, 74-80. Semiletowa, M.W. and D.N. Polubojarinow, 1971, Mosk. Chim.-Technol. Inst. im. D.I. Mendeleewa Trudi, 68, 136-139. Shimizu, S. and K. Fukami, 1972, J. Jap. Soc. Powd. Met. 18, No. 7, 259-265. Shirk, B.T. and W.R. Buessem, 1970, J. Amer. Ceram. Soc. 53, 192-196. Shtrikman, S. and D. Treves, 1960, J. Appl. Phys. 31, 58 S-66 S. Silber, L.M., E. Tsantes and P. Angelo, 1967, J. Appl. Phys. 38, 5315-5318. Sironi, G., G. Fagherazzi, F. Ferrero and G. Parrini, 1972, DE-OS 2 246 204. Sixtus, K.J., K.J. Kronenberg and R.K. Tenzer, 1956, J. Appl. Phys. 27, 1051-1057. Sloccari, G., 1973, J. Amer. Ceram. Soc. 56, 489-490. Sloccari, G. and E. Lucchini, 1977a, Ceramurgia Int. 3, 10-12. Sloccari, G., E. Lucchini and G. Asti, 1977b, Ceram. Int. 3, 79-80. Slokar, G. and E. Lucchini, 1978a, J. Mag. Magn. Mat. 8, 232-236. Slokar, G. and E. Lucchini, 1978b, J. Mag. Magn. Mat. 8, 237-239. Smit, J. and H.G. Beljers, 1955, Phil. Res. Rep. 10, 113-130. Smit, J. and H.P.J. Wijn, 1959, Ferrites, Phil. Techn. Lab., Eindhoven. Snoek, J.L., 1947, New Developments in Ferromagnetic Materials (Elsevier Publishing Comp., New York, Amsterdam). Stiiblein, F., 1934, Techn. Mitt. Krupp 127-128. Stfiblein, H., 1957, Techn. Mitt. Krupp 15, 165168. St~iblein, H., 1963, Techn. Mitt. Krupp, Werksber. 21, 171-184. St~iblein, H., 1965, unpublished. Stfiblein, H., 1966, Techn. Mitt. Krupp, Forsch.Ber. 24, 103-112.
Stiiblein, H., 1968a, Techn. Mitt. Krupp, Forsch.-Ber. 26, 81-87. St/iblein, H., 1968b, Techn. Mitt. Krupp, Forsch.-Ber. 26, No. 1, 1-10. Stiiblein, H., 1970, IEEE Trans. Magn. MAG-6, No. 2, 172-177, and Techn. Mitt. Krupp, Forsch.-Ber. 28, No. 3/4, 103-116. St~iblein, H., 1971, unpublished. St/iblein, H., 1972, AIP Conf. Proc. No. 5, Part 2, New York, 950-969. St~iblein, H., 1973, Z. Werkstofftechnik, 4, 133142. Stilblein, H., 1974, unpublished. St/iblein, H., 1975, Techn. Mitt. Krupp, Forsch.Ber. 33, 1-10. Stiiblein, H., 1978, Ber. Dt. Keram. Ges. 55, 305-307. Stilblein, H. and J. Willbrand, 1966a, IEEE Trans. Magn. MAG-2, No. 3, 459--463. St~iblein, H. and J. Willbrand, 1966b, Z. angew. Phys. 21, 47-51. Stiiblein, H. and W. May, 1969, Ber. Dt. Keram. Gesellsch. 46, 69-74 and 126-128. Stiiblein, H. and J. Willbrand, 1971, Z. angew. Phys. 32, 70-74. Stiiblein, H. and J. Willbrand, 1972, Proc. 7. Int. Symp. React. Sol. (Chapman and Hall) p. 589-597. Stiiblein, H. and J. Willbrand, 1973a, Science of Ceramics, 6, Proc. Int. Conf., Baden-Baden 1971, XXXII/1-12. Stiiblein, H. and J. Willbrand, 1973b, Proc. Int. Conf. Magnetism (ICM) Vol. IV, p. 232-236. Stanley, D.A., L.Y. Sadler, D.R. Brooks and M.A. Schwartz, 1974, Ceram. Bull. 53, 813-815 and 829. Stearns, F.S. and H.L. Glass, 1975, Mat. Res. Bull. 10, 1255-1258. Steingroever, E., 1966, J. Appl. Phys. 37, 1116-1117. Steinort, E., 1973, 1. IOS-Kolloquiun (Varese, Italy). Steinort, E., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam, 66--69. Stephens, R.A., 1959, Amer. Ceram. Soc. Bull. 38, 106-109. Stickforth, J., 1975, Techn. Mitt. Krupp, Forsch.-Ber. 33, 22-24. Stoner, E.C., E.W. Wohlfarth, 1948, Phil. Trans. Roy. Soc. London, Ser. A, 240,599-642. Strijbos, S., 1973, Chemical Engineering Science, 28, 205-213. Strijbos, S., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam, 102-105.
H A R D FERRITES AND PLASTOFERRITES Stuijts, A.L., 1956, Trans. Brit. Ceram. Soc. 55, 57-74. Stuijts, A.L., 1968, Ch. 19 in: Ceramic Microstructures, eds., R.M. Fulrath and J.A. Pask (Wiley, New York) 443-474. Stuijts, A.L., 1970, Ferrites, Proc. Int. Conf. Kyoto, 108-113. Stuijts, A.L., 1973, Ann. Rev. Mat. Sci. 3, 363-395. Stuijts, A.L., G.W. Rathenau and G.H. Weber, 1954, Phil. Techn. Rev. 16, 141-147. Stuijts, A.L., G.W. Rathenau and G.H. Weber, 1955, Phil. Techn. Rdsch. 16, 221-228. Suchet, J., 1956, Bull. Soc. Franc. Ceram. 33, 33-43. Sutarno and W.S. Bowman, 1967, Mines Branch Invest. Rep. IR 67-23 (Dept. Energy Mines and Resources, Ottawa, Canada). Sutarno, W.S. Bowman, G.E. Alexander and J.D. Childs, 1969, J. Canad. Ceram. Soc. 38, %13. Sutarno, W.S. Bowman and G.E. Alexander, 1970a, J. Canad. Ceram. Soc. 39, 33-41. Sutarno, R.H. Lake and W.S. Bowman, 1970b, Mines Branch Res. Rept. R 223 (Dept. Energy Mines and Resources, Ottawa, Canada). Sutarno, W.S. Bowman and G.E. Alexander, 1970c, J. Canad. Ceram. Soc. 39, 45-50. Sutarno, W.S. Bowman and G.E. Alexander, 1971, J. Canad. Ceram. Soc. 40, 9-14. Syono, Y., A. Ito and O. Horie, 1979, J. Phys. Soc. Japan, 46, No. 3, 793-801. Takada, T. and M. Kiyama, 1970a, Proc. Int. Conf. Ferrites, Japan, 69-71. Takada, T., Y. Ikeda, H. Yosbinaga and Y. Bando, 1970a, Proc. Int. Conf., Ferrites, Japan, 275-278. Tanasoiu, C., 1972, IEEE Trans. Magn., Sept. 348-351. Tanasoiu, C., P. Nicolau, C. Miclea and E. Varzaru, 1976a, J. Magn. Magn. Mat. 3, 275-280. Tanasoiu, C., P. Nicolau and C. Miclea, 1976b, IEEE Trans. Magn. 1VIAG-12, No. 6, 980982. Taylor, R.C. and V. Sadagopan, 1972, Solid State Sci. and Techn. 119, no. 6, 788-790. TDK, 1978, Data Handbook. Tenzer, R.K., 1957, Conf. Magnetism and Magn. Mat. Boston, 203-211. Tenzer, R.K., 1963, J. Appl. Phys. 34, No. 4, 126%1268.
601
Tenzer, R.K., 1965, J. Appl. Phys. 36, No. 3, 1180-1181. Tokar, M., 1969, J. Amer. Ceram. Soc. 52, 302-306. Torii, M., 1981, J. Jap. Soc. Pow. Met. 28, No. 3, 83-89. Torii, M., H. Kobayashi, F. Hashimoto and K. Saito, 1979, IEEE Trans. Magn. MAG-15, No. 6, 1864-1866. Torii, M., H. Kobayashi and M. Okuda, 1980, Ferrites, Proc. ICF 3, 370-374. Townes, W.D., J.H. Fang and A.J. Perrotta, 1967, Z. Kristallogr. 125, 437-449. Tul'chinskii, L.N. and V.N. Pilyankevich, 1971, Sov. Powd. Metallurgy and Met. Ceram. 10, 359-361. Ullmanns Encyklop/idie der techn. Chemie, 1965, 3rd ed., Vol. 16 (Urban and Schwarzenberg, Mfinchen, Berlin) p. 455. Ullmanns Encyklop~idie, 1974, 4th ed., Vol. 8, 301-311. Underhill (ed.), E.A., 1957, Permanent Magnet Handbook (Crucible Steel Comp., Pittsburgh, USA). Valvo, 1978/1979, Handbuch Permanentmagnete (FERROXDURE, FXD). Van den Broek, C.A.M., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam, 5361. Van den Broek, C.A.M., 1977, Ceramurgia International, 3, 115-121. Van den Broek, C.A.M. and A.L. Stuijts 1977/78, Phil. Techn. Rdsch. 37, Nr. 7, 169188. Van der Oiessen, A.A., 1970, Klei en Keramik, 20, 30-38. Van Hook, H.J., 1964, J. Amer. Ceram. Soc. 47, 579-581. Van Hook, H.J., 1976, Phase Equilibria in Magnetic Oxide Materials, in: Phase Diagrams, Vol. IV, ed., A.M. Alper (Academic Press, New York, London). Van ,Tendeloo, G., D. van Dyck, J. van Landuyt and S. Amelinckx, 1979, J. Solid State Chem. 27, 55-70. Van Uitert, L.G., 1957, J. Appl. Phys. 28, 317322. Veldkamp, J.D.B. and R.J. Klein Wassink, 1976, Philips Res. Repts. 31, 153189. Veldkamp, J.D.B. and N. Hattu, 1979, Phil. J. Res. 34, No. 1/2, 1-25. Vogel, E.M., 1979, Ceramic Bull. 58, No. 4, 453-454, 458.
602
H. ST)kt3LEIN
Vogel, R.H. and B.J. Evans, 1979a, J. Magnetism Magn. Mat. 13, 294-300. Vogel, R. and B.J. Evans, 1979b, J. Phys. Colloqu, 40, No. C-2, pt. 3, C2-277 to C2-279. Voigt, C., 1969, Z. Angew. Phys. 26, 160-165. Voigt, C. and K.A. Hempel, 1969, Phys. Status Solidi 33, 249-256. Vollmershaus, E. and K.A. Hempel, 1975, Bet. Dt. Keram. Ges. 52, 216-218. Von Aulock, W.H. (ed.), 1965, Handbook of microwave ferrite materials (Academic Press, New York). Von Basel, H.B., 1981, IEEE Trans. Magn. MAG-17, No. 6, 2654-2655. Von Basel, H.B. and K.A. Hempel, 1979, Phys. Status Solidi A, 55, K 183-K 184. Went, J.J., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1952, Phil. Techn. Rev. 13, 194-208. Wickham, D.G., 1970, Ferrites, Proc. Internat. Conf. Japan, 105-107. Willbrand, J. and U. Wieland, 1975, Techn. Mitt. Krupp, Forsch.-Ber. 33, 15-21. Wills, D. and J. Masiulanis, 1976, J. Canad. Ceram. Soc. 45, 15-19. Wilson, C.M., G.C. Bye, C.R. Howard, J.H. Sharp, D.M. Tinsley and S.A. WentworthRossi, 1972, React. Sol. 7, Int. Symp. (Chapman and Hall) 598~o09. Winkler, G., 1965, React. Sol. 5, Int. Symp. (Elsevier, Amsterdam) 572-582. Wippermann, A., 1968, thesis, Aachen. Wohlfarth, E., 1959, Advances in Physics
(suppl. of Phil. Mag.) 8, No. 30, 87-224. Wolski, W. and J. Kowalewska, 1970, Jap. J. Appl. Phys. 9, 711-715. Wullkopf, H., 1972, Intern. J. Magnetism 3, 179-187. Wullkopf, H., 1973, Intern. J. Magnetism 5, 147-155. Wullkopf, H., 1974, thesis, Bochum. Wullkopf, H., 1978, Ber. Dt. Keram. Ges. 55, 292-293. Yamamoto, H., T. Kawaguchi and M. Nagakura, 1978a, J. Jap. Soc. Powd. Met. 25, No. 7, 236-241. Yamamoto, H., T. Kawaguchi, M. Nagakura and Y. Kobayashi, 1978b, J. Jap. Soc. Powd. Met. 25, No. 7, 242-248. Yamamoto, H., T. Kawaguchi and M. Nagakura, 1979a, IEEE Trans. Magn. MAG15, No. 3, 1141-1146. Yamamoto,H. and Y. Kobayashi, 1979b, Res. Rept. Fac. Eng. Meiji Univ., Tokyo, No. 36, 63-72. Yamamoto, H., T. Kawaguchi and M. Nagakura, 1980, J. Jap. Soc. Powd. Met. 27. No. 7, 171-177. Zfiv~ta, K., 1963, Phys. Status Solidi, 3, 21112118. Ziolowski, Z., 1962, Prace Institut Hutniczych, 14, 155-163. Zijlstra, H., 1974, Phil. Techn. Rev. 34, no. 8, 193-207. Zijlstra, H., 1978, IEEE Trans. Magn. MAG-14, no. 5, 661-664.
chapter 8 SULPHOSPINELS
R.P. VAN S T A P E L E Philips Research Laboratories 5600 JA Eindhoven The Netherlands
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 603
CONTENTS 1. 2. 3. 4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Crystal chemistry . . . . . . . . . . . . . . . . . . . . . . . . . L o c a l i z e d a n d d e l o c a l i z e d s t a t e s in s u l p h o s p i n e l s . . . . . . . . . . . . . Sulphospinels containing copper . . . . . . . . . . . . . . . . . . 4.1. V a l e n c y of t h e c o p p e r i o n s . . . . . . . . . . . . . . . . . . 4.2. CuTi2S4 . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. CuVzS4 . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. CuCo2S4 a n d C u C o T i S 4 . . . . . . . . . . . . . . . . . . . 4.5. CuRh2S4 a n d CuRh2_xCoxS4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. C u R h 2 S e 4 a n d C u R h 2 - x S n x S e 4 4.7. CuCr2S4, CuCr2-xTixS4, C u C r 2 - x S n x S 4 a n d C u C r 2 - x V x S 4 . . . . . . . . 4.8. CuCr2Se4, C u C r 2 - x R h x S e 4 a n d CuCr0.3Rhl.7-xSnxSe4 . . . . . . . . . . 4.9. C u C r 2 T e 4 a n d Cul+~Cr2Te4 . . . . . . . . . . . . . . . . . . . 4.10. C u C r 2 ( X , X')4 w i t h X, X ' = S, Se a n d T e . . . . . . . . . . . . . . 4.11. CuCr2X4-xYx w i t h X = S, S e o r T e a n d Y = C1, B r a n d I . . . . . . . . 5. F e r r o m a g n e t i c a n d a n t i f e r r o m a g n e t i c s e m i c o n d u c t o r s . . . . . . . . . . . 5.1. G e n e r a l a s p e c t s . . . . . . . . . . . . . . . . . . . . . . 5.2. Z n f r 2 S 4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. CdCrzS4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. HgCr2S4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Z n C r 2 S e 4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. CdCr2Se4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.7. H g C r z S e 4 . . . . . . . . . . . . . . . . . . . . . . . . . 5.8. M i x e d c r y s t a l s b e t w e e n t h e c o m p o u n d s Z n C r z X 4 , CdCr2X4 a n d H g C r 2 X 4 w i t h X = S, S e . . . . . . . . . . . . . . . . . . . . . . . 5.9. M i x e d c r y s t a l s A172A3~2CrzX4 w i t h X = S, Se a n d d i a m a g n e t i c i o n s A . . . . 6. F e r r i m a g n e t i c s e m i c o n d u c t o r s . . . . . . . . . . . . . . . . . . . 6.1. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . 6.2. MnCrzS4 . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. FeCr2S4 . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. CoCr2S4 . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. T h e m i x e d c r y s t a l s Fea-xCoxCrzS4, Fel-x(CUl/zlnl/2)xCrzS4, Fel-xCdxCrzS4, Col-xfdxfr284 and Col-x(CumFem)xCr2S4 . . . . . . . . . . . . . 6.6. T h e m i x e d c r y s t a l s M l - x C u x C r 2 S 4 w i t h M = M n , F e a n d C o . . . . . . . . . . . 6.7. T h e m i x e d c r y s t a l s MI-xNi~Cr2S4 w i t h M = M n , Fe, C o , C u a n d Z n 6.8. T h e m i x e d c r y s t a l s MCr2-xInxS4, w i t h M = M n , F e , C o a n d Ni . . . . . . 6.9. T h e m i x e d c r y s t a l s M n C r z - x V ~ S 4 . . . . . . . . . . . . . . . .
604
607 608 616 618 618 62O 622 624 626 627 630 636 641 643 644 647 647 653 654 666 669 675 691 694 698 701 701 701 706 711 714 718 721 722 725
6.10. The mixed crystals FeCr2-xFe~S4 . . . . . . . . . . . . . . . . 6.11. The mixed crystals MCr2S4-xSex with M = Mn, Fe, Co or CUl/2Fem . . . . 7. Some rhodium and cobalt spinels . . . . . . . . . . . . . . . . . . 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 7.2. CoRh2S4, Col-xFexRh2S4 and FeRh2S4 . . . . . . . . . . . . . . . 7.3. The mixed crystals FeRh2-xCrxS4, CoRh2-xCr~S4 and NiRh2-xCrxS4 . . . . . 7.4. The mixed crystals Fel-xCuxRh2S4 and C01-xCuxRh2S4 . . . . . . . . . 7.5. Co3S4 and NiCo2S4 . . . . . . . . . . . . . . . . . . . . . . Notes added in proof . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
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726 726 728 728 728 730 732 736 737 737
1. Introduction
The denomination of "sulphospinels" will be used for materials with compositions (M, M', M")3X4 where M, M', M " . . . are metals and X = S, Se or Te. In contrast to the "oxyspinels" (X = O) the sulphospinels have not found applications. They exhibit however a much larger variety of physical properties, which makes them interesting from a scientific point of view. Whereas the oxyspinels are in general semiconductors with antiferromagnetic interactions, the sulphospine!s exhibit metallic conduction and superconduction as well as semiconductivity, and ferromagnetic as well as antiferromagnetic interactions. At the time that the first magnetic measurements on sulphospinels were carried out (Lotgering 1956) the oxyspinels had already been investigated for about ten years in many laboratories. The stimulation for an intensive study of sulphospinels came later, however, with the observation that CuCr2X4 (X = S, Se or Te) are metallic ferromagnets with Curie temperatures above room temperature (Lotgering 1964a, b). The subsequent discovery that MCr2X4 (M = Cd or Hg, X = S or Se) are semiconducting ferromagnets (Baltzer et al. 1965, Menyuk et al. 1966) with Curie temperatures not far below room temperature started numerous investigations of the physical and chemical properties, which resulted in an increasing number of articles on sulphospinels. After peak years in the early seventies, interest has been fading away. It may therefore be useful to review the results that have been obtained. The properties of magnetic semiconductors have earlier been summarized by Haas (1970), Methfessel and Mattis (1968), Nagaev (1975), and Wojtowicz (1969). Among the results of the study of sulphospinels the following are worth mentioning in advance: (1) The fact that superexchange interactions between transition metal ions can be ferromagnetic in semiconductors had been predicted theoretically and CrTe was considered to be an example (Anderson 1950). However, this compound, which was the only example known at that time, shows metallic conduction. The first indication of ferromagnetic superexchange in a real semiconductor was found in a sulphospinel, namely in MnCr2S4 (Lotgering 1956). (2) In magnetic semiconductors electrical and optical properties were observed that strongly depend on the magnetic state. These included an anomalous maximum in the resistivity near the Curie temperature, first observed in FeCr2S4 607
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R.P. VAN STAPELE
(Lotgering 1956); a negative magnetoresistance effect near the Curie temperature, first observed in n-type CdCr2Se4 (Lehmann and Harbeke 1967), and an anomalous shift to the red of the optical absorption edge of CdCr2Se4 (Busch et al. 1966, Harbeke and Pinch 1966). (3) As expected theoretically, an overlap of the d-orbitals of two magnetic ions may contribute to the exchange interaction (Wollan 1960, Goodenough 1960). Experimental evidence of this direct exchange was obtained from the asymptotic Curie temperature of ZnCr2X4 with X = O, S or Se (Lotgering 1964a, b). (4) Long-distance superexchange was observed in sulphospinels. A strong interaction via two sulphur ions occurs in CoRh2S4 (Blasse and Schipper 1964) and a fairly strong interaction via four sulphur ions occurs in Fel/2Cul/2Rh2S4 (Plumier and Lotgering 1970). (5) It was discovered that CuCr2X4 (X = S, Se or Te) are metallic ferromagnets in which the chromium spins are coupled ferromagnetically via interaction with delocalized conduction electrons. This provides an experimental confirmation of Zener's basic condition for strong ferromagnetism (Zener 1951) in simple, highly symmetric compounds. The chapter will be organized as follows. After a section (2) on the crystal structure and a section (3) on localized and delocalized electronic states, we will discuss in section 4 the metallic sulphospinels containing copper. In section 5 we deal with the ferromagnetic and antiferromagnetic semiconductors, in section 6 with the ferrimagnetic semiconductors and finally, in section 7 we consider some rhodium and cobalt spinels.
2. Crystal chemistry Compounds with the general formula AB2X4, where A and B are metal ions and X = S, Se or Te, crystallize in a large number of crystal structures. It is not possible to calculate the relative stability of the various structures for a given compound, but it has been found possible to define parameters that place different crystal structures in different regions of the parameter space. For that purpose Kugimiya and Steinfink (1968) used the radius ratio rA/rB of the cations A and B and a bond-stretching force constant KAB that is proportional to the product of the cation electronegativities and the inverse of the square of a suitably defined equilibrium distance. In the K ~ versus rA/rB plot the observed crystal structures separate nicely, with the exception of the spinel, the Cr3Se4 and the Ag2Hgh structure (Iglesias and Steinfink 1973). The difficulty in distinguishing between the spinel and the Cr3Se4 structure is reflected in the occurrence of both structures in one compound at different temperatures and pressures. Highpressure polymorphism in spinel compounds was first observed by Albers and Rooymans (1965), who succeeded in changing the spinel structure of FeCr2S4 into a structure related to Cr3Se4. Other examples have been found among the sulphides (Bouchard 1967, Tressler and Stubican 1968, Tressler et al. 1968), but not unambiguously among the selenides and the tellurides. Being concerned with
SULPHOSPINELS
609
the spinel structure only, we will not discuss these matters here. We conclude this passage with the remark that at room temperature and under normal pressures the number of AB2X4 compounds with the spinel structure decreases strongly in the sequence S, Se and Te. The only tellurides reported are CuCrzTe4 (Hahn and Schr6der 1952) and ZnMnzTe4 (Matsumoto et al. 1966). Since a description of the spinel structure has been given in chapter 4 by Krupi6ka and Novfik, we shall confine ourselves here to the main details of this structure (an extensive description was given by Gorter (1954)). The space group of the spinel structure is Fd3m. The chalcogenide anions approximate to a close-packed cubic lattice. The cations occupy twice as many octahedral sites B as tetrahedral sites A. The A sites form a diamond lattice and can be divided into two fcc Bravais lattices. Their local symmetry is purely tetrahedral (point group Td). The B sites are divided into four Bravais lattices. Their point group is D3a. The smallest unit cell is rhombohedral and contains two molecules AB2X4 (fig. 1). More commonly used is the cubic unit cell (fig. 2) which contains eight molecules. The structure is completely described by the cubic cell edge a and one parameter u that fixes the X positions. A deviation from the ideal close packing is caused by a variable A - X distance in one of the four [111] directions. The parameter u is defined by the shift a6X/3 with 6 = u - 3 of X from the ideal position (drawn in fig. 2) away from the A site. The distances A - X and B - X are then: (A-X) = aV'5(6 + ~), (B-X) = a ( ½ - ½6 + 362) m .
(1)
Each X belongs to the (perfect) tetrahedron of one A. With u # 3 two distances (X-X)1 for X of one tetrahedron and (X-X)2 for X of two neighbouring tetrahedra exist: (X-X)1 = 2aX/2(-~+ 6); (X-X)2 = 2aX/2(~- ~).
(2)
y
Fig. 1. T h e primitive rhombohedral unit cell which contains two AB2X4 units in the cubic cell.
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R.P. V A N S T A P E L E
A
G
Fig. 2. The cubic unit cell of the spinel structure with cell edge a. The structure can be described using two types of cubic octants (edge = a/2) that alternate like Na and C1 in rocksalt. Shaded circles A lying on the corner and in the centre of an octant. Black circles B and white circles X (for u = ~) lying on the body diagonals of the octants at ~ of its length.
With increasing u at constant a, A - X increases and B - X decreases. This gives an accommodation of the lattice to the radii of the ions. For the ideal close packing (u = 3) B - X is 16% larger than A - X , which is compensated by u > 3 in all spinels. Large values of u occur for large A ions like, for instance, Cd 2+. The octahedral sites are denoted by brackets. For two metals M and N the distributions M[Nz]X4 and N[NM]X4 among A and B sites are called "normal"
and "inverse", respectively. All sulphospinels with composition MN2X4 are normal. On the octahedral sites we will encounter the ions Ti, V, Cr, Co, In, Rh and Sn, and on the tetrahedral sites the ions Mn, Fe, Co, Cu, Zn, Cd and Hg. Table i lists u and a. Using these data a plot of u versus a (Raccah et al. 1966, TABLE 1 Lattice parameters at room temperature as determined by X-ray diffraction ((n) denotes results of neutron diffraction). Compound
a (A)
u
References
Cu/Ti2/S4
9.88 ± 0.008 9.994 ± 0.002 9.994 10.002 ± 0.003
0.382
Hahn and Harder (1956) Bouchard et al. (1965) Riedel and Horvath (1973a) Le Nagard et al. (1975)
Cu/V2/S4
9.824 9.808 9.803 9.805 9.800
± 0.008 ± 0.002
0.381 (0.3805) 0.384 0.382
± 0.005 ± 0.001
Hahn et al. (1956) Bouchard et al. (1965) Riedel and Horvath (1973a) Le Nagard et al. (1979) ibid.
611
SULPHOSPINELS T A B L E 1 (continued) Compound Mn/Cr2/S4
Fe/Crz/S4
Co/Cr2/S4 I
a (A) 10.129 10.110 ± 0.002 10.110 10.110 10.107 ± 0.002 10.11 10.108 9.97 ± 0.01 9.998 9.995 ± 0.002 9.995 9.995 9.983 ± 0.001 (9.97) 9.995 9.9893 ± 0.0008 9.91±0.01 9.934 9.923 ± 0.002 9.923
References
0.3876 (n) 0.3863
0.384 ± 0.002 (n) 0.3850 0.3858 (n)
0.3821 0.3830(n)
9.923 ±0.001 9.9213 ± 0.0007 9.936 9.923 9.918 9.9158± 0.0007 Cu/Cr2/84
9.63±0.006 9.822 9.814 ± 0.002 9.810 9.814 9.833 ± 0.019 9.820 9.820 9.813
0.381
0.383 ± 0.001 0.3841
0.384 0.385 Zn/Cr2/S4
9.983 9.988 9.986 ± 0.002 9.986 9.986± 0.001 9.983 9.983
0.385 0.3842 0.3854 ± 0.0005 0.3869
Lotgering (1956) Bouchard et al. (1965) Menyuk et al. (1965) Raccah et al. (1966) Tressler and Stubican (1968) Robbins et al. (1974) Darcy et al. (1968) Hahn (1951) Lotgering (1956) Bouchard et al. (1965) Shirane et al. (1964) Raccah et al. (1966) Tressler and Stubican (1968) Broq. Colominas et al. (1964) Robbins et al. (1970b, 1974) Shick and Von Neida (1969) Hahn (1951) Lotgering (1956) Bouchard et al. (1965) Raccah et al. (1966) Raccah et al. (1966) Tressler and Stubican (1968) Carnall et al. (1972) Robbins et al. (1974) Lutz and Becker (1973) Lisnyak and Lichter (1969) Shick and Von Neida (1969) Hahn et al. (1956) Lotgering (1964b) Bouchard et al. (1965) Riedel and Horvath (1973a) Raccah et al. (1966) Kanomata et al. (1970) Lutz and Becker (1973) Robbins et al. (1970a) Belov et al. (1973) Ohbayashi et al. (1968) Riedel and Horvath (1973b) Lotgering (1956) Baltzer et al. (1965) Bouchard et al. (1965) Raccah et al. (1966) Von Neida and Shick (1969) Riede! and Horvath (1973a) Riedel and Horvath (1969)
612
R.P. V A N S T A P E L E T A B L E 1 (continued)
Compound Cd/Cr2/S4
Hg/Cr2/S4
a (~,)
u 0.390
References
10.244 10.242 10.239 +- 0.002 10.238 10.238
0.3901 + 0.0007 0.3943
Baltzer et al. (1965, 1966) Busch et al. (1966) Von Neida and Shick (1969) Riedel and Horvath (1973a) Riedel and Horvath (1969)
10.206-+ 0.007 10.237
0.390
Hahn (1951) Baltzer et al. (1965)
Co/Coz/S4
9.416 9.399 + 0.002 9.391 -+ 0.004 9.405
Lotgering (1956) Bouchard et al. (1965) Heidelberg et al. (1966) Knop et al. (1968)
Ni/Co2/S4
9.392 9.384 + 0.002 9.387
Lotgering (1956) Bouchard et al. (1965) Knop et al. (1968)
Cu/Co2/S4
9.482 9.461 _+0.002 9.464 9.478 -+_0.001
Lotgering (1956) Bouchard et al. (1965) Riedel and Horvath (1973a) Williamson and Grimes (1974)
Co/Rh2/S4
Fe/Rh2/S4
9.72 9.74 9.805 9.76 9.86 9.902
0.382 0.388 - 0.001
0.383
0.385
Koerts (1963) Blasse (1965) Kondo (1976) Blasse and Schipper (1964) Koerts (1%5) Kondo (1976)
Ni/Rh2/S4
9.64 9.701 -+ 0.001 9.702
Koerts (1963) Tressler et al. (1968) Itoh (1979)
Cu/Rh2/S4
9.72 9.78 9.786 9.792-9.787 9.790-+ 0.001 9.7877 -+ 0.0005 9.790 9.788 9.73
Blasse and Schipper (1964) Van Maaren et al. (1967) Riedel and Horvath (1973a) Shelton et al. (1976) Schaeffer and Van Maaren (1968) Dawes and Grimes (1975) Robbins et al. (1967a) Riedel et al. (1976) Koerts (1963)
Cu/Cr2/Se4
10.356-+ 0.006 10.337 10.334
0.3802 -+ 0.0004
0.384-+ 0.001 0.384 0.380 0.384 (n) 0.3826 -+ 0.0003 (n)
10.321 -+ 0.014 10.334 0.383 0.385
Hahn et al. (1956) Lotgering (1964b) Robbins et al. (1967b) Colominas (1967) Kanomata et al. (1970) Belov et al. (1973) Ohbayashi et al. (1968) Riedel and Horvath (1973b)
613
SULPHOSPINELS T A B L E 1 (continued) Compound
Zn/Cr2/Se4
a (.~) 10.443 _+0.008 10.500 10.44 10.443 10.4973
u
References
0.376 ~< u ~<0.380
Hahn and Schr6der (1952)
0.3843 ± 0.0006 (n)
Lotgering (1964b) Plumier (1965) Baltzer et al. (1965) Kleinberger and de Kouchkovsky
(1966) 10.440 10.495 10.494 ± 0.001 10.493
0.3849
Raccah et al. (1966) Busch et al. (1966) Von Neida and Schick (1969) Riedel and Horvath (1969)
0.3843
10.721 ± 0.008 10.755 10.740 10.744 10.72 ± 0.01 10.741
0.383 0.390 0.3894
0.3889
Hahn and Schr6der (1952) Baltzer et al. (1965) Raccah et al. (1966) Busch et al. (1966) V o n Neida and Shick (1969) Riedel and Horvath (1969)
Hg/Cr2/Se4
10.753
0.390
Baltzer et al. (1965)
Cu/Rhz/Se4
10.259 10.34 10.260 10.2603 ± 0.0004 10.263 10.264
Cd/Cr2/Se4
Cu/Cr2/Te4
(n)
0.384 ± 0.001 0.379
Robbins et al. (1967a) Riedel et al. (1976)
11.137 0.3811 _+0.0003 (n) 11.127 11.049 ± 0.007 11.134
Robbins et al. (1967b) Van Maaren et al. (1967) Shelton et al. (1976) D a w e s and Grimes (1975)
0.379 0.376
Lotgering (1964b) Colominas (1967) Kanomata et al. (1970) Hahn et al. (1956) Riedel and Horvath (1973b) Robbins et al. (1968)
Riedel and Horvath 1973a) for MCr2S4 is given in fig. 3. Setting aside M = Cu, M has the sequence of increasing radius of the divalent ions. The figure illustrates the increase of u (see above) and of a with the M 2+ radius. This also appears directly from the increase of the distance M - S calculated from u and a using eq. (1) (table
2). Figure 3 shows that the Cu c o m p o u n d behaves differently from the others. This appears also from the Cr-S = B - X distances (table 2), which are 2.40 to 2.42 and are practically independent of M. For M = Cu, however, Cr-S is slightly smaller (2.38A). A n anomalously small Cr-Se distance occurs also in the selenides M[Cr2]Se4 for M = Cu: Cr-Se = 2.51 to 2.54 A for M = Zn, Cd or Hg, whereas Cr-Se = 2.49 to 2.50 A for M = Cu. S o m e sulphospinels, to which CuCr2S4 belongs, have an anomalously small a (Lotgering 1956). (This is the reason for the anomalous position of M = Cu in fig.
614
R.P. VAN STAPELE
Cd/
0 39o
/Hg
/
0388 0386
/0Mo
Zn
0.384 0382
/ 0.380 97
r
98 "
/l co /
i
i
99
10
10.1 a
I
(~}
10.2 10.3
Fig. 3. Lattice parameter a versus u parameter of the compounds MCr2S4.
3.) Using eq. (2) one finds am = 7.47 and 9.84 A for the cell edges of ideal spinel (u = 3) with X - X distances equal to the sum of the ionic X 2- radii of 02_ (1.32 A) and S 2- (1.74 A), respectively. According to the definition of this radius, a ~> am for ionic compounds, and this is indeed observed for oxyspinels (the smallest value a =-7.94 A occurs for LiomAls/204 (Blasse 1964). I n sulphides with spinel structure, a runs from 10.24A for CdCr2S4 to 9 . 3 9 A for NiCo2S4 (table 1). a < 9.84,~ means that the mean S-S distance is smaller than the shortest $2--S 2distance, i.e., the normal ionic S 2- state does not occur. We will see later that this is reflected in the electric and magnetic properties, which are essentially different from those of oxyspinels (and other oxides) for a < 9.84 A, but not for a > 9.84,~. For example (see table 1 and section 5.2) Zner204 and ZnCr2S4 (a = 9.99 A) are semiconductors and exhibit Curie constants corresponding to the metal ions (Zn 2+, Cr3+). This holds also for C o 3 0 4 (Wagner 1935, Cossee 1958) but C o 3 S 4 is metallic and the Curie constant does not agree at all with ionic C02+Co~+X2-, in contrast to CosO4. Since ions are not rigid spheres, the ionic S 2- radius and thus am are not determined exactly, so that the rule does not hold for a near oto am (e.g. CoRh2S4 with a = 9.80 has normal ionic properties). CuTi2S4 (a = 9.99 A), which is Pauli paramagnetic and metallic, is the only clear exception. Consequently the metallic conduction has another origin than in the o t h e r sulphospinels (section 4.2). A comparison of the A - X distances in the compounds CuM2S4 of table o 2 demonstrates that this distance is almost constant with an average value of 2.25 A, close to the value 2.26 A obtained from a more extensive analysis by Riedel and o H o r v a t h (1973a). In the selenospinets CuM2Se4 the average value is 2.38 A and in o the tellurospinel the C u - T e distance is 2.53 A. These distances compare well with the C u - X distances in other chalcogenides (Lotgering and Van Stapele 1968b). T h e A - X distances in MCr2X4 with M = Zn, Cd and Hg and X = S and Se compare well with the tetrahedral covalent radii as derived by Pauling (1960) from the sphalerite and wurtzite structures of the compounds M X (table 3).
TABLE 2 Cation-anion distances
Compound CoCr2S4
FeCr2S4 ZnCr2S4
MnCrzS4 CdCr2S4 HgCrzS4 CoRh2S 4
CuCr2S4 CuTizS4 CuVzS4 CuCo2S4 CuRh2S4 CuCr2Se4 ZnCr2Se4
CdCrzSe4
HgCr2Se4 CuRhzSe4 CuCr2Te4
A-X (~)
B-X (~)
References
2.27 2.32 2.34 2.34 2.32 2.34 2.39 2.41 2.48 2.48 2.48 2.26 2.26 2.28 2.27 2.26 2.24 2.16 2.26 2.27 2.23 2.38 2.40 2.43 2.44 2.46 2.61 2.59 2.61 2.61 2.38 2.34 2.53
2A1 2.41 2.40 2.40 2.41 2.40 2.42 2.41 2.42 2.42 2.42 2.38 2.38 2.37 2.44 2.44 2.38 2.30 2.25 2.36 2.39 2.50 2.49 2.52 2.51 2.52 2.54 2.54 2.53 2.54 2.48 2.50 2.72
Raccah et al. (1966) Shirane et al. (1964) Raccah et al. (1966) Baltzer et al. (1965) Raccah et al. (1966) Riedel and Horvath (1973a, 1969) Raccah et al. (1966) Menyuk et al. (1965) Baltzer et al. (1965) Riedel and Horvath (1973a, 1969) Baltzer et al. (1%5) Kondo (1976) Riedel and Horvath (1973a) Raccah et al. (1966) Riedel and Horvath (1973a) Le Nagard et al. (1975) Riedel and Horvath (1973a) Riedel and Horvath (1973a) Williamson and Grimes (1974) Dawes and Grimes (1975) Riedel et al. (1976) Riedel and Horvath (1973b) Robbins et al. (1967b) Plumier (1965) Raccah et al. (1966) Riedel and Horvath (1969) Baltzer et al. (1965) Raccah et al. (1966) Riedel and Horvath (1969) Baltzer et al. (1965) Dawes and Grimes (1975) Riedel et al. (1976) Riedel and Horvath (1973b)
TABLE 3 Cation-anion distance on tetrahedral sites in the compounds MCr2X4, compared with the distance in the compounds M X
Compound
A-X (A)
ZnCr2S4 CdCrzS4 HgCr2S4 ZnCr2Se4 CdCr2Se4 HgCr2Se4
2.33 2.48 2.48 2.44 2.60 2.61
compound M X ZnS CdS HgS ZnSe CdSe HgSe
615
M-X (A) 2.35 2.53 2.52 2.45 2.63 2.63
616
R.P. V A N S T A P E L E
3. Localized and delocalized states in sulphospinels
Many metallic conducting chalcogenides of transition metals are known. In most of them the magnetic moments do not agree with the spin-only value of magnetic ions. For example, CrTe and MnSb, which might be compounds of Cr z+ and Mn 3+, are metallic ferromagnets. The experimental ferromagnetic moments of 2.4 and 3.5 txB and the paramagnetic moments of 4.0 and 4.1 #B, respectively (Lotgering and G o r t e r 1957) deviate strongly however from the spin-only values 4/xB and 4.9/XB of the ferromagnetic and paramagnetic moment of the 3@ ions Cr z+ and Mn 3+. Metallic conduction and a non-integer number of d electrons per metal atom point to delocalized electrons in energy bands. In our opinion, an unambiguous interpretation of such properties has never been given (see, e.g., Bouwma and Haas 1973). A few metallic conducting chalcogenides exhibit magnetic moments that are in reasonable agreement with the presence of transition metal ions having the expected valency. This has been found clearly in Mel_~LaxMnO3 with Me = Ca, Sr or Ba (Jonker and Van Santen 1950), and in CoS2 (Benoit 1955, Ohsawa et al. 1976). Such "ionic" moments are also found in the non-oxidic spinels CuCr2X4, which makes an interpretation easier than in the case of the MnSb compounds. The metallic conduction of these spinels is to be attributed to delocalized electrons, their magnetic behaviour to electrons in localized 3d states of the Cr ions (section 4.8). We will now give a short review of the electronic structure of transition-metal chalcogenides*. This structure is characterized by two broad bands (with a width of 5 to 10 eV) separated by an energy gap, and narrow d bands or ionic levels of cations M n+ with a d m configuration. The broad bands arise from the strong overlap of the occupied outermost s and p states of the anions (e.g. 2s and 2p of 02-) with the first empty s states of the cations (e.g. 4s of Mn 2+) which gives rise to a "bonding" valence band and an "anti-bonding" conduction band. For a cation d orbital the overlap with the anion orbitals is much smaller. This overlap tends to break the highly correlated state of the d electrons in the cations Mn+(d m) and to delocalize the d electrons in a narrow d band. This delocalization is counteracted by the energy required for the excitation 2Mn+(dm)--->M~"+l)+(dm-l) + M("-l)+(dm+l). Delocalization or localization occurs if the effect of the overlap or the excitation energy dominates (Mott 1949). With an increasing ratio of the two factors, a sharp transition from a localized to a delocalized state is expected (Mott transition). The electrical and magnetic properties will be discussed with the help of schemes (fig. 4) which represent the relative energies of electrons in the broad valence and conduction bands and in d states, localized or otherwise. On the right-hand side of such a scheme the one-electron energy versus the density of states of the bands is sketched. The bands are occupied below and empty above a Fermi level EF. On the left-hand side of each scheme we place the ionic levels of cations M n+ with a d m electron configuration. Such an ionic level denotes the relative energy (with respect to the broad bands) of the localized mth electron. * See notes added in proof (a) on p. 737.
SULPHOSPINELS
E MIo-~
617
J --E
F
M~*__ ~ density of states
b
(3
Mn*~
F d
Mn*
c
F e
f
Fig. 4. Schematic band structure of chalcogenide spinels. O n the right-hand side the schemes show the conduction band and at a lower energy the valence band. T h e left-hand side shows the valency states of a transition metal ion. UF denotes the Fermi energy.
Each level can accommodate one electron only. If occupied (situated below Ev) it represents an ion with valency n, if empty (situated above UF) an ion with valency (n + 1). For a given metal M, the M (n-l)÷ level lies above the M n÷ level. The energy difference is the energy needed to excite an electron from Mn+(d m) to M(n-1)+(dm+l)), i.e., the transition 2 M " + ~ Mtn+~)+ + M (n ~)+. E F coinciding with M "+ levels indicates a mixed valency state (a mixture of M "+ and M (n+l)+) that gives an electrical conduction with a high concentration of charge carriers with a low mobility (~1 cm2/Vs). In oxides the valence and conduction bands are separated by a wide gap in which successive valency states are situated (fig. 4(a)). It has been proposed (Albers and Haas 1964, Albers et al. 1965) that the properties of chalcogenides and pnictides may be explained by cation levels that fall in one of the broad bands. The various possibilities are drawn in figs. 4(b), (c) and (d), Which represent semiconductors with conduction of electrons in a narrow band or holes in a broad band (b), of electrons in a broad band or holes in a narrow band (c) and of electrons or holes in a broad band (d). In figs. 4(e) and (f) there is metallic conduction of either holes in the valence band (e) or electrons in the conduction band (f). A narrow d band is expected to consist of two separated or overlapping branches arising from the cubic crystal field splitting (Goodenough 1969). In our energy schemes narrow bands are drawn schematically without such details, because experimental information is lacking.
618
R.P. VAN STAPELE
4. Sulphospinels containing copper
4.1. Valency of the copper ions The Cu oxides CuCr204 and CuFe204 with spinel structure are semiconductors and exhibit ferrimagnetic and paramagnetic properties that are consistent with the valencies c,, '~2. . . .2+g-~3+g-~22 ,-,4 and t~ u 2+12" , e 23 + g,-,4. In contrast with this, all non-oxidic TM
spinels CuM2X4 show metallic conduction and essentially different magnetic properties. For M = Cr they are ferromagnets with Curie temperatures above room temperature, and the others ( M # Cr) show a temperature independent paramagnetism. CuV2S4, CuRh2S4 and CuRh2Se4 become superconducting at low temperature. A survey of the electrical and magnetic properties of the compounds CuM2X4 is given in table 4. Detailed data will be given later, when each of the compounds is discussed separately. The striking difference in properties between the non-oxidic spinels CuM2X4 and the corresponding oxyspinels CuM204 points to an essential difference in electronic structure. Two explanations have been proposed. The first is based on the assumption that copper ions in the sulphospinels are monovalent, i.e., in the 3d 1° state, in contrast to their divalent state in the oxyspinels (Lotgering 1964a, b, Lotgering and Van Stapele 1968a). The second is based on the assumption that the copper ions are formally divalent, but that their 3d electrons are delocalized in a band formed by the copper 3d states (Goodenough 1965, 1967 and 1969). The crucial question in these matters is the valency of the tetrahedrally coordinated copper ions in non-oxidic chalcogenides. The following arguments and experimental results lead us to adopt the monovalent state: (a) Divalent Cu ions are known to have a great instability in a sulphur lattice (Akerstrom 1959), in agreement with the fact that no sulphides, selenides or tellurides are known with tetrahedrally coordinated Cu ions, exhibiting the properties of Cu e+, as CuCr204 does, for example. (b) The C u - X distances in the copper sulpho-, seleno- and tellurospinels do not differ significantly from the C u - X distances in other chalcogenides containing monovalent Cu (Lotgering and Van Stapele 1968b) (see section 2 and Sleight 1967). (c) A zero moment is observed at the A'sites in CuCr2Se4 and CuCr2We4 at temperatures down to 4 K by means of neutron diffraction (Colominas 1967, Robbins et al. 1967b) in contrast with 1/xB expected for a spin-ordered state at T = 0 with Cu 2+ on the tetrahedral sites (see also section 4.8). (d) The X-ray photo-electron spectrum of the copper 2p energy levels in CuCr2Se4 closely resembles the spectra of CuCrSe2, CuCrS2 and CuA1S2, in which compounds Cu is monovalent. All the spectra have the narrow peaks typical of Cu + at the same energy, while satellites due to the simultaneous excitation of an electron into empty states of the 3d shell are absent (Hollander et al. 1974). (e) The chemical Shift of the K absorption edge of copper in CuCr2S4, Cufr2Se4 and CuCrzTe4 with respect to Cu metal is small and indicative of Cu + (Ballal and Mande 1976) (table 5).
SULPHOSPINELS
619
...-t O~
E = .=
II ,,,..¢ vh +-
I
"~
~x x ',R.
,
x
x ~ " oo,~
i
,.- I "T'
Q
I
b,-
~.~. d~
e~
,
~,,
~,
+ +
÷
x××
×~
,~
3~ .,,-
8 ii
~...' E
x~
d
620
R.P. VAN STAPELE TABLE 5 Wavelengths of the K discontinuity of copper in various compounds, according to Ballal and Mande (1976).
A (x.u.) Compound
Valency
(-+0.09X.U.)
AA
Cu metal CuO CuSO4.SH20 CuC12.2H20 CuCO3
2 2 2 2
1377.67 1376.76 1376.42 1376.44 1376.65
0.91 1.25 1.23 1.02
CuC1 Cu20 Cu2Se
1 1 1
1377.10 1377.54 1377.41
0.57 0.13 0.26
1376.80 1377.36 1377.46 1377.56
0.87 0.31 0.21 0.11
CuCr204 CuCr2S4 CuCr2Se4 CuCraTe4
Especially the last three experiments provide a direct establishment of the monovalent state of copper in non-oxidic CuCrzX4. We adopt Cu ÷ in all sulphospinels, which is represented by a completely occupied Cu + level sufficiently far below the top of the valence band. The experimental data do not give information about the precise position of the Cu + state, so that this level will not be drawn in the energy level schemes.
4.2. CuTi2S4 CuTi2S4 is a normal spinel (Hahn and Harder 1956) with lattice parameters as given in table 1. Le Nagard et al. (1975) reported the existence of strongly Cu-deficient CUl-xTi2S4 compositions with 0 ~< x ~<0.44. The cell edge varies linearly with x, leading to a = 10.002-+ 0.003 A for x = 0. X-ray diffraction on a single crystal with a = 9.985 A and a corresponding composition Cu0.92Ti284 gave u = 0.3805. The compound has a nearly temperature-independent paramagnetic susceptibility, decreasing slightly with temperature (fig. 5). Le Nagard et al. (1975) measured on powders with a composition CuTi2S4 a room temperature susceptibility of 5 x 10-4cm3/mol after correction for the diamagnetic susceptibility. This agrees well with the value ( 4 . 5 + 0 . 1 ) x 10-4 cm3/mol reported by Lotgering and Van Stapele (1968a). The transport properties of powder samples have been measured by Bouchard et al. (1965). The electrical conduction is metallic with a room temperature resistivity of 4.8 x 10 -4 ~ c m (fig. 6). The Seebeck voltage is -11.8 ~xV/deg. These results are in accordance with those of Le Nagard et al. (1975), who measured on a single crystal a resistivity with a positive temperature coefficient and a value of
SULPHOSPINELS
621
"~mol l 10 xlO -~'
8 6 4
b
2
6;0 860 o'oo T(K) Fig. 5. Molar susceptibility of CuTizS4 corrected for the diamagnetic susceptibility. (a) According to Le Nagard et al. (1975). (b) According to Lotgering and Van Stapele (1968a).
?(f?crn]~
L
7 - x lOG
1 100 200 3(?0 a T(K) Fig. 6. The electrical resistivity of CuTi2S4and CuV2S4. (a) of a sintered powder of CuTi2S4, according to Bouchard et al. (1965). (b) of a single crystal with composition Cu0.92Ti2S4,according to Le Nagard et al. (1975). (c) of a sintered powder of CuV2S4, according to Bouchard et al. (1965).
4 . 2 x 10 4 ~ c m at r o o m temperature. T h e Hall constant was negative and ind e p e n d e n t of the t e m p e r a t u r e , with a value of 6.2 x 10 -4 cm3/C. Finally, V a n M a a r e n et al. (1967) searched for superconductivity. D o w n to 0.05 K they did not find a transition. T h e negative sign of the Seebeck and Hall voltages is indicative of conduction of electrons in a band. T h e extreme possibilities are a Ti 3÷ level well a b o v e the b o t t o m of the b r o a d conduction b a n d (as in fig. 4(f)) or well below it (as in fig. 4(c)). In the second case the Fermi level will fall in a partly filled and b r o a d e n e d Ti 3÷ band, since half of the Ti ions has d o n a t e d its d electron to the Cu ions, c o r r e s p o n d i n g to the valency distribution Cu+Ti3+Ti4+S42-. It is h o w e v e r questionable w h e t h e r the correlation b e t w e e n the remaining d electrons is strong e n o u g h to m a k e this f o r m u l a realistic in the sense that Ti 3+ and Ti 4+ exist, exchanging their valencies rapidly. G o o d e n o u g h (1969) argues that a 3d b a n d will be f o r m e d that is filled with half an electron per Ti ion. In the first case, w h e r e half of the Ti 3+ has already lost its 3d electron to the Cu ions, the o t h e r half of the Ti ions
622
R.P. VAN STAPELE
donates its 3d electron to the conduction band, which consequently contains one electron per molecule. However, the temperature-independent susceptibility of 5 × 10 -4 cm3/mole is much too large to be attributed to the Pauli paramagnetism of electrons in a broad band (Lotgering and Van Stapele 1968a). It can better be reconciled with a narrow 3d band, as is also the case with the rather large magnitude of the Seebeck coefficient. In this situation, where there is one type of charge carrier, the number of charge carriers is 1.3 per molecule as calculated from the value of the Hall constant. This agrees more or less with the expected number of about one electron per molecule. We therefore draw the energy bands as in fig. 7.
E~ n
band
EF Ti3dband ~ valenceband ~g(E) Fig. 7. Energy bands in CuTi2S4.
The magnetic moment x H induced by an applied magnetic field H in the 3d band of the Ti ions with a Pauli susceptibility X gives a hyperfine field Hh~ = K H on the nuclear spin of the Cu ions. The Knight shift K has been measured by Locher (1968). It decreases slightly with increasing temperature and is proportional to X (fig- 8), The ratio a = K/X = 5 can be compared with the corresponding ratio between the hyperfine field of 55 kOe on the Cu nuclear spin originating in the 6/~B of ordered C r s+ ions in semiconducting sulphospinels like CuuzInl/zCrzS4 (section 5.9). In such cases o~ = 1.63 (Locher and Van Stapele 1970). We can conclude that the strength of the interaction between the 3d moment and the Cu nuclear spin in CuTi2S4 is of the same order of magnitude as in semiconducting spinels with well localized 3d electrons on the octahedral sites.
4.3. CuVzS4 CHV2S 4 is a normal spinel (Hahn et al. 1956) with lattice parameters as given in table 1. Little is known about the physical properties of the compound. This is due to the difficulty of preparing sufficiently pure samples. As far as the susceptibility has been measured, a temperature-independent susceptibility with values of 13.5 x 10-4cm3/mol (Blasse, private communication) or 9.1x 10 4cm3/mol (Lotgering, private communication) has been found. At lower temperatures the susceptibility behaves irregularly or shows signs of a weak permanent moment. The Knight shift
SULPHoSPINELS
623 CuV2S4
0.5
% /
~o.3 0.2
CuTi 2 S~
0
._
Cu - metal
03 :3
I non- metallic compounds $4 - 0 , ro
-0.2~
• "
CuRhzSe Cu Rh2 $44
-o.#_ 0
100
200
3 0 - - ~ U '--d T(K)
Fig, 8. The Cu Knight shift with respect to CulnSea, in the COmpoundsindicated (/,ocher 1968). of the Cu nmr line (fig. 8) is positive and decreases with decreasing temperature ([,ocher 1968). The Cu nmr line suddenly broadens near 90 K and disappears at lower temperatures. This remarkable phenomenon, which is possibly due to a phase transformation, has not been investigated any further (Locher 1968). Both the Knight shift and the SUsceptibility corrected for the diamagnetic SUsceptibility of the sample Used in the nmr measurements (10.9 x I0-4) are about twice as large as in CuTi2S4. This means that the interaction between the Cu nuclear spin and the 3d mOmen!s are of COmparable strength in both COmpounds, (+5~.2e~V~d~1~hYyversus temperature cu ,,, 1965). The ~'" ~,w me occurrenceof~,_,.a~e (fig: 6/c)) and Seeh,~..,• t. ~yp~ metallic Cond,.~,;-_ ,L--~'r" voltage material superconductivity with transition temperatures range 4.45 to 3.95K exhibits measured on samples -~,.,,un (t~oncbardinetthe al. contaminated with 5 to 10% Cu3Vs4 (Van Maaren et al. 1967). The high Value of the Paul/ Susceptibility points to COnduction in a rather narrow band. It is reasonable to assume that this is the t2g band of the V ions. This is also in agreement with the Knight shift, which has a positive sign as in CuTi, S4. However, this cannot be the Whole Story. The t2g band o electrons per molecule. With Cu in the 3dI0 can contain twelve
statetheonly three electrons molecule will occupy the band. One therefore expects conduction to be thatper of electrons in a narrow band, with a negative and rather large Seebeck coefficient. EXperimentally, the Seebeck voltage is positive and this means that the COnduc_ tion is partly due to holes in another band. Because the t2g band of the V ions is expected to have a lower energy than that of the Ti ions, we assume that it verlaps with the broad band structure of the valence band, as sketched in fig. 9.
624
R.P. VAN STAPELE
E,
conduction band
EF ~
~"~/~
n
v 3d band d ~- g
(E)
Fig. 9. Energy bands in CuV2S4. This picture is essentially that given by Goodenough (1969). The simultaneous occurrence of itinerant electrons and itinerant holes coincides with the occurrence of superconductivity. The possibility of such a coincidence has been suggested in the interpretation of the behaviour of the superconducting transition temperature in the series CuRh>xSnxSe4 (Van Maaren and Harland 1969). Recent results of measurements on powder samples and single crystals of CuV2S4 confirm the earlier observations (Le Nagard et al. 1979). The electrical resistivity, the magnetic susceptibility, and the nuclear magnetic resonance of the nuclei 51V, 63Cu and 65Cu show a more or less sudden change below 100 K. However, X-ray diffraction fails to show a structural phase transition. Down to 4 K the c o m p o u n d r e m a i n s a cubic spinel with a cell edge that varies from 9.810 A at 300 K to 9.782 A at 4.2 K*. o
4.4. CuC02S4 and CuCoTiS4 CuCo2S4, which occurs in nature as the minerals carolyte and synchnodymite, is a normal spinel (De Jong and Hoog 1928). The lattice parameters are given in table 1. The compound exhibits a p-type metallic conduction, as appears from the resistivity versus temperature curve (fig. 10(a)) and the Seebeck voltage of +12.71xV/deg (Bouchard et al. 1965). CuCo2S4 has a temperature-independent paramagnetic susceptibility with a value of 3.7 to 3.8 × 10-4cm3/mO1 (Lotgering and Van Stapele 1968a). The part of the specific heat that depends linearly on the temperature is large (y = 24.4 mJmol-lK-2), which means a high density of states at the Fermi energy (Van Maaren, private communication). Replacement of Co by Ti removes the metallic conduction. This is shown by the properties of CuCoTiS4 (Lotgering and Van Stapele 1968a, Lotgering 1968b). The observed Seebeck voltage of +110 ixV/deg is much too high for metallic conduction and proves that the compound is a semiconductor. The resistivity versus temperature curve (fig. 10(b)) corresponds to a behaviour between that of a metal and a semiconductor. This is found in several semiconducting sulphospinels and has to be attributed to a small deviation from the stoichiometric composition, which gives a small number of charge carriers with a high mobility. The nearly temperature-independent magnetic susceptibility, corrected for the diamagnetic * See notes added in proof (b) on p. 737.
SULPHOSPINELS ?(#cm) 8x1()' 7 6 5 4 3 2 1
625
9(9cm)
160
260
1(]0
' 200
!
300
' 3.00
" T(K)
~ T(K)
Fig. 10. The electrical resistivity of: (a) CuCo2S4, according to Bouchard et al. (1965), (b) CuTiCoS4, according to Lotgering (private communication).
susceptibility ( - 1 . 8 x 10-4cm3/mol), was found to be 2.8 to 2.9x 10-4cm3/mol. The properties of CufoTiS4 can easily be understood on the basis of valencies, represented by Cu+fo3+Ti4+S4,with the Co 3+ ions in the low spin t6g state, as in oxyspinels. The empty 3d states of the Ti 4+ ions and the completely filled 3d states of the Cu 1+ ions explain the semiconduction. The temperature-independent susceptibility arises from the Van Vleck susceptibility of the Co 3+ ions (Lotgering and Van Stapele 1968a). On the assumption of monovalent copper ions the p-type metallic conduction of CuCo2S4 has been attributed to the conduction of holes in the valence band. This hole conduction can be compensated by the substitution of Ti for Co, since the Ti 3d states have a higher energy (fig. 7), which explains the semiconductivity of CuCoTiS4. If all the Co ions in CuCo2S4 were in the low spin t6g state, the Van Vleck susceptibility would amount to some 5.7x !0-4cm3/mol, about the measured value corrected for the diamagnetic susceptibility. This has led to the conclusion that all Co ions are trivalent and in the low spin state, and that the magnetic susceptibility of the conducting holes is small (Lotgering and Van Stapele 1968a). However, the specific heat, mentioned above, indicates a high density of states at the Fermi energy (10.3 states/eV molecule), which would mean a Pauli susceptibility of 3.3 x 10 -4 cm3/mol. This is of the same order of magnitude as the observed susceptibility. Such a poor agreement between magnetic and specific heat data has also been noted in the compounds CuRh2S4 (section 4.5) and CuRh2Se4 (section 4.6). In the last case the specific heat was found to be strongly enhanced by the electron-phonon interaction. An unexplained question is why CuCo2S4 behaves electrically and magnetically as CuRh2S4 and CuRh2Se4 but does not become superconducting as the two Rh compounds do. Locher (1968) has measured the Cu and Co nmr in CuCo2S4. The Knight shift of the Cu resonance is negative in this p-type conducting material, whereas it was positive in CuTi2S4 and CuV2S4, in which compounds the magnetic susceptibility is due to the Pauli paramagnetism of the 3d bands of Ti and V (fig. 8). The quadrupole splitting in the 59Co nmr spectrum, deduced from the complicated nmr
626
R.P. VAN STAPELE
powder spectrum, and confirmed by zero field nuclear quadrupole resonance, is much larger in CuC02S4 than in oxides such a s Z n C 0 2 0 4 and Co304 (Locher 1968).
4.5. CuRh2S4 and CuRh2-xCoxS4 The normal spinel CuRh2S4 (Blasse and Schipper 1964) exhibits essentially the same electrical and magnetic properties as CuRh2Se4, which compound will be discussed in the next section (4.6). We will therefore review experimental data without much comment. The resistivity at room temperature is 1.6x 10-3~cm (Lotgering and Van Stapele 1968a). The Hall coefficient is negative (Van Maaren, private communication). The compound becomes superconducting between 4 and 5 K. The transition temperature and width depend on the method of preparation (Van Maaren et al. 1967, Robbins et al. 1967a, Schaeffer and Van Maaren 1968, Dawes and Grimes 1975, Shelton et al. 1976). The reason for this dependence, which has been observed only in the case of CuRh2S4, is not known. The pressure dependence of the transition temperature To has been studied on samples with To between 3.8 and 4.8 K (Shelton et al. 1976). The pressure derivatives increase with increasing To from 2.73 × 10-5 K/bar at To = 3.81 K to 4.95 x 10-s K/bar at To = 4.76 K. The increase of To with pressure is ascribed to the increase of the Debye temperature, which primarily should determine To in compounds like CuRh2S4. It is doubtful, however, whether this conclusion is correct. In the series of mixed compounds CuRh2_xCoxS4, the lattice parameter varies linearly from 9.790 A at x = 0 to 9.498 A at x = 2 and the Debye temperature increases from 230 K at x = 0 to 310 K at x = 1 and 334 K at x = 2. However, To decreases fast for small increasing x and is about 1 K for CuRhCoS4 (Van Maaren, private communication). Above 50mK, CuCo2S4 has not been found superconducting (Van Maaren et al. 1967). At room temperature CuRh2S4 has a magnetic susceptibility of 1.6× 10 .4 cm3/mol (Blasse and Schipper 1964, Lotgering and Van Stapele 1968a). On the basis of Cu + ions, Rh > ions in the low spin t 6 state and hole conduction in the valence band the susceptibility can be explained as the sum of the diamagnetic susceptibility (-2.1 x 10 .4 cm3/mol), the Van Vleck susceptibility of the Rh 3+ ions (3 x 10-4 cm3/mol) and a Pauli susceptibility of 0.7 x 10 .4 cm3/mol (Lotgering and Van Stapele 1968a). As in CuCo2S4 (section 4.4) and in CuRh2Se4 (section 4.6), such a small Pauli susceptibility does not agree with the large linear temperature coefficient of the specific heat (y = 30 mJmol-lK -2) (Schaetter and Van Maaren 1968), which corresponds to a Pauli susceptibility of 4 x 10 .4 cm3/mol. The Knight shift of the Cu nmr lines measured on CuRh2S4 (Locher 1968) is negative and has nearly the same value as in CuRh2Se4 (fig. 8). A complete solubility has been observed in the series CuRh2(Sl_xSex)4 (Riedel et al. 1976). The lattice constant varies linearly with x. The anion sublattice shows a random distribution of chalcogen atoms with a mean value for the anion parameter u of 0.381.
SULPHOSPINELS
627
4.6. CuRh2Se4 and CuRh2-xSnxSe4 CuRh2Se4 is a normal spinel with lattice parameters as given in table 1. The c o m p o u n d has a p-type metallic conduction (Lotgering and Van Stapele 1968a) with at r o o m t e m p e r a t u r e a Seebeck coefficient of +7.3 p.V/deg and a resistivity of 1.3 × 10 -3 ~ c m . The magnetic susceptibility depends weakly on the temperature. At r o o m t e m p e r a t u r e the value is 1.1 × 10 -4 cm3/mol. Based on the assumption of monovalent copper ions, the properties of CuRh2Se4 have been attributed to Rh 3+ ions and hole conduction in the valence band, as sketched in fig. 4e, with the Rh 3+ states below the Fermi level (Lotgering and Van Stapele 1968a). At low temperatures the c o m p o u n d becomes superconducting. Van Maaren et al. (1967) found a transition at 3.47 K with a width of 0.04 K, which agrees with the findings of Robbins et al. (1967a) who observed the transition at 3.46 K with a width of 0.09 K, and those of Dawes and Grimes (1975), who obtained 3.50_+ 0.05 K. Shelton et al. (1976) measured the influence of a hydrostatic pressure up to 22 kbar on To. On samples with Tc -- 3.49 K and 3.38 K the pressure derivative has a value of 1.53 and 1.44 × 10 -5 K / b a r respectively. These m e a s u r e m e n t s were done to confirm the suggestion that in spinel compounds the transition to superconductivity occurs at a t e m p e r a t u r e determined by the D e b y e temperature, the strength of the electron-phonon interaction being roughly constant within the class of superconductive spinel compounds. However, a study of the properties of the system CuRh2_xSnxSe4 with 0~<x ~ 1 (Van Maaren and Harland 1969, Van Maaren et al. 1970a, b) has shown that the occurrence of superconductivity in CuRh2Se4 is determined critically by the details of the band structure. In this investigation use has been made of the possibility to change the n u m b e r of charge carriers drastically by substitution of Sn for Rh 3+. The Sn ions are expected to be tetravalent and to decrease the n u m b e r of holes in the band, which is responsible for the p-type metallic conduction. This turns out to be the case. T h e lattice p a r a m e t e r changes linearly with the composition from 10.26 ,~ at x = 0 to 10.62 at x = 1. T h e conduction changes from metallic for 0 ~< x ~< 1 to semiconductive at x = 1, at which composition the valencies are given by Cu+Rh3+Sn4+Se]-. The Seebeck voltage is positive in the complete range o f compositions, whereas the Hall coefficient RH is positive for 0.15 ~< x ~ 1 and negative for x ~< 0.15 (fig. 11). For 0.5 < x ~< 1, R~I1 at r o o m t e m p e r a t u r e is about proportional to the n u m b e r ( 1 - x) of charge carriers per molecule C u +Rh2_xSn 3+ 4+ x Se4 (fig. 11). For x < 0.5, however, R n behaves anomalously. The value of R ~ 1 increases strongly with decreasing x and R u changes sign at x -~ 0.15. The dependence of the transition to superconductivity on the Sn concentration is strongly correlated to that of RH. To decreases with x and no superconductivity above 0.05 K has been observed for x > 0.5 (fig. 11). Van Maaren and Harland (1969) conclude from these m e a s u r e ments that conduction takes place in at least two bands, one of which shows n-type behaviour for x < 0 . 5 . This can be reconciled with conduction i n the valence band, which at the top is split into a single narrow upper branch and a
628
R.P. VAN STAPELE
T
× 300 K o
i
77 K
A 4.2K
D u
_¢ O
E
I I I I
J lh-
4-1
.1
p-type
.3 /
.6
.8 X
,92 I
Fig. 11. Superconducting critical temperature To and reciprocal Hall constant R h 1 vs x of CuRh2-xSnxSe4 according to Van Maaren and Harland (1969).
broader two-fold degenerate lower branch (Rehwald 1967). The additional assumption which had to be made is that in the rigid band model the upper branch will show p-type conduction for 0 ~<x < 1, whereas the lower branch changes sign of conduction near x = 0.5. For x < 0.5 holes occur in the upper branch and electrons in the lower branch. The simultaneous presence of holes and electrons is apparently responsible for the appearance of superconductivity. At this point it should be noted that the transport properties have also been measured by Robbins et al. (1967b) and that they obtained a positive Hall coefficient at room temperature. However, the sample used in the measurements did not show superconductivity (Van Maaren and Harland 1969). Schaeffer and Van Maaren (1968) have measured the heat capacity of CuRh2Se 4 and Van Maaren et al. (1970a, b) extended the measurements to the series CuRh2-xSnxSe4 with 0 ~ x ~< 1. The Debye temperature, as calculated from the lattice contribution, increases linearly with x from 200 K at x = 0 to 267 K at x = 1. For x ) 0 . 6 the constant T in the linear term of the heat capacity is proportional to ( 1 - x) 1/3, the electronic density of states expected for a parabolic band with (1 - x) charge carriers per molecule. At smaller values of x, for which compositions the compounds are superconductive, y vs ( 1 - x ) 1/3 is again linear, but with a steeper slope. However, after correction of T for the enhancement of T by the electron-phonon interaction, y vs ( 1 - x) ~/3 is linear in the full interval 0 <~ x ~< 1 (fig. 12). This is in accordance with the two-band model, in which it is assumed that the density of states in the upper branch is much higher than in the lower branch.
SULPHOSPINELS
629
I \,
[\ I
o ,,2,,~ 1.0
.s,,
9 ,? ,9s ---~'~ .5
~
Fig. 12. The constant y in the linear term of the heat capacity of CuRh2-xSnxSe4 vs x according to Van Maaren et al. (1970a, b); (a) without and (b) with correction for electron-phonon interaction. T h e d e n s i t y of states of CuRh2Se4 o b t a i n e d f r o m t h e c o r r e c t e d v a l u e of y (12 m J / m o l K 2) is 5.1 s t a t e s / e V m o l e c u l e . T h i s w o u l d give a Pauli s u s c e p t i b i l i t y of 1.6 x 10 -4 cm3/mol. T h e m a g n e t i c s u s c e p t i b i l i t y of t h e m i x e d c o m p o u n d s CuRh2_xSnxSe4 has b e e n measured by Van Maaren and Harland (quoted by Van Stapele and Lotgering 1970) (fig. 13). T h e m a g n e t i c s u s c e p t i b i l i t y Xm is t h e s u m of t h e d i a m a g n e t i c 0(d),
I0£X~
T Q
•
i
0 0.5 ~ × 1.0 Fig. 13. Molar susceptibility at room temperature of CuRh2_xSnxSe4, according to Van Maaren, quoted in Van Stapele and Lotgering (1970).
630
R.P. VAN STAPELE
the Van Vleck 0(~) and the Pauli susceptibility 0(p). Since Xd, which arises mainly from the Se ions, is independent of x and X~, which is due to the Rh 3+ ions, is linear in x, the curvature is caused by Xp. Taking Xd = - 2 . 5 x 10 -4 cm3/mole, X~v can be estimated from Xm at x = 1 because Xp = 0 in the semiconductor CuRhSnSe4. This gives Xvv = 1.5 × 10 -4 cm3/mol Rh. From the susceptibility of CuRh2Se4 the Pauli susceptibility of this c o m p o u n d is then estimated to be 0.6× 10 _4 cm3/mol, which is smaller than, but of the same order of magnitude as, the value estimated from the specific heat data. The Knight shift of the Cu nmr lines in CuRh2Se4 (fig. 8) is negative and has nearly the same value as in CuRhzS4 (Locher 1968).
4.7. CuCr2S4, CuCr2-xTixS4, CuCr2-xgnxS4 and CuCr2-xVxS4 The normal spinels CuCr2X4 and X = S, Se and Te, which were first prepared by H a h n et al. (1956) have a metallic conduction and are ferromagnetic with a Curie t e m p e r a t u r e above r o o m t e m p e r a t u r e (Lotgering 1964a). Because much of our understanding of these interesting properties is based on the behaviour of mixed compounds like CuCrz-xTixS4, we will also discuss the properties of these compounds. C o m p a r e d with CuCrzSe4 and CuCrzTe4, the study of CuCr2S4 has the disadvantage that the preparation of pure samples is m o r e difficult. Samples of CuCrzS4 always contain some antiferromagnetic CuCrS2 (Lotgering 1964b), which makes magnetic data unreliable. Saturation magnetizations of 4.8 ~xB/molecule (Robbins et al. 1970a) and 4.85/xB/molecule (Van der Steen, private communication) were measured on the best samples, which also showed a lower Curie t e m p e r a t u r e than the samples first measured (fig. 14 and table 6). A b o v e the Curie t e m p e r a t u r e the magnetic susceptibility follows a Curie-Weiss law (fig. 15 and table 6). TABLE 6 Magnetic data of the compounds CuCr2X4 Compound CuCr2S4
CuCr2Se4
CuCr2Te4
Cm
0 (K)
Tc (K)
Saturationmagnetization (/xB/molecule)
2.40
390
420 398 390
4.6 4.8 4.85
2.0
365
364
3.9
Lotgering (1964b) Robbins et al. (1970a) Van der Steen (private communication). Kanomata et al. (1970)
2.50
465
2.3 2.55
460 441
460 433 414 430
4.94 4.77 4.5 5.07
Lotgering (1964b) Robbins et al. (1967b) Kanomata et. al (1970) Nakatani et al. (1977)
2.90 3.0
400 367
365 344
4.93 4.2
Lotgering (1964b) Kanomata et al. (1970)
Reference
SULPHOSPINELS
631
G(gauss cm3/g) 4.58.1J e I
80!
t
Cr? S~ 6C - -
4.9gJJ B - -
~.
"~"'*'-*-""~'~"~._
~ CuCr2Se~
4.93.1J B .
.
.
.
.
.
-
~%'~'--~
.
gu Cr2
Tez , " ~
o
I
0 100 200 300 400 500 °K Fig. 14. The magnetization o- per gram as a function of temperature in H = 20 kOe of CuCr2X4 (X = S, Se and Te) (Lotgering 1964b). T h e C u r i e t e m p e r a t u r e d e c r e a s e s with i n c r e a s i n g h y d r o s t a t i c p r e s s u r e . K a n o m a t a et al. (1970) a n d K a m i g a k i et al. (1970) m e a s u r e d a r e l a t i v e p r e s s u r e d e r i v a t i v e d In TJdp = - 3 . 1 x 10 -6 kg -1 c m 2. T h e o c c u r r e n c e of p - t y p e m e t a l l i c c o n d u c t i o n a p p e a r s f r o m a low resistivity (9 x 10 .4 ~ c m at r o o m t e m p e r a t u r e ) which i n c r e a s e s with i n c r e a s i n g t e m p e r a t u r e a n d a p o s i t i v e S e e b e c k v o l t a g e of + 16.0 ixV/deg ( B o u c h a r d et al. 1965).
Cm--2.40.e = 39o
K
/'
,,/
j j " ~';//'-.LCuCr2 Se~ ~~*~Cm=2.S0, I
~
e 465 K--
Cucrl2 Te~
c =z9o,e:,.oo
K
I
0 200 400 600 800 1000 K Fig. 15. Reciprocal molar susceptibility of CuCr2X4 (X = S, Se and Te) (Lotgering 1964b).
632
R.P. VAN STAPELE
The hyperfine fields on the nuclear spins of the ~'6~Cu and the S3Cr nuclei have been measured at various temperatures below the Curie t e m p e r a t u r e by Le Dang Khoi (1968) (table 7). In an applied magnetic field the nmr frequency of the Cu nuclear spins increases, while that of the Cr nuclear spins decreases. This means that the hyperfine field on the Cu nuclear spins is positive (parallel to the applied field) but that the hyperfine field on the Cr nuclear spins is negative. The magnitude of the hyperfine fields measured by Berger et al. (1971) agrees well with the results of Le Dang Khoi (table 7). The nmr spectrum measured at 4.2 K by Kovtun et al. (1978) was m o r e complicated. The relaxation of the Cu nuclear spins has been studied by Enokiya et al. (1977). In an applied magnetic field the spin-lattice relaxation time T1 increases with the field strength up to 6 k O e and remains constant in higher fields. The constant value, which can be considered to be the relaxation time of nuclei in Weiss domains, was measured as a function of temperature. The t e m p e r a t u r e dependence of T1 could be expressed as T ; 1= a T + b T 35 with a = 0.38 and b = 4.8 × 10 -7. The first term, which dominates at low temperature, is due to a process involving itinerant electrons, the second term has been attributed to a three-magnon process. TABLE 7 Hyperfine fields in CuCr2S4; (a)according to Le Dang Khoi (1968); co/according to Berger et al. (1971) 300 K (a) v MHz 63Cu
kG
65.6
77 K (") v MHz
70.35 27
kG
100.6 +58.1
65Cu 53Cr
4 K co}
-112
v MHz 102.0
+89.1 107.8 38.9
kG
-162
+90.3 109.2 39.8
-165
Recently, Ballal and Mande (1976) measured the chemical shift of the K absorption edge of Cu in CuCr2S4. T h e shift with respect to the position of the edge in Cu metal is small and typical of the 3d 1° electron configuration of the Cu + ion (table 5). The magnetic and electrical properties of CuCrzS4 are very similar to those of CuCrzSe4, which will be discussed in the next section. For the m o m e n t we mention that the valency distribution can be symbolized by Cu+Cr3+~Cr4-+sS4 with a small n u m b e r of holes (~ per molecule) in the valence band and that the high Curie t e m p e r a t u r e of CuCr2S4 is associated with the metallic conduction. The correlation between the electrical and the magnetic behaviour is clearly demonstrated in the series CuCr2_xTixS4 (Lotgering and Van Stapele 1968a). If we adopt Ti4++ Cr 3+ to be stable with respect to Ti 3+ + Cr 4+ (which holds in oxides) substitution of Ti for Cr compensates the p-type conduction. For x = 1 a semiconductor with valencies Cu+Cr3+Ti4+S24- is expected, which is experimentally confirmed by a relatively high resistivity ( 0 . 6 ~ c m ) and Seebeck voltage
SULPHOSPINELS
633
( - 2 5 0 txV/deg), and a c h a n g e of sign of the latter quantity (fig. 16). T h e Curie constant Cm = 1.84 is close to the spin-only value 1.88 of C r 3+. T h e Curie t e m p e r a t u r e decreases almost linearly with x to a low value (0 = 4 K) at x = 1 (fig. 17). This decrease, which is m u c h stronger than the reduction expected for dilution with n o n - m a g n e t i c Ti e+ ions, m e a n s that the strong ferromagnetic interaction is a b o u t p r o p o r t i o n a l to the n u m b e r of charge carriers giving metallic conduction. A further r e p l a c e m e n t of C r 3+ by Ti 3+ in Cu+Cr3+Ti4+S 2- formally gives a mixture of Ti 3+ and Ti 4+, so that n-type metallic conduction occurs for 1 < x ~< 2 (fig. 16) as in CuTi2S4 (section 4.2). T h e c h a n g e of sign of the Seebeck voltage at x = 1 (fig. 16) corresponds to the change f r o m p-type metallic conduction in the
Seebeck coeff
(j.JVldeg)
100
S
-100
-
200
- 300
0
~X
Fig. 16. Seebeck coefficient of CuCr2-xTixS4, according to Lotgering and Van Stapele (1968a).
LO0
T30£ x-"
-~ 200 B
Cu Cr2_xTix S L
¢-,
E 100 ,e 0
0.5
1
1.5
~X
2
Fig. 17. Curie temperatures (0) and asymptotic Curie temperatures (x) of CuCr2 xTixS4(Lotgering and Van Stapele 1968a) and CuCr2-xVxS4(Robbins et al. 1970a).
634
R.P. VAN STAPELE
valence band to n-type metallic conduction in a Ti 3+ band (fig. 7). With increasing n-type conduction the asymptotic Curie t e m p e r a t u r e also increases (fig. 17), which shows the ferromagnetic interaction between the Cr ions to be enhanced by the conduction electrons. In the interval 1 ~< x ~< 2 the Curie constant remains close to that of Cr 3+ (fig. 18), which confirms the assumption that Ti 4+ + C P + is stable with respect to Ti 3+ + Cr 4+ or, in other words, that the C1e+ levels have a lower energy than the Ti 3d band in fig. 7. The Curie constants of the compounds CuCr2_xTi~S4 with x < 1 gradually change from Ca = 1.88 at x = 1 to Ca = 2.40 for CuCr2S4 (fig. 18). The latter value is smaller than 2.88 expected for CuCr3+Cr4+S4 with spin-only values of 1.88 and 1.0 for Cr 3+ and Cr 4+ respectively. This lack of agreement also exists in the case of CuCr2Se4 (section 4.8). Cm
~2.88 •-, .,.... Cq3. Cry) x 2
1
ol o
1
~X Fig. 18. Molar Curie constant of CuCr2 xTixS4 (0) (Lotgering and Van Stapele 1968a) compared with the spin-only value of Cr3++ (1 - x) Cr 4+ for x < 1 and of (2- x) Cr3+ for x > 1. The substitution of Sn for Cr in CuCr2S 4 has the same effect as the substitution of Ti. The strongly ferromagnetic interactions between the Cr ions have disappeared in CuCrSnS4, which is paramagnetic down to 4 K with an asymptotic Curie t e m p e r a t u r e of - 2 0 K (Sekizawa et al. 1973). The ion distribution has been determined by Strick et al. (1968). Cu occupies the tetrahedral sites; the Cr and Sn ions occupy the octahedral sites. As shown in fig. 19, the lattice p a r a m e t e r increases and the Curie t e m p e r a t u r e decreases linearly with x in the series CuCr2_xSnxS4 in the interval 0~<x <~ 1 (Sekizawa et al. 1973). The electrical resistivity increases and the c o m p o u n d behaves like a semiconductor at x = 1. All these properties are understandable with tetravalent Sn ions replacing the Cr ions, as in CuCrz_xTixS4. Sekizawa et al. (1973) also measured the UgSn M6ssbauer spectra. At a low Sn concentration, as in CuCrl.9Sn0.1S4, they measured a hyperfine field of 580 k G at 80K. This agrees with the value of +530 k G measured by Lyubutin and Dmitrieva (1975) in CuCr0.95Sn0.05S4. The positive sign means a hyperfine field parallel to the Cr magnetization. This field is mainly due to the supertransferred hyperfine interaction between the Sn nuclear spin and the Cr spin density, which is partly transferred to the Sn 5s orbital. T h e hyperfine field due to one 5s electron is estimated by extrapolation of the experimental data of
SULPHOSPINELS
635
-
@t
Tc(K
T
I""
Q(,~) 10.0 l
t1¢"
9.8
40( \ 300
10.2
\
xTc oN
20C
N
oNN No N
10C 0
N\
I
0
"~:CTN)
0.5
Fig. 19. Cell edge and ferromagnetic Curie temperature of CuCr2-xSnxS4 according to Sekizawa et al. (1973).
Cd (Kelly and Sutherland 1956) and In (Campbell and Davis 1939) to be 16 MG. The observed hyperfine field o n ll9Sn thus corresponds to a spin density of 3.3% in the Sn 5s orbital. An interesting series of compounds is CuCr2-xVxS4, which has been investigated magnetically by Robbins et al. (1970a). The cell edge behaves anomalously; after an initial rise for x ~<0.375 it decreases to the smaller cell edge of CuV2S4. This and the initially slow decrease of the magnetic moment (see fig. 20) has been used g.825
.IJf lJJB )
al,&)
9.820 T o
9.815 9.810
9.805 9.800
0.15
110
ll5 ~X
2.0
Fig. 20. Lattice parameter a and magnetic moment per formula unit at 1.5 K and 15 kOe of CuCrz-xgxS4, according to Robbins et al. (1970a).
636
R.P. VAN STAPELE
by Robbins et al. (1970a) as arguments for a localized 3d 2 configuration of V 3+ for vanadium concentrations smaller than 0.375. The magnetic moment of the V ~+ ions is assumed to couple ferromagnetically with the Cr magnetization. The results of an nmr study of vanadium-substituted CuCr2S4, however, point in a different direction. Berger et al. (1971) interpret the splitting of the Cu nmr lines, observed in a sample with x = 0.1, and the shift of the broadening Cu lines at higher vanadium concentrations, as being due to non-magnetic V ions. The replacment of Cr 3+ ions by non-magnetic vanadium ions also splits the 53Cr nmr line. The magnitude of the splitting corresponds to a supertransferred hyperfine field of +87 k G exerted by the six Cr neighbours on a 53Cr nuclear spin. With a total field of - 1 6 5 k G (table 7) the sum of the fields from the core polarization and the band polarization is then estimated to be about - 2 5 2 kG. If the presence of holes in the valence band does not influence the supertransferred hyperfine interactions between the Cr ions, the field from the band polarization can be estimated by comparison of CuCr2S4 with the semiconductor CdCr2S4. The hyperfine field on the Cr nuclear spin in the last compound is - 1 9 0 k G (see section 5.3), which gives +25 k G from the band. The field from the core polarization is then - 2 7 7 kG, an acceptable 8% below the value of 300 kG measured in Cr ions in oxides (Geschwind 1967). The rapid decrease of the Curie temperature of CuCr2-xVxS4 with the vanadium concentration (Robbins et al. 1970a) parallels the behaviour of CuCr2_xTixS4 as shown in fig. 17. This suggests that the substitution of vanadium causes a rapid decrease of the number of holes in the band of Cufr2S4. Because T ~ 0 for x ~ 0.5 this might mean that the vanadium ions start to donate two electrons to the band, twice as many as the Ti ions in CuCr2_xTixS4. Such an occurrence of V 5+ (3d°) ions at low vanadium concentrations would also explain the non-magnetic character of the vanadium ions observed by Berger et al. (1971) and the slow decrease of the ferromagnetic moment, which is expected to decrease from 5/x~ per molecule to 4.5/zB in the hypothetical semiconductor C u ('~3+~tl'5+c~._.ll.5v0.4.5o However, as Robbins et al. (1970a) argue, the V ions start to form a partly filled 3d band from a vanadium concentration as low as 0.375. This changes the picture completely, giving rise to metallic conduction and ferromagnetism with a low Curie temperature and a low ferromagnetic moment that is difficult to saturate.
4.8. CuCr2Se4, CuCr2-xRhxSe4 and CuCro.3Rhl.7_xSnxSe4 CuCr2Se4 is a normal spinel (Hahn et al. 1956) with lattice parameters as given in table 1. The compound is, like CuCr2S4, a metallic ferromagnet (table 6) with Tc = 460 K, /xf = 4.94/xB/molecule (fig. 14), 0 = 465 K and Cm = 2.50 (fig. 15) (Lotgering 1964b). Since the material could be prepared in a pure state, the saturation value is considered to be reliable. Tc = 433 K has been found from measurements in a much lower field (50 Oe instead of 10 kOe), but on a sample not completely pure as seen from /xf = 4.77/xB/molecule (Robbins et al. 1967b). Measurements under hydrostatic pressure give d In Tc/dp = - 1 . 0 × 10 -6 kg icm2 (Kanomata et al. 1970, Kamigaki et al. 1970). The magnetic transition at Tc for
SULPHOSPINELS
637
increasing temperature at 50 Oe is accompanied by a large volume increase and a sudden change in magnetization, which points to a first-order transition (Belov et al, 1975). Magnetoscrystalline anisotropy constants Ka and /£2 of - 6 . 9 and - 0 . 9 x 10s erg cm -3 have been measured on a CuCr2Se4 single crystal. The anisotropy changed upon annealing in vacuum or in a Se atmosphere (Nakatani et al. 1977). Metallic p-type conduction occurs down to 1 K. A resistivity of 2 x 10 -4 ~'~cm at room temperature and a Hall constant of (1.0_+ 0.5)10 -l° Vcm-IG-1A -1 at 492 K were measured on a single crystal (Lotgering 1964b). The value of (1.5 + 0.5)10 -1° Vcm-IG-1A -1 given in the paper is incorrect. This Hall constant, which was measured in the paramagnetic state, gives 0.1 charge carrier per molecule. For the Seebeck voltage the values +20.5 txV/deg (Robbins et al. 1967b) and +40 p.V/deg (Lotgering and Van Stapele 1968a) are reported. As we have discussed in section 4.7, a striking correlation exists between metallic conductivity and strong ferromagnetism in the non-oxidic compounds CuCr2X4. Such ferromagnetism was interpreted by Zener (1951) as being due to an indirect coupling of localized incomplete d shells via the conducting electrons. A positive or negative exchange coupling between the localized spins and the spins of the conduction electrons results in a ferromagnetic coupling between the localized spins and in a positive or negative partial spin polarization of the conducting electrons. Goodenough (1965, 1967) assumed that in the compounds CuCrzX4 (X = S, Se and Te) the copper ions are formally divalent and that the conduction takes place in a narrow band of copper 3d states. The net magnetization of about 5 b~B/molecule was explained as the sum of 6 #B/molecule of the ferromagnetically coupled Cr 3+ spins and -1/xB/molecule of a fully polarized copper band. Lotgering and Van Stapele (1967, 1968a) assumed that the copper ions are monovalent and attributed the p-type conduction to a small number of 6 holes/molecule in the valence band. These holes are brought on by the presence of formally tetravalent Cr ions, i.e. holes in the Cr 3+ states, which were assumed to be situated below the top of the valence band, as sketched in fig. 21(a) for CuCr2Se4. The corresponding valence distribution in this compound can be symbolized by Cu +{Crl+~Cra-a}{Se4 3+ 4+ 2 - aSea} with 6 ~ 0.1, as determined by the Hall constant. In this model the net magnetization results from (5 + 6)/xB/molecule of the Cr ions, opposed by a spin polarization of the valence band. As discussed in section 4.1, measurements of the X-ray photoelectron spectrum of C u f r 2 S e 4 (Hollander et al. 1974) and of the shift of the K absorption edge (table 5, Ballal and Mande 1976) confirmed the monovalency of the copper ions. Neutron diffraction experiments on C u f r 2 S e 4 (Robbins et al. 1967b, Colominas 1967) and on CuCr2Te4 (Colominas 1967) showed the absence of a magnetic moment on the copper ions. The moment localized on the Cr ions was found to be close to 3/xR. However, the values of the magnetic moments derived from neutron diffraction experiments depend critically on the form factors used. In a recent study of the diffraction of polarized neutrons by a C u f r 2 S e 4 single crystal, Yamashita et al. (1979a) used measured form factors of the copper and the chromium ions. These authors determined a moment of -0.07___ 0.02/xB on the
638
R.P. VAN STAPELE EI
I
(1.8)CrL.÷T...~5: 0.1 hole/molecule ~~//~EF ~
g ( E ) o) Cu Cr2SeA E [1_8)Cr~,~ / 6 = 0.1hole/molecule A
v/////////////'A
~
g [E)
b) CuCrRhSe4 E r ~ 6 03 C r ~ ~
= 0.7 holeI molecule - E~ g(E)
C) Cu Cro3Rh17Sel, Fig. 21. Energy bands and localized Cr states in CuCr2 xRhxSe4, according to Lotgering and Van Stapele (1968a). copper ions and of 2.64_+ 0.04/zB on the Cr ions. T h e difference c o m p a r e d with the measured value of the saturation magnetization (5.01/zB/molecule) was attributed to a uniform polarization of - 0 . 2 0 _ 0.11/zB/molecule. A p a r t from the small negative m o m e n t on the copper ions, these results agree satisfactorily with the model of Lotgering and Van Stapele with 6 = 0.2 holes/molecule in the valence band. The crucial point in the Lotgering and Van Stapele model is the tetravaient state of Cr, which is known to exist in oxides (CrO2). Detailed experiments have been done to verify its occurrence in selenides. Because Rh 3+ + Cr 4+ is expected to be more stable than Rh 4+ + Cr 3+, a replacement of Cr > in CuCrzSe4 by Rh 3+ will ultimately give a material that contains exclusively Cr 4+. This has been investigated in the system CuCrz_xRhxSe4 (Lotgering and Van Stapele 1968a)*. It turned out that there is p-type metallic conduction throughout the series, the Seebeck coefficient being small and positive for all values of x (fig. 22). The asymptotic Curie t e m p e r a t u r e decreases gradually with increasing x (fig. 23), while ferromagnetic ordering remains down at x = 1.7. As fig. 23 shows, the magnetic m o m e n t in the ferromagnetic saturation is close to 2/xB per Cr ion for x > 1, while the paramagnetic Curie constant per g r a m a t o m Cr is close to 1.0, the spin-only value of Cr 4÷ (fig. 24). This confirms remarkably well the tetravalent state of the Cr ions in CuCr2_xRhxSe4 with x > 1. T h e behaviour of the system CuCr2_xRhxSe4 can qualitatively be understood on * See notes added in proof (c) on p. 737.
SULPHOSPINELS
639
seebeckcoeff.(jJV/deg)
2C 10 I
0
1
2 ~X Fig. 22. Seebeck coefficient of CuCrz_xRhxSe4, according to Lotgering and Van Stapele (1968a).
e(K)
%\ T/*00 '~ 300
N% xx~'~
20C
-Mf(JJB} l ~\
5
100
3 1 r
0
1
2
Fig. 23. Asymptotic Curie temperature ( 0 ) and ferromagnetic moment /x~ (O) of CuCr2_xRhxSe4 (Lotgering and Van Stapele 1968a, Van Stapele and Lotgering 1970). The solid lines represent/xf vs x for Cr 4+ (a) and Cr 3+ (b).
Cm
I
1
~X
Fig. 24. Molar Curie constant of CuCr2_xRhxSe4 (Lotgering and Van Stapele 1968a, Van Stapele and Lotgering 1970). The solid lines represent Cm vs x for Cr 3+ (a) and Cr 4+ (b).
640
R.P. V A N S T A P E L E
the basis of the energy level diagram for CuCr2Se4 (fig. 21(a)). Substitution of Rh replaces Cr 3+ levels by deeper Rh 3+ levels. This lowers the Cr 3+ concentration, leaving the number of holes in the valence band unchanged as long as the Fermi energy falls in the Cr 3+ levels. Figure 21(b) illustrates the situation in CuCrRhSe4 with 6Cr 3+ ions, (1 - 6)Cr 4+ ions and ~ holes in the valence band. If the resonance width of the Cr 3+ levels is sufficiently small, a further increase of the Rh concentration will finally increase the number of holes in the valence band, leaving the remaining Cr ions in the tetravalent state. This is sketched in fig. 21(c) for CuCr0.3Rhl.7Se4 with 0.3 Cr 4+ and 0.7 holes in the valence band. The consequence is that if the Fermi level is shifted to higher energies at a constant Cr concentration, the valency of the Cr ions should also change from C r 4+ to Cr 3+, This has been accomplished in CuCr0.3Rhl.ySe4 by substituting Sn 4+ for Rh 3+ (Van Stapele and Lotgering 1970). As we have discussed in section 4.6, this substitution reduces the number of holes in the band of CuRhzSe4 to zero in the semiconductor CuRhSnSe4. In the series of compounds CuRhl.7_xSnxCr0.3Se4 the properties change in the same way. As shown in fig. 25, the Seebeck coefficient is positive and increases strongly if x approaches 1, indicating that CuRh0.7SnCr0.3Se4 is a semiconductor. The asymptotic Curie temperature decreases strongly and, most important, the Curie constant per gramatom Cr changes gradually from the spin-only value 1.0 of Cr 4+ to the spin-only value 1.87 of Cr 3+. The change of valency cannot be detected from the magnetic moment in the ferromagnetic state, since for x >~0.3 the magnetization of CuRhl.y_xSnxCr0.3Se4 is difficult to saturate. It is difficult to account for the paramagnetic moment observed in CuCrzSe4 in terms of paramagnetic moments of Cr 3+ and Cr 4+ (Lotgering and Van Stapele 1968a, Yamashita et al. 1979b). The observed value of the molar Curie constant (Cm = 2.50) is lower than the spin-only values 2.97 and 3.06, which are expected
Cm/0.3
cdJaV,/deg)
e (K)
t 2.0
60'-
Cr 3+
a(A)
A
10.8
i6oo
40
10.6
20
IOL
1.5
1.0~ n
o o
o CFt~+
0 0
I
05 --I.-
O5
0
05
10.2
X
Fig. 25. Curie constant per gram atom chromium Cm/0.3, paramagnetic Curie temperature 0, Seebeck coefficient a and cell edge a of CuCr0.3Rhl.7 ,SnxSe4 as a function of the composition (Van Stapele and Lotgering 1970).
SULPHOSPINELS
641
for (1.1 C r 3+ + 0.9 Cr 4+) and (1.2 Cr 3+ + 0.8 Cr 4+) respectively. This means that in the paramagnetic state, too, the negative interaction between the Cr spins and the spins of the conducting electrons cannot be left out of account. Hyperfine fields in CuCrzSe4 have been measured on the nuclear spins of Cu, Cr and Se ions. Locher (1967) found the Knight shift K of the Cu nmr to be proportional to the magnetic susceptibility: K = c~X with c~ = 1.17x 103gcm -3. Extrapolation to the magnetic moment in the ferromagnetic saturation gave a hyperfine field of +68 kOe on the Cu nuclear spin. This agrees well with the hyperfine field actually measured by Yokoyama et al. (1967a, b) and Locher (1967) in the ferromagnetic state (table8). TABLE 8 Hyperfinefieldsin CuCr2Se4;(a) accordingto Locher (1967);(b) according to Yokoyama et al. (1967a, b).
63'65Cu 53Cr 77Se
77 K
Extrapol. to 0 K
+70.4 kOe +70.6 kOe - 159 kOe 71.4 kOe
+72.6 kOe - 161 kOe 73 kOe
4.2 K
Ref.
+72.1 kOe
(a) (b) (b) (b)
The positive hyperfine field on the Cu nuclear spin is larger than the positive field measured in semiconducting selenides: +72 kOe as compared to +32 kOe in CUl/2Inl/zCr2Se4. This means that the negative polarization of the band in CuCr2Se4 gives a hyperfine field of the opposite sign on the Cu nuclear spin. This sign agrees with the observations in the Pauli paramagnetic CuRhzS4 and CuRhzSe4, where a negative Knight shift of the Cu nmr has been observed (fig. 8). The hyperfine field on the 53Cr nuclear spin ( - 1 6 1 k O e of table 7) differs by 22 kOe from the - 183 kOe measured in the semiconducting CdCr2Se4 (see section 5.6). With Cr 3+ in both compounds this hyperfine field must be attributable to the (negative) polarization of the polarized band. The hyperfine field due to the Cr neighbours has been measured on the 119Sn nuclear spin in CuCrl.9Sn0.1Se4 (Lyubutin and Dmitrieva 1975) where it has the value of +490_+ 10 kOe. This compares well with the values found in CuCr2S4 (section 4.7).
4.9. CuCr2Te4 and Cul+xCrzTe4 CuCr2Te4, which was first prepared by Hahn et al. (1956), resembles CuCr2S4 and CuCrzSe4. It is a normal spinel (Colominas 1967), which can be prepared in a pure state like CuCrzSe4. The lattice parameters are given in table 1. CuCr2Te4 is a ferromagnet (Lotgering 1964b) with a Curie temperature Tc = 365 K and a saturation m o m e n t / ~ = 4.93/~B/molecule (fig. 14 and table 6). Above the Curie temperature the paramagnetic susceptibility follows a Curie-Weiss law with Cm = 2.90 and 0 = 400 K (fig. 15). The Curie temperature is not affected by hydrostatic pressure (Kanomata et al. 1970, Kamigaki et al. 1970).
642
R.P. V A N S T A P E L E
The small shift of the K absorption edge of the Cu ions, as measured by Ballal and Mande (1976), indicates these ions to be monovalent (table 5). Hyperfine fields have been measured on the nuclear spins of 63Cu, 65Cu, 53Cr and tZ~Te (see table 9). Locher (1967) measured the nmr of 63'65Cu in the paramagnetic state and found the Knight shift K to be proportional to the gram susceptibility gg: K = t~Xg with o~ = 0.80 x 103 gcm -3. Extrapolation to the ferromagnetic saturation moment gives a field of 32.5 kOe, in good agreement with the values actually measured. TABLE 9 Hyperfine fields in CuCr2Te4: (a) according to Yokoyama et al. (1967a, b); (b) according to Berger et al. (1968b); (c) according to Ullrich and Vincent (1967); (d) according to Frankel et al. (1968).
63'65Cu
77 K
Extrapol. to 0 K
+38.0 kOe
+39.9 kOe
1.4 K
Ref.
39.9 kOe 53Cr
-145 kOe
lZSTe
-181 kOe _+148 kOe _+160 kOe
-151 kOe 151.1 kOe -187.5 kOe
(a) (b) (a) (b) (b) (c) (d)
The Cu content can be strongly enlarged and single-phase CUl+xCr2Te4 with 0 ~< x ~< 1 has been obtained (Lotgering and Van der Steen 1971c). These materials are metallic and ferromagnetic. Figure 26 gives a, Tc and/xf (4.2 K) as a function of x. The crystallographic and magnetic properties can be attributed to a spinel lattice with the excess Cu occupying a part of the tetrahedral sites normally not occupied. QtA) _
,mc(k) ~f
11.30 " ' ~ ~ ~ ~ -
u f
o
-
400
4
200
2
0
0
11.2C
I
11.10 0
0.5
1.0
Y
Fig. 26. Cell edge a, ferromagnetic Curie temperature T~ and ferromagnetic moment /zf of CUl+yCrzTe4, according to Lotgering and Van der Steen (1971c).
SULPHOSPINELS
643
4.10. CuCr2(X ~St)4 with X, X ' = S, Se and Te O h b a y a s h i et al. (1968) o b s e r v e d c o m p l e t e solubility in the series CuCraS4_xSex. Their data agree well with the results of later investigations. T h e cell edge varies linearly with x, but the f e r r o m a g n e t i c Curie t e m p e r a t u r e does not, having a m i n i m u m value at x ~ 1 (fig. 27). T h e magnetic m o m e n t also has an a n o m a l o u s l y low value at x--~ 1 (fig. 28) (Belov et al. 1973, O b a y a s h i et al. 1968), the actual magnetic b e h a v i o u r d e p e n d i n g to a great extent on the firing conditions (Obayashi
!
I oIAI ,0L
..~o
10.2
O ~o ~' Sg ~
Tc(K)
. ..,.~.-"
T
10.0
"~
9.8
LLO
af' 400
Tc
: i ""
360 320 I
I
I
1
2
3
~X
Fig. 27. Lattice parameter and ferromagnetic Curie temperature of CuCr2S4-xSex. (n) Data of Ohbayashi et al. (1968); (×) Data of Riedel and Horvath (1973b); (O) Data of Belov et al. (1973).
5
~3 :a,
2 1 0 0
1
2
I 3 =X
Fig. 28. Ferromagnetic moment at 77 K and 12 kG of CufreS4-xSex, according to Below et al. (1973).
644
R.P. VAN STAPELE
et al. 1968). The anomalies in the X-ray intensities of CuCr2S3Se, observed by Obayashi et al. (1968), were not seen by Riedel and Horvath (1973b), who concluded that no deviations from a statistical distribution of the anions occur. Data on the electrical behaviour have not been published, except by Belov et al. (1973) who reported that the sample with x ~ 1 had a resistivity with a negative temperature coefficient, while the samples with a different composition had a resistivity with a positive temperature coefficient. A satisfactory explanation of the properties of CuCr2S4_xSex has not been given. However, the electronegativity of Se is smaller than that of the S ions. It is possible that the Se ions, substituted for S in CuCr2S4, start to act as traps for the holes in the valence band that are responsible for the metallic conduction and the strong ferromagnetic interaction. It at least suggests that in the case of an extremely strong binding of the holes to the Se ions, one can expect the compound Cu+Cr3+S~-Se - to be a semiconductor with a much lower Curie temperature than CuCr2S4 and CuCr2Se4. A broad miscibility gap has been observed in the series CuCr2Se4_xTe~ (Riedel and Horvath 1973b). Solid solutions are found only in the Te-rich samples with x > 2.8, where the cell edge increases approximately linearly with x.
4.11. CuCr2X4-xYx w i t h X = S, S e or T e a n d Y = Cl, B r or I The anions of sulphospinels can be replaced by halogen ions (Robbins et al. 1968, Miyatani et al. 1968). Starting from the electronic structure of CuCr2X4 discussed in section 4.8, one expects that the electrons produced by a replacement of X 2- by Y- occupy the holes in the valence band and the C r 3+ levels (fig. 21(a)). A semiconductor Cu+Cr~+X3Z-Y- is then expected to be the end of the series of mixed crystals. The Curie temperature of CuCr2X4-xYx is expected to decrease with increasing x, because the strength of the ferromagnetic interaction via the conducting electrons will decrease with the decreasing number of holes in the valence band. Although this behaviour has actually been observed, complications have arisen. A difficulty encountered in the study of these materials is the preparation of chemically pure and stable samples. The following experimental results have been reported. The series CuCr2S¢_xClx shows an increase of the cell edge and the saturation magnetization with x, and a decrease of the ferromagnetic Curie temperature (Sleight and Jarrett 1968). A sample with x ~ 1 and T c ~ 2 1 0 K exhibits an electrical behaviour typical of an impure semiconductor. Miyatani e t al. (1971a) prepared CuCr2Se4-~Clx with 0~<x ~<0.8. The lattice constant increases slowly with x. The Curie temperature decreases with x, but the magnetic moment remains constant at 5/xB/molecule. A sample of CuCr2Se3C1 was found to be ferromagnetic at room temperature but the material was found to be very hygroscopic, which prevented further measurements (Robbins et al. 1968). Recently, the magnetic behaviour of the series CuCr2Se4_xClx with x < 0.6 has been reinvestigated by Yamashita et al. (1979b). Their data confirm the decrease of the Curie temperature. However, the saturation magnetization was found to
SULPHOSPINELS
645
increase with x, which does not agree with the observations of Miyatani et al. (1971a). The series CuCr2Te4_xIx behaves anomalously. The cell edge passes through a maximum as a function of x and the ferromagnetic Curie temperature varies irregularly (Robbins et al. 1968). A M6ssbauer spectrum of i29I in a sample of nominal composition CuCr2Te3I has been reported by Granot (1973). The series CuCr2Se4_xBrx (Robbins et al. 1968) shows the best reproducible properties and is therefore the most extensively investigated system among the halogenide-substituted sulphospinels. The saturation magnetization /xf, the ferromagnetic Curie temperature Tc and the cell edge a are given as a function of x in figs. 29, 30 and 31. The differences in the results of measurements of /xf are considerable, which have to be attributed to impurities. From neutron diffraction experiments, a magnetic moment of 3+0.18/XB was derived for Cr ions in CuCr2Se3Br (White and Robbins 1968). In early papers on CuCr2Se4_xBrx the transition from the metallic to the semiconducting state is reported to take place at x ~ 0.5 in polycrystalline samples (Robbins et al. 1968) or at x ~ 0.8 in single crystals (Sleight and Jarrett 1968). More recent work on polycrystalline samples and single crystals indicates that the transition takes place at x = 0.98 and is accompanied by a sharp decrease of Tc (fig. 30) (Miyatani et al. 1971a). This illustrates again the close connection between the strong ferromagnetism and the metallic conduction. In a recent analysis of the asymptotic Curie temperature and the temperature dependence of the magnetization, Yamashita et al. (1979b) conclude that the first-neighbour C r - C r exchange interaction is only weakly influenced by the metallic conduction, whereas the second-neighbour interaction changes from strongly positive in CuCr2Se4 to weakly negative in CuCr2Se3Br. At the outset it was found that substitutions with x > 1 are not possible. However, more recent work has shown that materials with x > 1 can still be obtained. A single crystal with a = 10.444 A, corresponding to x = 1.06 (fig. 31), was found to be a semiconductor with Tc = 110 K and a band gap of 0.9 eV, as deduced from optical properties (Lee et al. 1973). A series of polycrystalline samples and single crystals from x = 0 to x - 2 could be prepared (Pinko et al. 1974). Figures 30 and 31 give a and Tc. In this series the largest a (10.444 A) and
61jdf
~'1 / ///+'1
(.uB)~ b
0
02
0.Z+
0.6
+
I
08 1 ~X Fig. 29. ]Ferromagnetic moment of CuCr2Se4 ~Br~; (a) in 10 kOe at 4 K, Robbins et al. (1968); (b) for 0.1 ~< x ~< 0.5, /xs = (5.0 + x) ~B, Sleight and Jarrett (1968); (c) Miyatani et al. (1971a).
646
R.P. VAN STAPELE i
o
&O0
Tc(K)
~.+ O ~+~"
3O0
\ x~ I
I I
4-
200
100
x 0
,
,
,
,
,
,
,
02_
0.4
0.6
08.
10
1.2
1.4
,
,
x
16 1.8 =X
2.0
Fig. 30. Ferromagnetic Curie temperature of CuCr2Se4-xBrx (symbols as in fig. 31).
10.46 10.44
x
10.42
[]
o
x x
x x
"E 10.40
t-I
x
,,F
x
+ +e
G~ 410
[3
10.38
+
O £.3
1036t 10.34]_~
o
uu~ u
,
o12
,
,
d4'o:6'o18'
~
1'.2
,
114 1'.6 P-X
, ,
,
118
2
Fig. 31. Cell edge of CuCr2Se4_xBrx according to: (0) Robbins et al. (1968); (C)) White and Robbins (1968); ([~) Sleight and Jarrett (1968); (+) Miyatani et al. (1971a) and (x) Pink et al. (1974).
SULPHOSPINELS
647
lowest Tc (84 K) of the halogen-substituted sulphospinels have been measured on a chemically analyzed sample with the composition Cu0.99CrzSe2.mBr2.02. Deviations from the stoichiometry according to CuyCr2Se4_zBr, with 0.8 ~< y ~< 1.2, 0 ~< x ~<2 and 0 ~ ( z - x ) ~ 0 . 2 have been found upon variation of the preparation conditions. Not all spinels are stable in air. Those with y < 1 are, but the spinels with y > 1 are not. The unstable spinels could be stabilized by means of a treatment with NH4OH, which mainly extracts the excess Cu. The Cu content of stable spinels depends on the Br content. It is always less than 1, with a minimum of y = 0.78 at x ~ 1 (fig. 32). The origin of this behaviour is not known. Since electridal and magnetic measurements have not been carried out, it is not possible to discuss the valencies in these complicated materials. Magnetostriction (Unger et al. 1974) and hysteresis loops (Unger 1975) have been measured on some CuCr2Se4_xBr~ single crystals.
0
1
~× Fig. 32. Composition of stable compounds CuyCr2Se4-zBrx,according to Pink et al. (1974).
5. Ferromagnetic and antiferromagnetic semiconductors 5.1. General aspects In this section we will treat the normal spinels ACr2X4 (X = S or Se) with
diamagnetic Zn 2+, Cd 2+ or Hg 2+ on A sites and magnetic Cr 3+ on B sites. The existence of this kind of compounds was discovered by Hahn (1951). The spinels CdCrzS4 and CdCrzSe4 exhibit the rare combination of quite strong ferromagnetism and semiconductivity (Baltzer et al. 1965, Menuyk et al. 1966). For this reason they have been investigated more than any other of the sulphospinels. In particular the influence of the magnetic ordering on the electrical and optical properties is the subject of many papers. Before treating the compounds separately we will discuss some general aspects. The first spinels of this type to be investigated were ZnCrzS4 and ZnCrzSe4. They are antiferromagnets and are anomalous in that they have a positive asymptotic Curie temperature 0. The corresponding oxyspinels ZnCr204 or
648
R.P. VAN STAPELE
MgCrzO4 exhibit a normal antiferromagnetism and have a strongly negative 0. The anomalous behaviour of the non-oxidic compounds has been attributed to the combination of a ferromagnetic nearest-neighbour interaction between the Cr 3+ ions and antiferromagnetic superexchange CrXXCr interactions at larger distances (Lotgering 1964b). The difference in sign of 0 for X = O and X = S or Se has been attributed (Lotgering 1964b) to a superposition of a ferromagnetic 90 ° Cr3+X2-Cr3+ superexchange interaction via the X 2- ion (Kanamori 1959) and an antiferromagnetic exchange interaction caused by the direct overlap of the d orbitals of the two Cr 3+ ions. The possibility of the latter interaction mechanism was anticipated (Kanamori 1959, Goodenough 1960, Wollan 1960) before a clear-cut example of it was known. In the oxyspinels the CrZ+-Cr3+ distance is small (2.94A in ZnCr204) so that a strong d - d overlap gives a dominating negative interaction. As a consequence of the much larger distance in the sulphospinels (3.53 A for X = S and 3.71 A for X = Se) the negative interaction is weakened so that the positive superexchange dominates. This is demonstrated in a plot of 0 versus a (fig. 33). The increase of 0 with increasing lattice parameter or Cr-Cr distance fits with the behaviour of a much wider class of Cr compounds with a dominating 90 ° C r - C r superexchange interaction (Rtidorf and Stegemann 1943, Bongers 1957, Lotgering 1964b, Baltzer et al. 1966, Menyuk et al. 1966, Bongers and V a n Meurs 1967, Motida and Miyahara 1970). The strength of the various terms that contribute to the 90 ° Cr3+-Cr3+ interaction has been determined in a detailed analysis of the optical spectrum of Cr 3+ pairs in Cr-doped ZnGa204 spinel (Van G o r k o m et al. 1973). The interaction - J S a " Su between the spins $ of two nearest-neighbour Cr ions a and b is the result of nine interactions -J~jsi • sj between the spins si of the three electrons in
M:Cd,Hg 200 100
--
o
0
,/ *--0~ x~
,t'×--s / 10 of-A) 11
100
200
300
Z,00
/ x=0
Fig. 33. Asymptotic Curie temperature versus lattice parameter of the compounds MCr2X4.
SULPHOSPINELS
649
the d states day, d~z and dax of ion a and the spins sj of the three electrons in the d states dby, dbyz and d~x of ion b. Due to the symmetry of a pair of nearestneighbour Cr ions there are four independent interactions among the nine £j: J~, the direct interaction between spins of electrons in the dxy orbits; J,~, the superexchange interaction between electrons in d states overlapping with the same ligand p state; J', the superexchange interaction between electrons in d states overlapping with two orthogonal p states of the same anion and Jc, the interaction between electrons in d states overlapping with p states on different anions (fig. 34). The direct interaction was indeed found to be by far the strongest (Jd = -561 cm-1), while J= = - 1 0 5 c m -1, J'c = +117 cm -1 and Jc = +39 cm -1. The existence of antiferromagnetic interactions MXXM via two anions X appears from the antiferromagnetic ordering in many layer structures, in which layers of magnetic ions M are separated by double anion layers. The sulphospinels under considerations are ferromagnetic or antiferromagnetic and the kind of ordering is determined by the relative strength of the positive MXM and negative M X X M interactions. The occurrence of both ferromagnets and antiferromagnets shows that the positive and negative interactions in sulphospinels are in equilibrium. From this it can be concluded that the M X X M interactions are about ten times weaker than the MXM interactions (Lotgering 1964b). It is difficult to derive the strength of the exchange interactions from the observed magnetic properties. The attempts that have been made, all except one, have been based on simplifying assumptions with regard to the more distant interactions. Lotgering (1965) analyzed the data of ZnCr2Se4, calculating the
dby
° ~ l
~~'-y o
b
Jo:dxy-dxy
~
~
,-y
dyz Jc
P~ dbz dyz -Pz ond dyz-Pz o
b
Z
- c / I d;x
x L.-"I
J.~ : dzx-Pz- y~
J~
d~×-p=± Px-dby
Fig. 34. (a) The negative interactions in the 90 ° Cr3+-Cr3+ superexchange. (b) The positive interactions in the 90 ° Cr3+-Cr3+ superexchange.
650
R.P. VAN STAPELE
interactions J1, J2, J3 and J4 from the asymptotic Curie temperature, the pitch of the observed helix a n d the magnetic susceptibility on the assumption that J3 = J4. (We use the notation of table 10 and fig. 35.) Plumier (1966a, b) used the same data to calculate J1, J2 and J3. Baltzer et al. (1966) used the interactions J1, J2, J4 and J5 and neglected J3 in a high temperature expansion of the magnetic susceptibility to calculate the Curie temperature. Assuming all the more distant interactions to be equally strong (e.g. K =-/2 = J4 = Js) they calculated J1 and K from the Curie temperature and the asymptotic Curie temperature for the ferromagnets CdCr2S4, CdCr2Se4 and HgCr2Se4 and the metamagnet HgCr2S4. A similar approximation has been made in a multi-sublattice molecular field analysis of these compounds (Holland and Brown 1972). However, the impressive analysis given by Dwight and Menyuk (1967) showed that the magnetic properties are very sensitive to the strength of J2 . . . . ./6 and that the validity of results obtained using simplifying assumptions is doubtful. They analyzed the stability of the various classical spin ground states, minimizing the Heisenberg exchange energy, and found that in the specific case of ZnCr2Se4 a spiral ground state with the observed properties can exist if the values of the interactions J~ . . . J6 fall inside a limited
TABLE 10 Notation of pairs of octahedral ions in the spinel lattice (fig. 35) and of exchange constants. Notation
According to
BoB1 BoB2 BoB3 BoBa Wo W1 W2 W3 J WJ UJ U'J.
BoB5 W4 VJ
BoB6 U2J
J1
J5
J6
J2
J3
J4
Baltzeret al. (1966) Lotgering (1965) Dwightand Menyuk (1967) this work
133
i
/
,
,
A
I
© [30 Fig. 35. Octahedral sites and anions in the spinel lattice.
e. 136
SULPHOSPINELS
651
region. In a similar analysis the stability at T = 0 of various possible spin configurations has been systematically investigated by Akino and Motizuki (1971) with the restriction that J3 = J4 and J6 = 0. Applying the Goodenough-Kanamori rules to the more distant exchange interactions Dwight and Menyuk (1968) expected a negative sign for J3, J4 and J6, a positive sign for Js, whereas the sign of J2 remained uncertain. However, a direct determination of the strength of the more distant exchange interactions between Cr 3+ ions in Cr-doped ZnGa204 by means of electron spin resonance revealed all interactions to be negative. The constants J~ of the exchange interactions -J~so" si were found to be: J 2 = - 0 . 9 4 c m -1, J 3 = - l . 2 2 c m -1, Y4=-0.80cm -I, Js = -0.45 cm -1 and J6 = -0.55 cm -1 (Henning 1980). The compounds under discussion are semiconductors, the behaviour of which is usually not intrinsic but determined by small deviations of the stoichiometry or the presence of impurities in small concentrations. The most striking property is a strong influence of the magnetic ordering on the resistivity and magnetoresistance in certain n-type compounds, e.g., in suitably doped CdCr2S4 and CdCr2Se4. Measured as a function of temperature these quantities show a maximum close to the ferromagnetic Curie temperature. These phenomena are due to the interaction between the spins of the charge carriers and the spins of the Cr 3+ ions. A generally accepted mechanism has not been found, and which of the proposed models applies depends on the type of conduction and the strength of the interaction between the spin of the Cr 3+ ions and that of the charge carriers. If the conduction is in a broad band and if the interaction between the spin of the charge carriers and the Cr 3+ spins is relatively weak, so that the influence of the charge carriers on the magnetic behaviour of the Cr 3+ spin system can be neglected, the theory of Haas (1968) applies. It describes the dependence of the number of charge carriers on the temperature and the strength of an applied magnetic field as it is due to the splitting of the conduction band and donor or acceptor levels in the exchange field from the Cr magnetization (Bongers et al. 1969). The scattering of the charge carriers at the spin disorder in the Cr spin system gives the carriers a mobility that can also be strongly dependent on the temperature and the magnetic field strength (Haas 1968, Patil and Krishnamurthy 1978, Aers et al. 1975). Both effects can give rise to a peak in the resistivity at the Curie temperature and to a negative magnetoresistance with a maximum at the Curie temperature. The critical behaviour of the resistivity has been studied theoretically by Alexander et al. (1976) and Balberg and Helman (1978). If the interaction between the spin of the charge carriers in a broad band and the Cr spins is sufficiently strong, the magnetic state of the Cr spin system changes and a magnetic polaron can exist. In this state the charge carrier is surrounded by a cloud of magnetic polarization of the Cr spins. Yanase et al. (1970) and Yanase (1972) have discussed the conditions for the stability of the magnetic polaron state. They find the magnetic polaron to be stable in a region around the Curie temperature, where it has a much smaller mobility than the original charge carrier would have had. Qualitatively, this can explain the observed anomalies in the electrical resistivity. The entropy of the polarized Cr spins gives rise to an
652
R.P. V A N S T A P E L E
anomalous thermoelectric power and, as Yanase (1971) has pointed out, this can explain the observation by Amith and Gunsalus (1969) that a maximum in the resistivity of Cdl-xInxCr2Se4 coincides with a minimum in the thermoelectric power. In the case of an impurity conduction influenced by the magnetic ordering, Yanase and Kasuya (1968a, b) and Kasuya and Yanase (1968) proposed the model of the magnetic impurity state. In this model the spins of the Cr ions, which are neighbours of an occupied impurity state, are polarized by the exchange interaction between the spin of the impurity electron and the Cr spins. This stabilizes the occupied impurity state and the stabilization energy will increase towards the Curie temperature, where the Cr spin system is highly susceptible. This leads to an activation energy that is maximum at the Curie temperature. Application of a magnetic field will decrease the activation energy. The model of the magnetic impurity state explains in this way a maximum in the resistivity and a maximum negative magnetoresistance at the Curie temperature.
T A B L E 11 Magnetic data of the semiconductors MCr2X4: the asymptotic Curie temperature 0, the ferromagnetic Curie temperature Tc or the antiferromagnetic N6el temperature TN, the molar Curie constant Cm and the ferromagnetic moment /zr. References: (1) Menyuk et al. (1966), (2) Lotgering (1956), (3) Plumier et al. (1975), (4) Lotgering (1964b), (5) Von Neida and Shick (1969), (6) Baltzer et al. (1966), (7) Srivastava (1969), (8) Hastings and Corliss (1968), (9) Le Craw et al. (1967), (10) Eastman and Shafer (1967).
Compound ZnCr2S4
0 (K)
Tc (K)
TN (K)
18 _+8
Cm
m (/xB/molecule)
3.34 18
CdCr2S4
152 156
HgCr2S4
142
84.5 86
3.70 3.8
5.15/./ 5.55 (,/ 6.02 co)
3.62
5.35 (a~
84
ZnCr2Se4
115
CdCr2Se4
204 210 172
HgCr2Se4
200
36.0 - 6 0 (c~ 36.1 -20 20 105 (dl 129.5 130 140 127.7 129_+2 106 105.5
Ref. (2) (1) (6) (1) (5) (7) (6)
(8) (7) (4) (1) (3)
3.54
3.82 3.66 4.48
5.62 (a) 5.6 (,/ 5.98 _+0.4 ~e~
3.79
5.94 -+ 0.04 5.64 (a)
(6) (1) (9)
(7) (10) (6)
(7)
(a) At 4.2 K in 10 kOe. co)At 1.5 K. (c)A spiral spin configuration in zero field. (d) A spiral spin configuration at T < 21 K, antiferromagnetic microdomains at T > 21 K. (e)At 1.5 K in 15 kOe.
SULPHOSPINELS
653
Effects of the magnetic ordering have also been seen in optical properties. The generally observed p h e n o m e n o n is an anomalous shift of the optical absorption edge (Busch et al. 1966, Harbeke and Pinch 1966) to a higher energy, as in CdCrzS4, or to a lower energy, as in CdCrzSe4. The interpretation of these observations depends heavily on the nature of the absorption at the edge. If a broad conduction band plays a role in the transition, a red shift of the absorption edge can be explained by the spin splitting of the band due to the exchange interaction between the Cr spins and the spin of the excited electron. Rys et al. (1967), Haas (1968) and Kambara and Tanabe (1970) have discussed this mechanism in detail. The critical behaviour of the band gap in this case has been treated by Helman et al. (1975) and Alexander et al. (1976). Helman et al. (1975) included the influence of an applied magnetic field. Callen (1968) has suggested another mechanism in which the shift of the absorption edge arises from a change of the band energy due to exchange striction, which distorts the lattice. The shift of the edge can have either sign, but it is estimated to be too small in all cases of interest, as we will discuss later on. White (1969) has pointed out that the absorption edge due to an indirect transition between the valence band and the conduction band can show a shift to the blue below the Curie temperature. Nagaev (1977) argued that a blue shift can arise from interband s-d exchange. Since the magnetic, the electrical and the optical properties and their mutual relation depend strongly on the detailed composition of the compounds, we will review in the following each of the compounds separately. The magnetic data are summarized in table 11".
5.2. ZnCr2S4 ZnCr2S4 is a normal (Hahn 1951) spinel (Natta and Passerini 1931) with lattice parameters, as given in table 1. In the paramagnetic region Lotgering (1956) observed above 100 K a CurieWeiss behaviour with 0 = 18 _+8 K and a molar Curie constant Cm = 3 . 3 4 - 0.06. According to Menyuk et al. (1966) the Cr spins order antiferromagnetically below TN = 18K. A b o v e TN Stickler and Zeiger (1968) observed a paramagnetic resonance with g ~ 2 and an antiferromagnetic resonance at lower magnetic fields below Ty. The zero-field antiferromagnetic resonance frequency follows an S = 3 Brillouin function fairly well. The antiferromagnetic spin structure is not known. A flat spiral, as observed in ZnCrzSe4, does not seem to fit the neutron diffraction spectrum of ZnCr2S4 (Stickler and Zeiger 1968). Bouchard et al. (1965) found the compound to be a semiconductor with p (300 K) = 5 x 10 l° f~cm and an activation energy q = 0.59_+ 0.03 eV at higher temperatures. The samples measured by Albers et al. (1965) had a much smaller resistivity and a small positive Seebeck coefficient. The cold-pressed samples studied by Lutz and Grendel (1965) had a p-type conduction with acceptor states 0.5 to 0.8 eV above the valence band. Doping with W for Cr or with In for Zn can compensate the p-type conduction. Above 200°C the activation energy in undoped samples is 1.5 eV, which is considered to be the band gap energy. * S e e n o t e s a d d e d in p r o o f (d) o n p. 737.
654
R.P. V A N S T A P E L E
5.3. CdCr2S4 is a normal (quoted by Hahn 1951) spinel (Passerini and Baccaredda 1931). Crystallographic data are given in table 1. As shown in fig. 36, the lattice constant a decreases in a normal way down to 100 K, but increases slightly below that temperature (Martin et al. 1969, Bindloss 1971 and G6bel 1976). More striking is the anomalous increase of the width of the X-ray diffraction lines (to A a / a ~ 10-3) observed by G6bel (1976) in CdCr2S4 and other sulphospinels below 200 K. This broadening is not correlated with the magnetic behaviour of the substances, and G6bel (1976) concludes that the spinel structure becomes rather soft at lower temperatures so that weak random stresses can give rise to remarkable random strains. The ferromagnetism of CdCr2S4 was discovered by Baltzer et al. (1965) and Menyuk et al. (1966). In the paramagnetic state the Curie constants are close to the value 3.75 for trivalent Cr ions (table 11). However, the moment in the saturated ferromagnetic state is often found to be less than the expected 6 txs per molecule (table 11). The observed moments depend strongly on the stoichiometry and the purity of the samples. For example at 1.5 K the single crystals grown by Von Neida and Shick (1969) have 3.01/xB per Cr ion in the ferromagnetic saturation. The asymptotic Curie temperature 0 is appreciably higher than the ferromagnetic Curie temperature (table 11). Baltzer et al. (1966) have analyzed this on the basis of a simplified model for the interactions between the Cr 3+ moments (see CdCr2S4
10.28
10.27
*d 10.26 113
g 10.2s u
.~ 10.24 O J
10.23
I I iiii i i
10.22 / I
I
I
I
200
300
400
I
I
I
500 600 700 T (K) Fig. 36. Lattice constant of CdCr2S4 versus temperature, according to Martin et al. (1969) (I), Bindloss (1971) (--) and G6bel (1976) (O). 0
100
SULPHOSPINELS
655
section 5.1). They find J/k = 11.8K for the nearest-neighbour interaction - 2 J S i ' N and K / k = - O . 3 3 K for the next-nearest-neighbour interactions - 2 K 8 i . ~. These values should be regarded with some caution since the results are expected to be very sensitive to the suppositions about the more-distantneighbour interactions (Dwight and Menyuk 1967). Under hydrostatic pressure the Curie temperature decreases at a rate dTJdP = -0.58 K/kbar, which corresponds to the value dTJda = +46 K / A for the rate of increase of T~ with the lattice parameter a (Srivastava 1969). The dependence of the magnetic moment on the details of the composition has been investigated by Pinch and Berger (1968). Annealing a polycrystalline sample with a magnetic moment of 5.79/xB (at 4.2 K and 10 kOe) for 46 h between 800 and 900°C in a sulphur pressure between 30 and 60 atm, they observed a small increase to a magnetic moment of 5.84/XB, while a reduction treatment in hydrogen at 800°C for 72h resulted in a smaller decrease to 5.73#B. They attribute these variations to Cr 2+ ions that charge-compensate the sulphur deficiency and that couple their magnetic moments of 4~B antiparallel to the moments of the Cr 3+ ions. They obtained larger variations by replacing Cd z+ with In 3+. At 4.2 K and 10 kOe polycrystalline samples of Cdl-xInxCr2S4 with x up to 0.15 showed a magnetic moment per molecule that decreased at a rate close to --7XtXB, corresponding to the replacement of 3 tXB of Cr 3+ parallel to the magnetization by 4 txB of C1a+ antiparallel to the magnetization (fig. 37). Pinch and Berger (1968) observed that the rate of approach to saturation was smaller the larger the In concentration, which they attributed to an increasing magnetic
6
-'X.
-5 o
-6 E ~5
\\'~
^Cdl_ x InxCr 2 $4
\
\
\
Z
o\ \
E 0 ~E
\ \ \ CdCr2-xInxS~ \
\
\ 3
\ \
=F 0
i
I 0.1
I
[
0.2 X
Fig. 37. Magnetic moment of Cdl xInxCr2S4 (Pinch and Berger 1968) and of CdCr2-xInxS4 (I.otgering and Van der Steen 1971a) at 4.2 K and 10 kOe.
656
R.P. VAN STAPELE
anisotropy, expected for Cr 2+. These results were in keeping with the existence of Cr 2+ in the inverse spinels CrIn2S4 and CrAlaS4 (Flahaut et al. 1961). However, Lotgering and Van der Steen (1969, 1971a, b) in a study of the paramagnetic properties of the latter compounds, found that the Curie constant corresponded to Cr 3+ instead of Cr 2+ and showed that the single phase compounds were the metal-deficient spinels Crs/9M16/9[[]l/3S4 3+ 3+ (M = A1 or In). Moreover, they discovered that the magnetization of CdCrzS4 decreased surprisingly fast if they replaced magnetic Cr 3+ ions by diamagnetic In 3+ ions in CdCr2_xInx 3+ 3+$4 (fig. 37). It is seen that the magnetic behaviour is comparable to that in Cdl_xInxCr2S4, though no Cr 2+ is present. The decrease of the ferromagnetic moment with x has been attributed by Lotgering and Van der Steen (1971a, b) to spin canting around the In ions due to negative exchange interactions between next-nearest Cr neighbours (see section 5.1)*. Two conclusions can be drawn from these experiments. The first is that the divalent state of chromium is not stable in CdCrz84. The second is that the ferromagnetic ordering in CdCr2S4 is easily disturbed. This last property makes it dangerous to use the magnetization of substituted CdCr2S4 as a measure of the magnetic moment of the substituted ions, as Robbins et al. (1969) had done. These authors prepared the spinels Cd0.sIn0.zCrl.80M0.2S4 with M = Co or Ni and CdCrl.sM0.2S4 with M = Ti and V. From the change in magnetization they concluded that the coupling between the spins of Ni 2+ and Co 2+ and the Cr 3+ spins is negative, while Ti 3+ and V 3+ appear to have no magnetic moment. Not only the magnetic moment, but also the ferromagnetic resonance spectra have been found to depend on the sample (Berger and Pinch 1967). Pinch and Berger (1968) studied the 9.49 G H z ferromagnetic resonance spectra of vapourgrown single crystals at 4.4 K. In the "as-grown" state the angular dependence o f the field for resonance was anomalous with sharp peaks in the [111] directions, while the line width was also anisotropic with a sharp maximum in the same direction. The angular variation could not be described by the usual cubic anisotropy constants K1 and /(2. Heating of the crystals in a sulphur p r e s s u r e reduced the anisotropy and produced samples with a small K~ = 3.8 x 103 erg/cm 3 and K2 = 1.3 x 10 3 erg/cm 3 and an isotropic line width. On a single crystal, exposed to air for 1½ years, Arai et al. (1972) measured at 9.5 G H z and 4.2 K an angular variation of the resonance field, corresponding to K1 = 1.6 x 10 4 erg/cm 3, and from the shift of the resonance fields while applying a uniaxial stress along the [110] direction they measured magnetostriction constants Am = - 2 . 9 x 10 -5 and h~oo= - 4 . 7 x 10-5. The observed variations in the magnetic anisotropy were attributed to the action of Cr 2+ ions, which could be present in non-stoichiometric crystals. However, Hoekstra and Van Stapele (1973) recognized the similarity between the angular variation of the anomalous resonance spectra and their spectra of Fe 2+ doped CdCr2S4 (Hoekstra et al. 1972, Hoekstra 1973). They showed that a small amount of 7 x 10 .4 tetrahedrally coordinated Fe 2+ per formula unit can explain the resonance spectra of the "as-grown" crystals of Pinch and Berger (1968). Hoekstra and Van Stapele (1973) also showed that Cr a+ ions on octahedral sites in the spinel lattice are * See notes added in proof (e) on p. 737.
SULPHOSPINELS
657
expected to give rise to peaks in the resonance field and the line width in the [110] and [112] directions, unless a static or a dynamic Jahn-Teller effect quenches most of the orbital moment. Anomalies in the [110] and [112] directions are not, however, specific to Cr2+; they can also be due to ions, such as Fe z+ on octahedral sites. In the ferromagnetic resonance spectrum at 9.5 G H z and helium temperatures of an "as-grown" single crystal of CdCr2S4 Hoekstra and Van Stapele (1973) actually observed small peaks in the [110] and [112] directions, additional to strong anomalies in the [111] directions, due to 7 x 10-5 tetrahedral Fe 2+ ions per formula unit. If the small peaks are due to Cr 2+ ions, their concentration is low: 2 x 10 -5 ions per formula unit. Single crystals of CdCr2S4, prepared from very pure starting materials, such that the Fe concentration was too small to be detected spectrochemically (<0.0006% by weight), had a weak anisotropy (K1 = +1 x 103 erg/cm 3) and Alll = - 2 × 10 -5, whereas A100 was found to be negative and one order of magnitude smaller (Hoekstra 1974). These values are in reasonable agreement with theoretical estimates of the magnetic properties of octahedral Cr 3+ ions (Hoekstra 1974). Studies of the paramagnetic resonance have been reported for polycrystalline samples (Samokhvalov et al. 1973, Stasz 1973, Shumulkina 1975, Shumilkina and Obraztsov 1975) and for single crystals (Krawczyk et al. 1973, Kaczmarska and Chelkowski 1977, Zheru et al. 1978). The g factor was observed to have a temperature-independent value close to 1.99 (Samokhvalov et al. 1973, Krawczyk et al. 1973, Kaczmarska and Chelkowski 1977). With the temperature decreasing towards the ferromagnetic Curie temperature the line width starts to decrease and passes a sample-dependent minimum, after which the resonance line broadens as the temperature approaches the Curie temperature. The increase of the line width at higher temperatures is attributed to Raman processes involving local phonons (Krawczyk et ak 1973). CdCrzS4 is a semiconductor. The cold-pressed samples studied by Lutz and Grendel (1965) had a p-type conduction, whereas the high density (99.6%) polycrystalline samples used by Lehmann and Robbins (1966) had an n-type conduction with a Seebeck coefficient of -601xV/K and a room temperature conductivity of 5 x 10-4 (Ocm) -1. The log o- versus T -~ plot was slightly curved, so that an activation energy could n o t be given, and did not show discontinuities around the Curie temperature. Like the samples of Lehmann and Robbins the polycrystalline hot-pressed samples studied by Larsen and Voermans (1973) did not show discontinuities in the conductivity around the Curie temperature either. These authors also measured the magnetoresistance and found only a slight decrease of the resistivity (less than 2 percent in a magnetic field of 7 kOe) at temperatures around the Curie temperature. Heat treatment of the samples in a high sulphur pressure led to high resistivities, whereas heat treatment in a low sulphur pressure decreased the resistivity and lowered the activation energyl which can be understood in terms of annihilation and formation of sulphur vacancies, that give rise to shallow donors. Samples of Cd0.98Ga0.02Cr254 have an n-type conduction and show in the ferromagnetic state an anomalous decrease of the resistivity with decreasing temperature (Bongers et al. 1969, Larsen and Voermans 1973). The maximum in the
658
R.P. V A N S T A P E L E
resistivity around the Curie temperature, which combines with a large and negative magnetoresistance in the same temperature region, has been ascribed by Bongers et al. (1969)to scattering of electrons in a broad band by a disorder in the Cr spin system and to a change in the concentration of charge carriers due to spin splitting of the conduction band (see section 5.1). However, Larsen and Voermans (1973) showed that the temperature at which the resistivity and the magnetoresistance are maximum depends on the heat treatment of the sample (figs. 38 and 39) and they concluded that the conduction in the ferromagnetic state is determined by electrons in an impurity band formed by Ga 3+ levels, whereas at high temperatures the conduction is dominated by electrons ionized in a broad conduction band. The impurity conductivity decreases with increasing temperature, because of the increasing stabilization of the magnetic Ga impurity state (see section 5.1), and the resistivity will be maximum at the temperature where
1012
~ b
1010
103/Tc (3
108 u
> 106
y
J
to 0) Or"
10 ~
102
100
C
Z, 6
8 10 12 1/-, 16 103/T (K-1)
Fig. 38. Resistivity of CdCr2S4 (a) annealed in a low sulphur pressure and of Cd0.98Ga0.02Cr2S4 (b) a highly compensated sample after annealing in a low sulphur pressure and (c) another sample without annealing, according to Larsen and Voermans (1973).
SULPHOSPINELS
659
1.0 0.8 ~- 06
e
0.1., 0.2 I
0
60
80
I
100 120 T(K)
t
I
1L0
I
I
160
Fig. 39. Magnetoresistanceof Cd0.98Ga0.02Cr2S4, accordingto Larsen and Voermans (1973)((b) and (c) see caption fig. 38). the conduction mechanism shifts from impurity conduction to band conduction. Although no definite explanation of the phenomena has yet been given, it is clear that the electrical transport properties show signs of an exchange coupling between the spin of the charge carriers and the Cr spins. Such effects have also been observed in optical properties, such as absorption and reflection spectra, photoconduction, magneto-optic spectra and Raman scattering, to which we will now turn our attention. A b o v e 2 eV the optical absorption of CdCr2S4 rises steeply. Towards longer wavelengths the absorption edge has a long tail with a complicated temperaturedependent structure (Busch et al. 1966), which also depends on the doping and the stoichiometry (Miyatani et al. 1971b). The absorption coefficient in the tail is so large that the optical density of the 4 x 10_3 cm thick single crystal studied by Harbeke and Pinch (1966) increased at room temperature to log(Io/I)= 3 at 1.57 eV. The position of the " e d g e " shifts to higher energies at lower temperatures, while a structure between 1.6 and 1.7eV develops most strongly between say 120 and 50 K. In the literature this behaviour has been known as the "blue shift of the band edge", but it was soon recognized that part of the absorption at energies below 2 eV is due to crystal field transitions of Cr 3+ and that the transitions between the valence band and the conduction band occur at higher energies (Berger and Ekstrom 1969, Wittekoek and Bongers 1969, 1970). All the lower energy crystal field transitions 4A2g~ 2Tlg + 2Eg' 4A2g i.) 4T2g' 4A2g__+2T2g' 4A2g~ 4Tlg have been observed. Their energies are listed in table 12 and we have indicated them at the left hand side of fig. 40. The transition 4A2g---~4Tlg has only been observed in the polar magneto-optic Kerr effect spectrum (Wittekoek and Rinzema 1971), where it occurs at the same energy (2.29eV) as in the absorption spectrum of Cr-doped CdIn2S4 (table 12). The other crystal field transition observed in the magneto-optic Kerr effect is 4A2g---~2T2g , but this transition,
R.P. V A N S T A P E L E
660
T A B L E 12 Crystal field transitions of Cr 3+, observed in CdCr2S4 and CdIn2S4: Cr 3+. Energy (eV) Transition
CdCr2S4
4A2g --> 2Tlg , 2Eg
1.64 1.62 1.61
4A2g -~ 4T2g
1.82
CdIn2S4: Cr 3+
Reference
1.85
Harbeke and Pinch (1966) Berger and Ekstrom (1969) Larsen and Wittekoek (1972) Berger and Ekstrom (1969) Koshizuka et al. (1978a) Larsen and Wittekoek (1972) Wittekoek and Bongers (1969, 1970) Berger and Ekstrom (1969) Koshizuka et al. (1978a) Wittekoek and Rinzema (1971) Larsen and Wittekoek (1972) Wittekoek and Rinzema (1971) Wittekoek and Bongers (1969, 1970)
1.76
4A2g -~ 2T2g
2.14
4A2g ~ 4Tig
2.12 2.1 2.29 2.29
- 2.60
••,otoconduction edge
2.50 2.LO
Z'A2 ~,,STlg ~-.-.-.
2,30 220
Z'A2-~2T2g
~
2.10 [~
g 2.o0 c~,
C,C"
LU
1.90 .
.
.
.
1.80
1.70 4A2-~Tlg ,2Eg~--~
Tc '~i
100
1.60 I
200
I
300 T IK)
i
LO0 5OO
Fig. 40. Energy of the transitions observed in CdCr2S4 as a function of temperature ( A, B and C, Berger and Ekstrom 1969, - - - - Wittekoek and Bongers 1969 and 1970, - . . . . . Wittekoek and Rinzema 1971, ,,~ Larsen and Wittekoek 1972, ~ A', A~ and C', Koshizuka et al. (1978a).
SULPHOSPINELS
661
together with the transitions from 4A2g t o *Tzg, 2Tlg and 2Eg, has also been observed in the absorption spectrum of thin films (less than llxm) (fig. 41, Berger and Ekstrom 1969, Koshizuka et al. 1978a) and in the photoconduction of poly: crystalline undoped n-type samples (fig. 42, Larsen and Wittekoek 1972). At 6 K the latter authors also observed a weak luminescence at 1.6eV due to the transition 2Tlg , 2Eg-->4A2g (fig. 43). A progression of 330+30cm 1 phonons, possibly associated with this transition, had been observed in absorption by Moser et al. (1971). The lower part of the absorption edge, as observed by Harbeke and Pinch (1966), consists of the crystal field transition 4A2g--">2ylg , 2Eg and the wing of the crystal field transition 4Azg~ 4T2e (Wittekoek and Bongers 1969, 1970). The blue shift of the edge is attributed by Wittekoek and Bongers (1969, 1970) to sharpening of the 4A2g--> 4T2g transition at lower temperatures. Berger and Ekstrom (1969) are of the opinion that another transition (A) is also present. It shows a small blue shift (fig. 43) and has a moderate oscillator strength of f ~ 10-3. Because no other crystal field transitions are expected in this region, Berger and Ekstrom (1969) conclude that A may be due to an indirect band-to-band transition or to a weak charge transfer transition. Below the Curie temperature the spectrum in the region around 2 eV shows even more structure. A peak C appears that shifts to lower energies with decreasing temperature (Berger and Ekstrom 1969, Wittekoek and Bongers 1969, 1970). The oscillator strength is small ( f ~ 10-4) and the absorption is strongly circularly polarized (fig. 41, Berger and Ekstrom 1969). In spite of the small oscillator strength, the transition has a considerable Kerr rotation (Wittekoek and
1.5
Z,A2 ~¢- 1.3
.2 1.1 O
I
A2
C
/.i/
0.9
Y...
0.7
_.// ,,,'"-
.~'
/ "~..~J" Am ----- + I
/ 0.5
-1
¢
---
0
I
1.7
,"'I
j
I
1.8
I
.r
I
I
19 2.0 Energy (eV)
I
21.1
I
2.2
Fig. 41. Circularly polarized absorption spectra of CdCr2S4 at 2 K in a magnetic field of several kOe, according to Berger and Ekstrom (1969). The m = +1 spectra are displaced by 0.12 to higher optical density.
662
R.P. V A N S T A P E L E
2.5
Energy (eV)
2.0
I
I
E
1.5
I
i
z' A2-.-~2 T2
T12E
cD 2 r~
& LL D o O
1
~5 ro_
~A2-~4T2
I
L
0.5
0.6
L
I
I
0.7
0.8
Wavelength (microns) Fig. 42. Photoconductivity of a polycrystalline undoped n-type sample of CdCr2S4 as a function of the wavelength in zero magnetic field and in a transverse magnetic field of 6 kOe, according to Larsen and Wittekoek (1972).
3.0 2.5 i
2.0
i
Energy (eV) 1.5
i
I
1.2 i
1.0 i
E
0.8 i
i
4A2--~4T2 2.0 / / ' 4 A 2 - ~ 2 T 2 ~ 4^
"41.0:/o / /
2T
2 E-
V i ~IR line of Cr3+ i. 200 x enhanced
A /
g E i
0.4
i
I
0.6
0.8 1.0 1.2 Wavelength {microns)
1.4
1.6
Fig. 43. Luminescence at 6 K (--) and excitation spectrum at 80 K (- . . . . . ) of undoped CdCr2S4 powders, according to Larsen and Wittekoek (1972).
SULPHOSPINELS
663
Rinzema 1971). These authors also found the position of the structure in the Kerr effect spectrum to depend on heat treatment and doping. This indicates that peak C is not due to an intrinsic excitation. A possible explanation is a transition from the valence band to an F-centre-like state of an electron bound to a sulphur vacancy (Harbeke and Lehmann 1970, Lehmann et al. 1971, Natsume and Kamimura 1972). In a repetition of the absorption measurements reported by Berger and Ekstrom (1969), Koshizuka et al. (1978a) found essentially the same structure in the region around 2 e V (see fig. 40). Apart from the peak C, however, these authors found a second red shifting peak A2, which was also observed by Berger and Ekstrom (1969) (fig. 41) at 2 K and which has the opposite circular polarization of peak C. Koshizuka et al. (1978a) interpret A2 and C as components of a transition to an exchange split state, separated at 4.2 K by 0.07 eV. The onset to strong absorption occurs at B (figs. 40 and 41). Berger and Ekstrom (i969) attribute this edge to transitions between the valence band and the conduction band. Its position 2.3 eV at low temperatures agrees well with the band gap of CdS (2.58eV) and of CdIn2S4 (2.2 eV). The direct edge in the photoconduction has been observed by Larsen and Wittekoek (1972) to occur at the slightly higher energy of 2.5 eV (fig. 40). The edge shifts weakly to higher energies at lower temperatures and shows no trace of a shift to the red in the ferromagnetic state. At still higher energies a transition at 3.4 eV has been found by Wittekoek and Rinzema (1971) as a strong resonance in the polar Kerr effect spectrum. This transition, which is responsible for the dispersive part of the Faraday rotation between 0.8 and 10 ~m (Wittekoek and Rinzema 1971, Moser et al. 1971) has been attributed by Wittekoek and Rinzema to a charge transfer transition of an electron from sulphur p orbitals to an empty Cr orbital. Reflection spectra (Wittekoek and Rinzema 1971, Fujita et al. 1971, Ahrenkiel et al. 1971), thermoreflectance spectra (Iliev and Pink 1979) and measurements of the reflectance d i c h r o i s m - o n e measures in a magnetic field 2 [ ( R + - R _ ) / ( R + + R )], where R+ and R_ are the specular reflectivities for right-handed and left-handed circularly polarized l i g h t - (Ahrenkiel et al. 1971, Pidgeon et al. 1973) have provided data that generally agree with the results reviewed above. This is also the case with the Faraday rotation of thin films of CdCr2S4, measured by Golik et al. (1976) in the visible region. Values of the refractive index have been derived by Wittekoek and Rinzema (1971) from the reflectivity and from interference patterns in thin hot-pressed polycrystalline samples by Moser et al. (1971) and Lee (1971), who measured n = 2.8 in the wavelength range of 2-10 Ixm. The data, which agree roughly, are given in fig. 44. Additional data were reported by Pearlman et al. (1973). T o conclude this review of the spectral properties of CdCr2S4, we return to the study of the photoconductivity reported by Larsen and Wittekoek (1972). The fact that they observe the crystal field transitions in the photoconductivity (fig. 42) reveals that excited C r 3+ ions are not stable with respect to either an indirect minimum of the conduction band or a direct minimum, to which optical tran-
664
R.P. V A N S T A P E L E
L
1
c o E~
"53
~ X ~ x ~ . x ~ x _ _
x c
'2 I
100
[
,
I
500 1000 W o v e l e n g t h (nm)
I
I
5000
Fig. 44. Refraction index of CdCr2S4; ( 0 ) data of Wittekoek and Rinzema (1971) at 80 K; (x) data of Moser et al. (1971) at 300 K.
sitions from the valence band are forbidden, at 1.6 eV or less above the valence band. The destabilized Cr ions give rise to holes in the valence band, which accounts for the observed photoconductivity. Larsen and Wittekoek (1972) observed that the photoconductivity depended strongly on the strength of an applied magnetic field (fig. 42), which they attribute to a hole mobility influenced by spin disorder scattering (Haas 1968). A strong fluorescence line observed at 0.9eV (fig. 43), which has an excitation spectrum showing the crystal field transitions, indicates that the holes can recombine with electrons from an acceptor state at 0.9 eV above the valence band (Larsen and Wittekoek 1972). Finally we mention that the photoconduction experiments have been extended to Ga-doped CdCr2S4 samples (Larsen 1973) and that the results corroborate the conclusion that the photoconduction is mainly due to photo-excited holes, which are responsible for the observed dependence on magnetic field and temperature. We now turn to the phonon structure of C d C r 2 S 4 . White and DeAngelis (1967) have shown that in normal spinels four vibrations (Tlu) are infrared and five (Alg + Eg + 3T2g) Raman-active. The four Tlu vibrations have been observed in infrared absorption and reflection studies and the observed frequencies at room temperature are given in table 13". Below the ferromagnetic Curie temperature at 79 K, the phonon frequencies are increased by only about 1%, while the oscillator strength of the highest two vibrations have not changed markedly (Lee 1971). This is at variance with the Raman-active modes, some of which show a strongly temperature-dependent intensity. Harbeke and Steigmeier (1968) were the first to observe this and by scattering light quanta of 1.96 eV they observed the Raman lines listed in table 14 (Steigmeier and Harbeke 1970). All lines were found to have an intensity that varies with temperature. This has to do with the temperature-dependent absorption at 1.96 eV, which is the only cause of the variation of the intensity of the light scattered by the Eg vibration (Raman line C), whereas * See notes added in proof (f) on p. 737.
SULPHOSPINELS
665
TABLE 13 Frequencies of the four infrared-active phonon modes of CdCrzS4. Frequencies (cm-1) at room temperature 381 385 376.9-+0.2 385
332 240 337 321.6-+0.3 347 234
Reference 97.0
Lutz (1%6), Lutz and Feh6r (1971) Riedel and Horvath (1969) Lee (1971) Moser et al. (1971)
TABLE 14 Raman lines of CdCr2S4, quoted from Steigmeier and Harbeke (1970). Line A C D E F G H I
Assignment 300 K 40 K mixed Eg T2g mixed Alg
mixed Eg T2g mixed mixed
Raman shift (cm-1) 300 K 40 K 101 -+2 256 -+2 280 -+ 1.5 351 _+2 394 -4-2 -460 -506 -600
105 _+2 257 + 2 281 -+ 1.5 353 -4-2 396 -+2
Rel. intensity 40 K 12 44 49 74 112 6 5 6
it is only partly the origin of the variation of the intensities of the other R a m a n lines. W h a t has strongly attracted attention was the observation of Steigmeier and H a r b e k e (1970) that the t e m p e r a t u r e variation of the ratio of the intensity of the lines A, D, E and F to the intensity of line C resembles that of the correlation function (Si • S j ) / S 2 of n e a r e s t - n e i g h b o u r Cr spins Si and S/. H o w e v e r , K o s h i z u k a et al. (1976, 1977a) subsequently s h o w e d that the way in which the R a m a n intensity varies with t e m p e r a t u r e d e p e n d s on the wavelength of the scattered light. A b o v e the ferromagnetic Curie t e m p e r a t u r e m a r k e d resonances are not observed, whereas at 15 K especially the R a m a n lines E and F show a strong r e s o n a n c e at 650 rim, which m e a n s that light q u a n t a are maximally scattered if their energy is a b o u t 1.9eV. A s can be seen in fig. 40, this is the wavelength region w h e r e the red-shifting absorption has been observed. T h e absorption in this region is strongly circularly polarized and Koshizuka et al. (1978a, b) o b s e r v e d that the R a m a n scattering of circularly polarized light d e p e n d e d systematically on the sense of the polarization of the incoming and the scattered light if the sample was placed in a magnetic field. These experiments were d o n e at 40 K with a Kr laser at 1.92 e V and with an A r laser at 2.01 e V in an a t t e m p t to observe the influence of the right-handed circularly polarized absorption C and the lefth a n d e d circularly polarized absorption A2 (figs. 40 and 41). A t 1.92 e V the effects of the polarization were m u c h m o r e p r o n o u n c e d than at 2.01 e V but neither spectra s h o w e d a c o m p l e t e right-left s y m m e t r y (see also Koshizuka et al. (1980)).
666
R.P. VAN STAPELE
An analysis of the phonon frequencies in terms of a simple force model has been given by Briiesch and D'Ambrogio (1972). These authors as well as Baltensperger (1970) and Steigmeier and Harbeke (1970) discussed the influence of magnetic ordering on the Raman and infrared-active phonons on the basis of the ion position dependence of the superexchange interaction. Suzuki and Kamimura (1972, 1973) formulated a phenomenological theory of spin-dependent Raman scattering, starting from the general form for a polarizability tensor that depends on the Cr spins. They obtained an integrated intensity I ( T ) IR + M ( S o . S~)/$212 with a temperature dependence that is determined by the signs of R and M and their relative magnitude. The values of R and M can be calculated for specific microscopic Raman scattering mechanisms. Suzuki and Kamimura (1973) did this for phonon-modulated transfer integrals and oildiagonal exchange and were able to explain the temperature dependence observed by Steigmeier and Harbeke (1970), mentioned above. However, the experimental situation turned out to be much more complex and a more definite theoretical picture will have to await more complete experiment data. Nuclear magnetic resonance studies of CdCrzS4 have been made by Berger et al. (1968a, 1969a) and Stauss (1969a, b). The spectrum of 53Cr is complex and has been analyzed by Berger et al. (1968). They described the spectrum by v = (y]2rr)Hi~o + [(y]2rr)Ha, is + vo(rn - ½)](3 cos 2 0 - 1), where u is the frequency, 3' the gyromagnetic ratio of 53Cr, m = 3, ½, _ ½for the three m = +1 transitions between the I = 3 nuclear spin states of 53Cr and 0 is the angle between the local trigonal axis of the octahedral site and the magnetization in the randomly oriented Weiss domains. At 4.2 K the isotropic hyperfine field Hiso = - 1 9 1 . 0 k O e , the anisotropic hyperfine field Hanis= +2.07kOe and the quadrupole interaction vQ = eZqQ/4h = 0.95 MHz. Berger et al. (1969a) discussed the strength of /-/~so in connection with the strength of the nearest-neighbour superexchange interaction, while Stauss (1969b) stressed the importance of transferred spin density in the Cr 4s states in the process that lowers Hiso from its purely ionic value. The hyperfine field on the 111Cd and H3Cd nuclei of the diamagnetic Cd ions is large, namely +167.0kOe at 4.2K (Stauss 1969b) and +168.10kOe at 1.4K (Berger et al. 1969a). This field is mainly due to transfer of spins from the filled Cr 3d states to the unfilled Cd 5s state. A density of 2.0% of an electron spin in the Cd 5s state can explain the observed strength of the hyperfine field (Berger et al. 1969a, Stauss 1969a, b).
5.4. HgCr2S4 HgCr2S4 is a normal spinel (Hahn 1951). Crystallographic data are given in table 1. In the paramagnetic region the magnetic susceptibility follows a Curie-Weiss law with a molar Curie constant close to the spin-only value 3.75 of Cre (table 11).
SULPHOSPINELS
667
As observed by magnetic measurements (Baltzer et al. 1966) and by neutron diffraction (Hastings and Corliss 1968a, b) the compound behaves as a metamagnet with an ordering temperature of 36.0 K or 60 K respectively. At 4 K the magnetic structure is a simple spiral, with a propagation vector parallel to the symmetry axis of the spiral and directed along a particular cube edge in a given domain. The spiral wavelength is 42 A at 4 K. It increases with temperature (fig. 45), reaching a value of about 90 A at 30 K, and shows little further variation up to the N6el point (Hastings and Corliss 1968a, b). Application of a magnetic field up to 4 kOe along a cube edge produces a growth of the domains in which the propagation vector is parallel to the magnetic field. In higher fields the spiral collapses in the field direction, saturating at about 10 kOe (Hastings and Corliss 1968a, b). These observations are consistent with the magnetization curves (fig. 46) measured by Baltzer 100
c-
8O c o [D
60 -8 t_ 5. O3
4O
10
20
30
40
T(K)
Fig. 45. Temperature dependence of the spiral wavelength of HgCr2S4 (Hasting and Croliss 1968b).
°1 ~5
o
0
0
2
4 6 8 Applied field H (kOe)
10
Fig. 46. Magnetizationof HgCr2S4 as a function of applied field and temperature (Baltzer et al. 1966).
668
R.P. V A N S T A P E L E
et al. (1966). The saturation magnetization measured by these authors at 4.2 K and 10 kOe corresponds to 5.35 p~B/molecule. This is lower than the theoretical 6/~B, probably for reasons of stoichiometry. Srivastava (1969) estimated the shift of the transition temperature with pressure by measuring the relative shift of the mutual inductance as a function of temperature and pressure. He did not observe anomalies around 60K, but reported the ordering temperature to be 36.1 K, in agreement with the value of 36.0 K given by Baltzer et al. (1966). This temperature increases with pressure at a o rate dTJdP = +0.14K/kbar, which means that dTJda = - 1 0 K/A. The pressure dependence, however, differs in sign from that of the Curie temperatures of CdCrzX4 and HgCrSe2 (Srivastava 1969). There have been hardly any measurements of the electrical properties. Baltzer et al. (1965) have reported that HgCrzS4 is a semiconductor. The behaviour of the absorption edge of HgCr2S4 has been studied by Harbeke et al. (1968) and Lehmann and Harbeke (1970). Using relatively thick samples (33 and 20 p~m) they did not observe any structure nor any change in the shape of the edge between 4 K and 600 K. The position of the edge, defined by the energy at which the absorption coefficient had risen to 1500 cm -1, showed a large red shift and a further shift to longer wavelength if a magnetic field was applied (fig. 47). Lehmann and Harbeke (1970) explain the temperature dependence and the magnetic field dependence in terms of the properties of the spiral spin structure and the nearest-neighbour spin correlation function. They also note that the magnetic field-induced shift at 8 kOe has a maximum at (60.0-+ 1) K, which they take to be the true N6el temperature. The infrared absorption spectrum of HgCrzS4 has been measured by Lutz (1966) and Lutz and Feh6r (1971). At room temperature four infrared-active vibrations were observed at 376, 336, 227 and 71.4 cm-L
1.5
1.L @ ,m
u
1233
H =0/.f'" . . . . . ~"-- .... . /" /
1.3
~ ~.2 c
1.1 i ! :
8kOe
1.0 0
[
I
100
200
I
I
~
300 400 500 Temperature (K)
I
600
Fig. 47. Energ y gap of HgCr2S4 as a function of t e m p e r a t u r e for H = 0 and H = 8 kOe, according to L e h m a n n and H a r b e k e (1970).
SULPHOSPINELS
669
Hyperfine fields on various nuclei have been measured by Berger etal. (1969a, b). At 1.4 K the isotropic hyperfine field on the nuclear spin of 53Cr w a s found to be -189.9 kOe (Berger e t a l . 1969a). The nmr lines of mgHg and 2°1rig were found to be very anisotropic, which is due to a reduction of symmetry by the spiral spin structure of HgCr2S4. The isotropic hyperfine field at the Hg nuclear spins, which corresponds to the high frequency peak, amounted to +524.3 kOe at 1.4 K (Berger et al. 1969a), while the centre of the Hg spectra was found at 507 kOe (Berger et al. 1969b). This means a spin density of 2.0% for an electron spin in the Hg 2+ 6 s state (Berger et al. 1969a). The same spin density was found in the 5s state of Cd 2+ in CdCr2S4 (see section 5.3). The much larger hyperfine field on the Hg nuclear spins is due to the larger amplitude of the 6s function on the site of the Hg nucleus.
.5.5. ZnCr2Se4 ZnCr2Se4 is a cubic spinel (Hahn and Schr6der 1952). Values of the lattice parameters are given in table 1. Using neutron diffraction, Plumier (1965) found the compound to be less than 1% inverse. The cell edge has been measured as a function of temperature down to 4 K by Kleinberger and De Kouchkovsky (1966). The compoufid is cubic down to 20.4 K. Below that temperature it shows a small tetragonal distortion (fig. 48), which is connected with the magnetic ordering. Magnetic data are summarized in table 11. Above 300 K, in the paramagnetic state, the magnetic susceptibility follows a Curie-Weiss law with a molar Curie constant Cm = 3.54 and an asymptotic Curie temperature 0 = +115 K (Lotgering 1964b). Ce(l edge (~,1
acubic
io.L8~ If
0
I
20
I
I
AO
I
I
60
I
/ 810 L
i
100
l
i
120
Temperature {K} Fig. 48. Cell edge of ZnCr2Se4 as a function of temperature, according to Kleinberger and De Kouchkovsky (1966).
In spite of the positive 0, the Cr spins order antiferromagnetically at 20 K as indicated by the minimum in the reciprocal susceptibility, shown in fig. 49. Subsequent neutron diffraction experiments by Plumier (1965) showed that the magnetic structure is a simple spiral with a propagation vector along the symmetry axis of the spiral and directed along a [001] axis. The turning angle between the magnetic moments in adjacent (001) Cr planes varies from 42_+ 1 degrees at 4.2 K (Plumier 1965) to 38 degrees at 2 1 K (Plumier et al. 1975b). Plumier (1966a, b) studied the influence of magnetic felds up to 15 kOe on the neutron diffraction
670
R.P.
300
VAN
STAPELE
6
I L~O~
2OO O0
20
100 l
S
/
If
O0
f
J I
200
I
I
z,o0
I
I
I
600 Temperature (K)
I
800
Fig. 49. Molar magnetic susceptibility of ZnCr2Se4, according to Lotgering (1964b). spectrum. His study shows that in zero magnetic field domains occur in which the helical axis is oriented along one of the cube edges. In magnetic fields up to 3 kOe the domains with a preferred orientation of the spiral axis grow. In higher fields a conical spin structure exists with an increasing net magnetization. The magnetization has been measured at 4.2 K in magnetic fields up to 30 kOe and 69 kOe by Lotgering (1965) and Siratori (1971) respectively and in pulsed magnetic fields up to 108 kOe by Allain et al. (1965). The magnetization, shown in fig. 50, saturates at 6.! #B/molecule in fields larger than 64kOe. Hydrostatic pressure shifts the N6el temperature to higher values at the rate dTN/dp = 0.90 x 10-3 K/bar (Fujii et al. 1973). As Lotgering (1964b) has stressed, the combination of a positive asymptotic Curie temperature and an antiferromagnetic behaviour is a clear indication of the important role of the more distant exchange interactions in ZnCr2Se4. Attempts have been made to extract quantitative information about the strength of the various exchange interactions from the paramagnetic data, the low temperature spin structure and its initial magnetic susceptibility. Lotgering (1965) and Plumier (1966a, b) have made such an analysis, assuming J5 = 3"6= 0 (see table 10, and fig. 35) and -/3 = J4. Lotgering (1965) used the experimental values of the turning angle and the asymptotic Curie temperature and calculated J1, J3 and the initial susceptibility Xi as a function of an antiferromagnetic J2 in the range - 7 < Jz/k < 0 K. Under these circumstances J1/k < 3 0 K , -5<J3/k < O K and Xi has a value close to the experimental one. Plumier (1966a, b) used the same experimental data, but calculated the al-
SULPHOSPINELS
671
:D (3 d~ O
E 3
3 E 2 E O ~E
1
I
I
I
I
I
I
I
20 40 60 80 Magnetic field (k0e)
100
Fig. 50. Magnetization versus magnetic field of powder samples of ZnCrzSe4. Curve (a) magnetization at 4.2K, according to Lotgering (1965); curve (b) according to Allain et al. (1%5) and curve (c) magnetization at 4.2 K, according to Siratori (1971). gebraic solution with a ferromagnetic -/2: J1/k = 24.9 K, J2/k = 7.8 K and J3/k = -10.65 K. Dwight and Menyuk (1967) analyzed the stability of the spiral spin configuration, taking into account all the interactions J 1 . . . J6. They showed that neither of these interactions can be neglected. Lotgering's set of interactions lies outside the region where the spiral spin configuration is stable. The values of Plumier are within this region, but Dwight and Menyuk (1967) judge them to be physically unreasonable from the point of view of the mechanism of the superexchange interactions. They do not give a better solution, but mention as an illustrative "zeroth approximation" the following set of interactions: J~/k = +25.4 K, J2/k = +2 K, J3/k = - 7 K, J4/k = - 7 K, Js/k = +1 K and J d k = - 1 K. In a similar analysis A k i n o and Motizuki (1971), who used the restriction -/3 = J4 and J6 = 0, came to the conclusion that the stability of the spiral spin configuration requires a negative J3 and that this stability is increased by a positive .15. Paramagnetic resonance with g = 2 had been observed in powder samples above TN = 21 K by Stickler and Zeiger (1968). Below TN, an antiferromagnetic resonance appeared abruptly in fields stronger than 4 k G , as the paramagnetic resonance line disappeared. The antiferromagnetic resonance faded out at lower fields. T h e antiferromagnetic resonance frequency, extrapolated to zero magnetic field, was found to follow an S = ~ Brillouin function. At the Ndel t e m p e r a t u r e the zero field frequency drops to zero abruptly. The magnetic resonance of single crystals has been studied by Siratori (1971) in the frequency range 38-83 GHz. His theoretical explanation of the frequency and angular dependence of the resonance field at 5.5 K gives the values of the Fourier c o m p o n e n t of the exchange and the magnetic anisotropy energy at three points 0,
672
R.P. VAN
STAPELE
k0 and 2ko in the reciprocal space (k0 is the spiral wave vector). Transformation to local exchange interactions via one and two Se ions gives values for J1 • • • J5 that do not stabilize the spiral spin configuration, from which Siratori concluded that superexchange interactions through more than two Se ions (like J6) cannot be neglected. With the temperature increasing from 5.5 K to 20 K Siratori (1971) observed a shift of the resonance field and a decrease of the angular dependence and the line width. Above 20 K, the resonance field is independent of the direction of the magnetic field, but the shift of the resonance field persists up to about 70 K. Specific heat measurements done by Plumier et al. (1975a, b) indicate that, in addition to a fairly large peak from 17 to 23 K with a mazimum at 20.5 K, two narrower peaks exist at 45.5 K and 105 K. The nature of these extra peaks is not yet clear. Plumier et al. (1975b), studying carefully the neutron diffraction spectrum of a powder sample, observed above 20.5 K broad satellites with angular positions corresponding to a pitch angle ~-/5, indicating that ZnCr2Se4 at such temperatures is a metamagnet with a centred tetragonal cell (a/V'-i, a/~/-i, 5a). The large line width is ascribed to the small size of the reflecting magnetic domains, 53 A ( - 5 a ) between 21 and 45 K and 32 A ( - 5 a / 2 ) between 45 and 105 K. When a magnetic field was applied below 20.5 K, Plumier et al. (1975b) observed that the sharp satellites of the helical spin configuration disappeared at a critical field strength and that broad peaks appeared at higher field strengths. The width and the position of these peaks corresponded to those observed in zero field above 20.5 K. The findings of Plumier et al. (1975a, b) prompted Akimitsu et al. (1978) to study the neutron diffraction of a single crystal and to reinvestigate the differaction on powder samples. They concluded that the broad peaks observed by Plumier can be ascribed to critical scattering, observed in their single crystal experiment in the wide temperature range from 20 to 40 K, and found that there is no reason to place the N6el temperature higher than 21.2K. However, the peaks at 45.5 and 105 K in the specific heat then remain unexplained. Another result of their work that is difficult to explain is the enormous deviation of the magnetic moment of the C13+ ions (1.71/xB) from the 3#B observed in the magnetic measurements. The weak temperature dependence of the turning angle (Akimitsu et al. 1978) and the susceptibility in the propagation direction (Kawanishi et al. 1978) have been correlated with the tetragonal deformation (Kleinberger and De Kouchkovsky 1966) mentioned above and shown in fig. 48. The reciprocal of both quantities was found to depend linearly on ~5= [1 - (c/a)] (Akimitsu et al. 1978, Kawanishi et al. 1978), which was interpreted as being due to exchange interactions with a strength depending on ~5 and the wave vector near the propagation vector of the spiral spin configuration*. The influence of stoichiometry and impurities on the magnetic properties has scarcely been investigated. The single crystals studied by Kawanishi et al. (1978) had a small residual ferromagnetic moment, varying from crystal to crystal. Small amounts of Cu (up to 0.04 per formula unit), substituted for Zn, had been * S e e n o t e s a d d e d in p r o o f (g) o n p. 737.
SULPHOSPINELS
673
reported to lower the N6el temperature from 20 to 11 K, while they decreased the high temperature magnetic susceptibility (Menth et al. 1972). Replacement of Zn by Mn had been reported to increase at 4.2 K the magnetization in magnetic fields up to 80kOe (Siratori et al. 1973). Neutron diffraction experiments on Znl-xMnxCr2Se4 with x = 0.1 showed that the spiral spin structure is not seriously changed by the presence of the Mn ions (Siratori and Sakurai 1975). It was concluded that the Mn-Cr exchange interaction is weakly ferromagnetic. Single crystals of Mn-doped ZnCr2Se4 have recently been reported to have a strong cubic paramagnetic anisotropy (Kawanishi et al. 1979). ZnCr2Se4 is a semiconductor (Lotgering 1964b, Albers et al. 1965). Replacement of 0.02 Zn per formula unit by Cu lowers the resistivity strongly (Lotgering 1968b). This result has been used as an argument for the monovalent state of copper because the replacement of Zn 2+ by Cu + gives rise to holes in the valence band. The miscibility in the series of mixed crystals Znx-xCuxCr2Se4 between the spinels ZnCr2Se4 and CuCr2Se4, which have about equal cell edges, has been reported to be limited to x ~<0.05 (Lotgering 1968b). Complete solubility has been observed in samples quenched from temperatures above 500°C (OkofiskaKozlowska and Krok 1978). These samples have a lattice parameter that varies linearly with x. They are ferromagnetic for x/> 0.2 with a ferromagnetic Curie temperature that varies slowly from 380 K at x = 0.2 to 415 K at x = 1. This behaviour is reminiscent of that of the series CuCrzSe4_yBry (fig. 30). In this system high Curie temperatures occur for 0 ~
'rE 2000
-E
1000 00,; 00I/ [I
0 1.10
I
I
1.20
L
I
I
1.30
Energy (eV) Fig. 51. Absorption coefficientversus energy of ZnCr2Se4(Lehmannet al. 1971).
674
R.P. V A N S T A P E L E
development of a precursor band, which shifts strongly towards the red with increasing absorption coefficient. The strength of this absorption was observed by Lehmann et al. (1971) to vary from sample to sample, indicating that the band has a non-intrinsic origin. It shows nevertheless the effects of the influence of the magnetic structure of ZnCr2Se4. Lehmann et al. (1971) observed that in a strong external magnetic field the position of the peak of the absorption of circularly polarized light in the precursor band depends on the sense of the rotation (fig. 52) and on the strength of the magnetic field (fig. 53). At 4.2 K, the latter curve has a
1.4
-
1.3
-
H--0
t_ co9
1.2 (3 O) 0-
1.1
1.0
= /. I
0.9
I
0
I
i
20
i
40
I
i
I
~
I
/
60 80 100 Temperature ( K )
Fig. 52. A b s o r p t i o n peak position of ZnCr2Se4 as a function of t e m p e r a t u r e in zero field and in 67 k O e for circularly polarized light ( L e h m a n n et al. 1971).
1.3
1.2
_~ 1.1
o~ 1.0
0.£
t
i
Li0
20 Megnetic
i
I
I
I
60 80 field (kOe)
Fig. 53. A b s o r p t i o n peak position of circularly polarized light of ZnCr2Se4 as a function of magnetic field strength at 4.2 K ( L e h m a n n et al. 1971).
SULPHOSPINELS
675
shape that is nearly identical to the magnetization curve, as measured by Allain et al. (1965) and given in fig. 50. Lehmann et al. (1971) proposed that the absorption in the precursor band be attributed to transitions from a fourfold valence band state with degeneracy lifted by the magnetic field to a spin-polarized singlet state, probably connected with Se vacancies. Finally, Riedel and Horvath (1969) have measured the infrared spectrum of powder samples of ZnCr2Se4. They observed at room temperature two infraredactive vibrations at 287 and 304 cm -1.
5.6. CdCr2Se4 CdCr2Se4 is a normal spinel (Hahn and Schrrder 1952). The lattice parameters are listed in table 1. The cell edge has been measured as a function of temperature by Martin et al. (1969), Bindloss (1971) and G6bel (1976). The results are shown in fig. 54. Whereas CdCr2S4 expands anomalously below its ferromagnetic Curie temperature, CdCr2Se4 is seen to contract in a normal way in the magnetically ordered state. As in CdCr2S4, anomalous broadening of the X-ray diffraction lines has been observed in CdCrzSe4 at lower temperatures, but not correlated with the magnetic phase transition ( G r b e l 1976), which suggests the existence of inhomogeneous lattice distortions. G r b e l (1976) also observed a shift of the anion parameter u from 0.389 at room temperature to 0.392 at 77 K, and he remarks that such a shift of u changes the atomic distances and bond angles considerably. This can be an important fact with a view to the understanding of other phenomena observed at low temperatures, like the red shift of the optical band edge. Banus and Lavine (1969) have reported that CdCrzSe4 transforms under high pressure and temperature to a monoclinic structure related to the defect NiAs structure. The physical properties of the monoclinic structure were found to differ completely from those of the spinel structure. CdCr2Se4 is a ferromagnet (Baltzer et al. 1965, Menyuk et al. 1966). In the paramagnetic region, the magnetic susceptibility obeys the Curie-Weiss law with an asymptotic Curie temperature of about 200 K and a Curie constant close to the spin-only value 3.75 of Cr 3+ ions (table 11). The ferromagnetic Curie temperature is 130 K and the saturation magnetization measured at 4.2 K in a magnetic field of 10 kOe amounts to 5.6/zB per molecule (Baltzer et al. 1966, Menyuk et al. 1966). The data given by Baltzer et al. (1966), measured on powder samples, differ from the single-crystal data reported by LeCraw et al. (1967). The latter authors measured a saturation moment of 2.99 + 0.2 txB per Cr 3+ ion, very close to the expected 3/xB, but their Curie constant is too high (table 11). The details of the magnetic properties apparently depend on the purity and the stoichiometry of the samples, and Pinch and Berger (1968) observed a small increase in the magnetization of their polycrystalline samples after annealing in excess Se. The ferromagnetic Curie temperature of In-doped CdCrzSe4 single crystals was found not to be affected by heat treatments in various atmospheres (Treitinger et al. 1978a).
676
R.P. VAN STAPELE
10.77
10.76
o~ 10.75 .,.go
g 10.7z, o 1.3
::- 10.73 'r
II
10.72
I 10.71
10.70~g 0
I
I
100
200
I
I
I
I
300 400 500 600 Temperature (K) Fig. 54. Lattice constant of CdCr2Se4 versus temperature, according to Martin et al. (1969) (I), Bindloss (1971) ( ) and G6bel (1976) (---). The values of the ferromagnetic and the asymptotic Curie temperature have been used by Baltzer et al. (1966) to estimate the strength J of the nearestneighbour exchange and the strength K of the more-distant-neighbour interactions (see section 5.1), which resulted in J/k = 14 K and K/k = - 0 . 1 0 K. The critical behaviour of CdCr2Se4 has been studied by Miyatani (1970), who measured the magnetization at temperatures close to the Curie temperature in magnetic fields between 6 0 e and 18 kOe. He was able to describe the temperature dependence of the spontaneous magnetization o-0 by o-0 ~ ( T - T 0 ) ~, where Tc = 127.67 + 0.005 K and /3 = 0.447 + 0.03, and that of the zero-field susceptibility X0 by ,to ~ (T - T*)% where T* = 127.7 -+ 0.2 K and 7 = 1.27 -+ 0.02. At the Curie temperature, the magnetic field dependence of the magnetization o- was given by o- ~ H 1/8 with 6 = 4.1 _+0.2. Within the experimental error, these values confirm the scaling law prediction y =/3(6 - 1). U n d e r hydrostatic pressure the Curie temperature decreases. Srivastava (1969) o measured dTddp = - 0 . 8 2 K/kbar, which corresponds to dTdda = +66 K/A, using the measured value of the compressibility. This agrees well with dTddp = - 0 . 7 6 K/kbar, measured by Fujii et al. (1970). Whereas these measurements were done with a mutual induction technique under pressures up to 10 and 6 kbar respectively, Shanditsev and Yakovlev (1975) used the much higher pressures of 60 and 90 kbar and measured the increase of the resonance line width to locate the Curie temperature. In this way they found dTddp = - 0 . 4 4 K/kbar. It should
SULPHOSPINELS
677
be noted, however, that Banus and Lavine (1969) observed traces of the highpressure modification of CdCr2Se4 at room temperature with pressures higher than some 80 kbar. The magnetic anisotropy of CdCr2Se4 is rather weak and dependent on the purity and the stoichiometry of the crystals. From~- ferromagnetic resonance measurements at 9.49 GHz, Berger and Pinch (1967) found the cubic anisotropy constant K1 to have values between 2.2 x 103 and 1.8 x 10 4 erg/cm 3 at 4.4 K. The temperature dependence differed considerably in the various crystals. The smallest uniform precession line width found was 37 G. A much smaller line width of 9.5 G was observed at 13 G H z and 4.2 K by L e G r a w et al. (1967). The crystals used by these authors has a g-factor of 1.983 + 0.003 and a K1 of approximately 1.5 x 104 erg/cm 3 at 4.2 K. Pinch and Berger (1968) observed an increase of the anisotropy after the crystal had been annealed in a hydrogen atmosphere, and a decrease to a very small anisotropy after an anneal in a selenium atmosphere. The resonance line width was isotropic and the angular dependence of the resonance field was normal. In contrast with these observations, the crystals studied by Gurevich et al. (1972) showed at 8.9 G H z a ferromagnetic resonance spectrum with an angle-dependent line width and resonance field. In one crystal the angular variation was anomalous, and it could not be described by the cubic anisotropy constants K1 and K2. The anomalous fe~/ture is the strong increase of the resonance field in the (111) directions, which was also found in the resonance spectrum of CdCrzSe4 crystals, in which a small amount of Fe 2+ was substituted for Cd (Gurevich et al. 1975). Although this suggests that contamination with Fe 2+ ions plays a role, Bairamov et al. (1977) prefer to think in terms of the Cr ions. This is based on the magnetic anisotropy of Ag-doped CdCr2Se4 crystals. Larson and Sleight (1968) observed that the positive cubic anisotropy of undoped crystals was strongly reduced to IKII < 0 . 7 x 103 erg/cm 3 in Ag-doped crystals, while K~ actually changed sign in more heavily doped crystals, reaching the value - 1 . 1 x 10 4 erg/cm 3 for 1.34 mole % Ag (Bairamov et al. 1976). When crystals doped with 1.5mole % Ag are annealed in vacuum a positive anisotropy is restored (Bairamov et al. 1977). The influence of Ag-doping on the ferromagnetic resonance line width has been investigated by Ferreira and Coutinho-Filho (1978). Eastman and Sharer (1967) measured the magnetostriction of a single crystal with a high ferromagnetic saturation moment of 2.97#B per Cr 3+ ion. Ferromagnetic resonance at 4 . 2 K and 23 G H z gave a cubic magnetic anisotropy constant K1 = 3.5 x 103 erg/cm 3. From the shift of the resonance field, caused by a compressional uniaxial stress, they found A~00=(2.6_+0.5)x10 -6 and Am = - ( 2 8 + 4 ) x 10-6. From the measured temperature dependence they concluded that Am is of single ion origin. Studies of the paramagnetic resonance have been reported for polycrystalline samples (Shumilkina 1975) and for single crystals (Samokhvalov et al. 1973, Krawczyk et al. 1973, K6tzler and Von Philipsborn 1978). The g-factor was found to have a temperature-independent value of 1.99 (Samokhvalov et al. 1973, Krawczyk et al. 1973), while the temperature dependence of the line width is characterized by a broad minimum around 200 K. The increase of the line width
678
R.P. VAN STAPELE
at higher temperatures has been attributed to Raman processes involving local phonons (Krawczyk et al. 1973). The critical increase of the line width, as the temperature decreases towards the Curie temperature, was found to depend on the strength of the applied magnetic field, quantitatively confirming the results of mode-coupling calculations in the limit of zero magnetic field (K6tzler and Von Philipsborn 1978). The paramagnetic resonance line width increases when Cd is replaced by Co (Grochulski and Gutowski 1975). Some magnetic properties of CdCr2Se4 are sensitive to light. Lems et al. (1968) discovered this so-called photomagnetic effect in Ga-doped CdCr2Se4. After cooling the crystals in the dark to 77 K (or a lower temperature), they observed that the low-frequency permeability (10 kHz) decreased by a factor of two upon illumination with white light. The return to the original higher-permeability state after the light was switched off was observed to occur at a rate that strongly depended on the temperature (fig. 55). Lems et al. proved experimentally that the lower permeability after illumination is due to a change throughout the material and not to changes local to domain wails. The spectral dependence of the effect roughly coincides with the absorption edge of CdCr2Se4 at 1 Ixm. In a simple model that accounts for the experimental data, stable centres I (probably filled Ga donors) are ionized, giving rise to less stable centres II. The inverse of the change in permeability is assumed to be proportional to the density n of centres II, while the recombination rate is proportional to n 2 as a consequence of the assumption of random recombination (Lems et al. 1968). The high-frequency permeabilty of pure and Ga-doped polycrystalline samples has been reported by Veselago et al. (1972a, b) to show a small decrease upon illumination. The spectral dependence of the effect shows that it starts at the optical band edge. A positive change of the ferromagnetic resonance field of illuminated undoped single crystals has been observed by Salanskii and Drokin (1975). Anzina et al. (1976) have reported that undoped and Ga- and Ag-doped samples show an increase in coercive force and a decrease in permeability when illuminated with white light.
300
light on
77
K
200
~ght
E¢ 100
off
L.2K
0
13_
0
510
I
100
I
150
time Is] Fig. 55. Influence of illumination by "white light" on the low-frequencypermeability of Ga-doped CdCr2Se4, according to Lems et al. (1968).
SULPHOSPINELS
679
Finally, Makhotkin et al. (1978b) studied the influence which illumination by white light and the application of short magnetic field pulses have on the high-frequency (4 MHz) permeability of Ga-doped CdCrzSe4 at 77 K. In the dark the permeability is decreased from 62 to 60 during the 5 ms long magnetic field pulse with an amplitude of 0.08 Oe. Illumination lowers the permeability to 31, but upon the rise and the decay of the magnetic field pulse the permeability increases rapidly to 33, decaying to 31 in about 2 ns. This shows that apart from the photomagnetic changes throughout the material, which reduce the permeability from 62 to 31, a photo-induced pinning of the domain walls exists, which is not apparent from the low-frequency permeability found by Lems et al. (1968). Before reviewing the electrical transport properties of CdCrzSe4, we mention the observation by Salyganov et al. (1973) of a DC electromotive force during ferromagnetic resonance at 77 K of a Ag-doped CdCr2Se4 single crystal. The emf was observed between gold electrodes in the centre and on the edge of the single-crystal platelet. The effect occurred not only during uniform precession, but also during a magnetostatic mode. It was observed that the sign and magnitude of the emf did not depend on the direction of the external magnetic field along the normal to the platelet. The mechanism of the effect is not known, but inhomogeneous heating of the conduction electrons or dragging of the charge carriers by propagating spin waves have been suggested as possible causes of the phenomenon. CdCr2Se4 is a semiconductor (Baltzer et al. 1965). High-density polycrystalline undoped samples have a resistivity that decreases with increasing temperature and the resistivity vs temperature curves do not show any discontinuity at the Curie temperature. This has been observed in undoped samples with p-type conduction (Lehmann and Robbins 1966, Haas et al. 1967, Lehmann and Harbeke 1967, Lehmann 1967, Lotgering 1968b) and in undoped samples with n-type conduction (Larsen and Voermans 1973). Most of the experimental resistivity curves are regularly curved (fig. 56) contrary to that of an n-type single crystal, which was observed to have a weakly temperature-dependent resistivity below the Curie temperature, a region with an activation energy of 0.18 eV between 130 and 310 K and of 0.6 eV between 350 and 800 K (Prosser et al. 1974). Substitution of Ag or Cu for Cd gives rise to strong p-type conduction. The conductivity of Ag-doped CdCrzSe4 decreases monotonically with decreasing temperature either without an anomaly (Haas et al. 1967) or with a change of slope of the log o- vs T ~ curve around the Curie temperature (Lehmann 1967) (fig. 57). The Cu-doped CdCrzSe4 samples studied by Lotgering (1968b) showed a similar change of slope. The Ag-doped crystals investigated by Coutinho-Filho and Balberg (1979) showed a slight "hump" in the resistivity around 130 K. Lehmann (1967) measured the Seebeck coefficient (fig. 58) and the Hall effect of hot-pressed Ag-doped samples and found the holes to have a large Hall mobility (10 to 100 cm2/Vs). The observed rapid decrease of the Seebeck coefficient below 170 K and the maximum of the normal Hall coefficient at 150 K were interpreted by Lehmann (1967) as being due to the onset of impurity conduction at lower temperatures. The magnetoresistance of Ag-doped CdCrzSe4 is small, with an
109
///a
107
>"
5
> 10 :,,.% u3
103
10~
I
2
z,
I
6
1
I
I
8
20 12 1/. 16 IOS/T (K -1 ) Fig. 56. Resistivity of hot-pressed polycrystalline undoped samples of CdCr2Se4: (a) with p-type conduction, according to Lehmann (1967); (b) with n-type conduction, according to Larsen and Voermans (1973); (c) sample b after 60 h at 600°C with Pse = 10-4 mm Hg and quenching to room temperature, according to Larsen and Voermans (1973).
T__ lOq {3
10-2 >,
:z. 10-3 *d D
-~ ~0-~ o O
10-s
@/rc 10-6 2
I
I
L
6
~'l
I
I
10 12 1L 103/T (K q ) Fig. 57. Electrical conductivity of p-type Ag-doped and n-type In-doped CdCr2Se4, according to Lehmann (1967). 680
8
SULPHOSPINELS
681
600
3
_••/•
400
oJ
200 o
0
i
]
300
250
Ag Tc ~
i
i /c
"~
200 150 100" T e m p e r a t u r e (K)
r
/
Fig. 58. Seebeck coefficientof p-type Ag-doped and n-type In-doped CdCr2Se4,accordingto Lehmann (1967).
2.0
0,8
0.6
?o_ 0.4
0,2
0100
~
, 120
I
I 140
l
i 160
i ....
T (K)
Fig. 59. Magnetoresistance of n-type Ga-doped CdCr2Se4 (2% Ga) in a magnetic field of 12 kOe, according to Haas et al. (1967).
anomalous magnetic field dependence at lower temperature (Lehmann 1967). Changes in the sign of the longitudinal magnetoresistance as a function of applied magnetic and electric fields were observed in Ag-doped single crystals (Balberg and Pinch 1972), Strong electric fields influence the properties of Ag-doped CdCr2Se4. The microwave absorption (Solin et al. 1976), the electrical conductivity (Samokhalov et al. 1978) and the magnetization (Samokhalov et al. 1979) decrease, which is attributed to the excitation of spin waves by electron-magnon interaction.
682
R.P. VAN STAPELE
The substitution of In and Ga for Cd gives rise to a strong n-type conduction. Unlike that of the p-type samples, the resistivity of the n-type samples shows a pronounced maximum around the ferromagnetic Curie temperature (fig. 57), while a large and negative magnetoresistance is maximum in that temperature region (fig. 59) (Haas et al. 1967, Lehmann and Harbeke 1967, Lehmann 1967, Amith and Gunsalus 1969, Feldtkeller and Treitinger 1973, Merkulov et al. 1978, Coutinho-Filho and Balberg 1979). The maximum in the resistivity has also been observed in the high-frequency conductivity of n-type Ga-doped hot-pressed samples, where it decreases with increasing frequency (Kamata et al. 1972). Lehmann (1967) and Amith and Gunsalus (1969) also studied the thermoelectric effect (fig. 58) and the Hall effect, and found that the Hall mobility of the electrons was of the order of i cm2/Vs, which is much smaller than that of the holes in p-type samples. The study reported by Amith and Gunsalus (1969) revealed a crucial anomaly, namely the coincidence at 150 K of a secondary minimum of the absolute value of the Seebeck coefficient with the maxima of the resistivity and the absolute value of the Hall coefficient. Amith and Friedmann (1970) concluded that this finding cannot be explained in terms of electrons in a single spin split conduction band which are scattered by the spin-disorder in the ferromagnetic Cr spin system (Haas 1968, Bongers et al. 1969) and these authors proposed a two-band model in which one band is an n-type conduction band and the other a p-type hole band in the band gap. As already discussed at some length in section 5.1, other models have been proposed. In particular the model of the magnetic impurity states seems to be applicable in the case of n-type Ga-doped or In-doped CdCr2Se4 (Larsen and Voermans 1973, Treitinger et al. 1978a). Treitinger et al. (1978a) varied the concentration of Se vacancies of In-doped single crystals of CdCrzSe4 and observed that the height of the maximum of the resistivity and of the magnetoresistance, as well as the temperature at which this maximum occurs, depended on the concentration of the Se vacancies (fig. 60), whereas the ferromagnetic Curie temperature was not affected. They ascribed these properties to conduction in magnetic impurity states at lower temperatures, the conduction at higher temperatures being dominated by electrons in the conduction band. In their study of In-doped CdCr2Se4 Treitinger et al. (1978a) also observed that the line width of the X-ray diffraction lines increases from the value in the as-grown state after annealing in Se vapour and also after annealing in hydrogen. Subsequent annealing in hydrogen after a heat treatment in Se vapour restores the as-grown value, indicating, as Treitinger et al. conclude, that the crystals in their as-grown state have a Se deficit that corresponds to a state of minimal internal stress. The optical absorption spectrum of stoichiometric pure CdCr2Se4 shows no structure between the bands near 17 txm, which are due to overtones of lattice vibrations, and the absorption edge near 1 Ixm (Bongers and Zanmarchi 1968), whereas doped or non-stoichiometric crystals have some characteristic absorption lines in that region (Miyatani et al. 1971b) (fig. 61). Hl/dek et al. (1977) have discovered that a similar absorption spectrum can be induced by illumination with
SULPHOSPINELS
683
T 200 160
107 300
J
i
120
100
i
i
105 3000
~103 400 C
(3-
10 L50C 10-1
10-3
I
I
5
7
103/T {K-1)
9
11
Fig. 60. Resistivity of n-type In-doped CdCr2Se4 with an increasing number of Se-vacancies, obtained by a heating in hydrogen at the temperatures indicated in the figure, after Treitinger et al. (1978a).
0.15
Photon energy (eV) 0.2 0.3 O.Z 0.6 1.0 2.0
i
i
i
i
i
i
JEll
.d c o) 1.3
o
In-doped
c 0 0-
undoped .13
<
110
i
i
8
i
I
6
I
I
~
4
i
2
0
Wave length (/urn)
Fig. 61. Absorption spectrum of undoped and In-doped CdCr2Se4between 0.1 and 1 eV at 78 K ( and 300 K (---), according to Miyatani et al. (1971b). light with a wavelength shorter than the absorption edge. T h e absorption edge shows a structure that has attracted considerable attention. Busch et al. (1966), w h o m e a s u r e d the diffuse reflectance of polycrystalline samples, and H a r b e k e and Pinch (1966), w h o m e a s u r e d the absorption of plane-parallel single-crystalline samples with thicknesses b e t w e e n 15 and 50 Ixm observed that the edge shifts to longer wavelengths at t e m p e r a t u r e s below 200 K (fig. 62). H a r b e k e and L e h m a n n (1970) f o u n d that the strength of the absorption at the lower energy edge d e p e n d s
684
R.P. VAN STAPELE 2.10 2.00
~.
1.90
~"
Ill
L fILl
,
1.50
\ "%
>,,
"
1.40 1.30
~
/,,
-.
/ /
1.20
./..~..
t I
1.10
/Tc 0
Fig. 62.
¢"~
t
100
200
f
i
300 T(K)
400
500
Energy of transitions observed in CdCr2Se4 as a function of temperature: Pinch 1966; (---) Sato and Teranishi 1970), (-.-.-.) Stoyanovet al.
( ) Harbeke (1976).
and
on the sample and that only the lowest energy absorption edge is shifted to the red with decreasing temperature, whereas the higher energy edge is weakly shifted to shorter wavelengths (fig. 63). The intensity at the lower energy edge could also appreciably be changed by a heat treatment (Prosser et al. 1974). Harbeke and Lehmann (1970) concluded that the red-shifting absorption is not due to an intrinsic excitation but most probably to vacancy states. Eagles (1978) explained the absorption profiles observed by Harbeke and Lehmann (1970) at photon energies below 1.6eV in terms of a combination of transitions between the valence band and hydrogen-like local 13 103
c 103 .£ .~ <
130
5.102 I
1.15
Fig. 63. Absorption
1.20
1,25
I
/7
1.30 1.35 Energy (eV)
2911K
1.40
edge of CdCr2Se4 at various temperatures, according to Harbeke and Lehmann
(1970).
SULPHOSPINELS
685
levels and an indirect band-to-band absorption, as suggested by Sakai et al. (1976). In his analysis Eagles also made use of the lower energy absorption data of Shepherd (1970) and the data at higher energies of Sakai et al. (1976). Application of a magnetic field shifts the absorption edge further to the red (Busch et al. 1966, Lehmann et al. 1971 and Hl~dek et al. 1976). Measurements have been done in the Voigt configuration with linearly polarized light and in the Faraday configuration with circularly polarized light (Lehmann et al. 1971, Hlidek et al. 1976 and Koshizuka et al. 1978a). They show that the lower energy edge in the magnetically saturated state is strongly polarized and has a triplet structure consisting of peaks separated by equal amounts for optical transitions with a change in magnetic quantum number m = +1, 0 and - 1 . This splitting was attributed by Lehmann et al. (1971) to a splitting of the valence band by the magnetic field. Reflectance spectra have been measured in a much wider range of photon energies. Ahrenkiel et al. (1971) measured them up to 4 eV, and observed at 4 K a maximum reflectance at 2.0 eV with a weak feature at 2.9 eV. Fujita et al. (1971) observed at room temperature a maximum at 1.9 eV and changes of slope at 1.4, 1.6 and 1.9eV. Itoh et al. (1973) measured at room temperature a maximum reflectivity around 2 e V and sub-bands at 1.6 and 2.9eV. The latter authors observed that the main peak at 2 eV splits into three overlapping peaks at 1.9, 2.0 and 2.1eV, when the temperature is lowered to 80K. Zv~ra et al. (1979) measured the specular reflectivity at room temperature up to 12eV. In their measurements the maximum reflectivity occurred at 1.82eV. They observed additional fine structure at 1.50, 2.6, 3.14, 4.10, 6.30, 7.25 and a triad around 9 eV. A Kramers-Kronig analysis resulted in a real part of the dielectric constant with a maximum at 1.38 eV, in good agreement with the optical absorption edge at room temperature, described above. The imaginary part of the dielectric constant showed a broad maximum around 2.05 eV and additional fine structure, in correspondence with that of the reflectivity. Theses results agree well with those of Itoh et al. (1973). Thermoreflectance spectra of CdCrzSe4 have been measured by Stoyanov et al. (1975) and Taniguchi et al. (1975). Although it is difficult to deduce the positions of the optical transitions from such spectra, the structure around 1.4 and 2.0 eV can be recognized as belonging to the optical absorption edge and the transition at about 2.0 eV, observed in the reflectance spectra. Reflectance magneto-circular dichroism spectra at 4 K show a doublet with opposite sense of polarization at 1.8 and 2.6eV (Ahrenkiel et al. 1971). Sato (1977) also measured the reflectance magneto-circular dichroism at 4 K and found a similar spectrum. A more involved analysis resulted in clear transitions at 1.9, 2.2 and 2.5 eV, a broad structure at 1.3 eV and some weaker transitions around 3 eV. Bongers et al. (1969) published a magneto-optical Kerr effect spectrum, measured at various temperatures between 4 and 140 K (fig. 64). Strong magnetooptical transitions were observed at 1.4, 2.0 and 2.6 eV, which values agree well with those of Sato. The transition at 1.4 eV shows a shift to longer wavelengths at lower temperatures. The Faraday rotation, measured in the transparent region
686
R.P. VAN STAPELE
2O u c~
"B c E
0
to
-20 o
~o
-40
-60
10
14 Weve
I I 2L2 i 18 n u m b e r (cm -1)
1 26 x 103
Fig. 64. Kerr rotation of CdCr2Se4as a function of the wave number at 140 K, 120 K and 4 K, accordingto Bongers et al. (1969).
between 1 and 17 Ixm, is composed of a constant part induced by ferromagnetic resonance transitions and of a large negative part due to an electronic transition at 2.6 eV (Bongers and Zanmarchi 1968). Sato and Teranishi (1970) studied the photoconductivity of undoped p-type single crystals. The spectral dependence (fig. 65) showed a narrow and weak peak, shifting from 1.3 eV at 200 K t o 1.1 eV at 70 K, and a broad and strong peak around 2 eV, which shifts slightly to higher energies with decreasing t e m p e r a t u r e (fig. 62). The results of later investigations of the photoconductivity are similar, but with m o r e detail. Using In-doped n-type single crystals Amith and Berger (1971) and Berger and Amith (1971) observed a red-shifting transition at 1.35 eV at 200 K and at 1.2eV at 1 0 0 K and transitions at 1.4 and 1.SeV, that have temperature-independent positions. Stoyanov et al. (1976) observed in undoped p-type single crystals that at 1.4 eV the peak (A) splits at 200 K into two branches, one shifting to the red and the other to the blue with decreasing t e m p e r a t u r e (figs. 62 and 66). These authors report two broad structures in the spectral dependence of the photoconductivity, one around 1.7 eV (B) and the other around 2.0 eV (C) (fig. 66). At the low energy of about 1.1 eV a shoulder was found, which also showed a shift to the red (fig. 62). T h e picture that emerges from the optical m e a s u r e m e n t s is still confused. There are arguments, however, for assigning the red-shifting precursor absorption to a transition from the valence band to localized vacancy states ( H a r b e k e and L e h m a n n 1970, L e h m a n n et al. 1971) and the part of the absorption edge above about 1.3 eV to an indirect transition from the valence band to the conduction band (Sakai et al. 1976). The m a x i m u m in the reflectivity around 2.0 eV suggests that the direct transitions from the valence band to the conduction band fall
SULPHOSPINELS 1.0
687
{a}
"~ 0.5 :3
3 ~
o
~
1.o
c
I
I
I
I
(b}
@ a2
0.5
0
J
I
1.0
1.5
I
2.0 Energy {eV}
I
2.5
Fig. 65. Spectral dependence of the photoconductivity of CdCr2Se4 at 300 K (a) and 77 K (b), according to Sato and Teranishi (1970). within this energy region (Sato and Teranishi 1970, Ahrenkiel et al. 1971, Sato 1977 and Zvfira et al. 1979). The wavelength dependence of the Faraday rotation finally suggests that the charge transfer transition from the valence band to the empty Cr 2+ 3d states has an energy of about 2.6eV (Bongers and Zanmarchi 1968). At this point the measurements reported by Batlogg et al. (1978) on the pressure dependence of the lower absorptive part of the absorption edge should be mentioned. At room temperature they observed that the edge shifted to higher energies under hydrostatic pressure, and they concluded from the measured value of the pressure coefficient that the edge could not be due to transitions involving s-band states, but that p ~ p interband or p ~ localized state could be reconciled with the observations. Using 100 Ixm thick single-crystalline samples, Balberg and Maman (1977) measured accurately the lower absorptive part of the optical absorption edge at temperatures close to the ferromagnetic Curie temperature. The position of the absorption edge, defined by the photon energy at which the absorption coefficient
688
R.P. VAN STAPELE
(/1 t-
b E0) t_
"(3 "x.
0J
(A C
o 0 ~D c o o 0 r12_
~'
1.5
2.0
Energy (eV) Fig. 66. Spectral dependence of the photoconductivity of CdCr2Se4 at various temperatures, according to Stoyanov et al. (1976).
equals 200 cm 1, was used in a determination of the critical parameters that was based on the theory of Alexander et al. (1976) for the critical behaviour of the direct optical gap of a ferromagnetic semiconductor. N o arguments were given for this assignment, which deviates from the view that the direct edge occurs at about 2 eV (see above). Much discussion has been devoted to the origin of the red shift of the absorption edge. In addition to the studies mentioned in section 5.1 Cfipek (1977) calculated the red shift of an absorption edge due to transitions to localized electronic states on lattice imperfections, influenced by an exchange interaction with the Cr spins. On the other hand, Zvfira et al. (1979) amplify a suggestion made by G6bel (1976) that the shift of the edge is not so much directly due to magnetic exchange interactions as to a magnetostrictive change of the u parameter with temperature. They argue that small changes of the u parameter give rather large variations in bond angles and distances, which are expected to give rise to an appreciable shift of the absorption bands. A small change of the u parameter has indeed been observed by G6bel (1976).
SULPHOSPINELS
689
As a normal spinel, CdCr2Se4 will have four infrared-active phonons and five Raman-active phonons (White and DeAngelis 1967). The frequencies of the infrared-active phonons at room temperature, as measured by far infrared absorption and reflection, are given in table 15. With decreasing temperature the frequencies continuously increase, which is largely due to the thermal expansion (Wakamura et al. 1976b). Below the ferromagnetic Curie temperature there is an additional small anomalous increase in energy (Arai et al. 1971, Br/iesch et al. 1971 and W a k a m u r a et al. 1976b), which arises from an interaction between the phonons and the ordering Cr spins (Baltensperger and Helman 1968, Baltensperger 1970 and W a k a m u r a et al. 1976b). The low-frequency phonon at 75 cm -1 not only shifts in the ferromagnetic state, but also increases in intensity (Wagner et al. 1971 and Brfiesch et al. 1971). Such effects have also been observed in the Raman-active modes. The frequencies of the Raman-active phonons observed by Steigmeier and Harbeke (1970) are listed in table 16. Three of the expected five Raman-active modes have been assigned by Steigmeier and Harbeke: F was observed to have the Alg symmetry, C the Eg and D a T2g symmetry. Brfiesch and D ' A m b r o g i o (1972), who analyzed the phonons of CdCr2Se4 on the basis of a simple force model, assigned T2g symmetry to the lines A and E. The temperature dependence of the frequency of the Raman lines is weak (see table 16) and similar
TABLE 15 Frequencies of the four infrared-active phonon modes of CdCr2Se4. Frequencies (cm 1) at room temperature 292 286.6 288.1 -+0.6 289.3
278 264.5 266.2± 0.2 271.2
188.0 7 4 . 5 189.2 7 5 . 5
Reference Riedel and Horwith (1969) Wagneret al. (1971) Lee (1971) Wakamuraet al. (1976b)
TABLE 16 Raman lines of CdCr2Se4, quoted from Steigmeier and Harbeke (1970). Line A B C D E F G H
Assignment
Raman shift (cm-1) 300 K 10 K
Eg T2g
84-+2 144±2 154± 1 169-+2
Alg
237 ± 2
85-+2 147-+2 158-+ 1 172 -+2 226 -+2 241 -+2 291 -+2 300 -+2
Rel. intensity 50 K 3 3 33 23 2.5 6.5 6 7.4
690
R.P. VAN STAPELE
to that of the frequency of the infrared-active phonons. More intriguing is the temperature dependence of the intensity of the Raman lines. Harbeke and Steigmeier (1968) were the first to notice that the intensity of the line D decreases with temperature in the same fashion as the nearest-neighbour spin correlation function, while the intensity of the lines A, B, C and F were found to be practically temperature independent (Steigmeier and Harbeke 1970). This has led to a number of proposed mechanisms for the coupling between the phonons and the Cr spin system (Baltensperger 1970, Brfiesch and d'Ambrogio 1972), culminating in Suzuki and Kamimura's theory (1973) of spin-dependent Raman scattering. Experimentally, however, the situation turned out to be rather confused. Steigmeier and Harbeke (1970) scattered H e - N e laser light with a photon energy of 1.96 eV, well above the absorption edge of CdCr2Se4. This can give the Raman scattering a resonant character and resonance effects have indeed been observed by Koshizuka et al. (1977a, b), who found the intensity of line C to depend only weakly on the temperature and the incident photon energy, whereas the shape of the temperature dependence of the intensity of the lines D and F relative to that of line C depends closely on the photon energy between 1.8 eV and 2.5 eV. In the ferromagnetic state, at 35 K, the intensity of line D was found to have a pronounced maximum around 2.0 eV, while that of line F had a broad, less pronounced maximum around 2.2 eV. These maxima fall in the region where the reflectivity has a maximum, which has been assigned to electronic transitions near the direct band gap. In the paramagnetic state the main dependence on the incident photon energy has disappeared. However, the results of the same measurement done by Iliev et al. (1978a), disagree completely with these findings. These authors observed that the intensity of line C had a pronounced resonance peak around 2.0 eV both in the paramagnetic and in the ferromagnetic state, the peak being slightly broadened in the ferromagnetic state. The intensity of line D also had a maximum around 2.0 eV, although the dependence on the incident photon energy was much weaker. At the much longer incident wavelength of 1.065 ~m the intensity of the Raman line C has been measured and analyzed by Shepherd (1970). The YAG : Nd 3+ laser had been chosen by Shepherd because its energy at 200 K is just below the low absorptive part of the absorption edge of CdCr2Se4, which shifts to the red if the temperature is decreased below 200 K. He explained the measured temperature dependence of the intensity of the Stokes l'ine as a combination of three effects: the change in absorption, the usual temperature dependence of the Stokes intensity, and the resonant term in the Raman cross section based on transitions between a parabolic valence and conduction band. The last assumption does not agree with the conclusion that the lower energy edge is not due to an intrinsic excitation (Harbeke and Lehmann 1970). The nuclear magnetic resonance spectra of CdCr2Se4 have been studied by Berger et al. (1968, 1969a), Stauss et al. (1968) and Stauss (1969a, b). The spectrum of 53Cr in CdCr2Se4 is very similar to that of 53Cr in CdCr2S4 and has been analyzed and discussed as described in section 5.3. At 4.2 K the isotropic hyperfine field Hiso is -182.5 kOe, the axially symmetric hyperfine field Hanis is
SULPHOSPINELS
691
+2.30 kOe, and the strength of the quadrupole interaction Vo is 0.90 MHz (Berger et al. 1968, Stauss et al. 1968). The hyperfine field on 77Se is large and negative. At 4 . 2 K the isotropic component is -98.0 kOe and the axially symmetric component is +9.2 kOe (Stauss et al. 1968, Berger et al. 1969a). On lnCd and i13Cd the hyperfine field is large and positive, +136.2 kOe (Berger et al. 1969a, Stauss 1969a, b). This is less than in CdCr2S4 and corresponds to 1.7% of an electron spin in the Cd 5s state (Berger et al. 1969a, Stauss 1969b).
5.7. HgCr2se4 HgCr2Se4 is a normal spinel (Baltzer et al. 1966) with lattice parameters as given in table 1. The lattice parameter has been measured as a function of temperature by Wakamura et al. (1976b). They found that it decreased steadily with decreasing temperature between 300 K and 90 K, deviating only Weakly from the GrfineisenDebye behaviour below 150 K. HgCr2Se4 is a ferromagnet with a Curie temperature at 106 K, an asymptotic Curie temperature of 200 K and a molar Curie constant of 3.79, close to the spin-only value of Ca~+ ions (3.75) (Baltzer et al. 1966). The magnetic moment at 4.2 K is 5.64 #B/molecule in an applied magnetic field of 10 kOe (Baltzer et al. 1966), while Minematsu et al. (1971) report a value of 5.8 _+0.2 ~B/molecule for the saturation moment. The last value agrees well with the 6 p.B/molecule expected for Cr 3+ ions. The Curie temperature is increased by doping with Cu (Lotgering 1968b, Okofiska-Kozlowska et al. 1977) and with Ag (Miyatani et al. 1970, Minematsu et al. 1971). Indium was found to substitute for Cr, and the Curie temperature was observed to decrease with increasing In concentration (Takahashi et al. 1971, Miyatani et al. 1970, Minematsu et al. 1971). From the values of the ferromagnetic and the asymptonic Curie temperature Baltzer et al. (1966) estimated the strength of the nearest-neighbour exchange interaction Y and the distant-neighbour interaction K (see section 5.1), which results in J/k = 15.8 K and K/k = -0.51 K. Under hydrostatic pressure the ferromagnetic Curie temperature decreases. Srivastava (1969) measured dTddP = - 0 . 9 5 K/kbar, which, in combination with the compressibility data, gives an increase of Tc with the lattice parameter at the rate dTdda = +99 K/A. HgCrzSe4 is a semiconductor (Baltzer et. al. 1965). Single crystals were observed to have a p-type conduction with a resistivity that has a maximum at 82K. At approximately the same temperature, a transition from p-type to n-type conduction was observed in the Hall coefficient (Lehmann and Emmenegger 1969). Ag doping (Miyatani et al. 1970, Minematsu et al. 1971) and Cu doping (Lotgering 1968b) results in a much higher p-type conduction. Ag-doped hot-pressed polycrystalline samples showed a small positive magnetoresistance at temperatures near the Curie temperature. The Hall and thermoelectric effects indicate that p-type carries dominate the electrical conduction of Ag-doped HgCrzSe4 (Minematsu et al. 1971).
692
R.P. VAN STAPELE
In doping increases the resistivity of hot-pressed polycrystalline samples. The resistivity reached a maximum around the Curie temperature and the samples have a strong, negative magnetoresistance in that region of temperatures. The Hall and thermoelectric effects show a complicated behaviour, indicating that more than one type of carrier takes part in the conduction (Miyatani et al. 1970, Minematsu et al. 1971). Similar properties have been observed by Takahashi et al. (1971) in the mixed crystals HgCr2-xInxSe4, in which In can be substituted for Cr up to x = 0.45. These authors conclude that In also substitutes for Cr in the In-doped polycrystalline samples studied by Minematsu et al. (1971). This means that impurities due to deviations from stoichiometry play a role in the conduction mechanism. Recently, Goldstein et al. (1978) and Selmi et al. (1980) found that the electrical transport properties of HgCrzSe4 crystals can be changed appreciably by annealing in a Hg or a Se atmosphere. Annealing in a Hg atmosphere results in highmobility n-type samples, whereas annealing in a Se atmosphere results in materials with p-type conduction at room temperature and n-type conduction at low temperatures. Although the analysis of the electrical transport phenomena is far from complete, the observed temperature dependence of the resistivity and the magnetoresistance reveals the active presence of an interaction between the charge carriers and the Cr spin system. A peculiar effect of this interaction has been observed by Toda (1970), who measured a decrease of the electrical resistivity and an induced DC voltage in the sample at ferromagnetic resonance. At wavelengths shorter than 2.5 ~m the optical absorption spectrum of HgCrzSe4 consists of a broad, weak absorption at 0.6 eV and of an absorption edge located at 0.84eV at room temperature, shifting strongly to longer wavelengths with decreasing temperature (Lehmann and Emmenegger 1969). The position of the absorption edge, which is depicted in fig. 67, starts to move to the red well above the Curie temperature. It shows a further shift to the red in the ferromagnetic state of the crystal (Lee et al. 1971, Arai et al. 1973). Application of a magnetic field shifts the edge further to the red (Lehmann and Emmenegger 1969, Arai et al. 1973), which indicates that the shift is related to the magnetic ordering. However, simple mechanisms like exchange split bands or magnetoelastic coupling fail to explain the observed temperature dependence of the position of the absorption edge (Arai et al. 1973). Doping of HgCrzSe4 single crystals results in a shift of the absorption edge. In In-doped crystals the edge is slightly shifted to shorter wavelengths, whereas in Ag-doped crystals the edge is shifted to the red (Miyatani et al. 1970). The Ag-doped crystals also show an additional broad absorption band at 0.62eV, which becomes sharper at lower temperatures (Miyatani et al. 1970). The frequencies of the observed optically active phonons are listed in tables 17 and 18. The frequencies of two of the four infrared-active phonons were derived from the reflectance at room temperature (Lee et al. 1971). In absorption, the frequencies were measured as a function of temperature (Wakamura et al. 1971, 1976b). Between 300K and 85 K, the frequencies increase continuously with decreasing temperature, showing a small additional shift to higher frequencies
SULPHOSPINELS
693
(] 0,8
0.6 Z O..
(D
/
I
/b
0.~
/ /
!
,J
0.2
Tc &
00
I1~
I
I
100
200
300
I
400 T(K)
I
I
500
600
Fig. 67. Shift of the optical absorption edge of HgCr2Se4. (a) The position at an absorption coefficient of 2000 cm -], according to Lehmann and Emmenegger (1969) and (b) the position at an absorption coefficient of 240 cm 1, according to Arai et al. (1973).
below the ferromagnetic Curie temperature. As in CdCr2Se4, this anomalous shift can be explained phenomenologically by assuming that the atomic potential depends on the magnetization (Baltensperger 1970, Wakamura et al. 1976b)*. The frequency and the intensity of the five Raman-active phonons have been measured as a function of temperature between 8 K and room temperature and as a function of the incident photon energy in the range 1.5 to 3 eV (Iliev et al. 1978b). The frequencies are listed in table 18. The assignments made by Iliev et al. T A B L E 17 Frequencies of the four infrared-active phonons of HgCr2Se4. Frequencies (cm -]) at room temperature 286.8 287.7
268.6 276.6
170.9
* See notes added in proof (h) on p. 737.
Reference
58.7
Lee et al. (1971) Wakamura et al. (1976b)
694
R.P. VAN STAPELE TABLE 18 Raman lines of HgCr2Se4, quoted from Iliev et al. (1978b).
Raman shift (cm 1) Line
Assignment
300 K
10 K
A B
T2g
6O.1
66.2 140.5
C D E F
Eg T2g T2g Alg
152.9 163.4 207 235.9
158.8 168.7 211 238
(1978b) are based on the analysis of Briiesch and D'Ambrosio (1972) of the lattice vibrations in the spinel structure, since selection rules are not always obeyed in the (resonant) Raman scattering of compounds like HgCr2Se4. The phonon frequencies in HgCr2Se4 and in CdCrzSe4 (table 16) have nearly the same value, except for line A, which means that the diamagnetic cations take part in the vibration only in mode A. The temperature dependence of the Raman intensities shows no anomaly at the ferromagnetic Curie temperature, but it depends significantly on the incident photon energy. This suggests, as Iliev et al. (1978b) conclude, that the observed changes in Raman intensity are due to temperatureinduced changes of the resonance conditions. We conclude this review of the properties of HgCr2Se4 with the nuclear magnetic resonance data published by Berger et al. (1969a). At 1.4K, these authors measured the hyperfine fields at the nuclear spins of 53Cr, 77Se, 199Hg and 2°~Hg. The isotropic part of the hyperfine field on 53Cr amounts to - 179.4 kOe and in comparison with the isotropic hyperfine fields in other ferromagnetic semiconductors can be correlated with the strength of the exchange interactions between the Cr spins (Berger et al. 1969a). The negative isotropic part of the hyperfine field on the Se nuclear spin (-91.7 kOe) could be understood in terms of a spin polarization of Se s orbitals by the Cr spins. The large and positive hyperfine field on the Hg nuclear spins (+446 kOe) was found to be isotropic and was ascribed to an unpaired spin density in the empty Hg 6s shell of 1.7% of an electron spin. This compares well with the data on CdCrzSe4 (Berger et al. 1969a).
5.8. Mixed crystals between the compounds ZnCrzX4, CdCr2X4 and HgCrzX4 with X = S, Se In this section we will briefly review the properties of mixed crystals between ZnCr2X4, CdCrzX4 and HgCrzX4. In the sulphides the only series that has been investigated is Cdl-xHgxCr2S4, between the ferromagnet CdCr2S4 and the metamagnet HgCr2S4, which have nearly the same cell edge (table 1). Baltzer et al. (1967) observed that the asymptotic Curie temperature 0 changes gradually from 0 = 152 K for CdCr2S4 to
SULPHOSPINELS
695
0 = 142 K for HgCr2S4, passing through a gentle maximum. The magnetic ordering temperature varies monotonically from the Curie temperature (84.5 K) of CdCrES4 to the N6el temperature (36 K) of HgCr2S4. The metamagnetic behaviour appears at x = 0.65. Within the limits of the model given by Baltzer et al. (1966), this variation of 0 and Tc could be described by a positive effective nearest-neighbour exchange J, depending only weakly on x, and a negative effective unified moredistant exchange /(, that drops rapidly in magnitude when the composition approaches that of CdCr2S4. In the selenides most attention has gone to the series Znl_xCdxCr2Se4, between the antiferromagnet ZnCr2Se4 and the ferromagnet CdCr2Se4. The latter compound has a 3 percent larger cell edge than ZnCr2Se4 (table 1). The cell edge of Znl_xCdxCr2Se4 has been reported to vary linearly with x (Busch et al. 1969, Wakamura et al. 1976a). The asymptotic Curie temperature increases linearly (Baltzer et al. 1967, Lotgering 1968b) or nearly linearly (Busch et al. 1969) with x (fig. 68). The transition from antiferromagnetism to ferromagnetism occurs at x = 0.4 according to Baltzer et al. (1967) and Lotgering (1968b) or, as measured by Busch et al. (1969) in very low magnetic fields, between x -- 0.5 and 0.6 (fig. 68). Although the large number of exchange parameters involved prevents a reliable analysis of the magnetic ordering in terms of x-dependent exchange interactions
200
/°
150
100 I
Q.
E t---
50
- - ~TN× ~ × "'"x
00.
I012101
.L
1
i
06
I
'
0.8
1
1.0
X
Fig. 68. Asymptotic Curie temperature, N6el temperature and ferromagnetic Curie temperature of Znl-xCdxCr2Se4 as a function of the composition: (Q) data of Baltzer et al. (1967), (O) data of Lotgering (1968b) and (x) data of Busch et al. (1969).
696
R.P. V A N S T A P E L E
(Lotgering 1968b), some authors conclude that the nearest-neighbour exchange interaction is essentially constant, but that the more distant interactions vary drastically with the replacement of Zn by Cd ions (Baltzer et al. 1967, Makhotkin et al. 1978a). Lotgering (1968b), on the other hand, mentioned the possibility that the main influence of this substitution is exerted on the nearest-neighbour exchange interaction. In CdCrzSe4, the ferromagnetic Curie temperature decreases under hydrostatic pressure. The rate of change, -0.76 x 10-3K/bar, increases with decreasing Cd concentration to - 1 . 3 x 10-3K/bar for Zn0.4Cd0.6Cr2Se4 (Fujii et al. 1970). Finally we mention that the small x-dependent shift of the frequencies of the four infrared-active phonons in Zn>xCdxCr2Se4 has been measured and analyzed (Wakamura et al. 1976a), and that the magnetic permeability of crystals with x/>0.76 has been observed to be sensitive to illumination (Makhotkin et al. 1975). In the system Cdl_xHgxCr2Se4, between the ferromagnets CdCr2Se4 and HgCr2Se4, the ferromagnetic Curie temperature decreases linearly from 130 K to 106K (Vinogradova et al. 1978). These authors observed that the dynamic permeability was sensitive to illumination throughout the series of mixed crystals. The long-wavelength edge of this photomagnetic effect and of the photoconductivity was observed to shift gradually to longer wavelengths with increasing Hg concentrations. In the system Zn~ xHgxCr2Se4, between the antiferromagnet ZnCr2Se4 and the ferromagnet HgCr2Se4, the cell edge varies linearly (Wakamura et al. 1973). Antiferromagnets have been observed for 0 ~<x ~<0.4, whereas at Hg concentrations higher than 0.5 a ferromagnetic behaviour was observed (Wakaki et al. 1975). The values of the asymptotic Curie temperature, the N6el temperature and the ferromagnetic Curie temperature are given in fig. 69. In the ferromagnetic compositions, the magnetic ordering has been analyzed in terms of a nearestneighbour exchange interaction and a unified more distant interaction, which both change with the composition (Wakaki et al. 1975). The optical absorption edge gradually shifts to lower energies with increasing Hg concentration, the magnitude of the anomalous red shift increasing from the value in ZnCr2Se4 to that in HgCr2Se4 (Wakaki and Arai 1978). Finally, the shift of the frequencies of the infrared-active phonons has been measured and analyzed by Wakamura et al. (1973)*. In the solid solution ZnCr2(S2-xSex)4 the cell edge increases linearly with x, whereas the chalcogen parameter remains constant (Riedel and Horvfith 1969). These authors have published some data on the infrared spectra, while the preparation of single crystals has been reported by Pickardt and Riedel (1971). Substitution of Te for Se turned out to be only partly possible. Single-phase samples of ZnCr2(Sei-xTex)4 with x >0.2 could not be obtained (Riedel and Horvfith 1969). The lattice parameter of CdCr2(Sl_xSex)4 increases linearly with x, whereas the u parameter remains constant (Wojtovicz et al. 1967, Riedel and Horvfith 1969). The asymptotic Curie temperature 0 increases linearly with x, but the ferromagnetic * See notes added in proof (i) on p. 737.
SULPHOSPINELS
697
200
(3
150
2
0) fl
E
(9 F-
100
50
TN
O0
1
i
012
i
II I
0 Z,
OIi~ I
I
0"8
I
I'0 X Fig. 69. Asymptotic Curie temperature 0, N6el temperature TN and ferromagnetic Curie temperature T¢ of Znl-xHgxCr2Se4, according to Wakaki et al. (1975).
200
150 D
g b--
100
0
I
I 0'.2 ' 0'.4 01.6 ' 018 ' 1.0
X Fig. 70. Asymptotic Curie temperature 0 and ferromagnetic Curie temperature Te of CdCr2(Sl-xSex)4, according to Wojtowicz et al. (1967).
698
R.P. VAN STAPELE
Curie temperature stays behind 0 for x ~<~ (fig. 70) (Wojtowicz et al. 1967). This finding has been analyzed by Wojtowicz et al. (1967) in terms of an effective nearest-neighbour exchange interaction J and an effective unified more distant interaction/(. Both parameters were found to vary in a non-linear way, the positive 37 passing through a weak maximum and the negative /£ having a pronounced minimum. The preparation of single crystals has been reported by Pickardt et al. (1970), data on the infrared spectra have been given by Riedel and Horvgtth (1969), and data on the position and the structure of the optical absorption edge have been published by Kun'kova et al. (1976).
5.9. Mixed crystals A1/2A1/2Cr2X4 1+ 3+ with X = S, Se and diamagnetic ions A An interesting class of compounds is formed by the spinels AlaA1/2Cr2X4, 1+ 3+ in which the tetrahedral sites are occupied by equal amounts of monovalent diamagnetic cations like Li +, Cu + or Ag ÷ and trivalent diamagneti c ions like AP +, Ga 3÷ or In 3+. These compounds are expected to be semiconductors, which has been ascertained experimentally in the case of CUl/2Inl/zCr2Se4 (Yokoyama and Chiba 1969) and Cumlnl/eCr2S4 (G6bel .et al. 1974). In a number of these compounds, and specifically the compounds that contain Li + or Cu ÷, the monovalent and trivalent cations order on the tetrahedral sites (table 19). This ordering will be discussed first. The spinel A sites form two equivalent fcc Bravais lattices (section 2, fig. 2). Since the sites of one Bravais lattice are surrounded tetrahedrally by four sites of the other, the A sites are suitable for ionic 1:1 ordering according to the two sublattices. The driving force is the electrostatic energy arising from a charge difference, while a difference in ionic radius may also play a role. The ordering was first observed by Lotgering et al. (1969) in CumFel/2Cr2S4 (section 6.6), Cul/2Inl/2CraS4 and CUl/2Inl/zCr2Se4. It has also been found in Cul/2Fel/2RhzS4 (section 7.4) and in many of the compounds listed in table 19. The 1 : 1 ordering on the tetrahedral sites lowers the space group from Fd3m (O 7) of spinel to F43m (T~). The inversion centres in the spinel lattice (being the B sites) have disappeared in T 2. The expected occurrence of piezoelectricity could not be detected (Pinch et al. 1970)*. Another consequence of the ionic ordering is that the X tetrahedra around the A + ions and around the A 3+ ions, which have no common X ions (fig. 2), are not equivalent, so that the A+-X and A3+-X distances are two parameters that determine the positions of the X lattice completely. Two X parameters have indeed been observed by means of neutron diffraction in CUl/2Inl/zCrzX4 for X = S and Se (Plumier, private communication). The differences between the Cu+-X and In3+-X distances is about 20% in the sulphide and about 5% in the selenide. Table 19 gives a survey of the properties of A1/zA1/z[Cr2 + 3+ 3+]X4 with diamagnetic A ions. Ionic ordering does not always occur and the data suggest that ordering occurs for Li + and Cu ÷ and not for Ag + (Pinch et al. 1970). The absence of ordering in Cul/zGal/z[Cr3+]S4(table 19) and in Cul/zInl/a[B2]84 with B = In or Rh * See notes added in proof (j) on p. 737.
SULPHOSPINELS
699
TABLE 19 Crystallographic and magnetic data of mixed spinels A1/2A1/2Cr2X4. 1+ 3+ u = chalcogen parameter, Cm = molar Curie constant, 0 = asymptotic Curie temperature, TN = Nrel temperature and Tc = ferromagnetic Curie temperature. References: (a) Yokoyama and Chiba (1969), (b) Lotgering et al. 1969, (c) Pinch et al. (1970), (d) Locher and Van Stapele (1970), (e) Plumier et al. (1971b), (f) Plumier and Sougi (1971), (g) Wilkinson et al. (1976), (h) Plumier et al. (1977a), (i) Plumier et al. (1977b).
Compound LiI/2Gal/2Cr2S4 Lil/2InmCr2S4
Cul/2A]I/zCr2S4
Cul/2Gal/2Cr2S4
u
9.974 10.127 9.915 9.920 9.918
0.385 0.385 0.382 0.381 0.382
10.065 10.060
0.388
10.067 10.063 10.215 10.24
0,385 0,387 0,390
no no ?
0.3876
no
0.381 0.385
yes ?
0.386
yes yes
Cul/2Inl/zCr2S4
AgmAll/2Cr2Sa AgmGal/2Cr2S~ Ag~/2Inl/2Cr2Sa
Cul/2AlmCr2Se4 Cul/2Gal/2Cr2Se4 Cu~/2InmCr2Se~
Ionic ordering on A sites
Celledge (A)
10.438 10.444 10.583 10.580
yes yes yes ? no yes yes yes
10.58
Cm
0 (K)
Critical temperature (K) TN -- 14 Ty = 27 TN = 14 TN = 31
3.83
-77
3.43
+142
TN -- 26 TN = 40 TN = 160.9 TN = 7 TN- 10 TN- 14 Ty = 17 TN = 138.9 Ty = 6 TN -- 7
3.8-+ 0.2
+ 135 _+5
3.4--+0.1 3.58
+105-+5 + 100
TN- 14 no 4.2 no ordering Tc = 50 T0 - 60
Ref. (c) (c) (c) (c) (g) (b) (c) (e) (i) (c) (c) (c) (e) (f) (h) (c) (c) (a) (b) (c) (d) (e)
at
Agl/2Inl/2Cr2Se4
10.724 10.72
0.390
no 3.86
+ 180
(g) (c) (e)
( L o t g e r i n g , p r i v a t e c o m m u n i c a t i o n s ) s h o w s t h a t t h e p r o b l e m is less s i m p l e . O n t h e o t h e r h a n d 1 : 1 o r d e r i n g o n t h e t e t r a h e d r a l sites s e e m s t o b e s u r p r i s i n g l y s t a b l e , as a p p e a r s f r o m t h e o c c u r r e n c e in F e x C u l - x R h 2 S 4 w i t h 0.46 ~ x < 0.7 ( B o u m f o r d a n d M o r r i s h 1978) a n d in Inz/3D1/3[In2/3Cr4/3]S4 3+ 3+ 3+ 3+ 34- 44a n d Inl/zDm[Cr3/2Sn m]S4 ( L o t g e r i n g a n d V a n d e r S t e e n 1971b), n o t w i t h s t a n d i n g a s t r o n g d e v i a t i o n f r o m t h e i d e a l composition. I n t h e i r p a r a m a g n e t i c state, t h e c o m p o u n d s t h a t h a v e b e e n i n v e s t i g a t e d h a v e a C u r i e c o n s t a n t t h a t m o r e o r less a g r e e s w i t h t r i v a l e n t C r i o n s (Cm = 3.75) ( t a b l e 19). A l t h o u g h a p o s i t i v e a s y m p t o t i c C u r i e t e m p e r a t u r e has b e e n f o u n d in m o r e cases, o n l y o n e of t h e c o m p o u n d s l i s t e d in t a b l e 19 o r d e r s f e r r o m a g n e t i c a l l y . T h i s c o m p o u n d , A g m I n m C r 2 S e 4 , h a s a f e r r o m a g n e t i c C u r i e t e m p e r a t u r e o f a b o u t 60 K. T h e m a g n e t i c m o m e n t has b e e n r e p o r t e d t o b e 4.7/xB at 4.2 K a n d 10 k O e ( P i n c h et al. 1970) a n d 5 . 1 / z ~ at 4.5 K a n d 30 k O e ( P l u m i e r et al. 1971b), b o t h v a l u e s b e i n g l o w e r t h a n t h e 6 tzB e x p e c t e d f o r C r 3+ ions. H o w e v e r , e v e n in 30 k O e t h e
700
R.P. V A N S T A P E L E
material was not saturated (Plumier et al. 1971b). Antiferromagnetic ordering has been found in all other compounds in table 19, with the exception of Cul/2Inl/2Cr2Se4, which shows no ordering at 4.2 K (Plumier et al. 1971b, Wilkinson et al. 1976). The spin configuration in AgmInmCr2S4 (Plumier and Sougi 1971) and CUl/2Gal/zCrzS4 (Wilkinson et al. 1976) is not commensurate with the crystallographic unit cell. In the former case a spiral arrangement like that in ZnCrzSe4 (section 5.5) was found, in the latter case a spiral arrangement with a propagation vector that does not point in a main crystallographic direction. The antiferromagnetic ordering found in Cu~/zInmCr2S4 (Plumier et al. 1971b) consists of four magnetic sublattices with magnetizations pointing along the four cube diagonals. This structure is commensurate with the unit cell and the four B sites in one octant (fig. 2) belong to different magnetic sublattices. It can easily be shown that the Heisenberg exchange energy is degenerate with respect to the mutual orientation of the sublattice magnetizations if the resulting magnetization vanishes. Other kinds of interactions must occur in order to remove the degeneracy. An isotropic biquadratic interaction J(Si • ~)2 with a positive J gives indeed a minimum energy for the configuration observed. This is a strong indication for the occurrence of biquadratic exchange in sulphospinels. The magnetic and electrical properties of Cu0.5+xln0.5-xCrzS4 with -0.1 ~<x ~<0.1 depend strongly on x (G6bel et al. 1974). The resistivity has a sharp maximum at x = 0, at which composition the conduction changes from p-type (for positive x) to n-type (for negative x). The paramagnetic Curie temperature shows a pronounced minimum at x = 0. A transition from ferromagnetism (established by measurements of the magnetic hysteresis) to antiferromagnetism occurs in the p-type region near x = 0. These results show Cul/21nl/2CrzS4 to be a semiconducting antiferromagnet and illustrate again the close connection between the strong ferromagnetic interaction in C u C r 2 S 4 and the hole conduction in the valence band (see section 3). Recent measurements of the magnetic susceptibility and the specific heat, together with neutron diffraction experiments, revealed that in Ag~/2Ina/2Cr2S4 a first-order transition from "helimagnetic macrodomains" to "metamagnetic microdomains" takes place at 12 K, a transformation to smaller microdomains at 42.5 K, and that the transformation to the paramagnetic state takes place at 138 K (Plumier et al. 1977a). Similar phenomena have been observed in ZnCr2Se4 (see section 5.5) and in Cul/2Inl/2Cr2S4. In the last compound the first-order transformation from long range magnetic order to a short range ordering takes place at 31 K, to yet another short range ordered state at 35 K and to the paramagnetic state at 158 K (Plumier et al. 1977b)*. Nuclear magnetic resonance of 63Cu, 65Cu and 115In in the compounds C u l / z l n l / z C r 2 S 4 and CumlnmCr2Se4 revealed the existence of large supertransferred hyperfine fields on nuclei of the diamagnetic cations. In terms of spin densities in the first empty s shell of the diamagnetic ion, these fields compare well with those measured in CdCrzX4 and HgCrzX4 (Locher and Van Stapele 1970). * See notes added in proof (k) on p. 737.
SULPHOSPINELS
701
6. Ferrimagnetic semiconductors 6.1. Introduction In this section we will discuss the properties of the normal sulphospinels MCr2S4 with M = Mn, Fe and Co and of some mixed crystal series connected with these compounds. The compounds MCrzS4 are interesting because they provide examples of ferrimagnetism in semiconducting non-oxidic compounds (Lotgering 1956). Their properties can be compared with the properties of the corresponding oxyspinels in order to study the influence of the anions. From this point of view it would have been interesting to compare oxyspinels MFe204 with sulphospinels MFezS4. However, the fact that many iron sulphides are not stable with respect to FeS2 prohibits the preparation of most of the sulphur analogues of the ferrites MFe204, which are important materials from a technical point of view. Nevertheless, the thorough investigation of the physical properties of the sulphochromites, which was started by Lotgering (1956), has yielded many interesting phenomena, a better knowledge of superexchange interactions and some insight into the relative stability of the valencies of cations and anions. Among the results, worth mentioning in advance is the magnetization versus temperature curve of MnCrzS4, which provided the first indication of the existence of a fairly positive exchange interaction between Crs+ ions (Lotgering 1956) (section 6.2). Another example is the occurrence of a semiconducting ferrimagnet FemCua/2Cr2S4 in the series of mixed crystals between the semiconducting ferrimagnet FeCrzS4 and the metallic ferromagnet CuCrzS4 (section 6.6), which implies Fe 3+ and Cu 1+ ions. It was found that these ions are ionically ordered on t h e tetrahedral sites (Lotgering et al. 1969). The same ordering has also been observed in a number of compounds with trivalent and monovalent diamagnetic ions on the tetrahedral sites (section 5.9) and later on in the fascinating antiferromagnet Fel/zCua/zRhzS4 (section 7.4), in which strongly° negative exchange interactions occur between Fe 3+ ions at a distance of 9.85 A (Plumier and Lotgering 1970). Finally, the compound FeCrzS4 itself is interesting because of its strong magnetic anisotropy at low temperatures and the cooperative Jahn-Teller effect below 9 K (Van Stapele et al. 1971, Spender and Morrish 1972b, Van Diepen and Van Stapele 1973). Both effects are connected with the 5E ground state of the Fe 2+ ions (section 6.3). The magnetic data of the compounds MnCrzS4, FeCr2S4 and CoCrzS4 are collected in table 20.
6.2. MnCr2S4 MnCr2S4 is a normal (Menyuk et al. 1965) cubic spinel (Passerini and Baccaredda 1931) with lattice parameters as listed in table 1. At high pressures and tern-
702
R.P. VAN STAPELE
0
L) ©
e~
'6 ~SNg
©
~
t
N
.e
p.. ,~
e~
E ¢)
•
~
~'.~
+1
I
~8 <
o
+1
e--
+l
~
+
I
cq I
I
SULPHOSPINELS
~t.,~ ~
~, ~
" ~ , ~ , ...~, .~. ~,.~ 1"'-, t"~
8
o
t"q
+1 t~
I
i
C)
J
i
703
704
R.P. V A N S T A P E L E
2.5
-5 2.0 0 o
S t
Ig
1.5
\
J 1.0 0
'1'0
i
i
3'0
1
temperature (K)
r
I
5'0 6'o
i
7'o
.~
Fig. 7]. Magnetization of MnCr2S4 as a [unction of temperature: (a) in 8.4 kOe (Lotgerin g 1956), (b) in 10 k O e (Menyuk et al. 1965) and (c) extrapolated to H = 0 (Lotgering 1968a).
peratures a transformation to a cation-defective NiAs structure has been observed (Bouchard 1967, Tressler and Stubican 1968, Tressler et al. 1968). According to the theory of Yafet and Kittel (1952) for ferrimagnetism in spinels, a canted spin configuration cannot transform at higher temperatures into the paramagnetic state directly, but has to pass through the collinear state. Further, the occurrence of a m a x i m u m in the magnetization versus t e m p e r a t u r e curve, as predicted by N6el (1948), cannot occur in the canted state but only in the collinear state. These theoretical conditions are nicely demonstrated in MnCr2S4. The c o m p o u n d is a ferrimagnet with a Curie t e m p e r a t u r e of about 8 0 K (Lotgering 1956, 1968a) or 66 K (Menyuk et al. 1965, Darcy et al. 1968). In the paramagnetic state the magnetic susceptibility follows at higher temperatures a Curie-Weiss law with a Curie constant which is in rough agreement with the spin-only value of Mn a÷ and C r 3÷, and an asymptotic Curie t e m p e r a t u r e of - 1 2 _+ 1 0 K (Lotgering 1956) or + 1 0 K (Darcy et al. 1968). In the ferrimagnetic state the magnetization has a m a x i m u m at about 40 K (fig. 71) (Lotgering 1956), decreasing to 1.3/xB/molecule at 4.2 K (Menyuk et al. 1965, Darcy et al. 1968). F r o m the low value of the asymptotic Curie t e m p e r a t u r e and the occurrence of a m a x i m u m in the magnetization versus t e m p e r a t u r e curve, Lotgering (1956) concluded that a fairly large positive exchange interaction IBB exists between the Cr 3÷ ions on the octahedral sites and a weaker negative exchange interaction IAB between the octahedral Cr 3+ ions and the Mn 2÷ ions on the tetrahedral sites. Subsequent m e a s u r e m e n t s of the magnetization down to 2 . 2 K in fields up to 30 k O e revealed the existence of a Yafet-Kittel spin configuration with canted " Mn 2÷ spins on the tetrahedral sites below 5 K and a collinear N6el configuration
SULPHOSPINELS
705
above 5 K (fig. 71) (Lotgering 1968a). The canting of the spins on the tetrahedral sites indicates a relatively strong exchange interaction IAA between the Mn 2+ spins. From the value of the magnetic moment extrapolated to zero magnetic field and zero temperature (1.18/zB), the temperature-independent differential susceptibility below 4.5 K and the value of the asymptotic Curie temperature Lotgering (1968a) found IAB/k = --1.79 K, IAA/k = --1.68 K and IBB/k +10 K. A similar/An, (--0.80 K) was observed in the antiferromagnet MnSc2S4 (Wojtowicz et al. 1969). The canted spin configuration has been observed by means of neutron diffraction (Plumier and Sougi 1969). The transition to the collinear N6el configuration takes place suddenly at 5.5 K. The temperature dependence of the sublattice magnetizations measured between 1.5 K and 45 K agrees well with that of the total magnetization as measured by Lotgering (1968a) and Menyuk et al. (1965). A molecular field calculation of the sublattice magnetization as a function of temperature agreed with the experimental results only when exchange striction effects were taken into account (Nauciel-Bloch et al. 1972). In high magnetic fields above 100 kOe (fig. 72) yet another magnetic phase exists at temperatures below 30 K (Denis et al. 1969, 1970). The spin structure in this phase and the magnetization in high fields have been the subject of molecular field calculations in which magnetostrictive effects play an important part (Plumier 1970a, b, 1980, Plumier et al. 1971a) (see also Plumier 1980). Other physical properties of MnCr2S4 have barely been studied. The compound is reported to be a semiconductor (Bouchard et al. 1965, Albers et al. 1965) and infrared-active phonons at 381, 323, 260 and 120 cm -1 have been observed in the infrared absorption spectrum in the course of a general study of the lattice vibrations of chalcogenide spinels (Lutz and Feh6r 1971). =
6
.,//7ji"
25 K
g3
E
1 I
300 200 H {kOe) Fig. 72. Magnetizationof MnCr2S4as a functionof magneticfield, accordingto Denis et al. (1970). 100
706
R.P. VAN STAPELE
6.3. FeCr2S4 FeCrzS4 is known as the mineral daubreelite, which Lundqvist (1943) demonstrated to have the cubic spinel structure. Neutron diffraction studies (BroquetasColominas et al. 1964, Shirane et al. 1964) showed that it is a normal spinel. The lattice parameters are given in table 1. At high pressures and/or temperatures FeCr2S4 adopts a cation-defective NiAs structure (Albers and Rooymans 1965, Bouchard 1967, Tressler and Stubican 1968, Tressler et al. 1968). At low temperatures down to 4 K, FeCr2S4 remains a cubic spinel (Shirane et al. 1964, G6bel 1976), but an anomalous broadening of the X-ray diffraction lines indicates inhomogeneous lattice distortions (G6bel 1976). FeCrzS4 is a ferrimagnet (Lotgering 1956) in which the Fe z+ spins on the tetrahedral sites are coupled antiparallel to the Cr 3+ spins on the octahedral sites in a collinear N6el configuration (Shirane et al. 1964, Broquetas-Colominas et al. 1964). Values of the asymptotic Curie temperature, reported in the literature, lie between - 2 3 4 K and - 3 3 0 K, that of the ferrimagnetic Curie temperature between 170 K and 195 K, while the saturation moment of powder samples lies between 1.55 and 1.79/xB/molecule (Lotgering 1956, Shirane et al. 1964, Haacke and Beegle 1967, Lotgering et al. 1969, Hoy and Singh 1968, Gibart et al. 1969, Shick and Von Neida 1969, Spender and Morrish 1971). Measurements on single crystals (fig. 73) showed the compound to have a strong magnetic anisotropy at
H f l [1001
30
t [111] 20 ',.3
D 121 O
o
H = 18kOe
*
H =12
[]
H:6
"
•
H=3
'"
'o
10
0, 0
50
'"
100 150 200 temperature (K) Fig. 73. Temperature dependence of the magnetization of a single crystal of FeCr2S4with H parallel to the [100] and [111] direction (Van Stapele et al. 1971).
SULPHOSPINELS
707
low temperatures (Van Stapele et al. 1971), as anticipated by Eibschfitz et al. (1967b). The magnetization lies preferentially along a cube edge, and the saturation magnetization is 1.86/~s/molecule. This corresponds to a magnetic moment of 4.14/~B for the Fe 2+ ions, if the Cr 3+ ions are assumed to have a moment of 3/~B (Van Stapele et al. 1971). These values agree well with those derived from neutron diffraction (Shirane et al. 1964). The magnetic anisotropy increases strongly with decreasing temperature (fig. 73). At 4 K the cubic anisotropy constant K1 is 3× 106erg/cm 3 and K2 is positive and of the same order of magnitude (Van Stapele et al. 1971). The anisotropy finds its origin in the 5E ground state of the tetrahedral Fe 2+ ions, whose splitting depends strongly on the direction of the magnetization (Eibschfitz et al. 1967b, Hoekstra et al. 1972). The straightforward crystal field theory, however, predicts a much larger anisotropy, which has indeed been observed for small concentrations of tetrahedral Fe 2+ ions in Cdl-xFexCrzS4 (Hoekstra et al. 1972). The fact that the magnetic anisotropy in FeCrzS4 is relatively weak is connected with the cooperative Jahn-Teller effect observed in the M6ssbauer spectrum of this compound (see below). The 57Fe M6ssbauer spectrum of FeCrzS4 in the paramagnetic state is in agreement with the perfect cubic symmetry of the tetrahedral sites occupied by the Fe 2+ ions (Yagnik and Mathur 1967, Eibschfitz et al. 1967b). In the ferrimagnetic state, however, the spectra show two anomalies: an electric field gradient on the Fe 2+ nucleus and a hyperfine field that decreases with decreasing temperature (Eibschfitz et al. 1967b). Both effects are due to the spin-orbit interaction that removes the orbital degeneracy of the 5E ground state of the Fe z+ ions in the magnetic state, in which the Fe z+ spins are oriented along the direction of the magnetization. This leads to a lowest orbital state with a tetragonal electronic charge distribution, a small induced orbital moment and a strong preference of the magnetization for the [100] directions (as discussed above). With such an electronic ground state the Fe z+ nucleus experiences a uniaxial electric field gradient with its main axis in the [100] directions, increasing in strength with decreasing temperatures, and a hyperfine field that decreases towards lower temperatures. Isolated Fe z+ ions on the tetrahedral sites, as in Cdl-xFexCrzS4 and Col-xFexCrzS4 with a small x, show the full effect, in agreement with the theory (Van Diepen and Van Stapele 1972, 1973). In FeCr2S4, however, the M6ssbauer spectrum is more complicated. Above 20 K a uniaxial electric field gradient has been observed in some cases (Eibschfitz et al. 1967b, Spender and Morrish 1972a, Van Diepen and Van Stapele 1973), in other cases a gradient with a lower symmetry (Hoy and Chandra 1967, Hoy and Singh 1968, Spender and Morrish 1972b). A sudden change in the spectrum occurs at about 10 K, which has been ascribed to a static Jahn-Teller distortion, that is too small to be detected by powder X-ray or neutron diffraction (Spender and Morrish 1972b, Van Diepen and Van Stapele 1973, Brossard et al. 1979). Subsequent investigations have shown that the M6ssbauer spectra and the specific heat are heavily influenced by the Fe/Cr ratio of the samples (Lotgering et al. 1975, Van Diepen et al. 1976). Carefully prepared samples in which Fe z+ ions exclusively occupy tetrahedral sites have M6ssbauer spectra with the narrowest lines. The specific heat of such
708
R.P. VAN STAPELE
O
E
8
-'3
--
6
•
.."
.
(D ¢o
&
:
E
.if
W"
/
2 tn
%
j 1'0 ' 2'0 temperature (K)
30 m
Fig. 74. Specificheat of Fe0.97Cr2S4as a function of temperature, according to Lotgering et al. (1975). samples has a lambda-type peak at 9.25 K (fig. 74), at which t e m p e r a t u r e the Jahn-Teller transformation occurs (Lotgering et al. 1975, Van Diepen et al. 1976)• The cooperative J a h n - T e l l e r effect in FeCr2S4 and the single ion behaviour can reasonably well be described within one model with quite satisfactory values for the spin-orbit splitting, the J a h n - T e I l e r coupling and the energy of the J a h n Teller active vibrations (Feiner 1977, 1982)• FeCrzS4 is a semiconductor with a resistivity that has an anomalous m a x i m u m (fig. 75) around the ferrimagnetic Curie t e m p e r a t u r e (Lotgering 1956, Albers et al. 1965). At both sides of the anomaly the Iog p vs T -1 curve is a straight line• Powder samples with a positive Seebeck coefficient of +338 ixV/deg at room temperature have an activation energy of 0.018 eV below 135 K and 0.038 eV above 200 K (Bouchard et al. 1965)• In p-type powder samples the thermoelectric power also shows an anomalous increase near the Curie t e m p e r a t u r e (Haacke and Beegle 1966)• Bongers et al. (1969) observed a negative magnetoresistance effect of Ap/p = - 0 . 0 5 in 12 k O e near the Curie t e m p e r a t u r e in p-type FeCrzS4. These
30 'oL A
20
I !
I i
t~ \i~
1o £
'
200 ' 400 I "'7- 600 temperature (K)
Fig. 75. The resistivity of a sintered sample of FeCr2S4 (Lotgering 1956).
SULPHOSPINELS
709
authors reported that powder samples with a n-type conduction do not show a maximum in the resistivity and the magnetoresistance effect near Tc (Bongers et al. 1969). Single crystals in the as-grown state are always reported to have a p-type conduction (Haacke and Beegle 1968, Goldstein and Gibart 1971, Watanabe 1973). The resistivity has been found to show a similar anomalous increase near the Curie temperature as in powder samples (fig. 76). The ordinary Hall coefficient has been observed to be too small to be measured (Haacke and Beegle 1968, Goldstein and Gibart 1969, 1971), the Hall resistivity being determined mainly by the spontaneous Hall effect (Goldstein and Gibart 1969, 1971). The resistivity and the magnetoresistance effect were found to be very sensitive to heat treatments (Watanabe 1973, Gibart et al. 1976). Annealing in a sulphur atmosphere slightly lowers the resistivity, whereas annealing in vacuum increases it (Watanabe 1973, Gibart et al. 1976) (fig. 76). In a qualitative way these observations can be understood from an energy level diagram (fig. 77) in which an Fe > band is situated in the energy gap between the valence and the conduction band (Lotgering et al. 1969). Hole conduction is attributed to holes in the Fe 2+ band, which are present because of deviations from the stoichiometric composition in as-grown samples (Watanabe 1973, Lotgering et al. 1975, Gibart et al: 1976). Sulphur deficiency gives rise to donor states, which are assumed to be situated above the Fe 2+ band. Annealing in vacuum will then decrease the number of:holes in the Fe z+ band and increase the resistivity, a s observed, whereas annealing in a sulphur atmosphere will have the reverse effect (Watanabe 1973).
102
I 1°1 U
.> 10o
10 -1
o
I
10
15 103/T (K41 Fig. 76. The resistivityof single crystals of FeCr2S4: (a) as-grown, (b) S-annealed at 700°C for 72 h and (c) vacuum-annealed at 575°C for 68 h 0Natanabe 1973).
710
R.P. VAN
STAPELE
E
T Fe2+
duction
band
EF
Cra÷V / ' / / ' / / / / / / / / ~
band
glE)
Fig. 77. Energy bands in FeCr2S4 (Lotgering et al. 1969).
Apart from the sharp negative magnetoresistance effect near the Curie temperature, p-type single crystals have an additional broad and positive magnetoresistance effect, which is maximal at a lower temperature (0.35 To) (Lyons et al. 1973, Goldstein et al. 1973) (fig. 78). The second effect was ascribed to a spontaneous anisotropic resistivity, which means a resistivity depending on the direction of the magnetization relative to the direction of the current and the crystal axes. A theoretical explanation for this anisotropy has not been given. The first effect was ascribed to spin disorder scattering of charge carriers in a broad band (Lyons et al. 1973, Goldstein et al. 1973), although an adequate theory will have to take acount of strong correlation and a strong exchange interaction, typical of charge carriers in a narrow Fe 2+ band (Bongers et al. 1969). The influence of doping has been reported for the dopants Cd and In (Goldstein and Gibart 1971) and Cu and Zn (Watanabe 1973). The resistivity of Zn-doped FeCr2S4 is higher than that of undoped samples, while the magnetoresistance peak is slightly shifted to lower temperatures. Doping with Cu strongly reduces the resistivity in accordance with the valency distribution 2+ 3+ , 1+ Fel-2xFex Cux Cr2S4 (section 6.6) (Lotgering et al. 1969). The magnetoresistance effect near the Curie temperature is strongly reduced (Watanabe 1973). Nuclear magnetic resonance of 53Cr nuclei in FeCr2S4 has been measured as a function of temperature below 150K. Extrapolated to OK the resonance frequency is 50.8 MHz, which corresponds to a hyperfine field of 211 kOe (Le Dang Khoi 1966).
SULPHOSPINELS
711
0.05
2-2 o
f
r -0.05
- 0.10
1
100 200 temperature (K)
Fig. 78. Spontaneous anisotropic resistivity (Aps/p(O)) and magnetoresistance (&p/p) in 15kOe of FeCraS4 (Lyons et al. 1973). The M6ssbauer spectrum of iagsn in Fel.lCrl.sSn0.1S4 consists of broad lines with an additional spectrum, indicating variations in the surrounding of the Sn ions. The large isomer shift relative to SnO2 points to an increased s-electron density. The hyperfine field was observed to be large and negative (-470 _+ 15 kOe at 80 K) (Lyubutin and Dmitrieva 1975). In the near infrared the reflectance circular dichroism of hot-pressed FeCr2S4 has been measured at 80 K. The normal remanence of the dichroism or the polar Kerr effect of the hot-pressed samples was found to be large (0.80) (Coburn et al. 1973). We conclude the review of properties of FeCr2S4 by mentioning the frequencies of the four infrared-active phonons observed in the absorption spectrum at 118, 260, 323 and 382 cm -~ (Lutz and Feher 1971). 6.4. CoCr2S4 In normal circumstances CoCr2S4 has the normal (Raccah et al. 1966) spinel structure (Hahn 1951). The lattice parameters are given in table 1. A transformation to the ordered cation-defective NiAs structure can be effected by the application of high pressure at high temperatures (Albers and Rooymans 1965, Bouchard 1967, Tressler et al. 1968, Tressler and Stubican 1968). The paramagnetic susceptibility of CoCr2S4 has a shape that is characteristic of a ferrimagnetic substance (fig. 79). Reported values of the asymptotic and the ferrimagnetic Curie temperature are - 3 9 0 ± 40 K and 240 _ 5 K (Lotgering 1956), - 4 8 0 K and 227 K (Pellerin and Gibart 1969), and T~ = 220 ± 1 K (Shick and Von Neida 1969). The spontaneous magnetization extrapolated to 0 K amounts to
712
R.P. VAN STAPELE
t :3 U (~ 0 E ea
200 l
3
I
I/ Ig I! o
I~
2o0
100 I
I
I
I
,,oo 660 860 ooo temperature(K) Fig. 79. Magnetization M and inverse molar susceptibilityX~1 of CoCr2S4,according to Pellerin and Gibart (1969). 2.55 +0.06 p,B/molecule (Lotgering 1956), 2.43 ~B/molecule (fig. 79) (Pellerin and Gibart 1969), and 2.4/~B/molecule (Shick and Von Neida 1969). With 6/~B of the Cr 3+ ions opposite to the Co moment in a simple N6el configuration, the Co ions have a moment of 3.45 to 3.57/~B. This corresponds to a g-factor of 2.30 to 2.38; a reasonable value for Co 2+ ions on tetrahedral sites (Gilbart et al. 1969). A molecular field analysis of the magnetic data indicates a dominating exchange interaction between the Cr s+ and Co 2+ ions and a weak interaction between the Cr ions (Gilbart et al. 1969). As-grown single crystals of CoCr2S4 were observed to have a cubic magnetocrystalline anisotropy with a cubic anisotropy constant of 3.45 × 105 erg/cm s at 77 K. Annealing in an oxidizing or a reducing atmosphere was found to influence the cubic anisotropy, while the annealed crystals show a weaker induced uniaxial anisotropy after cooling down to 77 K in a magnetic field (Gibart et al. 1976). CoCr284 is a semiconductor with a resistivity that is strongly sample-dependent. The slope of the log p vs T -1 curve is generally larger in the paramagnetic state than in the ferrimagnetic state, which observation has been made in polycrystalline samples (Bouchard et al. 1965, Albers et al. 1965) as well as in single crystals (fig. 80) (Pellerin and Gibart 1969, Watanabe 1973). Polycrystalline samples have either p-type (Bouchard et al. 1965) or n-type conduction (Albers et al. 1965), while single crystals show n-type conduction (Watanabe 1973, Gibart et al. 1973). The resistivity of undoped samples does not show an anomalous maximum near the Curie temperature. However, a magnetoresistance effect near T~ was observed in p-type doped polycrystalline samples (Bongers et al. 1969) and n-type single crystal (Watanabe 1973). Heating of single crystals in vacuum or in a sulphur atmosphere strongly affects the resistivity (fig. 80). The change was found to be opposite to that in FeCr2S4 (see section 6.3), namely an increase after annealing in a sulphur atmosphere and a decrease after annealing in vacuum (Watanabe 1973, Gibart et al. 1976). The mechanism of the n-type conduction is unknown, but the observed proper-
SULPHOSPINELS I
713 I
10 5
10 4
T
10 3
o
102 >,,, 4--
101
10o
I
0
5
[
110 103/T(K - )
15
Fig. 80. Resistivity of single crystals of CoCr2S4: (a) as-grown; (b) S-annealed at 700°C for 72 hr and (c) vacuum-annealed at 600°C for 68 hr (Watanabe 1973). ties point to donor states due to a sulphur deficiency, already present in as-grown crystals (Watanabe 1973). The optical properties of hot-pressed samples were investigated by Carnall et al. (1972). In the spectral range between 7 and 12 ~m the samples are transparent with a residual absorption coefficient of about 7 cm -1, a refractive index of 3.56 and a Faraday rotation that decreases with increasing wavelength from 2100 deg/cm at 5 ~m to 320 deg/cm at 10.6 ~m in the magnetic saturated state at 80 K. At longer wavelength the absorption spectrum shows four bands at 388, 330, 258 and 120 cm 1 due to the four infrared-active phonons of the spinel structure (Lutz and Feh6r 1971, Carnall et al. 1972). The onset of the strong absorption at the short wavelength side is due to crystal field transitions in the Co 2+ ions. Large Kerr rotations (fig. 81) were observed in dispersion-like peaks at 1.0 and 1.7 ~m, associated with the 4Az~4T1 transition of tetrahedrally coordinated Co 2+ ions (Ahrenkiel and Coburn 1973, Ahrenkiel et al. 1974). These transitions were also observed in the reflectance circular dichroism spectra (Ahrenkiel et al. 1973, Coburn 1973). The large remanence in the magneto-optical properties at normal incidence and the large Kerr effect has made hot-pressed CoCr2S4 interesting from the point of view of optical data-storage materials (Ahrenkiel et al. 1974). Nuclear magnetic resonance spectra of 53Cr nuclei in CoCr2S4 were measured at 77 K (Le Dang Khoi 1968) and of 53Cr and 59Co at 4.2, 55 and 78 K (Yokoyama et al. 1970). The last authors report the 53Cr resonance line to have a triplet structure, which was not analyzed. The central frequency is 50.0 MHz at 4.2 K,
714
R.P. VAN STAPELE
*8 •"
+6
\
+2 0)
o
o "[3
-2
\....'
U
-6 -8
10
1.5
2.0
wavelength (p) Fig. 81. Double polar Kerr rotation (a) and Kerr ellipticity (b) of C o C r 2 S 4 at 80 K in a saturating magnetic field (Ahrenkiel and Coburn 1973). which corresponds to a (negative) hyperfine field of 208 kOe. The nuclear magnetic resonance signal of 59Co was found around 31.2 MHz at 4.2 K. The increase of the resonance frequency in an applied magnetic field shows the hyperfine field to be positive. The small value of the hyperfine field (31 kOe at 4.2 K) is typical of tetrahedrally coordinated Co 2+ ions in which a positive orbital hyperfine field and a negative core polarization hyperfine field have nearly the same magnitude (Yokoyama et al. 1970). A large negative hyperfine field (-405 + 20 kOe at 80 K) was observed in the M6ssbauer spectrum of ngsn in a sample with the composition COl.lCra.sSn0.1S4. The spectrum is strongly broadened with an additional splitting of the lines, pointing to non-equivalent positions of the Sn ions in the lattice.The isomer shift relative to SnO2 is large and indicates an increased density of s electrons at the Sn ions (Lyubutin and Dmitrieva 1975). Finally, X-ray absorption spectroscopy has shown that the shift of the cobalt K absorption discontinuity agrees well with the divalency of the Co ions (Ballal and Mande 1977).
6.5. The mixed crystals Fel-xCoxCr2S4, Fel_x(Cl~l/2Irtl/2)xer2S4, Coa-xCdxCr2S4 and Col-x( Cul/2Fel/2)xCr2S4
Fel-xCdxCr2S4,
In the mixed crystal series Fel xCoxCr2S4 the lattice parameter decreases roughly linearly with x (Treitinger et al. 1976b). The Curie temperature increases almost linearly with x, the value at x = 0.15 being somewhat lower than that of pure
SULPHOSPINELS
715
FeCr2S4. Samples with x ~<0.95 have a p-type conduction with an anomaly in the resistivity and a negative magnetoresistance effect (3 to 4%) near the Curie temperature. Pure CoCr2S4 has an n-type conduction with a small Seebeck coefficient and a very small negative magnetoresistance effect (0.3%) (Treitinger et al. 1976b). Samples with x = 0.98 (Van Diepen and Van Stapele 1973) and CoCr2S4 samples with small unspecified amounts of Fe (Tanaka et al. 1973) have been used in a study of the 5E ground state of tetrahedrally coordinated Fe 2+ ions by means of Mrssbauer spectroscopy (section 6.3). Mixed compounds Fel-x(Cul/2Inl/2)xCrzS4 between the semiconducting ferrimagnet FeCrzS4 and the semiconducting antiferromagnet Cul/2Inl/zCr2S4 (see section 5.9) are single-phase spinels with a lattice parameter that varies linearly with x (Grbel et al. 1975). As measured by the intensity of the (200) X-ray reflection, ionic ordering of the Cu + and In 3+ ions on the tetrahedral sites exists down to x = 0.4. For smaller (Cut/2Inl/2) concentrations the Cu +, In 3+ and Fe 2+ ions are statistically distributed over the tetrahedral sites (Grbel et al. 1975). The compounds are ferrimagnets in the range 0 ~<x < 0.8 and antiferromagnets for x > 0.8 with critical temperatures as given in fig. 82 (Grbel et al. 1975). The compounds are semiconductors with a room temperature resistivity that increases with increasing x. In the iron-rich samples a negative magnetoresistance effect has been observed with a high-temperature maximum shifting in position with respect to the Curie temperature (fig. 83). An explanation of this phenomenon was not given (Treitinger et al. 1976a). In the mixed compounds Fel xCdxCr2S4 between the ferrimagnet FeCr2S4 and the ferromagnet C d C r 2 S 4 the lattice parameter varies linearly with x (Spender and Morrish 1971, Barraclough et al. 1974). With decreasing Fe content, the magnetic properties gradually change from ferrimagnetic to ferromagnetic. The asymptotic Curie temperature increases and the Curie temperature decreases as shown in figs. 84 and 85 (Bongers et al. 1969, Spender and Morrish 1971, Barraclough et al. 1974). In view of the rather large magnetoresistance effects the resistivity and the 200
150
t K
100
50 b e~.~e.--,.-
0
~ 0.2
I 0.4
I 0.6 X
01.8
1.0
~--
Fig. 82. Curie temperature (a) or Nrel temperature (b) of Fel_x(CumIn~/2)xCr2S 4 as a function of the composition (Grbel et al. 1975).
R.P. VAN STAPELE
716
T4
X=0.4
Ap Po
X=0.2
~,~ 050
100
X=0
150
200
250
temperoture (K)
Fig. 83. Magnetoresistance effect of Fel ~(Cumlnl/a)xCr2S4as a function of the temperature for x = 0, 0.2 and 0.4 (Treitinger et al. 1976).
8 (K)
%(K)
,,-200 l
I lgC I
[]
160
+ []
o
140
[]
-100 o r-I
+
80 0
6 -200
÷
I,
,,100 0
[]
120 100
.t+
•
I
Q2
I
I
04 '0'6 X
' 08
1.0
Fig. 84. Asymptotic Curie temperature 0 (O, +) and ferromagnetic Curie temperature Tc (©, [~) of powder samples of Fei-xCdxCr2S4, according to Bongers et al. (1969) (O, (3) and Spender and Morrish (1971) (+, E3).
magnetoresistance effect were measured in undoped single crystals (Barraclough et al. 1974), in hot-pressed Ag-doped powders with a p-type conduction (Bongers et al. 1969) and in Cu-doped single crystals with a p-type conduction (Treitinger et al. 1978b). The largest magnetoresistance effect (17%) was observed near the Curie temperature (147K) of an undoped single crystal with the composition Fe0.46Cd0.54CrzS4 (Barraclough et al. 1974). X-ray diffraction of a powder sample with the composition Fe0.83Cd0.17Cr2S4 showed the lattice parameter to decrease regularly with decreasing temperature, whereas the line width of the diffraction lines broadens unusually. This broadening, which was also observed in CdCr2S4 and FeCrzS4, indicates inhomogeneous lattice distortions (G6bel 1976). Complicated 57Fe M6ssbauer spectra were observed in the compounds
SULPHOSPINELS
717
u 5
•
+
•
O
E 4 3
E O E o ...., t'O I
I
'0.2
I
I
o14 o16'o'.8 X
Fig. 85. Magnetic moment of powder samples of Fel-xCdxCr2S4, (0) extrapolated to 0 K (Bongers et al. 1969) and (+) extrapolated to infinite magnetic fields at 4.2 K (Spender and Morrish 1971). The solid line represents a linear variation between 1.86 #B/molecule for FeCr2S4 (section 6.3) and 6 #B/molecule for CdCr2S4.
Fel_xCdxCrzS4 with 0 < x ~<0.9 (Spender and Morrish 1973). The simple M6ssbauer spectrum of Fe0.02Cd0.98Cr2S4 was described in terms of a magnetically induced orbital hyperfine field and quadrupole splitting (Van Diepen and Van Stapele 1972). In the series of mixed compounds C o l - x C d x C r 2 S 4 the lattice parameter varies linearly with x (Tret'yakov et al. 1975). The magnetic properties change gradually from the ferrimagnetic properties of CoCr2S4 to those of the ferromagnet CdCr2S4, the Curie temperature decreasing and the magnetic moment increasing with x (Coburn et al. 1972, Tret'yakow et al. 1975) (fig. 86). In view of applicable 250
-6 ÷+
2OO
+x
0 0 0
5
T
o
x
4
o
'~ 150
o
x
E
O
o
3 e e
~- 10(?
S c-
2 :£ N
@ 50
I
i
0.'2
' X
I
o16 o'8 ~--
I
C
0
1.o
Fig. 86. Curie temperature (O, C)) and magnetic moment (+, x) of Coi-xCdxCr2S4, according to Coburn et al. (1972) (0, +) and Tret'yakov et al. (1975) (O, x).
718
R.P. VAN STAPELE
magneto-optical properties, the absorption spectrum and the Faraday rotation of hot-pressed samples were measured. The absorption between 0.8 and 5 Ixm is roughly proportional to the Co concentration and shows at low Co concentrations absorption bands at 1.62, 1.72 and 1.95 g m due to the 4A2---~4Tl(F) crystal field transition of Co 2+ and a weaker band near 3 Ixm, probably due to the 4A2---~4T2(F) crystal field transition of Co 2+. In the spectral range between 4 and 14 ~xm the Faraday rotation increases with decreasing wavelength and increasing Co concentration (Coburn et al. 1972). The reflectance circular dichroism spectrum in the near infrared shows large dispersions at about 1 txm and 1.7 Ixm due to the crystal field transitions 4A2(F )--~ 4TI(P ) and 4A2(F ) ~ 4TI(F ) of the Co 2+ ions (Ahrenkiel et al. 1975). Single-phase spinels Col-x(CUl/2Fea/2)xCr2S4 between the semiconducting ferrimagnets CoCr2S4 and Cu +1/2Fe3+ 1/2Cr2S4 (section 6.6) were prepared in an attempt to realize sizable magnetoresistance effects near a magnetic ordering at room temperature. The Curie temperature varies linearly between 211 K at x = 0 and 350 K at x = 1. The magnetoresistance effect is rather small and negative with a maximum value near the Curie temperature (Treitinger et al. 1976a). 6.6. The mixed crystals ml-xCuxCr2S4 with M = Mn, Fe and Co
Single-phase spinels Mnl-xCuxCr2S4 between the semiconducting ferrimagnet MnCr2S4 and the metallic ferromagnet CuCraS4 have only been obtained for x i> 0.8 and x < 0.4. The Mn-rich compounds are metastable, heating at 300°C effects a decomposition into two spinel phases. In the single-phase regions the variation of the cell edge is smaller than would correspond to a linear variation between the lattice parameters of MnCr2S4 and CuCr2S4. From the magnetic moments measured for x = 0, 0.05, 0.2 and 0.8 between 1.6 and 50 K in magnetic fields up to 150 kOe, it was concluded that the Mn ions remain in the divalent state in the mixed compounds (Nogues et al. 1979, Mejai and Nogues 1980). A different situation is encountered in the series Fel-xCuxCr2S4. The electrical and magnetic properties of these compounds clearly indicate that the Cu ions ionize the ferrous ions to ferric ions (Lotgering et al. 1969)*. The series does not show a miscibility gap. Throughout the series, single-phase samples were prepared and the cell edge varies approximately linearly with x (Haacke and Beegle 1967). The electrical transport properties vary in a remarkable way (fig. 87) (Haacke and Beegle 1968, Lotgering et al. 1969). The occurrence of n-type conduction is observed at composition with x between 0.2 and 0.5, whereas samples with a smaller or larger Cu concentration have a p-type conduction (Haacke and Beegle 1968, Lotgering et al. 1969), and the observation that Fel/2Cut/2Cr2S4 is a semiconductor (Lotgering et al. 1969) led Lotgering et al. (1969) to the conclusion that the Fe z+ levels fall in the energy gap between the valence and the conduction band, as sketched in fig. 88. A replacement of 2Fe 2+ in FeCrzS4 by Fe3++ Cu + is represented by a hole in the Fe z+ level (section 3) and a filled Cu + level below the top of the valence band. The Fe 2+ levels are empty at x = ½. When x increases * See notes added in proof (1) on p. 737.
SULPHOSPINELS
719
500, 400t
T
3OO 2OO 100
:3, ml
o -100
.£3 -200 PA
-300 -4ooi
0
I 0
0.5 1 X----~
0.5 X
~-
Fig. 87. Seebeck coefficient c~ and resistivity p at room temperature of Fel-xCuxCr2S4, according to Haacke and Beegle (1%8) (©), Bouchard et al. (1%5) (0) and Lotgering et al. (1969) (11). Sample A has been quenched from 700°C, sample B has been slowly cooled with annealing at 500 ° and 100°C.
further, Fe 3+ is replaced by Cu ÷ with charge compensation by two holes in the valence band. The formal valence distribution is consequently written as 2+ 3+ + 3+ 2 3+ + Fel-2xFex CuxCr2 $4 in the range 0 ~< x < ½ and as Fel_xCuxCr2S4 with ( 2 x - 1) holes in the valence band and the Cr 3+ states for ½ < x ~< 1". This explains the observed p-type conduction for x >½ and for small x as well as the n-type conduction in the intermediate region, where the conduction is due to the simultaneous presence of ferro and ferric ions with less than half of the iron ions
nduction bGnd Fe3. (X) 2~ --g Fe *(1-2X
Fe3+{1/2)~
EF
Cr3*E;~NTZ,{~)~Volence
~r.'//,/~
Cr3÷
Fe3+(I_X)r(2X-1)holes C r ~ F
hood
g(E)~,,-
0~X<1/2
g(E) ~ X= 112
g(E) --~ 1/2<X<~1
Fig. 88. Energy level schemes of Fel-xCuxCr2S4 after Lotgering et al. (1969). The number of states per molecule is indicated between brackets. * See notes added in proof (m) on p. 737.
720
R.P. VAN STAPELE
in the divalent state. At x = ½, with all iron ions in the trivalent state, the gap between the empty Fe 2+ states (i.c. Fe 3+) and the filled Cu ÷, Cr 3+ and valence band states explains the semiconducting behaviour, with a large positive or negative Seebeck coefficient depending on the details of the preparation (Lotgering et al. 1969). The magnetic properties show a gradual change from ferrimagnetism in FeCrzS4 to ferromagnetism in CuCrzS4. The Curie temperatures are enhanced with respect to a linear variation with x (Haacke and Beegle 1967, Lotgering et al. 1969) (fig. 89), which was attributed to a negative Fe3+-Cr 3+ superexchange interaction that is stronger than the Fe2+-Cr 3+ interaction (Lotgering et al. 1969).
z,0C ,,
D (9
CL E
o
30c
o •
...,..:.i
o
:.,.
jo
I
f f f
20(
10( 01~2 I Oil& I 01,6 I 018
X
' 1.0
J,-
Fig. 89. Curie temperature of Fei-xCuxCr2S4, according to Haacke and Beegle (1967) (0) and Lotgering et al. (1969) (O). It is not possible to account for the magnetization data (Haacke and Beegle 1967, Lotgering et al. 1969). It is, however, difficult to measure the saturation magnetization correctly. At small Cu concentrations, the strong magnetic anisotropy of tetrahedrally coordinated Fe 2+ ions (section 6.3) makes polycrystaltine samples difficult to saturate, and it is not possible to prepare pure Cu-rich samples (Lotgering et al. 1969). The saturation m o m e n t of Fel/2CumCr2 3+ 1+ 3+S4 is 3.2/xB/molecule, 10% lower than the 3.5/xB/m01ecule expected for a simple N6el configuration with Fe in the trivalent state (Lotgering et al. 1969). M6ssbauer spectra of 57Fe, measured between 4 and 373 K in Fel/zCUl/zCr2S4 (Lotgering et al. 1969) and above the Curie t e m p e r a t u r e as well as at 77 K for the same and other compositions (Haacke and Nozik 1968) show the presence of Fe 2+ and Fe 3+ ions in Fel-xCuxCr2S4 with x <½ and of exclusively Fe 3+ ions for x ~>½. The hyperfine field on the iron nucleus in Fel/zCul/zCr2S 4 is positive, i.e. opposite to the m o m e n t of the Fe sublattice, in agreement with a simple N6el configuration. The hyperfine field versus t e m p e r a t u r e curve is m o r e concave than the magnetization curve (Lotgering et al. 1969). The absence of a quadrupole splitting and of dipolar contributions to the hyperfine field in the M6ssbauer spectrum of Fel/2Cua/zCrzS4 proves the local symmetry on the iron sites to be perfectly cubic, which is a strong indication of a 1 : 1 ordering of the differently charged Fe 3+ and Cu 1+ ions on the tetrahedral sites
SULPHOSPINELS
721
(Lotgering et al. 1969). Because of the too small difference in scattering power of the Fe 3+ and Cu 1+ ions, this ordering cannot be detected by means of X-ray diffraction. However, superstructure X-ray reflections were observed in In 3+ mCu 1+ 1/2CrzX4 with X = S or Se (Lotgering et al. 1969) and later on in a number of similar compounds (see section 5.9). The ionic ordering in Fel/2Cul/zCr2S4 permits the observation of Cu nmr lines, which would otherwise have been strongly broadened. The hyperfine field on the Cu nucleus was measured as a function of temperature. In terms of spin density in the empty 4s shell, the magnitude of the hyperfine field is comparable with that on the nuclei of other diamagnetic ions, like Cd 2+ and Hg 2+ (Locher and Van Stapele 1970). Finally we mention the recent confirmation of a N6el spin configuration in Fe0.sCu0.zCr2S4 by means of neutron diffraction (Babaev et al. 1975). The compounds COl-xCuxCrzS4 have been investigated in much less detail. Lutz and Becker (1973) have reported the existence of a complete series of solid solutions. The lattice parameter varies in a non-linear way. As a function of the composition the Seebeck coefficient does not change sign as in Fel-xCuxCrzS4, but is positive throughout the series. The conductivity of pressed samples increases rapidly with x with a positive temperature coefficient up to x = 0.2, and is metallic at larger Cu concentrations. At x = 0.2 the cell edge starts to decrease to the smaller value of CuCr2S4, which is reached at x = 0.80 (Lutz and Becker 1973). The only information on the valencies of the ions comes from the chemical shift of copper and cobalt K absorption discontinuities in COl/2CUl/2CrzS4, which shows that Co is in the divalent state, whereas Cu is monovalent (Ballal and Mande 1977). This result and the absence of a change in sign in the Seebeck coefficient indicates that the Co 2+ levels are well below the top of the valence band. 6. 7. The mixed crystals Ml-xNixCrzS4 with M = Mn, Fe, Co, Cu and Z n Attempts were made to prepare solid solutions with the spinel structure between a number of sulphospinels MCrzS4 and NiCr2S4 that itself crystallizes in the ordered cation-defective NiAs structure. It was found for M = Mn, Fe, Co, Cu and Zn that the spinel structure is stable in a limited range of Ni concentrations. This range is given in table 21 for each of the systems investigated. The table also summarizes some other properties. The lattice parameter generally decreases and the Curie temperature increases with increasing x. The only systems whose physical properties have been studied in some detail are Znl_xNixCrzS4 (Itoh et al. 1977) and Mnl_xNixCr2S4 (Mejai and Nogues 1980). The latter authors measured the magnetization of Mn0.9Ni0.1Cr2S4 at 7 and 9 K in magnetic fields up to 150 kOe. They discussed the influence of the Ni ions on the transitions between the various spin configurations in MnCr2S4 (see section 6.2). ZnCr2S4 is an antiferromagnetic semiconductor (section 5.2). Substitution of Ni for Zn does not change the type of conduction, as the resistivity of Zn0.6Ni0.4Cr2S4 (fig. 90) clearly shows. Itoh et al. (1977) consequently conclude that Ni is divalent, as represented by Zn0.~q'10.4Cr2 2+ .2+ 3+$4. The paramagnetic susceptibility is charac-
722
R.P. V A N S T A P E L E T A B L E 21 Some crystallographic and magnetic properties of the spinel systems M>xNixCr2S4 with M = Mn, Fe, Co, Cu or Zn. References: (a) Lisnyak and Lichter (1969), (b) Lutz et al. (1973), (c) R o b b i n s and Becker (1974) and (d) Itoh et al. (1977). o
Lattice constant (A)
System Mnt-xNixCr2S4 Fel-xNix Cr2S4 Col-xNixCr2S4
Cul-xNixCrzS4 Znl-.NixCr2S4
Curie t e m p e r a t u r e (K)
Stability range
x = 0
at maximal x
x = 0
x = 0.3
Ref.
x x x x x x x
10.11 9.995 9.918 9.923 9.936 9.820 9.986
10.068 9.953 9.898 9.909 9.898 9.801 9.945
74 185
110 214
235
250
TN = 16
-- 170 at x = 0.4
(c) (c) (a) (b) (c) (b) (d)
~0.3 ~ 0.3 ~<0.4 ~< 0.2 ~ 0.4 ~ 0.26 ~ 0.4
J
E 13
°° °%° °°.°, %°°
0
°. i
I
i
I
I
I
I
I
I
100 200 temperoture (K)
I
I
300
Fig. 90. Electrical resistivity of Zn0.6Ni0.4Cr2S4 as a function of temperature (Itoh et al. 1977).
teristic of a ferrimagnet which, for x = 0.4, has an asymptotic Curie temperature of - 2 9 9 K and a Curie constant that is consistent with the spin-only values of Cr 3+ and Ni >. The magnetization versus temperature curves measured in 16 k O e (fig. 91) show a m a x i m u m at low temperatures. The magnetization cannot be saturated except for the composition x = 0.4, where it reaches at 4 . 2 K a value of 3.0/xB/molecule. This is much smaller than the 5.2/xB/molecule expected for a simple Nrel configuration with 2/xB on the Ni 2+ ions (Itoh et al. 1977). 6.8. The mixed crystals MCrz-xlnxS4 with M = Mn, Fe, Co and Ni In this section we review briefly the properties of mixed crystals between the ferrimagnets MCr2S4 with M = Mn, Fe and Co and the corresponding indium sulphospinels MIn2S4. A m o n g the latter c o m p o u n d s MnIn2S4 is a partially inverse spinel, the other c o m p o u n d s MIn2S4 (M = Fe, Co and Ni) being inverse spinels
SULPHOSPINELS
60
I
i
i
,
723
i
•',•.
50 • X=O./.
l
•',;,
4O
c~ 30
X= 0.3 '
E
(11
2C
X=0.2
,....
10
x:ol ........ "'.... '
'
'
"...:.... '
temperature (K)
'
'2oo
~-
Fig. 91. Magnetization o- per gram of Znl xNixCr2S4 measured as a function of temperature in 16 kOe (Itoh et al. 1977).
(Hahn and Klingler 1950)• The indium sulphospinels are all paramagnetic down to 4.2 K (Schlein and Wold 1972)• The magnetic susceptibilities follow a Curie-Weiss law with a negative asymptotic Curie temperature. The molar Curie constant agrees with the spin-only value in the case of Fe and Ni, but deviates from it in the other cases (table 22). Electrical resistivity measurements at room temperature indicate that the c o m p o u n d s are semiconductors (Schlein and Wold 1972). The large negative asymptotic Curie temperature of NiIn2S4 is anomalous, since the 90 ° Niz+-S-Ni 2+ exchange interaction is expected to be positive• This anomaly and the lack of antiferromagnetic ordering have been discussed by G o o d e n o u g h (1972)• In the system MnCrz_xInxS4 single-phase spinels were prepared between x = 0 and x = i o(Darcy et al. 1968)• Theo lattice parameter changes linearly from a = 1 0 . 1 0 8 A at x = 0 to a = 1 0 . 4 1 8 A at x = 1. It was concluded from X-ray diffraction data that the In 3+ ions replace Cr 3+ ions on the octahedral sites, so that T A B L E 22 Cell edge (a), asymptotic Curie temperature (0) and molar Curie constant (Cm) of the compounds MIn2S4, according to (1) Schlein and Wold (1972) and (2) Eibschfitz et al. (1967a).
Cm
Cm
Compound
a (A)
0 (K)
(exp.)
(spin-only)
Ref.
Mnln2S4 FelnzS4
10.72 10.61 10.630 10.58 10.50
-78 -76 - 122 - 134 -144
4.00 3.10 2.94 2.84 1.16
4.38 3.00
(1) (1) (2) (1) (1)
Coln2S4 Niln2S4
1.87 1.00
724
R.P. VAN STAPELE
the tetrahedral sites are always occupied solely by Mn 2+ ions. MnCr2S4 is a canted ferrimagnet in which a strongly positive Cr3+-Cr3+ superexchange interaction combines with weaker negative Mn2+-Cr 3+ and MnZ+-Mn 2+ superexchange interactions (section 6.2). Substitution of In for Cr reduces the magnetic m o m e n t (at 4.2 K and 10 k O e from 1.27/xB/molecule at x = 0 to 0.85/zB/molecule at x = 0.3) as well as the Curie t e m p e r a t u r e (fig. 92), effecting a r e m a r k a b l e change from ferrimagnetism to antiferromagnetism at x = 0.4. The measured paramagnetic m o m e n t s are low c o m p a r e d to the theoretically expected values (Darcy et al. 1968). 100
I
50
'\% \
\ o
~J c~.
E
0
I~L
I
×~"
I
o
~
I
~ x ~ 0 ~°
~
o
I
I
I
X - - ~
I
1.'0
x~,~
-50
Fig. 92. Curie temperature Tc, Ndel temperature TN and asymptotic Curie temperature 0 of MnCrz-xInxS4, according to Darcy et al. (1968). MnCrInS4 was also prepared by Mimura et al. (1974). These authors confirm the cation distribution determined by Darcy et al. (1968), but their samples are paramagnetic down to 4.2 K. In the system FeCrz_xInxS4 a complete series of mixed crystals can be prepared. The lattice p a r a m e t e r increases linearly from 9.998 A at x = 0 to 10.610 A at x = 2 (Brossard et al. 1976). From the intensity of X-ray diffraction lines and from paramagnetic 57Fe M6ssbauer spectra the cation distribution was determined (Brossard et al. 1976). The fraction y of In ions on tetrahedral sites in Fel yIny[Cr2 xInx_yFey]S4 increases gradually with x (fig. 93). Magnetic m e a s u r e m e n t s (Goldstein et al. 1977a) show that the compositions 0 <~ x ~< 0.8 are ferrimagnetic. The Curie t e m p e r a t u r e decreases slowly with x. The measured saturation magnetizations agree with a collinear N6el spin structure with Fe 2+ spins on tetrahedral sites antiparallel to Fe 2+ and Cr 3+ spins on octahedral sites. Compositions in the range 1.3 ~< x ~< 2 are antiferromagnetic with relatively low N6el temperatures (20 K at x = 1.6). In the range 0.8 ~< x <~ 1.3 the magnetic behaviour changes from ferrimagnetic to antiferromagnetic. The compound FeCrInS4 with the cation distribution Fe0.41In0.59[CrIn0.41Fe0.59]S4 is ferro-
SULPHOSPINELS
725
1
Y
I 0.8 0.6 0.4 0.2 00-~
~
'
1'
'
'
'
~X
'
2
Fig. 93. Cation distribution Fez yIny[Cr2xInx yFey]S4,according to Brossard et al. (1976). magnetic with Tc = 75 K and a saturation moment of 0.8/xB/molecule. These results are at variance with the findings of Mimura et al. (1974), who found FeCrInS4 to be an antiferromagnet with a positive 0 of 82 K and TN = 20 K. In their sample the cation distribution is inverse, e.g., In[CrFe]S4. The M6ssbauer spectrum of octahedral Fe z+ ions in FeCrz_xInxS4 measured at room temperature as a function of x (Brossard et al. 1976) essentially agrees with the spectrum of FeCrInS4 measured by Mimura et al. (1974) and with the spectrum of FeIn2S4 measured by Eibschtitz et al. (1967a) and by Yagnik and Mathur (1967). The large quadrupole splitting of this spectrum is due to the trigonal crystal field splitting of the 5T2 ground state of octahedral Fe 2+ ions. In addition to MnCrInS4 and InCrFeS4, Mimura et al. (1974.) prepared InCrCoS4 and InCrNiS4. In these compounds the In ions occupy the tetrahedral sites. Both compounds order antiferromagnetically below 36 and 2 2 K respectively. The paramagnetic susceptibility follows a Curie-Weiss law in InCrNiS4 with a positive asymptotic Curie temperature of 26 K and a rather low molar Curie constant of 1.75. The paramagnetic susceptibility of InCrCoS4 deviates severely from a Curie-Weiss behaviour. At 4.2 K, the magnetic moment increases in a non-linear metamagnetic way in fields up to 8 kOe.
6.9. The mixed crystals MnCr2-xVxS4 The system MnCr2-xVxS4 was investigated by Goldstein et al. (1977b). The spinel phase exists up to x = 0.6 with lattice parameters that increase slightly with x. A neutron diffraction study of a sample with composition MnCq.sV0.2S4 shows that most of the V ions occupy octahedral sites. The material is ferrimagnetic with a N6el spin configuration. A transition to a canted spin configuration, as in MnCr2S4 (section 6.2), does not take place above 1.5 K. Measurements of the magnetization at 4.2 K in magnetic fields up to 150 kOe revealed a decrease of the spontaneous magnetization with increasing x. In high magnetic fields the materials show a transition from the N6el configuration to an "oblique" spin structure. The critical
726
R.P. VAN STAPELE
field for that transition decreases from 110 k O e at x = 0 to 75 k O e at x = 0.6. From the magnetic behaviour Goldstein et al. (1977b) conclude that the V 3+ spins couple antiferromagnetically to the Cr s+ spins. 6.10. The mixed crystals FeCr2_xFexS4 In this section we will briefly review the properties of solid solutions between FeCr2S4 and Fe3S4. The properties of the latter c o m p o u n d will not be discussed separately in this chapter. W e will confine ourselves to a short catalogue of properties, referring to the introduction given by Spender et al. (1972) for a m o r e detailed account. Two structures of the c o m p o u n d Fe3S4 have been found in nature. One is the mineral smythite, with a hexagonal crystal structure; the other is the mineral greigite, which has the spinel structure (Skinner et al. 1964). The spinel compound can be synthesized, but synthetic samples are often contaminated with other iron sulphides. The cell edge of the mineral is 9.876 A (Skinner et al. 1964); literature values of the lattice p a r a m e t e r of synthetic materials vary between 9.81 o and 9.90 A. Fe3S4 is ferrimagnet with the spins ordered in a simple N6el configuration (Spender et al. 1972). U d a (1968), who has studied the c o m p o u n d extensively, measured a Curie t e m p e r a t u r e of 580 K and a saturation m o m e n t of 1.3/xB/molecule. Spender et al. (1972) reported the values 6 0 6 K and 2.2/zB/molecule in their p a p e r on the magnetic properties and the M6ssbauer spectra of Fe3S4. From conductivity m e a s u r e m e n t s these authors obtained indications for a semimetallic behaviour. Single-phase samples of Fel+xCr2-xS4 were prepared between x = 0 and x = 0.5 (Robbins et al. 1970b). The solid solutions crystallize in the spinel structure with a lattice parameter, that decreases from 9.995 A at x = 0 to 9.984 A at x = 0.5. In agreement with the high Curie t e m p e r a t u r e of Fe3S4, the Curie t e m p e r a t u r e of Fel+xCr2_~S4 increases from 180 K at x = 0 to 302 K at x = 0.5. The magnetic m o m e n t measured at 1.5 K on polycrystalline samples (in which the magnetization is difficult to saturate because of the strong magnetic anisotropy) changes from 1.52/xB/molecule in FeCr2S4 to 1.71/xB/molecule at x = 0.5 with a m a x i m u m of 1.79/xB/molecule at x = 0.3 (Robbins et al. 1970b). From the low t e m p e r a t u r e resistivity m e a s u r e m e n t s it appears that the compounds are semiconductors. The Seebeck coefficient is positive, decreasing from +80 fxV/°C in FeCr2S4 to +3 IxV/°C at x __40.4 (Robbins et al. 1970b). A more recent investigation of the c o m p o u n d FemCrl.8S4 by means of neutron diffraction and magnetic m e a s u r e m e n t s (Babaev et al. 1975) shows the c o m p o u n d to be a ferrimagnet with the spins ordered in the N6el configuration. The magnetization versus t e m p e r a t u r e curve, measured on a powder sample, has a m a x i m u m at about 90 K. This, together with a large coercive force of 1.5 k O e at 4.2 K, indicates a strong magnetic anisotropy at low temperatures. 6.11. The mixed crystals MCr2S4-xSex with M = Mn, Fe, Co or C u m F e m In the system MCr2S4-xSex with M = Mn, Fe or Co, solid solutions with the spinel structure between the semiconducting ferrimagnetic spinels MCr2S4 and the
SULPHOSPINELS
727
corresponding selenides, which crystallize in the cation-defective NiAs structure, have been prepared in a limited range of sulphur-rich compositions. This range decreases from 0 ~< x ~<2 for MnCr2S4_xSex to 0 ~< x ~< 1.25 for FeCr2S4 xSex and 0 ~ x ~< 1 for CoCr2S4-xSex. The Curie t e m p e r a t u r e decreases slowly with increasing Se content, which is attributed to a weakening of the superexchange interaction between the octahedral Cr 3+ ions and the tetrahedral/VI~+ = Mn 2+, Fe 2+ or Co 2+ ions (Gibart et al. 1973). T h e system MnCr2S4 xSex has been investigated in m o r e detail by measurements of the paramagnetic susceptibility, the magnetization at 15.3kOe as a function of t e m p e r a t u r e and the magnetization at 1.5K as a function of the strength of the magnetic field up to 60 k O e (Robbins et al. 1973). The m a x i m u m in the magnetization versus t e m p e r a t u r e curve, which is typical of MnCreS4 (section 6.2), was observed to have disappeared at x = 0.5 (fig. 94), while the magnetization at 1.5 K remains a linear function of the strength of the magnetic field. At higher Se concentrations the magnetization at 1.5 K becomes an increasingly non-linear function of the magnetic field. The Curie t e m p e r a t u r e decreases from 74 K at x = 0 to 56 K at x = 2, whereas the asymptotic Curie t e m p e r a t u r e increases linearly from - 2 7 K for MnCr2S4 to +50 K for MnCrzSzSe2. 'The observed change of the magnetic properties is attributed to a decrease of the strength of the negative Mn2+-Cr 3+ superexchange interaction with increasing Se concentration (Robbins et al. 1973). In the system FemCul/zCrzS4_xSex a spinel phase exists between x = 0 and x = 2.75 with a lattice p a r a m e t e r that varies linearly with the Se concentration. The Curie t e m p e r a t u r e decreases monotonically from 350 K for x = 0 to 280 K for x = 2.75. Conductivity m e a s u r e m e n t s show that the compounds are semiconductors with a negative magnetoresistance effect of about 3% at the Curie temperature (Gyorgy et al. 1973).
3.6 3.2 -5 2.8 2.4
x=0.5 x=0.25
~, 2.0 g 1.6 :,= 1.2 0 .N_ 0.8 c~
E
0.4. 0
40
80
120
160
200
24.0
2~,0
temperature (K) Fig. 94. Magnetization versus temperature of MnCr2S4-xSex in a magnetic field of 15.3 k O e (Robbins et al. 1973).
728
R.P. VAN STAPELE
7. Some rhodium and cobalt spinels
7.1. Introduction In this section we will review some Rh and Co spinels, which are interesting because of their contrasting properties. Although both Rh 3+ and Co 3+ are in the zero spin t6g state and occupy octahedral sites, the properties of CoRh2S4 and C03S4, for example, differ strikingly. As will be described later on, CoRheS4 is a semiconducting antiferromagnet with a high N6el temperature and a lattice parameter of 9.8 A whereas C03S4 is a metallic paramagnet with a lattice parameter of 9.4 A. This correlates with a cell edge of C03S4 smaller than and a cell edge of CoRh2S4 about equal to 9.8A, which is the edge of the smallest cell that can accommodate sulphur ions with a normal radius of 1.74 A (section 1). In a tight lattice like that of C03S4 the d electrons of the tetrahedrally coordinated cations are apparently delocalized, which gives rise to metallic conduction and anomalous magnetic moments. Within the class of Rh compounds interesting phenomena were observed in the system C01-xCuxRh2S4 and Fel-xCuxRh2S4. The properties of Fel-xCuxRh2S4 are very similar to those of Fel-xCuxCr2S4 (section 6.6), indicating Fe 2+ levels w i t h i n the energy gap. However, the properties of C01-xCuxRh2S4 indicate Co 2+ levels below the top of the valence band as in Col_xCuxCr2S 4 (section 6.6).
7.2. CoRh2S4, C01-xFexRh2S4 and FeRh2S4 CoRh2S4 is a normal spinel with a lattice parameter of about 9 . 8 A (table 1) (Blasse 1965). Since Rh in oxy- and sulphospinels always occurs as trivalent ions in the low-spin t6g state, the Co ions are the only magnetic ions. In the reciprocal magnetic susceptibility (fig. 95) a rather sharp minimum has been observed at 400 K, which indicates a surprisingly strong antiferromagnetic ordering of the Co spins (Blasse 1965). Other susceptibility data in the literature show a less pronounced maximum around 4 0 0 K (Kondo 1976), which probably can be connected with the difficulty of preparing pure samples (Lotgering 1968b). In the paramagnetic region the susceptibility follows a Curie-Weiss law with an asymptotic Curie temperature of - 4 0 0 K and a molar Curie constant of 2.3 (Blasse 1965). Without correction for the Van Vleck susceptibility of the Rh 3+ ions the value of the Curie constant corresponds to a g value of 2.2, which compares well with values usually found for Co 2+ on tetrahedral sites (for example, g = 2.25 for ZnS : Co 2+ (Ham et al. 1960). The magnetic susceptibility clearly shows that the Co ions are divalent. The observed negative temperature coefficient of the electrical resistivity (Blasse 1965, Kondo 1976) shows the compound to be a semiconductor, in accordance with the valencies Co:+Rh3+S4. The superexchange interaction between neighbouring A ions in spinel takes place via two anions and is therefore in most cases weak. According to Blasse (1963) non-magnetic B ions like Rh 3+ or Co 3+ possibly play a part in superex-
SULPHOSPINELS
729
600
\ 500
\ \\
I 400
x:o/x/ \
x~
/
3oc
x--o.y /*
./'~'f /
"
.,'~" 2oc
/
f\%/
..-~qs , /
" ~ "~z*~ ....*/
*"~x=zo
,oo :?i" Oi
I
200
I
I
I
400 600 800 temperature (K)
i
1000
Fig. 95. Reciprocal molar magnetic susceptibility of CoRh2-xCrxS4 as a function of temperature (Lotgering 1968b). Curve for x = 0 after m e a s u r e m e n t s of Blasse (1965).
change interactions between neighbouring A ions. The anomalously strong antiferromagnetic interaction in CoRh2S4 might be enhanced by the Rh 3+ ions. However, the results of an analysis of the magnetic properties of the system CoRhz_xCrxS4 (section 7.3) do not confirm this assumption (Lotgering 1968b). It is not possible to prepare single-phase samples of FeRhzS4 (Koerts 1965, Riedel and Karl 1979). Tressler et al. (1968) have reported that the compound has an unidentified complex distorted spinel structure. Attempts were made to prepare solid solutions of FeRhzS4 in CoRh2S4 (Kondo 1976). Single-phase samples could not be obtained. The main phase was found to be spinel, the main contamination RhzS3. The magnetic susceptibility, the electrical resistivity and the M6ssbauer spectra were measured and the results are ascribed to the main phase Col_xFexRh2S4 (Kondo 1976). The compounds are semiconducting antiferromagnets with a N6el temperature that decreases linearly from about 400 K for CoRh2S4 to 250 K for Co0.25Fe0.75RhzS 4. The susceptibility of the Fegh2S4 sample (more contaminated than the samples with other compositions) has a maximum at 20 K, decreasing monotonically at higher temperatures. However, extrapolation of the linear variation with x gives a N6el temperature of 200 K, roughly agreeing with the temperature of 190 K below which a broad paramagnetic line in the complex M6ssbauer spectrum of the
730
R.P. VAN STAPELE
FeRh2S4 sample was observed to be split into six lines. These data are confirmed by Spender's findings, that FeRh2S4 is a semiconducting antiferromagnet with a N6el temperature of 205 K (Spender 1973, referred to in Boumford and Morrish 1978). The M6ssbauer spectra of Col_xFexRh2S4 with x ~<0.75 were observed to be superpositions of many Fe z+ spectra with different values of hyperfine fields and quadrupole splittings (Kondo 1976).
7.3. The mixed crystals feRh2-xCrxS4, CoRh2-xfrxS4 and NiRh;-xCrxS4 In the system FeRh2-xCrxS4 relatively pure spinels were prepared in the range 0.8 ~< x ~<2 (Riede! and Karl 1979). The cell edge increases from 9.935 A at x = 0.8 to 9.998 A at x = 2. All spinels are normal with only Fe 2+ on tetrahedral sites. The materials are p-type semiconductors. The room temperature Mrssbauer spectra of 57Fe consist of several overlapping doublets with almost identical isomer shift but different quadrupole splittings, which are attributed to tetrahedral Fe 2+ ions with different numbers of Rh ions as nearest octahedral site neighbours. In the system CoRh2_xCrxS4, investigated by Lotgering (1968b), single-phase samples with the spinel structure were prepared for all x. The magnetic properties vary in an interesting way between the strong antiferromagnetism of CoRh2S4 and the ferrimagnetism of CoCr2S4 (section 6.4). The paramagnetic susceptibility (fig. 95) follows a Curie-Weiss law with asymptotic Curie temperatures as given in fig. 96 and Curie constants that vary roughly linearly between the values for CoRh2S4 and CoCr2S4. From the magnetic susceptibility of CoRhlsCr0.sS4, which shows a kink at 360 + 10 K and a ferrimagnetic Curie temperature at 50 K (fig. 95), Lotgering (1968b) concluded that the Co spins order antiferromagnetically at 700 6O0
T 500 4001
TN
~
z 300 2 ~" 200 100
o;
I X
Fig. 96. Absolute value t01 of the negative asymptotic Curie temperature, Nrel temperature TN and ferrimagneticCurie temperature Tcof CoRh2-xCrxS4as a functionof the composition(Lotgering1968b).
SULPHOSPINELS
731
3 6 0 K and that at the lower temperature of 5 0 K a transition occurs to a Yafet-Kittel configuration with canted Co spins opposite to the Cr spins. The observed variation with x of the saturation magnetization (fig. 97) can be described with a constant ratio c~ of 1.37 between the strength JAA of the negative C o - C o superexchange interaction and the strength JAB of the negative C o - C r superexchange interaction. In this description a configuration with canted Co spins occurs for Cr contents up to x = 1.65. For higher Cr concentrations the moments agree with a simple N6el configuration. Although the absence of a N6el temperature for x > 0 . 5 and the observed variation of the asymptotic Curie temperature and the ferrimagnetic Curie temperature cannot be explained within a molecular field approximation, the behaviour of the saturation magnetization as a function of x is typical of an anomalously strong C o - C o interaction in the whole range of x. This shows that the strong C o - C o interaction is not due to the presence of Rh 3+ ions (Lotgering 1968b). In the system NiRh2_xCrxS4 single-phase spinels were prepared in the range 0.3 ~< x ~<0.8 (Itoh 1979). The cell edge increases slightly from 9.702 A at x = 0 to 9.715 A at x = 0.8. The samples are ferromagnetic and have a metallic electrical conduction. The Curie temperature increases with x (fig. 98). The paramagnetic moment is roughly proportional to the Cr concentration and is about 0.9 per gramatom Cr. The ferromagnetic moments are shown in fig. 99. Although the magnetic behaviour is reminiscent of that observed in the series CuRh2_xCrxSe4 with x > 1 (section 4.6), the anomalous values of the magnetic moments cannot be reconciled with a specific valency of the Cr ions. This points to delocalized Ni 3
I
2
D O
o o
•
/
I
1
/
1.65
2
~x Fig. 97. Saturation moment Ms at 4.2 K of CoRh2-xCrxS4.The straight lines have been calculated with a Co moment of 3.6/zB and a Cr moment of 3/x~ for: (a) a triangular spin configuration with a = J A A / J A B = 1.37 (Ms=3(1-a-1)x) and (b) a simple N6el configuration (Ms = 3x-3.6). After Lotgering (1968b).
732
R.P. VAN STAPELE
100
8O
o
o
B 60
o o
(9
E
40 o o
I 20 ' o'2 ' o'.~ ' o's ' o18 X
'110
Fig. 98. Asymptotic ((2)) and ferromagnetic (O) Curie temperature of NiRh2_xCrxS4(Itoh 1979).
1.0/,
:z,
081 Q
.~_ 0.E .N_ "$ 0.4 cE 0.2
l
o
I
I
I
I
o12 o.~ o;
I
0'.8
I
1'.o
-----.,. X
Fig. 99. Magnetization at 4.2 K and 14.5 kOe of NiRhz-xCrxS4 (ltoh 1979). electrons that are partially spin-polarized in a direction opposite to that of the ferromagnetically coupled Cr spins (Itoh 1979).
7.4. The mixed crystals Fel_xCuxRh2S4 and C01-xCuxRh2S4 Inspired by the 1:1 ionic ordering on the tetrahedral sites in Fet/2Cul/2Cr2S4, Plumier and Lotgering (1970) investigated the properties of the c o m p o u n d FemCUl/2Rh2S4. The c o m p o u n d has the spinel structure with a = 9 . 8 5 A and u = 0.3815. X-ray diffraction clearly showed a 1 : 1 ordering of Fe 3+ and Cu 1÷ ions on the tetrahedral sites. The material is semiconducting with a large Seebeck coefficient, the sign depending on the details of the preparation. The most remarkable observed property of FemCUl/2Rh2S4 is its strong antiferromagnetism. A b o v e 170 K, the magnetic susceptibility follows a Curie-Weiss law with an asymptotic Curie t e m p e r a t u r e 0 = - 4 2 0 K and a molar Curie constant Cm = 2.32. T h e magnetic susceptibility contains a rather large temperature-in-
SULPHOSPINELS
733
dependent part, due to the diamagnetic susceptibility and the Van Vleck susceptibility of the Rh 3+ ions. Correction for these terms gives 0 = - 3 6 7 K and Cm = 2.09 (Boumford and Morrish 1978). The value of Cm agrees fairly well with the value 2.19 for trivalent iron ions. The susceptibility shows a maximum at 145 K below which the iron spins order antiferromagnetically. Neutron diffraction experiments revealed that the antiferromagnetic ordering is of the second kind, as in MnO. In this type of ordering the second-neighbour interaction dominates the nearest-neighbour interaction, which leads in the case of Feu2CuuzRh2S 4 to the conclusion that a surprisinglYoStrong superexchange interaction exists between Fe 3+ ions at a distance of 9.85 A. A study of the 63'65Cu nuclear magnetic resonance as a function of temperature in the paramagnetic state indicates a N6el temperature of 135 K, slightly below the value of 145 K mentioned above (fig. 100). The Fe 3+ ions were observed to give a negative transferred hyperfine field at the Cu nucleus, which would amount to -12.5 kOe for a saturated Fe 3+ magnetization (Locher and Van Stapele 1970). The semiconduction and the valencies Fel/zCul/zRh2S4 3+ ~+ clearly indicate that the Fe 2+ levels fall in the energy gap between the valence and the conduction band as in Fel-xCuxCrzS4 (section 6.6 and fig. 91 with Rh 3+ instead of Cr3+). This was recently confirmed by a study of the properties of Fel_xCuxRh2S4 with X/>0.06 (Boumford and Morrish 1978). Using X-ray diffraction these authors observed an undistorted spinel structure with a linearly varying lattice parameter throughout the series. Ordering of copper and iron ions was detected in the range 0.3 ~< x ~< 0.54. Magnetic measurements indicate antiferromagnetic behaviour for all compositions. The N6el temperature, as determined from M6ssbauer spectra, and the
200
l
100
o!2 ' o',~ ' o:~
-200
o:a
I
1.0
X
G)
× X
-300 × •
x
X
-4.00
X
8 Fig. 100. Fel-xCuxRh2S4. N6el temperature (T~) (from M6ssbauer spectra) and asymptotic Curie temperature (0) before (O) and after correction for the Rh 3+ Van Vleck susceptibility (x), according to Boumford and Moorish (1978); ([~) data of Plumier and Lotgering (1970), (O) data of M.R. Spender, Ph.D. thesis (University of Manitoba, 1973, unpublished).
734
R.P. VAN STAPELE
asymptotic Curie temperatures are given in fig. 100. Iron-rich compounds with 0.06 ~< x ~< 0.5 exhibit remanence and displaced hysteresis loops after cooling to 4 K in an external magnetic field of 18kOe. Both the isomer-shift in the M6ssbauer spectrum and the paramagnetic m o m e n t s indicate the presence of solely Fe 3+ for x/> 0.5 and a gradual change from Fe 3+ to Fe 2+ for x decreasing from 0.4 to 0.06. The observed behaviour agrees with the valencies 2+ 3+ + + Fel-2xFex CuxRh2S4 in the range 0 ~ x ~< 0.5 and Fel3 + xCuxRh2S4 for x I> 0.5. In contrast to the behaviour of Fel_xCuxRh2S4 the properties of Col_xCuxRh2S4 do not indicate Co 2+ levels in the energy gap. As has been mentioned in section 6.6, this is not the case either in Col_xCuxCr2S4, in which system indications were found for Co 2+ levels below the top of the valence band. However, particularly in the system COl-xCuxRh2S4, this position gives rise to remarkable properties, i.e. antiferromagnetism for 0 < x ~< 0.4, spontaneous magnetization for 0.4 ~< x ~< 0.7 and paramagnetism for 0.7 ~< x ~< 1. Single-phase preparations of Col_~CuxRhaS4 were prepared for 0.1~<x ~< 1 (Lotgering 1969). X-ray diffraction, which shows the presence of a spinel phase with a lattice p a r a m e t e r of 9.78 A, cannot establish the formation of mixed crystals, because of the equal values of the lattice parameters of CoRh2S4 and CuRh2S4. However, the change in physical properties proves the existence of solid solutions. The samples have a nearly temperature-independent, low resistivity and a positive Seebeck coefficient, decreasing from 125 ixV/deg for x = 0.1 to 25 txV/deg for the Cu-rich compositions with x t>0.5. Measurements of the magnetic susceptibility show that the Co-rich compositions with x ~<0.4 are antiferromagnetic with a N6el t e m p e r a t u r e that decreases with increasing x (fig. 101). In the range 0 . 4 4 x ~<0.7 the samples are ferromagnetic with Curie temperatures that link up with the N6el temperatures (fig. 101). The small spon-
J
_~2,~ &OOt 2
3OO
E
\ 200
\
100
0 0
Tc
I 0.2
I 0.4 . ~ X
i 0.6
0.8
Fig. 101. N6el (TN) or Curie temperature (To) of Col xCuxRh2S4, according to Lotgering (1969) (measured on quenched (ff3)or on annealed samples (mE)).
SULPHOSPINELS I
i
735 I
0.8 o
E 0.6
:3, G O
0.4 g) c(31 O
E
!
0.2 !
I
i !
I
I
0~
02
0.4 X
0.6
0.8
Fig. 102. Magnetization at 4.5 K in 20 kOe of Col-xCuxRh2S4 after Lotgering (1969) (measured on quenched (O) or on annealed samples (0)). t a n e o u s magnetization reaches a m a x i m u m of 1.6/XB/CO ion at x = 0.5 (fig. 102). C o m p o s i t i o n s with x ~ 0 . 7 are paramagnetic. A definite explanation of these properties was not given. It was, however, n o t e d that three ranges of compositions can be distinguished, if o n e tentatively assumes that the valence b a n d can a c c o m m o d a t e 30 < 1 holes a b o v e the C o 2+ levels: (i) 0 ~< x ~< 60, in which there are x holes in the valence hand, while all the C o ions are divalent; symbolized by the f o r m u l a 2+ + 2Col_xCuxeh2{S4_xSx} ;
(ii) 30 ~< x ~< (1 + 60)/2, in which there are (x - 30) holes in the C o 2+ levels (i.e. C o 3+ ions) and 80 holes in the valence band, symbolized by the f o r m u l a
{COl+6o_2xCox_6o}Cux 2+
3+
+
Rh2
3+
2{S 4
3oS6o}; -
(iii) ( 1 + 30)/2 ~ x ~< 1, in which range all C o ions are trivalent, while there are (2x - 1) holes in the valence band, symbolized by 3+ + COl-xCux Rh23 + { S 5 -22-x S 2 x - 1- }
.
With 30 = 0.4, the first range possibly c o r r e s p o n d s to the antiferromagnetic range, the s e c o n d to the f e r r o m a g n e t i c range and the third to the p a r a m a g n e t i c range (Lotgering 1969). In Col/2Cul/2Rh2S4, X-ray absorption discontinuities were measured. T h e chemical shift of the c o p p e r and cobalt K-discontinuities indicate Cu + and C o 2+ ions
736
R.P. VAN STAPELE
(Ballal and Mande 1977) and do not provide evidence for a higher valency of a part of the Co ions. ZS. Co3S4 and NiCo2S4 Co3S4, which occurs in nature as the mineral linneite, has the spinel structure (Menzer 1926, de Jong and Willems 1927). The lattice parameter is small (9.4 A), like the other sulphospinels with low spin Co 3+ ions on the octahedral sites (table 1). This combines with a metallic conduction (Bouchard et al. 1965). The compound is paramagnetic down to 20 K (Lotgering 1956) with a magnetic susceptibility that is very sensitive to the purity of the sample. Literature data vary (Locher 1968) between temperature-independent susceptibilities of 3.9× 10-4cm3/mol (Serres 1953) and 10.4x 10-4cm3/mO1 (Heidelberg et al. 1966) to susceptibilities that are weakly temperature-dependent and at room temperature have a value of about 39 x 10-4cm3/mol (Lotgering 1956) or 11x 10-4cm3/mol (Lotgering (unpublished), quoted by Locher 1968). The small susceptibility and the metallic conduction are difficult to reconcile with paramagnetic Co 2+ ions on the tetrahedral sites and indicate a delocalization of the 3d electrons of the tetrahedral Co ions in a 3d band (Goodenough 1969). In the nuclear magnetic resonance spectrum of 59Co a strong, single symmetric line without quadrupole effects is attributed to tetrahedrally coordinated Co ions (Locher 1968, Saji and Yamadaya 1972, Locher 1973). In the spectrum due to octahedrally coordinated Co ions a considerable nuclear quadrupole interaction was observed, almost equal to the quadrupole interaction in the very similar spectrum of CuCo2S4 (section 4.4). This led Locher (1968) to suggest a similar charge distribution in the two lattices, which would mean effectively monovalent Co ions in Co3S4. NiCo2S4 is a normal spinel (Lotgering 1956) with a lattice parameter of 9.4 (table 1). The compound is paramagnetic with a low susceptibility, which does not agree with Ni 2+ ions on the tetrahedral sites, (Lotgering 1956), and has a metallic conduction (Bouchard et al. 1965). Other properties have not been measured, but the metallic conduction and the anomalous susceptibility point to delocalized Ni 3d electrons. o
Acknowledgements I am grateful to F.K. Lotgering for helpful discussions and critical reading of the text, to T.J.A. Popma and M.H. van Maaren for their comments and to S. Heymans for his help with the bibliography.
SULPHOSPINELS
737
Notes added in proof (a) The electronic structure of transition metal sulphospinels was recently discussed by Haas (Haas, C., 1980, Jpn. J. Appl. Phys. 19, suppl. 19-3, 171) (see p. 616). (b) R.M. Fleming, F.J. DiSalvo, R.J. Cava and J.V. Waszczak (1981), Phys. Rev. B24, 2850) observed charge-density-wave transitions at 90, 75 and 50 K in the resistance, magnetic susceptibility, and by X-ray diffraction (see p. 624). (c) More recently less clear data were obtained in the series CuCrz-xRhxS4 with 1.2 ~<x ~<2 (Itoh, H., 1980, J. Phys. Soc. Jpn. 48, 1130) (see p. 638). (d) Calculations of the electronic band structure were reported for CdCr2S4, CdCr2Se4 and HgCrzSe4. (Kambara, T., T. Oguchi and K.I. Gondaira, 1980, J. Phys. C: Solid State Phys. 13, 1493; Oguchi, T., T. Kambara and K.I. Gondaira, 1980, Phys. Rev. B22, 872 and B24, 3441 (1981)). The results of a photoemission study of CdCrzS4 and CdCr2Se4 were reported by W.J. Miniscalco, B.C. McCollum, N.G. Stoffel and G. Margaritondo, 1982, Phys. Rev. B25, 2947 (see p. 653). (e) CdCri.6In0.4S4was observed to show a typical spin-glass behaviour (Fiorani, D., M. Nogues and S. Viticoli, 1982, Solid State Commun. 41, 537) (see p. 656). (f) See also M.N. Iliev and G. Giintherodt (1980, Phys. Status Solidi, B98, K9) (see p. 664). (g) Recently a magnetoelectric effect in ZnCr2Se4 was observed and discussed by K. Siratori and E. Kita (1980, J. Phys. Soc. Jpn. 48, 1443) (see p. 672). (h) A. Selmi, R. le Toullec and P. Gibart (1980, Solid State Commun. 33, 889) reported on the plasmon reftectivity of HgCr~Se4 (see p. 693). (i) A neutron diffraction study and magnetic measurements in low fields showed that Zn0.3Hgi.TCr2Se4 has a spin-glass magnetic structure (Sadykov, R.A., A.V. Filatov, P.L. Gruzin, V.M. Novotortsev, I.S. Kovaleva and V.A. Levshin, 1980, JETP. Lett. 31, 642) (see p. 696). (j) Piezoelectricity of Cu0.sIn0.sfr2S4 was reported by N . A . Tsvetkova, K.P. Belov, L.I. Koroleva, V.V. Titov, Ya.A. Kesler and I.V. Gordeav (1979, JETP. Lett. 30, 533) (see p. 698). (k) See for more recent measurements in high magnetic fields and a further discussion R. Plumier, M. Sougi, M. Lec6mte and A. Miedan-Gros (1980, Z. Phys. B - Condensed Matter, 40, 227) (see p. 700). (1) Also in the system Cul-xFexCr2Se4 Cu was found to be replaced by Fe 3+ ions in the spinel phase, which occurred for 0 ~<x ~<0.6 (Hang Nam Ok, Yun Chung and Jung Gi Kim, 1979, Phys. Rev. B20, 4550) (see p. 718). (m) An X-ray photoelectron spectroscopy study of powder samples of Fel-xCuxCr2S4 with 0 < x ~< 1 confirmed the monovalent state of Cu ions throughout the series (Ando, K., 1980, Solid State Commun. 36, 165) (see p. 719).
References Aers, G.C., A.D. Boardman and E.D. Isaac, 1975, Phys. Lett. 54A, 373. Ahrenkiel, R.K. and T.J. Coburn, 1973, Appl. Phys. Lett. 22, 340. Ahrenkiel, R.K., F. Moser, S. Lyu and C.R. Pidgeon, 1971, J. Appl. Phys. 42, 1452. Ahrenkiel, R.K., T.H. Lee, S.L. Lyu and F. Moser, 1973, Solid State Commun. 12, 1113. Ahrenkiel, R.K., T.J. Coburn and E. Carnall, 1974, IEEE Trans. on Magn. 10, 2. Ahrenkiel, R.K., S.L. Lyu and T.J. Coburn, 1975, J. Appl. Phys. 46, 894. Akerstrom, S., 1959, Arkiv Kemi, 14, 403. Akimitsu, J., K. Siratori, G. Shirane, M. Iizumi
and T. Watanabe, 1978, J. Phys. Soc. Japan, 44, 172. Akino, T. and K. Motizuki, 1971, J. Phys. Soc. Japan, 31, 691. Albers, W. and C. Haas, 1964, Phys. Lett. 8, 300. Albers, W. and C.J.M. Rooymans, 1965, Solid State Commun. 3, 417. Albers, W., G. van Aller and C. Haas, 1965, Coll. Int. du C.N.R.S. sur les drriv6s semimrtalliques, Orsay 1965 (Editions du Centre National de la Recherche Scientifique, Paris, 1967), p.. 19. Alexander, S., J.S. Helman and I. Balberg, 1976, Phys. Rev. B13, 304.
738
R.P. VAN STAPELE
Allain, Y., F. Varret and A. Mi6dan-Gros, 1965, C.R. Acad. Sc. Paris 260, 4677. Amith, A. and S.B. Berger, 1971, J. Appl. Phys. 42, 1472. Amith, A. and L. Friedman, 1970, Phys. Rev. B2, 434. Amith, A. and G.L. Gunsalus, 1969, J. Appl. Phys. 40, 1020. Anderson, P.W., 1950, Phys. Rev. 79, 350. Anzina, L.V., V.G. Veselago and S.G. Rudov, 1976, JETP Lett. 23, 474. Arai, T., K. Wakamura and K. Kudo, 1971, J. Phys. Soc. Japan, 30, 1762. Arai, K.I., O. Kubo, N. Tsuya, F. Okamoto and P.K. Baltzer, 1972, IEEE Trans. on Magn. 8, 479. Arai, T., M. Wakaki, S. Onari, K. Kudo, T. Satoh and T. Tsushima, 1973, J. Phys. Soc. Japan, 34, 68. Babaev, G.Y., A.G. Kocharov, K. Ptasevich, LI. Yamzin, M.A. Vinnik, Y.G. Saksonov, V.A. Alferov, I.V. Gordeev and Y.D. Tret'yakov, 1975, Sov. Phys. Crystallogr. 20, 336. Bairamov, A.I., A.G. Gurevich, V.I. Karpovich, V.T. Kalinnikov, T.G. Aminov and L.M. Emiryan, 1976, Sov. Phys. Solid State, 18, 396. Bairamov, A.I., A.G. Gurevich, L.M. Emiryan and N.N. Parfenova, 1977, Phys. Lett. 62A, 242. Balberg, I. and J.S. Helman, 1978, Phys. Rev. B18, 303. Balberg, I. and A. Maman, 1977, Phys. Rev. B16, 4535. Balberg, I. and H.L. Pinch, 1972, Phys. Rev. Lett. 28, 909. Ballal, M.M. and C. Mande, 1976, Solid State Commun. 19, 325. Ballal, M.M. and C. Mande, 1977, J. Phys. Chem. Solids, 38, 843. Baltensperger, W., 1970, J. Appl. Phys. 41, 1052. Baltensperger, W. and J.S. Helman, 1968, Helv. Phys. Acta, 41, 668. Baltzer, P.K., H.W. Lehmann and M. Robbins, 1965, Phys. Rev. Lett. 15, 493. Baltzer, P.K., P.J. Wojtowicz, M. Robbins and E. Lopatin, 1966, Phys. Rev. 151, 367. Baltzer, P.K., M. Robbins and P.J. Wojtowicz, 1967, J. Appl. Phys. 38, 953. Banus, M.D. and M.C. Lavine, 1969, J. Solid State Chem. 1, 109.
Barraclough, K.G., W. Lugscheider, A. Meyer, H. Schaefer and L. Treitinger, 1974, Phys. Status Solidi, A22, 401. Batlogg, B., M. Zvfira and P. Wachter, 1978, Solid State Commun. 28, 567. Belov, K.P., Y.D. Tret'yakov, I.V. Gordeev, L.I. Koroleva, A.V. Ped'Ko, E.I. Smirnovskaya, V.A. Alferov and Y.G. Saksonov, 1973, Sov. Phys. Solid State, 14, 1862. Belov, K.P., L.I. Koroleva, M.A. Shalimova and S.D. Batorova, 1975, Sov. Phys. Solid State, 17, 197. Benoit, R., 1955, J. Chem. Phys. 52, 119. Berger, S.B. and A. Amith, 1971, J. de Phys., Coll. C.1.32, 934. Berger, S.B. and L. Ekstrom, 1969, Phys. Rev. Lett. 23, 1499. Berger, S.B. and H.L. Pinch, 1967, J. Appl. Phys. 38, 949. Berger, S.B., J.I. Budnick and T.J. Burch, 1968a, J. Appl. Phys. 39, 658. Berger, S.B., J.I. Budnick and T.J. Burch, 1968b, Phys. Lett. 26A, 450. Berger, S.B., J.I. Budnick and T.J. Burch, 1969a, Phys. Rev. 179, 272. Berger, S.B., J.I. Budnick and T.J. Burch, 1969b, J. Appl. Phys. 40, 1022. Berger, S.B., T.J. Burch, J.L Budnick and L. Darcy, 1971, J. Appl. Phys. 42, 1309. Bindloss, W., 1971, J. Appl. Phys. 42, 1474. Blasse, G , 1963, Philips Res. Rep. 18, 383. Blasse, G., 1965, Phys. Lett. 19, 110. Blasse, G. and D.J. Schipper, 1964, J. Inorg. Nucl. Chem. 26, 1467. Bongers, P.F., 1957, Dissertation (University of Leiden), unpublished. Bongers, P.F. and E.R. van Meurs, 1967, J. Appl. Phys. 38, 944. Bongers, P.F. and G. Zanmarchi, 1968, Solid State Commun. 6, 291. Bongers, P.F., C. Haas, A.M.J.G. van Run and G. Zanmarchi, 1969, J. Appl. Phys. 40, 958. Bouchard, R.J., 1967, Mat. Res. Bull. 2, 459. Bouchard, R.J., P.A. Russo and A. Wold, 1965, Inorg. Chem. 4, 685. Boumford, C. and A.H. Morrish, 1978, Phys. Rev. B17, 1323. Bouwma, J. and C. Haas, 1973, Phys. Status Solidi, B56, 299. Broquetas-Colominas, C., R. Ballestracci and G. Roult, 1964, J. de Phys. 25, 526. Brossard, L., L. Goldstein and M. Gu~ttard, 1976, J. de Phys., Coll. C6, 37, 493.
SULPHOSPINELS Brossard, L., J.L. Dormann, L. Goldstein, P. Gibart and P. Renaudin, 1979, Phys. Rev. B20, 2933. Brfiesch, P. and F. D'Ambrogio, 1972, Phys. Status Solidi, BS0, 513. Br/iesch, P., H. Kalbfleisch and F. Lehmann, 1971, Phys. Status Solidi, B46, K99. Busch, G., B. Magyar and P. Wachter, 1966, Phys. Lett. 23, 438. Busch, G., B. Magyar and O. Vogt, 1969, Solid State Commun. 7, 509. Callen, E., 1968, Phys. Rev. Lett. 20, 1045. Campbell, J.S. and J.R. Davis, 1939, Phys. Rev. 55, 1125. Cfipek, V., 1977, Phys. Status Solidi, B81, 571. Carnall, E., D. Pearlman, T.J. Coburn, F. Moser and T.W. Martin, 1972, Mat. Res. Bull. 7, 1361. Coburn, T.J., D. Pearlman, E. Carnall, F. Moser, T.H. Lee, S.L. Lyu and T.W. Martin, 1972, A.I.P. Conf. Proc. 10, 740. Coburn, T.J., R.K. Ahrenkiel, E. Carnall and D. Pearlman, 1973, A.I.P. Conf. Proc. 18, 1118. Colominas, C., 1967, Phys. Rev. 153, 558. Cossee, P., 1958, J. Inorg. Nucl. Chem. 8, 483. Coutinho-Filho, M.D. and I. Balberg, 1979, J. Appl. Phys. 50, 1920. Darcy, L., P.K. Baltzer and E. Lopatin, 1968, J. Appl. Phys. 39, 898. Dawes, P.P. and N.W. Grimes, 1975, Solid State Commun. 16, 139. De Jong, W.F. and A. Hoog, 1928, Z. Krist. 66, 168. De Jong, W.F. and H.W.V. Willems, 1927, Z. anorg, allg. Chem. 161, 311. Denis, J., Y. Allain and R. Plumier, 1969, C.R. Acad. Sc. Paris B269, 740. Denis, J., Y. Allain and R. Plumier, 1970, J. Appl. Phys. 41, 1091. Dwight, K. and N. Menyuk, 1967, Phys. Rev. 163, 435. Dwight, K. and N. Menyuk, 1968, J. Appl. Phys. 39, 660. Eagles, D.M., 1978, J. Phys. Chem. Solids, 39, 1243. Eastman, D.E. and M.W. Shafer, 1967, J. Appl. Phys. 38, 4761. Eibschtitz, M., E. Hermon and S. Shtrikman, 1967a, Solid State Commun. 5, 529. Eibsch/itz, M., S. Shtrikman and Y. Tenenbaum, 1967b, Phys. Lett. 24A, 563.
739
Enokiya, H., M. 5¢amaguchi and T. Hihara, 1977, J. Phys. Soc. Japan, 42, 805. Feiner, L.F., 1977, Electron-Phonon Interactions and Phase Transitions, ed., T. Riste (Plenum: New York) p. 345. Feiner, L.F., 1982, J. Phys. C: Solid State Phys. 15, 1515. Feldtkeller, E. and L. Treitinger, 1973, Int. J. Magn. 5, 237. Ferreira, J.M.C. and M.D. Coutinho-Filho, 1978, Solid State Commun. 28, 775. Flahaut, J., L. Domange, M. Guittard and S. Fahrat, 1961, C.R. Acad. Sc. Paris 253, 1956. Frankel, R.B., J.J. Huntzicker, D.A. Shirley and N.J. Stone, 1968, Phys. Lett. 26A, 452. Fujii, H., T. Kamigaichi and T. Okamoto, 1973, J. Phys. Soc. Japan, 34, 1689. Fujii, H., T. Kamigaichi, Y. Hidaka and T. Okamoto, 1970, J. Phys. Soc. Japan, 29, 244. Fujita, H., Y. Okada and F. Okamoto, 1971, J. Phys. Soc. Japan, 31, 610. Geschwind, S., 1967, Hyperline Interactions (eds. A.J. Freeman and R.B. Frankel) (Academic Press, New York-London, 1967). Gibart, P., J.L. Dormann and Y. Pellerin, 1969, Phys. Status Solidi, 36, 187. Gibart, P., L. Goldstein and L. Brossard, 1976, J. Magn. Magn. Mat. 3, 109. Gibart, P., M. Robbins and V.G. Lambrecht, 1973, J. Phys. Chem. Solids, 34, 1363. G6bel, H., 1976, J. Magn. Magn. Mat. 3, 143. G6bel, H., H. Pink, L. Treitinger and W.K. Unger, 1975, Mat. Res. Bull. 10, 783. G6bel, H., L. Treitinger, H. Pink, W.K. Unger and E. Bayer, 1974, Proc. XIIth Int. Conf. on the Physics of Semiconductors, ed., M.H. Pilkuhn (Teubner, Stuttgart 1974) p. 909. Goldstein, L. and P. Gibart, 1969, C.R. Acad. Sc. Paris, B269, 471. Goldstein, L. and P. Gibart, 1971, A.I.P. Conf. Proc. 5, 883. Goldstein, L., D.H. Lyons and P. Gibart, 1973, Solid State Commun. 13, 1503. Goldstein, L., L. Brossard, M. Guittard and J.L. Dormann, 1977a, Physica, 86-88B, 889. Goldstein, L., P. Gibart, M. Mejai and M. Perrin, 1977b, Physica, 86~88B, 893. Goldstein, L., P. Gibart and A. Selmi, 1978, J. Appl. Phys. 49, 1474. Golik, L.L., S.M. Grigorovich, Z.E. Kunikova, Y.M. Ukrainskii and N.M. Shtykov, 1976, Sov. Phys. Solid State, 17, 1420.
740
R.P. VAN STAPELE
Goodenough, J.B., 1960, Phys. Rev. 117, 1442. Goodenough, J.B., 1965, Coll. Int. du C.N.R.S. sur les d6riv6s semi-m&alliques, Orsay 1965 (Editions du Centre National de la Recherche Scientifique, Paris, 1967) p. 263. Goodenough, J.B., 1967, Solid State Commun. 5, 577. Goodenough, J.B., 1969, J. Phys. Chem. Solids, 30, 261. Goodenough, J.B., 1972, J. Solid State Chem. 4, 292. Gorter, E.W., 1954, Philips Res. Rep. 9, 295. Granot, J., 1973, Phys. Lett. 43A, 269. Grochulski, T. and M. Gutowski, 1975, Phys. Status Solidi, B72, K23. Gurevich, A.G., J.M. Jakovlev, V.I. Karpovich, A.N. Ageev and E.V. Rubalskaja, 1972, Phys. Lett. 40A, 69. Gurevich, A.G., V.I. Karpovich, E.V. Rubalskaja, A.I. Bairamov, B.L. Lapovok and L.M. Emiryan, 1975, Phys. Status Solidi, B69, 731. Gyorgy, E.M., M. Robbins, P. Gibart, W.A. Reed and F.J. Schnettler, 1973, A.I.P. Conf. Proc. 10, 1148. Haacke, G. and L.H. Beegle, 1966, Phys. Rev. Lett. 17, 427. Haacke, G. and L.C. Beegle, 1967, J. Phys. Chem. Solids, 28, 1699. Haacke, G. and L.C. Beegle, 1968, J. Appl. Phys. 39, 656. Haacke, G. and A J . Nozik, 1968, Solid State Commun. 6, 363. Haas, C., 1968, Phys. Rev. 168, 531. Haas, C., 1970, Crit. Rev. Solid State Sci. 1, 47. Haas, C., A.MJ.G. van Run, P.F. Bongers and W. Albers, 1967, Solid State Commun. 5, 657. Hahn, H., 1951, Z. anorg, allg. Chem. 264, 184. Hahn, H. and B. Harder, 1956, Z. anorg, allg. Chem. 288, 257. Hahn, H. and W. Klingler, 1950, Z. anorg, allg. Chem. 263, 177. Hahn, H. and K.F. Schr6der, 1952, Z. anorg. allg. Chem. 269, 135. Hahn, H., C. de Lorent and B. Harder, 1956, Z. anorg, allg. Chem. 283, 138. Ham, F.S., G.W. Ludwig, G.D. Watkins and H.H. Woodbury, 1960, Phys. Rev. Lett. 5, 468. Harbeke, G. and H.W. Lehmann, 1970, Solid State Commun. 8, 1281. Harbeke, G. and H. Pinch, 1966, Phys. Rev. Lett. 17, 1090.
Harbeke, G. and E.F. Steigmeier, 1968, Solid State Commun. 6, 747. Harbeke, G., S.B. Berger and F.P. Emmenegger, 1968, Solid State Commun. 6, 553. Hastings, J.M. and L.M. Corliss, 1968a, J. Appl. Phys. 39, 632. Hastings, J.M. and L.M. Corliss, 1968b, J. Phys. Chem. Solids, 29, 9. Heidelberg, R.F., A.H. Luxem, S. Talhouk and J.J. Banewicz, 1966, Inorg. Chem. 5, 194. Helman, J.S., I. Balberg and S. Alexander, 1975, A.I.P. Conf. Proc. 29, 495. Henning, J.C.M., 1980, Phys. Rev. B21, 4983. Hlidek, P., I. Barvik, V. Prosser, M. Vaneck and M. Zvfira, 1976, Phys. Status Solidi, B75, K45. Hlidek, P., M. Zvfira and V. Prosser, 1977, Phys. Status Solidi, B84, Kl19. Hoekstra, B., 1973, Proc. Int. Conf. on Magnetism, Moscow 1973, p. 117. Hoekstra, B., 1974, Phys. Status Solidi, B63, K7. Hoekstra, B. and R.P. van Stapele, 1973, Phys. Status Solidi, B55, 607. Hoekstra, B., R.P. van Stapele and A.B. Voermans, 1972, Phys. Rev. B6, 2762. Holland, W.E. and H.A. Brown, 1972, Phys. Status Solidi, A10, 249. Hollander, J.C.T., G. Sawatzky and C. Haas, 1974, Solid State Commun. 15, 747. Hoy, G.R. and S. Chandra, 1967, J. Chem. Phys. 47, 961. Hoy, G.R. and K.P. Singh, 1968, Phys. Rev. 172, 514. Iglesias, J.E. and H. Steinfink, 1973, J. Solid State Chem. 6, 119. Iliev, M. and H. Pink, 1979, Phys. Status Solidi, B93, 799. Iliev, M., G. Guentherodt and H. Pink, 1978a, Solid State Commun. 27, 863. Iliev, M.N., E. Anastassakis and T. Arai, 1978b, Phys. Status Solidi, B86, 717, Itoh, H., 1979, J. Phys. Soc. Japan, 46, 1127. Itoh, T., N. Miyata and S. Narita, 1973, Japan J. Appl. Phys. 12, 1265. Itoh, H., K. Motida and S. Miyahara, 1977, J. Phys. Soc. Japan, 43, 854. Jonker, G.H. and J.H. van Santen, 1950, Physica, 16, 337 and 16, 599. Kaczmarska, K. and A. Chelkowski, 1977, Phys. Status Solidi, B81, K95. Kamata, N., S. Yamazaki, S. Kabashima, T. Hattanda and T. Kawakubo, 1972, Solid State Commun. 10, 905.
SULPHOSPINELS Kambara, T. and Y. Tanabe, 1970, J. Phys. Soc. Japan, 28, 628. Kamigaki, K., T. Kaneko, H. Yoshida, H. Ido and S. Miura, 1970, Ferrites, Proc. Int. Conf. Japan, p. 614. Kanamori, J., 1959, Phys. Chem. Solids, 10, 87. Kanomata, T., H. Ido and T. Kaneko, 1970, J. Phys. Soc. Japan, 29, 332. Kasuya, T. and A. Yanase, 1968, Rev. Mod. Phys. 40, 684. Kawanishi, S., A. Tasaki and K. Siratori, 1978, J. Phys. Soe. Japan, 45, 80. Kawanishi, S., A. Tasaki and K. Siratori, 1979, J. Phys. Soc. Japan, 47, 1086. Kelly, F.M. and J.B. Sutherland, 1956, Can. J. Phys. 34, 521. Kittel, C., 1976, Introd. Solid State Physics (John Wiley, New York). Kleinberger, R. and R. de Kouchkovsky, 1966, C.R. Acad. Sc. Paris, B262, 628. Knop, O., K.I.G. Reid, Sutarno and Y. Nakagawa, 1968, Can. J. Chem. 46, 3463. Koerts, K., 1963, Rec. Trav. Chim. Pays-Bas, 82, 1099. Koerts, K., 1965, Dissertation (University of Leiden, unpublished). Kondo, H., 1976, J. Phys. Soc. Japan, 41, 1247. Koshizuka, N., Y. Yokoyama and T. Tsushima, 1976, Solid State Commun. 18, 1333. Koshizuka, N., Y. Yokoyama and T. Tsushima, 1977a, Physica, 89B, 214. Koshizuka, N., Y. Yokoyama and T. Tsushima, 1977b, Solid State Commun. 23, 967. Koshizuka, N., Y. Yokoyama, T. Okuda and T. Tsushima, 1978a, J. Appl. Phys. 49, 2183. Koshizuka, N., Y. Yokoyama, T. Okuda and T. Tsushima, 1978b, J. Phys. Soc. Japan, 45, 1439. Koshizuka, N., S. Ushioda and T. Tsushima, 1980, Phys. Rev. B21, 1316. K6tzler, J. and H. von Philipsborn, 1978, Phys. Rev. Lett. 40, 790. Kovtun, N.M., V.K. Prokopenko and A.A. Shamyakov, 1978, Solid State Commun. 26, 877. Krawczyk, M., H. Szymczak, W. Zbieranowski and J. Zmija, 1973, Acta Phys. Polonica, A44, 455. Kugimiya, K. and H. Steinfink, 1968, Inorg. Chem. 7, 1762. Kun'kova, Z.E., T.G. Aminov, L.L. Golik, M.I. Elinson and V.T. Kalinnikov, 1976, Sov. Phys. Solid State, 18, 1212.
741
Larsen, P.K., 1973, Proc. Int. Conf. on Magnetism, Moscow 1973, g, 484. Larsen, P.K. and A.B. Voermans, 1973, J. Phys. Chem. Solids, 34, 645. Larsen, P.K. and S. Wittekoek, 1972, Phys. Rev. Lett. 29, 1597. Larson, G.H. and A.W. Sleight, 1968, Phys. Lett. 28A, 203. LeCraw, R.C., H. von Philipsborn and M.D. Sturge, 1967, J. Appl. Phys. 38, 965. Le Dang Khoi, 1966, C.R. Acad. Sc. Paris, B262, 1555. Le Dang Khoi, 1968, Solid State Commun. 6, 203. Lee, T.H., 1971, J. Appl. Phys. 42, 1441. Lee, T.H., T. Coburn and R. Gluck, 1971, Solid State Commun. 9, 1821. Lee, T.H., R.M. Gluck, R.K. Ahrenkiel and T.J. Coburn, 1973, A.I.P. Conf. Proc. 10, 274. Lehmann, H.W., 1967, Phys. Rev. 163, 488. Lehmann, H.W. and F.P. Emmenegger, 1969, Solid State Commun. 7, 965. Lehmann, H.W. and G. Harbeke, 1967, J. Appl. Phys. 38, 946. Lehmann, H.W. and G. Harbeke, 1970, Phys. Rev. B1, 319. Lehmann, H.W. and M. Robbins, 1966, J. Appl. Phys. 37, 1389. Lehmann, H.W., G. Harbeke and H. Pinch, 1971, J. de Phys. Coll. C1, 32, 932. Lems, W., P.J. Rijnierse, P.F. Bongers and U. Enz, 1968, Phys. Rev. Lett. 21, 1643. Le Nagard, N., G. Collin and O. Gorochov, 1975, Mat. Res. Bull. 10, 1279. Le Nagard, N., A. Katty, G. Collin and O. Gorochov, 1979, J. Solid State Chem. 27, 267. Lisnyak, S.S. and B.D. Lichter, 1969, Trans. Metall. Soc. AIME, 245, 2594. Locher, P.R., 1967, Solid, State Commun. 5, 185. Locher, P.R., 1968, Z. Angew. Phys. 24, 277. Locher, P.R., 1973, Phys. Lett. 42A, 490. Locher, P.R. and R.P. van Stapele, 1970, J. Phys. Chem. Solids 31, 2643. Lotgering, F.K., 1956, Philips Res. Rep. 11, 218 and 11, 337. Lotgering, F.K., 1964a, Solid State Commun. 2, 55. Lotgering, F.K., 1964b, Proc. Int. Conf. on Magnetism, Nottingham 1964 (Institute of Physics and Physical Society, London), p. 533. Lotgering, F.K., 1965, Solid State Commun. 3, 347.
742
R.P. VAN STAPELE
Lotgering, F.K., 1968a, J. Phys. Chem. Solids, 29, 2193. Lotgering, F.K., 1968b, J. Phys. Chem. Solids, 29, 699. Lotgering, F.K., 1969, J. Phys. Chem. Solids, 30, 1429. Lotgering, F.K. and E.W. Gorter, 1957, Phys. Chem. Solids, 3, 238. Lotgering, F.K. and R.P. van Stapele, 1967, Solid State Commun. 5, 143. Lotgering, F.K. and R.P. van Stapele, 1968a, J. Appl. Phys. 39, 417. Lotgering, F.K. and R.P. van Stapele, 1968b, Mat. Res. Bull. 3, 507. Lotgering, F.K. and G.H.A.M. van der Steen, 1969, Solid State Commun. 7, 1827. Lotgering, F.K. and G.H.A.M. van der Steen, 1971a, J. Solid State Chem. 3, 574. Lotgering, F.K. and G.H.A.M. van der Steen, 1971b, J. inorg, nucl. Chem. 33, 673. Lotgering, F.K. and G.H.A.M. van der Steen, 1971c, Solid State Commun. 9, 1741. Lotgering, F.K., R.P. van Stapele, G.H.A.M. van der Steen and J.S. van Wieringen, 1969, J. Phys. Chem. Solids, 30, 799. Lotgering, F.K., A.M. van Diepen and J.F. Olijhoek, 1975, Solid State Commun. 17, 1149. Lundqvist, D., 1943, Ark. Kemi. Min. Geol. 17B, Nr. 12. Lutz, H.D., 1966, Z. anorg, allg. Chem. 348, 36. Lutz, H.D. and R.A. Becker, 1973, Monatshefte F. Chem. 104, 572. Lutz, H.D. and M. F6her, 1971, Spectrochem. Acta, 27A, 357. Lutz, H.D. and K. Grendel, 1965, Z. anorg. allg. Chem. 337, 30. Lyons, D., L. Goldstein and P. Gibart, 1973, Proc. Int. Conf. on Magnetism, Moscow 1973, 6, 208. Lyubutin, I.S. and T.V. Dmitrieva, 1975, JETP Lett. 21, 59. Makhotkin, V.E., G.G. Shabunina, T.G. Aminov, G.I. Vinogradova, V.G. Veselago and V.T. Kalinnikov, 1975, Soy. Phys. Solid State 16, 2034. Makhotkin, V.E., V.G. Veselago and V.T. Kalinnikov, 1978a, Sov. Phys. Solid State, 20, 777. Makhotkin, V.E., G.I. Vinogradova and V.G. Veselago, 1978b, JETP Lett. 28, 78. Martin, G.W., A.T. Kellogg, R.L. White, R.M. White and H. Pinch, 1969, J. Appl. Phys. 40, 1015. Matsumoto, G., K. Ohbayashi, K. Kohn and S. Iida, 1966, J. Phys. Soc. Japan, 21, 2429.
Mejai, M. and M. Nogues, 1980, J. Magn. Magn. Mat. 15-18, 487. Menth, A., A.R. von Neida, L.K. Shick and D.L. Maim, 1972, J. Phys. Chem. Solids, 33, 1338. Menyuk, N., K. Dwight and A. Wold, 1965, J. Appl. Phys. 36, 1088. Menyuk, N., K. Dwight, R.J. Arnott and A. Wold, 1966, J. Appl. Phys. 37, 1387. Menzer, G., 1926, Z. Krist. 64, 506. Merkulov, A.I., S.I. Radautsan and V.E. Tezlevan, 1978, Phys. Status Solidi, B87, K141. Methfessel, S. and D.C. Mattis, 1968, Magnetic Semiconductors, Encyclopedia of Physics XVIII/1 (Springer Verlag, Berlin). Mimura, Y., M. Shimada and M. Koizumi, 1974, Solid State Commun. 15, 1035. Minematsu, K., K. Miyatani and T. Takahashi, 1971, J. Phys. Soc. Japan, 31, 123. Miyatani, K., 1970, J. Phys. Soc. Japan, 28, 259. Miyatani, K., Y. Wada and F. Okamoto, 1968, J. Phys. Soc. Japan, 25, 369. Miyatani, K., T. Takahashi, K. Minematsu, S. Osaka and K. Yoshida, 1970, Ferrites, Proc. Int. Conf. Japan, p. 607. Miyatani, K., K. Minematsu, Y. Wada, F. Okamoto, K. Kato and P.K. Baltzer, 1971a, J. Phys. Chem. Solids, 32, 1429. Miyatani, K., F. Okamoto, P.K. Baltzer, S. Osaka and T. Oka, 1971b, A.I.P. Conf. Proc. 5, 285. Moser, F., R.K. Ahrenkiel, E. Carnall, T. Coburn, S.L. Lyu, T.H. Lee, T. Martin and D. Pearlman, 1971, J. Appl. Phys. 42, 1449. Motida, K. and S. Miyahara, 1970, J. Phys. Soc. Japan, 29, 516. Mott, N.F., 1949, Proc. Phys. Soc. (London) A62, 416. Nagaev, E.L., 1975, Soy. Phys. Usp. 18, 863. Nagaev, E.L., 1977, JEPT Lett. 25, 76. Nakatani, I., H. Nose and K. Masumoto, 1977, J. Japan Inst. Metals, 41, 939. Natsume, Y. and H. Kamimura, 1972, Solid State Commun. 11, 875. Natta, G. and L. Passerine, 1931, R.C. Accad. Lincei 14, 33. Nauciel-Bloch, M., A. Castets and R. Plumier, 1972, Phys. Lett. 39A, 311. Ndel, L., 1948, Ann. de Phys. 3, 137. Nogues, M., M. Mejai and L. Goldstein, 1979, J. Phys. Chem. Solids, 40, 375. Ohbayashi, K., Y. Tominaga and S. Iida, 1968, J. Phys. Soc. Japan, 24, 1173. Ohsawa, A., Y. Yamaguchi, H. Watanabe and
SULPHOSPINELS H. Itoh, 1976, J. Phys. Soc. Japan, 40, 986 and 40, 992. Okofiska-Kozlowska, I. and J. Krok, 1978, Z. anorg, allg. Chem. 447, 235. Okofiska-Kozlowska, I., M. Jelonek and Z. Drzazga, 1977, Z. anorg, allg. Chem. 436, 265. Passerini, L. and M. Baccaredda, 1931, R.C. Accad. Lincei, 14, 38. Patil, C.G. and B.S. Krishnamurthy, 1978, Phys. Status Solidi, B86, 725. Pauling, L., 1960, The Nature of the Chemical Bond (Cornell University Press, lthac~i). Pearlman, D., E. Carnall and T.W. Martin, 1973, J. Solid State Chem. 7, 138. Pellerin, Y. and P. Gibart, 1969, C.R. Acad. Sc. Paris, B269, 615. Pickardt, J. and E. Riedel, 1971, J. Solid State Chem. 3, 67. Pickardt, J., E. Riedel and B. Reuter, 1970, Z. anorg, allg. Chem. 373, 15. Pidgeon, C.R., R.B. Dennis and J.S. Webb, 1973, Surface Science, 37, 340. Pinch, H.L. and S.B. Berger, 1968, J. Phys. Chem. Solids, 29, 2091. Pinch, H.L., M.J. Woods and E. Lopatin, 1970, Mat. Res. Bull. 5, 425. Pink, H., W.K. Unger, H. Schaefer and H. Goebel, 1974, Appl. Phys. 4, 147. Plumier, R., 1965, C.R. Acad. Sc. Paris, 260, 3348. Plumier, R., 1966a, J. Appl. Phys. 37, 964. Plumier, R., 1966b, J. de Phys. 27, 213. Plumier, R., 1970a, C.R. Acad. Sc. Paris, B271, 184. Plumier, R., 1970b, C.R. Acad. Sc. Paris, B271, 277. Plumier, R., 1980, J. Phys. Chem. Solids, 41,871. Plumier, R. and F.K. Lotgering, 1970, Solid State Comrnun. 8, 477. Plumier, R. and M. Sougi, 1969, C.R. Acad. Sc. Paris, B268, 1549. Plumier, R. and M. Sougi, 1971, Solid State Commun. 9, 413. Plumier, R., R. Conte, J. Denis and M. Nauciel-Bloch, 1971a, J. de Phys. Coll. C1 32, 55. Plumier, R., F.K. Lotgering and R.P. van Stapele, 1971b, J. de Phys., Coll. C.1. 32, 324. Plumier, R., M. Lecomte, A. Miedan-Gros and M. Sougi, 1975a, Phys. Lett. 55A, 239. Plumier, R., M. Sougi, A. Miedan-Gros and M. Lecomte, 1975b, A.I.P. Conf. Proc. 29, 410.
743
Plumier, R., M. Lecomte, A. Miedan-Gros and M. Sougi, 1977a, Physica 86--88B, 1360. Plumier, R., M. Sougi and M. Lecomte, 1977b, Phys. Lett. 60A, 341. Prosser, V., P. Hlidek, P. Hoeschl, P. Polivka and M. Zvfira, 1974, Czech. J. Phys. B24, 1168. Raccah, P.M., R.J. Bouchard and A. Wold, 1966, J. Appl. Phys. 37, 1436. Rehwald, W., 1967, Phys. Rev. 155, 861. Riedel, E. and E. Horvath, 1969, Z. anorg, allg. Chem. 37!, 248. Riedel, E. and E. Horvath, 1973a, Mat. Res. Bull. 8, 973. Riedel, E. and E. Horvath, 1973b, Z. anorg. allg. Chem. 399, 219. Riedel, E. and R. Karl, 1979, private communication. Riedel, E., J. Pickardt and J. Soechtig, 1976, Z. anorg, allg. Chem. 419, 63. Robbins, M., R.H. Willens and R.C. Miller, 1967a, Solid State Commun. 5, 933. Robbins, M., H.W. Lehmann and J.G. White, 1967b, J. Phys. Chem. Solids, 28, 897. Robbins, M., P.K. Baltzer and E. Lopatin, 1968, J. Appl. Phys. 39, 662. Robbins, M., M.A. Miksovsky and R.C. Sherwood, 1969, J. Appl. Phys. 40, 2466. Robbins, M., A. Menth, M.A. Miksovsky and R.C. Sherwood, 1970a, J. Phys. Chem. Solids, 31,423. Robbins, M., R. Wolff, A.J. Kurtzig, R.C. Sherwood and M.A. Miksovsky, 1970b, J. Appl. Phys. 41, 1086. Robbins, M., P, Gibart, L.M. Holmes, R.C. Sherwood and G.W. Hull, 1973, A.I.P. Conf. Proc. 10, 1153. Robbins, M., P. Gibart, D.W. Johnson, R.C. Sherwood and V.G. Lambrecht, 1974, J. Solid State Chem. 9, 170. Rys, F., J.S. Helman and W. Baltensperger, 1967, Phys. Kondens. Materie, 6, 105. Riidorff, W. and K. Stegemann, 1943, Z. anorg. allg. Chem. 251, 376. Saji, H. and T. Yamadaya, 1972, Phys. Lett. 41A, 365. Sakai, S., T. Sugano and Y. Okabe, 1976, Japan J. Appl. Phys. 15, 2023. Salanskii, N.M. and N.A. Drokin, 1975, Sov. Phys. Solid State, 17, 205. Salyganov, V.I., Y.M. Yakovlev and Y.R. Shil'nikov, 1973, JETP Lett. 18, 215. Samokhvalov, A.A., V.S. Babushkin, M.I. Simonova and T.I. Arbuzova, 1973, Sov. Phys. Solid State, 14, 1883.
744
R.P. VAN STAPELE
Samokhvalov, A.A., V.V. Osipov, V.G. Kallinikov and T.A. Aminov, 1978, Sov. Phys. Solid State, 20, 344. Samokhvalov, A.A., V.V. Osipov, V.T. Kallinikov and T.G. Aminov, 1979, JETP Lett. 28, 382. Sato, K., 1977, J. Phys. Soc. Japan, 43, 719. 'Sato, K. and T. Teranishi, 1970, J. Phys. Soc. Japan, 29, 523. Schaetter, G.M. and M.H. van Maaren, 1968, Proc. 11th Int. Conf. Low Temp. Phys., St. Andrews, p. 1033. Schlein, W. and A. Wold, 1972, J. Solid State Chem. 4, 286. Sekizawa, H., T. Okada and F. Ambe, 1973, Proe. Int. Conf. on Magnetism, Moscow, 1973, 2, 152. Selmi, A., P. Gibart and L. Goldstein, 1980, J. Magn. Magn. Mat. 15--18, 1285. Serres, A., 1953, J. de Phys. 14, 689. Shanditsev, V.A. and E.N. Yakovlev, 1975, Sov. Phys. Solid State, 17, 1161. Shelton, R.N., D.C. Johnston and H. Adrian, 1976, Solid State Commun. 20, 1077. Shepherd, I.W., 1970, Solid State Commun. 8, 1835. Shick, L.K. and A.R. von Neida, 1969, J. Cryst. Growth, 5, 313. Shirane, G., D.E. Cox and S.J. Pickart, 1964, J. Appl. Phys. 35, 954. Shumilkina, E.V., 1975, Sov. Phys. Solid State, 17, 800. Shumilkina, E.V. and A.I. Obraztsov, 1975, Sov. Phys. Solid State, 17, 802. Siratori, K., 1971, J. Phys. Soc. Japan, 30, 709. Siratori, K. and J. Sakurai, 1975, J. Phys. Soc, Japan, 38, 701. Siratori, K., A. Tasaki and H. Asada, 1973, Int. J. Magnetism, 4, 273. Skinner, B.J., R.C. Erd and F.S. Grimaldi, 1965, Am. Min. 49, 543. Sleight, A.W., 1967, Mat. Res. Bull. 2, 1107. Sleight, A.W. and H.S. Jarrett, 1968, J. Phys. Chem. Solids, 29, 868. Solin, N.I., A.A. Samokhvalov and V.T. Kallinikov, 1967, Sov. Phys. Solid State, 18, 1226. Spender, M.R., 1973, Ph.D. Thesis, University of Manitoba. Spender, M.R. and A.H. Morrish, 1971, Can. J. Phys. 49, 2659. Spender, M.R. and A.H. Morrish, 1972a, Can. J. Phys. 50, 1125. Spender, M.R. and A.H. Morrish, 1972b, Solid State Commun. 11, 1417.
Spender, M.R. and A.H. Morrish, 1973, Proc. Fifth Int. Conf. Moessbauer Spectrometry, Bratislava 1973 (Czechoslovak Atomic Energy Commission, Nuclear Information Centre, Zbraslav, 1975) part I, p. 125. Spender, M.R.M., J.M.D. Coey a n d A.H. Morrish, 1972, Can. J. Phys. 50, 2313. Srivastava, V.C., 1969, J. Appl. Phys. 40, 1017. Stasz, J., 1973, Acta Phys. Polonica, A43, 177. Stauss, G.H., 1969a, J. Appl. Phys. 40, 1023. Stauss, G.H., 1969b, Phys. Rev. 181, 636. Stauss, G.H., M. Rubinstein, J. Feinleib, K. Dwight, N. Menyuk and A. Wold, 1968, J. Appl. Phys. 39, 667. Steigmeier, E.F. and G. Harbeke, 1970, Phys. Kondens. Materie, 12, 1. Stickler, J.J. and H.J. Zeiger, 1968, J. Appl. Phys. 39, 1021. Stoyanov, S.G., M.N. Iliev and S.P. Stoyanova, 1975, Phys. Status Solidi, A30, 133. Stoyanov, S.G., M.N. Iliev and S.P. Stoyanova, 1976, Solid State Commun. 18, 1389. Strick, G., G. Eulenberger and H. Hahn, 1968, Z. anorg, allg. Chem. 357, 338. Suzuki, N. and H. Kamimura, 1972, Solid State Commun. 11, 1603. Suzuki, N. and H. Kamimura, 1973, J. Phys. Soc. Japan, 35, 985. Takahashi, T., K. Minematsu and K. Miyatani, 1971, J. Phys. Chem. Solids, 32, 1007. Tanaka, M., T. Tokoro and T. Mori, 1973, Proc. Fifth Int. Conf. Moessbauer Spectrometry, Bratislava, 1973 (Czechoslovak Atomic Energy Commission, Nuclear Information Centre, Zbraslav, 1975) part I, p. 118. Taniguchu, M., Y. Kato and S. Narita, 1975, Solid State Commun. 16, 261. Toda, M., 1970, Appl. Phys. Lett. 17, 1. Treitinger, L., H. Pink, H. Mews and R. Koepl, 1976a, J. Magn. Magn. Mat. 3, 184. Treitinger, L., H. Goebel and H. Pink, 1976b, Mat. Res. Bull. 11, 1375. Treitinger, L., H. Pinl~ and H. Goebel, 1978a, J. Phys. Chem. Solids, 39, 149. Treitinger, L., K.G. Barraclough and E. Feldtkeller, 1978b, Mat. Res. Bull. 13, 667. Tressler, R.E. and V.S. Stubican, 1968, J. Am. Cer. Soc. 51, 391. Tressler, R.E., F.A. Hummel and V.S. Stubican, 1968, J. Am. Cer. Soc. 51, 648. Tret'yakov, Y.D., M.A. Vinnik, Y.G. Saksonov, V.K. Kamyshova and I.V. Gordeev, 1975, Sov. Phys. Phys. Solid State, 17, 1184. Uda, M., 1968, Sci. Pap. Inst. Phys. Chem. Res. 62, 14.
SULPHOSPINELS Ullrich, J.F. and D.H. Vincent, 1967, Phys. Lett. 25A, 731. Unger, W.K., 1975, J. Magnetism Magn. Mat. 1, 88. Unger, W.K., O. Scherber and H. Stremme, 1974, Int. J. Magnetism, 6, 313. Van Diepen, A.M. and R.P. van Stapele, 1972, Phys. Rev. B5, 2462. Van Diepen, A.M. and R.P. van Stapele, 1973, Solid State Commun. 13, 165L Van Diepen, A.M., F.K. Lotgering and J.F. Olijhoek, 1976, J. Magn. Magn. Mat. 3, 117. Van Gorkom, G.G.P., J.C.M. Henning and R.P. van Stapele, 1973, Phys. Rev. BS, 955. Van Maaren, M.H. and H.B. Harland, 1969, Phys. Lett. 30A, 204. Van Maaren, M.H., G.M. Schaeller and F.K. Lotgering, 1967, Phys. Lett. 25A, 238. Van Maaren, M.H., H.B. Harland and E.E. Havinga, 1970a, Solid State Commun. 8, 1933. Van Maaren, M.H., H.B. Harland and E.E. Havinga, 1970b, Proc. 12th Int. Conf. on Low Temp. Phys. Kyoto 1970, p. 357. Von Neida, A.R. and L.K. Shick, 1969, J. Appl. Phys. 40, 1013. Van Stapele, R.P. and F.K. Lotgering, 1970, J. Phys. Chem. Solids, 31, 1547. Van Stapele, R.P., J.S. van Wieringen and P.F. Bongers, 1971, J. de Phys., Coll. C1 32, 53. Veselago, V.G., E.S. Vigeleva, G.I. Vinogradova, V.T. Kalinnikov and V.E. Makhotkin, 1972a, JETP. Lett. 15, 223. Veselago, V.G., E.S. Vigeleva., G.I. Vinogradova, V.T. Kalinnikov and V.E. Mokhotkin, 1972b, Proc. Int. Conf. Phys. Semicond., Warsaw, p. 1300. Vinogradova, G.I., V.G. Veselago, V.E. Makhotkin, I.S. Kavaleva, V.A. Levshin, G.G. Shabunina and V.T. Kalinnikov, 1978, Sov. Phys. Solid State, 20, 827. Wagner, C., 1935, Z. Tech. Phys. 16, 327. Wagner, V., H. Mitlehner and R. Geick, 1971, Optics Commun. 2, 429. Wakaki, M. and T. Arai, 1978, Solid State Commun. 26, 757. Wakaki,x M., T. Arai and K. Kudo, 1975, Solid State Commun. 16, 679. Wakamura, K., S. Onari, T. Arai and K. Kudo, 1971, J. Phys. Soc. Japan, 31, 1845. Wakamura, K., T. Arai, S. Onari, K. Kudo and T. Takahashi, 1973, J. Phys. Soc. Japan, 35, 1430. Wakamura, K., T. Arai and K. Kudo, 1976a, J. Phys. Soc. Japan, 40, 1118. Wakamura, K., T. Arai and K. Kudo, 1976b, J. Phys. Soc. Japan, 41, 130.
745
Watanabe, T., 1973, Solid State Commun. 12,
355. White, R.M., 1969, Phys. Rev. Lett. 23, 858. White, W.B. and B.A. DeAngelis, 1967, Spectrochim. Acta 23A, 985. White, J.G. and M. Robbins, 1968, J. Appl. Phys. 39, 664. Wilkinson, C., B.M. Knapp and J.B. Forsyth, 1976, J. Phys. C: Solid State Phys. 9, 4021. Williamson, D.P. and N.W. Grimes, 1974, J. Phys. D: Appl. Phys. 7, 1. Wittekoek, S. and P.F. Bongers, 1969, Solid State Commun. 7, 1719. Wittekoek, S. and P.F. Bongers, 1970, IBM J. Res. Develop. 14, 312. Wittekoek, S. and G. Rinzema, 1971, Phys. Status Solidi, B44, 849. Wojtowicz, P.J., 1969, IEEE Trans. on Magn. 5,840. Wojtowicz, P.J., P.K. Baltzer and M. Robbins, 1967, J. Phys. Chem. Solids~ 28, 2423. Wojtowicz, P.J., L. Darcy and M. Rayl, 1969, J. Appl. Phys. 40, 1023. Wollan, E.O., 1960, Phys. Rew 117, 387. Yafet, Y. and C. Kittel, 1952, Phys. Rev. 87, 290. Yagnik, C.M. and H.B. Mathur, 1967, Solid State Commun. 5, 841. Yamashita, O., Y. Yamaguchi, I. Nakatani, H. Watanabe and K. Masumoto, 1979a, J. Phys. Soc. Japan, 46, 1145. Yamashita, O., H. Yamauchi, Y. Yamaguchi and H. Watanabe, 1979b, J. Phys. Soc. Japan, 47, 450. Yanase, A., 1971, Solid State Commun. 9, 2111. Yanase, A., 1972, Intern. J. Magnetism, 2, 99. Yanase, A. and T. Kasuya, 1968a, J. Appl. Phys. 39, 430. Yanase, A. and T. Kasuya, 1968b, J. Phys. Soc. Japan, 25, 1025. Yanase, A., T. Kasuya and T. Takeda, 1970, Ferrites, Proc. Int. Conf. Japan, p. 604. Yokoyama, H. and S. Chiba, 1969, J. Phys. Soc. Japan, 27, 505. Yokoyama, H., S. Chiba and N. Ichinose, 1970, Ferrites, Proc. Int. Conf. Japan, p. 611. Yokoyama, H., R. Watanabe and S. Chiba, 1967a, J. Phys. Soc. Japan, 22, 659. Yokoyama, H., R. Watanabe and S. Chiba, 1967b, J. Phys. Soc. Japan, 23, 450. Zener, C., 1951, Phys. Rev. 81, 440 and 82, 403. Zheru, I.I., I.G. Lupya, K.G. Nikiforov, S.I. Radautsan and V.E. T6zl6van, 1978, Sov. Phys. Solid State, 20, 884. Zvfira, M., V. Prosser, A. Schlegel and P. Wachter, 1979, J. Magn. Magn. Mat. 12, 219.
chapter 9 TRANSPORT PROPERTIES OF FERROMAGNETS
I.A. C A M P B E L L A N D A. FERT Laboratoire de Physique des Sofides Universit6 Paris-Sud, 91405 Orsay France
Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth O North-HollandPublishing Company, 1982 747
CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1. G e n e r a l p r o p e r t i e s of t r a n s p o r t in f e r r o m a g n e t s . . . . . . . . . . . . . 1.1. R e s i s t i v i t y a n d H a l l effect of a m o n o d o m a i n p o l y c r y s t a l . . . . . . . . . 1.1.1. S p o n t a n e o u s resistivity a n i s o t r o p y . . . . . . . . . . . . . . 1.1.2. E x t r a o r d i n a r y H a l l effect . . . . . . . . . . . . . . . . . 1.1,3. P l a n a r H a l l effect . . . . . . . . . . . . . . . . . . . . 1.2. R e s i s t i v i t y a n d H a l l effect in single c r y s t a l f e r r o m a g n e t s . . . . . . . . . 1.3. T h e r m a l a n d t h e r m o e l e c t r i c effects in p o l y c r y s t a l s . . . . . . . . . . . 2. E l e c t r i c a l resistivity of f e r r o m a g n e t s . . . . . . . . . . . . . . . . . 2.1. T h e o r e t i c a l m o d e l s . . . . . . . . . . . . . . . . . . . . . 2.1.1. S p i n d i s o r d e r s c a t t e r i n g . . . . . . . . . . . . . . . . . 2.1.2. T w o c u r r e n t m o d e l . . . . . . . . . . . . . . . . . . . 2.2. R e s i s t i v i t y of p u r e m e t a l s . . . . . . . . . . . . . . . . . . . 2.2.1. T a b u l a r r e s u l t s . . . . . . . . . . . . . . . . . . . . 2.2,2. R e s i s t i v i t y at l o w t e m p e r a t u r e s . . . . . . . . . . . . . . . 2.2.3. R e s i d u a l resistivity . . . . . . . . . . . . . . . . . . . 2.2.4. H i g h field b e h a v i o u r . . . . . . . . . . . . . . . . . . . 2.3. A l l o y s : r e s i d u a l resistivity a n d t e m p e r a t u r e d e p e n d e n c e o f resistivity . . . . 2.3.1. N i c k e l h o s t . . . . . . . . . . . . . . . . . . . . . . 2,3.2. C o b a l t h o s t . . . . . . . . . . . . . . . . . . . . . . 2.3.3. I r o n h o s t . . . . . . . . . . . . . . . . . . . . . . . 2.3,4. A l l o y s c o n t a i n i n g i n t e r s t i t i a l i m p u r i t i e s . . . . . . . . . . . . . . 2.4. H i g h t e m p e r a t u r e a n d critical p o i n t b e h a v i o u r . . . . . . . . . . . . 3, O t h e r t r a n s p o r t p r o p e r t i e s of Ni, C o , F e a n d t h e i r all~oys . . . . . . . . . . 3.1. O r d i n a r y m a g n e t o r e s i s t a n c e . . . . . . . . . . . . . . . . . . 3.2. O r d i n a r y H a l l coefficient . . . . . . . . . . . . . . . . . . . 3.3. S p o n t a n e o u s resistivity a n i s o t r o p y . . . . . . . . . . . . . . . . 3.4. E x t r a o r d i n a r y H a l l effect . . . . . . . . . . . . . . . . . . . 3.5. T h e r m o e l e c t r i c p o w e r . . . . . . . . . . . . . . . . . . . . 3.6. N e r n s t - E t t i n g s h a u s e n effect . . . . . . . . . . . . . . . . . . 3.7. T h e r m a l c o n d u c t i v i t y . . . . . . . . . . . . . . . . . . . . . 4. D i l u t e f e r r o m a g n e t i c a l l o y s . . . . . . . . . . . . . . . . . . . . 4.1. P a l l a d i u m b a s e d a l l o y s . . . . . . . . . . . . . . . . . . . . 4.1.1. R e s i s t i v i t y a n d i s o t r o p i c m a g n e t o r e s i s t a n c e . . . . . . . . . . . 4.1.2. M a g n e t o r e s i s t a n c e a n i s o t r o p y . . . . . . . . . . . . . . . 4.1.3. E x t r a o r d i n a r y H a l l effect . . . . . . . . . . . . . . . . . 4.1.4. T h e r m o e l e c t r i c p o w e r . . . . . . . . . . . . . . . . . . . 4.2. P l a t i n u m b a s e d a l l o y s . . . . . . . . . . . . . . . . . . . .
748
751 751 751 752 754 754 755 756 757 757 757 758 762 762 762 764 765 766 768 771 771 772 773 776 776 778 779 783 790 792 792 793 793 793 794 794 794 795
5. A m o r p h o u s alloys . . . 5.1. Resistivity of a m o r p h o u s 5.2. Hall effect and resistivity References . . . . . . . .
. . . . . alloys . anisotropy . . . .
. . . . . . . . . . . . . . . . . . . . . . . . of a m o r p h o u s alloys . . . . . . . . . . . . . . .
749
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795 795 800 800
Introduction The scope of this chapter will in fact be rather more restricted than its title might suggest. W e will outline some very general properties of transport in ferromagnets and will summarize the models that have been used. We will then review in detail results on particular systems. W e will not treat magnetic semiconductors, and we only occasionally mention rare earth metals and their alloys, as they will be treated in another chapter*. Because of the lack of systematic data, we will not review the properties of magnetic intermetallic compounds as such, but will mention results on these compounds as and when they exist. A section is devoted to a m o r p h o u s ferromagnets. However, we will be mostly concerned with the transport properties of the transition ferromagnets Fe, Co and Ni and their alloys, while drawing examples from other classes of magnetic metals to illustrate particular types of behaviour. The subject has advanced so much over the last 25 years that this chapter has little to do with the equivalent one in Bozorth's book. However, a n u m b e r of books and review articles have been very useful; a list of them is given at the end of the chapter (Jan 1957, Mott 1964, H u r d 1974 and 1972, Dorleijn 1976).
1. General properties of transport in ferromagnets W e will discuss effects which arise quite generally as a consequence of the symmetry properties of the ferromagnetic state.
1.1. Resistivity and Hall effect of a monodomain polycrystal The components Ei of the electric field inside a conductor are related to the current density ~ through J~i ~" E PiJJ] , J
( 1)
* Vol. 1, oh. 3, by Legvold. 751
752
I.A. CAMPBELL AND A. FERT
where the pij coefficients form the resistivity tensor. Suppose we have a random polycrystal with its magnetization saturated in the direction z. From symmetry arguments (Birss 1964, H u r d 1974) one finds that such a magnetized isotropic medium has a resistivity tensor of the form: [P~i] = |[_ p H (orP±(B) B ) -pH(B) pa(B) 0
00 1 .
(2)
RjI(B)
This form of the resistivity tensor corresponds to the following expression of the electric field E: E = p I ( B ) J + [PlI(B)- p±(B)][o~ • J ] ~ +
pH(B)oz x J,
(3)
where J is the current vector and a is a unit vector in the magnetization direction. functions of the induction B, which depends on the external field H and on the demagnetizing factor D of the particular sample geometry,
The pii(B) are
B = H + 4rrM(1 - D ) .
(4)
This is because of Lorentz force effects which exist in any conductor. That the effective field acting on the electron trajectories in a ferromagnet is indeed B seems physically reasonable (Kittel 1963) and has been verified experimentally (Anderson and Gold 1963, Tsui 1967, Hodges et al. 1967). Conventionally, the coefficients Pij are split up into two parts pij(B) = pij + p°(B) where the p~j are the " s p o n t a n e o u s " or "extraordinary" coefficients, and the p°(B) are the "ordinary" coefficients. It should be noted that the Pit cannot be measured directly without some form of extrapolation because of the presence of the internal Lorentz field. In practice, this extrapolation causes little difficulty except for fairly pure samples at low temperatures where B/p can be high and the ordinary effects become large. Assuming that this extrapolation to zero B has been made we have the three spontaneous parameters: Pll = the resistivity for J parallel to M at B = 0, p± = the resistivity for J perpendicular to M at B = 0, PH = the extraordinary Hall resistivity.
1.1.1. Spontaneous resistivity anisotropy The fact that the diagonal elements Pll and p± in (2) are unequal means that the resistivity depends on the relative orientation of M and d. Taking the geometry of fig. 1 and calling 0 the angle between M and J, as by definition the resistivity is p = E.
J/fJI 2 ,
we have from eq. (3),
TRANSPORT PROPERTIES OF FERROMAGNETS
7
753
[
Fig. 1. Experimental geometry for transport properties. T h e current J is constrained to flow along the direction x, and whatever the applied field or magnetization direction, the resistivity is proportional to the voltage between probes A and B, p = ( V B - VA)bt/J1. For the conventional Hall geometry, the applied field or magnetization direction is along z and the Hall voltage is m e a s u r e d between C and D. T h e n PH = ( V O - Vc)t/J and R0 = ( V D - Vc)t/JH or R~ = ( V D - Vc)t/J 4~rM.
ps=0 = Pll + 32p~ + (cos 2 0 - ½)(Pll- P~)
(5)
The relative spontaneous anisotropy of the resistivity is defined as: Ap _ PlI- P± 1 P 3Pll + 2p±
(6)
It can have either sign, and while generally values of a few percent are typical, certain systems show more than 20% anisotropy. Figure 2 shows schematically typical resistivity changes as a function of applied field, and the method of extrapolation to obtain Pll and p± is indicated. N o t e that the resistivity of the zero field state depends on the exact domain configuration, so it is history dependent and is not well defined even for a given sample at a given temperature. In the same way, the change of resistivity with field below technical
{8=0}. . . . .
~a=01--
, H
B/p
8=0,1
I1
Fig. 2. Schematic extrapolation for a ferromagnetic of p(H) resistivity curves to B = 0. T h e heavy lines indicate observed resistivity as a function of field when the field is applied parallel (11) or perpendicular (±) to the current direction. Arrows show the regions of incomplete technical saturation. Dotted lines indicate extrapolations from the saturated regions to the respective B = 0 points (B = H + 4~-M(1 - D ) where D is the demagnetizing factor for transverse or longitudinal fields).
754
I.A. C A M P B E L L A N D A. F E R T
saturation depends on the magnetization process. We have assumed above that in the saturated region only Lorentz force effects are important for the variation of Pll or p± with B. In fact, the external field H may also increase the magnetization of the sample which will affect p, because of a reduction in spin disorder resistivity. This is particularly important near T¢.
1.1.2. Extraordinary Hall effect The off-diagonal terms +pH in (2) lead to the extraordinary Hall voltage,
(7)
E H ( B = 0) = p H a × J ,
perpendicular to M and J. This is usually measured in the conventional Hall geometry with M perpendicular to J (fig. 1). We can also define the extraordinary Hall angle
¢hH= P~/Pi
(8)
and, by analogy with the definition of the ordinary Hall coefficient R0 = p ° / B we have the extraordinary Hall coefficient
Rs = pn/4~M.
(9)
Once again, extrapolation of the Hall voltage curve as a function of B from the saturated region back to B = 0 is necessary to obtain PH (fig. 3). This is easy in the low field regime oJc~ 1 (we is the cyclotron frequency and ~- is the electronic relaxation time) but the separation between ordinary and extraordinary effects is difficult when ~o~-~ 1 where the ordinary Hall voltage is no longer linear in B.
~(~0] -
/ H I,
B=O 0 Fig. 3. Schematic extrapolation for a ferromagnet of a Hall resistivity curve to B = 0. On (B = 0) is the extraordinary Hall resistivity.
1.1.3. Planar Hall effect This is a misnomer, as was already pointed out by Jan (1957). When J is in the direction x, the voltage is measured perpendicular to J in the direction y and M is rotated in the plane xy, then from eq. (4):
TRANSPORT PROPERTIES OF FERROMAGNETS
755
Ey = (P/I- P±) cos 0 sin OJ , where j r . M = cos 0. This is a manifestation of the resistivity anisotropy and is an effect even in field which has nothing to do with the Hall effect. 1.2. Resistivity and Hall effect in single crystal ferromagnets The symmetry arguments can be extended to single crystals (see, e.g., Hurd 1974). It is found that even for cubic crystals, the resistivity becomes dependent on the orientations of the current and the magnetization with respect to the crystal axes , and the extraordinary Hall effect depends on the magnetization direction. For a cubic ferromagnet with M in the direction (11, 12, 13) and J in the direction (/31,/32,/33) we have the D6ring expression (D6ring 1938): O ~. Oo[l+k1(a2/321+
2 2 ..{- 0/3/33 2 2 -- ~) 1 Of 2/32
+ k2(20L1o~2/31/32 + 2ol2o,3/32/33 + 2ce3oq/33/31 ) + k 3 ( S ..~ k , ( ~ 14 / 321 + ~ / 3 2 +
_ 1)
4 2 + z3S - I) 13/33
+ k5(2~i~2,~2/31/3~ + 2~2,~,-,~/32/3, + 2 - , ~ 1 - ~ / 3 , / 3 3 1 , where
(10)
S = O /2l a 22.~_ OL20~3 2 2 -}- 0~30~ 2 21
Other equivalent definitions have been given. Kittel and Van Vleck (1960) suggested that a physically more significant definition for the magnetoelastic coefficients (which have the same symmetry as the resistivity coefficients) would regroup the terms to give new coefficients: K1 = k l + 6k4; K2 = k2 + ~k5;I K3 = k3 + 2k4; K4 = k4; /(5 = }ks and p; = p0(1- 2k4). This would separate out terms homogeneously second order (K1,/£2) and fourth order (/(3, K4, Ks) in the magnetization. The resistivity p = t~ + ( p , - a i ) ( c o s 2 0 - 1)
(11)
for a magnetized cubic polycrystal is related to the two types of coefficients by: t~ = t~o(1 - ~ k 3 ) -= o ;
and 2
3
12
3
2
Pfl- P. = po(~kl + 3k2 + ggk4 + 5~k5) ~ po(~K1 + 3/(2).
(12)
The resistivity of a demagnetized cubic polycrystal is memag = P ~--p0(1 -- ~k3) --=p ;
(13)
756
I.A. CAMPBELLAND A. FERT
if the magnetization is randomly oriented with respect to the crystal axes. In contrast, if there are easy axes, Pdemagis different from/5, for example, Pdemag = /90
for (111) easy axes. The D6ring expression only gives the leading terms in an infinite expansion. Higher order terms can be necessary in interpreting experimental results. For the extraordinary Hall effect in a cubic monocrystal, instead of defining the z-axis as the M direction, we use the crystal axes to define x, y and z. Then the asymmetric part of the resistivity tensor becomes (Hurd 1974).
[ A3 o -a3 0 -A2 A1
A2 1 0
-A1
with
Ai = o~i(eo+ ela~ + e2c~4+ e3S).
(14)
This gives a Hall voltage which must be perpendicular to J, but is no longer necessarily perpendicular to M, and which is anisotropic. We might note that in cubic crystals the ordinary Hall effect is isotropic in the low field limit. For ferromagnetic monocrystals with other symmetries such as hexagonal, analogous expressions can be derived (Birss 1964, Hurd 1974).
1.3. Thermal and thermoelectric effects in polycrystaIs The thermal conductivity and the Righi-Leduc effects are the pure thermal analogues of the resistivity and the Hall effect, with heat currents replacing electrical currents and thermal gradients replacing electrical field gradients. The phenomenological separation into spontaneous and ordinary effects carries over entirely. The only difference lies in the necessity to define whether the experimental conditions are isothermal or adiabatic (Jan 1957). Similarly, for a magnetized ferromagnetic polycrystal subject to a temperature gradient VT, the resultant electric field is
E, = E Si,V,T, with S/j =
NE
S±
0
0
.
S~l
Here, SII and Sl are the isothermal thermoelectric powers in parallel and perpendicular geometries. SNE represents the spontaneous Nernst-Ettingshausen effect.
TRANSPORT PROPERTIES OF FERROMAGNETS
757
For both the thermal effects and the thermoelectric effects the generalization to monocrystals is just the same as for the electrical effects.
2. Electrical resistivity of ferromagnets 2.1. Theoretical models
For non-magnetic metals, current is carried by electrons which are scattered by phonons and by impurities or defects. To a first approximation the two scatterings give additive contributions to the resistivity p ( r ) = Po + pp(T),
where p0 is the residual resistivity and pp(T) is the pure metal resistivity at temperature T. This is known as Matthiessen's rule. Deviations from this rule are small and are generally explained in terms of differences in the anisotropies of the relaxation time of impurity and of phonon scattering over the Fermi surface (Dugdale et al. 1967). In magnetic metals a number of new effects appear. 2.1.1. Spin disorder scattering
On the simple model of well defined local moments in a simple conduction band, an exchange interaction between the local and conduction electron spins, J and s respectively, of the type F s . J will give rise to spin disorder scattering (Kasuya 1956, 1959, De Gennes and Friedel 1958, Van Peski Tinbergen and Dekker 1963). Well above the ordering temperature there will be a temperature independent paramagnetic resistivity - kv(mF)2 J ( J + 1) pM - 4~e2zh3
(15)
where kF is the Fermi wave vector and z the number of conduction electrons per atom. This paramagnetic resistivity is actually the sum of a non-spin-flip term (due to szJz interactions and proportional to j2) and a spin-flip term (due to s - J + + s+J and proportional to J). For the region around Tc the resistivity depends on the spin-spin correlation function (see section 2.4). As T drops both the spin-flip and non-spin-flip scattering begin to freeze out. Kasuya (1956) finds
~m -- j ( j
PM (J-I<S)I)(J + 1 + KS)t) _}_ 1)
(16)
Finally, at low temperatures magnetic scattering only remains as magnon-electron scattering. A number of authors have calculated the low temperature form of this scattering. If the spin '~ and spin + conduction electron Fermi surfaces are assumed to be identical spheres with the same relaxation rates, the contribution to
758
I.A. CAMPBELL AND A. FERT
the resistivity is proportional to T 2 (Vonsovskii 1948, Turov 1955, Kasuya 1959, Mannari 1959). Mannari (1959) finds*
Pm
_ ¢r3 N J m F 2 (_~) 2 32 eZzhE~ (kT)2 '
(17)
where/xe is the effective mass of the magnons (/Xe= h2/2D). The resistivity varies as T 2 because the loss of momentum of the total electron system due to collisions with the magnons is proportional to
f
q exp(Dq~/kT)-
1
q2 dq
'
which is equal to a constant times T 2. Here q is the magnon wave vector. The final q2 factor inside the integral is a small angle scattering factor, and the rest of the integrand represents the number of magnons with vector q at temperature T which undergo a collision. The reasoning is essentially the same as that leading to the well known T 5 limiting dependence for electron-phonon scattering in nonmagnetic metals except that: (i) the dispersion relation for magnons is E = D q 2 instead of E = aq for phonons. (ii) the coupling strength for electron-magnon collisions is independent of q instead of proportional to q as it is for electron-phonon collisions. If the conduction band is polarized or if there is scattering from s to d Fermi surfaces or if there is a magnon energy gap, the electron-magnon scattering will tend to drop off exponentially at low temperature instead of the T 2 behavior (Abelskii and Turov 1960, Goodings 1963). Other mechanisms giving various temperature dependences have been also suggested (Vonsovskii 1955, Turov and Voloshinskii 1967) but appear to give extremely small contributions (see section 2.2). The previous models generally assume that the spin T and spin { electrons have the same relaxation times and carry the same current. If there are different spin 1' and spin { currents, there will be a contribution of the magnons to the resistivity through spin mixing. This appears to be the major magnon contribution in many ferromagnetic alloys. This question Will be treated in section 2.1.2. Finally, in dilute random ferromagnets (Pd_Fe at low concentrations is the best example of this type of system) the incoherent part of the magnon scatteringwithout momentum c o n s e r v a t i o n - b e c o m e s predominant. The scattering rate is then simply proportional to the number of magnons giving p ( T ) - p o - T 3/2 (Turner and Long 1970, Mills et al. 1971). 2.1.2. T w o current model All the discussion given up to now has neglected any spin independent potential. If there is a scattering potential V at magnetic sites in addition to Fs • J, then at
* Note that the result of Kasuya (1959) differs from eq. (17) by a factor 3z/'n'.
TRANSPORT PROPERTIES OF FERROMAGNETS
759
low temperatures the spin I' and spin + electrons will be subject to potentials V + F J and V - F J respectively, together with weak spin-flip scattering by magnons (from F(s+J - + s-J+)). This will give rise to different spin t and spin $ currents. Alternatively, in terms of the s-d band model which is widely used for transition ferromagnets, the d t and d + densities of states at the Fermi level are different so the s to d scattering rates will be different for spin 1' and spin $ conduction electrons. This approach was used early on to explain the p ( T ) of transition ferromagnets up to and above the Curie temperature (Mott 1936, 1964). It now appears that the simple s-d band model approach is questionable at high temperatures where the local spin aspect seems to be dominant even for a typical " b a n d " ferromagnet such as Ni. At low temperatures however where Sz is almost a good quantum number the s-d model is more appropriate. The electronic structure of the transition ferromagnets has been studied intensively, and low temperature measurements such as the de Haas van Alphen effect in pure metal samples show that they have complex Fermi surfaces of much the same type as those of non-magnetic transition elements except that k 1' and k ~ states are not equivalent. Detailed band structure models have been set up which are in good agreement with the measurements and which show that the electrons wave functions are s and d like, generally hybridized (Visscher and Falicov 1972). An extreme s-d model where s-d hybridization is assumed to be weak provides a good basis for the discussion of a wide range of alloy properties (Friedel 1967). We will now consider the resistivity again. Quite generally, at low temperature the electron spin direction is well defined if we ignore magnon scattering and spin-orbit effects. Then in any model we will have conduction in parallel by two independent currents. If the corresponding resistivities are Pt, P+ the total observed resistivity is*:
P
(18)
= PtP+ Pt + P+
Inside each p~ we can have complications such as s and d bands but eq. (18) still remains strictly valid. If now there is transfer of momentum between the two currents by spin mixing scatterings (e.g. electron-magnon or spin-orbit scattering) then again quite generally (Fert and Campbell 1976), P=
PtP+ + Pt +(Pt + P+) , pt+p~+4pt~
(19)
where P* = P * t / X ~ + P t $ / X t X ~ ,
P$ = P ~ $ / X 2 ~ + P t $ / X t X ~ ,
(2o)
and * Electrons with magnetic moment parallel to the total magnetization, i.e., electrons of the majority spin band, are indicated by t ; electrons of the minority spin band by $ :
760
I.A. C A M P B E L L A N D A. F E R T
P~ ~ = - P t + / X , X+ . H e r e p~, are integrals over the transition rates p(kcr, k'cr') for scattering from one electronic state to another and X~ are integrals over driving terms: Vk " (e Ofk/OEk)E where E is the electric field, vk the electron velocity andfk the Fermi function (Ziman 1960). If the occupation n u m b e r of each k state under zero electric field is ~ , then we can write the occupation n u m b e r under applied field as fk
= ~
-
(21)
4)k(df°kldEk).
We can use the variational principle, using k . u as a trial function for the function k, where u is a unit vector parallel to the applied field. We then get:
1
P'~ - X ~ k B T
~,
1
P* ~
f (k.
X t X,t k B T
f
u)[(k - k')" u]P(ko-, k'o") d k d k '
(22)
(23)
(k' • u)(k • u ) P ( k t k'+ ) d k d k ' ,
where P(ko-, k'o-') is the equilibrium scattering rate between (kcr) and (k'o-'). Matthiessens' rule is assumed for each of the three terms
x
x
where x refers to different types of scattering centres (phonons, magnons, each sort of impurity). T h e r e are t e m p e r a t u r e independent " p u r e metal" terms Pit ( T ) , pi+(T) and p~ ~(T) which go to zero at zero t e m p e r a t u r e and are assumed to be independent of impurity concentration in dilute alloys, and there are impurity terms which are assumed to be t e m p e r a t u r e independent. The spin-flip scattering by impurities (via spin-orbit coupling) is generally neglected, which leaves two impurity terms P0 t and p0 ~. The model then predicts a deviation from Matthiessens' rule in the residual resistivity of ternary alloys (Fert and Campbell 1976):
A p = PAB -- (PA + PB) --
(O/A -- aB)2pAPB a , , ) 2 a B p A + (1 + aB)Za
oB '
(24)
where a A = P A $ / P A "r
and
O/B = PB $/PB t "
The analysis of the deviations in alloys with different relative concentrations of A and B can be used to determine aA, aB (Campbell et al. 1967, Cadeville et al.
TRANSPORT PROPERTIES OF FERROMAGNETS
761
1968, Dorleijn and Miedema 1975a, Fert and Campbell 1976, Dorleijn 1976). For a binary alloy at finite temperature the general equation (19) can be used, with P~ = Po~ + pi~(T). For the low temperature range where Pot, po+ >>p~t (T), pi+ (T), Pt +( T ) , this reduces to:
(1
p~(T)+ k ~ + - l ] Pt $ ( T ) ,
(25)
where tx = Pil (T) pi~: ( T) ' Po = PotPo+ Pot +Po~
(residual resistivity)
and pi(T) = PiT(T)Pi~(T) pi,r(T)+ pi$ (T)
(which is not the ideal pure metal resistivity).
The term of eq. (25) proportional to p$ ~(T) will give a strong variation of the resistivity as a function of the temperature when a is very different from unity; in nickel, for example, Co, Fe or Mn impurities enhance the low temperature resistivity variation by almost an order of magnitude. The form of the electronmagnon contribution to p~ $(T) has been calculated by Fert (1969) and Mills et al. (!971) using a spin-split spherical conduction band model. In alloys with a -~ 1 the temperature dependence of the resistivity will nearly be that of pi(T). Using experimental data on binary and ternary alloys, it turns out to be possible to obtain consistent values for the parameters for a number of impurities, together with estimates of the temperature behaviour of the pure metal terms (see section 2.3). It is important to note that it is not possible to obtain a full description of the pure metal behaviour, i.e., the three pure metal terms, without analyzing alloy data. Another way of treating the two current conduction has been presented by Yamashita and Hayakawa (1976). They start from a realistic band structure model for Ni and calculate the resistivity by numerically solving coupled spin 1' and spin $ Boltzmann equations for series of k vectors. They find that the electronmagnon contribution to the resistivity is very small when there is no impurity or
762
I.A. CAMPBELL AND A. FERT
phonon scattering but becomes important when impurity or phonon scattering makes the spin 1" and spin $ mean free paths different; in the latter case, there is no more "cancellation between outgoing and incoming scatterings". This is another way of describing the spin-mixing effect of the magnons.
2.2. Resistivity of pure metals 2.2.1. Tabular results The resistivity (and also the thermoelectric power and thermal conductivity) of pure Fe, Co and Ni are given in tabular form over a wide range of temperatures by Laubitz et al. (1973, 1976) and and Fulkerson et al. (1966). Data on polycrystalline hexagonal Co should be treated with caution, as the transport properties of monocrystals are highly anisotropic. At room temperature (Matsumoto et al. 1966) pc = 10.3 ixf~cm,
Po = 5.5 ixlIcm
where Pc is the resistivity measured along the c axis while pp is measured in the plane perpendicular to the c direction. Texture effects in polycrystals will certainly be important.
2.2.2. Resistivity at low temperatures With high purity samples at low temperatures the presence of the induction in each ferromagnetic domain means that the Lorentz wO- is not negligible even in zero applied field. There is an associated "internal" magnetoresistance and to get meaningful results for the intrinsic low field resistivity this effect must be eliminated as well as possible. Careful extrapolations to B = 0 using Kohlers' law 2Xp/po = f(B/po) have been done for Ni (Schwerer and Silcox 1968), Co (Volkenshtein et al. 1973) and Fe (Volkenshtein and Dyakina 1971). For Fe in particular the "internal" magnetoresistance is very important, partly because of the high value of 4~-M and partly because Fe behaves as a compensated metal (see section 2.2.4) so that the transverse magnetoresistance can become very strong, whereas the longitudinal magnetoresistance is relatively much weaker. This means that the observed resistivity of a high purity Fe sample at low temperature is strongly dependent on the domain configuration, which regulates how much of the sample is submitted to transverse magnetization and how much to longitudinal; the domain configuration is a function of applied field, stresses and measuring current. The resistivity behaviour arising from such effects of internal magnetoresistance has been studied in detail in Fe whisker monocrystals (Taylor et al. 1968, Shumate et al. 1970, Berger 1978); an example of experimental results is given in fig. 4. A contribution to the resistivity from the internal Hall effect has also been found in Co monocrystals; this contribution is associated with the zig-zag path of the conduction electrons which is induced by the Hall effect in a polydomain sample (Ramanan and Berger 1978, Berger 1978). The low temperature resistivity of Ni, Co and Fe has been found to vary as
TRANSPORT PROPERTIES OF FERROMAGNETS
763
18001600-
-~ 14001200g N % ~3
~-
1000800 0
U I
~
I
{
I
I
L
I
I
I
I
I
I
-0.2 -0,4 0_.
~-- -0.6
oo>
-0.8 I
I
100 200 300 400 500 600 700 800 Oe Magnetic FieLd
Fig. 4. Magnetization of iron single crystals (above) and magnetoresistance (below) of (100) and (111) iron whiskers at 4.2 K as a function of applied field (after Taylor et al. 1968).
p o + A T 2 by most workers; above 1 0 K an additional term in T 4 is generally needed (White and Woods 1959, Greig and Harrison 1965, White and Tainsh 1967, Schwerer and Silcox 1968, Beitcham et al. 1970). In early work no magnetoresistance corrections were made, with the result that rather varied values of A were obtained. In a number of samples a term linear in T was also needed, but careful experiments on the effect of magnetic fields show that this linear term is not intrinsic but is a result of the internal magnetoresistance (Volkenstein et al. 1971, 1973). The best values of A from data to which the magnetoresistance correction was applied to obtain values at B = 0 are: A = 9.5 x 10-12 ~ c m K -2 for Ni (Schwerer and Silcox 1968) A = 16 × 10-12 l"~cmK-2 for Co (Volkenstein et al. 1973) A = 15 × 10-12 ~ c m K -2 for Fe (Volkenstein et al. 1971, 1973). These values however are not quite consistent with measurements on other samples, even if internal magnetoresistance effects are taken into account. It is likely that p(T) depends in some way on the nature of the residual impurities. As the scattering by residual impurities is still predominant up to 10 K in the purest samples, p(T) is actually expected to show deviations from Matthiessens' rule similar to those observed in alloys and explained in the two-current model
764
I.A. CAMPBELL AND A. FERT
(section 2.3). More precisely, the two-current model relates p(T) to the parameter a characteristic of the impurity scattering (eq. (25)). According to whether a is large or close to unity p(T)-po is large and varying as p , +(T) or small and varying as pi(T). The values of p(T)-po for pure metals, although scattered, are relatively small, which suggest that a is generally close to unity. The variation in T 2 can be then ascribed to pi(T). The variation in T 2 has been attributed either to electron-magnon scattering or to s-d electron-electron scattering (Baber 1937) of the same type as leads to a T 2 term in the resistivity of non-magnetic transition metals at low temperatures, and which is much the same magnitude as the T 2 term in the ferromagnets. If the thermal conductivity of the ferromagnetic metals is also measured at low temperatures the Lorentz ratio corresponding to the non-impurity scattering is about 1 × 10-8 W~)K -2 both in Ni (White and Tainsh 1967) and in Fe (Beitcham et al. 1970). This is close to the value estimated theoretically (Herring 1967) for s-d electron-electron scattering. However the way in which the experimental data are analyzed has been criticized (Farrel and Greig 1969). Secondly, we can consider data on pit(T), pi+(T) and p~ +(T) obtained from an analysis of dilute Ni alloys (see section 2.3). The spin-flip magnon-electron resistivity p~ +(T) is roughly 5 × 10 9 l~cm at 10 K in Ni (see fig. 9); because of the small angle scattering factor the electron-magnon contributions to p~, (T), pi+ (T) should be lower by a factor of the order of T/Tc, giving pi~ ( m a g n o n s ) - 1 0 - 1 ° ~ c m ; as the "observed" pi~ values in Ni at 10 K are much higher (these are higher than 10 -9 ~~cm), we can infer that the electron-magnon contributions to the p~r are not dominant. This actually is in agreement with predictions of calculations based on a realistic band structure model of Ni (Yamashita et al. 1975). It thus turns out that electronelectron collisions play the major role in the low temperature T 2 term of the pure metals.
2.2.3. Residual resistivity In pure ferromagnetic metals the "internal magnetoresistance" enhances the resistivity which is no longer proportional to the concentration of impurities. This effect is particularly important for Fe which has a high value of 47rM and a high transverse magnetoresistance (fig. 5). For demagnetized Fe polycrystals it was pointed out that the apparent residual resistivity ratio p(300 K)/p(4.2 K) would never increase beyond about 300 however pure the sample (Berger and de Vroomen 1965). It is now standard practice to measure the low temperature resistivity of Fe samples in a saturating longitudinal magnetic field so as to eliminate transverse magnetoresistance. This can reduce the apparent resistivity by a factor of 5 or more. In principle a correction should still be made for the longitudinal magnetoresistance. In Ni samples the enhancement of the residual resistivity by the internal magnetoresistance is less important than in Fe but still significant (Fujii 1970, Schwerer and Silcox 1970). The contribution of the domain walls to the residual resistivity of ferromagnetic metals has been subject to many discussions. It now appears that domain walls are too thick to scatter electrons appreciably. However, as it has been pointed out in
TRANSPORT PROPERTIES OF FERROMAGNETS
765
1000 -
x
500 o " c~ .4.. ~"
B 0 xrl x O V ^Jm x
200
nO O0
O 0 O A
n On 0
100 - -
o
c,l
0...
x[3 X
50
x
°o 0 *o
Increasing p u r i t y
20 x
I 20
,
i
i , ~,,I 50 100
I 200
,
i
I L,,,I 500 1000
, 2000
((3295 / (34.2)mox.
Fig. 5. Residual resistance ratio in zero field and in longitudinal applied field for iron samples of increasing purity (after Berger 1978).
the preceding section, the resistivity depends indirectly on the domain walls as it depends on the domain configuration in the sample (Berger 1978).
2.2.4. High field behaviour It is well known that the magnetoresistance and Hall effect of pure metals under high fields such that wc~">> 1 give information on the Fermi surface. In Ni under high fields applied along a non-symmetry direction of a monocrystal, the transverse magnetoresistance saturates, and R0 corresponds to an effective carrier density of 1 electron per atom, even though Ni has an even number of electrons and so would normally be expected to behave as a compensated metal. Reed and Fawcett (1964a) showed that a ferromagnetic metal did not have to obey the same rules as non-magnetic metals because of the inequivalence of spin 1' and spin $. They deduced from their results that the minority d band in Ni was electron-like in character. The behaviour of the magnetoresistance for certain field directions indicated the presence of open orbits for certain field orientations. The results could be compared with de Haas-Van Alphen data (Hodges et al. 1967, Tsui 1967, Ruvalds and Falicov 1968). No obvious transition corresponding to a major difference in mobility for d-like and s-like parts of the Fermi surface was observed. In Co the transverse magnetoresistance is again saturated (Coleman et al. 1973) with open orbit behaviour for certain special directions. In Fe up to fields of about 100kG, the magnetoresistance tends to a B 2 dependence indicating that the metal is compensated (Reed and Fawcett 1964b). There appears to be a considerable spread of o)c~-values. In the same field range at low temperatures the ordinary Hall coefficient R0 is strong, negative and
766
I.A. C A M P B E L L A N D A. F E R T
weakly field dependent (Klaffky and Coleman 1974). This also is consistent with a metal having compensated character, for which R0 bears no relationship to any effective number of electrons per atom. At still higher values of ~o~- the magnetoresistance increases much more slowly than B 2 (Coleman 1976); magnetic breakdown and intersheet scattering have been invoked.
2._3. Alloys: residual resistivity and temperature dependence of resistivity The residual resistivity per atomic percent impurity has been measured for a wide range of impurities in Ni, Co and Fe (p0 in tables 1, 2, 3) and the deviations from Matthiessens' rule have been studied both for ternary alloys (fig. 6) and for binary alloys as a function of temperature. Using the two current model equations of section 2.1.2 the experimental data have been used to determine the spin t and spin ~, residual resistivities Pot and p0~ for each impurity in each host (tables 1, 2,
3). TABLE 1 Values of a = P o l / P o t , po, Pot, Po,, for dilute impurities in nickel*. Po (ixf~cm)
po t (ix~cm)
13 ("), 300,), 20 (c), 13(d) 20(f), 20(g)
0.16 ± 0.03
0.18 --+0.03
3.5 --+1
Fe
11 ("), 200,), 7.3 (d)
0.36-+0.04
0.4-+0.04
6-+ 1.5
Mn
6.3 ("/, 150,), 5.4 (d)
0.7 -+ 0.1
Cr
0.21 ("), 0.45 (b), 0.4 (c), 0.21(a), 0.2#), 0.4(g)
V Ti
c~ = Po ~/Po t
Impurity in nickel Co
Po (~f~cm)
0.75 -+ 0.2
7.5 + 2.5
5 -+ 0.1
22 -+ 6
6.5 -+ 0.5
0.45 ("), 0.55 °,), 2.3 (d)
4.4-+0.2
13-+ 1
6.7-+0.5
0.9 (a), 40,), 2.7 (d)
3.3 -+ 0.6
5.6 -+ 2
Pd
1(d)
0.2 -+ 0.05
Rh
0.3 ("), 0.17 ("), 0.290)
1.8 _+ 0.1
10 _+ 2
2.1 _+0.2
Ru
0.075 ("/, 0.15 (e)
4.8 _+ 0.2
56 -+ 15
5.8 -+ 0.5
Mo
0.28 e), 0.37 °)
6.4 -+ 0.6
25 + 4
8+ 1
5 _+0.2
16 -+ 1
7 _+ 0.2
Nb
0.44 ("/, 0.470)
Zr
7.5 (e)
Pt
0.24 (a), 0.17 (~)
0.3 Id)
10.5 -+ 4
2.8 ± 0.5
4 (e)
0.85 ± 0.2
5.3 ± 1.6
0.3 (a)
30 (e) 1 _+0.2
Ir
0.24 ("), 0.13 (~)
3.8 ± 0.2
28 ± 7
4.8 ± 0.2
Os
0.13 ("~, 0.13 o)
5.5 _+0.5
50 ± 2
6.4 ± 0.5
Re
0.3 ("), 0.26 e)
5.8 ± 0.5
26 ± 3
7.5 ± 0.5
T A B L E 1 (continued)
Impurity in nickel
Po (txf~cm)
a = po ~/Po t
W
0.4 (e), 0.5 o)
Ta
pot (ixf~cm)
Po ,~ (pf~cm)
6 ±0.5
16.5 -+ 1
7 -+ 0.5
0.53 (e), 0.46 o)
5.2 ± 0.5
16 ± 1
7.5 ± 0.5
Hf
8.6 (~), 8.1 o)
3.6 ± 0.5
3.5 ± 0.5
30 - 1
Cu
2.9 (a), 3.7 (d)
0.9 ± 0.1
1.1 ± 0.2
3.7 ± 0.2
Au
5.9 (")
0.36 (")
0.44 (a)
2.6 (a)
AI
1.7 (a)
2.13 (a)
3.4 (a)
5.8 (a)
Si
1.3 (")
2.83 °)
5 (a)
6.4 (a)
Zn
2.2 (~)
1.3 (a)
2.9 (a)
1 ± 0.1
Ga
1.7(g)
1.91 (g)
3cg)
5.2 (g)
Ge
1(g)
2.84 (g/
5.7 (g/
5.7 (g)
In
1.50')
3.60')
6 °`)
90`)
Sn
1.6(a), 1.350')
3.2 ± 0.4
5.2 -+ 0.8
7.7 ± 0.5
Sb
0.8 ~)
1.6c~)
3.60')
2.90')
* For a we give the values found by: Dorleijn and M i e d e m a (1975a), Dorleijn (1976); 0`) Fert and Campbell (1976); (c) Leonard et al. (1969); ca) Farrell and Greig (1969); (e) D u r a n d and Gautier (1970); (a)
(0 Cadeville et al. (1968); ~) Hugel (1973); 0') Ross et al. (1978); (i) D u r a n d (1973).
T h e values of a given in (a), (b), (f), (g) have been mostly derived from m e a s u r e m e n t s of the residual resistivity of ternary alloys, which is the most direct method. T h e values of a given in (d), (e), (h), (i) have been obtained on binary alloys from the deviations from Matthiessen's rule at low temperature (h), 77 K (i), 300 K with the assumption of complete spin mixing (d) or 300 K with the assumption of no spin mixing (e). T h e values that we give for p0, Pot, p0~ have been estimated from the spread of the values found in the literature.
lo]
2
0.5[
o_£ 1
t
//
N.~ (AUl_xCO x)
Ni (Co1_xRhx) i
05
0
10
×
01
0
015
1.0
X
Fig. 6. Residual resistivities of Ni(COl-xRhx) and Ni(Aul xCox) alloys. The large deviations from Matthiessen's rule (broken line) for the Ni(COl-xRhx) alloys are accounted for by very different values of C~coand aRh; the solid curve is calculated from eq. (24) with aco = 13 and aRh = 0.3. T h e very small deviations from M R in the Ni(Aul-xCox) are associated with values of aAu and aCo both m u c h larger than 1 (after Dorleijn 1976). 767
768
I.A. C A M P B E L L A N D A. F E R T TABLE 2 Values of a = Po ~/po ~, po, Po t , po ~ for dilute impurities in cobalt*.
Impurity in cobalt Fe (") Mn c°/ Cr e°} V (b) Ti (u~ Rh c°~ Ru ("/ Mo c°~ Nb ~ Zr c°~ Ir (a~ Os (a~ Re c°) W (b~ Ta c°~ Hf (b) Sn (c~ Sb (c)
c~ = Po +/Po ~
12 0.8 0,3 1 1.4 1 0.22 0.7 1 3.3 0.33 0.29 0.43 0.84 1.23 2.5 1.2 0.9
Po
Po ~
po;
0xf~cm)
(Ixf~cm)
(~ftcm)
0.5 5.5 1.8 3.8 4.5 1.4 4.0 6.0 6.5 4.0 2.9 5,3 5.3 5.7 5.5 4.0 2.9 2
0.54 12 7.3 7.7 7.6 2.8 22.4 14.4 13 5.2 11.7 23.5 18 10.5 10 5.5 5.3 4.2
6,7 10 2.4 7.7 11 2.8 4,86 10 13 17 3.82 6.84 7.7 12.5 12.3 14 6.4 3.8
• ca)Loegel and Gautier 1971; ~b~Durand 1973; to) Ross et al. 1978. The data have been obtained from deviations from Matthiessen's rule in the residual resistivity of ternary alloy (a) or in the resistivity of binary alloys at low temperature (c) or at 77 K (b). We have preferred the results given by Durand (1973) to slightly different ones given previously by Durand and Gautier (i970).
2.3.1. Nickel host The general picture of c~ (=p0~/p0t) values for impurities in Ni estimated by different groups is consistent, although numerical values are not in perfect agreement (table 1, fig. 7). It is found that Co, Fe, Mn, Au and Cu have a >> 1 while Cr, V and a number of other transition impurities have a < 1. As has been pointed out (Durand and Gautier 1970, Fert and Campbell 1971, 1976, Hagakawa and Yamashita 1975) there is a very clear connection between the electrical and the magnetic properties of the impurities. Those impurities with high values of o~ are those which, on the Friedel analysis of the magnetic properties (Friedel 1967), do not have d I' virtual bound states at or near the spin 1' Fermi energy. These impurities have low P0t values because the d 1" phase shift at the Fermi energy is small; in contrast, when the impurity is such that a d ]' virtual bound state is close to the Fermi energy, Pot is large so a is small. The difference in Pot values between these two types of impurities can be quite striking: Pot -~ 0.16 Ixf~cm/% for Co impurities while Pot = 5 6 1 x ~ c m / % for Ru impurities! Detailed comparisons between calculated and experimental values of spin 1' and spin resistivities have been made. The temperature dependence of the resistivity of binary alloys of Ni can be
TRANSPORT PROPERTIES OF FERROMAGNETS
769
TABLE 3 Values of a = PoUPot, Po, Pot, P01 for dilute impurities in Fe*.
I m p u r i t y in Fe Ni Co Mn Cr V Ti Rh Ru Mo Pt Ir Os Re W Be A1 Si Ga Ge Sn Sb
Po (Ixl~cm)
oL = po ~ Ipo t
3 (a), 70") 1("), 3.70') 0.09 (a), 0.170') 0.17 ("), 0.37 (8) 0.12 C"), 0.13 °') 0.25 (a), 0.66 (8) 5.8 (8) 0.380') 0.210') 80') 90') 0.33 °') 0.31 c°) 0.240') 6.2 °') 8.6 °') 5.60') 8.1 (8) 6.2 °') ~ 1(c) ~ 1(~)
2 _+0.2 0.9_+0.1 " 1.5 _+0.2 2.2_+0.3 1.1_+0.3 2.75 _+0.25 0.95 ~ 2 _+0.1 1.75 ~ 0.2 1.3 (8) 2 (8) 3.5 _+0.5 2.7 _+0.5 1.6 _+0.1 40') 5.3 _+0.2 6 _+0.6 4.8 °') 6.8 _+0.2 8.7 _+ 1 9.8 _+0.4
* F o r a we give the values derived by: and M i e d e m a (1977), Dorleijn (1976); resistivity of ternary alloys (b) or f r o m there are data f r o m several a u t h o r s we
Po i' (ixf~cm) " 2.4 _+0.2 1.6_+ 0.4 13 _+5 12.5_+6 10.5_+3 10.5 _+4 1.1 °') 7.3 °') 110') 1.5 °') 2.2 °') 130') 8.7 °') 7.50') 4.7 °') 5.6 °') 6.40') 5.40') 7.9 (8)
Po $ (Ixf~cm) 12 _+5 3.3_+ 1.3 1.7 _+ 0.2 2.8_+0.2 1.3_+0.3 4 _+0.4 6.4 0')
2.80') 2.30') 120') 200') 4.3 °') 2.7 (8) 1.8 °') 29 °') 48 °') 36 °') 440') 49 °')
(~) Fert and Campbell (1976); 0") Dorleijn
(C)Ross et al. 1979, f r o m the residual p ( T ) of binary alloys (a) and (c). W h e n have estimated m e a n values of p0, p0t,
Po~.
ID
,
E
J,
20.
15 0_.~_~ 10
c~_
Ti
I
I
!
V
Cr
iqn
I
Fe
Co
Z
Ni
Fig. 7. S u b - b a n d residual resistivities p0 t and p0 ~ of 3d impurities in nickel. (References in f o o t n o t e to t a b l e 1.)
770
I.A. C A M P B E L L A N D A. F E R T
analyzed by using the two-current model equations to estimate the pure metal parameters Pt ~(T), Pit (T) and pi,(T). Figure 8 shows the agreement between experimental results below 50 K for series of Ni alloys and curves obtained from eq. (25) by using a values derived from independent measurements on ternary alloys, /x = 3.6, pi(T) = 9.5 x 10-12T2+ 1.7x 1 0 - 1 4 T 4 (in f~cm if T is expressed in K) and Pt +(T) of fig. 9 (dashed line). At temperatures up to about 50 K the analysis can be done unambiguously but at higher temperatures different sets of solutions fitting the experimental data are possible. At 300 K a reasonable estimate is Pt ~(300) = 11 tx~cm, pit (300) = 6.7 tM2cm, pi~(300) = 27 FxlIcm (Fert and Campbell 1976). The contribution to Pt ~(T3 from electron-magnon collisions has been calculated by Fert ~(1969) and Mills et al. (1971) in a model of spin-split spherical Fermi surfaces. The calculation gives the correct order of magnitude. The variation obtained for p~ $(T)/T 2 as a function of T is shown in fig. 9 (solid line) together with the variation needed to fit the experimental results (dashed line). The calculated curve drops at low temperature, which results from a freezing out of electron-magnon, scattering in the presence of a gap between spin I' and spin Fermi surfaces; the experimental curve shows a similar drop below about 30 K and then an upturn below 5 K; this upturn seems to be associated to a variation in T 3/2 at very low temperature and has been ascribed to electron-magnon scattering
~ T (10-115~cm °K-2)
x
×
x
{Cx'C
°
10
x
o
/~"/~:atc. _. / /* /NiMnOA*/, d ,¢// o/O
?
,//.x./ x
x
,,x x ~ / x7 7
- o °
r
o
/
o
cole.
"~ /_~a_NiCrt6°lo~
a
4 "'-u
~,1°
tx
~
•
cole. _
%M.n0
t~
10
20
30
40
50
Fig. 8. pr/T 2= Co(T)-p(O))/T 2 against T for several nickel based alloys. The solid curves are calculated from eq. (25) in the way described in the text (after Fert and Campbell 1976).
TRANSPORT PROPERTIES OF FERROMAGNETS
771
in regions where the spin 1' and spin $ Fermi surfaces touch or are very near (Fert and Campbell 1976). The resistivities pi~(T) are expected to include contributions from electronelectron, electron-phonon and electron-magnon collisions. Because of the small angle scattering factor the electron-magnon contributions to pi~, pi+ should each be equal to roughly (T/Tc)p~ + and therefore relatively small at low temperatures. If then the electron-electron or electron-phonon contributions are dominant, the possibility of scattering of the spin $ electrons to the d $ band makes pi$(T) larger than pi~(T), in agreement with /~ > 1. At very low temperatures the variation of pi(T) in T 2 can be attributed to electron-electron scattering, as it has been concluded in section 2.2.2. Above 10K the electron-phonon collisions become progressively more important. When approaching room temperature the electron-magnon collisions should begin to make a substantial contribution to pi~(T). Theoretical estimates of the electron-phonon contributions to Pit and pi+ at 300 K are 4.25 ~ c m and 19.2 ~l"~cm respectively (Yamashita and Hayakawa 1976); we can reasonably infer that additional contributions of a few ~ c m from electron-magnon scattering account for the experimental pi~(300). Without magnon contributions to pi~(300) and without p~ ~ term the resistivity of pure nickel at 3 0 0 K would be predicted to amount to roughly 4.25x 19.2/(4.25+ 1 9 . 2 ) 3.5 ~ c m , instead of 7 p ~ c m experimentally. We conclude that: (i) at low temperature the main contributions to p~(T) arise from electronelectron and electron-phonon scatterings; electron-magnon collisions come into play through p~ ~(T) and are important in alloys with ~ very different from unity; (ii) at near room temperature the electron-magnon collisions contribute to both pi~ and p~ +; they will become increasingly important as temperature increases. The analysis of the experimental data on Ni alloys by Yamashita and Hayakawa (1976), although based on a different treatment of the two current conduction, arrives at similar conclusions.
2.3.2. Cobalt host The o~ values of a large number of impurities have been obtained in Co metal (Durand and Gautier 1970, Loegel and Gautier 1971, Durand 1973, Ross et al. 1978), table 2. They are again consistent with the magnetic structures of the impurities. The parameters Pit (T), pi+ (T) and p, +(T) of Co have been evaluated by Loegel and Gautier (1971); the behaviour of p~ ~(T) is similar to that of Ni.
2.3.3. Iron host Extensive work has been done on Fe based alloys (Campbell et al. 1967, Fert and Campbell 1976, Dorleijn 1976, Dorleijn and Miedema 1977, Ross et al. 1979), table 3. The resulting ~ values from different authors, both from ternary alloy data or from temperature dependence, are in reasonable agreement with each other. The range of c~ values is very great, po ~/po ~ varies from 0.13 for F__eeVto 9 for FeIr (table 3). There is a good correlation between the resistivity p0 in each band and the charge screening in that band for each impurity (Dorleijn 1976).
772
I.A. C A M P B E L L A N D A. F E R T
,_NC
12
T C) v k-4P
J
I
I
I
I
I
10
20
30
40
50
Temp6rature (K) Fig. 9. Experimental (dashed line) and calculated (solid line) curves for p$ ,~/T 2 in nickel. The experimental curve is after Fert and Campbell (1976); the calculated curve is obtained from the model calculation of Fert (1969) with 01 = 38 K.
The behaviour of p, +(T) in Fe is similar to that in Ni and the value of pi+/pi, seems to be near 1 (Fert and Campbell 1976). More complete low temperature measurements would be necessary to decide this. As in Ni, the low temperature p(T) data cannot be understood without including the p, ~ term.
2.3.4. Alloys containing interstitial impurities Ni, Co or Fe based alloys containing small concentrations of interstitial impurities of B or C can be prepared by rapid quenching. Swartz (1971), Schwerer (1972) and Cadeville and Lerner (1976) have investigated the resistivity of NiC, C__o_oC, Nil_xF_eexC alloys. The residual resistivity of these alloys is equal to about 3.4 ~flcm/at.% for C in Ni and 6.6 txOcm/at.% for C in Co. From the deviations from Matthiessens' rule in N__iiCrCand CoCuC alloys, Cadeville and Lerner (1976) have estimated that the resistivity P0+ was about twice as large as Pot. This result, together with magnetization and thermo-electric data by the same authors, are consistent with a predominant screening by the electrons of the d + band. In Ni~-xFexC alloys the resistivities Pot and p0+ of the C impurities are found to become nearly equal for x >0.4, which has been ascribed to the change from strong to weak ferromagnetism (Cadeville and Lerner 1976). The resistivity of B impurities in Ni and Co have been found to be fairly small ( - 1 ixl)cm/at.%). This has been ascribed to a predominant screening by the d ~, electrons resulting in a small resistivity for the spin 1' electrons (Cadeville and Lerner 1976).
TRANSPORT PROPERTIES OF FERROMAGNETS
773
2.4. High temperature and critical point behaviour It was observed a long time ago that the resistivities of ferromagnetic metals changed slope as a function of temperature at the Curie temperature. For Ni this was originally interpreted by Mott (1936) as indicating a reduction of the spin T resistivity on ordering. Later work (Kasuya 1956, Yoshida 1957, Coles 1958, Weiss and Marotta 1959) showed that spin disorder scattering provided a more general explanation. When the resistivities of the 3d ferromagnetic metals are compared with those of their non-magnetic 4d and 5d counterparts it can be seen clearly that there is an extra magnetic scattering contribution which is approximately constant above T~ and which decreases gradually below T~ (fig. 10). The simplest disorder model shows that the paramagnetic term above T~ is equal to kv(mF)2 t t r Pm = 4~e2zfi3 ~ + 1),
(26)
where J is the effective local spin and f ' the local spin conduction electron spin coupling parameter. De Gennes and Friedel (1958) suggested that the critical magnetic scattering near Tc was similar in type to the critical scattering of neutrons and that it should lead to a peak in p(T) at To. Later work by Fisher and
I0[
[3
Tc
Qcm
~/
80
6C
Tc
Pd 20
~ I r 0 0
I 1
T//80 L 2
I 3
I /~
Fig. 10. Resistivity of several transition metals as a function of T/OD. OD is the D e b y e t e m p e r a t u r e .
774
I.A. CAMPBELL AND A. FERT
Langer (1968), using a better approximation for the spin-spin correlation function near To, modified this prediction to that of a peak in dp/dT at To. They also made the important remark that just above To the same leading term in the spin-spin correlation should dominate dp/dT and the magnetic specific heat, so that these two parameters should have the same critical behaviour as T tends to Tc from above. Both magnetic entropy S and magnetic scattering rate should be proportional to
fo2kvF(k, T)k 3dk,
(27)
where F(k, T) is the spin-spin correlation function. Later theoretical work showed that the same correspondence should hold equally in the region just below Tc (Richard and Geldart 1973). Renormalization theory can predict the critical coefficients for dp/dT (Fisher and Aharony, 1973) but it is difficult to decide over what range of temperature each side of To the strictly "critical behaviour" should be observed; Geldart and Richard (1975) discussed the cross-over from a regime near To where the shortrange correlations dominate to a long-range correlation regime. The theory of resistivity behaviour at To in weak ferromagnets has been developed by Ueda and Moriya (1975), Der Ruenn Su and Wu (1975). Experimentally, the critical behaviour of dp/dT has been studied very carefully for Ni, Fe, Gd and the compound GdNi2 (Craig et al. 1967, Zumsteg and Parks 1970, Shaklette 1974, Kawatra et al. 1970, Zumsteg and Parks 1971, Parks 1972, Zumsteg et al. 1970). For Ni (Zumsteg and Parks 1970) and Fe (Shaklette 1974) it is found that dp/dT and the specific heat do indeed show the same A point type of behaviour around To (fig. 11). The data are parameterized using I
J
i
i
i
l
l
, ooo
o°
oo
.0.05 o o
oo
o
1.04
o
1.03
oo
oO o o
.OOl o o
o
o
1.02
o
1.01 -~ .005
1,00 n,-
.002
099
o°°2 o
,001
n*"
0.98
o
o
0.97
o o
.000 348
096 ~
,
352
,
,
356
I
i
I
360 T(oC)36&
I
I
368
I
I
372
I
I
376
Fig. 11. Resistivity R(T) of nickel and dR/dT versus temperature in the region of the Curie point (after Zumsteg and Parks 1970).
TRANSPORT PROPERTIES OF FERROMAGNETS 1 dp A pcdT-h (e-*-l)+B,
T > To,
775 (28)
and 1 dp
A'
p o d T - -h (lel-~'- 1 ) + B "
T < To,
(29)
where
e = ( T - Tc)lTc.
(30)
Renormalization theory predicts h = h ' ~ 0 . 1 0 and A/A'~-1.3 (Zumsteg et al. 1970) for a 3 dimensional exchange ferromagnet. The accurate determination of A and h' is extremely delicate especially as Tc must be fitted self-consistently from the data and it appears essential to have the theoretical predictions as a guide. In pure Fe, Kraftmakher and Pinegina (1974) find h, h ' = 0-+ 0.1 while Shaklette (1974) observes A, A'=-0.12--_0.01 by imposing h----h'. Agreement with the magnetic specific heat data in Fe is very good (Shaklette 1974, Connel!y et al. 1971). For Ni, the values obtained were h = 0.1 _+0.1, h' = 0.3_+0.1 (Zumsteg and Parks 1970) but within the fitting accuracy this is presumably also consistent with theoretical values. In G d which is hexagonal the critical behaviour looks very different when measured along the c- and the a-axes. Zumsteg et al. (1970) suggest that the resistivity changes are complicated by the critical behaviour of the lattice parameters, but this has been questioned (Geldart and Richard 1975). GdNi2 was investigated in the hope that it would correspond to a simple local moment system, dp/dT shows similar critical behaviour to Fe and Ni but has more complicated temperature dependence a few degrees above Tc (Kawatra et al. 1970, Zumsteg and Parks 1971). The significance of this has been discussed (Geldart and Richard 1975). The resistivity variation has also been measured at the structural and ferromagnetic transition in T b Z n (Sousa et al. 1979). The critical behavi0ur of dp/dH has been studied for Ni (Schwerer 1974) and for Gd with the current in the basal plane (Simons and Salomon 1974). The behaviour of transport properties near Tc can also be studied in alloys, but local inhomogeneity leads to a spread in the local values of Tc at different parts of the sample and so the critical behaviour is smeared out. This has been observed in NiCu alloys (Sousa et al. 1975) and in PdFe (Kawatra et al. 1970, Kawatra et al. 1969). Finally, behaviour at the critical concentration for ferromagnetism (the concentration at which To-> 0) can be studied. Very varied behaviour has been found in different alloy systems. In N iCu alloys there is a peak in dp/dT at T~ as long as Tc exists and there is a maximum in p(T) some degrees higher, while for c > cent a minimum in p(T) is observed (Houghton and Sarachik 1970). In NiAu (splat cooled to avoid segregation) p(T) shows a maximum at T0 for c < cent (Tyler et al.
776
I.A. CAMPBELL AND A. FERT
1973). For NiCr, Yao et al. (1975) find weak minima in p ( T ) for c > Ccrit while Smith et al. find giant minima in the region c - cent (Smith et al. 1975). In NiPd alloys, Tari and Coles (1971) express the low temperature resistivity behaviour as p = po = A T n and find A is sharply peaked at cc~t while n has a minimum with n - 1. The Curie point "is not easy to detect on the p ( T ) curves". A m a m o u et al. (1975) using the same way of expressing the resistivity behaviour found n --> 1 and strong peaks in A at the critical concentrations of a large number of alloys systems. The transition from low temperature two current behaviour to high temperature spin disorder behaviour has been studied in Fe based alloys (Schwerer and Cuddy 1970). The high temperature resistivity behaviour of the alloy seems to depend essentially on the local impurity moment.
3. Other transport properties of Ni, Co, Fe and their alloys Here we will summarize results on different transport properties in these metals and alloys and outline the interpretations which have been given. We will generally find that Ni has been studied in most detail while rather less is known about Fe and Co. In the interpretation of the results, we will refer to what has been learnt about the different systems from the resistivity measurements which we have already discussed. 3.1. Ordinary magnetoresistance We have outlined the situation for pure metals in section 2.2. For non-magnetic alloys the low temperature magnetoresistance behaviour generally follows Kohler's rule ( p ( B ) - p ( O ) ) / p ( O ) = f(B/p(O)), where f is a function which varies from metal to metal but which is rather insensitive to the type of impurity present for a given host. In a ferromagnet above technical saturation the same effect, due to the Lorentz force on the electrons, can be observed but as B includes the magnetization term 47rM, p(0) cannot be attained except by extrapolation. Schwerer and Silcox (1970) showed by a careful study of dilute Ni alloy samples that for a given series of alloys (e.g. NiFe samples) the ordinary magnetoresistance follows a Kohler's rule, but that the Kohler function f varied considerably with the type of scatterer (fig. 12). Other work (Fert et al. 1970, Dorleijn 1976) is consistent with these data. It can be seen in fig. 12 that the strongest magnetoresistances are associated with impurities having large values of p0+/P0t (i.e. N__iiFe, __NiCo...). The longitudinal magnetoresistance of these alloys is also high [Apll/P(O ) saturates at about 10 in NiFe (Schwerer and Silcox 1970)] considerably greater than that observed for Cu based alloys for instance, where ApJp(O) saturates at about 0.7 (Clark and Powell 1968). Attempts have been made to understand this behaviour in the two current model. In its simplest form the two types of electron (spin 1' and spin $ ) can be represented by electron-like spheres in k space with different relaxation
TRANSPORT PROPERTIES OF FERROMAGNETS
,.,o
777
oo////
1.05
IDO ~ ~ R u 0 10
~ 20
, 30
, &O
, 50
B/~O (k G/,u.~.cm)
Fig. 12. Kohler plots for the transverse magnetoresistance at 4.2 K of nickel containing Co, Fe, Mn, Ti, A1, Cr, Pt, V or Ru impurities (after Dorleijn 1976). times. In this approximation (Fert et al. 1970) the transverse magnetoresistance is indeed an increasing function of p~ (O)/pt (0), but the model is not satisfactory as it predicts a zero longitudinal magnetoresistance in disagreement with experiment. As a next step, it is possible to invoke relaxation time anisotropy within each spin band. Dorleijn (1976) suggests that the intrinsic magnetoresistivity of the spin 1' band of Ni is much greater than that of the spin band so that the longitudinal and transverse magnetoresistances are much greater when the current is carried mainly by the spin 1' electrons. Jaoul (1974) proposes that there is a mixing between spin 1' and spin ~ currents which is an increasing function of B/p(O). This is because spin-orbit effects mean that an electron on a given orbit on the Fermi surface passes continuously between spin 1' and spin +, progressively mixing currents as B/p(O) increases. This model predicts the saturation magnetoresistances of the different alloy series reasonably well. The ordinary magnetoresistance in Fe based alloys is m o r e difficult to express in the form of Kohler curves, because the much higher value of 4 ~ M in Fe means that extrapolations to B = 0 are always very extended. D a t a given by Dorleijn (1976) again indicate different Kohler curves for Fe samples containing different impurities, but the correlation with the value of p+ (O)/p, (0) is much less clear than in the case of Ni based alloys. There is an additional effect that appears under similar experimental conditions as the Lorentz force ordinary magnetoresistance, but which is due to the high field susceptibility of the ferromagnetic metal. This high field susceptibility can have two origins. First, there is an increasing magnetic order in an applied field which can also be thought of as a reduction in the n u m b e r of magnons with increasing field. This term is m a x i m u m around Tc and goes to zero as T goes to zero. Secondly, for a band ferromagnet, the local magnetic m o m e n t s can be altered by an applied field at any temperature, even T = 0 (Van Elst 1959).
778
I.A. CAMPBELL AND A. FERT
Insofar, as an increasing field produces increasing magnetic order and hence lower spin disorder scattering, dp/dH due to the first term will be negative. The second type of effect can in principle give either positive or negative magnetoresistance depending on the electronic structure of the system. Van Elst (1959) measured at 300 K (1/p)(dp/dH)l I~- (1/p)(dp/dH)l with effects of the order of 10-4/kG and with significant variations from one alloy to another. This behaviour is due to the first effect. At low temperatures the Lorentz-force magnetoresistance dominated except for NiMn alloys which showed negative dp/dH even at low temperature; this is probably due to an unusual band susceptibility in these alloys.
3.2. Ordinary Hall coefficient In non-magnetic metals it is known that the ordinary Hall coefficient R0 behaves to a rough approximation as Ro oc 1/en* where n* is the effective density of current carriers and e is their charge (e is negative for electron-like carriers and positive for hole-like carriers). The actual values of R0 can be considerably modified by Fermi surface and scattering anisotropy effects (Hurd 1972); for the high field condition wc >> 1, R0 depends only on the Fermi surface geometry and can be highly anisotropic in single crystals. In ferromagnetic metals the ordinary Hall effect can be separated from the extraordinary Hall effect by measurements above technical saturation, as long as the susceptibility of the sample in high fields is negligible so that there is no paramagnetic extraordinary Hall effect correction (see section 3.4). The ordinary Hall coefficient in Ni at room temperature is R0-~ - 6 x 10 1312cm/G (Lavine 1961), which corresponds to conduction by electronlike carriers with an effective electron density n* of about 1 electron per atom. R0 varies by about 20% between room temperature and 50 K; at lower temperatures the low field condition ~0c~-'~ 1 no longer holds for high purity Ni samples so R0 tends towards the high field value (Reed and Fawcett 1964). Pugh and coworkers (Pugh et al. 1955, Sandford et al. 1961, Ehrlich et al. 1964) and Smit (1955) showed that for a number of Ni based alloys, in particular NiFe and NiCu, the low temperature Hall coefficients in concentrated samples correspond to much lower effective carrier concentrations, n * - 0 . 3 electrons per atom. They pointed out that this low number of carriers was probably, associated with a regime where only the conduction band for one direction of spin was carrying the current. Later work on Ni and NiCu alloys (Dutta Roy and Subrahmanyam 1969) showed that R0 is very temperature dependent in the alloys, and that above the Curie point n* returns to a value of about 1 electron-atom, i.e., to a situation where both spin directions carry current. This would seem to fit in well with other data on the two current model. However, careful measurements by Huguenin and Rivier (1965) and by Miedema and Dorleijn (1977) on a wide range of Ni based alloys have shown that the situation is more complicated. The data can be summarized as follows: the low temperature R0 is very close to zero in dilute alloys (concentration - 0 . 5 % ) for
TRANSPORT PROPERTIES OF FERROMAGNETS
779
which Po+/Pot > 1 (i.e. NiFe, N__iiCu, N i C o . . . ) but then increases rapidly with impurity concentration to a value corresponding to n* - 0.3 in samples where the impurity resistivity is greater than about 5 txf~cm. For alloys for which po ~/po t < 1, R0 is essentially independent of impurity concentration at about - 6 x 10-13 l~cm/G (note that only samples of this type having p > 2 ix~cm were studied). Now in a two current model R0 is given by
Ro= p2 Rot/p2 + Ro+/p~ ,
(31)
where Rot, R0+ are the ordinary Hall coefficients for the two spin directions taken separately. From the experimental data it can be concluded that R0+ is reasonably constant, while Rot varies strongly with p~. Dorleijn and Miedema suggested that the effect is due to a "smudging out" of the details of the spin 1' Fermi surface of Ni with increasing Pt and they associated this with the observed changes of the magnetocrystalline anisotropy with alloy concentration (Miedema and Dorleijn 1977). As we will see in section 3.3, the resistivity anisotropy of the same alloys changes similarly with impurity concentration until a certain residual resistivity value is reached. The R0 data suggest that the "smudged out" Fermi surface situation corresponds more closely to the extreme s-d model with conduction entirely by an s t like band containing about 0.3 electrons per atom. The results on R0 in Fe based alloys are less clear, partly because the separation into ordinary and extraordinary Hall components is more difficult because of the large value of 4~-M. Fe has a positive ordinary Hall coefficient, as have the dilute Fe based alloys except for FeCo (Beitel and Pugh 1958) although R0 for __FeNi alloys changes sign with temperature and with concentration (Softer et al. 1965). There appears to be evidence (Carter and Pugh 1966) that alloys for which pt(O)/p+(O)> 1 such as FeCr, behave similarly to Ni in that R0 is high at low temperatures and drops considerably at higher temperatures as both spin directions begin to participate in the conduction.
3.3. Spontaneous resistivity anisotropy This was defined in section 1 and is a spin orbit effect. The mechanism can vary from system to system. The simplest case to understand, at least in principle, is that of dilute rare earth impurities (Fert et al. 1977). Because of the unclosed f shell, the magnetic rare earths can be regarded as ion-like with a non-spherical distribution of charge (apart from the spherical ion Gd3+). A conduction electron plane wave encounters an object with a different cross section depending on whether it arrives with its k vector parallel or perpendicular to the rare earth moment, which provides an axis for the non-spherical charge distribution. The anisotropy of the resistivity is proportional to the electronic quadrupole moment of the particular rare earth. The theory of this effect has been worked out in detail (Fert et al. 1977). In transition metals, the spin orbit coupling is usually a weak perturbation on the spin magnetization. The lowest order terms leading to a resistivity anisotropy
780
I.A. CAMPBELLAND A. FERT
will be either mixing terms of the type ( L + S - ) 2 o r polarization terms of the type (LzSz)2. Smit (1951) calculated the resistivity anisotropy to be expected on an s-d model from the mixing terms acting between spin 1' and spin ,~ d bands. When data became available for both the anisotropy and the p ~/p t ratios in various Ni alloys, it was found that there was good agreement between the results and predictions which could be made using the Smit approach (Campbell et al. 1970). Agreement is however less good for impurities having a virtual bound d state near the Fermi surface, and an additional (LzS~) 2 mechanism was suggested for these cases (Jaoul et al. 1977). The relative anisotropy of the resistivity (Pll- P±)/P defined in section 1 has been measured for Ni and a large number of Ni alloys as a function of concentration and temperature (Smit 1951, Van Elst 1959, Berger and Friedberg 1968, Campbell et al. 1970, Vasilyev 1970, Campbell 1974, Dedi6 1975, Dorleijn 1976, Dorleijn and Miedema 1976, Kaul 1977, Jaoul et al. 1977) and for many dilute Fe based alloys, mainly at He temperature (Dorleijn and Miedema 1976). We will first discuss the Ni data. The anisotropy ratio for pure Ni is near +2% from nitrogen temperature up to room temperature, and then gradually drops as the temperature is increased up to the Curie point (Smit 1951, Van Elst 1959, Kaul 1977). Below nitrogen temperature the anisotropy is difficult to estimate for pure samples because of the rapidly increasing ordinary magnetoresistance, but it appears t o remain fairly constant. For most dilute N__iiXalloy series the limiting low temperature anisotropy ratio is relatively concentration independent for a given type of impurity X over a fairly wide concentration range but the value depends strongly on the type of impurity, table 4. For NiCo, NiFe and N__iiCu (fig. 13) the anisotropy ratio increases continuously with concentration up to concentrations corresponding to residual resistivities of about 2 p~cm. It is a disputed point as to whether the appropriate characteristic value of the anisotropy ratio for these alloys is the plateau value (Jaoul et al. 1977) or a value at some lower concentration (Dorleijn and Miedema 1975b, 1976). When the temperature is increased, the anisotropy ratio of a given sample tends towards the pure Ni value and finally becomes zero at the Curie point of the alloy (Vasilyev 1970, Kaul 1977). There is a clear correlation between the value of a and the low temperature a n i s o t r o p y ratio (Campbell et al. 1970). Alloys having high values of a N(~Co, NiFe, N i M n . . . ) have high positive resistivity anisotropies while alloys with c~ ~ 1 have small positive or negative anisotropies. A spin-orbit mixing model originally suggested by Smit (1951) gives a convincing explanation of the overall variation of the anisotropy ratio with the value of a. As Ni metal has a fully polarized d band, there are no d 1' states at the Fermi surface for the conduction electrons to be scattered to. However because of the spin-orbit mixing by the matrix element AL+S- some d 1' character is mixed into the d $ band. The resulting weak s ]' to d $ scattering can be shown to depend strongly on the relative orientation of the k vector of the s conduction electron and the sample magnetization. This leads to a resistivity anisotropy of the form
T R A N S P O R T P R O P E R T I E S OF F E R R O M A G N E T S
781
TABLE 4 Anisotropy of the residual resistivity of dilute nickel based alloys*. Impurity PJ - P± x 102 t~
Impurity P_JI- P± x 102
Co
Fe
Mn
Cr
V
Pd
20 Ca)
13.6 o')
9.9 °)
--0.3500)
0.6 C")
14.8 Cb)
14 Cd)
7.8 Cb)
--0.28 (a)
O. 15 c°)
28 (c)
19.5 Cc)
9.5 Co)
-0.23 Cd)
Ru
Mo
0.05 C°)
-0.600')
0.1 Ca)
0.05 C~)
- 0 . 8 2 C~)
0.05 (0)
W
Cu
Au
Rh
Nb
Impurity
Re
pp!- Pa x 102
- 0 . 5 0 C°)
0.4 Ca)
6.8 C°)
- 0 . 4 5 Cc)
0.8 ¢ )
7.8 Co)
0.15 (~)
2 C~)
Pt
Ir
0.4 C°)
- 1 . 5 2 C~)
0.4 C~)
A1
Si
Zn
Sn
7.5 C°)
4.7 (a)
2.5 (")
5.7 Ca)
3.4 Ca)
7.9 Co)
3.9 Co)
2.1 co)
4..7 (b)
2.9 Co)
4.6 Co)
2.8 (c)
6.5 ¢)
3.5 Co)
*After: ca)Van Elst 1959, C°)Dorleijn and Miedema 1974, Dorleijn 1976, e)Jaoul et al. 1977, ca)Schwerer and Silcox 1970. We indicate - when this is possible - the resistivity anisotropy of alloys in the concentration range where the concentration dependence is weak (see fig. 13). The experimental data on (P/I- P±)/Pll has been re-expressed in terms of (PH- P±)/P.
aOtf (%) 3C
25
I
20 oo
ooo i
15
\
10
x
5
~\ ""x
x
%,
x
0
io
i
40
"x
60
Impur i ty concentrat
L
on, at °/o
Fig. 13. Concentration dependence of the resistivity anisotropy at 4.2 K for several nickel based alloys. AA: NiCo, OC): N iFe, ×: N_iiCu (after Jaoul et al. 1977).
782
I.A. CAMPBELL AND A. FERT (32)
P l l - P . / P = ~(o~ - 1 ) ,
where y is a spin-orbit constant which can be estimated to be about 0.01 from the Ni g factor. This model explains the sign, the magnitude and the general variation of the anisotropy with a (fig. 14). In addition, it has been shown (Ehrlich et al. 1964, Dorleijn and Miedema 1976, Jaoul et al. 1977) that an analysis of the anisotropy ratio of ternary alloys can lead to estimates of the individual anisotropies for the spin 1' and spin $ currents and that for alloys with a > 1 the results are in agreement with the predictions of the Smit mechanism. However, for a number of alloys of Ni for which c~ < 1, although the resistivity anisotropies remain small as would be expected from the Smit mechanism, eq. (32) is not accurately obeyed and the anisotropies of the two spin currents do not obey the Smit rules (Ehrlich et at. 1955, Jaoul et al. 1977). A further mechanism needs to be invoked for these systems, which are characterized by virtual bound states at the spin I' Fermi level. A mechanism has been proposed involving the )tLzSz spin-orbit interaction on the impurity site, particularly for impurities which have strong spin-orbit interactions (Jaoul et al. 1977). Dorleijn and Miedema (1976) pointed out that for most impurities, whatever the value of c~, (Ap/p)t > 1 and (Ap/p)$ < 1 but they did not explain this regularity. The temperature variation of the anisotropy ratio can also be understood using the Smit model (Campbell et al. 1970). As phonon and magnon scattering increases with increasing temperature, the effective value of a for an alloy tends to approach the pure metal value. Data on NiCu alloys have been analyzed in this
30
l
//
20
I0
I
1o
20
3'0
Fig. 14. Resistivity anisotropy of Ni based alloys at 4.2 K as a function of a = P0J,/P0t- The straight line is Ap/~ = 0.01 (a - 1) (after Jaoul et al. 1977).
TRANSPORT PROPERTIES OF FERROMAGNETS
783
way over a wide temperature and concentration range (Kaul 1977) so as to estimate
pit(T), pi~(T) and p~ ~(T). High concentration effects in certain alloy series have been interpreted as due to characteristic changes in the electronic structure with concentration (Campbell 1974). The resistivity anisotropy of a large number of Fe based alloys has also been studied (Dorleijn and Miedema 1976). Here, the alloys having p,(O)/p+(O),> 1 have strong positive resistivity anisotropies while those with Pl (O)/p+(0) < 1 have small anisotropy ratios (table 4). Again, an analysis in terms of the anisotropies of the spin ]' and spin $ currents has been carried out and the predictions of the Smit approach seem well borne out (Dorleijn 1976). As we have seen in section 1 the resistivity anisotropy in cubic ferromagnetic monocrystals can be expanded in a series of D6ring coefficients k l . . . ks. Once again, Ni and Ni alloys have been the most studied [pure Ni (Bozorth 1951), Ni 15% Fe (Berger and Friedberg 1968), Ni 1.6% Cr and N_j 3% Fe (Jaoul 1974), N__ii 0.5% Fe, Ni 0.55% Pt and Ni 4% Pd (Dedi6 1975)]. Very roughly the individual ki coefficients are simply proportional to the average polycrystal anisotropy with the exception of k3 (table 5). This coefficient may behave differently from the others because it does not strictly represent an a n i s o t r o p y - i t corresponds to an average change of the sample resistivity with the moment direction which is independent of the current direction. TABLE 5 Magnetoresistance anisotropy in Ni and Ni alloy single crystals. D6ring coefficients ki are givenin percent. References: (a~D6ring 1938,Co)Berger and Friedberg 1968, (c~Jaoul 1974, cd~Dedi6 1975. kl Ni, 300 K (a)'(d) NiFe 15% 4.2 K(b~ NiCr 1% 4,2K(c~ NiPd 4% 4.2 K(d~
55.0 -3.0 4.0
ke 14.5 -0.3 1.0
k3
k4
k5
-3.4 -26.3 -1.2 -5.5
-5.2 -37.8 +2.3 -4.0
+ 1.7 +24.7 0_+0.7 -3.0
There are also measurements of the D6ring coefficients for Fe at room temperature (Bozorth 1951). No convincing model has been proposed to explain the monocrystal anisotropy coefficients which presumably depend on the detailed band structure of the metal. The fact that the terms which are fourth order in the direction cosines of the magnetization (k3, k4, k5) are as large as the second order terms (kl, k2) is remarkable.
3.4. Extraordinary Hall effect Apart from the resistivity, the property of ferromagnetic metals which has attracted the greatest theoretical attention is the extraordinary Hall effect, Rs; the extraordinary Hall voltage is remarkable in being both strong and rapidly varying
784
I.A. CAMPBELL AND A. FERT
with temperature and impurity concentration. The fundamental mechanisms which are believed to produce this effect were proposed some years ago by Smit (1955) and Luttinger (1958) but the physical understanding of these effects has been considerably improved quite recently (Berger 1970, Lyo and Holstein 1972, Nozibres and Lewiner 1973). We will outline the discussion given byNozibres and Lewiner (1973); although this theory was developed specifically for semiconductors the same physics can broadly be used for ferromagnetic metals. An electron in a band submitted to the spin-orbit interaction acquires an effective electric dipole moment p= -Akxs,
where A is a spin-orbit parameter, k is the k vector and s the spin of the electron. If there were no scattering centres, the effective Hamiltonian would he Ygen = k 2 / 2 m - e E . (r + p )
(where r is the centre of the electron wave packet) for a metal in a uniform electric field E. Local scattering potentials give local terms in the Hamiltonian
V ( r ) - A(k × s). v v . Here, the second term arises from spin-orbit coupling in the lattice. An additional contribution to A can also arise from a local spin-orbit interaction. There are two distinct effects: (a) the scattering matrix elements between plane wave states are expressed as (k'] V - A(k x s ) . V V I k ) : Vu,[1 - iA(k x k')- s] (by applying the general commutator rule If(x), kx] ~ i 0 f ( x ) / 0 x to V(r)). This means that the probability of scattering k ~ k' is not the same as the probability k'~k because of interference between the spin-orbit term and the potential scattering. For a weak 3 function potential, Wkk' = V2[1 + 2A V r r n ( k x k ' ) . s] , where n is the density of states at the Fermi level. This "skew scattering" leads to a Hall current such that the Hall angle ~bn oc A V, which is independent of scattering centre concentration, but which can be of either sign, depending on the sign of V. (b) Now we come to the "side jump" term. The total Hamiltonian is = k2/2m + V(r)-
eE. r+p
• [VV- eE],
TRANSPORT PROPERTIES OF FERROMAGNETS
785
and the total velocity is: v : / ~ - i[r, gel = k/m + A [ V V - eE] x s + p . Without scattering, p changes as k increases under the influence of E, and secondly, the energies of the different k states are altered by the second term in v. However, when scattering is introduced, both of these currents are exactly cancelled out in static conditions; the first because ( p ) = - A ( t ~ ) × s --- o ,
and the second because the electron distribution readjusts itself to minimize energy, and this new distribution automatically has an average velocity perpendicular to E equal to zero. It would thus appear that the spin orbit terms do not lead to any extra current. But, during each scattering event there is also a "side j u m p " or shift of the centre of gravity of a scattered wave packet
8r = f 6v d t = - A A k × s (as 6v --- A V V × s = -A/¢ x s during the scattering event). Now, there are two side j u m p contributions: (i) electrons travelling with a c o m p o n e n t of k parallel to E jump sideways on being scattered; the resultant of these jumps is a current. (ii) electrons with a c o m p o n e n t of k perpendicular to E gain or lose an energy - e , 3 r . E on scattering. This shifts the total electron distribution to provide a second current. These terms are not cancelled out by any compensating terms. They lead to a total Hall current of 2ANe2E x (s), which is proportional to the electric field E but independent of the scattering rate. The definition of R, is Vy/IxMz, where y is the Hall p r o b e direction, x the current direction and z the m o m e n t direction. Putting Vy = ply and E = pIx, with the Hall current just given we clearly obtain R, ~ Ap2. Note that the p a r a m e t e r h represents the rate of change of the spin-orbit dipole - A k x s with k. This is a band property. However, local spin-orbit interactions on scattering centres can give an additional contribution to A and complicate the picture. We can now turn to the experimental data. The skew scattering term can be expected to dominate in dilute alloys at low temperatures, and indeed in Ni based alloys for which p(0) ~< 1 tzf~cm at helium temperatures (fig. 15) it has been shown that the Hall angle ~bH is independent of impurity concentration, but depends strongly on the type of impurity (Jaoul 1974, Fert and Jaoul 1972, Dorleijn 1976). It is possible to define Hall angles for each direction of spin, ~bHt and 4~H~ and experiments on ternary alloys (Dorleijn 1976) or on the t e m p e r a t u r e dependence
786
I.A. CAMPBELL AND A. FERT - ? H ('1"1.~. cm) "XTRAORDINARY 10
HALL RESISTIVITY AT /-,.2°K
Cu
Mn~Fe
5
Co 2
0
1
-5
c tat*l,)
Cr lr
Os
Fig. 15. Extraordinary Hall resistivity of several types of Ni based alloys as a function of their impurity concentration. The data are limited to alloys having a resistivity smaller than about 1 Ixf~cm; in more concentrated alloys, a side-jump contribution progressively appears and becomes predominant for p = 10 ixf~cm (see fig. 16) (Jaoul 1974). of t h e H a l l angle (Jaoul 1974) allow o n e to e s t i m a t e t h e s e two H a l l angles for each i m p u r i t y . R e s u l t s a r e given in t a b l e 6. T h e v a l u e s of t h e s k e w s c a t t e r i n g H a l l angles can b e discussed in t e r m s of t h e e l e c t r o n i c s t r u c t u r e of t h e v a r i o u s i m p u r i t i e s (Fert a n d J a o u l 1972, J a o u l 1974). F o r s a m p l e s with h i g h e r resistivities (either b e c a u s e of h i g h e r i m p u r i t y c o n c e n t r a t i o n o r b e c a u s e t h e y are m e a s u r e d at h i g h e r t e m p e r a t u r e s ) t h e side j u m p t e r m b e c o m e s i m p o r t a n t . C o n s i d e r i n g only d a t a t a k e n at low t e m p e r a t u r e s , results for a given alloy series can g e n e r a l l y b e fitted (Jaoul 1974, D o r l e i j n 1976) b y t h e
TABLE 6 Skew scattering Hall effect in dilute Ni based alloys. For each impurity, qSH is the dilute limit Hall angle in millirad, and ~bHt, ~bH~ are the corresponding spin 1" and spin $ Hall angles. References: * Dorleijn 1976, *Jaoul 1974. Impurity 42H ~bH1' qSH~
Impurity ~bH ~bat ~bH;
Ti +1.5", -4.5 -3.4* +5.5*
Fe --6.2, --10t -7", -10 t +6", +10 t
V -3", -2.5* -4*, -79 +6", -3*
Co --6.2*, --10.5' -6", -10 t +2.5", +7 t
Cr
Mn
+2.8", +2 t - 3*, - f +4", 3t
Cu --10", --23t -14", -24* +3.5", +10'
-6.5", -9.5 t - 10* +1.5 t
Ru +2.5*, +3 t -4.7", +3 t +3", +3 t
Rh 0", --4t -1.4", - 3 t +1.3", -5*
TRANSPORT PROPERTIES OF FERROMAGNETS
787
expression (33)
Rs = ap + bp :2,
or alternatively (fig. 16)
(34)
c/:,H = ~b° + B p ,
if the variation of the magnetization with impurity concentration is neglected. It is usually assumed that this represents a separation into the skew scattering term and the side jump term. For most Ni based alloy series, as we have seen the values of 4~° vary considerably, but the values of B hardly vary from one impurity to another, with B -~ - i m i l l i r a d / ~ c m . However, for those Ni based alloys with p+ (O)/pt (0)>> 1, the data as a function of concentration cannot be represented by eq. (33) unless only a very restricted range of concentration is considered. It is interesting to note that these particular alloys are those which also show anomalous R0 and resistivity anisotropy behaviour as a function of concentration. At room temperature, p in Ni and Ni alloys is always "high" so that the side jump mechanism can be assumed to dominate. The experimental value of the ratio R d p 2 increases from the pure Ni value, R s / p 2 ~ 0.1 (~cmG) -1, as a function of impurity concentration and rapidly saturates at a plateau value of about 0.15 (f~cmG) -~ for a wide range of Ni alloys (K6ster and Gm6hling 1961, K6ster and R o m e r 1964), (fig. 17). The room temperature R s / p 2 values for the alloys are close to the values at low temperatures for the same alloys (Dorleijn 1976). However, for certain alloy systems R s / p 2 measured at room temperature changes steadily with impurity concentration. Thus for NiFe, R~ changes sign at about 15% Fe (Smit 1955, Kondorskii 1964). Alloys with this concentration of Fe show low values of R~/p: even if a second high resistivity impurity is introduced (Levine 1961). In pure Fe and FeSi alloys, R s / p 2 is remarkably constant over a wide range of concentrations and temperatures (Kooi 1954, Okamoto et al. 1962, where this ratio remains constant although R~ varies over three decades) (fig. 18). For other Fe based alloys the ratio generally approaches the pure Fe value at moderate or
20
EL°
-r-
t
10
-r 1C
./"
//
to
/ 1'0 2~0 . ~ (p~cm)
¢0 20 9±(#.O_cm)
Fig. 16. The extraordinary Hall. angle at 4.2 K as a function of the residual resistivity of FeA1 and NiRu alloys (Dorleijn 1976).
788
I.A. C A M P B E L L A N D A. F E R T
Rs/ )2 (~.cm9)._i o
~
-0.15 o
i /~
.0
/t
-0.1 o CF Ru Mo
oNb • Ti
-0.05
x V
Concentration, %
0
I
I
I
I
I
/
1
2
3
4
5
6
•
Fig. 17. The ratio Rs/p 2 in Ni and Ni alloys at room temperature (after K6ster et al. 1961 and 1964).
l
Fe
o
#
A 2.04% Si-Fe * 3.83% Si-Fe
/
xO,
109 g b. E o
-
E
fc~0
o
? 1611
,
156
,
,,I
lO-5
,
,,
I
lo-~ Resistiv'lty ~o (D.cm)
Fig. 18. Log-log plot of R5 against p for Fe and some Fe alloys above nitrogen temperature (after Okamoto et al. 1962).
TRANSPORT PROPERTIES OF FERROMAGNETS I
I
I
[
789
A I
A12.7% Cr IN Fe o 5.1% CF IN Fe
50
/ / /~/~ / /
• 0.75 °/o CFIN Fe
// /
x 2.3 % CFIN Fe
20
t
#j/,y'
~" 10 o.~~ , t o
N
s
! 0.5
I
2
I
5
I
10
I
20
50
~ (10-8OHMM) Fig. 19. Log-log plot of Rs against p for FeCr alloys, with temperature as an implicit variable (after Carter and Pugh 1966).
high temperatures (Softer et al. 1965, Carter and Pugh 1966). However, at low temperatures where skew scattering can be important, the behaviour can be completely different (fig. 19) (Carter and Pugh 1966). It seems that in the F__~eCr case, there is a strong skew scattering effect at low temperatures which has disappeared by room temperature (but see Majumdar and Berger 1973). Dorleijn (1976) has made an analysis in terms of skew scattering, side jump and ordinary Hall effect in Fe alloys at helium temperatures, but the interpretation is tricky, particularly because samples frequently show a field dependent Hall coefficient. The extraordinary Hall coefficient has been measured as a function of temperature in pure Co (Cheremushkina and Vasileva 1966). Kondorskii (1969) suggested that the sign of the side jump effect was related to the charge and polarization of the dominant carriers, which can be compared with the model outlined above. No satisfactory quantitative estimates of the size of the effect seem to have been made for ferromagnetic metals, and other basic questions concerning this mechanism remain open. The anisotropy of the Hall effect in single crystals is technically difficult to study, and, as a result, the existence of an anisotropy in the extraordinary Hall coefficient of cubic metals has been uncertain. Now evidence has been provided for the anisotropy in Rs for Fe (Hirsch and Weissmann 1973) and for Ni (Hiraoka 1968) at room temperature. In hexagonal Co both R0 and Rs are highly anisotro-
790
I.A. C A M P B E L L A N D A. F E R T
pic (Volkenshtein et al. 1961) which means that measurements on hcp Co polycrystals are subject to severe texture problems.
3.5. Thermoelectric power In non-magnetic metals under elastic scattering conditions, the thermoelectric power (TEP) coefficient depends on the differential of the resistivity at the Fermi surface through the Mott formula: dp s=
3 lel
p
In ferromagnets the situation is complicated by the existence of the two spin currents at low temperatures and by magnetic scattering at higher temperatures. The TEP curves as a function of temperatures for Fe, Co and Ni metals show effects which are clearly due to ferromagnetic ordering (fig. 20). For Co and Ni, the curve of S(T) shows a bulge towards negative values of S in the ferromagnetic temperature range, and a distinct charge of slope at To. For Fe, the behaviour is similar but complicated by a positive hump in S(T) just below room temperature. The critical behaviour of S(T) has attracted considerable attention. In Ni, the curve for dS/dT near Tc resembles the specific heat curve in the same way as does dp/dT (Tang et al. 1971). Although it has been argued that the TEP anomaly represents strictly the specific heat of the itinerant electrons (Tang et al. 1972) a more reasonable interpretation is in terms of the critical behaviour of the elastic scattering (Thomas et al. 1972). Combining the Mott formula and the expression 20
10
0 _10 ¸ iI
"T
x,¢
> -20 (13
-31 -41
Tc -50
400 Tc(Ni) 8 00
1200
T (K)
Fig. 20. T h e absolute thermoelectric power of Ni, Fe, Pd and Co (Laubitz et al. 1976).
TRANSPORT PROPERTIES OF FERROMAGNETS
791
for the resistivity as a function of k near Tc leads to
Pn/P),
S = Sp - 1 A o T ( 1 +
where AQ = 27r2k~/3[elEv, and Sp is the background non-magnetic TEP. Results on GdNi2 were discussed in terms of this approach (Zoric et al. 1973). The systematics of S(T) were studied at room temperature and above in a number of Ni based alloys (Vedernikov and Kolmets 1961, Kolmets and Vedernikov 1962, K6ster and Gm6hling 1961, K6ster and R o m e r 1964). S at room temperature becomes rapidly more positive with impurity concentration for those alloys for which p;(O)/p~(O)~<1 ( ~ V , N i C r . . . ) while S becomes more negative for alloys with p+(O)/pt (0) ~> 1 (fig. 21). The negative bulge in S(T) remains very strong for a wide range of NiFe alloys measured up to Tc (Basargin and Zakharov 1974), but tends to disappear in NiV alloys (Vedemikov and Kolmets 1961). The low temperature T E P of Ni based alloys has been analyzed using the two current model (Farrell and Greig 1969, 1970, Cadeville and Roussel 1971). If the intrinsic T E P coefficients for the two spin directions are S t and S+ then the observed value of S should be S = (p; S t + Pt S;)/(p~ + p+) at low temperatures; at high temperatures where the two currents are mixed, the impurity diffusion thermopower becomes S = ½(St + S+). Using these two expressions, Farrell and Greig (1969) extracted S t , S , for a number of impurities in Ni and similar analyses have been done in Ni and Co based alloys (Cadeville et al. 1968, Cadeville 1970, Cadeville and Roussel 1971). A detailed discussion has been given
26
T (K)
8.8%Cr
(a)
2O
24
'
22
11.
20
5.2
18
.8
40
60
80
100
i
-2 -4
16
-6
14 -Q
12
::k ~'4C 8 -1;
6 Ni Cr
4
--ld
2 r
i
,
i
,
i
,
i
,
i
.
i
.
i
40 80 120 160 200 2z,0 280
J (K) Fig. 21. The absolute thermoelectric power of some nickel based alloys as a function of temperature (after Beilin et al. 1974 and Farrell and Greig 1970). (a) NiCr; (b) Ni alloys.
792
I.A. CAMPBELL AND A. FERT
of the relationship between the electronic structure of the impurity and the T E P coefficients (Cadeville and Roussel 1971). Another aspect of the two current situation is the influence of magnon-electron scattering (Korenblit and Lazarenko 1971). Scattering of a spin $ electron to a spin I' state involves the creation of a magnon, which needs positive energy, while spin 1' to spin + scattering is through the destruction of a magnon. The electron-magnon scattering will then lead to a positive term in S at moderate temperatures in alloys where the spin $ current dominates, and a negative term in alloys where the spin 1' current dominates. The T E P due to this effect will be superimposed on the elastic electron-impurity term except at very low temperatures, and will complicate the analysis of the diffusion terms. Results on Ni alloys have been interpreted with this mechanism (Beilin et al. 1974). A magnon drag effect has been suggested (Bailyn 1962, Gurevich and Korenblit 1964, Blatt et al. 1967). Measurements on the T E P in a NiCu and a NiFe alloy in applied fields appear to be consistent with this mechanism (Granneman and Berger 1976). However, the strong positive T E P hump in pure Fe does not have this origin (Blatt 1972). The value of S is anisotropic with respect to the magnetization direction in a ferromagnet. Measurements on Fe and Ni single crystals at room temperature (Miyata and Funatogawa 1954) gave AS100 = + 0.70 IxV/K,
ASm -- - 0.13 txV/K
in F e ,
AS~00 = +0.57 ~xV/K,
ASm = +0.69 txV/K
in Ni.
and
The Fe result was confirmed by Blatt (1972). 3.6. Nernst-Ettingshausen effect
This is the thermoelectric analogue of the Hall effect. It has been studied in the pure ferromagnetic metals and in a number of alloys (Ivanova 1959, Kondorskii and Vasileva 1964, Cheremushkina and Vasileva 1966, Kondorskii et al. 1972, Vasileva and Kadyrov 1975). Like Rs, this coefficient varies strongly with temperature in ferromagnets. Kondorskii (1964) proposed the phenomenological relationship Q = - (a + jgp)T,
and the origin of the effect was discussed in terms of the side jump mechanism by Berger (1972) and Campbell (1979). 3. 7. Thermal conductivity
This is not a purely electron transport effect, as heat can be carried also by phonons and even magnons, and separating out the different contributions is difficult. Farrell and Greig (1969) in careful measurements on Ni and Ni alloys have shown that a coherent analysis of the alloy data needs to take into account
TRANSPORT PROPERTIES OF FERROMAGNETS
793
the two current character of the conduction. They found that it was not possible to decide for or against the presence of any electron-electron term in pure Ni at low temperatures (White and Tainsh 1967). At higher temperatures, Tursky and Koch (1970) have shown that it is possible to use the spontaneous resistivity anisotropy to separate out phonon and electron thermal conductivity. By measurements in strong fields, Yelon and Berger (1972) identified a magnon contribution to the low temperature thermal conductivity in N_iiFe. The thermal conductivity of Ni shows an abrupt change of slope at Tc (Laubitz et al. 1976). This property is very difficult to measure with high precision.
4. Dilute ferromagnetic alloys 4.1. Palladium based alloys
It has been known for some time that P dFe, PdCo, PdMn and P__ddNialloys are "giant moment" ferromagnets at low concentrations; the transport properties of these systems have been well studied. 4.1.1. Resistivity and isotropic m agnetoresistance PdFe alloys are soft ferromagnets down to at least 0.15% Fe. The Fe magnetization at T ~ Tc saturates completely in small applied fields (Chouteau and Tournier 1972, Howarth 1979). The magnetic disorder at relatively low temperatures is in the form of magnons; for the dilute alloys (C < 2% Fe), it appears that the magnon-electron scattering is essentially incoherent so the magnetic resistivity is proportional to the number of magnons present, leading to a temperature dependent resistivity proportional to T 3/2 for T ~ Tc and a characteristic temperature dependent negative magnetoresistance (Long and Turner 1970, Williams and Loram 1969, Williams et al. 1971, Hamzi6 and Campbell 1978). At higher concentrations a T 2 resistivity variation replaces the T 3/2 behaviour (Skalski et al. 1970). At the Curie temperature there is a change in slope of the p ( T ) curve but it is difficult to analyze the results in terms of critical scattering behaviour because of smearing due to the spread of Tc values in the samples (Kawatra et al. 1969). PdMn alloys are "ferromagnets" below 4% Mn concentration in that they show a high initial susceptibility below a well defined ordering temperature (Rault and Burger 1969, Coles et al. 1975). In fact, high field magnetization measurements (Star et al. 1975) show that the Mn magnetization only becomes truely saturated when very strong magnetic fields are applied. The temperature dependence of the resistivity of these alloys is qualitatively similar to that observed in PdFe, with a change of slope in p ( T ) at Tc and a T 3/2 variation of the resistivity at low temperatures (Williams and Loram 1969). In contrast to the PdFe alloys the magnetoresistance remains strongly negative even when T tends to zero (Williams et al. 1973).
794
I.A. C A M P B E L L A N D A. F E R T
PdCo alloys have very similar ordering temperatures and total magnetic moments per atom as the PdFe alloys (Nieuwenhuys 1975), and the temperature dependence of the resistivity is again of the same type (Williams 1970). However the paramagnetic resistivity at T > Tc is proportional to the Co concentration (Colp and Williams 1972) whereas in P__ddFealloys it increases as the square of the Fe concentration (Skalski et al. 1970). The PdCo alloys below 5% Co show a negative magnetoresistance at T ~ Tc which indicates that they are not true ferromagnets (Hamzi6 et al. 1978a)*. PdNi alloys are ferromagnets above a critical concentration of 2.3% Ni (Tari and Coles 1971). Near this concentration the low temperature variation of the resistivity of the alloys becomes particularly strong (Tari and Coles 1971). Both the paramagnetic and ferromagnetic alloys show a large positive magnetoresistance due to an increase in the local moments at the Ni sites with the applied field (Genicon et al. 1974, Hamzi6 et al. 1978a).
4.1.2. Magnetoresistance anisotropy PdFe, P__d_dCoand PdNi alloys all show positive anisotropies Pll > P± at moderate magnetic impurity concentrations. At low concentrations P_ddFe samples show vanishingly small anisotropies (Hamzi6 et al. 1978a). From this and other evidence it has been concluded that the Co and Ni impurities carry local orbital moments. 4.1.3. Extraordinary Hall effect Over a broad concentration range the Hall coefficient in PdFe alloys behaves similarly to that in concentrated NiFe alloys, changing sign near 20% Fe (Matveev et al. 1977, Dreesen and Pugh 1960). At low concentrations the Hall angle tends to zero for PdFe and P__d_dMnbut takes on a concentration independent value for P dNi and PdCo (Hamzi6 et al. 1978b, Abramova et al. 1974). This should be related to the local orbital moments of Co and Ni impurities. 4.1.4. Thermoelectric power In the concentrated ferromagnets, features clearly associated with the ferromagnetic ordering are visible in the temperature dependence of the TEP. For the Pd based alloys this does not seem to be the case except perhaps when the magnetic impurity concentration is greater than 5% (Gainon and Sierro 1970). At 1%, or lower, concentrations PdFe and PdMn show weak negative or positive TEP below 20 K varying in a rather co'--mplex way with concentration and temperature (Gainon and Sierro 1970, Macdonald et al. 1962, Schroeder and Uher 1978). P_dd1% Co shows a negative TEP hump at 20 K (Gainon and Sierro 1970); this hump becomes more pronounced and goes to lower temperatures as the concentration is decreased (Hamzi6, 1980). Below the critical concentration PdNi alloys show a strong negative hump in the TEP around 15 K which disappears once the concentration exceeds the critical value (Foiles 1978). * They can he considered to be "quasiferromagnets", i.e., systems having an overall magnetic m o m e n t but where the local m o m e n t s are each somewhat disoriented with respect to the average m o m e n t direction.
TRANSPORT PROPERTIES OF FERROMAGNETS
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4.2. Platinum based alloys Again, Pt__Fe and Pt___Coare giant moment ferromagnets at concentrations of a few percent, but at lower concentrations the behaviour is more complicated. For Pt__Fe below about 0.8% spin glass order sets in (Ododo 1979). In the ferromagnetic concentration range there is the usual step in p(T) at the ordering temperature, but below 0.8% Fe this step disappears (Loram et al. 1972). The isotropic magnetoresistance is strongly negative at concentrations less than about 5% Fe (Hamzi6 et al. 1981). PtCo alloys below 1% Co show resistivity variations which are complex because of competing tendencies to Kondo condensation and to magnetic ordering (Rao et al. 1975, Williams et al. 1975). At concentrations above about 1% Co a step can be seen in p(T) at To. The isotropic magnetoresistance is positive at low concentrations, becoming negative by 2% Co (Lee et al. 1978, Hamzi6 et al. 1980). Both Pt__Fe and PtCo alloys show concentration independent resistivity anisotropies and extraordinary Hall angles at low concentrations (Hamzi6 et al. 1979). The low temperature thermoelectric power of PtCo alloys becomes strongly negative below about 2% Co concentration (Lee et al. 1978). This TEP is sensitive to applied magnetic fields. PtMn alloys are spin glasses (Sarkissian and Taylor 1974), and Pt___Nialloys are not magnetically ordered below 42% Ni.
5. Amorphous alloys Since the early 1970s considerable effort has been devoted to the study of the electrical and magnetic properties of amorphous alloys. The resitivity minimum observed in many systems has been subject to much controversy.
5.1. Resistivity of amorphous alloys The amorphous alloys have a very high resistivity (p ~ 100 Ixllcm) which changes relatively little as a function of temperature. Figure 22 shows that, in series of NiP alloys, the temperature coefficient changes from positive to negative as the concentration of P increases. This behaviour is well explained in the Ziman model of the resistivity of liquid metals (Ziman 1961) and its extension to amorphous alloys (Nagel 1977). In the Ziman model the resistivity turns out to be proportional to a(2kv) where kv is the Fermi wave vector and a(q) the atomic structure factor. If 2kv is close to the first peak of a(q), the resistivity is high and decreases as a function of T owing to the thermal broadening of the p~ak. In contrast, if 2kv lies well below (or well above) the peak, the resistivity is relatively low and increases as a function of T. In the NiP alloys (fig. 22) the additional conduction electrons provided by the higher concentrations of P raise 2kF to the first peak of a(q), which accounts for the experimental behaviour (Cote 1976). On the other hand, the small resistivity upturns observed in NiP at low temperature (fig. 22)
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cannot be explained by the Ziman model. Such resistivity upturns, which generally give rise to a resistivity minimum, have been found in many amorphous systems. They have been found in both ferromagnetic and non-ferromagnetic amorphous alloys and, up to now, only in alloys containing transition (or rareearth) metals. Their origin has been subject to much controversy. Resistivity minima have been first found by Hasegawa and Tsui (1971a, b) in amorphous PdSi containing Cr, Mn, Fe or Co impurities (fig. 23). The classical features of the Kondo effect are observed: the resistivity varies logarithmically over a large temperature range and becomes constant in the low temperature limit; at low concentration of magnetic impurities the logarithmic term increases with the concentration, there is a negative magnetoresistance. But, surprisingly, the resistivity minimum still exists in the most concentrated alloys which are ferromagnetic. These results seem to indicate that weakly coupled moments subsist in amorphous ferromagnets and can give rise to Kondo scattering. Results on many other systems have suggested that the coexistence of ferromagnetism and Kondo effect is quite general in amorphous alloys; thus large logarithmic upturns have been observed (fig. 24) in ferromagnets of the series FeN•B, FeNiPB, FeN•PC, FeNPBS (Cochrane et al. 1978, Babi6 et al. 1978, Steward and Phillips 1978), FeNiPBA1, FeMnPBA1, CoPBA1 (Rao et al. 1979), PdCoP (Marzwell 1977); in
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798
I.A. CAMPBELLAND A. FERT
many cases the addition of small amounts of Cr strongly enhances the resistivity upturn. On the other hand, Cochrane et al. (1975) found that the logarithmic resistivity upturn of several amorphous alloys was field independent, in contrast to what is generally observed in Kondo systems. They also noticed a logarithmic upturn in NiP alloys with high P concentration in which the Ni atoms were not supposed to carry a magnetic moment. On the basis of these observations they ruled out the explanation by the Kondo effect and proposed a non-magnetic mechanism. Their model treats the electron scattering by the two level systems which are supposed to be associated with structural instabilities in amorphous systems; a variation of the resistivity in - l n ( T 2 + A2) is predicted, where A is a mean value of the energy difference between the two levels. The resistivity curves of several amorphous alloys fit rather well with such a variation law. At the present time (1979) however the trend is in favour of an explanation of the resistivity minima by the Kondo effect rather than by a non-magnetic mechanism. Clear examples of logarithmic resistivity upturns in non-magnetic systems are still lacking: alloys such as NiP or YNi c a n be suspected to contain magnetic Ni clusters (Berrada et al. 1978). On the other hand, systematic studies of the resistivity of FeNiPB (BaNd et al. 1978), FeNiPBAI, FeMnPBA1 (Rao et al. 1979) have shown definite correlations between the resistivity anomalies and the magnetic properties (logarithmic term large when Tc is small, etc.); it has been also found in several systems that the logarithmic upturn is lowered by an applied field. Finally, M6ssbauer experiments on FeNiCrPB alloys have found very small hyperfine fields on a significant number of Fe sites, which seems to confirm the coexistence of ferromagnetism and Kondo effect (Chien 1979). What we have written up to now concerned the metal-metalloid alloys which have been the most studied amorphous alloys. Studies of metal-metal amorphous alloys of rare-earths with transition or noble metals have been also developed recently. Resistivity minima have been again observed in these systems but appear to be generally due to contributions from magnetic ordering and not to Kondo effect. In Ni3Dy (fig. 25) the resistivity increases either if a magnetic field is applied or if the temperature is lowered below the ordering temperature To. This suggests a positive contribution from magnetic ordering to the resistivity, in contrast to what is observed in crystalline ferromagnetics. This has been ascribed by Asomoza et al. (1977a, 1978) to coherent exchange scattering by the rare-earth spins (Ni has no magnetic moment in these alloys). The model calculation predicts a resistivity term proportional to m(2kv) where re(q) is the spin correlation function 1
m ( q ) = NCelj( J + 1) R , ~ , exp[iq • ( R - R')IJR " JR'.
Here C1 is the concentration of magnetic ions, having local moments J and placed at R, R ' ; the sum is over the pairs of magnetic ions. The resistivity will depend on the magnetic order through m(2kv); for example,
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ferromagnetic correlations will increase or decrease p according to whether the interferences are constructive or destructive. The Ni3-RE alloys should correspond to the case of ferromagnetic correlations and constructive interferences. The A g - R E , A u - R E and A I - R E amorphous alloys also show a clear contribution from magnetic ordering to the resistivity, but the interpretation seems to be a little more complicated than for the Ni3-RE alloys (Asomoza et al. 1979, Fert and Asomoza 1979). Finally, alloys of the series F e - R E and C o - R E generally show a monotonic decrease of the resistivity from the helium range to room temperature (Cochrane et al. 1978, Zen et al. 1979). In these alloys of high Tc the variation of the resistivity due to magnetic ordering must be displayed over a wide temperature range and is certainly difficult to separate from the normal variation due to the phonons and the thermal variation of the structure factor. We believe that this normal variation should be predominant, specially at low temperature. Similarly, in the alloys such as FeNiPB discussed above, a contribution from magnetic ordering to p(T) certainly exists but is likely covered up by other contributions (Kondo or structural effects) at low temperature.
800
I.A. CAMPBELL AND A. FERT
5.2. Hall effect and resistivity anisotropy of amorphous alloys The amorphous ferromagnetic alloys have a very large extraordinary Hall effect which generally covers up the ordinary Halt effect. This is because the extraordinary Hall resistivity, in contrast to the ordinary one, is an increasing function of the scattering rate (the contributions from skew scattering and side-jump are roughly proportional to p and p2 respectively). Thus pi~(B) is practically proportional to the magnetization in many systems and, for example, is frequently used to record hysteresis loops (McGuire et al. 1977a, b, Asomoza et al. 1977b). The extraordinary Hall effect of ferromagnetic alloys of gold with nickel, cobalt or iron has been studied by Bergmann and Marquardt (1979) and ascribed to skew scattering; the change of sign of pn between Ni and Fe has been accounted for by a model based on a virtual bound state picture of the 3d electrons. On the other hand, the extraordinary Hall effect of FeNiPB alloys rather suggest a side-jump mechanism (Malmhfill et al. 1978). The extraordinary Hall effect has been also studied in amorphous alloys of transition metals with rare-earths and related to the magnetization of the transition and rare-earth sublattices in phenomenological models (Kobliska and Gangulee 1977, McGuire et al. 1977, Asomoza et al. 1977b). The spontaneous resistivity anisotropy is rather large in amorphous alloys of gold with nickel or cobalt (/911-p± -~ 1 ix12cm) and has been interpreted in a model of virtual bound state for the 3d electrons (Bergmann and Marquardt 1979). The resistivity anisotropy seems to be smaller in alloys of the FeNiP type (Marohnid et al. 1977). The resistivity anisotropy has been also studied in amorphous alloys of nickel or silver with rare-earths and turns out to be mainly due to electron scattering by the electric quadrupole of the 4f electrons (Asomoza et al. 1979).
Reference Abelskii, Sh. and E.A. Turov, 1960, Fiz. Met. Metalloved. 10, 801. Abromova, L.I., G.V. Fedorov and N.N. Volkenshteyn, 1974, Fiz. Met. Metalloved. 38, 90. Amamou, A., F. Gautier and B. Leogel, 1975, J. Phys. F 5, 1342. Anderson, J.R. and A.V. Gold, 1963, Phys. Rev. Lett. 10, 227. Armstrong, B.E. and R. Fletcher, 1972, Can. J. Phys. 50, 244. Asomoza, R., A. Fert, I.A. Campbell and R. Meyer, 1977a, J. Phys. F 7, L 327. Asomoza, R., I.A. Campbell, H. Jouve and R. Meyer, 1977b, J. Appl. Phys. 48, 3829. Asomoza, R., I.A. Campbell, A. Fert, A. Li6nard and J.P. Rebouillat, 1979, J. Phys. F 9, 349.
Baber, W.G., 1937, Proc. Roy. Soc. A 158, 383. Babic, E., Z. Marohnic and J. Ivkov, 1978, Solid State Commun. 27, 441. Bailyn, M., 1962, Phys. Rev. 126, 2040. Basargin, O.V. and A.I. Zakharov, 1974, Fiz. Met. Metalloved. 37, 891. Beitcham, J.G., C.W. Trussel and R.V. Coleman, 1970, Phys. Rev. Lett. 25, 1970. Beitel, F.P. and E.M. Pugh, 1958, Phys. Rev. 112, 1516. Beilin, V.M., T.I. Zeinalov, I.L. Rogel'berg and V.A. Chernenkov 1974, Fiz. Met. Metalloved. 38, 1315. Berger, L., 1970, Phys. Rev. B 2, 4559. Berger, L., 1972, Phys. Rev. B 5, 1862. Berger, L., 1978, J. Appl. Phys. 49 (3), 2156. Berger, L. and S.A. Friedberg, 1968, Phys. Rev. 165, 670.
TRANSPORT PROPERTIES OF FERROMAGNETS Berger, L. and A.R. de Vroomen, 1965, J. Appl. Phys. 36, 2777. Berrada, A., N.F. Lapierre, L. Loegel, P. Panissod and C. Robert, 1978, J. Phys. F 8, 845. Bergmann, G. and P. Marquardt, 1978, Phys. Rev. B 18, 326. Birss, R.R., 1964, Symmetry and magnetism (North-Holland, Amsterdam). Blatt, FJ., D.J. Flood, V. Rowe, P.A. Schroeder and J.E. Cox, 1967, Phys. Rev. Lett. 18, 395. Blatt, F.J., 1972, Can. J. Phys. 50, 2836. Boucher, B., 1973, J. of Non-Cryst. Sol. 7, 277. Bozorth, R.M., 1951, Ferromagnetism (Van Nostrand, Princeton). Cadeville, M.C., F. Gautier, C. Robert and J. Roussel, 1968, Solid State Commun. 7, 1701. Cadeville, M.C., 1970, Solid State Commun. 8, 847. Cadeville, M.C. and C. Lerner, 1976, Phil. Mag. 33, 801. Cadeville, M.C. and B. Loegel, 1973, J~ Phys. F 3, L 115. Cadeville, M.C. and J. Roussel, 1971, J. Phys. F 1, 686. Campbell, I.A., 1974, J. Phys. F 4, L 181. Campbell, I.A., 1979, J. Magn. Magn. Mat. 12, 31. Campbell, I.A., A. Fert and A.R. Pomeroy, 1967, Phil. Mag. 15, 977. Campbell, I.A., A. Fert and O. Jaoul, 1970, J. Phys. C 3, S 95. Carter, G.C. and E.M. Pugh, 1966, Phys. Rev. 152, 498. Cheremushkina, A.V. and R.P. Vasil'eva, 1966, Sov. Phys. Solid State, 8, 659. Chien, C.L., 1979, Phys. Rev. B 19, 81. Chouteau, G. and R. Tournier, 1972, J. de Phys. 32, C1-1002. Clark, A.L. and R.L. Powell, 1968, Phys. Rev. Lett. 21, 802. Cochrane, R.W., R. Harris, J.O. Str6m-Olsen and M.J. Zuckermann, 1975, Phys. Rev. Lett. 35, 676. Cochrane, R.W. and J.O. Str6m-Olsen, 1977, J. Phys. F 7, 1799. Cochrane, R.W., J.O. Str6m-Olsen, Gwyn Williams, A. Lirnard and J.P. Rebouillat, 1978, J. Appl. Phys. 49, 1677. Coleman, R.V., 1976, AlP Conf. Proc. 29, 520. Coleman, R.V., R.C. Morris and D.J. Sellmeyer, 1973, Phys. Rev. B 8, 317. Coles, B.R., 1958, Adv. Phys. 7, 40.
801
Coles, B.R., H. Jamieson, R.H. Taylor and A. Tari, 1975, J. Phys. F 5, 572. Colp, M.E. and G. Williams, 1972, Phys. Rev. B 5, 2599. Connelly, D.L., J.S. Loomis and D.E. Mapother, 1971, Phys. Rev. B 3, 924. Cote, P.J., 1976, Solid State Commun. 18, 1311. Craig, P.P., W.I. Goldberg, T.A. Kitchens, and J.I. Budnick, 1967, Phys. Rev. Lett. 19, 1334. Dedir, G., 1975, J. Phys. F 5, 706. De Gennes, P.G. and J. Friedel, 1958, J. Phys. Chem. Solids, 4, 71. Der Ruenn Su and T.M. Wu, 1975, J. Low Temp. Phys. 19, 481. D6ring, W., 1938, Ann. Phys. 32, 259. Dorleijn, J.W.F., 1976, Philips Res. Repts, 31, 287. Dorleijn, J.W.F. and A.R. Miedema, 1975a, J. Phys. F 5, 487. Dorleijn, J.W.F. and A.R. Miedema, 1975b, J. Phys. F 5, 1543. Dorleijn, J.W.F. and A.R. Miedema, 1976, AIP Conf. Proc. 34, 50. Dorleijn, J.W.F. and A.R. Miedema, 1977, J. Phys. F 7, L 23. Dreesen, J.A. and E.M. Pugh, 1960, Phys. Rev. 120, 1218. Dugdale, J.S. and Z.S. Basinski, 1967, Phys. Rev. 157, 552. Durand, J. and F. Gautier, 1970, J. Phys. Chem. Sol. 31, 2773. Durand, J., 1973, Thesis (Strasbourg) unpublished. Dutta Roy, S.K. and T.M. Wu, 1975, J. Low Temp. Phys. 19, 481. Erlich, A.C., J.A. Dreesen and E.M. Pugh, 1964, Phys. Rev. 133, A, 407. Etin Wohlman, O., G. Deutscher and R. Orbach, 1976, Phys. Rev. B 14, 4015. Farrell, T. and D. Greig, 1968, J. Phys. C, 1 sur 2, 1359. Farrell, T. and D. Greig, 1969, J. Phys. C, 2 sur 2, 1465. Farrell, T. and D. Greig, 1970, J. Phys. C, 3, 138. Fawcett, E., 1964, Adv. Phys. 13, 139. Fert, A., 1969, J. Phys. C, 2, 1784. Fert, A. and R. Asomoza, 1979, J. Appl. Phys. 50, 1886. Fert, A. and I.A. Campbell, 1968, Phys. Rev. Lett. 21, 1190. Fert, A. and I.A. Campbell, 1971, J. de Phys. (Paris) 32, Sup. no. 2-3, C1--46.
802
I.A. CAMPBELL AND A. FERT
Fert, A. and I.A. Campbell, 1976, J. Phys. F 6, 849. Fert, A. and O. Jaoul, 1972, Phys. Rev. Lett. 28, 303. Fert, A., I.A. Campbell and M. Ribault, 1970, J. Appl. Phys. 41, 1428. Fert, A , R. Asomoza, D. Sanchez, D. Spanjaard and A. Friederich, 1977, Phys. Rev. B 16, 5040. Fischer, M.E. and A. Aharony, 1973, Phys. Rev. Lett. 30, 559. Fisher, M.E. and J.S. Langer, 1968, Phys. Rev. Lett. 20, 665. Foiles, C.L., 1978, J. Phys. F 8, 213. Friedel, J., 1967, Rendicanti della Scuola Intern. di Fisica '°Enrico Fermi" XXXVII Corso (Academic Press, New York). Fulkesson, W., J.P. Moore and D.L. McElroy, 1966, J. Appl. Phys. 37, 2639. Fujii, T., 1970, Nippon Kinsoku Gakkaishi (Japan) 34, 456. Gainon, D. and J. Sierro, 1970, Helv. Phys. Acta, 43, 541. Geldart D.I.W. and T.G. Richard, 1975, Phys. Rev. B 12, 5175. Genicon, G.L., F. Lapierre and J. Soultie, 1974, Phys. Rev. B 10, 3976. Goodings, D.A., 1963, Phys. Rev. 132, 542. Grannemann, G.N. and L. Berger, 1976, Phys. Rev. B 13, 2072. Greig, D. and J.P. Harrisson, 1965, Phil. Mag. 12, 71. Gurevich, L.E. and I.Y. Korenblit, 1964, Sov. Phys. Solid State, 6, 1960. Guenault, A.M., 1974, Phil. Mag. 30, 641. Hamzid, A., 1980, Thesis (Orsay). Hamzid, A. and I.A. Campbell, 1978, J. Phys. F 8, L33. HamziG A. and I.A. Campbell, J. Phys. (Paris) 42, L17. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1978a, J. Phys. F 8, 1947. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1978b, Solid State Commun. 26, 617. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1980, J. Magn. Magn. Mat. 15-18, 921. Hasegawa, R. and C.C. Tsuei, 1971a, Phys. Rev. B 2, 1631. Hasegawa, R. and C.C. Tsuei, 1971b, Phys. Rev. B 3, 214. Hayakawa, H. and J. Yamashita, 1976, Progr. Theor. Phys. 54, 952. Herring, C., 1967, Phys. Rev. Lett. 19, 1131. Hiraoka, T., 1968, J. Sci. Hiroshima Univ. 32, 153.
Hirsch, A.A. and Y. Weissmann, 1973, Phys. Lett. 44A, 230. Hodges, L., D.R. Stone and A.V. Gold, 1967, Phys. Rev. Lett. 19, 655. Houghton, R.W. and M.P. Sarachik, 1970, Phys. Rev. Lett. 25, 238. Hugel, J., 1973, J. Phys. F 3, 1723. Howarth, W., 1979, Thesis, London. Huguenin, R. and D. Rivier, 1965, Helv. Phys. Acta, 38, 900. Hurd, C.M., 1972, The Hall Effect (Plenum Press, New York). Hurd, C.M., 1974, Adv. Phys. 23, 315. Ivanova, R.P., 1959, Fiz. Met. Metalloved. 8, 851. Jan, J.P., 1957, Solid State Phys. 5, 1. Jaoul, O., 1974, Thesis (Orsay), unpublished. Jaoul, O., I.A. Campbell and A. Fert, 1977, J. Magn. Magn. Mat. 5, 23. Jayaraman, V. and S.K. Dutta Roy, 1975, J.P.C.S. 36, 619. Kasuya, T., 1956, Progr. Theor. Phys. 16, 58. Kasuya, T., 1959, Progr. Theor. Phys. 22, 227. Kaul, S.N., 1977, J. Phys. F 7, 2091. Kawatra, M.P., S. Skalski, J.A. Mydosh and J.I. Budnick, 1969, J. Appl. Phys. 41), 1202. Kawatra, M.P., J.I. Budnick and J.A. Mydosh, 1970, Phys. Rev. B 2, 1587. Kawatra, M.P., J.A. Mydosh and J.I. Budnick, 1970, Phys. Rev. B 2, 665. Kittel, C., 1963, Phys. Rev. Lett. 10, 339. Kittel, C. and J.H. Van Vleck, 1960, Phys. Rev. 118, 1231. Klaffky, R.W. and R.V. Coleman, 1974, Phys. Rev. B 10, 2915. Kobliska, R.J. and A. Gangulec, 1977, Amorphous Magnetism II, eds., R.A. Levy and R. Hasegawa (Plenum, New York). Kolmets, N.V. and M.V. Vedernikov, 1962, Sov. Phys. Sol. St. 3, 1996. Kondorskii, E.I., 1964, Sov. Phys. JETP, 18, 351. Kondorskii, E.I., 1969, Sov. Phys. JETP, 28, 291. Kondorskii, E.I. and R.P. Vasil'eva, 1964, Sov. Phys. JETP, 18, 277. Kondorskii, E.I., A.V. Cheremushkina and N. Kurbaniyazov, 1964, Soy. Phys. Sol. St. 6, 422. Kondorskii, E.I., A.V. Cheremusbkina, R.P. Vasil'eva and Y.N. Arkipov, 1972, Fiz. Met. Metalloved. 34, 675. Kooi, C., 1954, Phys. Rev. 95, 843.
TRANSPORT PROPERTIES OF FERROMAGNETS Korenblit, I.Y. and Y.P. Lazarenko, 1971, Sov. Phys. JETP, 33, 837. K6ster, W. and W. Gm6hling, 1961, Zeit. Met. 52, 713. K6ster, W. and O. Romer, 1964, Zeit. Met. 55, 805. Kraftmakher, Y.A. and T.Y. Pinegina, 1974, Sov. Phys. Sol. St. 16, 78. Laubitz, M.J., T. Matsumara, 1973, Can. J. Phys. 51, 1247. Laubitz, M.J., T. Matsumara and P.J. Kelly, 1976, Can. J. Phys. 54, 92. Lavine, J.M., 1961, Phys. Rev. 123, 1273. Lee, C.W., C.L. Foiles, J. Bass and J.R. Cleveland, 1978, J. App. Phys. 49, 217. L6onard, P., M.C. Cadeville and J. Durand, 1969, J. Phys. Chem. Sol. 30, 2169. Loegel, B. and F. Gautier, 1971, J. Phys. Chem. Sol. 32, 2723. Loram, J.W., R.J. White and A.D.C. Grassie, 1972, Phys. Rev. B 5, 3659. Luttinger, J.M., 1958, Phys. Rev. 112, 739. Lyo, S.K. and T. Holstein, 1972, Phys. Rev. Lett. 29, 423. MacDonald, D.K.C., W.B. Pearson and I.M. Templeton, 1962, Proc. Roy. Soc. A 266, 161. McGuire, T.R. and R.I. Potter, 1975, IEET Transactions on Magnetics, Vol. Mag. 11, 1018. McGuire, T.R., R.J. Gambino and R.C. Taylor, 1977a, J. Appl. Phys. 48, 2965. McGuire, T.R., R.J. Gambino and R.C. Taylor, 1977b, I.E.E.E. Transactions on Magnetism M A G 13, 1977. Majumdar, A.K. and L. Berger, 1973, Phys. Rev. B 7, 4203. Malmh~ill, R., G. B~ickstr6m, K. Rao, S. Bhagat, M. Meichle and M.B. Salamen, 1978, J. Appl. Phys. 49, 1727. Mannari, J., 1959, Prog. Theor. Phys. 22, 335. Marohnic, Z., E. Babic and D. Pavuna, 1977, Phys. Lett. 63A, 348. Marzwell, N.I., 1977, J. Mag. Mag. Mat. 5, 67. Matveev, V.A., G.V. Fedorov and N.N. Voltenshteyn, 1977, Fiz. Met. Metalloved. 43, 1192. Matsumoto, H., H. Saito, M. Kikuchi, 1966, J.J. Inst. Meta. 30, 885. Miedema, A.R. and J.W.F. Dorleijn, 1977, J. Phys. F 7, L 27. Mills, D.L., A. Fert and I.A. Campbell, 1971, Phys. Rev. B 4, 196. Miyata, N. and Z. Funatogawa, 1954, J. Phys. Soc. Japan, 9, 967. Mott, N.F., 1936a, Proc. Roy. Soc. 153, 699.
803
Mott, N.F., 1936b, Proc. Roy. Soc. 156, 368. Mott, N.F., 1964, Adv. Phys. 13, 325. Nagel, S.R., 1977, Phys. Rev. B 16, 1694. Nieuwenhuys, G.J., 1975, Adv. Phys. 24, 515. Nozi6res, P. and C. Lewiner, 1973, J. de Phys. 34, 901. Okamoto, T., H. Tange, A. Nishimura and E. Tatsumoto, 1962, J. Phys. Soc. Japan, 17, 717. Ododo, J.C., 1979, J. Phys. F 9, 1441. Parks, R.D., 1972, AIP Conference, 5, 630. Pugh, E.M., 1955, Phys. Rev. 97, 647. Ramaman, R.V. and L. Berger, 1978, Proc. Int. Conf. Physics of Transition Metals (Toronto 1977), Institute of Physics, Conf. Ser. No. 39. Rao, K.V., O. Rapp, C. Johannesson, J.I. Budnick, T.J. Burch and V. Canella, 1975, AIP Conf. Proc. 29, 346. Rao, K.W., H. Gudmundsson, H.U. Astr6n and H.S. Chen, 1979, J. Appl. Phys. 50 (3), 1592. Rapp, O., J.E. Grindberg and K.V. Rao, 1978, J. Appl. Phys. 49, 1733. Rault, J. and J.P. Burger, 1969, C.R.A.S., 269, 1085. Reed, W.A. and E. Fawcett, 1964a, J. Appl. Phys. 35, 754. Reed, W.A. and E. Fawcett, 1964b, Phys. Rev. 136 A, 422. Richard, T.G. and G.J.W. Geldart, 1973, Phys. Rev. Lett. 30, 290. Ross, R.N., D.C. Price and Gwyn Williams, 1978, J. Phys. F, 8, 2367. Ross, R.N., D.C. Price and Gwyn Williams, 1979, J. Mag. Mag. Mat. 10, 59. Ruvalds, J. and L.M. Falicov, 1968, Phys. Rev. 172, 508. Sakissian, B.V.B. and R.H. Taylor, 1974, J. Phys. F 4, L 243. Sandford, E.R., A.C. Erlich and E.M. Pugh, 1961, Phys. Rev. 123, 1947. Schroeder, P.A. and C. Uher, 1978, Phys. Rev. B 18, 3884. Schwerer, F.C. 1969, J. Appl. Phys. 40, 2705. Schwerer, F.C., 1974, Phys. Rev. B 9, 958. Schwerer, F.C. and L.J. Cuddy, 1970, Phys. Rev. B 2, 1575. Schwerer, F.C. and J. Silcox, 1968, Phys. Rev. Lett. 20, 101. Schwerer, F.C. and J. Silcox, 1970, Phys. Rev. B 1, 2391. Skalski, S., M.P. Kawatra, J.A. Mydosh and J.I. Budnick, 1970, Phys. Rev. B 2, 3613. Shacklette, L.W., 1974, Phys. Rev. B 9, 3789. Shumate, P.W., R.V. Coleman and R.C. Eiwaz, 1970, Phys. Rev. B 1, 394.
804
I.A. CAMPBELL AND A. FERT
Simons, D.S. and M.B. Salomon, 1974, Phys. Rev. B 10, 4680. Smit, J., 1951, Physics, 17, 612. Smit, J., 1955, Physica, 21, 877. Smith, T.R., R.J. Jainsh, R.N. Shelton and W.E. Gardner, 1975, J. Phys. F 5, L 96. Softer, S., J.A. Dreesen and E.M. Pugh, 1965, Phys. Rev. 140, A 668. Sousa, J.B., M.R. Chaves, M.F. Pinheiro and R.S. Pinto, 1975, J. Low Temp. Phys. 18, 125. Souza, J.B., M.M. Amado, R.P. Pinto, J.M. Moreira, M.E. Brago, M. Ausloos, J.P., Leburton, P. Clippe, J.C. van Hay and P. Morin, 1979, J. de Phys. (Paris) 40, sup. no. 5, *C5--42. Star, W.M., S. Foner and E.J. McNift, 1975, Phys. Rev. B 12, 2690. Steward, A.M. and W.A. Phillips, 1978, Phil. Mag. B 37, 561. Su, D.R., 1976, J. Low Temp. Phys. 24, 701. Swartz, J.C., 1971, J. Appl. Phys. 42, 1334. Tang, S.H., F.J. Cadieu, T.A. Kitchens and P.P. Craig, 1972, AIP Conf. Proc. 5, 1265. Tang, S.H., T.A. Kitchens, F.J. Cadieu, P.P. Craig, 1974, Proceedings LT 13 (Plenum Press, New York) 385. Tari, A. and B.R. Coles, 1971, J. Phys. F 1, L 69. Taylor, G.R., Acar Isin and R.W. Coleman, 1968, Phys. Rev. 165, 621. Thomas, G.A., K. Levin and R.D. Parks, 1972, Phys. Rev. Lett. 29, 1321. Tsui, D.C., 1967, Phys. Rev. 164, 669. Turner, R.E. and P.D. Lond, 1970, J. Phys. C 3, S 127. Turov, E.A., 1955, Isv. Akad. Nauk SSSR, Ser. fiz. 19, 474. Turov, E.A. and A.N. Volshinskii, 1967, Proc. 10th Intern. Conf. Low Temperature Phys., Izd. Viniti, Moscow. Tursky, W. and K.M. Koch, 1970, Zeit. Nat. 25A, 1991. Tyler, E.H., J.R. Clinton, H.L. Luo, 1973, Phys. Lett. 45A, 10. Ueda, K. and T. Moriya, 1975, J. Phys. Soc. Japan, 39, 605. Van Elst, H.C., 1959, Physics, 25, 708. Van Peski Tinbergen, T. and A.J. Dekker, 1963, Physica, 29, 917. Vassilyev, Y.V., 1970, Phys. St. Sol. 38, 479. Valil'eva, R.P. and Y. Kadyrov, 1975, Fiz. Met. Metalloved. 39, 66. Vedernikov, M.V. and N.V. Kolmets, 1961, Sov. Phys. Sol. St. 2, 2420. Visscher, P.B. and L.M. Falicov, 1972, Phys. St. Sol. B 54, 9. Volkenshtein, N.V., G.V. Fedorov and V.P.
Shirakovskii, 1961, Fiz. Met. Metalloved. 11, 152. Volkenshtein, N.V. and V.P. Dyakina, 1971, Fiz. Met. Metalloved. 31, 773; The Phys. of Met. and Metallog. 31, no. 4, 101. Volkenshtein, N.V., V.P. Dyakina and V.C. Startsev, 1973, Phys. St. Sol. (b) 57, 9. Vonsovskii, S.V., 1948, Zh. Eksper. Teor. Fiz. 18, 219. Vonsovskii, S.V., 1955, Izv. Akad. Nauk 555 B, Ser. fiz. 19, 447. Bull. Acad. Sc. USSR, 19, 399. Weiss, R.J., A.S. Marotta, 1959, J. Phys. Chem. Sol. 9, 3202. Weiser, O. and K.M. Koch, 1970, Zeit. Nat. 25A, 1993. White, G.K. and S.B. Woods, 1959, Phil. Trans. Roy. Soc. (London) A 251, 273. White, G.K. and R.J. Tainsh, 1967, Phys. Rev. Lett. 19, 105. Williams, G., 1970, J. Phys. Chem. Solids, 31, 529. Williams, G. and J.W. Loram, 1969a, J. Phys. Chem. Solids, 30, 1827. Williams, G. and J.W. Loram, 1969b, Solid State Commun. 7, 1261. Williams, G., G.A. Swallow and J.W. Loram, 1971, Phys. Rev. B 3, 3863. Williams, G., G.A. Swallow and J.W. Loram, 1973, Phys. Rev. B 7, 257. Williams, G., G.A. Swallow and J.W. Loram, 1975, Phys. Rev. B 11, 344. Yamashita, J. and H. Hayakawa, 1976, Progr. Theor. Phys. 56, 361. Yamashita, J., S. Wakoh and S. Asano, 1975, J. Phys. Soc. Jap. 39, 344. Yao, Y.D., S. Arajs and E.E. Anderson, 1975, J. Low Temp. Phys. 21, 369. Yelon, W.B. and L. Berger, 1970, Phys. Rev. Lett. 25, 1207. Yelon, W.B. and L. Berger, 1972, Phys. Rev. B 6, 1974. Yoshida, K., 1957, Phys. Rev. 107, 396. Zen, D.Z., T.F. Wang, L.F. Liu, J.W. Zai, K.T. Sha, 1979, J. de Phys. 40, C5-243. Ziman, J.M., 1960, ELectrons and Phonons (Clarendon Press, Oxford) p. 275. Ziman, J.M., 1961, Phil. Mag. 6, 1013. Zoric, I., G.A. Thomas and R.D. Parks, 1973, Phys. Rev. Lett. 30, 22. Zumsteg, F.C. and R.D. Parks, 1970, Phys. Rev. Lett. 24, 520. Zumsteg, F.C. and R.D. Parks, 1971, J. de Phys. 32, C1-534. Zumsteg, F.C., F.J. Cadieu, S. Marcelja and R.D. Parks, 1970, Phys. Rev. Lett. 15, 1204.
SUBJECT INDEX abbreviation, see phases absorption coefficient, a, of BaO-6Fe203 as a function of wavelength 359 AC magnetization of the alnicos 18l activation energy 101, 103 of pinned wall 103 of thin wall 104 additives 462-464, 468, 476, 499, 500, 514, 522 after-effects dielectric relaxation 276 elastic relaxation 286 magnetic, spinels 249ff aging, see stability air gap 44, 46 amorphous alloys 795ff ribbons 524 Anderson localization 268 anhysteretic magnetization of the alnicos 179 anilin process 465 anisotropy C O 2+ contribution 236, 240, 247, 251 exchange 52 induced 246ff experimental data for spinels 251ff magnetic 49ff, 55 magnetocrystalline 50, 53ff, 56, 57, 102, 120, 133 magnetocrystalline constant BaCox/2Tix/2Fe12-x019 379 BaCu~Fe12-~O19-xFx 386 BaInxFel2-xO~9 376 BaNixFe12-xOa9-xFx 386 BaO.6Fe203 329-332, 376, 386 LaFe12Oi9 367 LaFeZ+Fe~-O19 367 Na0.sLa0.sFe12019 367 PbO.6Fe203 329-332 SrO-6Fe203 329-332
temperature dependence of BaScxFe12-xO19 375 magnetocrystalline, formulae 233 shape 50, 52ff alnicos 1-4, 113-120 alnico 5 and alnico 5 D G (alnico 5-7) 121-133, 149 alnicos 8 and 9 145, 149 Fe2NiA1 120, 133 single ion, spinels 235ff surface 52 uniaxial 50 anisotropy constant 67 anisotropy energy 49, 62, 85, 96 anisotropy field 49ff, 50, 446, 493, 499, 537 BaAlxFe12-xO19 373 BaCox/2Tix/2Fe12-x019 378 BaCrxFe12-xO19 373 BaGaxFe12-xO19 373 Ba(TiCo)xFe12_xO19 379 BaO.x(TiCoO3)-(6- x)Fe203 347 BaO.6Fe~O3 332-335, 349, 381 BaZnx/2Ge~/zFe12-xO19 380 B aZn:,/2Irx/2Fe12-~O19 381 BaZn2x/3Nbx/3Fe12_xO19 380 BaZn2x/3Tax/3Fe12-x019 380 BaZnx/2Tix/2Fe12-x019 347, 381 BaZr~Tir Mnz Fea2-x-r_z O19 380 BaZn2x/3Vx/3Fe12-x019 380 CaO--A1203-Fe203 375 PbO.6Fe203 332-334 SrAlxFe12-xOt9 373 SrO-xA1203.(6- x)Fe203 347 SrO-6Fe203 332-334, 374 temperature dependence of BaO.6Fe203 333 PbO-6Fe203 333 SrO.6Fe203 333 W-type compounds 433 833
834
SUBJECT INDEX
Y-type compounds 432 Z-type compounds 433 antiferromagnetic 52, 89 antiferromagnetism oxide spinels 224 antiparallel coupling 89 application of hard ferrites 535, 581, 582 plastoferrites 585, 586, 592 assemblage 463, 484 atomizer 469, 483 attritor 469, 481, 483, 485 (BH)m,x value
angular dependence 561, 564 (BpH)max value 579, 580 binder 463, 471, 483, 484, 527 blending, see raw materials, mixing Bloch wall thickness of PbO.6Fe203 358 Boltzmann constant 101 Brown's paradox 60 bubble memory 23 bubbles 21 bulk modulus K, variations with temperature BaO.6Fe203 360, 361 calcination, see reaction sintering calendering, see rolling calenders 585 calibration 510, 517 charge-density waves (in CuV2S4) 624 chemical analysis BazZn2Fe12022 (Zn2Y) 436 chemical vapour deposition 534 cobalt, effects of in alnicos 154 coercive force 334-342 angular dependence of BaO.6Fe203 361 effect of milling time on BaO.6Fe603 337 effect of packing factor on BaO.6FeeO3 336 effect of particle size on BaO-6Fe203 338 temperature dependence of (Ba or Sr)(Cu+ Ge)xFe~2-xOx9 383 (Ba or Sr)(Cu + Si)xFe12-xO19 383 (Ba or Sr)(Cu + Ta)xFe12-xO~9 383 (Ba or Sr)(Cu+ V)xFe12-xO19 383 coercivities of alnicos 1-4 112-114 alnicos 5-9 127, 131, 133 alnico 8, extra high 141 coercivity 49, 50, 59, 60 angular dependence 561, 564-566 flux 42 magnetization 41
magnetocrystalline anisotropy 66ff of antiphase boundary 92-94 of buckling mode 63 of curling mode 61, 63 of discrete sites 100 of fanning mode 65 of planar defect 87 , 88 of powder 486, 553, 566 of thin wall 94ff of twisting mode 63 of wall pinned by cavities 76, 77, 79 of whiskers 64 particle packing density 62 shape anisotropy 60ff temperature dependence 447, 551-554, 579, 580 uniform rotation 61, 63 columnar crystallization of alnico 9, 142 compass 4 compaction anisotropy 492, 540, 561 compensation material 560 complex permeability, temperature dependence of BaO.6FeaO3 344 compressive strength BaO-6Fe203 361 core loss 12 creep, by compressive deformation BaO.6FezO3 361 critical behaviour 773 stress intensity factor 573 volume for thermal stability 102 critical radius 77 cylinder 59, 63 fine particles 55ff resistivity phenomena 773ff sphere 62 upper and lower bounds 55, 59 crystal field splitting of 3d n ions in oxide spinels 202ff crystal field transitions of Cr 3+ (in CdCr2S4) 659ff of Co 2+ (in CoCr2S4) 713, 718 crystal growth, see grain growth crystal structure U-type and other compounds 402 W-type compounds 396 X-type compounds 401 Y-type compounds 397 Z-type compounds 400 crystallographic texture of alnicos and effects on magnetic properties 161 Curie constant 343 Curie temperature 74, 113, 126, 155, 156, 550
SUBJECT INDEX Ag0.sLa0.sFe12019 367 BaAlxFe12-xO19 371, 372 BaCoxFea2-xO19-xFx 386 BaCrxFelz-xO19 372 BaCuxFe12-xO19-xFx 386 BaGaxFe12-~O19 371, 372 BalnxFe12-xO19 376 Bal-~(K or Bi)x(Cu, Ni or Mn)xFe12-xO~9 383 BaNixFe12-x O19Fx 386 BaO.6Fe203 326, 327, 386 Ba(TiCo)xFe12 xO19 379 BaZnx/2Irx/2Fe12 xO19 381 BaZnx/2Tix/2Fe12-xOa9 381 Ca0.88La0.14Fe12019 367 LaFe2+Fe3~ O19 367 LaFe12019 367 Na0.sLa0.sFe12019 367 Nrel theory 222 oxide spinels 225, 296 PbO-6Fe203 326, 327 SrAI4.sFeT.2019 374 SrAlxFe12-xO19 371,372 SrO.6Fe203 326, 327 cutting 463, 584 cyclic heat treatment of alnico 5 129
DC electrical conductivity oxide spinels 260ff deagglomeration 463 Debye temperature Ba-6FezO3 361 spinel ferrites 289 demagnetization 510-512 curves 535, 539, 588, 589 curves, comparison of various materials 578, 579 curves, temperature dependence 555-557 factor 49, 53 influence of method 512 mode 56 demagnetizing field 42, 44, 53, 60 at conical pit 80 at surface defects 59 density 322, 326, 349, 384 apparent powder 464, 466, 471 green 490, 514 sintered 498, 502 tap 465, 471 uniformity 491 X-ray 575 designation, see phases dewatering 482, 494
die 489 pressing 489, 513, 584, 585 dielectric behaviour 569 dielectric constant BaNizAlxFe16-xO27 (NiA1)W 435 oxide spinels 275ff dielectric constant, real part temperature dependence of BaO-6Fe203 365 diffusion couples 472, 534 dilute ferromagnets 793 dipole 55 directional ordering 54 dispersants 483 domain observation BaO.6Fe403 354-358 domain wall detachment 92ff nucleation 59, 66, 67, 81 180 degrees 67ff, 84 pinning 59, 67, 81 thickness 62, 67ff domain wall energy 59, 67ff, 68, 334, 335 BaO.6Fe203 335, 355 PbO-6FezO3 335 SrO.6Fe203 335 domain wall mobility BaFeH.3AI0.7019 358 BaO-6Fe203 358 domain width BaO.6Fe203 355, 358 PbO-6Fe203 358 SrO.4.2Fe203-1.8A1203 355 SrO.4.5Fe203.1.5A1203 355 domain width effect of crystal thickness on BaO.6Fe203 357-358 PbO-6Fe203 357-358 SrO'6Fe303 357-358 SrO.(6- x)Fe203-xA1203 357 domain width effect of magnetic field on BaO-6Fe203 355-356 SrO-4.2Fe203-1.8A1203 355 SrO.4.5Fe203-1.5A1203 355 DS processes 519, 525 dynamic excitation of alnicos 180 easy axis 49 economic aspects of magnetism 6, 7 effects of y-phase in alnicos 138-140 elastic constants of oxide spinels 285ff elastic moduli 572 BaFe12019 361 electric conductivity ferroxplana-type compounds 434
835
836
SUBJECT INDEX
electric conductivity, temperature dependence of BaO.6Fe203 364, 365 PbO-6Fe203 364 electric steels 9-11 electrical properties of sulpho- and selenospinels 607ff ellipsoid 53 energy anisotropy 49, 57, 62, 85, 96 conversion capability 579 coupling 90 domain wall 59 exchange 57, 62, 68, 78, 85, 90, 96 interaction between magnetized bodies 47 magnetocrystalline anisotropy 56, 78 magnetostatic 49, 55, 57, 59, 62, 96 energy product 27, 42 maximum 44 of alnicos 112-114 ESR Camll2 xFexO19 370 Euler's equation 68, 84 eutectic composition 455, 458, 524 temperature 455, 458 exchange biquadratic 218, 230 constant of PbO.6Fe203 335 coupling 56 energy 57, 62, 68, 78, 85, 90, 96 coefficient 68, 69ff of body-centred cubic lattice 70, 73 of face-centred cubic lattice 71, 73 of hexagonal close-packed lattice 71, 73 of simple cubic lattice 71, 73 integrals, values in oxide spinels 218ff resonance frequency 256 striction spinels 244 exchange interaction 55, 60 between Cr 3+ ions in semiconducting sulphoand selenospinels 647ff, 701if, 728ff in metallic sulpho- and selenospinels 608, 632ff, 644ff existence range 449 extrusion 513, 515, 526, 527, 532, 584 fanning asymmetric 65 symmetric 64 far infrared absorption data oxide spinels 284 Faraday rotation BaO-6Fe203 358, 359
feed materials, s e e raw materials ferrimagnetism 216ff collinear, s e e Nrel configuration effect of diamagnetic substitution, spinels 227ff effect of magnetic field 224, 229 spiral 223ff theory, spinels 221ff triangular arrangement, s e e Yafet-Kittel configuration ferrite(s) 12 components 19 electrical properties 262ff ferromagnetic resonance data 258ff magnetization data 294ff magnetocrystalline anisotropy data 292ff magnetostriction data 294ff survey of intrinsic magnetic properties 296 ferromagnetic resonance, s e e FMR 101 ferromagnetism oxide spinels 224 ferroxdure 28 fibre texture 473, 526, 562 field anisotropy 50, 53, 60, 64 demagnetizing 42, 44, 53, 60 nucleation 66, 81 Weiss 60 filter press 469 fine particles 55ff Fisher sub-sieve-sizer 485 fluidized bed 466, 513, 525 flux density, magnetic 445 fluxes 522 FMR BaO-6Fe203 345-347 BaO-x(TiCoO3).(6- x)Fe203 347 BaZnx/2Irx/2Fe12-xO19 380-381 B aZnx/2Tix/2Fe12-xO19 380-381 SrO.xAI203(6- x)Fe203 347 FMR effect of DC field on the frequency of BaO.6FezO3 345, 346, 348 SrO-6Fe203 348 formation kinetics ferroxplana-type compounds 402 formation process BaO.6FeaO3 315-317 PbO-6Fe203 315-317 SrO-6Fe203 315-317 fracture surface energy 574 free energy magnetic 46ff reversible change 47 free drying 518
SUBJECT INDEX gangue 464 garnets 20 geometric defects 509 glass melt process 523 glassy phase 457, 499 grain growth 462, 480, 497, 498, 505-507 anisotropic 475 discontinuous 472, 498, 501, 505, 506, 517 inhibition 457, 459, 499 granulate 462, 469-471, 478, 484, 492 granulation 463, 468, 471, 472 grinding 463, 508, 513, 573, 579, 580, 584 mechanism 484, 509 gyromagnetic factor g BaO-6Fe203 348 SrO-6Fe203 348 gyrator 15 gyromagnetic ratio 102 effective 256
Hall coefficient extraordinary 752, 754, 783ff, 793 ordinary 752, 778 Hall effect 751ff extraordinary definition 754 of dilute ferromagnets 794 theory and experimental data 793 ordinary 778 planar 754 hard ferrite particles aligning 462, 463, 479, 482, 492-494, 497, 583 grain size determination 485 shape anisotropy 475, 485, 514, 518, 583 hard ferrites 443 annual mass production 577, 592 bonded 582 hardness 502, 574, 575 H - C process 519 heat capacity BaO.6Fe203 361, 362 heat treatment of alnicos annealing 112, 118, 119, 121-123, 138, 141, 142 homogenization 111, 112, 121, 123, 125, 138, 141, 142 thermomagnetic 121, 125, 130, 137, 138, 141, 142 Heisenberg model 73 hematite, s e e iron oxide, natural hexaferrites, s e e hard ferrites hexagonal ferrites 443, 454, 473
837
high field behaviour 765 history of ferrites 12 garnets 20 iron silicon alloys 10 magnetism 3 permanent magnets 24 homogeneity range 451, 454, 457, 459 homogeneous nucleation 81 honeycomb domain, stability against ternperature BaO-6Fe203 358 PbO'6Fe203 358 hot deformation techniques 525, 526, 530 pressing 489, 513, 518, 525, 528 hydrothermal method 518 hyperfine fields Fe 57 in oxide spinels 298 hyperfine magnetic field BaMg2Fe16027 423 hysteresis loop(s) 41, 44, 48, 50, 51, 67, 541543 after annealing 81, 82 after polishing 81, 82 ilmenite 467 impurities 464, 499 indirect shaping 463, 510 induction (magnetic) 445 injection moulding 484, 585 interaction domain wall with cavities 74ff domain wall with crystal lattice 81ff exchange 55, 60 magnetostatic 54 interracial energy of al and a2 phases 117 intermediate product 457, 472, 473, 476, 477, 522 internal field, temperature dependence of LaO.6F~O3 354, 368 SrO.6Fe203 352 ionic radii, list of several ions 317 iron oxide natural 465-467 synthetic 465, 468, 469 isomer shift, temperature dependence of SrO.6Fe203 352 isotropic pressing 489 Jahn-Teller effect cooperative in oxide spinels 213ff elastic constants 285
838
SUBJECT INDEX
far infrared spectra 284, 286 in Ba2Cu2Fex2022 (Cu2Y) 435 in FeCr2S4 701, 707 magnetic anneal 249, 255 Kerr rotation, as a function of wavelength BaO.6Fe203 358, 359 (K1)m/M~, temperature dependence BaO.6Fe203 339 kilns 470, 478-480, 507, 508 rotary 478, 479 kneaders 585 Kondo effect 796 Kopp's rule 288 lattice constant(s) 575 Ag0.sLa0.sFe12019 366 BaA112019 370, 385 BaAlxFe12-xO19 369 BaCozA112 xO19-xFx 385 BaCoxFelz-xO19-xFx 385 B aCo0.sZnzA19.5O16.5F2.5 385 BaCoZnAI10OlyF2 385 BaCrsFe4019 370 BaCr~Felz-xO19 369 BaCuxFelz_xO19 xFx 385 BaFe22+Ni0.58Fels.~2018.42F0.58 385 BaGa12019 370 BaGaxFelz_~O19 369 BalnxFea2-xO19 376 BaNixAl~2-xO19 xFx 385 BaNixFex2-xO19-xFx 385 BaNi0.sZn2A19.5016.sF2.5 385 BaO.6Fe203 322, 376 BaScxFe~2-xO19 376 Bal-xSr~Fe12019 368 BaZn~/zlrx/2Fe12 ~O19 380 Ca(AIFe)12019 369-370 CaA112019 369-370 Ca0.ssLa0.14Fe12019 366 LaMgGa11019 369-370 Pbl-~Ba~Fex2019 368 PblnLgFe10.1019 376 PbO-6Fe203 322 SrAl12Ot9 370 SrAl~Fe12-xO19 369 SrCr6Fe6019 370 SrCr~Fe12-xO19 369 SrGa12Ox9 369-370 SrO.6Fe203 322 Sra-xPbxFe~2019 368 temperature dependence of BaO-6Fe203 363
of
lattice defects 59, 60 leakage factor 46 light switching matrix 34 linear thermal expansion 569-571,580 liquid phase 476, 499 epitaxy 534 lodestone 4 Lorentz microscopy 94 lubricants for milling 483 pressing 492 Lurgi process 466 machining, see grinding Madelung constant oxide spinels 207 magnetic after-effect 569 of BaO-6Fe203 344 anneal 245 constant ~0 445 domain of ferroxplana-type compounds 436 hardness 443 pressure 98 viscosity 101, 102 of the alnicos 173 magnetic properties dependence on sintering temperature 503, 504 of isotropic magnets 457, 459 of powder 479 of pressed parts 491 of sulpho-, seleno- and tellurospinels 607ff primary 459, 462 magnetic structure BaCoxFelz-x O19 384 BaO'6Fe203 323-325 BaScxFe12-xO19 377 magnetization (quantity) 445 magnetization (remagnetization) 463, 510, 512, 541, 584 magnetization buckling 62, 65 changes coherent reversal 518 irreversible 550, 557-560 reversible 550, 554, 557-559, 579 curling 62, 63 in the alnicos 169 curve, initial 41 fanning . 64 field dependence of BaO-6FeeO3 330 PbO.6Fe203 329, 330
SUBJECT INDEX remanent 41, 42, 44 saturation 41 twisting 62 uniform 57 magnetizing process 341 magnetocrystalline anisotropy 120, 133 ferroxplana-type compounds 412 magnetomotoric force 46 magnetooptical effects of oxide spinels 282ff magnetooptical properties, of sulpho- and selenospinels 663, 685, 687, 711, 713, 718 magnetoresistance 776ff, 793 in sulpho- and selenospinels 607, 651ff, 657ff, 679ff, 691, 692, 708ff, 712, 715, 718, 727 ordinary 776 magnetoresistive element 32 magnetostatic energy 49, 55, 57, 59, 62, 96 of cavity 76 interaction domains in the alnicos 170 magnetostriction 54, 567 alnico 5 133, 134 alnico 5DG (alnico 5-7) 133, 134 dipole-dipole 242 linear, basic relations 234 single ion 238ff BaFe2FelrOz7 (Fe2W) 425 BaO-6Fe203 360 magnons, dispersion relation for spinels 231ff main components 464 manufacturing process hard ferrite, usual 462, 463 hard ferrite, special 513 plastoferrite 583, 584 mass efficiency 579, 580 material length l BaFe12019 358 PbFe12019 358 Maxwell's equations 43 mechanical properties of BaO-6Fe203 361 work 47 melting congruent 453 incongruent 457 point 455 techniques 519 memory cores 17 micromagnetic 55, 57, 60, 81, 84 microstructure alnicos 1--4 113 alnico 5 134, 136 alnico 8 146
839
alnico 9 146 FezNiAI 113, 118, 120 microwave linewidth W-type compounds 432 Y-type compounds 431 Z-type compounds 431 milling particle size after 484 reaction with water 488 wet 463, 472, 481,485 mills 469, 481-483 miscibility 461 mixers 585 mixing, s e e raw materials Mott's formula for variable range hopping 264 Mrssbauer effect ferroxplana-type compounds 421 AI, Cr, ZnTi, ZnGe, ZnSn, ZnZr, CuTi, CoTi, CoCr and NiTi substituted M-type compounds 353354 BaAIxFe12 xO19 370 BaO.6Fe203 351-354 BaZnxTir Mnz Fe12_x_y-zO19 380 CaAllz-xFexO19 370 LaO-6Fe203 354 PbO-6Fe203 351-354 SrAlxFea2-xOl9 370 SrO-6Fe203 351-354 Tl05La0.sFelzO19 368 M6ssbauer spectra of n9I (in CuCr2Te3I) 645 57Fe in sulphospinels 707, 715, 716, 720, 724-726, 729, 730, 733 119Sn in sulphospinels 634, 641, 711, 7'14 M6ssbauer spectroscopy of the alnicos 148 moulded alnico 149 multipole 55
Nrel configuration 222 stability conditions, spinels 222, 224 temperature, oxide spinels 225 neighbouring phases 454, 455, 458, 461 Nernst-Ettinghausen effect 792 neutral zone 491 neutralization 511 notched-bar impact test, s e e strength values, impact NMR (nuclear magnetic resonance) Y-type compounds 427 frequency temperature dependence of BaO.6Fe203 350 spin-echo amplitude versus resonance frequency, BaO.6Fe203 350
840
SUBJECT INDEX
of BaO.6Fe203 347-351 of nl'n3Cd in semiconducting sulpho- and selenospinels 666, 691 of 59Co in sulphospinels 625, 713, 736 of 53Cr in metallic sulpho- seleno- and tellurospinels 632, 636, 641, 642 of 53Cr in semiconducting sulpho- and selenospinels 666, 669, 690, 694, 710, 713 of 63'65Cu in metallic sulpho-, seleno- and tellurospinels 622, 623, 625, 626, 630, 632, 636, 641, 642 of 63'65Cu in semiconducting sulpho- and selenospinels 700, 721, 733 of 119'2°1Hgin sulpho- and selenospinels 669, 694 of rain in sulpho- and selenospinels 700 of 77Se in selenospinels 641, 691, 694 of ~2STein tellurospinels 642 of 51V in sulphospinels 624 nucleation field 66, 81 reverse domains 66, 67, 89 wall 80, 93 olivine 198 operating point 43 optical properties BaO-6Fe203 358-360 PbO.6Fe203 358-360 sulpho- and selenospinels 607, 645, 653, 659ff, 668, 673, 682ff, 692, 696, 713, 718 optical transition in oxide spinels 277ff
paramagnetic properties 342, 343 paramagnetic susceptibility, temperature dependence of BaM 342 PbM 342, 343 SrM 342 particle(s) accelerator 17 fine 55ff interactions 164--166 misalignment, effects on coercivity 163 remanence 161 orientation determination 563, 564 Peierls force 98 pellet density 471 peritectics 461 peritectoid reaction temperature 455 permanent magnet materials 443
permeability 565 permanent magnet characteristics 536, 540 influence of mechanical stress 565, 567 influence of neutron irradiation 567 optimum values 538, 585, 587, 588 temperature dependence 550 perovskite 477 phase diagram(s) 449 BaO-Fe203 310-313 BaO-MeO-Fe203 308 PbO-Fe203 313-315 SrO-Fe203 312-314 phases abbreviations 450 designations 451 phenacite 198 photoluminescence BaGaa2019 375 LaMgGa11019 375 MgGa204 375 SrGa12019 375 photon structure of sulpho- and selenospinels 664, 668, 675, 689, 692, 696, 705, 711, 713 photomagnetic effect oxide spinels 250 selenospinels 678ff, 696 pinning force 75, 79 plasticising agents 515, 527 plastoferrites 443, 479, 486, 582 Poisson's number 572 ratio of BaFe12019 361 polarization (magnetic) 445, 492 porosity 502 pot cores 14 potential energy of magnetic field 44 precursor phases, s e e intermediate product preferred direction 462, 473, 510 press forging, s e e hot deformation techniques pressed alnicos 149 presses 494, 496, 497 pressing 489 dry 463, 495, 517 orienting field 489 wet 517 pressure filtration, s e e compression moulding, wet pressure sintering, s e e hot pressing P - T diagram BaO.6Fe203 311 Fe304 311 2FeO.BaO.8Fe203 311 2FeO.SrO-8Fe203 311 pyrite 465, 467
SUBJECT INDEX quadrupole splitting, temperature dependence of SrO.6Fe203 352
raw materials 462-465, 499 coprecipitation 473, 477, 518 mixing 468, 469, 471, 472 precipitation 513, 517 reaction kinetics 462, 476 layers 473 mechanism 473, 476 model 475 product 462, 472 sequence 472, 476, 477 sintering 462, 463, 472, 477 thermal quantities 476, 477, 498 recording heads, integrated 33 reflectance spectra BaCo0.sGall.5Oas.sF0.5 386 BaNil.sAI10.5017.sF1.5 386 B aNi0.sGan.5018.sF0.5 386 relaxation, see after-effect resonance linewidth, oxide spinels 257 slowly relaxing ions (impurities) 257 reluctance 46 remanence angular dependence 510, 511, 561-563 calculation from texture 540, 562, 563 remanence, temperature dependence 551, 579, 580 of alnicos 112 of (Ba or Sr)(Cu+ Ge)xFe12-xO19 383 of (Ba or Sr)(Cu + Nb)xFel2-xO19 383 of (Ba or Sr)(Cu + Si)~Fe12-~O19 383 of (Ba or Sr)(Cu + Ta)~Fea2-xO19 383 of (Ba or Sr)(Cu + V)xF'elz-~O19 383 remanent magnetization 41, 42, 44 resistance factor 46 resistivity 751, 752ff, 762, 793, 795 anisotropy 752, 753, 779ff, 800, 850 high field 765 low temperature 762 of alloy 766ff, 793ff of amorphous alloys 795 of magnons 757 of pure ferromagnets 762 of single crystals 755 minimum 7 9 5 f f residual 764, 766 tensor 752 reversal mode 55 reverse domain at surface defect 80
841
nucleation 66, 67, 89 of cavity 78 Righi-Leduc effect 756 rigidity modulus, temperature dependence of BaO.6Fe203 360, 361 rolling techniques 513, 515, 527, 532, 584 rotational hysteresis in alnicos 177 rubber 584, 585 Ruthner process 465, 466 salt bath process 513, 523 saturation magnetization 41 ferroxplana-type compounds 404 Ba/MxFe12-~O19 370-372, 374 BaCoxFe12-xO19-xFx 384, 386 BaCrxFe12-xO19 370-372 BaCuxFel2-xO19-xFx 386 BaFz-2FeO-5Fe203 384 BaGaxFe12-xO19 370-372 BalnxFe12_xO~9 376 Bal-x(K or Bi)x(Cu, Ni or Mn)xFe12-~Oa9 383 BaNixFe12-xO19-xFx 386 BaO-6Fe203 325-328, 335, 349, 376, 384, 386 Ba(TiCo)xFela-~ O19 379 BaZnx/2Irx/2Fe12-x019 381 Ca0.88La0.14Fe12019 366 CaO-AI203--Fe203 375 LaFe2+Fe~O19 366 LaFe12019 366 Na0.sLa0.sFe12019 366 PbO.6Fe/O3 325-328 SrAI4.sFe7.zO19 374 SrAlxFe11-~O19 370-371, 374 SrCrxFelzOi9 370-372 SrO.6FezO3 325-328, 335 saturation magnetization, temperature dependence of BaO.6Fe203 326-328, 382 BaSb0.sFe 2+ 1.0Fe3+ 10.5019 382 Ba(SbFe)12019 382-383 BaSc~Felz-x O19 375 B aTi0.8Fe2+6Fe3~.8019 382 BaTiO3.5Fe203 382 BaZnxTiyMn~Fel~-~-y-~019 380 PbO'6Fe203 326-327 Sr(AsFe)12019 382-383 saturation polarization, magentic 445, 446, 462, 499, 536 of powder 487, 488 temperature dependence 446, 551 Seebeck coefficient values for spinels 269ff
842
SUBJECT INDEX
segment magnets 494, 509, 535 self cleaning effect 517 shape anisotropy of alnicos 1-4 11%120 alnico 5 and alnico 5DG (alnico 5-7) 131133, 145, 149 alnicos 8 and 9 120 FezNiA1 148 shrinkage 462, 463, 497, 507, 508, 514 ratio 502 temperature dependence 502 single crystals 755, 765, 778, 783 shunt 560 single domain particle, critical diameter of BaO.6Fe203 335, 355 BaZnx/zGex/aFetz-x Oa9 380 BaZn2x/3Nbx/3Fetz-x019 380 BaZn2x/3Tax/3Felz-xOt9 380 BaZnzx/sVx/3Felz-x019 380 PbO.6FezO3 335 SrO.6Fe203 335 single sintering techniques 513, 514 sintered alnicos 148 sintering 463, 480, 497, 513 promotion 457, 459, 514 slurry 469 small-defect-width approximation 87, 88 small-deviations approximation 85, 88 small-field approximation 87, 88 solid solution 458, 461 solid state reaction 468 solubility range, see homogeneity range specific heat 572 of sulpbo- and selenospinels 624, 626, 628, 672, 700, 708 specific resistivity 568, 569, 580 specific surface 465 spheroid, prolate 60 spin disorder scattering 757ff spin dependent Raman scattering 665ff, 689ff spin Hamiltonian 3d" ions with orbital singlets 235 values of parameters, oxide spinels 242 spin mixing 759 spinel crystal structure 609ff cation-anion distances in spinel compounds 613ff, 618 lattice parameters of spinel compounds 610ff polymorphism in spinel compounds 608 spinel structure cation distribution 208ff cation ordering 211ff crystal energy 206ff
description 191 inverse 193 ionic radii 194ff normal 193 thermodynamic properties 196ff spinodal decomposition in alnicos 1-4 115, 116 alnico 5 126 alnico 8 146 alnico 9 146 FezNiA1 115, 116 spontaneous resistivity anisotropy 752, 800 splat-cooling 522 spray drying 524 wasting 464, 525 stability chemical 445, 448, 575-577 magnetic 510, 578, 579 natural 545, 549 structural 445, 448, 550 thermal 453, 461, 545 standardization 541,545-546, 590 Stoner-Wohlfarth theory of hysteresis in alnicos 166 strength values 573, 580 substitution 450, 461 of M-type compounds with anions 384-386 suitability criterion 42ff super-exchange interactions in spinels 217ff superconductivity in sulpho- and selenospinels 623, 626, 627 superparamagnetic crystals 487 temperature compensation 560 dependence of magnetic properties of alnicos 180 influence of 100ff tensile strength, BaFex2019 361 thermal activation of wall displacement 102 agitation 101 conductivity 572, 792 excitation 101 expansion, BaO-6Fe203 362, 363 fluctuation 100 hydrolysis of salts 518 properties, oxide spinel data 288ff thermoelectric behaviour 569 effect 756, 790 thermomagnetic treatment Cahn theory of 173
SUBJECT INDEX dependence of magnetic properties on field direction 151 effects on al particles shape anisotropy 149 N6el-Zijlstra theory of 172 of alnicos 121, 125 of alnico 5DG (alnico 5-7) 129 of alnico 8 137 of alnico 8 (extra high coercivity) 141 of alnico 9 142 relationship between field direction and preferred direction of magnetization 151 thermoplastics 584 thermosettings 584, 585 thin layer techniques 534, 535 ticonal 26 titanium, effects of in alnicos 155 topotactic mechanism 475 trade marks 541, 544, 591 transport 751ff trends in magnetism research 31 two-current model 758ff two-domain state 56ff uniform rotation 49-51, 55, 60, 63, 93 units (SI, cgs) 443 valency of copper ions in sulpho- and selenospinels 618ff variational calculus 68, 91 Verwey transition 264ff volume efficiency 579, 580 volume functions of the Fe-Co rich c~l phase particles determination of the optimum value 164 in alnico 5 135, 136 in alnico 8 146
843
volumetric feeding 492 vulcanization 584, 585
wall creep 100, 104 wall energy at anti-phase boundary 90 in applied field 91ff, 95 wall nucleation at antiphase boundary 93ff at surface defects 80 wall pinning 81 at antiphase boundary 88ff at discrete sites 98ff at large cavities 76ff at line defects 99 at planar defects 83ff at point defects 99 at small cavities 78ff wall thickness 94 parameter 96 Weiss field energy 73 model 69 wettability 583 whiskers 64 working point 44, 46 X-ray absorption of Co ions 714, 721, 735 of Cu ions 620, 632, 642, 721, 735 X-ray photoelectron spectra of sulpho- and selenospinels 618, 637, 653, 719 Young's modulus E, temperature dependence of BaO.6Fe203 360-361
MATERIALS INDEX * Me = divalent metal ion, M = magnetoplumbite type compound Agl/2All/2Cr2S4 698ff AgxCdl xCr2Se~ 67%681 AgmGamCr2S4 698ff AgxHgl-~Cr2Se4 691,692. AgmlnmCr2S4 698ff AgmlnmCr2Se4 698ff Ag0.sLa0.sFe12019 366-367 AI substituted M-type compound 354, 368374, 385 alnico 39, 53, 54, 63, 64, 102, 445, 448, 578-580, 582 alnicos 1-4 111 alnico 5 121 alnico 5DG (alnico 5-7) 129 alnico 6 137 alnico 8 137, 141 alnico 9 137, 142 A1203 204, 205, 462, 464, 499, 500, 519, 522, 526, 528, 531 A1203-BaO-Fe203 454 A1EO3-BaO-Fe203-SrO 461 AI203-Fe2Oa-SrO 458 All/2CumCrzS4 698ff All/2Cul/2Cr2Se4 698ff A15/2Lil/204 614 ec-FeaO3, see Fe203 amorphous alloys 795ff B, see BaO, BxFy and BaO-Fe203 fl-A1203 444 BF 449-456, 458, 461, 473, see also BaFe203 and BaO.Fe203 BF2 450, 454, 455, see also BaO.2Fe203 and T B2F 449-451, 473, see also Ba2Fe205 B2F3 453-455, 473 BsF7 453
B7F2 450 B203 498-500, 514, 522-524, 529, 534 B203-BaO-Fe203-GeO2 524 BzO3-Fe203-GeOz-PbO 524 B203-FezO3-SiOz-SrO 524 BSF2 461 BaAll2019 370, 385 BaAlo.TFelL3019 358 BaAlxFelz-xOl9 368-375 Ba(CH3COO)2 468, 519, 521 BaCO3 444, 463, 467, 471-473, 499, 501, 515, 516, 519, 520, 522-525, 533, 534 BaC12 520 BaCoFe12-xO19-xFx 385 BaCoOaal.5018.sF0.5 386 BaCox/2Tix/2Fel2-xO19 378-379 BaCo0.sZn2AI9.sO~6.sFz5 385 BaCoZnAIa0017F2 385 Ba-Co--Zn-W 317 Ba-Co--Zn-Z 317 BaCo2Fe16027 (Co2W) 403, 434-436 Ba2Co2Fe12022 (C@Y) 406, 407, 410, 411, 414, 425, 427, 429 Ba2Co2Fee80~ (Co2X) 409, 414, 418 Ba2CoZnFe120~ (CoZnY) 403, 413 Ba2CoZnFez8046 (CoZnX) 418 Ba3CozFe24041 (Co2Z) 407, 408, 411, 414, 424, 425, 428, 436 Ba3CoL75Zn0.~Fe24041 (Coa.75Zn0.25Z) 414 BaCrsFe4019 370 BaCrxFe12-xO19 353, 354, 368-375 Ba(Cu+Ge)xFe12_xO19 383 Ba(Cu + Nb)xFe12-xO19 383 Ba(Cu+Si)xFe12_xO19 383 Ba(Cu + Ta)xFe12-xO19 383 Ba(Cu + V)xFei2-xO19 383 BaCuxFe12-xO19~ ~Fx 385 Ba2Cu2Fe12022 (Cu2Y) 435 BazCu2Fe~O4~ (Cu2X) 411 845
846
MATERIALS INDEX
Ba3Cu2Fe24041 (Cu2Z) 411 BasCuNiTi3Fe12031 (CuNi-18H) 411,420, 421 BaFeO3_x 308 BaFe204 453, 454, 518, 534, see also BF and BaO.Fe203 3+ BaFe22+Nlo.58Fe15.42018.42Fo.s8 385 BaFe2Fet6027 (Fe2W) 403, 406, 407, 411, 422, 425-427, 434 BaFe42A17.8019 454 BaFelo.92017.38 568 BaFe12019 433-448, 451, 452, 454, 455, 457, 479, 519, 522-524, 534, see also, BaO.6Fe203, BaM and M BaFe12Olg-Na20 524 BaFe12.59019.89 568 BaFe15023 453, see also BaO.FeO.7Fe203, BaO-MeO.7Fe203 and X Ba2Fe2Os 534, see also B2F BaGa12019 370, 375 BaGaxFe12-xO19 368-375 Ba-hexaferrite 55 BaInxFe12-xO19 375-378 Bal_x(K or Bi)x(Cu, Ni or Mn)xFe12-x019 383 Bal_xLaxMnO3 616 BaM 450, 536, 537, 551-553, 556-575, see also BaFe12019, BaO-6Fe203 and M Ba-Me-U 307, 309 Ba-Me-W 307, 309, 311 Ba-Me-X 307, 309, 312 Ba-Me-Y 307, 309 B a - M e - Z 307, 309 BaMg2Fe16027 (Mg2W) 405, 421-423 BaMn2Fe16027 (Mn2W) 411 Ba2Mg2Fe12022 (Mg2Y) 406, 407, 411, 414, 429 Ba2Mn2Fe12Oz~ (Mn2Y) 406, 407, 411 Ba2MnZnFe12022 (MnZnY) 407, 425 BasMg2Ti3Fex2031 (Mgz-18H) 410, 411, 420, 421 BasMgZnTi3Fe12031 (MgZn-18H) 420 Ba(NO3)2 468, 520, 521, 528 BaNil.sAlmsO17.sF15 386 BaNio 5Gan.sOls.sFo5 386 BaNio.sZn2A19.5016.sFz5 385 BaNixAl12-xO19-~Fx 385 BaNixFel2 xO19-xFx 385 BaNi2Fe16027 (Ni W) 405 BaNi2Al~Fe16-xO27 (NiA1W) 435 BaNiFeFe16027 (NiFeW) 406, 411 BaNio.sZno5FeFea6027 (Nio.sZno5FeW) 406 Ba2NiZnFe12022 (NiZnY) 413 Ba2Ni2Fe120~ (Ni2Y) 406, 411, 414 BaO 449, 450, 454, 455, 467, 468, 472, 473, 488, 522-524 BaO.4.6AI203 535
BaO-6AI203 444, 535 BaO.6.6A1203 535 BaO-CaO-Fe203 454 (BaO)x (CaO)l-x- nFe203 457 BaO-Fe203 449, 451~454, 458, 522 BaO-FeO-Fe203 454 BaO-FeO-7Fe203 308, 453, 454, 456, see also BaFelsO23, BaO-MeO.7Fe203 and X 3BaO.4FeO- 14Fe203 454 BaO.FeO.3Fe203 308 BaO.Fe203 (B) 308-310, 449-454, 456, 458, 468, 472, 474, 488, 522, see also BaFe204 and BF BaO.2Fe203 (T) 308, 309, 316, 321, 456, see also BF2 and T BaO.4.5Fe203 452 BaO-5Fe203 452 BaO-5.3Fe203 498 BaO@Fe203 453 BaO.5.5Fe203 529 BaO-5.6Fe203 484 BaO.5.9Fe203 498 BaO.6Fe203 30%366, 444, 449-453, 456, 461, 464, 468, 472, 475, 488, 522, see also BaFe12019 and BaM BaO-nFe203 449, 453 2BaO.Fe203 308 2BaO.3Fe203 308, 312, 313 3BaO.Fe203 308 5BaO.Fe203 308 5BaO.TFe203 308 7BaO.2Fe203 308 3BaO.4FeO. 14Fe203 308 BaO.Fe203-Fe203-S 456 BaO-Fe203-MeO 454, 456 BaO-Fe203PbO--SrO 461 BaO-Fe203-SiO2 457 BaO-Fe203-SrO 461 BaO-Fe203-ZnO 454 BaO-2Fe203-8Fe203 (Ba-Fe-W) 308, 311,312 BaO2 468 Ba(OH}2 468, 488, 517, 519, 521 BaO-MeO-Fe203 307, 308 BaO.MeO-3Fe203 456, see also Y BaO.MeO.7Fe203 456, see also X BaO.2MeO-8Fe203 456, see also W 2BaO-MeO-9Fe203 456, see also U 2BaO.MeO- i3Fe203 456 3BaO-MeO- 19Fe203 456 3BaO.2MeO.12Fe203 456, see also Z BaO-PbO-Fe203 367, 368 BaO-SrO-Fe203 367, 368 BaSO4 519, 523 Ba(SbFe)12019 382
MATERIALS INDEX B aSbo.sFeZ+oFe3~.5Oa9 382 BaSc~Fe~z-xO19 375 Bao.2Sro.sFe12019 575 Bao.4Sro.6Fea2019 575 Bao.6Sro.4Fe12Oa9 575 Bao.vsSro.zsFe12O19 367 Bao.sSr0.2Fe12019 575 Bal-xSr~Fea2Oa9 443, 461 (Ba, Sr)(Fe, A1, Ga)12019 535 BaTiO3-5Fe203 380 • 2+ + BaT10.6Fe 0.?,Fe310.8019 382 BaZn2A12Fe12027 405 BaZn2AIxFe12-~O27 405 BaZn2Fe16027 (Zn2W) 404, 412, 422 BaZnFeFe16027 (ZnFeW) 406, 411 Ba2Zn2Fe1202z (Zn2Y) 404, 407, 410, 411, 414, 425, 427, 429 Ba3Zn2Fe24041 (ZnzZ) 407, 408, 411, 429, 430, 433 Ba2Zn2Fe28046 (Zn2X) 409, 411,414, 416, 418, 433 Ba4Zn2Fe36Oeo (ZnzU) 409, 410, 414, 419, 430, 433 Ba4Zn2Fe52084 401 BaZn2GaFexsO27 405 BaZn2Ga3Fe13027 405 BasZn2Ti3Fe12031 (Zn2-18H) 410, 411, 419421 BaZn~/2Gex/2Felz-x019 380 BaZn~/2Ir~/2Fe12-~O19 380, 381 BaZnz~/3Nb~/3Fe~z xO19 380 BaZnzx/3Tax/3Felz-xOa9 380 BaZn~/zTi~/2Fe12 ~O19 381 BaZnxTiyMn~Felz-x-r-zO~9 380 BaZn2~/3V~/3Fea~-~O19 380 Ba-Zn-W 317 Ba-Zn-Y 317 Ba-Zn-Z 317 Bi~O3 500, 519, 522 C-steel 45 CO 477 CsH~2 477 CaAI~20~9 370 Ca(AIFe)~20~9 370 CaFesO13 454, 459 Cao.88Lao.~4Fe~zO~9 366, 367 Ca~_xLaxMnO3 616 CaO 461, 467, 519 CaO-6AI~O3 444, 475 CaO-AI~O3-Fe203 375 CaO-Fe~O3 462 CaO-Fe~O3-SrO 458 (CaO)~_~(SrO)x •nFe~O3 459
847
CaSiO3 503 CdxCol-xCr2S4 717 CdCr2S4 607, 612-615, 647,-650-654ff, 675 CdCr2Se4 697, 608, 613-615, 641, 647, 650653, 675ff CdCr2(S~-xSe~)4 696 CdCrz-xlnxS4 656 CdCrl.sTi0.2S4 656 CdCrI.sV0.2S4 656 Cdl-xCuxCr2Se4 679 CdFe204 260, 286 CdxFel-xCr2S4 656, 707, 715-717 Cdx_xFexCr2Se4 677 Cd0.98Ga0.02Cr284 657 Cdl-xGaxfr2Se4 678, 679, 682 Cdl-xHgx Cr2S4 694 Cdl-xHg~Cr2Se4 696 Cdln2S~: Cr3+ 659, 662 Cdl-xlnxCr2S4 655, 656 Cdl_xlnxCr2Se4 652, 675, 680-683, 686 Cdo.sluo.2Cr1.80C00.2S4 656 Cdo.8In0.2Cra.80Ni0.2S4 656 CdMnzO4 215 CdxZn~-xCr2Se4 695 CI 465, 466 Co 52, 762ff, 773, 776ff, 789, 790 Co alloys 766, 768, 771,772, 776, 799 Co-steel 45 Co~ 467, 472, 473, 476, 477, 498, 501, 518, 520, 523 Co-Cr, Co-Ti and Cu-Ti substituted M-type compounds 353, 354 COA1204 225, 261 CoCo2-2xMn2xOa 216 CoCrz-xlnxS4 725 CoCr2-2xMnzxO4 216 CoCr204 284, 286 CoCrxRh2-xS4 729-731 CoCr2S4 611, 613-615, 701, 703, 711ff CoCr2S4-xSex 726 ColaCrl.sSn0.1S4 714 COl_xfuxfr2S4 721,728 Coi-x (CUl/2Fel/z)xCr2S4 718 COl-xCuxRh2S4 728, 734, 735 Co~Fex-~Cr2S4 707, 714 CoFe204 196, 197, 220, 231, 242, 258, 276, 286, 288, 289, 291,296, 298 CoxFe3-xO4 248, 250-252, 269, 273, 282, 294 CoFe204 :Ti 270, 271 COl-xFe~Rh2S4 729, 730 CoFeVCr 578, 582 Co2GeO4 195, 197, 199 Coln2S4 723 CoMn204 215
848
MATERIALS INDEX
CoxMnl-xFe204 244 CoNiZn ferrite 251 COl-xNixCrzS4 722 Co304 220, 614, 626 CoRhl.5Feo.504 284 CoRh2S4 608, 612, 614, 615, 728 Co354 612, 614, 728, 736 CoS7 616 Co7/3Sb2/304 195 CozSiO4 199 CozTiO4 197 Co0.zZnl.sSnO4 205 Coo.2Znl.sTiO4 205 Cr substituted M-type compounds 353, 354, 368-375 CrAI2S4 656 CrFeCo 578, 579, 582 Crln2S4 656 CrMn204 213 CrO2 638 CrTe 616 Cu 620 CuA1Sz 618 CuA1204 205 CuCO3 620 CuC1 620 CuC12.2H20 620 CuCozS4 612, 614, 615, 619, 624ff, 736 CUCOxRhz-xS4 626ff CuCoTiS4 624ff CuCr204 215, 224, 286, 618, 620 CuCr2S4 607, 608, 611-615, 618-620, 630ff, 701 CuCr2S4-xClx 644 CuCr2S4_~Se~ 643 CuCr2Se4 607, 608, 612-615, 618-620, 630, 631, 636tt CuCr2Se4-xBr~ 645, 673 CuCr2Sea-xClx 644 CuCr2Se4_~Te~ 644 CuCr2Te4 607-609, 613-615, 618-620, 630, 631, 637, 641ff Cu~+~Cr2Te4 641ff CuCr2Te4_~I~ 645 CuCr2-~RhxSe4 636ff CuCr0.3Rhl.7-xSn~Se4 636ff Cufr2-x SnxS4 630ff CUfl'l.9Sn0.1Se4 641 CuCr2 ~TixS4 630tt CuCr2-~V~S4 630ff CuFe204 213, 215, 243, 258, 259, 269, 289, 291, 296, 618 CuFel.vCr0.304 213 Cu~Fel xCr2S4 698, 710, 718ff, 728, 732, 733 Cul/2Fel/2Cr2S4-~Se~ 726
CuxFea-xRh2S4 608, 698, 701, 728, 732, 733 Cul/zGamCr2S4 698ff Cul/zGal/zCrzSe4 698ff CuGa204 2O5 ChaxHgl-xCrzSe4 691 CumInmCr2S4 622, 698ff, 715 Cu0.5+xIn0.5-xCr2S4 700 CumInmCr2Se4 641, 698ff (C'umlnl/2)xFel_xCr2S4 715 CuxMl-xCr204 (M = Cd, Co, Mg, Zn) 216 CuMg0.sMnl.504 225 CuxMnl-~Cr2S4 718 Cul-xNixCr2S4 722 CuNiFe 578, 582 CuNi0.sMnl.504 195, 225 CuO 620 Cu20 620 CuRhMnO4 195 CuRh204 215, 225 CuRh2S4 612, 614, 615, 618, 619, 625, 626ff, 641 CuRh2Se4 613-615, 618, 619, 615~17ff, 641 CuRh2(Sl_xSe~)4 626 CuRh2_~SnxSe4 624, 627ff CuSO4-5H20 620 Cu2Se 620 CuTi2S4 610, 614, 615, 619, 620tt, 623, 625 CuV2S4 610, 614, 615, 618, 619, 621, 622ff, 625 Cu0.2Zn0.4Cd0.4Al204 205 Cu~Znl_xCr2Se4 672, 673 CuZn ferrite 275 CuZnGeO4 205 Dy 98 DyNi3 799 Dy3A12 98 F, see Fe203, BxFy, and PxFy Fe 53, 56, 63, 64, 77, 78, 80, 762ff, 773, 775, 776tt, 788, 790, 792 Fe alloys 766, 769, 771, 772, 779, 783, 787ff, 797tt Fe(CI-I3COO}2 519, 521 FeC204 519, 521 Fe(CO)5 467, 534 FeCI2 464 FeCI3 520, 524 FeCo 64 Fe~Col_~Cr204 216 FeCr2-xInxS4 724, 725 FeCr204 215, 285, 287 Fe3-xCrxO4 214 FeCrzS4 607, 608, 611,613-615, 701, 702, 706ff Fel+xCr2-xS4 726
MATERIALS INDEX FeCr2S4-xSex 726 FeCrxRh2_x$4 730 FeL1CrI.sSn0.1S4 711 Fel-sCusFel+sCuz~Ml-2~-804 (M= Co, Mg, Ni) 216 Fe2GeO4 199, 286 FeIn2S4 723 FeMnzO4 215 Fe(NO3)3 519-521 Fe-Ni-A1 alloy 45 Fe2NiA1 111 Fel-~Ni~CrzS4 722 FeO 201 FeO2 459 FeOOH 515, 521, 525 Fe203 195, 201, 444, 448-469, 471-477, 487, 499, 514-516, 519, 520, 522-525, 528, 533, 534 Fe203-2(FeO2)-SrO 459 Fe203-MeO-SrO 458 Fe203-PbO 449, 459-461, 522 Fe203-SiO2-SrO 459 Fe202~SrO 449, 457, 458, 522 Fe203-SrO-ZnO 458 Fe304 196, 197, 200, 201, 212, 213, 220, 231, 232, 235, 242, 258, 259, 262ff, 269, 270, 277, 278, 286, 287, 289, 291, 292, 296, 311, 451, 452, 457, 458, 462 Fe304: Mn 255 Fe304 : Zn 254 FeRhzS4 612, 729 FeS2 465, 467, 701 FeSO4 525 Fe2SiO4 199 Fe3S4 726 FeTiO3 467 Fe2TiO4 195, 227 Fe3-xTixO4 244 FeVzO4 196, 215, 262 Gal/2Li1/2Cr284 698ff Gd 775 GeCo204 224 GeFe204 206, 224, 225 GeNi204 224, 225 HC1 464-466, 471 H2504 466 hexaferrite 39, 49, 55 HgCr2S4 607, 612-615, 650, 652, 666ff HgCr2Se4 607, 613-615, 650, 652, 691ff HgCrz-xInxSe4 691, 692 Hgl xInxCrzSe4 692 HgxZnl xCr2Se4 696
Inl/2LimCr2S4
849 698ff
KCI 523, 524 KOH 524 K2SO4 522, 523 La(Co, Ni)5 98 LaFe2+Fe3i~O19 366, 367 LaFe12019 354, 366, 367, 368 LaMgGanO19 369, 370, 375 La203 462 LaxSrl_xMnO3 616 Lio.sAlzsO4 204, 219, 286 LiCO3 500 LiF 476 Lio.5Feo.sCr204 212 LiFeO2 476 LiFesO8 476 Lio.sFezsO4 195, 212, 220, 229, 231, 235, 238, 242, 251, 257, 260, 269, 271, 277, 282, 283, 287-289, 291, 296, 298 Lio.sFe2.504:Mn 255 Lio.sGazsO4 206, 219 Lio5Mnz504 195 LiV204 195, 261, 262 M 449-458, 460, see also BaFel2019, SrFe12O19 and PbFe12019 MS 456, see also W M2S 456, see also X MaS 456 M6S 456 MY 456, see also Z M2Y 456, see also U 2MeO-BaO-8F~O3 (2MEW) 307, 312, 316 2MeO.2BaO.6FezO3 (3MeY) 307, 309, 316 2MeO.3BaO.12Fe203 (2MeZ) 307, 309, 316 2MeO.2BaO-14Fe203 (3MeX) 307, 309, 312 2MeO.4BaO.18FezO3 (MeU) 307, 309 MeO.Fe203 309, 321,456 MgAI204 191, 197, 204, 206, 219, 260, 261, 284, 286, 287, 289, 295 MgCr204 225, 245, 648 Mga-xFexAleO4 290 Mg ferrite 252, 253, 270, 295 MgFe204 197, 209, 210, 220, 239, 242, 251, 257-259, 277, 279, 283, 288, 289, 291, 296, 298 MgFe204 : Mn 272 MgGa204 375 MgxMno.6Fez4 xO4 239, 242 MgMn204 210, 215, 269 MgO 201, 205, 499 Mg2SiO4 199
850
MATERIALS INDEX
Mg2TiO4 196, 204 MgV204 225, 262 Mg2VO4 199 MnA1 55, 89, 94 MnAIC 578, 580 MnA1204 220, 225 MnBi 578, 579 MnCr ferrite 255 MnCr204 196, 230 Mnl+2xCr2_2xO4 214, 216, 246 IVlnCrz-xInxS4 723 MnCr2S4 607, 611, 613-615, 701ff, 724 MnCr2S4-xSe~ 726 MnCr2-~VxS4 725 MnFeCrO4 230 MnFe204 196, 197, 209, 210, 230, 233, 242, 258, 259, 269, 276, 286, 289, 291, 296, 298 Mn~Fe3-xO4 213, 220, 238, 250, 253-256, 259, 260, 269-271, 273, 278, 280, 282, 293, 294 Mnln2S4 722, 723 MnMg ferrite 255, 259 Mnl-xNixCrzS~ 721,722 Mn203 195, 215, 466 Mn304 215, 224, 286 MnRh204 225 MnSb 616 MnV204 245, 262 Mn0.6Zn0.4Fe204 220 MnZn ferrite 255, 258, 259, 275 MoAg204 195 NH3 518, 520 NI-I40H 517, 519, 520 (NH4)2CO3 517, 519, 520 Na2CO3 517, 519, 510, 522, 523 NaC1 523, 524 NaF 476 NaFeO2 522, 523 Na20 524 Na0.sLa0.sFe12019 366, 367 Na2Mn2Si207 204 Na20.11AIzO3 444 NaOH 517, 520, 521, 524 NaSO4 522, 523 NazWO4 261 Nd203 462 Ni 762ff, 764, 773-776ff, 783, 788, 790, 792 Ni alloys 766ff, 772, 775, 777ff, 781ff, 786ff, 791,796ff NiAI204 261 NiCo ferrite 251 NiCo.eS4 612, 614, 736 NiCr2-xInxS4 725 NiCr204 205, 215, 285, 287
NiCrxRh2 xS4 731, 732 NiFeCo ferrite 251, 272 NiFe, Cr2_~O4 213 NiFe204 195-197, 235, 242, 257-259, 275-277, 279, 281, 286, 288, 289, 291, 296, 298 NixFe3-xO4 252, 253, 258, 259, 269-271, 282, 292, 293 NiFe2 xVxO4 228 Ni2GeOa 199, 286 Niln2S4 723 NiMn204 210 NiO 281, 499 NiRh204 215, 225 NiRh2S4 612 Ni2SiO4 199 Ni-Ti substituted M-type compound 354 NiZnCo ferrite 251 NixZnl-xCr204 285, 287 NixZnl-xCr2S4 721, 722 NiZn ferrite 243, 270, 271, 275-277, 290 PbO and PxFr PF2 460, 461, 477 PzF 460, 461, 477 PbAlxFe12-xO19 374 Pb(C2H5)4 534 PbCO3 529, PbF2 529 PbFe7.sMn3.sAlii.sTi0.sO19 444, 574 Pb2FelsMn7(A1Ti)O38 307 PbFe12019 443, 534, s e e a l s o PbO-6Fe203, PbM and M PbM 450, 536, 537, 551, 569, 574, 575, s e e a l s o PbFe12019, PbO.6FezO3 and M Pb(NO3)2 520 PbO 449, 450, 460, 461, 468, 471, 477, 507, 514, 522, 529 PbO-2Fe203 313, 315 2PbO.2Fe203 314, 315 PbO.2.5Fe203 461 PbO.!~Fe203 461 PbO-5Fe203 315, 459, 461,501 PbO.6Fe203 307-366, 444, 449, 450, 461, 464, 477, 527, 532 PbO-nFe203 449 Pd 790 Pd based alloys 775, 793ff Pt based alloys 795 PtCo 578, 579 P, see
RE-alloys 49 RE-Co 580, 582 RECo5 578, s e e a l s o SmCos RE(Co, Cu, Fe, Mn)x 578, 579
MATERIALS INDEX S 456, s e e SrO and SxFy SF 458, 459, 476 SF6 459, s e e a l s o SrFe12019 and SrO.6Fe203 S2F 457, 459, 476 S3F 457, 459 $3F2 458, 459 $4F3 457-459, 477 87F5 457-459, 461,477, 522 SO2 467 SiC 526, 531 Si3N4 527 SiO2 457, 459, 462, 464, 465, 467, 498-503, 514, 519, 522 SmCo5 45, 55, 67, 81, 83, 88, 103, 490 SmCo5.3 81 Sm2Co17 83 Smz(Coo.85Feo11Mn0.04)17 45 SnO2 499 SrAI3.8Fes.20|9 374 SrAl4.aFe7.2Ol9 374 SrAl12019 370, 458, s e e a l s o SrO-6A1203 SrAlxFe12 1019 355, 368-375 Sr(AsFe)12019 382 SrCH3(CH2)10COO2 477, 519 SrCO3 463, 467, 476, 477, 515, 516, 519, 520, 522-525, 533 SrCr6Fe6019 370 SrCrxFe12-xO19 368-375 Sr(Cu + Ge)xFe~2 xO19 383 Sr(Cu+Nb)xFe12_xO19 383 Sr(Cu+ Si)~Fe12-xOa9 383 Sr(Cu+Ta)~Fe12-xOa9 383 Sr(Cu+V),Fe12 xO~9 383 SrFeO3 x 314, 458, 459, 476, 477 SrFesA14019 535 SrFel2019 443, 448, 457-459, 479, 519, 522524, s e e a l s o SrO-6Fe203, SrM and M SrFe18027 457, 458, s e e a l s o W Sr-Fe-W 311, 313, 314 Sr-Fe-X 313, 314 Sr2FeO4-/ 459 Sr3Fe207-~ 459 Sr4Fe3Om-x 459 SrGaxFe12-~O19 368-375 SrGal2019 370, 375, 535 Sr-hexaferrite 55 SrM 450, 536, 537, 551-553, 566, 570, 571, 573-575, s e e a l s o SrFe12019, SrO-6Fe203 and M Sr(NO3)2 519, 520 SrO 449, 450, 457-459, 467, 468, 519, 522 SrO.6A1203 4 4 4 , s e e a l s o SrAl12019 SrO.2FeO-8Fe203 311-314, 457, s e e a l s o W SrO-FeO.7Fe203 458, s e e a l s o X
851
SrO.4.2Fe2Oy 1.8AlzO3 355 SrO-4.5Fe203.1.5A1203 355 SrO.5.5Fe203 501 SrO.5.9FeeO3 501 SrO-6Fe203 307, 366, 444, 449, 461, 464, 476, 522, s e e a l s o SrFe12019, SrM and M SrO.nFe203 449 3SrO.2Fe203 313, 314 Sr0.75Pb0.25Fe12019 368 SrO-PbO-Fe203 367, 368 SrSO4 519, 520, 523 Sr(SbFe)12019 382 T 456, s e e a l s o BaO.2Fe203 and BF2 Th(Co, Ni)5 98 Ticonal G 45 Ticonal GG 45 Ticonal II 45 Ticonal XX 45, 54 TiFe204 235, 285, 287 TiO2 464, 499, 519 T10.sLao.sFe12019 366-368 U
454, 456, 473,
see
2MeO.4BaO. 18Fe203
V205 499 W
450, 451, 454, 456-458, 2MeO-BaO-8Fe203 W-steel 45 X 450-454, 456-458, 461, 2MeO.2BaO- 14Fe203
461,
see
also
see also
Y
454, 456, 461, 473, s e e a l s o 2MeO-2BaO.6Fe203 Y(Co, Ni)s 98 YCos 81 Y3AI5012 204 Y3FesO12 251, 277-279, 281-283 Z
454, 456, 473, s e e a l s o 2MeO-3BaO. 12Fe203 ZnAlxCr2 xO4 285 ZnA1204 242, 260, 261 ZnCo204 626 ZnCr204 196, 285, 287, 608, 614, 647 ZnCr2-2,Mn2xO4 216 ZnCr2S4 608, 611, 613-615, 647, 652, 653ff ZnCr2Se4 608, 613-615, 647, 649, 650, 652, 653, 669tt ZnCr2(Sl-xSex)4 696 ZnCr2(Sea-xTe,)4 696 ZnFe2-2xMn2xO4 216
852
MATERIALS INDEX
ZnFe204 195--197, 225, 260, 285, 286, 288, 289, 298 ZnxFe3 xO4 270, 271 ZnGa204 204, 206, 219, 242, 284 ZnGa204 : Cr 3+ 648, 651 Zn-Ge, Zn-Ti and Zn-Zr substituted M-type compounds 353, 354 Zn2GeO4 198, 199 ZnLiSbO4 212 ZnxMl-xFe203 (M=Co, Fe, Li0.sFe0.5, Mn, Ni) 228
Zn~-xMnxCr2Se4 673 ZnMn204 215, 225, 286 ZnMn2Te4 609 ZnNbLiO4 195, 212 ZnNiSnO4 205 ZnO 534 ZnRh204 285 Zn2TiO4 204 ZnV204 262 ZrO2 526, 529, 530