Handbook of Magnetic Materials, Volume 6

Handbook of Magnetic Materials, Volume 6 Elsevier, 1991 Edited by: K.H.J. Buschow ISBN: 978-0-444-88952-2

by kmno4

PREFACE TO VOLUME 6 The Handbook of Magnetic Materials has a dual purpose. As a textbook it is intended to help those who wish to be introduced to a given topic in the field of magnetism without the need to read the vast amount of literature published. As a work of reference it is intended for scientists active in magnetism research. To this dual purpose, the volumes of the Handbook are composed of topical review articles written by leading authorities. In each of these articles an extensive description is given in graphical as well as in tabular form, much emphasis being placed on the discussion of the experimental material in the framework of physics, chemistry and materials science. The original aim of Peter Wohlfarth when he started this Handbook series was to combine new developments in magnetism with the achievements of earlier compilations of monographs, to produce a worthy successor to Bozorth's classical and monumental book Ferromagnetism. It is mainly for this reason that Ferromagnetic Materials was initially chosen as title for the Handbook series, although the latter aims at giving a more complete cross-section of magnetism than Bozorth's book. Here one has to realize that many of the present specialized areas o1' magnetism were non-existent when Bozorth's book was first published. Furthermore, a comprehensible description of the properties of many magnetically ordered materials can hardly be given without considering, e.g., narrow-band phenomena, crystal-field effects or the results of band-structure calculations. For this reason, Peter Wohlfarth and I considered it desirable that the Handbook series be composed of articles that would allow the readers to orient themselves more broadly in the field of magnetism, taking the risk that the title of the Handbook series might be slightly misleading. During the last few years magnetism has even more expanded into a variety of different areas of research, comprising the magnetism of several classes of novel materials which share with ferromagnetic materials only the presence of magnetic moments. Most of these areas can be regarded as research topics in their own right, requiring a different type of expertise than needed for ferromagnetic materials. Examples of such subfields of magnetism are quadrupolar interactions and magnetic superconductors. Chapters dealing with these materials were included in Volume 5 of this handbook series, which appeared in 1990. In the present Volume it is primarily

vi

PREFACETO VOLUME 6

the Chapter on quasicrystals that has not much in common with ferromagnetism. Magnetic semiconductors, to be considered in Volume 7, is a further example of a class of materials with properties distinctly different from those of ferromagnetic materials, and the same can be said of substantial portions of the materials considered in the remaining Chapters of Volume 6. This is the reason why the Editor and the Publisher of this Handbook series have carefully reconsidered the title of the Handb o o k series and have come to the conclusion that the more general title Magnetic Materials is more appropriate than Ferromagnetic Materials. At the same time this change of title does more credit to the increasing importance of materials science in the scientific community. The task to provide the readership with novel trends and achievements in magnetism would have been extremely difficult without the professionalism of the NorthHolland Physics Division of Elsevier Science Publishers and I would like to thank A. de Waard and P. Hoogerbrugge for their great help and expertise. K.H.J. Buschow

Philips Research Laboratories

CONTENTS Preface to V o l u m e 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C o n t e n t s o f Volumes 1-5 List o f c o n t r i b u t o r s

..............................

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. M a g n e t i c P r o p e r t i e s o f T e r n a r y R a r e - e a r t h T r a n s i t i o n - m e t a l C o m p o u n d s H.-S. L I a n d J . M . D . C O E Y . . . . . . . . . . . . . . . . . . . . . . . . . . 2. M a g n e t i c P r o p e r t i e s o f T e r n a r y I n t e r m e t a l l i c R a r e - e a r t h C o m p o u n d s A. S Z Y T U L A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. C o m p o u n d s o f T r a n s i t i o n E l e m e n t s with N o n m e t a l s O. B E C K M A N a n d L. L U N D G R E N .................... 4. M a g n e t i c A m o r p h o u s A l l o y s P. H A N S E N . ..................... . ........... 5. M a g n e t i s m a n d Q u a s i c r y s t a l s R.C. O ' H A N D L E Y , R . A . D U N L A P a n d M . E . M c H E N R Y . . . . . . . . 6. M a g n e t i s m o f H y d r i d e s G . W l E S I N G E R a n d G. H I L S C H E R ....................

v vii ix xi

1 85 181 289 453 511

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

585

Subject I n d e x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

635

Materials Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

643

vii

CONTENTS OF VOLUMES 1-5 Volume 1 I. 2. 3. 4. 5. 6. 7.

Iron, Cobalt and Nickel, by E.P. Wohlfarth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dilute Transition Metal Alloys: Spin Glasses, by J.A. M y d o s h and G.J. Nieuwenhuys . . . . . . Rare Earth Metals and Alloys, b y S. Legvold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rare Earth Compounds, b y K . H . J . Buschow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Actinide Elements and Compounds, b y W. Trzebiatowski . . . . . . . . . . . . . . . . . . . . . . . . Amorphous Ferromagnets, b y E E . L u b o r s k y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetostrictive Rare Earth-F% Compounds, by A . E . Clark . . . . . . . . . . . . . . . . . . . . .

1

71 183 297 415 451 531

Volume 2 1. 2. 3. 4. 5. 6. 7. 8.

Ferromagnetic Insulators: Garnets, b y M . A . Gilleo . . . . . . . . . . . . . . . . . . . . . . . . . . . . Soft Magnetic Metallic Materials, b y G.Y. Chin and J.H. Wernick . . . . . . . . . . . . . . . . . . Ferrites for Non-Microwave Applications, b y P.L Slick . . . . . . . . . . . . . . . . . . . . . . . . . Microwave Ferrites, b y J. Nicolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystalline Films for Bubbles, b y A . H . Esehenfelder . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amorphous Films for Bubbles, b y A . H . Esehenfelder . . . . . . . . . . . . . . . . . . . . . . . . . . . Recording Materials, b y G. B a t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferromagnetic Liquids, by S . W . Charles and J. Popplewell . . . . . . . . . . . . . . . . . . . . . . .

1

55 189 243 297 345 381 509

Volume 3 1. Magnetism and Magnetic Materials: Historical Developments and Present Role in 2. 3. 4. 5. 6. 7. 8. 9.

Industry and Technology, by U. Enz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permanent Magnets; Theory, b y H. Ziflstra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Structure and Properties of Alnico Permanent Magnet Alloys, b y R . A . M c C u r r i e . . . . . . Oxide Spinels, b y S. Krupidka and P. Novd*k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Properties of Hexagonal Ferrites with Magnetoplumbite Structure, b y H. Kojima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Ferroxplana-Type Hexagonal Ferrites, b y M . Sugimoto . . . . . . . . . . . . . . . . Hard Ferrites and Plastoferrites, b y H. Stiiblein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulphospinels, b y R . P . van Stapele . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transport Properties of Ferromagnets, b y L A . Campbell and A. Fert . . . . . . . . . . . . . . . .

ix

1

37 107 189 305 393 441 603 747

x

CONTENTS OF VOLUMES 1-5

Volume 4 1. 2. 3. 4. 5.

Permanent Magnet Materials Based on 3d-rich Ternary Compounds, b y K . H . J . Busehow Rare Earth-Cobalt Permanent Magnets, b y K . J . Strnat . . . . . . . . . . . . . . . . . . . . . . . . . Ferromagnetic Transition Metal Intermetallic Compounds, b y J.G. Booth . . . . . . . . . . . . . Intermetallic Compounds of Actinides, b y V. Sechovsk~ a n d L. Havela . . . . . . . . . . . . . . . Magneto-optical Properties of Alloys and Intermetallic Compounds, b y K . H . J . Buschow . . .

1

131 211 309 493

Volume 5 1. Quadrupolar Interactions and Magneto-elastic Effects in Rare-earth Intermetallic Compounds, 2. 3. 4. 5. 6.

b y P. M o r i n a n d D. S e h m i t t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magneto-optical Spectroscopy of f-electron Systems, b y W. R e i m a n d J. Sehoenes . . . . . . . . INVAR: Moment-volume Instabilities in Transition Metals and Alloys, b y E . E Wasserman . Strongly Enhanced Itinerant Intermetallics and Alloys, b y P . E . B r o m m e r and J . J . M . Franse . First-order Magnetic Processes, b y G. A s t i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Superconductors, b y O. Fischer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

133 237 323 397 465

chapter 1 MAGNETIC PROPERTIES OF TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

Hong-Shuo LI and J. M. D. COEY Department of Pure and Applied Physics Trinity College, Dublin 2 Ireland

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991

CONTENTS 1. I r t r o d u c t ! o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. C o m p o u n d s w i t h s t r u c t u r e s r e l a t e d fo N a Z n 1 3 . . . . . . . . . . . . . . . . . 3. C o m p o u n d s w i t h s t l u c t u r c s r e l a t e d fo T h M n 1 2 . . . . . . . . . . . . . . . . . 3.1. O y s l a l s t r u c t u r e . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. A l l o ) s r i c h in F e o r C o . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 M a g n e t i c p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . . 3.2.1.1. N o n m a g n e t : c ~are e a r t h s . . . . . . . . . . . . . . . . . 3.2.12. M a g n e t i c r a r e e a i t h s . . . . . . . . . . . . . . . . . . . 3.2.2. Ce ercivi~y . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. A l l c y s rich in A1 . . . . . . . . . . . . . . . . . . . . . . . . . .

3 4 6 6 8 8 13 22 31 33

3.3.1. RT4AI8 . . . . . . . 3.3.2. R F e 5 A17 . . . . . . . 3.3.3. RT6A16 . . . . . . . 4. C o m p o u n d s w i t h , t l u ~ t u r e s r e l a : e d fo 4.1. R T 9 S i 2 . . . . . . . . . . 42. RTloSiCo.5 . . . . . . . . 5. C o m p o u n d s w i t h s t l u c t u r e s r e l a t e d lo 5.1. R 2 T 1 7 C 3 _ ~ . . . . . . . . 5.2. R 2 T l v N 3 - ~ . . . . . . . . 6. C o m p o u r d s w i t h s t l u c t u r e s 1elated ~o 6.1. R T 4 B . . . . . . . . . .

34 39 40 41 41 42 43 43 46 49 50

. . . . . . . . . . . . . . . . . . . . . . . . . . . BaCdl~ . . . . . . . . . . . . . . . . . . . . . . . . T h 2 Z n l v o r ~/h2Nil7 . . . . . . . . . . . . . . . . . . CaCu 5 . . . . . . . . . . . . . . .

. . . .

. . . .

. . . . . . .

. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .

62. R3CollB4, R2CoTB 3 and RCoaB z . . . . . . . . . . . . . . . . . . . 6.3. C e T P t 4 (T = C u , G a , R h , F d e r P t ) . . . . . . . . . . . . . . . . . . . 7. C o m p o u n d s w i t h ~,tJuctures l e l a t e d fo C e N i 3 . . . . . . . . . . . . . . . . . 8. C o m p o u n d s w i t h | e r n a r y s t r u c l r r e t y p e s . . . . . . . . . . . . . . . . . . . 8.1. R 3 F e 6 2 B 1 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. R C o l 2 B6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. R 2 T 2 3 B 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. R 2 T 1 4 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. R T 6 S n 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. R1 +~T4B4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7. R 6 T l l G a 3 ~ n d N d 6 F e 1 3 S i . . . . . . . . . . . . . . . . . . . . . . 8.8. R 2 T l z P 7 a n d R C o s P 5 . . . . . . . . . . . . . . . . . . . . . . . 8.9. R A u N i 4 a r d C e l + x l n l _ x P t 4 . . . . . . . . . . . . . . . . . . . . . 9. C o n c l r s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54 55 55 56 56 56 57 58 64 65 67 69 71 71 75

1. Introduction

The magnetism of pure elements concerns the properties of about 20 metals, mostly from the 3d or 4f series. Binary intermetallic compounds are much more numerous. Magnetic binaries may involve one or both elements with magnetic moments (and even a few examples where both constituents are individually nonmagnetic, e.g., ZrZn/). Composition adds a further dimension, with many binary diagrams exhibiting ranges of solid solubility and a number of intermetallic phases, each with its particular structure. Sometimes, the distinction is a matter of site preference, e.g., ordered substitution of one quarter of the sites of the fcc structure leads to a Cu3 Autype structure (space group Pm3m) compound, whereas complete disorder produces an A75B25 fcc solid solution. The magnetic properties of binary intermetallic compounds, usually involving a 3d or 4f element, and sometimes both, have been reviewed by many authors (Taylor 1971, Wallace 1973, 1986, Buschow 1977, 1979, 1980, Kirchmayr and Poldy 1979, Buzo et al. 1991). Ternaries are at another level of complexity, with three elements and two composition variables. In magnetic ternaries, usually one or two of the constituent elements are magnetic. The structure is sometimes a specific ternary structure, unrelated to any known binary structure type (e.g., NdzFe14B). Otherwise, the ternary may be related to a binary by preferential occupation of one of the sites (e.g., CeCo3B/is related to CaCus by substituting B on the 2c sites of the latter structure). Degrees of preferential ordering of elements over the sites are possible; the extreme is a pseudo-binary, where two of the elements substitute at random over a set of sites, while the third has a unique site occupancy. Another way of generating a ternary structure from a binary is by introducing small interstitial atoms X, such as carbon or nitrogen in YzFe17X3_~, which are interstitial ternary phases. In the search for novel compounds, theories predicting the stability of intermetallic phases, like Miedema's 'macroscopic atom model' (de Boer et al. 1988c), Pettifor's structure maps (Pettifor 1988), and the structural stability diagrams of Villars (1985a,b) provide helpful guidelines. The parameter values which are assigned to the elements in these models give an impression of the chemical similarity of the elements. They are useful when trying substitutions in well-known compounds. Out of approximately 100 000 possible ternary systems, phase diagram information is available on fewer than 6 000 of them. Often, this information is far from complete, relating to only a single isothermal section or a limited compositional field. Therefore, it is

4

H.-S. LI and J. M. D. COEY

reasonable to suppose that many novel ternary structure types are still awaiting discovery. In the circumstances, it is inevitable that our knowledge of the magnetic properties of ternary compounds is far from complete. Some systems have been studied in great detail, others hardly at all. The systems of most interest magnetically involve a 3d element, and a 4f element, the other component being a metal or metalloid, particularly boron or carbon. Oxides and chalcogenides are generally nonmetallic, and they are treated elsewhere. Compounds with the Nd2Fe~4B structure are of particular importance, and they have already been discussed by Buschow (1988c). Here, in sections 2-7, we present in order of decreasing transition-metal content the magnetic properties of ternaries with structures related to a binary structure type. The true ternary compounds are discussed in section 8. Work on the magnetism of these compounds has often been inspired by the search for new materials for highperformance permanent magnets. The iron-rich ThMn12-structure compounds, the interstitial R2T17X 3_~ carbides and nitrides and the R 2 T~4C ternaries have all been studied with this in mind. Other ternary compounds of comparatively low transition-metal content are discussed by SzytuIa, chapter 2 in this volume.

2. Compounds with structures related to NaZn13 The cubic NaZnla structure (space group Fm3c) has Na on 8a, and Zn on 8b and 96i sites. The only rare-earth-transition-metal binary with this structure is LaCo13, which is ferromagnetic with a cobalt moment of 1.58#B and Curie temperature Tc = 1290K (Buschow and Velge 1977). Among the rare-earth-3d compounds it has the highest 3d-metal content and is of potential interest for application. The structure type can be stabilized for other 3d elements, including Fe and Ni, by substituting Si or A1. The cubic La(Fel_xSix)~3 phase is found to be formed for 0.12 < x < 0.19 (see table 2.1). Magnetic studies showed that Tc increases with x in this range (Palstra et al. 1983). For La(Fet~Sia) (x = 0.15), Tc is 230K and the average iron moment is 1.95#B. There is apparently no site preference of iron or silicon for the 8b site, so these alloys should be regarded as pseudo-binaries rather than ternaries. La(Nil~ Si2) is a Pauli paramagnet. La(Fet -xAlx)~3 compounds can be stabilized with x between 0.08 and 0.54 (Palstra et al. 1985). At high x values (0.38 < x ~<0.54), a mictomagnetic regime occurs with distinct cusps in the AC susceptibility at about 50 K. The large positive Curie-Weiss temperature 0 = + l l 0 K , indicates the presence of predominantly ferromagnetic exchange interactions. With the decrease of silicon concentration (0.14 < x ~<0.38), a soft ferromagnetic phase was found which at lower temperatures shows anisotropy effects related to re-entrant mictomagnetic behaviour (fig. 2.1). The Curie temperature increases with decrease of x up to a maximum Tc = 250 K and then decreases. When 0.08 < x ~<0.14, an antiferromagnetic order appears along with a sharp metamagnetic transition in external field of 4 T (Palstra et al. 1984). Ido et al. (1990a) have reported the studies on La(Cox_xAlx)13 with x up to 0.3,

TERNARY RARE-EARTH TRANSITION-METAL C O M P O U N D S

5

TABLE 2.1 Structural and magnetic data for La(Ta-xSixh3 compounds (T = Fe, Co or Ni), after Palstra et al. (1983). Compounds La(T1 _xSi:,)13

x

Tc(K)

Psa (#B)

Ref.*

LaFe~1.5 Sil.s LaFe11.2Sil.8 LaFeal.1 S i l . 9 LaFell.oSiz. o LaFelo.gSi2.1 LaFelo.8 Si2. 2 LaFe lo.5 Si2.5

0.115 0.139 0.146 0.154 0.162 0.169 0.193

198 211 219 230 234 245 262

2.08

1.85

[1] [1] 1-1] 1-1] 1-1] 1-1] [1]

LaCol3 LaCo 11.s Si1.5 LaColl Si2 LaColo.s Si2.s

0.000 0.115 0.154 0.193

1290

1.58 1.29 1.14 0.88

[1, 2] [1] [1] [1]

LaNilo Si2

0.154

4.2 K

1.95

~ = 2.5 x 10- 7 m s kg - 1

[1]

* References: [1] Palstra et al. (1983). 1-2] Buschow and Velge (1977). 12.0

i

i

11.8

o~ 11.6 (a) 11.4 I '.'

2 . 5

I ,.,

I '.'

I ,•,

2.0 [] []

~..-t 1.5 ~ 1.o

[]

[]

0.5 z

~8

[] •

i

,

,

i i

.

.

i

,

,

i i

(b ,

,

i

.

,

TN 200

lOO

T c u s p

(cl

o o.o

0.2

0.4

0.6

Fig. 2.1. Dependence on A1 concentration in La(Fel_xAlx)ls of (a) lattice parameter, (b) iron saturation magnetic moment and (c) the cusp temperature (solid triangle), the Curie temperature (solid circle) and the N6el temperature (solid square).

6

H.-S. LI and J. M. D. COEY

La(Col_x_rFe~Alr)13 with y = 0.15 and x up to 0.3, (Lao.TNdo.3)(Coo.TFeo.3)13 and La(Col_~Fe~)a3 with x up to 0.6. It is found that the N-substitution decreases the Co moment as well as the Curie temperature and the Fe-substitution increases the magnetization significantly, but decreases the Curie temperature. The magnetization at 77 K increases by 20% in La(Coo.ss-~FexAlo.~5)13 on Fe substitution of x = 0.4. These authors conclude that it is possible to produce a NaZn~3-type compound having a large magnetization, comparable to that of F e - C o alloys.

3. Compounds with structures related to ThMn12 3.1. Crystal structure Examination of numerous ternary Fe-rich R - F e - M alloys by means of X-ray or neutron diffraction has shown that the tetragonal ThMnt2 structure forms quite generally for RFe12_xMx when M = Ti, V, Cr, Mn, Mo, W, A1 or Si and x is in the range 1.0 ~<x ~<4.0 (Yang et al. 1981, de Mooij and Buschow 1987, Ohashi et al. 1987, 1988b, Wang et al. 1988, Bigaeva et al. 1987, Mfiller 1988, Buschow and de Mooij 1989). However, the RFe12 end-member does not exist for any rare earth. The ThMn12 structure, illustrated in fig. 3.1, is tetragonal with space group I4/mmm and Z = 2. The rare-earth atoms occupy the single 2a thorium site which has a high point symmetry, 4/mmm, while the transition elements are distributed over the three manganese sites, 8f, 8i and 8j. Iron atoms are found to occupy 8f and 8j site fully while the 8i site is populated by a mixture of Fe and M atoms. An exception occurs when M = Si. The Si atoms share the 8f and 8j positions with the Fe atoms in RFe10 Si2 (Buschow 1988a). The site occupancies were studied in RFeIoV2 compounds with R = Y, Tb or Er by Helmholdt et al. (1988) and Helmholdt and Buschow (1989) using neutron diffraction; in YFez~ Ti by Moze et al. (1988a) and Yang et al. (1988c) using neutron diffraction and in NdFeaoMo2 by de Mooij and Buschow (1988a) from a detailed X-ray structure determination. It follows from these results that Ti, V and Mo atoms have a strong preference to occupy the 8i sites, but the distribution of Fe and M atoms within the 8i sites seems to be disordered. Formally, it is this M site preference

a

(~2a

~ 8f

~ 8i

~ 8j

Fig. 3.1. Structure of ThMn12.

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

7

that justifies considering these compounds as ternaries rather than pseudo-binaries. A number of binary structures, the ThMn12 structure included, can be derived from the hexagonal CaCu5 structure (Yang et al. 1989a,b, Hu et al. 1990b). Replacement of Ca atoms by a dumbbell of Cu atoms leads to the different phases. When a third of the Ca atoms are thus replaced, one obtains the ThzZn17 or Th2Ni~7 structure, depending on the sequence of replacements. When half the Ca atoms are replaced, the ThMn~2 structure results. Then, half of the transition-metal atoms on 2c sites in the CaCus cell become equivalent to the substituting dumbbell atoms and together form the 8i site, one third of the atoms on 3g and the other half of the 2c atoms constitute the 8j site and the remaining atoms on 3g site form the 8f site. Figure 3.2 shows the structural relationship between ThzNil, z or ThMn~2 and CaCus. There is also a considerable resemblance between the ThMn~2 structure and the cubic Th6Mn23 structure (Johnson and David 1985, Solzi et al. 1989). The Fe-Fe nearest-neighbour distances range from 2.40 A for 8f-8f to 2.97 A for 8i-8i in YFel~Ti (Moze et al. 1988a). The number of nearest-neighbour sites for 2a are (0, 8, 4, 8), for 8f are (2, 2, 4, 4), for 8i are (1, 4, 5, 4) and for 8j are (2, 4, 4, 2), where the numbers in brackets refer to 2a, 8f, 8i and 8j site neighbours, respectively. The average Fe-Fe distances are 2.49, 2.69 and 2.57 A for 8f, 8i and 8j sites, respectively (Hu et al. 1989a). The structures observed for the various RFelz_~Mx compounds may be analysed in terms of metallic radii and enthalpy effects. The shortest R - T distances in the

b

a

(~

2b

~)

2d

•

4f

o ~ i

6g

(a)

®

12j

(D

12k

c b

~

© 2a { e 8f }

•

8

i-1

®

8 i-2

e

S j

a

(b)

Fig. 3.2. Schematic representation of the relationship between (a) the ThzNilT-type and (b) the ThMn12type structures and the CaCu s structure.

8

H.-S. LI and J. M. D. COEY

structure of RFe,z_xMx occur between R atoms and the T atoms at the 8i sites. Progressively larger R-T distances are involved for the 8f and 8j sites, respectively. Since the metallic radii of all of the M elements, except for Si, are substantially larger than that of Fe, one might have expected the M atoms to preferentially occupy 8j sites rather than 8i sites (Buschow 1988a). However, on the basis of average T-T distances, the 8i site is expected to be preferred over the 8f or 8j sites for T atoms larger than Fe. This latter argument seems to be in accord with the observed preferential occupancies in these systems, so it can be concluded that the distances between the transition-metal atoms play a critical role. It follows that Si, which is smaller than Fe, should prefer 8f and 8j sites rather than the 8i site. This is in fact observed in LuFeloSiz (Buschow 1988a). Enthalpy also plays a part in reinforcing the site preference. The difference in structure between RFeaoSi2 on the one hand and RFe,0T2 (T = Ti, V, Mo) on the other may be related to the fact that the heat of mixing between R and Si is negative and the heat of mixing between R and Ti, V or Mo is positive (Niessen et al. 1983). Since an R atom has only four nearest 8i-site neighbours compared with eight nearest 8f- and 8j-sites neighbours, it follows that the 8i sites have by far the smallest area of contact with the R sites. In view of the positive enthalpy contribution associated with R and Ti, V or Mo contents, one may expect therefore that the 8i site will be preferred by those three elements. The comparatively large negative heat of mixing between R and Si leads to an equally large stabilizing effect if the contact between the R and Si atoms is as large as possible. Hence, from enthalpy considerations, one would again expect the Si atoms to occupy the 8f and 8j sites (Buschow and de Mooij 1989). 3.2. Alloys rich in Fe or Co 3.2.1. Magnetic properties Lattice parameters and magnetic data for all the RFe12_xMx, RCo12_xMx and RFe,2 _,(M]-yM;')x compounds are listed in table 3.1. Some general features emerge from the mass of data on the iron series: (a) The average iron magnetic moment is observed to be 1.35#B--1.93~B depending on the specific M element. The iron compounds appear to be weak ferromagnets (Coey 1989). (b) Curie temperatures are in the range 400-650 K (except for the Mo series where they vary from 260-500 K), with the highest values for the Gd compound in each series. (c) The anisotropy due to the iron sublattice is uniaxial. The magnitude of K, (Fe) is a monotonic function of temperature, decreasing from 1.93 MJ m - a at 4.2 K to 0.89 MJm -a at room temperature for YFe**Ti (Li and Hu 1988). (d) The second-order crystal field coefficient A2o at the 2a, rare-earth site is negative and considerably smaller in magnitude than that found for either RCo5 or R2Fe,+B (Li et al. 1988a, Buschow et al. 1988a). This implies that the contribution to the uniaxial anisotropy is relatively small for those rare-earth ions, R = Sm 3 +, Er 3+, Tm 3+ and Yb 3+, having a positive second-order Stevens coefficient ~j. The room-temperature anisotropy field observed in all these RFe12_xM~ compounds is

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

9

TABLE 3.1 Structural and magnetic data for RT~z-xMx (T = Fe and Co) compounds with ThMn~2-type structure. Compounds NdFellTi SmFellTi GdFellTi TbFellTi DyFellTi HoFellTi ErFeilTi TmFell Ti LuFellTi YFellTi Ero.5 Smo.sFel~Ti CeFelo.sTil. 2 NdFelo.sTil.2 SmFelo.8 Til.2 GdFelo.sTil.2 ErFelo.sTil.2 YFelo.sTil.2 NdFeloTi 2 YFe!oTi 2 GdFelo.sTil.5 Gdl_xFelx+xTi Y(Feo.8 Coo.z)ilTi Y(Feo.s Coo.5)ll Ti Y(Feo.sNio.z)u Ti Y(Feo.gNio.1)lx Ti GdFesCo3Ti GdFesCo6Ti GdFe2Co9Ti DyFelo CoTi DyFe 8Co3Ti DyF%Co6Ti DyFezCogTi HoFe8 Co3Ti ErF%Co3Ti Ero.sSmo.sFesCo3Ti GdCollTi HoColiTi ErCollTi YCo11Ti SmFelo.s Sio.sTi SmFe~oSiTi SmFe9.5 Sil.sTi SmFe9 SizTi SmFes.8 Si2.2Ti SmFeio,s Alo.5Ti SmFelo A1Ti SmFe9.5 All.5 Ti SmFe9A12Ti SmFelo.2 Sio.sTi

a (A)

c (A)

8.5740 8.5572 8.5476 8.5372 8.5212 8.5056 8.4951 8.46 8.46 8.5028 8.507 8.543 8.594 8.561 8.523 8.494 8.509 8.584

4.9074 4.7994 4.7988 4.8078 4.7990 4.7986 4.7948 4.77 4.77 4.7946 4.784 4.787 4.793 4.792 4.783 4.794 4.789 4.806

8.56 8.56 8.521 8.495

4.79 4.79 4.784 4.769

8.462 8.512 8.471 8.419 8.500 8.492 8.447 8.393 8.317 8.469 8.507 8.394 8.416 8.381 8.3479 8.569 8.533 8.501 8.508 8.498 8.545 8.601 8.581 8.675 8.678

4.788 4.772 4.752 4.727 4.779 4.765 4.742 4.714 4.730 4.761 4.769 4.716 4.653 4.726 4.7004 4.842 4.804 4.793 4.796 4.789 4.793 4.826 4.811 4.873 4.804

Tc (K) 547 584 607 554 534 530 505 496 488 524 533 495 545 585 600 500 520 504 498 600 600 736 945 568 478 834 995 1119 636 820 1022 1095 810 796 823 1080 1073 1066 943 544 557 545 550 552 588 562 546 567 582

Ms (/~B/f.u.) 4.2K 293K 21.27 20.09 12.46 9.7 9.7 9.58 9.2

19.0 14.5"

16.8 16.97 12.5 10.6 11.3

4.2K

#o Ha (T) 293K

>15 7.81

12.4

8.3

15.7 16.6 14.8

4.0 15.18"

13.36 19.12 10.1 11.8 13.7 19.73 18.65 16.99 15.46 13.4" 13.6" 10.9" 11.4" 11.7" 10.2" 8.0* 12.1" 13.0' 16.3' 7.8* 6.0* 7.5* 12.69" 17.258 15.862 13.650 12.807 12.579 16.460 14.549 13,841 13.148 16.456

14.0 13.9 11.6 13.1 13.9 13.0 10.5 15.1 16.5 17.9 9.3 10.6 12.7 12.93 15.857 14.022 11.800 10.978 10.830 14.903 13.104 11.761 10.270 15.083

2.5 N0 2.8 5.5 6.69*

6.89* 9.00*

2.48* 15.46 17.54 16.70 15.87 15.24 17.68 17.36 12.62 10.22 18.28

Ref.t

I-1, 5] 10.5 1,1-3,5,6] 3.34 1,1,4,5,8] [1,5] 2.3 [1,5] 1,1, 5, 13] 2.4 [1,5,7] 1,1,5] 2.2 [1,5] 2.1 1,1,4,7] 6.77 1-24] 1-9] 1,9] [9] 1,9,22] [9] 1,9,22] 2.68 [10, 18] 2.29 [10] [20] [20] 1,11,27] 1,11,27] [11,25] [11] 5.38 [24] 1,24] [24] 4.42 [24] 4.72 1,24] 1,24] 1,24] 4.80 [24] 4.07 [24] 4.05 1,24] [24] [24] [24] 1.27 1,7,11] 9.65 [12] 8.50 [12] 8.35 1,12] 8.23 1,12] 8.06 [12] 9.97 1,12] 10.34 1,12] 9.66 1,12] [12] 9.46 [12]

10

H.-S. LI and J. M. D. COEY TABLE 3.1

Compounds

a (/~)

c (A)

Tc (K)

SmFes.sAlz.sTi SmFeaxTiH1,2 SmFeaa TiNo.s SmFetlTiCo.8 YFell TiHi.2 YFellTiNo. 8

8.696 8.554 8.64 8.64 8.511 8.62

4.894 4.796 4.84 4.81 4.794 4.81

456 627 769 698 567 733

CeFeloV2 NdFeloV 2 SmFexoV 2 GdFeloV 2 TbFeioV2 DyFeioV2 HoFexoV 2 ErFeloV2 TmFeloVz LuFeloV2 YFeioV z CeFelo.5 V1.5 NdFelo.5 Vl.s NdFelo.2Va.8 NdFe9.sV2.2 Ndl.2Feg.sV2, 2 SmFelo.sV1.5 GdFe~o.s V1.5 GdFe9.s V2.5 YFelo.6V1, 4 YFelo.sVi.5 YFelo.4V1. 6 YFelo.2VI.8 YFe9.sVz. 2 YFe9.4V2. 6 YFe9.zV2. 8 YFes.sV3.5 YFesV4 ThFeioV2 YCoaoV2

8.502 8.5630 8.5368 8.5167 8.5023 8.4877 8.4790 8.4713 8.4553 8.4468 8.4938

4.754 4.7772 4.7722 4.7741 4.7743 4.7733 4.7672 4.7650 4.7608 4.7606 4.7723

440 570 610 616 570 540 525 505 496 483 532

8.565 8.5 8.5 8.55 8.533 8.524 8.518 8.487 8.4727 8.488 8.488 8.427 8.500 8.506

4.774 4.7 4.7 4.77 4.774 4.778 4.776 4.769 4.7699 4.769 4.770 4.774 4.775 4.778

600 630 580 570 620 635 545 577 575 575 556 516 478 455

8.529 8.583 8.364

4.796 4.775 4.706

350 515 611

NdFeloSi2 SmFeloSi2 GdFeloSiz TbFeloSi 2 DyFeaoSiz HoFeloSi 2 ErFeloSi 2 TmFeloSi2 LuFe~oSi 2 YFeloSi 2 UFeloSi 2 SmFesCozSi 2 SmFeTCosSi 2

8.464 8.467 8.437 8.415 8.404 8.390 8.386 8.369 8.370 8.373

4.771 4.755 4.757 4.747 4.748 4.749 4.743 4.733 4.740 4.737

8.447 8.431

4.742 4.729

574 606 610 585 566 558 550 546 540 540 700 714 765

(continued) Ms (/tB/f.u.) 4.2K 293K 1 2 . 1 0 2 9.156 21.1 12.6

19.1

17.5

4.2K

/t on . (T) 293K

9.68 25.0

17.0

9.0

6.0

Ref.t [12] [34] [36] [36]

[34] [36]

18.07 8.93 7.92 6.66 6.35 8.37 11.17 15.49 16.15

20.7* 17.6" 17.2

17.2 11.55

~15

~10 10.60

14.21 15.67 19.86 18.2 15.7 15.05

4.0

[30] [30]

12.22 9.13 16.33 17.93

14.91

4.73*

2.99~' 13.11

[4,2] [9] [9, 17] [9, 17] [9] 2.59 [7, 17] [9, 22] [9] 1.61 [9, 7] [9, 22]

[9] [22] [9] [9]

9.64

[29]

7.19" 15.30

14.05" 20.0

[9] 1.89 [14, 10, 30] 5.4 [14, 15] 3.34 [14, 8] [14,31] [14,31] [14,31] 1.76 [14,7,31] [14] [14] 1.97 [14,7,22] [17] [9, 17]

13.05"

3.65*

1.75 [lO] 5.2 [9, 15] 3.3 [9, 8] [9] [9] [9] [9] [9] [9] 2.18 [9, 7] [32] [9]

[9]

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS TABLE 3.1 Compounds

a (A)

c (A)

Tc (K)

SmF%CosSi z LuFelo.5 Sil. 5 YFe8 Coz Si2 YFe6C0gSi 2 YFe4Co6Si2 YFe2Co8Si2 UFeloSi2

8.420 8.371 8.424 8.421 8.359 8.328 8.24

4.708 4.751 4.743 4.730 4.684 4.665 4.63

850 528 670 790 820 788 550

Gdl.1Fe9.s Crz. 5 NdFeloCr 2 SmFe~oCrz GdFeloCr 2 TbFeloCr/ DyFeaoCr2 HoFexoCr2 ErFeloCr 2 TmFe~oCr2 LuFexoCr2 YFeloCr 2 YFexo.5 CrLs YFe9.3Cr2. 7 YFe9.oCr3. o YFes.sCr3. 5 YFeloCrV

8.45 8.532 8,496 8,515 8,444 8,419 8,39 8,432 8,416 8.412 8,463 8.442 8.463 8.445 8.442 8.473

4.75 4.769 4.760 4.766 4.745 4.733 4.730 4.749 4.732 4.736 4,756 4.745 4.739 4,751 4.748 4.758

608 530 565 580 525 495 485 475 465 450 510 540, 420 385 360 515

CeFeaoMo 2 PrFeloMo 2 NdFeloMo2 SmFeloMoz GdFeloMo2 TbFeloMo2 DyFelo Mo/ HoFeloMo2 ErFejoMo 2 TmFeloMo 2 LuFe lo Mo2 YFeloMo2 UFeloMo2 NdF%o.~ Mol. s NdFe9.sMo2. 5 SmFellMo SmFelo.5 Mol.5 Sml.z Felo Mo2 GdFelo.sMol.5 YFelo.5 Moa. 5 YFeg.sMoz. 5 GdM Feg.sMo2. 2 Gdl.1FeaoMo / Gdl.1 Felo.2Mol. 8 GdFelo.2Mol. 8

8.567 8.634 8.606 8.590 8.581 8.546 8.538 8.523 8.517 8.513 8.511 8.541

4.786 4.808 4,798 4.804 4.806 4.785 4.790 4.788 4.785 4.781 4.780 4.792

8.590 8,612 8.566 8.572

4.791 4.809 4.778 4.788

8.557 8.513 8.576 8.58 8.56

4.791 4,783 4.815 4.80 4.80

8.54

4.79

260 385 400 483 430 390 365 345 310 290 260 360 256 440 350 510 460 460 520 460 300 370 440 484 446

11

(continued) Ms (/tB/f.u.) 4.2 K 293 K

4.2 K

#o Ha (T) 293 K

[9] [9] [9] [9] [9] [9] [32]

10.0

19.8"

10.62 16.2 12.28

4.6 5.9 2.7

11.2" 9.3* 9.8* 9.9* 10.2" 10.1"

9.6 10.0 10.9 11.4 11.0

4.9 4.0 2.7 2.8

16.67

14.9

2.6

16.4 15.2 9.79 4.9 4.4 3.5 3.6 5.5 10.6 13.0

12.6 10.48 7.04

15.0

8.0 8.3 9.9

Ref.i"

4.52 5.69 7.00

[21] [9,16] [9,15] [9,16] [9,16] [9,16] [9,16] [9,16] [9,16] [9] [9,16,22] [9] [9] [9] [9] [9]

[9] [9] [9, 18, 35] 3.7 [15, 28, 35] 2.19 [9, 8, 22, 35] [35] [35] [35] [35] [35] [35] [9, 28, 35] [32] [9] [9] [9] [9] >5.0 [4] [9] [9] [9] [4,21] 2.8 [4, 21] [4] [21]

12

H.-S. LI and J. M. D. COEY TABLE 3.1 (continued)

Compounds Yl.lFel0Mo2 CeFexo Feao Mo 1.~ NdFeloMol. 5 SmFeloMol. s GdFelo Mot.5 DyFeloMoa.5 ErFeao Moa.5 YFeloMol. 5 SmFesCo/Mo z

a (•)

c (A)

8.568

4.790

SmFelo.5 W1.5 GdFelo.sWx.2 GdFelo.5 W1.5 GdFelo.4Wo.sMs.s GdFelo.sWo.5 Mo YFe~o.sW1.5 YFelo.sW1.2 YFeloW2 NdzFejoW/ SmFeloW 2 GdFeloW2

8.557 8.540 8.565 8.561 8.569 8.516

4.791 4.773 4.777 4.780 4.786 4.763

8.548 8.553 8.549 8.549

4.779 4.740 4.780 4.780

GdFeloMnz Nd2FeloMn2 Nd(Coo.s Mno.5)12 Nd(Coo.6 Mno.4)a2 Nd(Coo.7 Mno.3)~e

8.494 8.604

4.759 4.695

GdFesA14 GdFeloA12

8.57 8.49

Tc (K) 360 358 458 475 478 415 381 408 490 520 570 550 550 500 500 500 500 547 532 569

*at 77K. "~References: [1] Hu et al. (1989a). [2] Liu et al. (1988). [3] Yang et al. (1989a). [4] Christides et al. (1988). [5] Yang et al. (1989b). [6] Kaneko et al. (1989). [7] Solzi et al. (1989). [8] Chin et al. (1989a). [9] Buschow and de Mooij (1989). [10] Chin et al. (1989b). [11] Yang et al. (1988a). [12] Xing and Ho (1989). [13] Yang et al. (1988b). [14] de Boer et al. (1987). [15] Ohashi et al. (1988a). [16] Wrzeciono et al. (1989). [17] Ho and Huang (1989). [18] Chin et al. (1989b).

13.5

12.7 15.32

20.82 14.5 11.29

[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

/~oHa (T) 293K

Ref.1" [4] [33] [33] [33] [33] [33] [33] [33] [35]

[9] [9,22] [9] [9] [9] [9] [22,23] [9] [18] 2.47 [8] 2.52 [8]

7.81 9.5

2.17 [8] [18] [26] [26] [26]

6.07 10.6

[19] [19]

0.37 5.14 11.16

385 498

4.2K

2.1

445 5 128 370

4.95 4.89

M~(/tB/f.u.) 4.2K 293K

Wang et al. (1988). Cochet-Muchy and Pai'dassi (1989). Christides et al. (1989a). Verhoef et al. (1988). Buschow et al. (1988a). Sinha et al. (1989a). Yang and Cheng (1989). Allemand et al. (1989). Yang et al. (1990a). Yang et al. (1990b). Jurczyk and Chistyakov (1989). Christides et al. (1990). Christides et al. (1989b). Baran et al. (1990). Mfiller (1988). Zhang and Wallace (1989). Christides (1990). Coey et al. (1991c).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

13

approximately 2.0 T, except for the Sm compounds which have a room-temperature anisotropy field around 10T. This large anisotropy field in SmFellTi is due to an unusual increase of A20 compared to other rare-earth compounds, which is only partly explained by J-mixing effects for the Sm 3 + ion (Li et al. 1988b, Kaneko et al. 1989, Moze et al. 1990a). The sign of A2o is changed by the presence of interstitial nitrogen (Yang et al. 1991, Coey et al. 1991c) or carbon (Hurley and Coey 1991). (e) These series show a variety of spin reorientations when there are contributions to the anisotropy from the iron sublattice and the rare-earth sublattice of comparable magnitude and opposite sign. Figure 3.3 summarizes the magnetic structure diagram for the R(Fet~Ti) series (Hu et al. 1989a). As these spin reorientations reflect the different thermal variations of crystal-field terms of different order acting on the rare earth, they can be used to determine the crystal-field parameters in an accurate way. 3,2.1.1. Nonmagnetic rare earths. The magnetic moments of 3d transition elements depend in a complex way on the local density of electronic states, reflecting the nature, number, distance and spatial configuration of the neighbouring atoms. These features are taken into consideration in band-structure calculations based on the real structure and site occupancies. Calculations using the augmented spherical wave method (neglecting spin-orbit coupling) have been performed by Coehoorn for the hypothetical YFe12 end-member and YFesM4 (M = Ti, V, Cr, Mn, Mo or W) R(Fe]l Ti ) V

I

Nd

ilililiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiilililililil

1

I

Sm Gd

ilililililili i i iliSi i!i i2i i i i i i i i i!i i i i i i i I iiiii!i!i!iiiiiliiiiiiiiiiiiiiii!iiiill Dy Tb

Ho Er

!iiiiiiiiilililil

I I I

Tm Lu I

i

i

0

200

400

I I

I

I

I

i~

600

T(K)

bl II c-axis

Iv[a. c-axis

complex

Fig. 3.3. Temperature dependence of magnetic phases for RFellTi series, results by Hu et al. (1989a).

14

H.-S. LI and J. M. D. COEY

TABLE 3.2 Fe moment on the three different crystallographic sites of the ThMn12 structure, determined by neutron diffraction and 57Fe M6ssbauer spectroscopy (conversion factor was taken as 15.7T//tB). The theoretic results are included as well. Compound

Method

#Ve(#B) at 4.2K 8f

8i

8j

1.53(5) 1.80 1.32(3) 1.23(3)

1.70(9) 1.92 1.74(3) 1.67(3)

1.16(11) 2.28 1.51(3) 1.43(3)

Re~t

[1] [2] [3,4] [3,4] [5]

YFeloV2 YFellTi YFellTi LuFellTi YFe~oMo2

Neutron Neutron M6ssbauer M6ssbauer M6ssbauer

1.83(7)

1.95(13)

1.50"(3) 1.43"(3) 1.16

1.97"(3) 1.75"(3) 1.90"(3) 1.67"(3) 1.92 1.55

YFeloV 2 YFexoV2

M6ssbauer Calculation

1.25 1.68

1.75 2.1

1.47 1.99

[5] [6]

YFeloCr 2 YFeaoCr 2

M6ssbauer Calculation

1.20 1.77

1.82 2.23

1.57 2.08

[5] [6]

YFe 12 YFe12

Extrapol. Calculation

1.77 1.86

2.31 2.32

2.17 2.26

[5] [7]

YFe8 V4 YFesV4

Extrapol. Calculation

0.75 1.41

1.24 -0.57

0.81 1.48

[5] [7]

*at 77K t References: [1] Helmholdt et al. (1988). [2] Yang et al. (1988c). [3] Hu et al. (1989a). [4] Hu et al. (1989b).

t.52(16)

#Fe(PB) at room temperature 8f 8i 8j

[5] Denissen et al. (1990). [6] Jaswal et al. (1990). [7] Coehoorn (1990a).

(Coehoorn 1988, 1990b), and by Jaswal et al. for Y F e l o M 2 (M = V or Cr) (Jaswal et al. 1990). M o m e n t s are 1.86pB, 2.32#R and 2.26#B for 8f, 8i and 8j sites in YFe12 (table 3.2), respectively. All binary Y - F e c o m p o u n d s are weak ferromagnets, meaning that both 3d T and 3d ~ states are occupied at the Fermi level. The formation of magnetic m o m e n t s in alloys, both crystalline and a m o r p h o u s , of the transition metals Fe and Co was interpreted by Friedel (1958) and developed by Terakura and K a n a m o r i (1971, T e r a k u r a 1977), Williams et al. (1983) and M a l o zemoff et al. (1984). W h e n b a n d calculations are impracticable, some pointers are provided by the magnetic valence model (Williams et al. 1983, M a l o z e m o f f et al. 1984), which assumes strong ferromagnetism (i.e., only 3d ~ states lie at the Ferni level) and ignores details of the crystallographic environment. The magnetic m o m e n t depends only on the composition, via the total n u m b e r of electrons. The magnetic valence of an a t o m Z m is defined as 2N~o-Z, where N~ is supposed to be 5 for the late 3d elements (Fe, Co and Ni), but it is zero for the early transition elements, the rare earths and the metalloids, e.g., B, C, A1 or Si. Z is the chemical valence. The average atomic m o m e n t is given by a simple formula < # ) =
(1)

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

15

where (Zm) is the magnetic valence averaged over all the constituents and N~p is the number of electrons in the unpolarized s-p conduction bands. The average magnetic moment per atom, ( # ) , in the alloy is also the average over all the constituents. This formula has achieved great success, in the case of strong ferromagnets, when applied to explain a large amount of experimental data on the concentration dependence of magnetization of binary transition-metal alloys (Williams et al. 1983), transition-metal-metalloid alloys (Malozemoff et al. 1984) and rareearth-transition-metal (Fe and Co) intermetallics (Gavigan et al. 1988, Coey 1989). As shown by Malozemoff et al. (1984), the essential fact that makes eq. (1) correct, without the necessity of considering any detailed hybridization and local-environment effects, is the existence of gaps or deep minima in the density of states of the 3d band as a function of energy. Such band gaps provide a necessary condition for strong magnetism in the framework of Stoner's 'collective electron ferromagnetism' theory (Stoner 1939) and give rise to the important conservation law for the integrated density of states under alloying (Terakura and Kanamori 1971). In fact, the magnetic moment depends only on the total number of d and s-p electrons, not on the band shape. The argument of the rigid band model (Slater 1936, Pauling 1938) is avoided, which presumes that the d band as well as the s-p bands of the alloy form common bands, invariant under alloying. Friedel (1958) first proposed that in mixtures of early and late transition metals, the relatively repulsive d potential on the early transition-metal solute created a separate high-energy d band containing precisely ten states per solute. Based on this argument, eq. (1) can be used to describe the Co-Cr, Co-V and rare-earth-(Fe, Co) systems (where rare earths are seen as early transition metals). For transition-metalmetalloid systems, Terakura and Kanamori (1971) showed how the metalloids can have a larger number of s-p electrons than typical transition metals without increasing the value of N~p appearing in the formula. The extra s-p electrons tend to occupy the states made up from linear combinations of states originally from nearestneighbour sites, thus there is no change in N~p, because the metalloid states are made up of states which are already below the Fermi level and, therefore, already filled. This makes it possible to use eq. (1) in the case that the alloys include a metalloid such as B, C, N, Si, etc. Figure 3.4 shows the predicted variation of (kt) with (Zm) for N~p between 0.3 and 0.4. Data are taken from table 3.1. The points for many of the 1 : 12 compounds are close to the predicted line, especially for those alloys rich in cobalt, but YFe 11Ti, YFelo.sV1.5 and YFeloMz (M = Cr or Si) and pure e-Fe are exceptions which indicates they are weak ferromagnets. The measured average iron magnetic moments in R(Fe12_xMx) are in the range 1.35#B to 1.93pB, with the lowest values 1.35#n and 1.41#a for YFe~oMo 2 and YFeloSi2, respectively; and the largest values, 1.77pB and 1.93pa for YFelo.sTil.2 and YFe~0.8 W~.2, respectively. More detailed experimental information on the individual iron moments of the three different crystallographic sites was obtained from neutron diffraction and 5VFe M6ssbauer spectroscopy. Table 3.2 summarizes the results together with the theoretic values. There are some discrepancies in these data; Helmholdt et al. (1988) found the largest iron moment for atoms at 8i sites by neutron

16

H.-S. LI and J. M. D. COEY / / 1 Y (Fe0.3Co0.7)11Ti

/ ,/

2 Y (Fe0.5Co0.5)11Ti

2.5

3 Y (Fe0.7Co0.3)llTi

/

5 Y (Fe0.9Co0.I}llTi / 6 Y (Fe0.92Ni0.08)llTi

/

/•0.6/ / '

/

7 Y (Fe0.sNi0.2)11Ti

Fe

/

/

8 Y (Fe0.7Ni0.3}llTi

/

9 ~e8.5V3. 5

/

/

/ s'

10 ~.10v2

9&

11 ~Fe9.4V2.6

,,'

i'

YFel0.8WI. ~/ ,/ ,m i / 3/4

~-~ ::t. ~'~

,J

2Nqsp = 0.8/' / t/

4 Y(Fe0.8Co0.2)IITi

2.(

/ ,'

1.5

'~rv5 ~

ellTi

%

~ e l 0 C r

A

,,'~ ,'

V

~/~ /' • •

0.5 •

t

/

i i

i

i

/

/

/

t

i

/

/

t

t

/ i

"YFel0Si2

/' t /'Ni I

/

i

~Fel0.5Vl.5

,'"/','"Y,9°llTi

i

•

2

/ J

i

o.o,-0'.5

o'.o

015

1;0

1'.5

2.

Fig. 3.4. Plot of the average atomic moment <#> against magnetic valence for YFe12_xM~, including Fe, Co and Ni for comparison.

diffraction, which is in accordance with the 57Fe M6ssbauer results of Hu et al. (1989a,b) and the calculation of Coehoorn (1988) while Yang et al. (1988d) found the greatest moment was at 8j sites. On the other hand, the smallest iron moments are associated with atoms at 8f sites following Hu et al., Yang et al., and Coehoorn while Helmholdt et al. (1988), Cadogan (1989) and Sinnamann et al. (1989) prefer 8j sites. In order to draw an acceptable conclusion, we use the previous arguments relating to crystal structure. Ti and V prefer to occupy 8i sites; a quarter of 8i sites are occupied by Ti atoms in YFellTi and one half of them are occupied by V atoms in YFeaoV2. So, iron on 8i sites has 11.75 and 10.5 iron nearest-neighbours for YFela Ti and YFeloV2, respectively, while iron on both 8f and 8j site has 9 iron neighbours in YFI~Ti and 8 iron neighbours in YFeloV2. The average Fe-Fe distances follow the relation dveve (8i) > dFoF~(8j) > dF~F, (8f). On the basis of the coordination number

TERNARYRARE-EARTHTRANSITION-METALCOMPOUNDS

17

of iron (Gavigan et al. 1988) and average Fe-Fe distances, there is little doubt that the 8i site should have the largest magnetic moment. The shortest average Fe-Fe distances are for the 8f sites, which have the same number of iron nearest-neighbours as the 8j sites, suggesting that #Fe(8i) > #Ve(8j) > #Ve(8f). Band calculations for YFe12 (Coehoorn 1988, 1990a), YFel0M2 (M = V or Cr) (Jaswal et al. 1990) and YMn12 (Shimizu and Inoue 1987) all support this view. The iron magnetic moments in RFe12-xMx are a function of x and the specific M element. Figure 3.5 shows the variation in the RFele_xV~ series, where there is a reduction of 0.23#B per vanadium. All the early transition-metal elements, Ti, Cr, V, Mn, Mo, W and metalloids Si and A1 are more effective than yttrium or the other rare-earths elements at reducing the iron moment in an alloy. The composition dependences of the 3d atomic moment in Y(Fel_xCox)l~Ti and Y(Fel_~Nix)llTi, observed by Yang et al. (1988a) are plotted in fig. 3.6. It is seen that, for both cases, there is a peak, occurring at x ~ 0.28 for Co and at x ~ 0.07 for Ni. This behaviour can be understood in terms of 3d band structure. According to the Slater-Pauling curve, there is a crossover from weak to strong ferromagnetism in binary Fe~ _~Co~ or Fel _~Nix alloys with increasing x (Friedel 1958, Williams et al. 1983).

•

1.8

.

.

,

.

.

.

.

,

~

.

=

.

.

.

,

•

.

YFel2"xVx

"~1.6 --t ~ 1.4 ::::k

1.2 1

2 X

3

Fig. 3.5. Vanadium concentration dependence of Fe magnetic moment in YFe12_xV x compounds, from Verhoef et al. (1988) (solid square) and from Ho and Huang (1989) (solid circle), respectively.

i

2.0

Y ( F e l . x M x ) l l Ti 1 . 8

1.6 ::3-

"o M = N i 1.4 1.2 0.0

012

014

' 016 X

018

1.0

Fig. 3.6. Concentration dependence of the 3d metal magnetic moment in Y(Fel-xMx)llTi Ni) compounds, after Yang et al. (1988a).

(M = Co or

18

H.-S. LI and J. M. D. COEY '

i

. . . .

i

. . . .

,

. . . .

RFel0M2

700

V 600

M = W

Si

~

r

V W

Si

Cr

.

50O d

Mn

a MO

400

,Mo 1.0

1.5

2.0

2.5

2 (IXB2) Fig. 3.7. Plot of Curie temperature as a function of the square of the average atomic moment for RFe12_~M~ compounds.

The Curie temperature of YFeloM 2 compounds is greatest for M = Si (540 K) and M = V (532 K) and it is smallest for M = Mo (360 K). Figure 3.7 plots the variation of Tc for YFelo Mz and GdFelo M2 as a function of the square of the average atomic magnetic moment (#)z, assuming strong ferromagnetism. The weak dependence of Tc on (#)2 in these iron compounds contrasts with the result Tc ~: (#)2 usually found in compounds of cobalt and nickel (Givord and Lemaire 1974). It follows that the exchange interactions in the iron compounds decrease as the moment increases. The effect of composition on the Curie temperatures of some RFe 12-x Mx compounds is shown in fig. 3.8. It is seen in figs. 3.8a and 3.8b that the effect of substitution of nonmagnetic elements for Fe in RFe12 leads to a reduction in Tc that is most drastic for Mo and A1. It follows by extrapolation that the hypothetical YFe12 compound would have a Curie temperature of about 700 K. The value of the magnetic coupling constants Jveve and Jgvo in RFela-xVx compounds, deduced from the high-field dependence of magnetization measurements are 52K and - 8 . 5 K , respectively (Zhong et al. 1990a). It is worthy to note that the Curie temperature of an yttrium compound is a little higher than that of the corresponding Lu compound, as it is for both R2Fe17 and RzFe14B series (Buschow 1977, Givord et al. 1984b). Unlike the early transition metals or the metalloids, cobalt and even nickel substituted for iron in Y(Fel-~Tx)lz-yMy (T = Co or Ni) increases the Curie temperature as can be seen from fig. 3.9 (Yang et al. 1989a). The 3d-sublattice anisotropy favours the c-axis for Fe compounds and is planar for Co compounds. As is customary, it can be well represented by a quadratic term KIT sin 20a- in the anisotropy energy where 0T is the angle between the c-axis and the 3d-sublattice magnetization direction. Figure 3.10 shows the temperature variation of K1T for YFellTi and YCo~ITi as well as for Y2Fe14B compounds (Coey et al. 1989, Solzi et al. 1989). The anomalous temperature dependence on YaFe14B is absent in YFellTi. At OK, KI(Fe)= 1.93MJm -3 for YFellTi (Li and Hu 1988) compared to 0.75 M J m -3 for YaFe14B (Givord et al. 1984b) and -0.89 M J m -3 (at

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

19

700

YFe12.xT x 600

+ -+, +. ~. - - ~ Sl "-. +

Ti

500

T = V

400

', M o

C r "%.

"'-.

(a) 300 ,

i

.

.

.

.

2

1

'

,

'

'

3

•

,

'

•

•

4

1

,

600

Gd(Fel.xAIx)12 500

400

~300 200 (b)

lO0

012

o.o

0 1 4 ' 016

0.8

700

600

-~.

C
500

400

(c) . . . .

~ " ' ~ ~ i 1

. . . .

i

,

,

2 X

Fig. 3.8. Concentration dependence of Curie temperature of RFexz-~Mx compounds: (a) R = Y and M = Ti, V, Cr, Mo, W or Si (Buschow and de Mooij 1989), (b) R = Gd and M =A1 (Wang et al. 1988), (c) R = Nd, Sm or Gd and M = V or Mo (Buschow and de Mooij 1989). 77 K) for YCollTi (Solzi et al. 1989) compared to - 0 . 8 0 MJm -3 for Y z C o l 4 B (Thuy et al. 1988a). This similarity in magnitude and sign of 3d anisotropy for ThMn12type and Nd 2 Fel~ B-type compounds can be ascribed to the close structural similarity between both of them and cubic Th6Mn23 (Johnson and David 1985, Shoemaker et

20

H.-S. LI and J. M. D. COEY .

~

,

,

.

,

1200

Y ( F e l . x M x ) l l Ti 1000 jr~ a"

,"

M=Co

800 /

.•

600

,' ="

,.0

M = Ni

.-~"

o2~

o'.4

oi,

018

1,0

x

Fig. 3.9. Concentration dependence of the Curie temperature of Y(Fel_xMx)llTi (M = Co and Ni) compounds, after Yang et al. (1988a) and Yang and Cheng (1989). . . . .

i

Y C o l I T

. . . .

i

. . . .

T

~ -

o

i

o

-1 0

100

200

300

T (K)

Fig. 3.10.Temperaturedependenceof Fe sublatticeanisotropyconstant Ka for YFell Ti (Li and Hu 1988), Y2Fe14B (Givord et al. 1984b) and YCollTi (Solzi et al. 1989). al. 1984). Compounds with the hexagonal CaCu5 and Th2Ni17 structures exhibit stronger uniaxial symmetry. The origin of 3d anisotropy is the residual orbital moment (Deportes et al. 1976), which is largely quenched by the crystal field. It is well established that the uniaxial anisotropy observed in YCo5 (Schweizer and Tasset 1969) stems from the relatively large orbital moments of the cobalt atoms on 2c sites, while the contribution from the atoms on the 3g sites is much smaller. Judging the discontinuities of the hyperfine field at the spin reorientation temperature observed by 57Fe M6ssbauer spectroscopy in NdFel 1Ti, TbFell Ti and DyFell Ti (Hu et al. 1989a), the largest orbital moment for iron in the ThMn12 structure is on 8i sites as can be seen from fig. 3.11. These discontinuities in the hyperfine field are closely related to the second-order anisotropy (Thuy et al. 1988b, Gubbens et al. 1989b), and 57Fe M6ssbauer experiments on a YzFe17 single crystal by Averbuch-Pouchot et al. (1987) show that the iron atoms at the dumbbell sites (4e, 4f), which correspond to the 8i site in the ThMn12 structure,

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS '

30

"

'

*------.......~

"

'

.

"

'

=-f 8

~

21

1I

,8i

J

A

1--25 m 20 15 I

,

I

100 35

,

I

150

I

,

I

200

I

,

I

250

I

i

•

8f

T8i *Sj

30 A

I,~25 m 20 T b ( F e 1 1 T i ) ~ ~ 15

I

,

100 ' ~ '

35

I

,

I

200 I

,

I

300 "

i

•

,

400 I

,

I

~

•

•

!

8f

11125 Dy(Fe11Ti) 20

I

I

I

I

I

I

50

100

150

200

250

300

T(K)

Fig. 3.11. Temperature dependence of the Fe nuclear hyperfine field of individual crystallographic sites 8f, 8i and 8j, the discontinuities marked by arrow correspond to the spin reorientation; results by Hu (1990).

show a large difference of hyperfine field, ABhf = 3.0 T when the magnetization is saturated in plane and along c-axis. The value of the orbital moment for Fe atoms at these sites is estimated as AML ~ 0.05#B. As in many other R,(Fel_xCox),, systems (Thuy et al. 1988b), the Fe end-member of R(Fel_xCOx)llTi shows a uniaxial anisotropy, but, as the Co content increases, the uniaxial anisotropy decreases and passes to planar anisotropy (i.e., K1 changes sign) at the composition x ~ 0 . 5 (Yang et al. 1988a). Low concentrations of Ni substituting Fe in Y(Fea-xNi~)ll Ti also reduce the uniaxial anisotropy. Magnetic properties of the YFeHTi and SmFealTi hydrides were reported by Zhang and Wallace (1989). After the hydrogenation, the Curie temperature increases

22

H.-S. LI and J. M. D. COEY

TABLE 3.3 Magneto-optical and magnetic properties of some polyerystalline YFe12_xMx compounds at room temperature (van Engelen and Buschow 1990). Data for LuzFe14X (X = B or C), UF%oSi 2 and for Fe are given for comparison, cr is the magnetization measured at a field of 1.16T. Photon energy (hv) and Kerr rotation (OK)are taken at the first negative peak in the rotation spectrum. The quantity ~oK/eris the reduced Kerr rotation. Compound

Tc (K)

a (A m2 kg- 1)

hv (eV)

(PK(°)

cpK/cr(x 10- 3)

YF%o.6V1.4 YFeg.8V2.2 YFe8.TV3.3 YF%oCr2 YFel0Mo2 YFelo Wz

577 516 415 510 430 500 540 635 495 539 1040

110 85 45 72 56 83 110 77 96 97 213

0.7 0.7 0.7 1.6 0.8 0.8 0.9 0.5 0.8 0.8 1.2

0.25 0.24 0.13 0.23 0.06 0.18 0.26 0.5 0.24 0.21 0.53

2.3 2.8 2.9 3.2 1.1 2.2 2.4 6.5 2.5 2.2 2.5

YFel0Si2 UFeloSi 2 LuzFe14C Lu2Fe14B Fe

from 520 to 5 6 7 K and magnetization increases 5% for YFel~Ti. The m a x i m u m h y d r o g e n content is a b o u t 1.2 atoms per formula unit. A larger increase in magnetization and Curie temperature (to 743 K) is found after nitrogenation of Y F e ~ T i (Coey et al. 1991c). The m a x i m u m nitrogen content is a b o u t 0.8 atoms per formula. Magneto-optical properties of Y F e l z - x M x (M = V, Cr, Mo, W or Si) polycrystalline samples have been reported by van Engelen and Buschow (1990). D a t a obtained are shown in table 3.3. It can be seen that the c o m p o u n d for T = Cr has the highest reduced Kerr rotation a m o n g the c o m p o u n d s studied. Indications were obtained that the uranium sublattice also contributes to the Kerr effect in UFe~o Si2.

3.2.1.2. Magnetic rare earths.

The R F e 1 2 - x M x c o m p o u n d s with a magnetic rare earth have a Curie temperature higher than corresponding c o m p o u n d s with n o n m a g netic Lu or La; the greatest values occur with Gd. As an example, fig. 3.12a shows the variation of Curie point with rare earth for the RFel~ Ti series (Hu et al. 1989a). The 3 d - 4 f exchange interactions can be deduced in the molecular-field approximation, following Beloritzky et al. (1987). The magnetic ordering temperature is given by

(2)

Tc = ½[Tve + (TZe + 4T~w)l/2], where

(3)

TF~ = nFeFeNve[4S*(S* + 1)#g/3kB], and TRFe : nRFel~l (NFeNR) lie [2x/S*(S* +

1)gjX/JR(JR + 1)#2/3ka],

(4)

with 7 = 2 ( g s - 1)/gj. The exchange interactions between rare earths are neglected as they are expected to be less than 5% of the rare-earth iron interactions. 2x/S*(S* + 1)/~B is the effective m o m e n t of iron in the paramagnetic state, Nvo and

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS i

,

,

i

,

i

i

i

i

i

i

,

,

,

,

23

600 ~

550

500

(a) I

I

[

i

I

1

I

I

I

I

[

I

I

I

I

i

i

i

i

i

i

i

i

r

i

i

p

i

i

i

La

ee

Pr

Nd

Pm

Yb

Lu

350

-~300

~250

200 150

Srn Eu Gd Tb Dy Ho Er Tm

Fig. 3.12. Variation of (a) Curie temperature, (b) exchange coefficient nRFe, on rare-earth partner for RFexlTi (Hu et al. 1989a).

NR are the number of Fe and R atoms per unit volume, respectively. The rare-earthiron exchange coefficients deduced from Curie temperatures of the RFe11Ti series in this way (Hu et al. 1989a) are shown in fig. 3.12b, the value of 2~/S*(S* + 1) is taken as 3.7. nRvo is roughly twice as large for the light rare earths as for the heavy rare earths. The systematic decrease for nRa-by a factor two or more from the beginning to the end of the rare-earth series appears to be a general feature of intermetallic compounds of rare earths (Beloritzky et al. 1987, Radwanski et al. 1990). It may be related to 4f-5d overlap (Beloritzky et al. 1987, Brooks et al. 1989, Li et al. 1991). The RFe 12-x M~ series of compounds show a variety of spin reorientations (figs. 3.3 and 3.13), e.g., RFellTi (Li et al. 1988a, Hu et al. 1989a, Boltich et al. 1989), RFeloV2 (Gubbens et al. 1988c, Christides et al. 1988, 1989b, Moze et al. 1988b, Haije et al. 1990), R(Fel_xCox)11Ti (Sinha et al. 1989b, Cheng et al. 1990), RFeloCra and RFe~oSia (Stefanski et al. 1990). Figure 3.13 compares thermo-magnetic measurements on RFel~Ti (Hu et al. 1989a, 1990a,b) and RFel0Va (Christides et al. 1988). These unusual variations in the low-field magnetization are attributed to the spin reorientation. At room temperature and above, the uniaxial iron anisotropy usually determines the magnetization direction, but at lower temperatures the rare-earth anisotropy may be dominant. Spin reorientation transitions are expected, when the balance of competing iron and rare-earth anisotropies changes sign. Figure 3.14 shows the corresponding temperature variation of 0, the angle between the magnetization direction and the e-axis, (Hu et al. 1989a, Christides et al. 1990). These have been explained in terms of the interplay of the terms of different order in the crystalfield, which have different temperature dependences (Hu et al. 1989a). The crystal-field Hamiltonian at the rare earth 2a site (point symmetry 4/mmm)

24

H.-S. LI and J. M. D. COEY

(a)1-151 Y' 1.oo

~

I[

I' ' '

'

~ l

1,00 1.21

L"

1.0o

I 1.00 1.93

Er

\

1.00

•

R{FenTi} B.=0.1T

I

,

I

I

I

,

t

200

100

3 O0

T(K)

,b,2 i

M,,

F

TbIFeloV2)

_

nw Ov2'u°'=el-"-'

--v. k"~_,

I

,

~/

I

,~'6i1

I

DylFelOV21 22

,

I

'

ErlFeloV2 I

13:

11

i

I

100

i

I

~

I

200

I

I

100

I

I

200

TtK

Fig. 3.13. Low-field thermo-magnetization curves for (a) RFellTi (R=Y, Nd, Tb, Dy, Ho or Er), spin reorientations are marked by arrows (Hu et al. 1989a), (b) RFeloVz (R = Tb, Dy, Ho or Er), measured with the applied field along and perpendicular to the oriented direction, after Christides et al. (1990).

in the ThMn12 structure takes the comparatively simple form Hcf = B2o 020 "q- B40 040 --~ ~,~4n(c),-'44r~(c)+ B6 ° 060 + "u64u(e)v64"/ql(c)

(5)

Where {B(kq)} (a = C, S) are the crystal-field parameters depending on the specific rare

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

25

earth ion and {0~ )} are the Stevens operator equivalents as defined by Hutchings (1964), which are directly related (within a constant factor) to the cosine (e = c) and sine (e = s) part of teseral harmonics. In order to distinguish from the operator equivalents related to the tensor normalized spherical harmonics {C~k)} (Smith and Thornley 1966), here the index q is denoted as subscript rather than superscript as used by Hutchings (1964). In practice, it is more convenient to deal with the socalled crystal-field coefficients {A~)}, as defined by n(,)_ .CXkq - - u(,)m X.,kq / u k , where {Ok} are the Stevens coefficients (02 = ~j, 04m-flj and 06 =7s) and {} a r e expectation values over the 4f shell; r[f values have been given by Freeman and Desclaux (1979). The crystal-field coefficients, defined in this way, are expected to be independent of the rare-earth ion and only determined by the crystallographic structure type. The matrix elements of operator equivalents {0~ )} can be found in tables IX-XIII of Hutchings (1964) paper (for k = 2, 4, 6 and q = 0, 2,3, 4, 6), and the values of{0k} are listed in table 3.4 for some rare-earth trivalent ions, including those for the first excited J-multiplet. However, these quantities can also be expressed by using 3j- and 6j-symbols (see, e.g., Judd 1963, Wybourne 1965) as:

[JJSJ

L(2J + k + 1).J x <3 IIC (k) 113><4f"LII U (k) 114f"L>,

-(2J-~i

<J, MlOkoIJ, M'> = ~/(--1)

(_I/j_MF(2J +k + 1)q L OJ ~ k-)( J

<J, MIO~q lJ, M') =

JkJ

x[(-M-qM,]

<J, MIO~IJ, M'> =

k

i

~(-1)

-MOM' '

x/~c k

(6)

+(-1)q( JkJ

" (~---k-)i

-MqM'J.J'

1),],,2

Gk

× L \ - M - qM / - (- 1)" \ _ MqM'].J' where Gk are G2 = 2, G4 = 8 and G6 = 16, and the numerical factors {ck} are found in table3.5 (Rudowicz 1985). The reduced matrix elements <3LICtk)II3> and <4f"LI[ U (k) 114f"L> for ground state of R 3 + are listed in table 3.6 (Nielson and Koster 1963). The anisotropy of the rare-earth sublattice may be described by the phenomenological expression, E aRn i _- -

K 1 sin20 + (K 2 + K~ cos 4~b)sin 40 + (Ka + K; cos 4q5)sin 60,

(7)

where 0 and q~ are the polar angles for the sublattice magnetization relative to the crystallographic axes. From the transformation properties of the Stevens operator equivalents (Rudowicz 1985), when the conditions (O~)> = 0 (q v~0) are satisfied, the

26

H.-S. LI and J. M. D. COEY i

90

R=Tb

R (FellTi) 60

Nd

o o

"g 30"

~x 0

i

i

i

i

i

(a) ]

i

i

i

[

90

~-Dy

T (g) ]

60

R(Fel0V2)

Ho

o i,.i eto o

30

,-5 II

0

,

,

Co) ,

I

I

100

200

300

T (K) Fig. 3.14. Temperature dependence of the angle between the magnetization and tetragonal e-axis: (a) RFexlTi compounds (Hu et al. 1989a), (b) RFeloV2 compounds (Christides et al. 1990).

relations between the {Ki} for the rare earth and the {B~)} are (Hu et al. 1989a) K , = --3B20 (Ozo) -- 5B4o ( 0 4 0 ) -- ~B60 (060), K 2 = 715B4o ( 0 4 0 ) + 27B6o ( 0 6 0 ) ] ,

K'2 = ~ [B~] ( 0 4 o ) + 5B~)4( 0 6o )],

(8)

K 3 = --21~B60(060), Kt3 =

--

11 FI(e) / t'~

16U64NV60

>"

The second-order crystal-field coefficient A2o at the 2a site can be deduced from the principal component of the electric field gradient V~=determined by *ss Gd M6ssbauer spectroscopy; A2o = -[el¼V= (1 - 7 o ~ ) = A2o/(l -o-2), where 7o~ is a constant equal to - 9 2 (Bog6 et al. 1986) and o-2 is a screening factor approximately equal to 0.5. Values of V== and A2o obtained by this method for RFe12_,M~ are included in table 9.1. We can see the sign of A2o is negative, the same as the la site in RCos, but opposite to that for 4f and 4g sites in R2Fe,4B. This implies that the rare-earth

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

27

TABLE 3.4 Stevens factors Ok for R a + ground J-multiplet and first excited J-multiplet, except for Sm3+ where three low-lying J-multiplets are given. Quantities of Ok(rk) (Oko) (in units of a~) are the measures of the magnetocrystalline anisotropy at 0 K for specific R elements when A~) = 1. Values of (r k ) are taken from Freeman and Desclaux (1979), and (Oko) = (JJ ]Oko[JJ ). R 3+

4f"

zS+ILs

Pr 3+

2 3H 4 3H 5

Nd 3+

3 419/2

Sm 3+

5 6H5/2

4Ii1/2 6H7/z 6H9/2 6Hll/2 Tb 3+

8 7F 6

Dy 3+

7F 5 9 6H15/2

Ho 3+ Er 3+ Tm 3+ Yb 3+

6H13/e 10 5I s 5I 7 11 4115/2 4113/2 12 3H 6 3H 5 13 2F7/2 2F5/2

as × 10/ -2.101 -1.333 -0.6428 --0.4117 4.127 1.651 1.010 0.7823 --1.010 -0.7407 --0.6349 -0.6838 -0.2222 -0.2564 0.2540 0.3077 1.010 1.333 3.175 5.714

fls x 104

Ys × 106

fl]<04o> 7./<06o)

as(r2><020>

-7.346 60.99 -2.565 7.400 --2,911 --37.99 -0.9773 --2.979 25.01 -2.021 152.5 -0.8446 23.46 -0.02691 6.267 1.224 --1.121 --1.924 12.33 -0.5920 1.035 -0.3767 -1.207 -0.3330 -1.294 -0.3532 -0.4312 0 . 4 4 4 0 2.070 0.5651 1.811 1.632 -5.606 2.565 -7.400 --17.32 148.0 --63.49 -

-0.713 -0.727 --0"258 -0.252 0.398 0.334 0.350 0.414 --0.548 --0.274 -0.521 -0.417 -0.199 -0.174 0.190 0.171 0.454 0.408 0.435 0.373

-2.12 -2.22 -1.28 --1.13 0.339 -0.192 -0.289 -0.241 1.20 --0.800 --1.46 -0.486 -1.00 -0.585 0.924 0.616 1.14 0.759 --0.792 --0.415

5.89 5.36 --8.63 -3.72 0 2.03 3.74 5.50 -1.28 3.19 5.64 -2.26 -10.0 -1.25 8.98 2.69 -4.05 -1.21 0.733 0

TABLE 3.5 Values of the numerical factors c~ for Stevens operator equivalents (Rudowicz 1985), occurring in eq. (6). k/q

0

1

2

3

4 .

.

5

6

2

1

2~/3

~/3

.

4

1

2.,/10

2x/5

2x/70

x/35

. -

-

6

1

2~/21

½~/105

~/210

3~/7

3~/154

½~/231

ions, S m 3 +, E r 3 +, T m 3 + a n d Y b 3 +, h a v i n g a positive s e c o n d - o r d e r Stevens coefficient e j (see table 3.4), c o n t r i b u t e to the u n i a x i a l a n i s o t r o p y while the r a r e - e a r t h i o n s P r 3 +, N d 3 +, T b 3 +, D y 3+, H o 3 +, h a v i n g a n e g a t i v e as, c o n t r i b u t e to the p l a n a r a n i s o t r o p y . H o w e v e r , the c o m p l e x s p i n r e o r i e n t a t i o n s o b s e r v e d c a n n o t be s i m p l y r a t i o n a l i z e d i n t e r m s of the s e c o n d - o r d e r crystal field. E r F e l l T i a n d E r F e l o V a , for e x a m p l e , s h o w a tilted m a g n e t i c s t r u c t u r e at t e m p e r a t u r e s b e l o w 60 K (see fig. 3.13), a l t h o u g h b o t h the i r o n a n d r a r e - e a r t h s e c o n d - o r d e r crystal field c o n t r i b u t i o n s to the a n i s o t r o p y f a v o u r the c-axis. T h e tilting a n g l e m e a s u r e d o n a n E r F e t l T i crystal at 4.2 K is 0 = 16 +_ 2 ° a n d decreases p r o g r e s s i v e l y w i t h i n c r e a s i n g t e m p e r a t u r e ( A n d r e e v et al. 1988). T h e h i g h e r - o r d e r (fourth- a n d sixth-order) t e r m s m u s t be t a k e n i n t o a c c o u n t to e x p l a i n the data. A m o n g the R F e l z _ x M x c o m p o u n d s , the R F e H T i series a n d the R F e l o V 2 series

28

H.-S. LI and J. M. D. C O E Y

have been well studied by high-field magnetization measurements, 57Fe M6ssbauer spectroscopy, singular point detection techniques and neutron diffraction (Moze et al. 1990a,b, Haije et al. 1990). Figures 3.15 and 3.16 show the high-field magnetization curves on the single crystal of DyFell Ti (Hu et al. 1990a) and SmFell Ti (Kaneko et al. 1989). For DyFe~ Ti compounds, there is a sharp increase of magnetization when a field of 0.5 T is applied along [001] at temperatures below 58 K; also abrupt increases of magnetization are observed when a field of about 1-3 T is applied along [100] or [I 10], at a temperature in the range 58-150 K. These discontinuities indicate firstorder magnetization processes (FOMPs, Asti and Rinaldi 1972), type-I along [100] and type-II along [100] and [001]. There is a remarkably large in-plane anisotropy TABLE 3.6 Values for the reduced matrix elements of normalized spherical operators C ~k) and Racah tensor unit operators U k (see, e.g., Nielson and Koster 1963). f"

L

1 2 3

F H I



( f " L IIU" I]f"L)

1 ~/(11 x 13)/(2 x 32 x 7) ~/13/(2 x 3 x 11)

(f"LI] U 6 Ilf"L)

1 - ~ / ( 2 z x 13)/(32 x 7) - x / ( 2 x 13 x 17)/(32 x 112)

1 - x / ( 5 x 17)/(32 x 7) ,,/(5 z × 17 x 19)/(3 x 7 x 112)

(fT-,Lll U k IIf7-"L) = - (f"Lll U k IIf"L) (fT+"L[I U k [If7 +"L) = + (f"LFI U k [If"L) ( f a 4 - ' z IrU k 1]f l " - " z ) = - (f"LIP u k Ill"L) (3If cc~)ir3)= - x / ( 2 2 x 7)/(3 x 5)

(3 IIC~')l13)= ~/2x 7)/11 (3[IC¢6)F13) = - ~ / ( 2 2 × 52 × 7)/(3 x 11 x 13)

• -

12

"

[001]

~ . _ .

[100] [OOl]

.

• _

'

'

"

.

.

8 [11Ol 4 I

4.2 K

100 K

f

200 K

-n I

I

I

I

[

I

--

' I

'ran1, ]

t

I

~

[

[100]

j y

y,,,o,

[110] 50 K

2

4

300 K

6

2

4

6

0

2

4

6

Bo(T) Fig. 3.15. Magnetization curves on a DyFel~Ti single crystal, solid lines are theoretic values (see text), results by Hu et al. (1990a).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS .

.

.

.

i

.

.

.

.

i

.

.

.

29

i

.

[ 0~l

~

Sm(FellTi)

5 ~

T = 300 K

/0

'.

20

•

: •

: •

: •

1 •

. . . . •

•

I

•

•

•

. . . . •

•

i

•

t

--

H II [001]

5 ~

0

-

,

O

,

,

,

I

,

T=4.2K

,

,

,

5

I

10

,

,

,

,

I

15

~t0H (T) Fig. 3.16. Magnetization curves on a SmFellTi single crystal, solid lines are experimental values (Kaneko et al. 1989) and full symbols represent theoretical points (Moze et al. 1990a).

persisting to room temperature. SmFellTi shows a type-II F O M P below 150K, which can be seen in fig. 3.16. At room temperature, its uniaxial anisotropy field is about 10 T. The low-lying excited J states must be taken into account. The splitting of the J-multiplets for Sm in the ThMn12 structure has been measured directly by inelastic neutron scattering (Moze et al. 1990a). The spin reorientations occurring in DyFe11Ti are more complicated, and the variation of the tilting angle 0 as a function of temperature shown in fig. 3.14a has been confirmed by single-crystal measurements (Hu et al. 1990a). The spontaneous magnetization direction in DyFellTi is parallel to [100] below 58 K, and it is parallel to the [001] above 200K. There is a firstorder transition at 58 K to an intermediate orientation in an (010) plane, at an angle 0 = 42 °, then it decreases continuously to zero at 200 K. In order to explain the intrinsic magnetic properties of RFe~2_xMx series of compounds, a model including crystal field (single ion) and exchange interactions (mean-field treatment) was employed by Hu et al. (1989a, 1990a), which was originally developed to handle the single-crystal magnetization curves of Nd2Fet4B (Li 1987, Cadogan et al. 1988, Coey et al. 1989). The model is based on two coupled equations which describe the iron and rare-earth sublattices. For the iron sublattice, the energy

30

H.-S. LI and J. M. D. COEY

per RFe12-x Mx formula is given by /~Fe = /~e --

(B~ + BaPP) • M F e ,

(9)

where e~o = KI(Fe)sin20ve and B ~ = -/'/RFeTMR [7 = 2 ( g j - 1)/gs] , are respectively the iron sublattice anisotropy energy and the exchange field acting on the iron magnetization. The sublattice magnetizations in a RFe12_xM, formula are defined as MFe = (12 - x ) ( m F e ) and Ms = ( m R ) , where ( m F e ) is the average atomic moment of the iron and mR = -gsJl~B is the atomic moment of the rare-earth ion. For the rare-earth ion H R = Hcf -

(BIx + BaPp) - M R ,

(10)

where B~x = -nRF, TMFe is the exchange-field acting on rare-earth ions (R-R interactions are neglected), and the crystal-field Hamiltonian is given by eq. (5). In the intersublattices exchange energy: eex = nRF~MF," MR, the factor 7 = 2 ( g j - l)/gs is included because the exchange fields act on the spin magnetic moment of the 4f and 3d shell of rare earth and iron. The magnetic structure at any given temperature or applied field is determined by solving eqs. (9) and (10), while minimizing the total energy (11)

etotal = gFe + FR -- eex,

where F~ = -kBTln(ZR) is the rare-earth free energy, resulting from direct diagonalization of the rare-earth Hamiltonian defined by eq. (10). Using the procedure described above, Hu et al. (19900 were able to find a complete set of crystal-field parameters, listed in table 3.7, from the fit of the magnetization curves on a D y F e u Ti single crystal measured in the temperature range 4.2-300 K. These parameters were successfully scaled to reproduce the spin reorientations found in the other members of RFe~ITi (Hu et al. 1989a) and in the RFe~oV2 series (Christides 1990). In the case of the Sm 3 + ion, the low-lying excited J-multiplets must be taken into account (Sankar et al. 1975, de Wijn et al. 1976, Ballou et al. 1988, Li et al. 1988b). Instead of eq. (10), the total Hamiltonian for the Sm 3 + ion takes the form H R = 2L. S -

2,ttB rtSmFe ( M F e ) " S + #B(L +

2S) "Bo + Hcf,

(12)

where first term is due to spin-orbit coupling with 2 = 411.1 K (Williams et al. 1987); the second term represents the exchange interaction between Sm and Fe sublattices and the third term is the Zeeman term (Bo is applied field). The crystal-field Hamiltonian in the case of J-mixing should be treated by using Racah unit tensor operators (U~) (Racah 1942, 1943); instead of eq. (5), we have H ~ f = N O A O ( r 2 ) U ~ + N aoA 4o( r 4 ) U ~ + N 4 ( r 4 )(A4U4 4 4 + A~gU4_4) + N 60A 60( r 6 > Uo6 + N~(A~ U 6 + A 6 4 U 6 - , ) ,

(13)

where the numerical factors {N~} are N O= Gk

(3 IIC (~° 113>,

N[ = (Gk/~/2 c~ql)(3 IIC (k)II3),

(14)

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS

31

and the crystal-field coefficients {Ag}, defined by eqs. (13) and (14), are related to {At) } by

A ° = Ako, A~=(-1)q(A~ ) --LCXkql,;A(S)] ( q > 0). A~q = [A(e) ~,-O-kq±T ;A(s)'~ J,Z~-kq)

(15)

The matrix elements for Racah operators are (Wybourne 1965)

< 4f"LSJMIUkl4fnL'S'J'M'> = (--1)S-M+L+S+J'+kE(2J "4- 1)(2J' + 1)] 1/2 x ( JkJ' k-MqM'

"~L'Lk / [ J J ' S J <4fnLll ok [14f"L>gss,,

(16)

where the reduced matrix elements of Racah operators were found in table 3.6. Following the same procedure for the case of the ground J-multiplet, eqs. (9) and (12) are solved while minimizing the total energy given by eq. (11) to determine the magnetic structure fo;r given temperature and applied field. For the S m F e l l T i compound, Li et al. (1988b) and Kaneko et al. (1989) have studied the magnetization curves on polycrystalline and single-crystal samples (fig. 3.16), respectively. Moze et al. (1990a) have measured directly the splittings between 6H5/2 and 6H7/2 for the Sm a + ion in the SmFell Ti compound, and the crystal-field splittings in SmMn4Als compound (Moze et al. 1988c). The values of the crystal-field coefficients found by these authors are listed in table 3.7. Interstitial nitrogen is found to change the sign of A2o from negative to positive in SmFellTiNo.8 (Yang et al. 1991, Coey et al. 1991c).

3.2.2. Coercivity Coercivities have been developed in S m - F e - M materials (with main phase of ThMn12 structure) by means of melt-spinning (e.g., Hadjipanayis et al. 1987, Zhao et al. 1988, Singleton et al. 1988, Saito et al. 1988, Yamagishi et al. 1989, Pinkerton and van Wingerden 1989, Yamamoto et al. 1989. Ding and Rosenberg 1989, 1990,

TABLE 3.7 Values of the crystal-field coefficients A~) (in units of Kao k) in ThMn12 structure, determined from analyses of single-crystalmagnetizationcurves and from inelastic neutron scattering. Compound

Method

DyFellTi

Thermoscan Single crystal Orientedsample Single crystal Neutron Thermoscan

SmFellTi SmMn4Als ErFeloVz

* References: [1] Li et al. (1988a). [2] Hu et al. (1990a). [3] Li et al. (1988b).

A2o

A4o

-61 -32.3 -170 - 143 -161 --140

-5.9 -12.4 27.0 4.0 144

~4,,a(¢) 118 -432

A60 0.15 2.56 -16.0 6.7 1.75

1-4] Kaneko et al. (1989). [5] Moze et al. (1988c). I-6] Moze et al. (1988b).

~64A(~) 0.64 -24.5

Ref.* 1-1] [2] 1-3] [4] I-5] 1-6]

32

H.-S. LI and J. M. D. COEY

Cochet-Muchy and Paidassi 1990, Sun et al. 1990b), sputtering thin films (Cheung et al. 1986, Cadieu et al. 1987, Liu et al. 1988, Kamprath et al. 1988a,b) and mechanical alloying (Schultz et al. 1987, 1990, Schultz and Wecker 1988). Data obtained with the materials prepared by melt-spinning are summarized in table 3.8. The value of coercivity depends on the composition of the starting material, the wheel speed, annealing temperature and time, and the annealing atmosphere. The highest value of coercivity was found to be #o~Hc = 0.98 T in SmFeloTiV ribbons (Yamagishi et al. 1989). The ribbons were prepared with a wheel speed of 40 m s-1 and then annealed at 800°C for 1 hour in a Sm atmosphere. In the Sm-Fe-Ti sputtered films, the ThMn12 phase was relatively soft with a coercivity of 0.1-0.2T (Liu et al. 1988); while a additional magnetic phase was found with tetragonal symmetry and a = 8.931 A and c = 12.297A, which has a high

TABLE 3.8 Parameters of 1 : 12 Sm-Fe-M magnets prepared by melt-spinning. Compound SmsFes4A1 s SmsFeTs Co6Mos SmFel~Ti

SmT.9Fe75.gV16.2 SmTa.s Fevs.s Vls.7 Sm-Fe-Ti-B Sm-Fe-Ti-(A1, Si) SmFe aoA12 SmFe~oSi 2 SmFeloTi 2 SmFeao V2 SmFeloCr2 SmFeloMo2 SmFeloTiA1 SmFeloTiSi SmFeloTiV SmFeioTiV SmFeaoTiCr SmFeloTiMo SmFe 11Ti SmFe 11Ti SmFea 1Ti SmFe 1~Ti SmFel aTi SmFellTi SmFeioTi2

v(ms - i )

20 16 32

20 20 20 20 20 20 20 20 20 40 20 20 50 50 50 50 50 50

* References: [ll Hadjipanayis et al. (1987). [2] Zhao et al. (1988). [3] Schultz and Wecker (1988). 1-4] Singleton et al. (1988). 1-5] Saito et al. (1988).

Ta(°C)

t(min)

#oHo(T)

650 700

10

0.25 0.19 0.30 0.55 0.63 0.77 0.65 0.03 0.25 0.32 0.13 0.08 0.05 0.05 0.08 0.55 0.98 0.55 0.41 0.26 0.49 0.56 0.37 0.14 0.10 0.57

as-spun as-spun 850

800

60

700 800 800 800 700 800 800

10 10 20 30 10 10

[6] [7] [8] [9]

as(Am2kg - i )

Tc(°C) Ref.* 250 295 320 312

117 98 64 81 72 61 90 88 50 34 51 47

Pinkerton and van Wingerden (1989). Yamagishi et al. (1989). Sun et al. (1990a). Ding and Rosenberg (1989).

[1,2] [3] [4] [5] [5] [6] [6] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [8] [8] [8] [8] [8] [8] [9]

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

33

coercivity of 2.4-5.8 T at room temperature (Kamprath et al. 1988a,b). The nominal composition was Sin2 FeTTi (Kamprath et al. 1990). Microcrystalline S m - F e - M permanent magnets prepared by mechanical alloying show some promising properties. The data are listed in table 3.9. For Sm-Fe-V, with the ThMnl2 structure, a coercivity of 1.17 T was obtained (Schultz et al. 1990), the highest value reported for 1:12 magnets. Giant coercivities up to 5.03T and remanences of #oMr = 0.3 T were found in a resin-bonded SmzoFeToTilo sample (annealed for 30minutes at 725°C), a new and possibly metastable e~-phase with a Curie temperature of 380°C. 3.3. Alloys rich in Al

Since Zarechniuk and Kripyakevich described the CeMn4A18 structure in 1963 as a superstructure of ThMnl2, a wide range of ternary rare-earth aluminium compounds with the formula RT4+xAls_x (0 ~<x ~<2) have been shown to crystallize in the ThMniz-type structure, where T = Cr, Mn, Fe or Cu. In the RT4A18 series, 3d atoms occupy only 8f sites (Zarechniuk and Kripyakevich 1963), while in R T s A 1 7 and RT6A16 the 8j site is further occupied by a mixture of 3d and A1 atoms (Felner 1980, Felner et al. 1983). A detailed investigation of the site occupancy of Fe atoms in RFe4+xA18_~ (R = Gd, Er, Y and 0 ~<x ~<2) by 57Fe Mrssbauer spectroscopy has led to a slightly different conclusion (W.-L. Liu et al. 1987, Kamimori et al. 1988) as can be seen in fig. 3.17. High-resolution neutron powder diffraction studies on YT4+xA18_~ (x = 0, 1, 2) revealed a strong preferential site occupancy, in particular, the 8f site is found to be populated by Fe atoms while there is a preference of A1 for the 8i site (Moze et al. 1990a). Magnetic properties of RT4÷~A18_x (x = 0, 1, 2) have been studied in great detail by Felner, Buschow and their co-workers (see table 3.10). All the iron series exhibit TABLE 3.9 Magnetic data for 1 : 12 S m - F e - M magnets prepared by mechanical alloying (Schultz et al. 1990). Compound SmloFesoTilo SmloFe~oColoTilo Smlo F%oCo2oTilo SmioFesoCo3oTilo SmloFesoMOlo Sm10FevsB2Molo SmloFev6B4Molo SmloFe78B2 Tilo SmloFesoTivV3 Sm lo Feso TiT Si3 Smlo FesoTigGa Sm lo Feso Mo s Tis SmloFeTsB2M%Ti 5 SmloFevoCoaoMosTis

/toHo (t)

Tc (°C)

0.44 0.50 0.41 0.23 0.47 0.55 0.51 0.50 0.54 0.42 0.36 0.56 0.54 0.47

323 438 530 595 232 242 261 329 341 317 327 288 292 366

34

H.-S. LI and J. M. D. COEY i . . . .

i ....

i . . . .

J ....

4

93 o

~

2

o

., ~' . . , '

.GIFI4+xAI.8.'x.

0

0.0

0.5

1.0

1.5

2.0

X

Fig. 3.17. Concentration dependence of Fe occupancy for f and (i,j) sites in GdFeg+~A18_~(0 ~<x ~<2) compounds, deduced from s7Fe Mfssbauer spectroscopy(W.-L. Liu et al. 1987). complex magnetic behaviour due to the relatively weak iron-iron exchange interactions. For example, in a certain range of x up to four different magnetic phases have been identified in G d F e , + x A18 _x; the full magnetic phase diagram of this compound is shown in fig. 3.18 (W~-L. Liu et al. 1987).

3.3.1. RT4AIs The RT4A18 series consists of strictly ternary compounds. The Curie temperatures for T = Fe are in the range 100-200K, and depend in a bizarre way on the rare earth (see table 3.10); something similar was found for the series with T = Cr where Curie temperatures are less than 20 K whereas the T = Cu series is antiferromagnetic and shows the familiar maximum in Ty at gadolinium (32 K). As an illustration, fig. 3.19 compares the critical temperature as a function of rare earth for RCu4A18 and RCr4Als. The 3d magnetization is about 0.5#B/f.u. for T = Fe and R = La, Lu or Y. With magnetic rare-earth ions, the total magnetization varies from 0.2#B/f.u. for Nd to

300

200

~.

.L

.

_

0

/~"

0.0

,~//

GdFe4+xAl8"x

TS- F "R 0.5

1.0

1.5

2.0

X

Fig. 3.18. Magnetic phase diagram as a function of temperature and Fe concentration for GdFe4+xA18_~ after W.-L. Liu et al. (1987). The symbols P, A, F, F' signifyparamagnetic antiferromagnetic, ferromagneticand ferrimagnetic,respectively.

(0 ~< x ~< 2)

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS i

i

30

i

i

i

i

i

i

i

i

i

i

~ R M 4 A I

q

i

i

i

i

i

Tm

Yb

Lu

35

8

~ 20 10

/,

0

_t,

La

,

i

i

i

Ce

Pr

Nd

i

i

Sm

,

,

1

Gd

i

Tb

i

Dy

~

I-Io Er

i

Fig. 3.19.Rare-earth dependenceof Curie temperature for RCu,AI8 seriesand for RCr4A18series(Felner and Nowik 1979). 2.8#B/f.u. for Er and Yb compounds. For T = Cr or Mn, the total magnetizations are maximum for Dy and Ho compounds, reaching 4.8~tB/f.u. A 57Fe M6ssbauer study by Buschow and van der Kraan (1978) shows that the hyperfine field at the Fe nuclei is close to 11 T and apparently independent of the magnetic moment of the rare earth. Even in the temperature region where the magnetization falls off rapidly with increasing temperature, the variation of the hyperfine field is unexceptional; this is shown in fig. 3.20 for NdFe4Als (Buschow and van der Kraan 1978). Similar values of Bhr ll.2T and ll.0T, are observed for ThFe4A18 and UFe4AIs, respectively (Baran et al. 1985). Magnetic susceptibility measurements of YFe4A18 show a single transition, at the magnetic ordering temperature, whereas for R = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er or Yb two magnetic transitions are observed (Felner and Nowik 1978a). The first one is at about 20 K and second at about 120 K. According to Felner and Nowik, this is due to the existence of two decoupled magnetic lattices in RFe4AI8 compounds with a magnetic rare earth. The rare earth orders at low temperatures while the hightemperature magnetic transition corresponds to the ordering of iron. In contrast to the detailed studies of magnetization, the anisotropy of RT4Als has been little examined. A single-crystal magnetization study on GdFe4A18 by Fujiwara et al. (1987) shows that the easy direction of magnetization is the a-axis at 4.2 K, while at temperatures larger than the spin-reorientation temperature TR= 20 K the spontaneous magnetization tilts out of the c-plane. Figure 3.21 shows the temperature dependence of tilt angle 0 (Fujiwara et al. 1987). However, the Curie temperature found by these authors is only 28 K, in contrast to the much higher values reported on polycrystalline material, 172 K. Dilute STFe in RCr4AI8 and RCu4A18 shows no magnetic hyperfine field. In RMn4A18, there are magnetic hyperfine fields at the Fe probe site only when R is a magnetic rare earth (Felner and Nowik 1979). These results confirm the view that the Cr atoms have no moment of their own, and the Mn atoms order only under the influence of the rare-earth lattice. 161Dy and 166Er M6ssbauer studies at 4.2 K for RT4A18 (T = Cr, Mn, Fe or Cu) show that, in all systems, the Dy and Er ions have their full free ion magnetic moments of 10#B and 9#B, respectively. Comparison

36

H.-S. LI and J. M. D. COEY

TABLE 3.10 Structural and magnetic data for RT~AI12-x (T = Cr, Mn, Fe or Cu) compounds with ThMnaz-type structure (rich in M). Compound

a(A)

c(A)

Tc(K) 4.2 K

M~ (#B/f.u.) Room temperature

0(K)

P¢ff(PB) Ref.*

PrFe6A16 EuFe6AI 6 GdFe6A16 TbFe6A16 DyFe6AI 6 HoFe6A16 ErFe6 A16 TmFe6 A16 YbFe6A16 YFe6A16 UFe6A16

8.845 8.937 8.687 8.651 8.650 8.636 8.619 8.605 8.662 8.646 8.638

5.106 5.160 5.015 5.029 5.001 4.985 5.016 5.005 5.001 4.992 4.987

GdCu6Al 6 TbCu6 A16 DyCu 6A16 HoCu6 A16 ErCu 6A16 TmCu6 A16 YbCu6 AI6 LuCu 6AI6 YCu6A16

8.691 8.657 8.662 8.651 8.630 8.624 8.643 8.605 8.662

5.062 5.053 5.042 5.039 5.029 5.040 5.043 5.050 5.058

21 33.4 3.9 1.9 2.6 3.9

-22 - 54 - 14 - 11 - 3 - 5

[3,6] [3, 6] [3, 6] [3, 6] [3, 6] [3, 6] [-3,6] [3, 6] [3, 6]

GdMn6A16 TbMn 6A16 DyMn6 A16 HoMn6 A16 ErMn 6A16 TmMn6A16 YbMn 6 A16 LuMu 6AI6 YMn6A16

8.845 8.820 8.800 8.777 8.768 8.765 8.751 8.760 8.796

5.108 5.092 5.080 5.067 5.062 5.060 5.053 5.057 5.079

15 8 6

-9 - 26 - 7

[3,6] [3, 6] [3, 6] [3, 6] [3, 6] [3,6] [3, 6] [3, 6] [3, 6]

GdCr6A16 DyCr6A16 ErCr6AI 6 TmCr6A16 LuCr6A16

8.893 8.890 8.878 8.872 8.866

5.186 5.132 5.126 5.122 5.119

170 20 15

SmFe 5A17 GdFesA17 TbFesA17 DyFesA17 HoF%A17 ErFesA17 TmFesA17 YbF% A17 LuF%AI7

8.763 8.709 8.706 8.701 8.685 8.675 8.680 8.678 8.662

5.056 5.025 5.026 5.020 5.014 5.009 5.001 5.008 4.988

220 268 248 227 227 218

135 345 335 325 310 320 320 210 308 355

2.11

8.4 6.84

2.6 2

207 212

[2-4] [2-4] [1-4] [2-4] [2-4] [2-4] [2-4] [2-4] [2-4] [2-5] [12]

- 4 -18 - 23

1.4 1.2 1.2

-44

1.4

158 -5 -1

5.1 0.4 0.6 1.8 2.3 1.7 0.5 3.6 5.4

265 241 174 177 186 192 109 224 224

1.6

3.9 3.8 2.5 3.4 3.5 3.6 3.9 4.2

[3,6] [3,6] [3,6] [3, 6] [3,6] [7] [7] [7] [7] [7] [7] [7] [7] [7]

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

37

TABLE 3.10 (continued) Compound

a (/~)

c (]k)

Tc(K) 4.2 K

Ms (#B/f.u.) Room temperature

0 (K)

P, fr (#B) Ref.*

YFesAI7 UFesAI7

8.706 8.692

5.026 5.018

215 268

5.8 6.16

230

4.4

[7] [12]

LaFe4A18 CeFe4AI8 PrFe4AI8 NdFe4AI8 SmFe4AI8 EuFe4AI8 GdFe4AI8 TbFe4AI s DyFe4AI8 HoFe4AI8 ErFe4AI8 TmFe4AI8 YbFe4AI8 LuFe4AI8 YFe~AI8 ThFe4AI8 UFe4Als

8.900 8.805 8.834 8.813 8.773 8.784 8.758 8.749 8.715 8.720 8.704 8.697 8.714 8.689 8.740 8.842 8.749

5.075 5.048 5.058 5.058 5.051 5.051 5.048 5.043 5.037 5.035 5.037 5.034 5.026 5.036 5.045 5.076 5.036

135.4 159.7 107 142.0 108 137 172.3 165.3 122 137 183.0 186.6 103 197.3 184.7 147.2 160

0.36 0.26 1.06 0.18 0.46 0.27 2.40 2.10 2.30 1.65 2.80 2.00 2.80 0.6 0.28

-68 23 35 44 68 -148 -151 -105 -80 -66 -38 7 62 79 - 16

4.4 4.2 4.2 4.4 4.0 4.5 4.5 4.4 4.2 4.4 4.3 4.3 4.6 4.3 4.6

[8,9,15] [8,9,15] [8,9,15] [8,9,15] [8,9,15] [9-11] [8,9,14,15] [8,9,15] [8,9,15] [8,9,15] [8,9,15] [8,9,15] [8,9,15] [8,9,15] [8,9,14,15] [8,9,12,15]

CeCu4Al8 PrCu4AI8 NdCu4Al8 SmCu4Als EuCu4Als GdCu4AI8 TbCu4AI8 DyCuaAl8 HoCu4AI8 ErCu4AI8 TmCu4AI8 YbCu~AI8 LuCu4Al8 YCu4AI8 ThCu4AI8

8.839 8.817 8.789 8.797 8.886 8.746 8.752 8.725 8.720 8.712 8.674 8.746 8.670 8.721 8.818

5.153 5.150 5.143 5.143 5.156 5.146 5.134 5.137 5.122 5.130 5.114 5.122 5.098 5.139 5.165

LaCr4AI8 CeCr4AI8 PrCr4AI8 NdCr4AI8 SmCr4A18 GdCr4AI8 TbCr4AI8 DyCr4AI8 HoCr4AI8 ErCr4AI8 TmCr4AI8 YbCr4AI8

9.131 9.042 9.023 9.000 8.973 8.950 8.925 8.926 8.910 8.903 8.903 8.945

5.127 5.128 5.135 5.136 5.136 5.133 5.130 5.132 5.126 5.124 5.131 5.132

[12]

15 20 ~25

-17 -15 -18 -40

32 22 17 7 6 5

-16 -14 -5 -7 -10 -6

[8,13] [8,13] [13] [13] [13] [8,9,13] [13] [13] [13] [8,13]

[131 [8,13]

[13] [8] [8]

6

0.38

19 8 12 16 8 14 11

0.03 1.5 3.3 4.2 4.1 3.8 2.4

-16 -11 -24 -9 -5 - 5 -5 -4 -11 7

0.16 0.12 0.61 0.15 0.08 0.12 o.08 0.07 0,1

[8, 13] [8, 13] [8,13] [13] [13] [8,13] [13] [13] [13] [8,13] [13] [8,13]

38

H.-S. L1 and J. M. D. COEY

....

TABLE 3.10 (continued) Compound

a (/~)

c (A.)

Tc(K)

LuCr4A18 YCr4AI8 ThCr4A18 LaMn4A18 CeMn4AI 8 PrMn4AI8 NdMn4A18 SmMn4A18 EuMn4A18 GdMn4AI 8 TbMn4A18 DyMn4A18 HoMn4A18 ErMn4A18 TmMn4A18 YbMn4 AI8 LuMn4A18 YMn4A18 ThMn4A18

8.884 8.920 9.012

5.119 5.130 5.140

9.057 8.910 8.952 8.925 8.902 8.982 8.911 8.865 8.849 8.845 8.837 8.848 8.875 8.814 8.857 8.937

5.167 5.150 5.142 5.133 5.120 5.161 5.116 5.108 5.112 5.097 5.093 5.080 5.111 5.083 5.101 5.639

Poff(,uB) Ref.*

[13] [8,133 [83

11 7 12 20 28 21 19 14 15 13

0.38 0.48 0.14 0.46 3.1 4.3 4.0 4.8 4.1 3.7

* References: [1] Wang et al. (1988). [2] Chelkowska et al. (1988). [3] Felner (1980). [4] Felner et al. (1981a). [5] Zarek and Winiarska (1988). [6] Felner et al. (1981b). [7] Felner et al. (1983). [8] Buschow et al. (1976).

[9] [10] [11] [12] [13] [14] [15]

. . . .

1.5

0(K)

Ms (#B/f.u.) Room temperature

4.2 K

~

i

. . . .

,

8 -1 -8 -18

0.9 1.6 1.7 1.4

4 7 -26 --2 -2 5

1.6 1.7 1.9 1.5 1.0 1.5

10 5

0.9 0,8

[8,13] [8,13] [8,13] [13] [13] El3] [8,13] [131 [133 [13] [8,13] [133 [8,13] [13] [8,131 [8]

Felner and Nowik (1978a). Felner and Nowik (1987b). Darshan and Padalia (1984). Baran et al. (1985). Felner and Nowik (1979). van der Kraan and Buschow (1977). Buschow and van der Kraan (1978).

. . . .

,

•

•

12

e4Al 8 10

8

1.0

4

0.5 2

0

0.0 50

.....

100

150

T (K)

Fig. 3.20. Temperature dependence of the Fe hyperfine field Bhf and magnetization at a fixed field of 0.3 T for NdFe4A18 compound, after Buschow and van der Kraan (1978).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

39

40 GdFe4AI 8 30

.-g ,

.83

\

20

-,,,

T

oa

10

~,

0

I

TR

:. :. :.',.~[

,T_

_! ,~

\ ,

20

, "~

40

,

,

,

610

T (K) Fig. 3.21. Temperature dependence of the tilting angle 0 of the easy direction with respect to the a-axis in the a-c-plane. The dotted curve is for zero applied field, results by Fujiwara et al. (1987).

with the macroscopic saturation moments suggests an antiferromagnetic structure of rare-earth sublattices. Neutron diffraction studies for RCugAI8 when R = Dy, Ho or Er, reveal a simple antiferromagnetic structure, the moments at the corners and those at the centre of the cell are antiparallel, and lie along the c-axis. However, for TbCu4A18, the moments lie in the plane, and the structure is an antiferromagnetic staking layer (Deportes et al. 1979). Magnetic measurements on antiferromagnetic RCu4A1 a and RZn12 by Deportes et al. (1979) show that an applied field in excess of 15 T is needed to approach saturation of the rare-earth magnetization. In EuCu4A18, the Eu is divalent (Felner and Nowik 1979), in contrast to EuFe4AI8 (Felner and Nowik 1978b, Darshan and Padalia 1984) and EuMn4A18 (Felner and Nowik 1979) where it is in a mixed-valent state. Yb in YbMngA1 s and YbFe4Als is divalent and trivalent, respectively, but in YbCr4Ala and YbCu4Als it is in a mixedvalent state (Felner and Nowik 1979).

3.3.2. RFe5A17 Curie temperatures for RFesA17 are in the range from 200 to 268 K with a maximum value for the Gd compound (Felner et al. 1983). Iron magnetization is 5.4#B/f.u. in LaFe5A17 and 5.8#B/f.u. in YFesA17. The rare-earth moments lie antiparallel to the 8j site iron moments and parallel to a ferromagnetic component of canted antiferromagnetic structure of iron in the 8f sites. Iron in the 8i sites is nonmagnetic. The population of Fe atoms over three sites determined by 57Fe M6ssbauer effect (Felner et al. 1983) is 8f: 58%, 8i: 6% and 8j: 36%, respectively. RF%A17 compounds display a variety of unusual magnetic phenomena, including huge thermal hysteresis of the magnetization in as-cast samples; fig. 3.22a shows the hysteresis loop of HoFesA17 at 4.2 K as an example. The magnetic anisotropy in RFesA17 originates in part from the rare-earth crystal field but also, to a large extent, from the iron sublattice. The relatively high Curie temperature compared to RFe4A18 series is attributed to the intrasublattice exchange interaction for 8j sites. The temperature dependence of the

40

H.-S. LI and J. M. D. COEY 2

H°Fe5Ai7 . ' * ~

TbFe6A! 6 1

T = 4.1K ¢

=1. "~J

)

A

.2

-1 (a)

(b) . . . .

-4

-2

0 2 B 0 (T)

4

~2

. . . .

-| 1

. . . .

. . . .

B 0 (T)

Fig. 3.22. Hysteresis loop of (a) HoFesA17 at 4.2 K (Felner et al. 1983) and (b) TbFe6AI6 at 122 K (Felner et al. 1981b).

magnetization of the Sm, Tb and Lu compounds show a negative value of magnetization when the sample is quickly cooled down in a relatively weak field. The hysteresis curves of the systems with Yb, Lu and Y are also exceptional because the virgin curves extend to a region beyond that covered by the hysteresis loop.

3.3.3. RT6Al6 Compared to RFe4A1a and RF% A17, RFe6A16 has much higher Curie temperatures (except for the Eu and Yb compounds). A maximum value of 350 K is found for Gd. However, investigations by Zarek and Winiarska (1988) show that thermal or mechanical treatment can alter the distribution of the iron and aluminium atoms over the three sites in the crystal lattice, clearly changing the Curie temperature and the magnetic moment of the alloys. The magnetization and Curie temperature reach a maximum value for quenched samples, 8.4~B/f.u. and 308 K in YFe6A16, and have minimum values for annealed samples, 4.4#B/f.u. and 255K. 57Fe M6ssbauer spectroscopy revealed that the average hyperfine field at 4.2 K is about 16 T for all the compounds and that there is no nonmagnetic iron. Felner et al. (1981 a,b) observed that, in certain ranges of temperature, the alloys exhibit large hysteresis effects, even at relatively high temperatures, e.g., fig. 3.22b shows the effects observed in TbFe6 A16. These authors also performed extensive M6ssbauer studies, fig. 3.23 shows their results for DyFe6 A16. In order to analyse experimental results, they proposed a four sublattice molecular-field model, assuming collinear moments for the rare earths at 2a sites and the iron at 8j sites, and a canted antiferromagnetic structure for the iron at 8f sites. Relatively strong Fe-rare-earth exchange causes the rare earth to order at the ordering point of the iron, which is in contrast to RFe4AI8, where rare-earth and iron lattices order independently. Yb and Eu compounds are again thought to exhibit mixed valences. In RM6A16 (M = Cu, Mn or Cr) the R - R exchange is weak and antiferromagnetic, leading to N6el temperatures below 20K. An exception is GdCr6A16 where the ordering is ferromagnetic and Tc is 170 K (Felner et al. 1981a,b). The magnetization studies reveal strong crystal field effects on the rare-earth ions, as also indicated by the low Curie constants found in TbCu6AI6 and DyCr6A16 (Felner et al. 1981a,b).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS .

.

.

.

i

.

.

.

.

i

.

.

.

.

i

.

41

J

1.0 0.8

Fe

~ 0.6 [.., "~ 0.4 O.2

DyFe6AI6

0.0 100

200 T (K)

300

Fig. 3.23. Temperature dependence of the reduced hyperfine field for Dy and Fe in DyFe6 A16 (Felner et al. 1981b).

In RMn6A16, the Mn ion probably carries a moment. A value of ~l,4ktB is derived from the susceptibility of YMn6A16. The Cr in RCr6A16 may also have a small moment, although L u C r 6 A16 is diamagnetic. 4. Compounds with structures related to

BaCd11

4.1. RTgSi 2 N d C o 9 Si 2 crystallizes in a tetragonal structure (space group 141/amd) derived from

the BaCdll-structure type (Bodak and Gladyshevskii 1969). The cobalt atoms occupy two different sites: 32i and 4b, while neodymium and silicon atoms are located in 4a and 8d sites, respectively. Each cobalt atom has eight cobalt nearest neighbours, but the average Co-Co distances are significantly different, namely 2.537 A for 32i sites compared to 2.623 A for 4b sites. N d C o 9 S i 2 is ferromagnetic with a Curie temperature of 454 K (Malik et al. 1989). The magnetization at 4.2 K is 11.1#B/f.u., from which a value of 0.9#B was deduced for the Co moment. This is lower than the values in Co metal, RCos, R2Co17 (Wallace 1986) o r R2Co14B (Buschow et al. 1988c), and reflects the relatively large silicon content. The low moment accounts for the comparatively low Tc of N d C o 9 Si 2 . The anisotropy field deduced from the magnetization curves of an oriented powder sample of NdCogSi2 was 1.2T at 295K and more than 2.0T at 77K (Malik et al. 1989). A spin reorientation is observed below 77 K in SmCo9Si2 (Pourarian et al. 1989), but there is no such effect in N d C o 9 Si2, which indicates that the contributions to the anisotropy of the cobalt and Sm sublattices are opposite in sign. The Nd(Co 1 -xFex)9Si2 series of compounds are isostructured with N d C o 9 S i 2 when 0 < x < 0.55 (Berthier et al. 1988, Sanchez 1989). Figure 4.1 shows the concentration dependence of the average 3d magnetic moment, iron moment and the Curie temperature for the Nd(Col_xFe~)gSi2 series. The average 3d moment increases monotonously with x, whereas the Curie temperature passes through a maximum of 556 K

42

H.-S. LI and J. M. D. COEY I

I

550

2,0

500 ::1.

.~1.5 ::::L

450

1.0 4O0 •

O.O

I

0.1

,

,

I

0.2

,

,

I

0.3

.

,

I

0.4

.

,

I

0.5

,

,

0.6

X

Fig. 4.1. Iron concentration dependence of Curie temperature, average 3d moment and Fe moment which is deduced from 5VFe M6ssbauer spectroscopy in Nd(Col-xFex)gSi2 (Berthier et al. 1988, Sanchez 1989).

at x = 0.22, and then falls. The Fe atoms preferentially occupy the larger 4b sites, and the iron moment is a maximum (1.74#B) for x = 0.33 whereas the cobalt moment increases uniformly with x. It is suggested that the Co moments are canted away from the ferromagnetic axis.

4.2. RTloSiCo.5 Studies of the N d ( C o l - x Fex)9 Si2 system showed that the solubility limit of iron was x = 0.55 (Berthier et al. 1988). In order to stabilize the iron phase, a small amount of carbon was added by Le Roy et al. (1987), who succeeded in preparing RFelo SiCo.5 for R = Ce, Pr, Nd or Sm. An X-ray diffraction study on a NdFeloSiCo.5 crystal showed the B a C d ~ - t y p e structure (I41/amd), with the carbon atoms filling a quarter of the 8c octahedral interstitial sites formed by four iron atoms and two neodymium atoms. The NdFe~oSiC0.5 structure is a disordered version of LaMnl~C2_~ (Jeitschko and Block 1985). The Curie temperatures for RFeloSiCo.5 lie between 390 K for R = Ce and 460 K for R = S m (table 4.1). Magnetization curves show that the field required for saturation of compounds with R = Nd and Pr at 4.2 K is somewhat higher than for R = Sm and Ce (Le Roy et al. 1987) which suggests axial anisotropy for the former compounds. The isostructural RCo~oSiCo.5 compounds have much higher Curie temperatures than their iron counterparts, namely 950 K for R = Nd and 670 K for R = Sin. However, the magnetization of 9.02#B/f.u. and 7.50/~B/f.u., respectively, is much lower than that of the corresponding iron compounds. Figure 4.2 shows the concentration dependence of the Curie temperature and the magnetization for R(Fel-~Cox)loSiCo.5 (R = Nd or Sm); in the case of R = Nd, Tc increased linearly with x whereas for R = Sm the behaviour is more surprising (Allemand et al. 1989). For R = Sm, the magnetization is linearly decreasing with x while for R = Nd the

TERNARYRARE-EARTHTRANSITION-METALCOMPOUNDS 1000

i

i

i

i

i

43

i

R(Fel-xC°x)10SiC0.5~ 800

[., 600

18

I6

'14

R = Nd

~ - - S m

~

~12

10

T = 4.2 K °

01.0' 0.2

~

01.6

01.4

0.8

11.0

X

Fig.4.2.Cobalt concentrationdependenceof Curie temperature and saturation magnetizationfor R(Fel-xCo~)loSiCo.s(R= Nd or Sm)series,resultsby Allemandet al. (1990). variation is nonlinear. The value of the spontaneous magnetization is 13.2#B/f.u. at 4.2K in CeFeloSiCo.s which corresponds to an average iron moment of 1.32#B, assuming ferromagnetic order. Higher values of the magnetization for R = Pr, Nd or Sm are due to ferromagnetic coupling between these light rare earths and the iron moments (Allemand et al. 1989). The average cobalt moment of about 0.6/~B in the RCo~o SiCo.5 compound is also quite small.

5. Compounds with structures related to Th 2zn17

or

Th2Ni17

5.1. ReT17C3-~ Ternary interstitial manganese carbides R 2 Mn17Cx which crystallize in the rhombohedral Th2ZntT-type structure (R3m) for R = La, Ce, Pr, Nd or Sm were reported by Block and Jeitschko (1986). Similar rare-earth iron carbides RzFelvCx were synthesized by Gueramian et al. (1987), who succeeded in preparing the compounds with R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu or Y, and more recently by Zhong et al. (1990b) for x ~- 1. The C content was fixed at 6.5 at.% and the R content

44

H.-S. LI and J. M. D. COEY

TABLE 4.1 Structural and magnetic data for RCo 9 Si2, Nd(Col _xFex)9Si2 and R(Col-xFe~)ll SiCo.s compounds. Compound

a (A)

c (A)

Tc(K) 4.2 K

Nd(Co 1-~ Fex)9 Si2 x=0 0.11 0.22 0.33 0.44 0.55 SmCo 9 Si 2

GdCo9 Si2 TbCo 9Si2 CeFelo SiCo.5 PrFelo SiCo.5 NdFelo SiCo.5 SmFe l0 SiCo.s NdColo SiCo.5 SmColo SiCo.5

9.796 9.819 9.842 9.885 9.900 9.913

6.328 6.360 6.365 6.400 6.408 6.423

454 521 556 551 521 492

9.755 9.718 9.690

6.303 6.290 6.262

473 483 463

10.049 10.107 10.083 10.092 9.874 9.874

6.528 6.534 6.629 6.538 6.379 6.396

390 430 410 460 950 670

* References: [1] Bodak and Gladyshevskii (1969). [2] Malik et al. (1989). [3] Chevalier et al. (1987). [4] Berthier et al. (1988).

M (#B/f.u.) Room temperature

I 1.1 11.97 13.32 14.69 15.31 16.24

7.35 8.98 10.34 11.39 12.12 12.91

Ref.*

[1, 2] I-3,4] [3, 4] [-3,4] [-3,4] I-3,4] [5] 1-5] [5]

13.2 17.1 17.5 14.8 9.02 7.50

6.5 9.2 8.4 11.1

1-6,7] [6, 7] [6, 7] [-6,7] [7] [-7]

[5] Pourarian et al. (1989). [6] Le Roy et al. (1987). [7] Allemand et al. (1990).

was varied between 11.4 and 13.5 at.%. The arc-melted samples consist of a majority phase having the r h o m b o h e d r a l T h z Z n l T - t y p e structure (R = Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy) or the hexagonal Th2NilT-type structure (R = Dy, Ho, Er, Tm, Lu). Both structure types coexist in the D y c o m p o u n d . An X-ray structure determination on a single-crystal Pr2Mn17Ci.77 (Block and Jeitschko 1986) shows that c a r b o n atoms occupy 59% of the 9e interstitial sites. The m a x i m u m value of x is therefore 3, but m u c h less carbon than this usually enters the structure. A similar conclusion is drawn from X-ray (de Mooij and Buschow 1988b) and neutron diffraction (Helmholdt and Buschow 1989) studies of polycrystalline N d z F e i T C 0 x . The R 2 M n l 7 C x phase is formed at temperatures above a b o u t 1000°C; at lower temperatures it transforms to the R2Fe~4C phase (fig. 8.2). The concentration dependence of the lattice constants and Curie temperature of Y2Fei7Cx (0 ~< x ~< 1.5) is shown in fig. 5.1. (Sun et al. 1990a). The i r o n - i r o n exchange is unusually low in the pure iron Y2Fei7 c o m p o u n d , Jvev~ = 23 K ( G u b b e n s et al. 1989b). With the introduction of interstitial carbon, both unit cell volume and the Curie temperature increase strongly at first, but level off at a b o u t x = 1.0. The c a r b o n solubility limit is a b o u t x = 0.6 at 900°C for N d 2 F e l T C x (Helmholdt and Buschow 1989) and is a b o u t x = 1.0 in Y2FelTC~ as in the cast samples (Sun et al. 1990a). M u c h greater a m o u n t s of c a r b o n (x ~ 2.2) can be introduced at lower t e m p e r a t u r e by gas-phase reaction with a h y d r o c a r b o n gas (Coey et al. 1991b).

TERNARY RARE-EARTH TRANSITION-METAL

COMPOUNDS

45

The correlation between the unit cell volume and the Curie temperature is initially linear, with Tc rising from 327 K for x = 0 to 424 K for x = 0.5, while the unit volume increases from 794 to 805/~3 in Nd2Fe17C x. Similar effects are observed with certain substitutional impurities in Nd2Fe17 (Hu and Coey 1988). Coey et al. (1991b) have shown that the samarium compound Sm 2 Felt C2. 2 has a Curie temperature of 673 K. Figure 5.2 shows the variation of Curie temperature with the rare-earth partner for R2Fe~TC and R2Fe~7. For the YzFet7C x series, Tc increases from 321 K for x-- 0 to about 520 K for x >/1.1 with a transformation of crystal structure: Th2Ni~7 type for x ~< 1.0 and Th2Zn17 type for x ~< 1.1 (fig. 5.1). At the transformation point, the volume shows a anomalous upturn, from 527A 3 for x = 1.0 to 532A 3 for x = 1.1. Detailed investigation by means of electron diffraction, at the concentration near the phase transition, reveals that the phase cannot be described by a random stacking in the c-direction of hexagonal Th2Ni17 type layers and rhombohedral Th2Zn17 type layers. The disorder is a novel type of stacking in which homogeneous sheets of dumbbell pairs of Fe atoms and homogeneous sheets of rare-earth atoms are stacked at random (Coene et al. 1990a,b). Y2Fe17C2.2 produced by treating Y2Fe~7 in butane has Tc = 660 K, but it retains the Th2NixT-type structure (Coey et al. 1991b). The rhombohedral Th2 Zn ~Tcrystal structure is shown in fig. 5.3. The 9e interstitial sites, occupied by carbon atoms, are adjacent to the rare-earth atoms. Therefore, the crystal-field interaction in the ternary carbides may be expected to differ significantly from those in the corresponding binaries. Preliminary results obtained from the 169Tm M6ssbauer resonance in Tm2FelTCx (Th2Ni~7 type) have shown that there is a large negative shift on the value of the crystal field coefficient A2o [fig. 5.4, from .

.

.

.

i

.

.

.

.

t

(a)

.

.

.

.

,

8.6

a

..S

-" ~ ~

a ~ o~S.~ ______.._I---.I Hex.

Rhomb.

8.4 c

'I- 2/3 c = =" ----

8.3

t i

. . . . 500

I . . . .

I . . . .

(b)

,.],-i--r-s--~

Tea/~ ~" 450

., 530

V '< 525 ,--,

"'"

%." o

;~o

400

~.~

52o

Y2Fel7Cx 35O 0.0 . . . .

015 . . . . x

1'.0 . . . .

1.5

Fig. 5.1. C a r b o n concentration dependence of (a) the lattice p a r a m e t e r s 6 a n d c, (b) Curie t e m p e r a t u r e and unit cell v o l u m e (for the r h o m b o h e d r a l case this is ~2 of the unit cell volume) for Y2 F e l t C~ (0 ~< x ~< 1.5), after Sun et al. (1990a).

46

H.-S. LI and J. M. D. COEY I

I

I

I

I

I

I

800

600 v

u 400

200

I

I

I

Ce Pr N d

]

[

Sm

I

I

[

I

I

I

I

Gd Tb Dy Ho Er Tm

I

I

Lu

Fig. 5.2. Variation of Curie temperature with the rare-earth partner for R 2 Fe17 , R2 Felv C and R 2 Fe 17N~ (x = 2.6) series (Zhong et al. 1990b, Sun et al. 1990c).

Gubbens et al. (1989a)]. The effect, measured with 155Gd M6ssbauer in GdzFelTCx (ThzZn17 type) shows that the value of A2o reaches a maximum, - 8 1 1 K a o 2 for x = 1.2 (Dirken et al. 1990, Jacobs et al. 1990) which is of similar magnititude as in permanent magnet materials of the type R2 Fe14 B or RCos. This effect, together with the dramatic increase in Curie temperature due to the carbon, brings the R2 FelTCx compounds into the range of interest for permanent magnet applications (Buschow 1989). High-field magnetization measurements on magnetically aligned powders indicate that the axial anisotropy field at 4.2 K is about 25 T for Sm2 Fe17C (Zhong et al. 1990b). It falls to 6 T at room temperature. The electron transfer to the Fe 3d majority band, which normally is not fully occupied in the weak ferromagnetic R 2 Fe17 compounds, makes R2 Fe17 C compounds stronger ferromagnets. This effect is related to the large increase in Curie temperature. The main effect of the C atoms is to increase the lattice constants as observed in R2Fe17Cx series. For the GdzCo17C x and GdzNilTCx compounds, such a lattice expansion has not been seen (Dirken et al. 1989b). However, a55Gd M6ssbauer spectra show that the Gd2Co17 takes up some amounts of carbon, although less pronounced than that of R 2 Felt series. This is in contrast with Gd2 Ni~7, which does not seem to absorb any carbon. 5.2. ReT17N3_:,

The R 2 Fe17 compounds with most of the rare earths (see table 5.1), have been found to absorb large quantities of nitrogen when treated at about 500°C in gaseous NH3 or N2 (Coey and Sun 1990, Sun et al. 1990c). The diffusion process of nitrogen in fine powder has been found to follow an exponential law D = D o exp(-Em/kT ) with

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

6c 06c

a

a • 9e

~9d

47

(~)2d

(~18f

4f

(D18h

02b

e6h

~ 6g

@12j

([) 12k

Fig. 5.3. Th2Znl7 (left) and Th2Ni17 (right) structures showing the octahedral intestitial 9e or 6h sites that m a y be occupied by C or N.

3

Y2(Fel.xCox)17Ny

(a 200 e4~

E

100

T = 293 K 0

I

,

I

'

I

,

I

(b

15 E

% "~

10

5 0

-5

T = 293 K i

0.0

0.2

,

I

~

r

0.4

0.6

0.8

(c) I 1.0

Fig. 5.4. Cobalt concentration dependence of (a) nitrogen content y, (b) room temperature saturation magnetization Ms, (c) room temperature anisotropy constant K1. Solid balls and circles represent the data of Y2(Fel -xCox)lTNy and Y2(Fe 1-xC0~)17, respectively.

48

H.-S. LI and J. M. D. COEY TABLE 5.1 Structural and magnetic data for R2T17C3_,~ (T = Fe or Mn) and R2FelTN3_ a compounds.

Compound

a(A)

c(h)

Tc(K)

Ce2Fe17C Pr2Fe17C Nd2Fe17C Sm2Fe~vC Sm2 Felt C2.2 Gd2Fe17C Tb2FexvC Dy2Fe17C Ho2Fe17C Er2FexvC Tm2Fe17C Lu2Fe17C

8.534 8.615 8.633 8.562 8.74 8.562 8.618 8.507 8.507 8.493 8.476 8.461

12.436 12.478 12.479 12.450 12.57 12.501 12.469 12.441 8.328 8.319 8.307 8.311

297 370 449 552 673 582 537 515 504 488 498 490

Y2 Fe17 Co.25 Y2FetvCo.s Y2Fe17Co.75 Y2FelvC Y2FeI7Ca.t Y2Fe17C2.2 Y2Fel7CH2.2

8.484 8.503 8.517 8.567 8.597 8.66 8.589

8.314 8.326 8.336 12.489 12.466 8.40 12.789

365 427 461 502 519 660 566

Ce2Fe17N2.s Pr2 FelvN2.5 Nd2FelTN2.3 Sm2FelTN2.a Gd2FelTN2.4 Tb2Fe17N2.3 DY2 FelTN2.8 Ho2FelTN3.0 ErzFelTN2.7 Tm/Fe17 Nz. 7 Lu2FelvNz.7 Y2FelTN2.6

8.73 8.77 8.76 8.73 8.69 8.66 8.64 8.62 8.61 8.58 8.57 8.65

12.65 12.64 12.63 12.64 12.66 12.66 8.45 8.45 8.46 8.47 8.48 8.44

713 728 732 749 758 733 725 709 697 690 678 694

YzFeavCN1.4 Sm2FelvCI.IN

8.674 8.737

8.512 12.702

701 744

La/MnaTC3-o Ce2 Mn17C3-~ PrzMnlvCa-o Nd2 Mn17C3-~ SmzMn17C3-o

8.983 8.785 8.871 8.847 8.810

12.940 12.683 12.783 12.750 12.777

* At room temperature. t References: [-1] Gueramian et al. (1987). [2] de Mooij and Buschow (1988b). [-3] Luo et al. (1987). [4] Zhong et al. (1990b). [5] Gubbens et al. (1989a).

Ms(/~B/f.u.) 4.2 K Room temperature

Ba(T) 4.2 K

Ref.'["

32.8 40.6 34.0

3-4 ~4 ~25 ~ 25

23.6 19.0 17.0 17.4 18.8 24.4 35.2

5-6 >35 25 20 6 9 4-5

[1, 4] [1,4] [1,2,4] [1, 3, 4] [-11] [1,4] [1,4] [1,4] [,1,4] [1,4] [,1, 5, 4] [,1,4]

35.5

4-5

36.4 37.9 40.5 31.9 26.7 22.3 27.1 27.2 31.7 32.5 35.2 34.2 34.0 35.4

14"

> 8*

[6] [6] [6] [1,4,6] [6] [11] [-6] [-8] [-8] [-8] [7, 8, 9] [-8] [-8] [-8] [8] [8] [-8] [8] [7, 8] [-7] [-7] [10] [,10] [10] [I0] [10]

[6] [-7] [8] [-9] [-10] [11]

Sun et al. (1990a). Coey and Sun (1990). Sun et al. (1990b). Katter et al. (1990). Block and Jeitschko (1986). Coey et al. (1991b).

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS

49

a diffusion constant D O= 1.95 x 10 -1° m2/s and an activation energy E m = 0.81 eV (Coey et al. 1991a). The structures of the interstitial nitrides are related to those of the hexagonal Th2Ni17 or rhombohedral ThzZnx7 parent compounds. The R2FeiTN r nitrides with y ~ 2.5 have Curie temperatures that are in the range from 678 to 758 K, compared to those for y = 0 which are in the range from 2z[1 to 477 K. This enormous increase in Curie temperature in the nitrides is due to more than doubling of the Fe-Fe exchange interactions, associated with an increase in cell volume of about 7% (Coey et al. 1990, Sun et al. 1990a). The R-Fe exchange interaction is slightly reduced in the nitrides. All compounds exhibit easy c-plane anisotropy at room temperature, except for R = Sin, which is easy c-axis. The negative sign of the iron sublattice anisotropy constant K~ is unchanged after nitrogenation (K1 is -1.3 M J m -3 for YzFei7N2.6 at 4.2K, compared to - 2 . 4 M J m -3 for YzFe~7). The room temperature anisotropy field in Sm compound is found to be 14 or 22 T (Katter et al. 1990, 1991), which is largest of any of the iron-rich rare-earth intermetallies. The anisotropy field decreases monotonically with increasing temperature, and the easy magnetization direction lies always parallel to the c-axis. Spin reorientations from the c-axis at low temperatures to the c-plane at higher temperatures are observed for other rare earths with positive as (Hu et al. 1990e). The transition temperature is 120 K in the Er compound and 200 K in the Tm compound. At 15 K, M6ssbauer data show that the iron moments are slightly larger in nitrides than in the parent compounds (Hu et al. 1991). The combined effects of carbon and nitrogen have been examined in the samarium compound, Sm2 Fel7 C i.i N l.o, where a large uniaxial anisotropy field at room temperature has also been observed (Coey and Sun 1990). Solid solutions Yz(Fei _xCox)iTN3_~ exhibit a broad maximum in magnetization at x = 0.2 (Hurley and Coey 1991). The effect of nitrogen on solid solutions is indicated on fig. 5.4. Figure 5.4a shows the nitrogen content y as a function of cobalt concentration x. A broad maximum in the magnetization at room temperature is found in the solid solution Y 2 ( F e l -xCOx)17Nywhen x ~ 0.2 (see fig. 5.4b). The 3d sublattice anisotropy is also modified in the nitrides and Ka becomes increasingly positive on cobalt substitution [see fig. 5.4c, after Hurley and Coey (1991)]. For example, the parent compound with x = 0.4 has easy plane anisotropy (K~ = - 0 . 7 MJ/m 3 at 4.2 K), but the anisotropy of the corresponding nitride is easy e-axis with K1 = +1.0 MJ/m 3. These materials possess a unique combination of high Curie temperature, strong uniaxial anisotropy and large iron moment. A coercivity of 3.0 T has been achieved by mechanical alloying (Schnitzke et al. 1990). Many studies on RzFelTN r nitrides were reported in late 1990 by Coey et al. (1990), Buschow et al. (1990b), Huang et al. (1990b), Zhang et al. (1990), Wang et al. (1990) and Zouganelis et al. (1990b); Yang et al. (1990c) also reported the results on R2FelTNr and R F e l i T i N r nitrides. 6. Compounds with structures related to CaCus There exists a series of crystal structures, RCo4 B, R 3 Co i i B4, R2 CoT B 3 and RCoa B 2 , which can all be regarded as derivatives of the CaCu5 structure (Kuz'ma and

50

H.-S. LI and J. M. D. COEY

Bilonizhko 1974). The basic CaCu5 structure compound RCo5 is built up alternately of layers of Co3 atoms and RCo2 layers where Co and R atoms are accommodated. Ordered replacement of the Co atoms in the mixed layers by B atoms leads to the various structure types which are schematically represented in fig. 6.1 (Smit et al. 1988). It can be seen from this figure that all R sites are equivalent in RCo5 and RCo3B2; two inequivalent R sites of equal occupancy occur in RCo4B; there are two inequivalent R sites with an occupancy ratio of 1:2 in R3CollB4; and in R2Co7B3, there are three inequivalent R sites with an occupancy ratio of 1:2:1.

6.1. RT4B Iron compounds, RFe4B, with the hexagonal CeCo4B structure only form with R = Er, Tin, Lu (Spada et al. 1984, van Noort et al. 1985, Hong et al. 1988), while the cobalt (Kuz'ma and Bilonizhko 1973) and nickel (Niihara et al. 1973, Chernyak et al. 1982) compounds form with all rare earths except Eu and Yb. We see in table 6.1 that the CeCo4B structure is obtained by ordered replacements of cobalt by boron on the 2c sites in every second RCoz mixed layer. The average iron moment in the RFe4B compounds is only about 1.3#B/Fe which is much lower than that in ~-Fe. Cobalt moments in RCo4B are smaller and strongly dependent on the rare-earth partner, increasing from 0.28#B for Ce to 0.68#B for Pr and saturating at 0.95#B for the heavy rare-earths (see fig. 6.2a, from Burzo et al. 1989a). This behaviour is reminiscent of the exchange enhanced magnetism found in compounds such as RCo2 (Bloch and Lemaire 1970, Gignoux et al. 1977), where a large fraction of the cobalt moment is induced by exchange interactions due to a magnetic rare earth. In contrast to the saturation behaviour exhibited by the RCo4 B series, the cobalt moments show a linear dependence on the exchange field in Y(Co4_xFex)B solid solutions (fig. 6.2b, from Burzo et al. 1989b). A study of the magnetic anisotropy in the Lu(Col_xFe~)4B system by Hong et al. (1988) showed that at low temperatures the anisotropy favours the c-axis for the Fe-end members, whereas the Co-end members are planar. The x-dependence of K1 o GcoGcoO

Co

o

B

•

QO000

~ccOoo~

~eoOooO

¢ooo$

®ooo®

..o.. T , o . o . . ,

000~000~

Iioooioooo. oeOoo

GdCo 5

GdCo4B

~oeOoeO

Gd2COlIB 4 Gd2Co7B 3

GdCo3B 2

Fig. 6.1. Schematic representation of the structures derived from the CaCu5 type for Gd(Co a -xBx)5 series.

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

51

TABLE 6.1 Structural and magnetic data for RT4B (T = Fe, Co or Ni) compounds. Compound

a(A)

c(/k)

Tc(K)

Ms (#B/f.u.) 4.2 K

CeCo4B PrCo4B NdCo4B SmCo4B GdCo4 B TbCogB DyCo4B HoCo4B ErCo4B LuCo4B YCo4 B ErFe4 B TmFe4B LuFe4B YFel.5 Coz.5 B YFel.oCo3.oB YFe0.5 C%.sB SmFe2CozB GdFe2CozB DyFezCozB SmF%CoB SmFezNizB SmFeNi3 B SmCo~NiB

5.011 5.114 5.079 5.081 5.034 4.995 4.987 4.978 4.979 4.95 5.020 5.028 5.023 4.985 5.057 5.055 5.038 5.116 5.104 5.052 5.118 5.083 5.066 5.065 5.065 4.95 4.96 4.98 4.989 4.980 4.979 4.977 4.962 4.949 4.960 4.938 4.934

6.944 6.880 6.879 6.861 6.879 6.863 6.870 6.873 6.869 6.85 6.875 6.971 6.985 6.927 6.824 6.823 6.819 6.921 6.924 6.884 6.860 6.947 6.953 6.901 6.888 6.86 6.90 6.92 6.947 6.933 6.944 6.940 6.935 6.931 6.931 6.929 6.918

297 455 458 510 505 455 427 396 386 396 382 620 610 573 633 586 519 768 770 650 721 495 404 424

1.10 5.10 5.80 3.8 3.25 5.17 6.20 6.10 5.10 2.14 2.65 2.08 1.16 5.22 4.98 4.47 3.86 6.0 1.2 4.0 4.5 3.9 2.0 2.5 3.4 4.33 5.69 5.73

GdFeo.zsC03.75B LuFeCo3B LuFe2 Co2 B LuFe3CoB EuNi4 B GdNi4B TbNi4B DyNi4B HoNi4B ErNi4 B TmNi 4 B YbNi4B LuNi4 B

* References: [1] Burzo et al. (1989a). [2] Pedziwiatr et al. (1987). 1-3] Hong et al. (1988). [4] Dung et al. (1988). 1-5] van Noort et al. (1985). 1-6] Spada et al. (1984).

460 482 510

[7] I-8] [9] [-10] [11] [12]

#0H,(T) 77 K 295 K

12.2 90.6 3.2

15.8 11.0

7.8 1.5

2.15

1.46

3.3

60.2

43.9 49.0 62.8 76.3

Burzo et al. (1989b). Drzazga et al. (1990). Chernyak et al. (1982). Oesterreicher et al. (1984). Drzazga et al. (1989). Ido et al. (1990b).

Ref.* I-I] [2,6] [-2, 12] [6, 10] I-2,6, 8, 11] [1] [1, 11] [I] [-2] [3] [2, 4, 6, 7] [-5] [-5] [3, 5, 6, 10] 1-7] [-7] [7] [10] [11] [11] [10] [10] [-10] [-10] [8, 11] [-3] [-3] [3] 1-9] [-9] [9] 1-9] [-9] [-9] I-9] [-9] [9]

52

H.-S. LI and J. M. D. COEY i

1.0 ,~,

i

,

,

,

Er

RCo4B

i

Dy_Tb

6d

0.8

0.6 O 0.4

a =C

/ (a)

0.2 0.0

,

I

,

I

,

I

,

[

,

I

~

1.2

Y(C°4"xFex)

1.0

,

B

o.8 0

I

x=l~.a

=

.

0.6 0.4

=

0.2

Bex

(b)

(T)

Fig. 6.2. Exchange field dependence of Co magnetic moment: (a) RCo4B compounds (Burzo et al. 1989a), and (b) Y(Col-xFe;)4B compounds (Burzo et al. 1989b).

for Lu(Col_xFex)4B and Y(Col_xFe~)4B is shown in fig. 6.3. At 4.2K, K 1 is - 0 . 3 9 6 M J m -3 for LuCo4B and it is +0.549MJm -3 for LuFe4B. NMR studies showed that the Co atoms at 2c sites have an easy c-axis while those at 6i sites prefer the easy c-plane, resulting in a c-plane anisotropy of YCo4B at 4.2 K (Kapusta et al. i

r

i

o Y (co1_~r~) 4~

i

[

I -5

-10

... '

'014 '.[6 '

'1..

X

Fig. 6.3. Iron concentration dependence of the anisotropy constant K1 for Lu(Col_xFex)4B and Y(Col _~Fex)4B, results by Hong et al. (1988).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

53

1990). KI changes sign above 145 K in YCo4B where the magnetic moments turns from the basal plane to the c-axis (Hong et al. 1988). No such change is found in YCo5, where K1 is positive at all temperatures. A relative small concentration of Fe in Gd(Co4_xFex)B (x ~ 0.15) causes the easy direction of magnetization to tilt from the c-axis to the basal plane (Drzazga et al. 1990). Magnetic coupling in (R1 _xLux)Fe4B (R = Ho, Er or Tm) was studied by temperature dependence of the magnetization and its high-field dependence (up to 30 T). It was found that the value of the coupling constants are Jwvo = 75 K in all the cases and JRF~= - 9 . 7 to -11.0 K (Buschow et al. 1990a), respectively. An interesting feature of the R T 4 B series is the huge rare-earth anisotropy found in these systems; a value of 90.6 T has been measured for the uniaxial anisotropy field in SmCo4B (Oesterreicher et al. 1984). 155Gd M6ssbauer effect and magnetic measurements on the series G d C o 4 B, Gd3 Co 11B4, Gd2 Co7 B3 and GdCo3 B2, show that the second-order crystal-field coefficient -4zo increases with increasing B substitution (Smit et al. 1988). Averaged over the rare-earth sites, Azo reaches -1000Kao z in RCo4B compared with - 7 0 0 K a o z in RC% and 670Kao z in RzFe~4B. The negative sign of Alo means that the rare earths having a positive second-order Stevens coefficient as (Sm 3+, Er a+, Tm 3+ and Yb 3+) show uniaxial anisotropy, similar to that of RCo5 and unlike R z F e 1 4 B . 57Fe M6ssbauer spectroscopy on oriented ErFe4B and TmFegB absorbers confirm the uniaxial anisotropy (Gros et al. 1988a). There was no indication of spin reorientation from 57Fe M6ssbauer study for R = Tm and Er (Zouganelis et al. 1990a). It is reported that NdCo4B has an easy c-axis and NdCo3FeB has an easy c-plane, which indicates that Fe atoms mainly occupy 2c sites where the transition metal has a crucial effect on the uniaxial anisotropy (Gros et al. 1989). Large intrinsic coercivities were observed in as cast RFezNizB for R = Sm or Er (Strzeszewski et al. 1988), as shown in fig. 6.4. In SmFe2NizB, the coercivity is greater than 8 T at 4.2 K. In contrast, NdFezNi/B is quite soft because of its planar anisotropy. RCO4_nFe,B alloys with R = N d , Sm or Er have been examined by i

.

.

.

.

I

.

.

.

.

I

RFe2Ni2B

0

-4

Nd (4K) _ . . . . -6

, -5

,

,

,

,

,

,

0

,

,

,

, 5

],tOH (T) Fig. 6.4. Hysteresis loop of RFe2Ni2B (R = Nd, Sm or Er) compounds, after Strzeszewski et al. (1988).

54

H.-S. LI and J. M. D. COEY

magnetometry and X-ray diffraction by Aly et al. (1988). The CeCo4B-type phase is found for all n with Er, for n ~< 3 with Sm, and for n ~<2 with Nd. Maximum coercivities, #0He> 1.7T at room temperature were obtained in a crystallized SmFezCozB sample. The unusually high achievable ratios of extrinsic coercivities to anisotropy fields in these metalloid-stabilized materials are related to their chemically relatively inert layer structure. This appears to lead to less corrugated surface structures and is so responsible for the characteristic domain-waU nucleation processes (Oesterreicher et al. 1984). Several other studies of R(Col_xFe~)4B pseudoternaries have been published by Spada et al. (1984) (Sm), Jiang et al. (1986) (Pr), Hong et al. (1988) (Lu), Burzo et al. (1989b) (Y) and Gros et al. (1988b) (Pr, Nd, Sin, Er). 6.2. R3CollB4, R2Co7B 3 and RCo3Be Table 6.2 lists crystallographic and magnetic data for a series of G d - C o - B compounds (Smit et al. 1988). The data are presented on fig. 6.5 as a function of the B concentration (as well as B/Co ratio). Both the Curie temperature and the cobalt atomic moment decrease linearly as this ratio increases. However, the second-order crystal-field coefficient A2o is an increasing function of the B/Co ratio, rising from - 6 9 8 K a o 2 for SmCo5 to - 2 2 0 3 K a o 2 for SmCo3Bz (Smit et al. 1988). Thus, the extremely large coercive field found by Oesterreicher et al. (1977) in SmCo3 Bz (5 T, as compared with 3.5 T in SmCo4B) reflects the enormous magnetocrystalline anisotropy due to Sm 3+ in this compound. Substantial coercivity (up to 3 T at room temperature is also found in Rz(FexCol-~)7 B3 material crystallized from melt-spun TABLE 6.2 Structural and magnetic data for R(Co 1- ~X~)5 (X = B or Ga) and Ce(Rh 1_ xIrx )3 B2 compounds. Compound

a (A)

c (A)

Tc (K)

Ms (#B/f.u.)

/tco (#B/f.u.)

GdCo 5 GdCo4B Gd3CollB 4 Gd2Co7B 3 GdCo3B2 CeRh 3B 2 Ce(Rho.slro.2) 3 B2 Ce(Rho.5 Iro.5)3 B2 Ce(Rh0.4Iro.6)a B2 Nd 2Co 7Ba Nd 2Fe 7B a Nd2 Fe4.2 Co2.s B3 TbCo 3Ga 2 YCo 3Ga 2

4.973 5.059 5.072 5.067 5.065 5.649 5.473 5.475 5.476 5.140

3.969 6.904 9.839 12.94 3.018 3.090 3.088 3.088 3.092 12.654

1014 517 460 345 58 115 125 118 90 330

1.37 2.85 11.9 9.8 6.9 0.324 0.301 0.266 0.215 8.0 16.5

1.67 1.04 0.83 0.60 0.00

8.813 8.818

4.063 4.062

885 205 < 85

* At an applied field of 1.8 T. t References: [1] Smit et al. (1988). [2] Hsu and Ku (1988).

3.2* 0.73*

[3] Huang et al. (1990a). [4] Felner et al. (1989).

Ref.t [1] [1] [1] [-I] [1] 1-2] 1-2] 1-2] [2] [-3] 1-3] 1-3] [4] [4]

TERNARY RA RE-EARTH TRANSITION-METAL COMPOUNDS ....

loOOsoo ~

i ....

.

.

.

t ....

_

i ....

55

i

Gd(C°l'xBx)5

1.5 3=

~

N~ 600 B/Co = [" 400 200

~

gCo

1.0

Tc ~

o 0.5

0/5

1/4

4/3.1 3 / 7

"~[: 0.0

0.0

0.1

0.2

0.3

0.4

X

Fig. 6.5. Boron concentration dependence of Curie temperature and Co moment for Gd(Co l_~B~)s series of compounds (Smit et al. 1988). TABLE 6.3 Structural and magnetic data for CeTPt 4 (T = Cu, Ga, Rh, Pd or Pt) compounds. Compound

a(/k)

¢(•)

CeCuPt 4 CeGaPt 4 CeRhPt 4 CePdPt 4 CePt 5

5.338 5.328 5.346 5.168 5.365

4.347 4.402 4.385 4.157 4.379

#eff ( ~ B / C e )

2.54 2.46 2.37 2.51 2.48

0(K)

Z(x 104emu/mol.f.u.)

- 8 - 7 -16 -9 - 8

2.0 0.3 0 1.0 3.2

ribbons (Aly et al. 1988). Melt-spun ribbons of Pr2 Fe7 B3 alloys develop coercivities up to 2.0T upon annealing between 620 and 660°C (Dracopoulos et al. 1990). However, 57Fe M6ssbauer spectra and X-ray powder diagrams show that the samples consist of two phases, Pr2Fe14B and PrFe4B4. Finally, ferromagnetic RCo3 Ga2 compounds have been reported for R : Y (Tc = 100 K) and R = Tb (Tc = 210 K). The structure is again related to CeCus, except that the Ga substitution now occurs in the Cu3 layers rather than the CeCu2 mixed layers (Felner et al. 1989).

6.3. CeTPt4 (T= Cu, Ga, Rh, Pd or Pt) The CeTPt4 compounds, with T = Cu, Ga, Rh, Pd or Pt, were found to crystallize in the hexagonal CaCus-type structure (Adroja et al. 1989). The susceptibility of all these compounds follows Curie-Weiss behaviour with a slight deviation at low temperatures. The cerium is essentially in a trivalent state. The paramagnetic Curie temperature is negative for all the compounds, see table 6.3. 7. Compounds with structures related to CeNi3 A series of ternary rare-earth-nickel compounds, R 3Ni 7B2, crystallize in a structure related to CeNi 3 (space group P6a/mmc) when R is a heavy rare earth. The nickel

56

H.-S. LI and J. M. D. COEY

is nonmagnetic, and the compounds order antiferromagnetically as a result of R - R exchange interactions. There are two crystallographic sites for the rare earth, and it is of interest that the magnitude of-42o at the 2c site measured using the 155Gd M6ssbauer resonance is --2000Kao 2 (Felner 1983), second only to the values found in Gdt +eFegB4.

8. Compounds with ternary structure types 8.1. R3Fe62B14

A metastable cubic (space group Im3m) compound Y3Fe62B14 has been prepared by crystallizing melt-spin ribbons. There is one Y site and four Fe sites. The compound shows a ferromagnetic order with a Curie temperature of 510K (de Mooij and Buschow 1987, de Mooij et al. 1987). The saturation magnetization at 4.2K in a field of #o H = 1.81 T amounts to 162 A m 2 kg-1, which corresponds to an average Fe moment of 1.9#B. 8.2. RCozeB 6

The R C o l z B 6 compounds crystallize in the rhombohedral SrNi12 B 6 structure with space group R3m (Niihara and Yajima 1972, Chaban and Kuz'ma 1977). A systematic account of the magnetic properties of the series was given by Jurczyk et al. (1987a) and Mittag et al. (1989). Curie temperatures (table 8.1) range from 154 to 177K. Unlike RCo2 or RCo4B, the average cobalt moment in RCo12B 6 is practically independent of the rare earth; it is 0.44pB in YCo12B6 and 0.43#B in GdCo12B 6 (Rosenberg et al. 1988). The small difference in cobalt moment or Curie temperature between YCOl2B 6 and GdCo12B 6 reflects the weakness of the G d - C o exchange interaction compared to the Co-Co exchange interaction, which largely TABLE 8.1 Structural and magnetic data for RT12B 6 (T = Fe or Co) compounds. Compound

a (A)

c (A)

Tc (K)

NdFe12B 6 CeColzB 6 PrCo12B 6 NdCo12B6 SmCoa2 B6 GdCo 12B6 DyCox2B 6 YCoI2B ~

9.605 9.496 9.493 9.491 9.470 9.454 9.445 9.418

7.549 7.442 7.475 7.475 7.458 7.457 7.443 7.442

230 154 177 174 172 169 165 151

* References: [1] Buschow et al. (1986). [2] Mittag et al. (1989). [3] Jurczyk et al. (1987a). [4] Niihara and Yajima (1972).

Ms ( #B/f.u.) 4.2K 77K 19.5 5.4 8.4 8.8 6.8 2.1 5.9 6.5 [5] [6] [7] [8]

4.5 5.6 6.0 5.5 1.5 1.9 5.5

Teomp

47.8 72.0

E1 Masry et al. (1983). Rosenberg et al. (1988). Chaban and Kuz'ma (1977). Rosenberg et al. (1989).

Ref.* [1] [2,3,4] [2,3] [2,3] [2, 3, 5] [2, 3, 6, 7, 8] [2, 3] [3,6,8]

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

57

determines the value of Tc. The ineffectiveness of the rare earth in influencing the magnetic properties is probably due to the low concentration of rare-earth atoms in the structure, and the fact that they are relatively isolated by a surrounding cage of boron atoms (Kuz'ma et al. 1981). The exchange integral IJ6acol=5.54K in GdCot2B 6 is four times smaller than that in Gd2Co~,B (Rosenberg et al. 1988), whereas the Jcoco integral is similar. Figure 8.1 shows the temperature dependence of the magnetization of RCo12B 6 for R = Ce, Nd, Pr, Sm, Gd or Dy in a field of 2T (Jurczyk et al. 1987a). The R - C o coupling follows the usual trend with R and Co moments coupling ferromagnetically for the light rare earths and antiferromagnetically for the heavy rare earths. A ferrimagnetic spin compensation phenomenon is observed in GdCo12B 6 and DyCoI2B6 at 46 and 72K, respectively. Buschow et al. (1986) found a metastable compound with the rhombohedral SrNi12 B6 structure in the N d - F e - B system. NdFe~2 B 6 w a s obtained by crystallizing amorphous melt-spun flakes at relatively low temperatures. The Curie temperature is 230 K and the magnetization at 4.2 K is 19.5#~/f.u. 8.3. R2T23B 3

Cubic rare-earth iron borides R2T23B 3 (R = Pr, Nd, Sm or Gd) have been prepared by crystallizing melt-spun ribbons (de Mooij et al. 1987). Some magnetic properties of these compounds are given in table 8.2 (de Mooij and Buschow 1987). A similar metastable compound Nd4.5 ± 1F%2.5 +_s B12.5 _+3.5 has been obtained during the crystallization of Fe-rich N d - F e - B amorphous materials, which has an

RCoI2B6 6

:i

4

U ,

,

,

,

I

,

,

,

100

,

I

200

+

,

,

,

300

T (K) Fig. 8.1. Temperature dependence of the magnetization of RCo~286 compounds in an applied field of 2 T (Jurczyk et al. 1987a).

58

H.-S. LI and J. M. D. COEY TABLE 8.2 Structural and magneticdata for RzFez3B3 compounds(de Mooij and Buschow 1987, de Mooij et al. 1987). Compound

a (A)

Tc(K)

Pr2Fe23B3 Nd2Fe23B3 Sm2Fe23B3 Gd2Fe23B3

14.18 14.19 14.06 14.11

644 655 663 689

Ms(#B/f.u.) 49.1

unknown bcc structure with a = 12.38 A. It is ferromagnetic, with a Curie temperature of 548 K and a saturation magnetization of 19 J T-~ kg-~ (Altounian et al. 1988).

8.4. ReT14C The first report of a ferromagnetic tetragonal ternary carbide, whose composition was given as Gd 3 Fe2o C, came from Stadelmaier and Park in 1981 (Stadelmaier and Park 1981) in their study of the G d - F e - C phase diagram. The discovery of 'Gd 3 Fe2o C', therefore, preceeded that of Nd2 Fe14 B. Furthermore, the carbide crystal structure was determined by Marusin et al. (1985) for La2 Fel~ C, independently and at roughly the same time as the Nd2Fe~4B structure determination (Herbst et al. 1984, Givord et al. 1984a, Shoemaker et al. 1984). Unlike the 2 : 14 : 1 borides which form peritectically from the melt at about 1400 K (Matsuura et al. 1985) the 2 : 14 : 1 carbides result from a solid-solid transformation below 1200 K, carbides generally need prolonged annealing of several weeks at these temperatures. A systematic synthesis was made by Gueramian et al. (1987); they found the Nd2Fe~4B structure for R2FeI4C for R = Pr, Sm, Gd, Tb, Dy, Ho, Er, Tm or Lu. Nd2FeI4C was added later by Buschow et al. (1988b). As-cast ingots contain a rhombohedral RzMnxTC3-a-type phase (Block and Jeitschko 1986) which transformed to the La2Fe~4C-type phase after 20-30 days annealing at 1170 K. Alloys with Y and Pr were annealed between 1070 and 1 110 K for 50 days, and then cooled down to 700K in 100K steps over several months. Initially, Bolzoni et al. (1985), Liu et al. (1985) and Gueramian et al. (1987) reported that Nd2Fe14C could not be formed. A subsequent investigation by Buschow et al. (1988b), however, showed the Nd2Fe14C compound does exist, but that it is only stable below about 1160 K. At higher temperatures, it transforms into Nd2 Fe17 C3_a and NdzC 3. Figure 8.2 illustrates the temperature range where the R2Fe14C phase can be obtained (de Mooij and Buschow 1988b). Kinetics in the region below the dashed line are prohibitively slow, the transformation temperature T~ increasing monotonical from light to heavy rare earths. Assuming the solubility limit of carbon in Nd2 Felt Cx can slightly exceed x = 0.6, de Mooij and Buschow proposed a reaction scheme for formation and decomposition of the 2 : 14 : 1 phase, T
T>Tt

17RzFe14C,~ 14R2Fe17Co.64 + 3RzC3.

(17)

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS

59

1200

1100

1000

900

800 I

Nd

I

I

Sm

I

I

~

I

I

2b I~

Fig. 8.2. Variation of the transition temperature Tt (below which R2Fe14C can be formed) on the rare earths (de Mooij and Buschow 1988b). The fall in Tt towards the beginning of the lanthanide series suggests that for R = La or Ce the value of Tt would be in the temperature range where the diffusion limited reaction rates are too low to allow the RzFe14C phase to form from the primary crystallization products of the as-cast melt. If the reaction rates below Tt can be enhanced by other means, e.g., by applying fast cooling, by mechanical treatment of the alloys or by additives, formation of the R2Fel~C phase is still possible. Despite these difficulties, La 2 Fe 14C was obtained by prolonged low-temperature anneals (Marusin et al. 1985) and CezFe14C was successfully prepared by substituting 2% manganese for iron in CezFe14C (Jacobs et al. 1989). The intrinsic magnetic parameters of R 2 Fe14C are listed in table 8.3. It is interesting to make a comparison with R 2 Fe14 B (see Buschow 1988c). The lattice parameters a and c are displayed in fig. 8.3a for the two series. The a parameter is similar for borides and carbides, but the c parameter is much lower in R2Fe~4C than in RzFe~4B. The variations of the Curie temperatures across the rare-earth series are presented in fig. 8.3b. Values of Tc for RzFe14C are systematically lower by 40-50 K than for RzFe14B. This fact might be attributed to a weakening of the exchange with the shortening of some F e - F e distances, due to the smaller c/a ratio and cell volume of the carbides or else to a reduction in iron moment due to the different electron transfers (Deppe et al. 1988) between iron and the metalloid (boron and carbon), as described in the 'donor model' (Cadeville and Daniel 1966). At low temperatures, the iron magnetization in Lu2Fe14C is 27.61~B/f.u. (1.97#B/Fe) compared to 29.30#B/f.u. (2.09#B/Fe) in L u 2 Fe~gB (Denissen et al. 1988a,b); this indicates that the average iron moment in the carbides is slightly lower (6%) than in the borides which is sufficient to explain the difference in Tc. Iron magnetic moments for each individual crystallographic site were measured by Buschow et al. (1988b), Denissen et al. (1988a,b) and Jacobs et al. (1989) using 57Fe M6ssbauer spectroscopy; the results are listed in table 8.4 where R 2 Fe14B data are included for comparison. Site moments are reduced by about 5% at all except

H.-S. LI and J. M. D. COEY

60

TABLE 8.3 Structural and magnetic data for Ra Fe14C compounds. Compound

a(A)

c(A)

La2Fe14C Ce2Fe14C Pr2Fe14C Nd2Fe14C SmzFe14C Gd2Fex4C Tb2Fe14C Dy2Fe14C Ho2Fe14C Er2FeI4C Tm2Fe~4C Lu2Fea4C Ndl.sDyo.2Fe14C Ndl.6DYo.4Fea4C Ndl.zDyo.sFe14C Nda.aLuo.zF%,C Ce2Fe13.7Mno.3C Pr2Fe13.7 Mno.3C Pr2 FelEMn2C Pr2Fel~ Mn3C Pr2 Fes Mn6 C Nd2Fe13.v Mno.3C Nd2 Fe13.5Mno.s C Nd2FelaMnC Nd2Fe12.sMn1.sC Nd2Fe12Mn:C

8.819 8.74 8.816 8.827 8.802 8.795 8.771 8.763 8.752 8.742 8.732 8.719 8.810 8.804 8.786 8.788

12.142 11.84 12.044 12.022 11.952 11.902 11.864 11.836 11.813 11.791 11.766 11.726 11.998 11.969 11.925 11.964

Tc(K)

345 513 530 580 630 585 555 525 510 500 495 535 537 540 530 480 412 305 230 85 506 491 451 401 354

Ms (#~/f.u.) #oHa (T) ~R(K) Ref.~ 4.2 K Room Room temperature temperature 27.5*** 23.9** 34.5 32.5 30.2 18.1 12.0 10.5 10.9 12.3 18.4 27.2 30.9 26.9 24.8 34.1 33.8 30.6 23.8 16.9 -

9.5 23.5 15.9" 8.0* 9.0* 12.5" 18.2" 22.3* 25.0*

120

3.53

0.1 0.4 3.1

35 3O8 310 108 98 98 117

27.2

102

21.3

69

[1,4, 5] [8] [1,9] [3,5,6,7, 10, 13] [1, 10, 13] [1,10,11,12,13] [1,10,13] [1,2,6,10,13] [1, 6, 10, 13] [1,2,10,13] [1, 10, 133 [1, 10, 133 [6] [6] [6] [6] [9] [9] [9] [9] [9] [7] [7] [7] [7] [7]

* at an applied field up to 7 T ** extrapolated values from R2Fe14_xMn~C series *** from 57Fe M6ssbauer spectroscopy t References: [1] Gueramian et al. (1987). [8] Jacobs et al. (1989). [2] Pedziwiatr et al. (1986). [9] Buschow et al. (1988d). [3] Buschow et al. (1988b). [10] de Boer et al. (1988b). [4] Marusin et al. (1985). [11] Abache and Oesterreicher (1985). [5] Denissen et al. (1988a,b). [12] Kou et al. (1990). [6] de Boer et al. (1988a.). [13] Gr6ssinger et al. (1990). [7] Buschow et al. (1988c).

the 8j site, where the r e d u c t i o n is a b o u t 14%. U n l i k e L u 2 F e 1 4 X ( X = B , C ) , G d 2 F e 1 4 X c o m p o u n d s have a l m o s t the same m a g n e t i z a t i o n for X = B o r C, suggesting that the p a r t of the i r o n m o m e n t i n d u c e d b y a m a g n e t i c rare e a r t h is larger in the c a r b i d e s t h a n in the borides. H o w e v e r , the m a g n e t i z a t i o n m e a s u r e m e n t s b y a p u l s e d field of 1 2 T give 16.73pB/f.u. for G d 2 F e 1 4 C a n d 18.01#B/f.u. for G d 2 F e l g B ( K o u et al. 1990). F i g u r e 8.4 c o m p a r e s the m a g n e t o v o l u m e effects as a function of t e m p e r a t u r e for

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS 0.96

i

,

i

.

i

,

i

,

i

i

,

61

i

•

R-Fe-B

0.94 ,-,0.92

1.22 1.20 e~

"-'0.90

1.18,-~

0.88 1.16 0.86

(a) I

I

I

I

I

I

I

I

I

l

I

I

I

700 •

R-Fe-B

600

500

400

La Ce Pr Nd

Sm

Gd Dy Ho Er Tm Yb Lu

Fig. 8.3. Comparison of (a) the lattice parameters a and c and (b) the Curie temperature, for the R2Fe14C and RzFe14B series. Data were taken from table 8.3 for the carbides and from Buschow (1988c) for the borides.

TABLE 8.4 Fe moments on the different crystallographic sites of Nd2 Fe14 B structure for some R 2Fe~4C and R 2Fe14 B compounds, values deduced from 57Fe M6ssbauer spectroscopy. Compound

T(K)

8j2

16k 2

16k 1

8jl

4c

4e

Ms (#B/f.u.)

Lu2Fe14C

10 300 10 300 10 300 10 300 300 300 20

2.26 1.90 2.38 2.07 2.65 2.36 2.53 2.33 2.19 2.31 2.24

L99 1.67 2.07 1.81 2.38 2.11 2.30 2.08 1.97 2.07 1.92

1.94 1.62 2.04 1.78 2.19 1.94 2.20 1.95 1.80 1.95 1.78

1.81 1.49 2.06 1.62 2.19 1.90 2.13 1.89 1.80 1.89 1.65

2.02 1.71 2.15 1.83 2.06 1.85 2.39 1.88 1.78 1.91 1.82

1.73 1.46 1.83 1.60 1.91 1.69 1.92 1.77 1.55 1.76 1.33

27.61 23.11 29.30 25.17 31.93 28.26 31.63 28.21 26.39 28.15 25.73

LuzFelgB Gd2Fel~C Gd/Fea4B Nd2Fe14C Nd2Fe14B Ndz(Fe13.7 Mno.3)C

* References: [1] Denissen et al. (1988a,b). I-2] Buschow et al. (1988b). [3] Jacobs et al. (1989).

Ref.* [1] [-1] [1] [1] I-1] [1] [1] [1] 1-2] [2] [3]

62

H.-S. LI and J. M. D. COEY

-~

~"

/

20

0

-'-.

Lu2FeI4B ,

-20

,

,

.

r

200

.

,

,

i

,

400

,

,

i

,

,

600

T (C °) Fig. 8.4. Magnetovolume effect as a function of temperature for Lu2Fe14C and Lu2Fe14B (Buschow 1988b).

Lu2 Fe14B and Lu2Fe14C (Buschow 1988b), a highly anomalous thermal expansion behaviour is manifest at T~< To, but the negative volume magnetostriction is less pronounced in the carbides. The major contribution to this anomaly was shown to originate from the spontaneous volume magnetostriction of the iron sublattices. The persistence of the effect at temperatures substantially above the Curie temperature in the ternary compounds lends credence to the view that the local iron moments do not disappear at Tc (Holden et al. 1984). Preliminary singular point-detection measurements carried out on the Y2 Fe14Bl-xCx series, reported by Bolzoni et al. (1985), indicate that the anisotropy field does not change on varying the carbon content (#oHa = 2.15 T at room temperature). High-field measurements performed on an oriented powder sample of Lu2FelgC give that the anisotropy field associated with the Fe sublattice in R2 FeI4C is about 4.0 T at 4.2 K (de Boer et al. 1988b), which is larger in magnitude than that in the Y2 Fet4 B compound (Givord et al. 1984b). Singular point detection measurements reveal that the value of K~ is 11.1 M J m -3 at 4.2K for GdzFe14C , compared to 9.0 M J m -a for Gd2Fe~4C (Kou et al. 1990). This difference in magnitude of K~ was attributed to the lower c/a ratio for Gd 2 Fe~4C than that for Gd2 Fe14B. There is a composition dependence of anisotropy field on the Nd2Fez4Bl_xC~ series, as shown in fig. 8.5 (Bolzoni et al. 1985). It appears that the increase in anisotropy with increasing carbon content is mainly due to an increasing contribution of the Nd ions to the anisotropy field. Generally, the 2:14:1 carbides are more anisotropic than the corresponding borides. Figure 8.6 shows the magnetization curves at 4.2 K of the polycrystalline Dy2FeIgX and Er2Fel,~X (X = B, C) after Pedziwiatr et al. (1986). 16aDy M6ssbauer studies on Dy2Fe14C and Dy/Fea4B by Gubbens et al. (1988b) confirm that there is an increase in rare-earth second-order crystal-field parameter B2o, namely --1.1 + 0.5K for Dy2Fe14B and -1.7 + 0.5K for Dy2Fe14 C. The magnetic phase transitions of the R2Fe~4C series as function of temperature

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS t

~9~1° ~ g

i

i

Nd2F~ / T

~'

"~

8 S

0.0

63

[]

'

' 012

'

' 014'

T/Tc

' 0'.6

= 0.5

'

0.8

X

Fig. 8.5.Carbon concentrationdependenceof the uniaxial anisotropyfieldin the NdzFe 14B1--xCx series (Bolzoni et al. 1985). 16

. . . .

i

. . . .

i

. . . .

i

. . . .

8 4

~[[ ~/

0,'0 . . . .

• •

015 . . . .

1'.0 . . . . p_0H (T)

Er-Fe-C Er-Fe-B

1'.5 . . . .

2.0

Fig. 8.6. Magnetizationcurveson REFe14X (R = Dy or Er; X = C or B) polycrystallinesamples(Pedziwiatr et al, 1986).

are schematically represented in fig. 8.7, with those for R2Fe14B for comparison. These two series are very similar, the Pr, Gd, Tb, Dy and Lu compounds have an easy e-axis at all the temperatures, while the Sm compound is planar. A tilted spin structure occurs for Nd2Fe14C at temperatures below 120 K (Denissen et al. 1988a,b) and for Ho2 Fe14C at temperatures below 35 K (de Boer et al. 1988a), the corresponding temperatures for Nd2Fe14B and HozFe~4B are 135 and 57 K, respectively. Plane to c-axis spin reorientations occur near room temperature for TmEFe14C and Er2Fe~4C (de Boer et al. 1988b), just as they do in the corresponding boride. The similarity between the R2Fe~4C and RzFe~4B series has led to an interest in these materials, with a view to their potential application in permanent magnets. The microstructure of the carbide formed by solid-state transformation has been exploited to obtain coercivity, (Liu and Stadelmaier 1986, N. C. Liu et al. 1987), above 1.2 T in cast and annealed materials without any additional processing step. The high coercivity is related to a cellular microstructure of the R2Fe~Ba_xC~ phase in which the cell size is approximately 1 ktm. The cell structure, which originates in a peritectoid-like transformation from primary R2Fe~TX3-~ (X = B or C), is quite

64

H.-S. LI and J. M. D. COEY

R2Fel 4B

Y[

I

La Ce Pr

R2Fe 14c Pr Nd S nl Gd Tb Dy Ho

Nd Sm Gd Tb Dy Ho Er Tm Yb

Er Tm Yb

LoI

Lu I

0

,

,

J

I

i

i

400

i

I

0 T(K)

J T

i

i

[

i

L

400 T(K)

Fig. 8.7. Magnetic phase diagrams of R2Fe14C and R2Fe14B series (Buschow 1988c). White denotes m I]c; black m / c ; and shaded the canted structure.

stable and does not change during prolonged annealing. The coercivity was found to depend sensitively upon the alloy composition: 0.95T for R15Fe76X9; 0.85T for R15Fe77X8; and 0.7T for R14.sFe77.sX8, where X = Bo.lCo. 9 and R = Ndo.6Dyo. 4. The maximum value of #oiHc, found in Nd9Dy6Fe77Bo.8CT.2, is as high as 1.25T. Hadjipanayis and co-workers have reported a value of 2.1 T for the coercivity developed in as-cast Dya5 Fe77 C 8 alloys after a heat treatment at 900°C (Hadjipanayis et al. 1988, Llamazares et al. 1989). The high coercivities are attributed to localized domain-wall pinning at the boundaries between the hard, magnetic Dyz Fe14C phase and a D y - F e - C phase (Tc~40K), Coehoorn et al. (1988, 1989) have achieved #oiHc = 1.0 T and Br = 0.7 T in Nd13.5 Fe79.6C6.9 alloys obtained by annealing meltspun flakes. They found the amount of Nd2 Fe14C formed, the presence of secondary phases, and the magnetic properties all depend sensitively on the composition, with optimum results being found in a narrow composition range. 8.5. RTaSn 6

No information is available on the magnetic properties of RFe 6 Sn6, but the isostructural manganese stannides RMn6Sn 6 (hexagonal HfFe6Sn 6 structure, space group P6/mmm) are reported to be ferromagnetic for R = Gd, Tb, Dy or Ho, and antiferromagnetic for R = Er, Tm or Lu. Magnetic ordering temperatures range from 449 K for Gd to 337 K for Tm (Malaman et al. 1988).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

65

8.6. RI+,T4B 4

A tetragonal phase of approximate composition RFe4B4 was first mentioned for R = Ce by Bilonizhko and Kuz'ma (1972), and then for R = Nd, Sm or Gd by Chaban et al. (1979). It attracted more attention after NdFe4B, was found as a minor phase in Nd2Fe14B magnets (Oesterreicher and Oesterreicher 1984). Systematic synthesis and crystal structure determination was carried out by Bezinge et al. (1985) for R = Ce, Pr, Nd, Sin, Gd, Tb; by Givord et al. (1986) for R = Nd; and by Tian et al. (1989) for R = Ce. Niarchos et al. (1986) and Rechenberg et al. (1986) have studied the magnetic properties for the series with all rare earths except Eu and Yb. The crystal structure of R I+~Fe4B 4 is formed of two substructures, one for R atoms and another for Fe and B atoms, both having tetragonal symmetry and repeat distances ca and eve. Rare-earth atoms form infinite linear chains along the tetragonal c-axis, while the iron and boron atoms form chains of edge-sharing tetrahedra along the same directions (see fig. 8.8). Single-crystal X-ray diffraction data on Sm1.13Fe4B4 can be explained on a commensurate structure with composition SmlT(Fe4B~)15 and space group P4 2/n, which includes a periodic twist modulation of the iron tetrahedral chains around c-axis (Bezinge et al. 1985). The single-crystal structure determination on Nd~0(FegB4)9 by Givord et al. (1985) showed that the whole structure can be described in the Pccn orthorhombic space group with c = 35.07/~, while the Nd sublattice is described by the space group I4/mmm and the Fe-B sublattice is described by the space group P42/ncm. Tian et al. (1989) claim that the structure of the Ce compound is actually incommensurate, and refer to it as a one-dimensional 'chimney-ladder' structure. The series of rare-earth iron borides have very low Curie temperatures, with a maximum Tc = 37K for R = Sm, (Rechenberg and Sanchez 1987) compared with Tc = 20 K for R = Gd. It is unusual to find that the Gd member of an R-T series does not have the highest To but here, there is an exceptionally strong uniaxial crystal field which stabilizes the magnetic order in the Sm case. STFe M6ssbauer measurements by Rechenberg et al. (1986) indicated that all the iron in Rs Fe~8B18 Fe

B

NdFel+~Fe4B 4 Fig. 8.8. Schematic representation of the c-plane of the Ndl +.Fe~B4 structure (Givord et al. 1986).

66

H.-S. LI and J. M. D. COEY

(R = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er or Lu) shows no trace of magnetic ordering for temperatures down to 1.5 K. The low Tc values for the series clearly indicate that the Fe atoms are not magnetic. The loss of the iron moment results from the high concentration of B and R atoms. For comparison, the critical concentrations for the appearance of magnetism in amorphous FexMloo-x alloys is xc = 38 for B and xc = 36 for Y (Coey and Ryan 1984). The destruction of the 3d magnetic moment may be attributed mainly to 3d(Fe)-5d(R) and 3d(Fe)-2p(B) hybridization. The magnetic properties of R~+~Fe4B4 are, therefore, due to the rare earths. Temperature dependence of the magnetization and the susceptibility for the Gd2Fe7B 7 compound is shown in fig. 8.9 (Tenaud 1988). High-field magnetization data on a Ndl.~ Fe4B4 crystal (Givord et al. 1985, Givord et al. 1986) are shown on fig. 8.10, which revealed a hard c-axis anisotropy, with the anisotropy constant Ks reaching - 6 . 9 M J m -3. A large anisotropy of the paramagnetic susceptibility was also observed. The ferromagnetic Nd moment at 4.2 K is 2.2#B/Nd compared to the free ion value of 3.27#B. This reduction is due to the crystal field. 155Gd and 161Dy M6ssbauer spectroscopy on Gdl.I~Fe4B4 and DyLEFe4B4 compounds led to a determination of the second-order crystal-field coefficient .~zo = - 2 4 5 0 K a o 2 (Rechenberg et al. 1987, Bog6 et al. 1989) which is a record for any rare-earth intermetallic. It is about 3.5 times greater and opposite in sign to the average over two rare-earth sites in Nd2Fe14B (670Kao2). This implies that the crystal-field interactions are comparable or stronger than the exchange interactions in the R~ +~Fe4B4 series. M6ssbauer measurements (Rechenberg et al. 1987, Oddou et al. 1988) were also used to determine the easy direction of magnetization, which is found to be the c-axis for Sm and the c-plane for Nd and Dy as expected from the

T (K) 50 •

100

i

'

150

i

•

200

i

'

i

250 •

300

i

8

•

i

t

~

Ms

15 ~"

lOt~

4 O~

2

/

0

,

0

~

,

,

1

,

I

10

,

,

,

,

I

Gd2Fe7B7

,

,

20

,

,

I

30

,

,

5

,

,

I

,

..../

0

40

T (K)

Fig. 8.9. Temperature dependence of the magnetization and the susceptibility for Od 2Fe 7B7 (Tenaud 1988).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

67

12 ~

[1101

10 [1001

S"

8

Nasre18~8

6

T=4.2K 4

2 0

[001] I

I

I

2

4

6

gOH (T) Fig. 8.10. High-field magnetization curves of Ndl. 1Fe4 B4, results by Givord et al. (1985).

sign of the second-order Stevens coefficient as (positive for Sm and negative for Nd and Dy). The R C o 4 B 4 series was first described by Kuz'ma et al. (1979). These compounds have the CeCo4B 4 structure, with c = 2OR. Magnetic measurements on the SmCo4B 4 compounds (El Masry and Stadelmaier 1984) and the R = Pr, Nd or Sm compounds (Jurczyk et al. 1987b) show relative high Curie temperatures around 180K for the three compounds. There is little evidence for a Co moment, see table 8.5. Table 8.6 lists data on ROs4B4 and RIr4B4 (Hiebl et al. 1982).

8.7. R6TllGa3 and Nd6Fej3Si Ternary rare-earth-iron gallides, R6FetlGa 3 (R = Pr, Nd, Sm) crystallize in the tetragonal La6ColtGa3 structure with space group I4/mcm (Sichevich et al. 1985), see table 8.7. There are two R sites (161 and 8f), one Ga site, three Co sites and another site occupied at random by Coo.sGao.5. The structure is formed only with the light rare earths while the heavy rare earths form the C15 Laves phase. Three compounds R6FellGa 3 (R= Pr, Nd, Sm) are ferromagnetic with Tc in the range 320-424K (Li et al. 1990). The average iron moment is 1.6#B. Anisotropy fields are greater than 7 T at room temperature. A sharp change of the slope in the magnetization curves (fig. 8.11) has been observed, which was attributed to the existence of two rare-earth sublattices with opposite anisotropy. However, observation of a similar effect in the compound with R = La (Hu et al. unpubl.) suggests an exchanged-based origin. Another version of the La 6Co 1t Ga3-type structure was identified in the Nd 6Fe t 3Si compound (Allemand et al. 1990), in which the 161 sites previously occupied by a mixture of Co and Ga in R6FeltGa3, are now entirely occupied by Fe atoms.

68

H.-S. LI and J. M. D. COEY TABLE 8.5 Structural and magnetic data for Rx +~Fe4B 4 and RCo4B 4 compounds.

Compound

a(A)

CR(A)

La 1+, Fe4 B4 Ce 1+,Fe4B 4 Prl +~Fe4B4 Ndl+~Fe4B 4 Sin1 +Xe4B4 Gdl+~Fe4B 4 Tbl +~Fe4B 4 Dyl+~Fe4B 4 Hol+~Fe4B4 Erl +~FegB4 Tml +~FegB4

7.20 7.090 7.158 7.141 7.098 7.073 7.049 7.00 6.98 6.97 6.96

3.64 3.4889 3.5301 3.5241 3.4574 3.442 3.4109 3.390 3.36 3.32 3.31

PrCo4B 4 NdCo,~ B4 SmCo4B4

7.108 7.126 7.067

Cve(A) 3.9102 3.9042 3.9073 3.9124 3.9217 3.919

10.694 11.400 11.552

* References: [1] Niarchos et al. (1986). [2] Givord et al. (1985). [3] Bezinge et al. (1985).

Tc(K)

Ms (#B/f.u-) Ref.*

7.5 14 37 20 16 11.5 6.5 ---

[ 1] 1.1,3] [1, 3] [1,2,3] [1, 3, 4] [1,3] [•,3] [1] 1.1] [1] [1]

1.5 2.4 6.1 3.5 5.7 5.5

171 182 176

1.7 1.9 0.2

[5] 1-5] [5]

[4] Rechenberg and Sanchez (1987). [5] Jurczyk et al. (1987b).

TABLE 8.6 Structural and magnetic data for RT4B4 ( T = Os or Ir) compounds, results by Hiebl et al. (1982). Compound EuOs 4 B4 Eulr4B 4 SmOs~B4 SmOsalrB4 SmOs2 Ir2 B4 SmOslraB4 Smlr4B~ PrOs2 Ir2 B4

a (A)

c (A)

0 (K)

7.5262 7.6219 7.526 7.5406 7.5538 7.5742 7.590 7.599 l

4.0159 3.9771 4.009 3.9949 3.9860 3.9822 3.976 3.9835

#err (#B)

0 2.5

7.20 7.84 1.69 1.87 1.71 1.62 1.55 3.55

22

TABLE 8.7 Structural and magnetic data for R6Fel~Ga3 (R = Pr, Nd or Sm) and Nd6Fe13Si compounds. Compound Pr6Feax Ga 3 Nd6Fell Ga 3 Sm6FealGa 3 Nd6Fe13Si

Tc

(K)

320 397 462

a (A)

c (A)

Ms* (flB/f.u.) 4.2K 300K

Bcr (T) 4.2K 300K

8.105 8.090 8.056

23.06 22.96 22.94

22.5 28.9 17.1

4.3 4.8 >7.0

8.056

22.78

* Values at maximum applied field of 7 T ? References: [1] Li et al. (1990). [2] Allemand et al. (1990).

14.2 16.1 15.6

2.3 2.7 5.5

(Bhf) (T) 8.9 12.4 22.8

#Fe (/~B) Ref.'[ 0.60 0.84 1.54

[1] [1] [1] [2]

TERNARY RARE-EARTH TRANSITION-METAL C O M P O U N D S

15

69

Pr~

R=Sm

112 :::L

T = 300 K 0

20

10 T

0

Sm

,

I

2

,

L

4

,

I

,

.

6

~o H (X) Fig. 8.11. Magnetization curves on magnetically aligned R 6Ga 3 Fell (R = Pr, Nd or Sm) powder samples. External fields were applied perpendicular to the alignment direction (Li et al. 1991).

8.8. R2TleP 7 and RCosP5

The ternary system of R - T - P (T = Fe, Co or Ni) contains many compounds which crystallize with about a dozen different structure types (Reehuis and Jeitschko 1989). Systematic investigations of the magnetic properties were reported by Jeitschko, Reehuis and their co-workers on the series RT2P2 (Jeitschko and Reehuis 1987, Reehuis and Jeitschko 1987, M6rsen et al. 1988, Reehuis et al. 1988b), RCo8P5 (Reehuis et al. 1988a) and R2 T12 P7 (Reehuis and Jeitschko 1989). Among these rareearth-transition-metal phosphide ternary series, R2TIEP 7 and RCosP5 are richest in transition metal and rare earth. R2 T12 P7 compounds crystallize in the Zr2 Fe12 PT-type structure (space group P6) (Jeitschko et al. 1978), see table 8.8. Rare-earth atoms occupy the two Zr crystallographic sites, which have very similar local environments. The transition-metal atoms are distributed over four different crystallographic sites. The iron atoms carry essentially no magnetic moment and Lu2 FelfP7 is weakly paramagnetic with a minimum of the susceptibility of X = 4.3 x 103 m~ 3 mo1-1 at about 100K. The magnetism of these compounds is, thus, dominated by the magnetic properties of the R atoms. In contrast, all cobalt compounds order ferromagnetically with Curie temperatures of between Tc= 142K (Pr2Fe~2P7) and Tc = 160K (Ho2FelEPT). The magnetic moment per Co atom deduced from LUECO12P7 is 1.14 +_0.02/zB, similar to the value (1.44#B) obtained for the cobalt atoms in RCo2P2 (Mrrsen et al. 1988). It is worth

H,-S. LI and J. M. D. COEY

70

TABLE 8.8 Structural and magnetic data for R2TI2P7 (T = Fe or Co) compounds, results by Reehuis and Jeitschko (1989). Compound

a (A)

c (A)

Ce2 Fe12 P7 Pr2Fe12P 7 Nd2Fe12P7 Sm2Fe12P7 Gdz Fex2 P7 Tb/Fe12 P7 Dyz Fe12 P7 Ho2 Fe12 P7 Er 2Fexz P7 Tin2 Fe12 P7 Yb2 Fe12 P7 Lu2 Fe12 P7

9.132 9.198 9.190 9.167 9,140 9.129 9.118 9.109 9.100 9.098 9.091 9.083

3.6728 3.689 3.683 3.6670 3.6562 3.6428 3.6393 3.6363 3.6293 3.6250 3.6210 3.6146

Ce2 Co12 P7 Pr2Co12P v Nd2 Co12 P7 Sm2 Co1~ P7 Eu2 Co12 P7 Gd2Co12P7 Tb2 Colz P7 DY2Co12 P7 Ho 2Co 12P7 Er2 Co12 P7 Tm2 Colz P7 Yb2 Co 12P7 Lu2 Co12 Pv

9.077 9.129 9.109 9.083 9.078 9,068 9.049 9.046 9.043 9.032 9.025 9.020 9.018

3.651 3.665 3.649 3.628 3.6265 3.617 3.609 3.603 3.5997 3.5918 3.5859 3.5793 3.576

Tc(K)

/~3d(PB)

Pgf (#B)

0 (K)

3.8 3.8 2.0 7.8 9.7 10.6 10.9 9.5 7.5 4.5 48 136 140 148 151 145 150 152 152 146 147 134 150

10 3 3 5 5 4 3 7 0

1,21

56 142 147 153 156 154 158 159 160 155 155 142 158

3.5 3.5 1.9 4.1 8.1 9.9 10.5 10.4 9.5 7.4 4.2 1.14

noting that the maximum Curie temperatures occur for the rare earth with the highest moment, Dy2FelePT and HozFe12PT. A similar correlation was observed in the ternary carbide series R 2 Cr2C3 (Jeitschko and Behrens 1986). RCo8 P5 compounds for R = La, Pr or Eu are found to crystallize in the LaCo8 P5type structure (space group Proton), see table 8.9. The rare earth occupies one crystallographic site and the cobalt atoms occupy five inequivalent sites (Reehuis et al. 1988a). The cobalt atoms are not magnetic and LaCo8Ps is a Pauli paramagnet. The susceptibility of LaCos P5 exhibits Curie-Weiss type behaviour, and indicating ferromagnetic order of the praseodymium atoms at below 20K. Europium in LaCo8 Ps is divalent. TABLE 8.9 Structural and magnetic data for RCosP 5 compounds (Reehuis et al. 1988a). Compound

a (•)

b (A)

c (/~)

LaCosP 5 PrCos Ps EuCo s Ps

10.501 10.479 10.526

3.596 3.570 3.559

9.342 9.295 9.321

/~eff(#B)

0 (K)

Z = 1.62 x 10 -9 m3/f.u. (300K) 3.67 (3) 20 (1) 7.70 (8) 6 (I)

TERNARY RARE-EARTH TRANSITION-METAL C O M P O U N D S

71

8.9. RAuNi4 and Cel+xlnl-xPt4 The RAuNi4 compounds (R = heavy rare earths) and Cel + x l n l _ x P t 4 (0 ~<x <~0.4) crystallize in an fcc structure with space group F43m (Dwight 1975, Adroja et al. 1989), see table 8.10. The structure is closely related to that of the well-known C15 Laves phase. The R atoms occupy the 4a sites with Au/In in the 4e sites and Ni or Pt in the 161 sites. The RAuNi4 compounds with R = Gd, Tb, Dy, Ho or Er are ferromagnetically ordered at low temperatures, whereas for R = Tm or Yb they are paramagnetic down to 4.2 K. Nickel and gold are nonmagnetic. The magnetic susceptibility of the CeInPt4 compound exhibits a Curie-Weiss behaviour in the temperature range of 100 to 300 K, but shows large deviation below 100 K. A very large and negative value of 0 (,-~225 K) suggests the presence of Kondo type interactions in this compound. 9. Conclusions (1) Rare-earth (R)-transition-metal (T) ternary compounds extend the scope of RT binary compounds, offering a wide range of structure and physical properties. An effective way of finding new ternary phases is to begin with a binary intermetallic phase where at least one of the constituent elements has two or more crystallographically inequivalent sites. Preferential occupation of one of these sites by a third element M leads to a ternary compound such as RCo4B. An alternative method of generating a ternary from a binary structure, is by introducing interstitial atoms, particularly carbon and nitrogen, into suitable vacant sites, e.g., Rz F e l t C= and Rz FelTNx. Gasphase reactions at temperatures of order 500°C are a good way of generating interstitial modifications of existing intermetallics. True ternary phases which have TABLE 8,10 Structural and magnetic data for RAuNi4 (Felner 1977) and R1 +~Inl_xPt4 (Adroja et al. 1989). Compound

a (A)

Tc (K)

M~ (/zB/FU)

#~ff ( PB)

GdAuNi 4 TbAuNi4 DyAuNi4 HoAuNi4 ErAuNi4 TmAuNi4 YbAuNi~

7.136 7.094 7.052 7.034 7.011 6.982 6.952

38 28 23 14 24 -

5.9 4.5 5.4 6.1 15.0

8.1 9.6 11.4 11.9 10.3 9.8 6.4

CelnPt 4 Cea .2 Auo.8 Ni4 Ce i .4 Auo.6 Ni¢

7.602 7.624 7.657

* at an applied field of 1.5 T. t References: [1] Felner (1977). [2] Adroja et al. (1989).

2.54 2.54 2.54

0 (K)

Ref.t

22 12 5 4 4 - 14

[1] [-1] [1] [1] [1] [-1] [1]

- 225 - 84 - 63

[2] [-2] [2]

72

H.-S. LI and J. M. D. COEY

no close relationship with binary phases are difficult to find. Villars (1985a,b) has shown that true AxByCz ternaries (x/> y ~>z, x + y + z = 1) occur only for x ~<0.85 and z ~>0.05. (2) From a magnetic point of view, solid solutions between isostructural end members and the existence of long isostructural series with many rare-earth elements, permit a more systematic approach to the experimental study of magnetism than is possible for simpler structures. Ternary compounds with useful magnetic properties (i.e., those that are ferromagnetic with Tc > 300 K) are found only when the concentration of Fe, Co or Ni is sufficiently large. Alloying, whether with rare earth and early transition metals or metalloids tends to destroy the 3d moment. The magnetic valence model (presented in section 3.2.1.1) relates the average atomic moment to the electron concentrations via the average magnetic valence, assuming strong ferromagnetism. All the data collected in fig. 9.1 show the general tendency predicted by the model for Nsp ~ 0.6-0.8. In particular, all the cobalt-rich alloys appear to be strong ferromagnets, whereas a number of the iron-rich compounds, including ~-Fe, R2Fe17, RFeuTi, RFeioM2 and RFeloSiCo.s, are weak. Increasing (y + z) pushes the iron compounds towards strong ferromagnetism, but dilutes the magnetization in all cases except for R2 Fei7 Cx and R2 Fe~7Nx. (3) As in binaries, there is a tendency for cobalt-rich compounds to have higher Curie temperatures than either iron or nickel counterparts. In fact, the Co-Co exchange tends to be rather independent of structure or cobalt moment, in the range 130K < J < 150K. By contrast, the iron-iron exchange is unpredictable. In some structures such as 2:17, where it is unusually low, it may be greatly increased by interstitial modification. (4) The 3d magnetocrystalline anisotropy in uniaxial crystals is generally opposite in sign for isostructural iron and cobalt compounds. (5) The magnetocrystalline anisotropy of rare-earth-transition-metal intermetallic compounds is frequently dominated by the rare-earth contribution. When the rareearth ion possesses an orbital moment, the crystal-field parameters of the rare-earth sites are then the key to understanding magnetocrystalline anisotropy. There has been some progress towards calculating these parameters accurately in metals from first principles (Coehoorn 1990a,b). Also, Coehoorn has shown that a qualitative estimation of the sign and magnitude of A2o is better obtained from values of the charge density at the boundaries of the cell surrounding the rare-earth atom than from traditional point charge calculation, which fail in metals because the electric field gradient is mainly created by the rare earth's own 6p and 5d electrons. The charge density at the edge of the atomic Wigner-Seitz cells is described by the Miedema parameter nws, which generally shows n o simple correlation with the electronegativity (fig. 9.2). It is concluded that -~2o is positive if neighbours with highest nw~are on the z-axis through the R-atom and that -~2o is negative if they are in the x-y-plane around the R-atom. Experimental methods for determining the crystal-field coefficients include the single-crystal magnetization or torque measurements, inelastic neutron scattering and measurements of rare-earth hyperfine interactions, particularly by M6ssbauer spectroscopy. The last technique provides only the leading, second-order terms -42o and ~22~-(c)from the electric field gradient

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS i

i

i

i

73

L it it

Y (Fe0.30-o0.7) 11Ti Y (Fe0.5C°0.5) 11Ti X (Fe0.7C°0.3) 11Ti 4 x (Fe 0 .8Co0.2) 11 Ti 1

i

2 3

2.5

/ it

2NTsp = 0.8/"

5 Y (Fe0.9C°0.1) 11 Ti

6

i

,,/

t

/

,/0.6 /

Y (Fe0.92Ni0.08) Ii Ti

7 X (Fe0.8Ni0.2) 11 Ti

/

8 Y (¥e0.7Ni0.3) 11 Ti

I /

9 YFe8.5V3.5

2.0

tl ,i

/

I0 ~ez0v2 11 YFeg. 4V2.6

/ i ,

Ct~

i•

I'

(I

'

Fe

/ tI i i

/ t /

/ b Lu2FeI4B

YFel0. sWI.~'A ff'ALu2Fel4C / '~,~ 5

1.5 A -A V

///'-~

Y2co14~// ~//

,'

,'

~'Z/

1.0

8

~ez0.5vL

"

• c,,r~losieo.5

7./,o' .1/

0.5

5

. YFel0Si2

o.

14 Yg.l.sC02.sB

/'Ni

t~ / / YCo~B y Co~I2B6, '

15 LuFe2Co2B 16 LuFe3CoB

tt t• i i iI tI iI

0.0

iI

iI /

-015

010

015

1.'0

115

2.0

Fig. 9.1. Plot of the average atomic moment (#) against the average magnetic valence (Zm) for some ternary R-T-X (T = Fe, Co or Ni and X = B or C).

(EFG) at the nucleus. Many ternary alloys have been examined using 155Gd M6ssbauer spectroscopy, which has the advantage that there is no 4f orbital contribution to the field gradients, so the results are only from the contributions of the lattice, including conduction electrons, and is, therefore, proportional to the electric field gradient acting on the 4f electrons, which produces the second-order crystal field interactions. "~20 and x(o) ~22 are related to the principal component of EFG by the following expressions A2o

=

--

¼lelV=/(1

__

y~);

-

-(c)

[A2o/Az21

=

rh

(18)

74

H.-S. LI and J. M. D. COEY

where -lel is the electronic charge and ?o is the Sternheimer antishielding factor [7~o = - 9 2 for 155Gd (Bog6 et al. 1986)]. Table 9.1 lists the values of-~2o which are deduced without taking any account of the screening effects due to outer electronic shells. The true second-order crystal-field coefficients A2o and ~22A(c)experienced by 4f electrons are often related to ~t~) -'~-2m by A~) 2m - tl ~x -

-

-

-

.. ~X~)

(~ = c. s),

u2t,,Zt2m

(19)

where the value of the screening factor 0-2 (Sternheimer et al. 1968, Blok and Shirley 1966) is normally taken to be about 0.5. Values of V~z and A20 deduced from the 155Gd M6ssbauer spectroscopy (table 9.1) indicate that there is a variation of a factor 80 between the most and least anisotropic rare-earth sites. Of the compounds listed, only Gd2 FeI4B and related materials turn out to have a positive sign for Jzo, which is an important fact for permanent magnet applications because Nd and Pr (which show uniaxial magnetocrystalline anisotropy when A2o > 0) are more abundant than Sm, for which the opposite is true. Note that Azo is only about half as large as A2o listed in table 9.1. (6) The giant coercivity ( # o i H e = 5.03 T) obtained in Sm z F e 7 Ti magnets (made by mechanical alloying) is among the highest measured in permanent magnets at room temperature, but the comparatively low saturation magnetization (~<½ of the N d Fe-B value) will limit its applications to special cases. The coercivity of the 1 : 12 Sm-Fe-Ti magnets reaches values (#oiH¢ "~ 1.0 T) which are typical for Nd-Fe-B, but their saturation magnetization is 25-30% lower than that of Nd-Fe-B. There are chances of developing coercivity in interstitially modified iron-rich 1 : 12 alloys with R = Nd (a quaternary system with positive Azo), but the new tenary system which may have the best prospect of challenging N d - F e - B for certain hard magnet applications is Sm-Fe-N, where a coercivity #oH~ =3.0T has been achieved in nitrides of mechanically alloyed Sm2Fe17.

I

.

.

.

.

I

.

.

.

.

I

'

r ~

I

_

}

-

.

-

.

.

.

G c

2V

[ Y,~I II

,

3

i

.

,

I

4

.

.

.

.

I

.

.

.

.

5

I

.

.

.

.

6

Elect ronegativity

Fig. 9.2. Plot of the Miedema's parameter nw~ versus the electronegativity parameter q5' (Coehoorn 1990b).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

75

TABLE 9.1 Values of the second-order crystal-field coefficient -42o, deduced from the principal electric field gradient, V~ acting on Gd nuclei, which is determined by ~55Gd M6ssbauer spectroscopy. Value of y~ was taken to be -92. Several values of A2o are listed when there are two or more nonequivalent sites present in the structure. Compound

Structure

Tc(K)

GdFellTi GdFelo.8Til.z GdFeloVz GdFeloMo2 GdFeloSi2 GdFel0.8Wl.2 Gd2Cox7 Gd/Co 17C 1.2 Gd2Fe17 Gd2Fe17C1.2 Gd2Ni17 Gd2Ni17C1.2 GdzFe14B Gd2Fel~C GdzCo14B GdCo5 GdCo4B Gd3CollB4 Gd2CoTB 3 GdCo3B 2 Gd3NiTB / Gdl +,Fe4B 4

ThMn12

Th2Mn17

607 600 616 430 610 550 1218

Th2Ni~v

476 582 196

Nd2Fea4B

CaCu 5 CeCo4B Ce3ColIB4 CezCOTB3 CeCo3 Bz Ce3CoTB z Ndx+~Fe4B4

V~z(1021 V m -2 ) +0.34 +0.9 +1.65 +1.35 +1.41 +1.60 +4.3 + 6.67 +4.4 +9.28 +7.5 +8.7 -7.75 - 8.2 -6.64 +8.2 +8.9 +9.6 +9.7

660 620 1053 1014 517 460 345 58 37 +22.9 20 +28.1

* Not at the principal direction of EFG. t References: [1] Czjzek (1989). [2] Dirken et al. (1989a). [3] Buschow et al. (1988a). [4] Gubbens et al. (1988b). [5] Dirken et al. (1989b). [6] Dirken et al. (1990).

+5.1 +3.6 11.37' 10.2" 6.95 +14.0 +18.8 +19.2 +4.89

[7] [8] [9] [10] [11]

+25.8 +25.3

A20 (Kao 2) -30 -79 -144 -118 -123 -140 -376 - 582 -384 -811 -655 -759 +677 + 716 +580 -716 -777 -839 -847 -2001 -2455

-445 -314 +670 + 588 +410 -1223 -1642 -1677 -427

-2254 -2210

Ref.'~ [1] [-2] [3] [3] [3] [2] [4,6] [6] [6] [5,6] [6] [6] [7] [3] [8] [5] [9] [9] [9] [9] [10] [11]

Bog6 et al. (1986). Smit et al. (1987). Smit et al. (1988). Felner (1983). Rechenberg et al. (1987).

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chapter 2 MAGNETIC PROPERTIES OF TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

A. SZYTULA Institute of Physics Jagellonian University 30-059 Krak6w, Reymonta 4 Poland

In memory of my friend ZVONKO BAN

Handbook of Magnetic Materials, Vol. 6 Edited by K.H.J. Buschow © Elsevier Science Publishers B.V., 1991 85

CONTENTS I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Electronic states in rare-earth intermetallic compounds . . . . . . . . . . . . . . 3. Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Basic information . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Magnetic interactions . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Crystalline electric fields . . . . . . . . . . . . . . . . . . . . . . . 3.4. Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. The case Hox > Hcf . . . . . . . . . . . . . . . . . . . . . . 3.4.2. The case Hox < H~f . . . . . . . . . . . . . . . . . . . . . . 3.4.3. The case Hex ~ Hcf . . . . . . . . . . . . . . . . . . . . . . 4. Magnetic properties of ternary compounds . . . . . . . . . . . . . . . . . . 4.1. RTX phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Compounds with the MgCuz-type structure . . . . . . . . . . . . . 4.1.2. Compounds with the MgAgAs-type structure . . . . . . . . . . . . . 4.1.3. Compounds with the LaIrSi- (ZrOS-) type structure . . . . . . . . . . . . . . . . . . . . . 4.1.4. Compounds with the Fe2 P- (ZrNiA1-) type structure . . . . . . . . . . . . . 4.1.5. Compounds with the MgZnz-type structure 4.1.6. Compounds with the AIB2- or Ni2In-type structure . . . . . . . . . . . 4.1.7. Compounds with the CaIn2-type structure . . . . . . . . . . . . . . 4.1.8. Compounds with the LaPtSi-type structure . . . . . . . . . . . . . . 4.1.9. Compounds with the PbFCl-type structure . . . . . . . . . . . . . . 4.1.10. Compounds with the TiNiSi-type structure . . . . . . . . . . . . . . 4.1.11. Compounds with the CeCu2-type structure . . . . . . . . . . . . . . 4.2. RTX 2 phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. RT2X phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. RTX3 phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5, RTzX z phases . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1. Compounds with the ThCr2Si2-type structure . . . . . . . . . . . . . 4.5.1.1. Magnetic properties . . . . . . . . . . . . . . . . . . . 4.5.1.2. Magnetic phase transitions . . . . . . . . . . . . . . . . . 4.5.1.3. Magnetic structures . . . . . . . . . . . . . . . . . . . 4.5.1.4. Magnetic properties of solid solutions . . . . . . . . . . . . . 4.5.1.5. Magnetic properties of RMn2 Si2 and RMn2 Ge2 compounds . . . . . 4,5.1.6. Other RTzX 2 compounds . . . . . . . . . . . . . . . . . 4.5.2. Compounds with the CaBezGe2-type structure . . . . . . . . . . . . 4.5.3. Compounds with the CaA12Si2-type structure . . . . . . . . . . . . . 4.6. Other ternary compounds . . . . . . . . . . . . . . . . . . . . . . 86

88 90 93 93 94 95 96 96 96 97 97 97 97 98 99 100 104 105 107 108 108 108 110 110 114 117 119 120 120 131 136 137 139 148 152 154 155

TERNARY INTERMETALLIC 4.6.1. R 2 R h S i 3 c o m p c t n d s 4.6.2. R 2 N i 2 X c o m p o u n d s 5. C o n c l u s i o n s . . . . . . . . 5.1. M a g n e t f c m o m e n t . . . 5.2. E x c l : a n g e i r t e r ~ c t i o n s . . 5.3. Crystalline electric f e l d . Refeler ces . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

RARE-EARTH COMPOUNDS

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87 155 157 157 157 159 165 172

I. Introduction

During the past years, intermetallic compounds containing rare-earth elements have been the subject of intensive studies because of their intriguing physical properties. Apart from a manifold of magnetic properties, they show a mixed valence and a heavy fermion behaviour. They may also give rise to superconductivity, including its coexistence with a long-range magnetic ordering. One of the many 'families' of intermetallic compounds are ternary R - T - X systems where: R is a rare-earth element including Y and Sc; T is a transition 3d, 4d and 5d element; and X is a main group element from the boron, carbon or nitrogen group. The family of ternary rare-earth intermetallics comprises several hundreds of ternary compounds. The existence of intermetallic compounds and the reason for their formation represent an old problem in chemistry and metal science, which has not completely been solved. Intermetallic compounds are formed according to the thermodynamic stability of certain types of crystal structures, but quantum chemistry is unable to predict their existence. Phase equilibria have been investigated for only a small number of the possible ternary combinations R-T-X, and, for the large number of ternary systems, only a few compounds have been identified up to date. Most of the ternary phase-diagram studies have been carried by Gladyshevskii and coworkers at Lvov University, USSR (Bodak and Gladyshevskii 1985). Since that time, phasediagram studies have shown that the number of ternary phases is surprisingly large, e.g., 21 phases in Ce-Ni-Si according to Bodak et al. (1973). A typical ternary phase diagram for R-Rh-Si systems is given in fig. 1. It contains seven phases with different composition and crystal structure. In table 1, data of the structural, magnetic and super-conducting properties of these systems are summarized. Of the RxTyXz compounds, only the phases with 1 : 2 : 2 ratio were systematically studied. The data concerning these latter phases are about 50% of the data of all materials considered in this chapter. The nature of the constituent elements of these compounds involves large electronegativity differences between the two metals and/or between the metals and the nonmetal. These differences, therefore, appear to be crucial for the occurrence of the structures and properties observed. These electronegativity differences are favourable 88

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

89

Si

R

Si2~Rh

S? /

3Si4

v:

R..........

i

'Rh

_T-RRh3Si2, I_]-RRh2Si2, IT_I-RRhSi, ~-R;Rh3Sis, - RRhSi2, ~-R2RhSi 3 , ~lI-RsRh4Silo Fig. 1. The rare-earth-rhodium-silicon ternary phase diagram (Chevalier et al. 1983).

TABLE 1 Crystallographic, magnetic and superconductive data of ternary silicides in R-Rh-Si systems. I

II

III

IV

V

VI

VII

RRh3 Si 2

RRh2 Si2

RRhSi

R2RhaSi s

RRhSi 2

R2 RhSi 3

R5 Rh4Silo

Structure Hexagonal Tetragonal Orthorhombic Orthorhombic type CeC%B2 ThCr2Si2 NiTiSi Sc2Co3Si5 (P6/mmm) (I4/mmm) (Pnma) (Ibam) or cubic ZrOS (P213) La S S S T~= 74K T~= 4.4 K T~= 4.5 K Ce AF TN= 36K Nd P AF P TN= 56K Sm F AF P Tc = 34K TN = 46K Eu AF T~= 25K Gd F AF F P T c = 3 1 K TN=98K T c = 1 0 0 K Tb F AF AF AF T c = 3 7 K TN=94K TN=55K TN=8.5K Dy F AF AF P T c = 2 9 K TN=55K TN=25K Ho AF AF AF P TN=10K TN=27K T N = 8 K Er F AF AF P Tc = 24K TN = 12.8KTN = 7.5K

Orthorhombic Hexagonal Tetragonal CeNiSi2 Sc5Co4Si (Cmcm) (P62c) (P4/mbm)

S

T~

= 3.4K AF TN=6K F Tc= 15K

AF TN= 14K AF TN= l l K P

90

A. SZYTULA

for the formation of stoichiometric compounds, as was graphically illustrated by Ku~ma et al. (1979). The essential characteristic of a ternary compound is that it contains three elements, each occupying distinct set or sets of crystallographic sites. This crystallographic definition clearly distinguishes ternary compounds from binary or pseudo-binary phases in which only two sets of lattice sites are occupied or which contain only two kinds of atoms. The structural characteristics of ternary intermetallic rare-earth compounds were presented in a review paper by Parth6 and Chabot (1984). Ternary intermetallic compounds may crystallize in different types of crystal structures. The realization of a certain crystal structure can be related to several factors: to geometric, electronic, electrochemical factors and to chemical bonds, which, in limiting cases, correspond to an ionic, covalent or metallic type of bonds. Lacking dominant factors, the structures of intermetallic compounds tend to reach the highest symmetry, the highest space filling and the highest number of connections among atoms. In a more quantitative approach, one has to take account of the dimensions of the constituent atoms and the interatomic distances realized after the formation of the compound. The aim of this chapter is to summarize the up-to-date knowledge, derived mainly from experimental investigations, of the magnetic behaviour of the ternary intermetallic compounds RT, X,, with n + m ~<4. The general features and tendencies in the 4f electron systems are sketched in sections 2 and 3. Section 4 reviews the properties of ternary compounds with a stoichiometry of 1 : 1:1, 1 : 1:2, 1:2: 1, 1 : 1:3 and 1:2:2. The topics presented in section 4 were selected in order to support the conclusions drawn from these systematics. We have highlighted some of the current problems of the magnetic interactions in these materials in section 5. For a more complete review of rare-earth intermetallic compounds, we recommend the following review papers and monographs, Buschow (1979, 1980), Rogl (1984), Leciejewicz (1982), Suski (1985) and Szytuta and Leciejewicz (1989).

2. Electronic states in rare-earth intermetallic compounds Rare earths occupy a special position in the periodic table, since they correspond to the filling up of the 4f electron shell. In rare-earth metals, the 5d and 6s electrons are delocalized and give rise to the conduction band. On the other hand, the 4f electrons remain localized on the atoms and there is really no overlap between the 4f wave functions centred on two neighbouring atoms, the 4f shell can be described as being the same as in the free atom. Moreover, the 'normal' electronic configuration of rare-earth metals in 4f"5d 16S2 and the conduction band contains, therefore, three conduction electrons. It is well-known that some rare-earth metals have an anomalous behaviour corresponding to an electronic configuration different from the normal one. From the experimental data on atomic volume, electronic specific heat and magnetic moment, one deduces that europium and ytterbium metals are divalent, while the valence, defined as the number of conduction electrons, varies from three to four in the different phases of cerium metal (Koskenmaki and Gschneidner Jr. 1978). An anoma-

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

91

lous behaviour has been observed not only for many alloys or compounds containing, as could be expected, cerium, europium or ytterbium, but also in alloys containing one of three other rare-earths, namely samarium as in SmS, thulium as in TmSe or praseodymium as in PrSn3 (Coqblin 1982). The mixed-valence state is observed also in ternary intermetallic compounds, e.g., in the group of compounds CeT2X2, EuT2X2 and YbT2X2. In this case, the mixedvalence phenomena are correlated with structural properties of these compounds. The variation in the unit cell volume in the RT2 X2 series exhibits a regular increase with increasing ionic radius of the R 3+ ions (fig. 2). The anomalous behaviour observed in the case of Ce, Eu and Yb compounds is connected with the occurrence of a divalent, tetravalent or mixed-valence state. The definite valence state in a given compound is a function of the chemical composition and the associated 'intrinstic' (chemical) pressure. Data on a mixed valence are well documented for the CeT2X2 family of compounds, where T is a 3d electron metal. For this group of compounds, mixed-valence data and volumes of the unit cell correlate very well (fig. 3). For the CeT2Si2 compounds, a decrease in the volume of the unit cell leads to an increase in 'intrinstic' (chemical) pressure, and this, in turn, leads to an increase in the Ce valence. For the CeT2 Ge2 family, any change in valence as a function of the volume of the unit cell was not observed (Groshev et al. 1987), because the atomic radius of the Ge atom is larger than the one of Si. In all CeT2X2 compounds the Ce-Ce distance within the (001) plane has a value equal to the lattice constant (a -~ 4/k), while the next-neighbour distance, i.e., the one

/° 0,19r A R__ ~T 2 S ~ 0.1~

u

~/7°

0.19 ) RT2Ge2 --

1~' ]/ ~* ~="', /~//i

Ru x/,~Rh Cu

,,o o

"¢ ~ ~ 0 0

0"18I

x/.~-'°"

Fe

,

Pd Os

0'17I

~u1:'"~S/" J ~ / \ j

o16 ~h~-:y _ f l V ~ ~J

4n+-+'÷"

0:1

0.15 Fe Ni~ ./ TmHoTbEu LuYbErDyGdLSmNdPrCeLa 0.09 0.10 0.105 rR3+(nm) I, I I I L , I

I

I

I,I

I,,J

]l~

OJ5F | TmHoTb Eu | LuYbEr Dy GdSmNdPrCeLa 0.09 0.10 0.105 rR3+(nm} hll

I

hi

I I I

I

h

I

I

,I

Fig. 2. The unit cell volume in RT 2Si2 (left) and RT 2Ge2 (right) series of compounds versus the radius of rare earth rR3+.

92

A. SZYTULA

<'~>[- CeT2X2 3'~I ~','"°"~°''',o 3.2 3

.." ~ - ' - ~

"

i

b

190

V{,E3) '~ 180 ~\~,

." P i

170

"--,__.."

Q"~. 16C 15C

t

In

""o I

Fe

p

z

," i Co

~ Ni

I Cu

Fig. 3. The unit cell volume (bottom) and valence (top) of CeT2Si 2 and CeT2Ge 2 compounds versus the 3d element. Data of the valence of CeT2 Si2 compounds were taken from the following papers, (1) Groshev et al. (1987), (2) Liang et al. (1987), (3) Sampathkumaran et al. (1985).

between the planes, is ~ 5 A. Therefore, a direct overlap of the 4f wave functions of the different Ce atoms cannot be responsible for the delocalization of the 4f electrons or, to express it equivalently, for the formation of a narrow 4f band. The delocalization essentially occurs through hybridization of the 4f electron wave function with s, p or d wave functions of neighbouring atoms. The valence instability leads to a strong temperature and pressure dependence of the average occupation of the 4f shell. Reviews on that problem and its theoretical treatments have been given by Lawrence et al. (1981) and Nowik (1983). The behaviour of ternary intermetallic compounds is most intriguing from a physical point of view. They behave as, e.g., 'heavy fermions' (HF); concentrated Kondo systems (CKS); or superconducting systems (SS). The first group of compounds has anomalous properties at low temperatures. The observed values of the magnetic susceptibility and specific heat are, however, some orders of magnitude larger than in common metals. In conventional metals, where the metallic properties originate from itinerant s, p and d electrons, the values of the coefficient ? in the electronic specific heat are 1 - 1 0 m J K -2 mo1-1. For 'heavy fermion' systems, these coefficients are larger by a factor 103 than those of ordinary metals. The large values of ? and Cp indicate strong interactions in the electronic systems and, therefore, the system may be regarded as a Fermi liquid of quasiparticles with large effective masses rather than as a Fermi gas. Several ternary intermetallic compounds were found to exhibit such 'heavy fermion' behaviour: CeCuzSiz (Assmus et al. 1984), CeRu2Siz (Mignot et al. 1988), CePt2Si2 (Gignoux et al. 1986b), CePtSi and CeRuSi (Rebelsky et al. 1988). The CKS metallic substances are characterized by a transition from classical to quantum-statistical behaviour at low temperatures. At low temperatures these substances display anomalous electrical, thermoelectric and magnetic properties. The resistivity shows a logarithmic increase followed by the Fermi liquid resistivity behaviour p ~ A T z, with a large coefficient A. The temperature dependence of the

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

93

susceptibility for C e C u 2 S i 2 is shown in fig. 4 (Steglich et al. 1982). It indicates a transition from the Curie-Weiss behaviour at T ~ TK to the Fermi liquid behaviour, TK being the Kondo temperature. These properties are related to the formation of a narrow kB TK high-amplitude Abrikosov-Suhl resonance in the vicinity of the Fermi level EF. In ternary intermetallic systems, one may observe, e.g., a coexistence between magnetism and super-conductivity within the heavy electron state (Steglich 1989) or a balance between magnetism and intermediate valence behaviour (Ott et al. 1978). Several compounds have now been identified as 'heavy fermion' superconductors. For example, CeCu2Si2 (Steglich et al. 1979) shows type II superconductivity. This behaviour is in total contrast to the type I superconductivity observed in the isostructural 'normal' RT2 X2 compounds in which R represents La, Lu or Y (Palstra et al. 1986a).

3. Magnetic properties 3.1. Basic information In order to obtain a general view on the magnetic properties of rare-earth compounds, the reader is referred to the 'Handbooks on the Physics and Chemistry of Rare Earths' (Gschneidner Jr. and Eyring 1978-1989). In the rare-earth elements, the incomplete 4f shell, which becomes more filled in going from La to Lu, is responsible for their magnetic properties. Excepting Ce, Eu and Yb, all rare-earth elements are present in the trivalent state. The abnormal valence of the former three elements is closely related to a general rule in elementary quantum mechanics which states that empty, completely filled or half-filled shells are energetically preferred. Spin, orbital and total angular momentum of the single rare-earth ions are determined by Hund's rules. For the free R 3 + ions, the magnetic moment is proportional to gjlzBJx/fO+ 1) in the paramagnetic state and to gjJ#B in the ordered state. i

,

,

5i 2

200 _15C E 0 ~100

Q..

lstc'cu2si2

01

,

.~

. .-.~P;-,

0

-.,

I

0.5T2[K211

50

510

100

150

I 200 250 T [K ]

Fig. 4. Temperature dependence of the resistivity of CeCu2Si 2 and LaCu2Si 2. The inset shows the normalstate resistivity of CeCu2Si2 versus T 2 (Steglich et al. 1982).

94

A. SZYTULA

The Hamiltonian which describes the magnetic properties of rare-earth ions is usually presented in the form Htot = Hcoum+ Hex~h+ Her + Hms + Hext,

(1)

where the term Hcoul represents the Coulomb interactions, Hox~h describes the exchange interactions, H~f is the crystal electric field term, Hms accounts for magnetostriction effects and Hext takes account of the interaction in an external magnetic field. The available experimental data clearly indicate that the terms Hooch and Hef are dominant in the description of the magnetic properties of the R ions in a crystal, so we shall discuss them in detail.

3.2. Magnetic interactions In most of the models, the magnetic coupling energy between two localized moments is taken to be proportional to Si'Sj. In the case of rare earths, two mechanisms have been proposed in which the 4f moment can interact in an indirect way. In the first of these, called the RKKY interaction, the magnetic coupling proceeds by means of spin polarization of the s conduction electrons. In the second mechanism, the spin polarization of the appreciably less localized rare-earth 5d electrons plays an important role. These two mechanisms and their implications for the magnetic properties of the various intermetallic compounds are briefly discussed below. The essential form of the indirect interaction between localized moments was introduced by Ruderman and Kittel (1954) to describe the hyperfine interactions between nuclear moments. This was then applied to the exchange interaction between localized moments (Kasuya 1956, Yosida 1957). The spin polarization of localized spin moment involves exchange interactions, H = -- 2Jsfs " S,

(2)

where s represents the spin of the Fermi surface conduction electrons, S denotes the localized rare-earth spins and Jsf the exchange integral. The conduction electron spin polarization interacts with a localized spin moment on a neighbour ion at a distance Rij from the scattering centre. The total exchange energy of the indirect interaction between i and j is

E-

18rcn2 2

~

JsfSi" SjF(2kFRij).

(3)

Substituting this interaction energy into the molecular field expression (Bleaney and Bleaney 1965) of Tc or 0p for ferromagnets, it can be shown that

Tc =

3rcn2

_

Op --

_

2

kBEFJsf(gJ -- 1)2J(J + 1) i*o ~ F(2kFR°~)'

(4)

TERNARYINTERMETALLICRARE-EARTHCOMPOUNDS

95

where 0 p is proportional to the molecular field at the central ion O resulting from the interaction with all neighbours i at a distance Roi. This type of summation is, of course, valid only when all magnetic ions are crystallographically identical. In antiferromagnetic materials, there may exist various types of spin arrangements represented by a propagation vector k ¢ 0. Here, k may represent, e.g., the wave vector of some spin spiral structure whose wavelength 2 is equal to 2~r/k. Conical spin arrangements need not to be considered here since they are only stabilized by the presence of an anisotropy. The stable structure (described by ko) is that for which the energy of system is minimum. This gives (see Mattis 1965) 37zn2 2 TN= k - ~ Jsf(gl - 1)2J(J + 1)i,~o F(ZkFRoi) cos(k0 • Ro, ).

(5)

Within the RKKY theory, it was shown that for isostructural rare-earth compounds the ordering temperatures are expected to scale with (gs- l)2j( J + 1) (de Gennes 1962). A different coupling scheme between the localized 4f moments was proposed by Campbell (1972). In this model, the 5d electrons of the rare-earth component play an important role. These 5d electrons are far less localized than the 4f electrons and a considerable overlap might occur between the 5d wave functions of neighbour atoms. In compounds of sufficiently high rare-earth concentration, one can expect, therefore, a direct d - d interaction. According to Campbell, this offers the possibility for an alternative form of interaction involving a positive ordinary f-d exchange, combined with the positive direct d - d interaction mentioned above. The overall indirect interaction between the 4f moments is, therefore, always ferromagnetic. In contrast to the RKKY interaction, it has a short range and treats d and s electrons separately.

3.3. Crystalline electric fields Another feature which largely determines the magnetic properties of rare-earth compounds is the interaction of the 4f electrons with the electric charges due to the surrounding ions. Each rare-earth ion, placed in a crystal, is submitted to an inhomogeneous electrostatic potential originating from the electric charges of the surrounding ions and the conduction electrons in the case of metallic compounds. This contribution to the energy can be divided into a one-ion contribution which corresponds to the crystal electric field (CEF) term and a two-ion contribution which accounts for the dipolar or multipolar interactions between magnetic ions. The interaction of the CEF with the multipole moments of the rare-earth atom electrons is given by the Hamiltonian,

Hoe=

~

B'~O'~(J),

(6)

n = O t/l = --n

where n' can take the maximum value of n appropriate to the rare-earth atom

96

A. SZYTULA

considered, B~ are the crystal field intensity parameters and O"~(J) represent polynomials of the angular momentum operators Jz, j2, j ÷ , j _ . For a particular crystal symmetry, the Hamiltonian Hcf can become reduced, e.g., for (1) cubic symmetry with z chosen in the (001) direction, H~f = B4(O ° + 50**) + B6(O ° - 210~);

(7)

(2) tetragonal symmetry with 4/mmm point symmetry, H e f = B 0 02

o2 .TB o O 4 4o "b 8 44. 0 44 "]- B 6o0 6 o -[- B 64 0 6o. ,

(8)

(3) hexagonal symmetry with 3m point symmetry, H e f = B 200 2 0 -4- B 40 0 40 -[- n 43 0 43 .

(9)

The energy splitting of the ground multiplet [J, M > by the crystal field will depend on both the rare-earth ion and the crystal structure considered. Usually, it is of the order of a few hundredths of a Kelvin, thus, the CEF is a very important contribution for determining the magnetic anisotropy. The values of the B~ coefficients can be determined from experimental data such as magnetic susceptibility, magnetization, heat capacity, inelastic neutron scattering, spin-disorder resistivity and the M6ssbauer effect. 3.4. Magnetic anisotropy

In this section, we want to emphasize the importance of the relative strength of the crystal field (Hcf) and the magnetic interactions (H~x) in determining the anisotropy, i.e., the momentum direction. This problem can be treated in a purely one-ion approach, and will depend very much on the relative ratio of Her and H~x. 3.4.1. The case Hox > Hcf

This situation occurs when the exchange interaction is very large, or when the CEF splitting is very small. In that case, Hcf can be treated as a perturbation in comparison with H~x, and the anisotropy can be expressed by the classical formulation as E A = K 1 sin20 + K 2 sin40 + ....

(10)

The magnetic moment reaches the maximum value g j J . The preferred magnetization direction depends on the crystal structure via the CEF parameters B~' and the shape of the 4f electron charge cloud via the so-called Stevens coefficients. In the case of uniaxial crystal structures the lowest-order parameters are B ° and c~s, respectively. 3.4.2. The case Hox < Her

This situation applies usually to ionic rare-earth compounds, but it also occurs very often in rare-earth intermetallics that have a low ordering temperature (RossatMignod 1983). We must define two parameters: 6 which is the energy of the first excited CEF level and A which is the total CEF-splitting. A simple and more common situation corresponds to the case where the magnetic

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

97

interactions are lower than 6. Then, the Hamiltonian He, can be projected on the crystal-field ground level. In this case, the CEF anisotropy may lead to noncollinear magnetic structures. For rare-earth compounds in which the magnetic interactions are smaller than the energy 6 of the first excited CEF level, the magnetic behaviour is dominated by the CEF anisotropy.

3.4.3. The case Hex Hcf When Hex "~ Hcf, no simple approximation can be made and the complete Hamiltonian H~x + Hcf must be diagonalized. The problem is then much more complex, but qualitative results can be obtained by using also a semiclassical description. By decreasing the temperature, the population of excited levels decreases and a rotation moment may occur due to the competition between the CEF anisotropy and the entropy. Such a rotation moment has been observed, e.g., in HoA12 (Barbara et al. 1979). In that case, it is not possible to formulate general trends, the magnetic properties depending very much on the strength of both CEF and exchange terms. The symmetry of the rare-earth site remains always an important parameter, but a large variety of anomalous magnetic behaviours can occur. "~

4. Magnetic properties of ternary compounds The variation in magnetic properties of rare-earth intermetallic compounds through several systems has been discussed briefly before. The data discussed in this section were obtained mostly for polycrystalline samples. Only in a few cases, single-crystals were available for measurements of the magnetic anisotropy.

4.1. R T X phases A large number of equiatomic ternary rare-earth intermetallic compounds with the general formula RTX (R = rare earth, T = transition element and X = metalloid) are known to exist (Hovestreydt et al. 1982, Ba~ela 1987). These compounds crystallize in several different types of structure, such as MgCu2, MgAgAs, ZrOS, Fe2 P, A1B2, Ni2 In, LaPtSi, LaIrSi, PbFC1, MgZn2, TiNiSi and CeCu2. The two crystal structure parameters a/c and (a + c)/b can be used for grouping the various RTX type structures. This is illustrated in fig. 5. Each group of RTX metallic phases has different values of these parameters. Shoemaker and Shoemaker (1965) and Rundqvist and Nawapong (1966) found that the a/c ratio contains information on the number of nearest neighbours. The length of the short b-axis parameter is a further quantity determining the coordination number. A convenient expression for the coordination number is the ratio (a + c)/b. This section is on the systematics in the magnetic properties of a large family of RTX rare-earth intermetallic compounds.

4.1.1. Compounds with the MgCu2-type structure The ternary RMnGa (R = Ce or Ho) compounds have a crystal structure of high symmetry. It belongs to the cubic Laves phases (C15, fcc structure, MgCu 2 type,

98

A. SZYTULA

2.O a/c 1.8

~

Fe2P (ZrNiAt}

=,,

1.6 1.4 1.2

MgCu2 MgAgAs ", ZrOS Ata 2 ~,

1.C

.•NiTiSi E° ~-

0.8

CeCu2 Coin2 •~t, MgZn2 PbFC[q..... Ni21 n

O.B

0.t

LaPtSi a.

0.2 0.0 1.0

I

I

2.0

I

I

3.0

I

I

4.0

I

I

5.0

(o*c)/b Fig. 5. Grouping of RTX compounds according to their axial ratios.

space group Fd3m). This structure is depicted in fig. 6a. In this type of structure, the R atoms occupy the 8a site, while the Mn and Ga atoms are randomly situated in the 16d site (Tagawa et al. 1988). The temperature dependence of the electrical resistivity and the magnetic susceptibility of the compounds with R = Ce, Pr or Nd in the temperature range 4.2-300 K indicate spin glass-like behaviour (Tagawa et al. 1988). The neutron diffraction, the electric resistivity and the magnetic measurements for the D y M n G a compound show a spin glass state with a spin glass temperature T~g= 40 K (Sakurai et al. 1988). The TbMnA1 and ErMnA1 compounds are antiferromagnets with a N6el temperature TN = 34 K and 15 K, respectively (Oesterreicher 1972). Neutron diffraction data for TbMnA1 suggesting a modulated magnetic structure similar to that found in TbMn2 (Corliss and Hastings 1964).

4.1.2. Compounds with the MgAgAs-type structure Only a small number of RTX compounds crystallize in the cubic MgAgAs-type structure (space group FT~3m) in which the R atoms occupy the corners of a regular tetrahedron, as may be seen in fig. 6b. Such a structure is frequently found in transition-metal intermetallic compounds (e.g., NiMnSb). It is closely related to the structure of ordinary Heusler alloys of the X2YZ type, to be discussed in section 4.3.2. Both structures can be described by means of four positions: v n 1 h v ta 3 3x

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

ol

99

c)

b)

I,

OR

oT, X

OR

e)

oT

oX

OR

o'r2- oX

g)

f)

OR

oT

oX

h) or oX

oR

OR

OT, X

ox

oT, X

j)

.LL_ Z_-_°_-_## . . . . . . . . . q,¢ OX

OR

,.(

oT OR

OT

o X

OR

oT, X

Fig. 6. The structure of (a) cubic MgCu2, (b) cubic MgAgAs, (c) cubic LalrSi, (d) hexagonal Fe2P , (e) hexagonal MgZn2, (f) hexagonal Cain2, (g) hexagonal Ni2In, (h) tetragonal LaPtSi, (i) tetragonal PbFCI, (j) orthorhombic TiNiSi and (k) orthorhombic CeCu2.

Y(000) and z.42221.7/-111~In the case of RTX compounds, the R, T and X atoms occupy the X~, Y and X2 positions, respectively. The Z sites remain vacant again. The magnetic and other bulk properties of RNiSb compounds were reported by Aliev et al. (1988). For RNiSb compounds in which R = Ho, Er, Tm or Yb, there is no magnetic ordering observed above 5 K. The magnetic susceptibility of YbPdX (X = Sb or Bi) satisfies the Curie-Weiss law in the temperature range 4.2-300 K (Dhar et al. 1988). GdPtSn is a paramagnet with a paramagnetic Curie temperature 0p = 24 K and the effective magnetic moment equals #eff 8.28/~B (de Vries et al. 1985). =

4.1.3. Compounds with the LalrSi- (ZrOS-) type structure The RTSi compounds, in which R is a light rare-earth atom (La-Eu) and T represents Rh or Ir, crystallize in a primitive cubic structure (space group P213). In the crystal structure of the LaIrSi (ZrOS) type, the R, T and Si atoms are placed on the fourfold 4e sites of the P213 group. Its crystal structure is shown in fig. 6c. LaRhSi and LaIrSi exhibit a superconducting transition at 4.35 K and 2.3 K, respectively. Above the superconducting transition temperature, T~, the measured susceptibility is positive and almost temperature independent (Chevalier et al. 1982a).

100

A. SZYTULA

NdlrSi has a spontaneous magnetization below the Curie temperature, Tc = 10 K. The fact that the magnetic saturation is not reached up to 20 kOe suggests that a noncollinear magnetic ordering occurs below Tc. A hysteresis loop was obtained at 4.2 K with a coercive field of 0.5 kOe. Above Tc, the magnetic susceptibility obeys the Curie-Weiss law with a positive value of the paramagnetic Curie temperature, 0p = 12K, and the paramagnetic moment is equal to #elf = 3.62#B (Chevalier et al. 1982a). EuPtSi and EuPdSi are isomorphous with the LaIrSi-type structure. The magnetic susceptibility for both compounds obeys the Curie-Weiss law between 10-300 K with an effective paramagnetic moment close to the free E u 2 + ion value. At 4.2 K, a symmetric unresolved hyperfine split M6ssbauer spectrum is observed in EuPtSi, indicating the onset of magnetic ordering. For EuPdSi, at T = 4.2 K only a single M6ssbauer line is observed (Adroja et al. 1988b).

4.1.4. Compounds with the Fe2P- (ZrNiA1-) type structure The hexagonal structure of the F e 2 P type has the space group P6m2. In the ternary RTX compounds, the T atoms occupy the phosphorus sites and the R and X atoms are situated in the two inequivalent iron sublattice sites, as seen in fig. 6d. Compounds of the type RNiA1 and RCuA1 crystallize in the hexagonal Fe 2 P-type structure (Dwight et al. 1968). They are ferromagnets at low temperatures. The magnetic data obtained for these compounds are summarized in table 2 (Buschow 1980). TABLE 2 Magnetic data for RTX compounds. Compound

Crystal structure

Type of magnetic ordering

TC,N(K)

NdMnGa DyMnGa TbMnA1 ErMnA1 GdPtSn YbPdSb YbPdBi NdlrSi PrNiA1 NdNiA1

MgCu2 MgCu 2 MgCu2 MgCu2 MgAgAs MgAgAs MgAgAs ZrOS Fe2 P Fe2P

Spin glass Spin glass AF AF

10 40 34 15

GdNiA1

Fe2P

TbNiAI DyNiA1 HoNiAI ErNiA1 TmNiA1 LuNiAI PrCuA1 NdCuA1 GdCuA1

FezP Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P

F

10

F 15-17 F 61-70 F 57-65 F 39-47 F 25-27 F 15-16 F 4.2, 12 Pauli paramagnetic F 36 F 25 F 67-90

0p(K)

,t/err(b/B)

- 11 0-18

10.6

+ 24 - 9 - 9 + 12 - 10 +5 53-70 45-52 30 11-12 -1-0 -11

8.28 4.39 4.04 3.62 3.73 3.84 8.5-8.9 10.1-10.2 11.0-11.1 10.6-10.8 9.8-9.85 7.8

55-90

8.2

PR(Pn)

1.5 1.6 7.38-7.42 7.48-8.01 7.38-7.82 7.25-8.86 7.39-7.4 4.72 1.7 1.8 7.01

Ref.*

[I] [2] [3] [3] [4] [5] [5] [6] [7, 8] [7, 8] [7-10] [7-10] [7-10] [7-10] [7-10] [7, 10] [7, 10] [7, 10] [7,10] [7-10]

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

101

TABLE 2 (continued) Compound

Crystal structure

Fe2P Fe2 P Fe2P Fe2P FezP Fe2 P Fez P Fe2 P Fe2P FezP Fe2P Fe2 P Fe2P Fe2P FezP MgZnz MgZnz MgZn2 MgZnz MgZn 2 MbZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 AIB2 A1B2 A1Bz A1B2 A1B2 Ni2In A1B2 HoCuSi Nizln TmCuSi A1B2 CeZnSi A1Bz NdZnSi AIBz GdZnSi A1B2 TbZnSi A1Bz HoZnSi GdCuGe A1B2 A1Bz NdAgSi EuAgo.67 Sil.33 AIBz NdNio.67 Si1.33 A1B2 A1Bz CeCoo.4Sil.6 A1Bz NdNio.4Sil.6 SmFeo.4.Sil.6 A1Bz GdCoo.4.Sil.6 A1B2 A1Bz GdFeo.4Sil.6

TbCuA1 DyCuA1 HoCuA1 ErCuA1 TmCuA1 YbCuA1 LuCuA1 GdNiIn GdPdIn GdCuA1 GdPtSn GdCuIn CePtIn CePdIn CeAuIn YFeA1 GdFeAI TbFeA1 DyFeA1 HoFeA1 ErFeA1 TmFeA1 LuFeA1 TbCoA1 DyCoA1 HoCoA1 ErCoA1 CeCuSi PrCuSi NdCuSi GdCuSi TbCuSi

Type of magnetic ordering

Tc,N(K)

F 52 F 35 F 23 F 17 F 13 No C.-W. Pauli paramagnetic F 83 F 102 F 90 AF 30 AF 20 AF AF F F F F F F F F F F F F F F

1.8 5.7 38 260 195 125-144.5 92 56 38 39 48 47 34 25 15.5 14

F F AF

49 47 16

F

AF F F F

0p(K)

+42 + 29 +13 +3 -8

80 103 90 20 -73 -15 -10

+ 36

,Ueff(/AB)

]2R(~B )

10.1 11.0 10.9 10.0 7.6

7.41 8.66 8.59 7.27 4.71

7.28 7.73 8.56 7.99 7.90 2.58 2.56 2.1

10.9

-30 +8 - 45 30-58 + 52

10.4 3.3 3.39 4.2 7.0-8.32 9.62

+ 30

10.2

+ 12 + 30 + 63 +40 +50

2.54 3.62 7.94 9.72 10.61

+17 +21 +12 -- 9 0 0 0 -30

3.62 7.94 3.68 4.9 4.9 5.75 9.0 9.06

9

16 20 34 23

0.1 5.81 6.44 7.12-7.6 8.11 6.32 2.93 0.1 6.42 6.55 8.54 8.3 1.25 2.02 6.9 7.3 8.7 6.1

0.2 0.2 1.0

Ref.*

[7,10] [7,10] [7,10] [7,10] [7,10] [7,10] [7, 10] [4,9-11] [4,9-11] [4] [4] [4]

[12] [12] [13] [14] [14] [14] [14-16]

[14] [14] [14]

[14] [17] [18, 19] [17]

[20] [2 I,22] [23]

[21] [21,23] [23] [24] [21] [25] [26] [26] [26] [26] [26] [27] [28] [28] [283 [28] [283 [28] [293 [29]

102

A. SZYTULA TABLE 2

(continued)

Compound

Crystal structure

Type of magnetic ordering

Tc,N (K)

0p(K)

SmFeo.67 Gel.a3 NdA1Ga TbA1Ga DyA1Ga HoA1Ga ErA1Ga CeCuSn GdCuSn GdAuSn CePtSi NdPtSi SmPtSi YMnSi LaMnSi GdMnSi DyMnSi HoMnSi GdCoSi YNiSi LaNiSi CeNiSi PrNiSi NdNiSi SmNiSi GdNiSi TbNiSi DyNiSi HoNiSi ErNiSi TmNiSi YbNiSi LuNiSi TbCoSn DyCoSn HoCoSn ErCoSn TmCoSn LuCoSn CeRhGe CeIrGe GdAuGa TbAuGa DyAuGa HoAuGa ErAuGa TmAuGa CePdSn GdPdSn CePtGa

A1B2 A1B2 A1B2 AIB 2 " A1Ba A1B2 Cain 2 Cain 2 Cain2 LaPtSi LaPtSi LaPtSi PbFC1 PbFC1 PbFC1 PbFC1 PbFC1 PbFCI TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi

AF AF AF AF AF AF AF AF AF

26 2.5 47, 23 51.5, 17 30, 17.8 2.8 4.2 24 35

+ 33

AF 15 AF 4 F, AF 275,130 F 295 F 314-320 AF 30 AF 36 F 250 Pauli paramagnetic Pauli paramagnetic 57 +17 -15 Pauli paramagnetic 0 -2 0 0 +5 +8 -65 Pauli paramagnetic

AF

9.3

AF

6

AF AF AF

7.5 14.6 3.2

+1

+5 - 32 -I0 -47

290 295 220-314 30 - 10 131

~¢ff([~B)

~R(~B)

0.07

10.8

0.9 6.7 6.8 8.2 4.9

2.59 2.3 1.6 2.56

2.0 7.8 10.6 11.7

1.3 0.24 5.37 6.7 7.35

Ref.*

[29] [30] [31] [32] [31] [30] [33] [34] [34] [35] [36] [36] [37] [38] [38, 39] [38] [38] [39] [40]

[40] - 57 +17 -15

2.86 3.56 3.50

0 -2 0 0 +5 +8 -65

8.12 9.83 10.4 10.4 9.53 7.58 4.57

+30 + 27 +9 +11 +5 +31 - 56 -10 8.5 -10 -4.5 +3.5 +1.5 -2.0 - 67

10.43 10.47 9.42 7.57 0.79 2.30 0.27 8.06 9.7 10.63 10.58 9.6 7.59 2.67

[40] [40]

[40] [40] [40] [40] [401 [401 [40] [40]

[40] [40] [41] [41] [41] [41] [41] [41] [42] [42]

[43] [43] [43] [43] [43] [43] [44] [44] [45]

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

103

TABLE 2 (continued) Compound

Crystal structure

Type of magnetic ordering

Tc,N(K)

CePdGa GdRhSi TbRhSi

TiNiSi TiNiSi TiNiSi

DyRhSi HoRhSi ErRhSi TbRhGe CePdGe CePtGe TbNiGa PrAgGa NdAgGa GdAgGa TbAgGa DyAgGa HoAgGa ErAgGa TmAgGa EuCuGa

TiNiSi TiNiSi TiNiSi TiNiSi

AF F F AF F AF AF AF AF AF AF

1.7 100-102 55 13, 29 25 8-11 7.5-12 15 3.4 3.4 23

CeCu 2

CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCuz CeCu2 CeCu2

AF AF AF AF

AF

* References: [1] Tagawa et al. (1988). [2] Sakurai et al. (1988). [3] Oesterreicher (1972). [4] de Vries et al. (1985). [5] Dhar et al. (1988). [6] Chevalier et al. (1982a). [7] Oesterreicher (1973). [8] Leon and Wallace (1970). [9] Buschow (1975). [10] Buschow (1980). [11] Ba~ela and Szytuta (t986). [12] Fujii et al. (1987). [13] Pleger et al. (1987). [14] Oesterreicher (1977b). [15] Lima et al. (1983). [16] Bara et al. (1982). [17] Oesterreieher (1973). [18] Oesterreieher (1977a). [19] ~lebarski (1980). [20] Oesterreicher et al. (1970). [21] Kido et al. (1983b). [22] Gignoux et al. (1986b). [23] Oesterreicher (1976). [24] Ba~ela et al. (1985b). [25] Allain et al. (1988). [26] Kido et al. (1983a). [27] Oesterreicher (1977c).

0 v (K)

#eff(/AB)

60-90 48

7.55-7.95 9.92

11.5 10.5 -3

10,31 10.71 9.54

-37 -82

2.55 2.54

+31 +4 + 52 +20 +17 +14 +12 +9

3.18 3.65 7.95 10.03 10.6 10.43 9.43 7.38

#R(#B)

2.2 2.0 8.1 8.7-9.1 6.6 9.26

6.8

27 18 4.7 3 l0 [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]

Felner and Schieber (1973). Felner et al. (1972). Martin et al. (1983). Girgis and Fischer (1979). Doukour6 et al. (1986). Adroja et al. (1988b). Oesterreicher (1977a). Lee and Shelton (1987). Braun (1984). Kido et al. (1985c). Nikitin et al. (1987). Kido et al. (1982). Skolozdra et al. (1984). Skolozdra et al. (1982). Rogl et al. (1989). Sill and Hitzman (1981). Adroja et al. (1988a). Malik et al. (1988). Chevalier et al. (1982b). Szytuta (1990). Ba~ela et al. (1985a). Quezel et al. (1985). Szytula et al. (1988a). Kotsanidis and Yakinthos (1989). Sill and Esau (1984). Malik et al. (1987).

Ref.*

[45] [46,47] E46] [48,49] [46] E46,48, 49] [46,48] [50] [42] [42] [51] [523 [523 [52] [52] [52] [52] [52] [523 [533

104

A. SZYTULA

Ternary GdTAI and GdTSn compounds were investigated by Buschow (1971, 1973) and found to be ferromagnets, too. A rather unusual variation of the paramagnetic Curie temperature 0p was observed in the Gdl_~ThxCuA1 series, passing through a maximum for x = 0.3. In the Gdl _xThxPdln series, a change in the sign of 0p from positive to negative was observed at about the same concentration. Taking into account the 27A1 N M R data on GdCuA1, attempts have been made to explain such behaviour in terms of the RKKY model (Buschow et al. 1971, 1973). 155Gd M6ssbauer spectra obtained for some GdTX compounds showed a magnetic ordering at 4.2 K. The analysis of these spectra indicates that the magnetic moment of the Gd atoms is oriented parallel to the c-axis in GdCuA1, GdNiln and GdPdln and has an angle of ~b= 47 ° with the c-axis in GdPdSn and GdPdA1 (de Vries et al. 1985). Also, CeTIn (T = Ni, Pd, Pt or Rh) crystallize in the Fe2 P-type crystal structure. The temperature dependence of the inverse susceptibility gg- 1 for CePdIn and CePtIn follows the Curie-Weiss law with effective moments which are in agreement with the theoretical free-ion value for the Ce 3 + ion. At low temperatures, CePdIn exhibits antiferromagnetic order below TN= 1.8 K, whereas CePtIn is a heavy fermion (Fujii et al. 1987). The temperature dependence of the magnetic susceptibility and the electrical resistivity suggests that CeNiIn is an intermediate valence compound (Fujii et al. 1987). Also, the temperature dependence of the magnetic susceptibility of CeRhIn indicates the mixed-valent behaviour of this compound (Adroja et al. 1989). The temperature dependence of the magnetic susceptibility and the specific heat of CeAuIn indicate antiferromagnetic ordering below TN= 5.7 K. Above TN, the magnetic susceptibility obeys the Curie-Weiss law with an effective moment that appears to be reduced with respect to that expected for the 4f 1 configuration of Ce (Pleger et al. 1987). 4.1.5. Compounds with the MgZn2-type structure The groups of intermetallic compounds RTA1 with T = Fe or Co have the hexagonal MgZn2- (C14) type structure (space group P6a/mmc) represented schematically in fig. 6e. This space contains three nonequivalent sets of crystal sites. The 4f sites are occupied by R atoms. The sites 2a and 6h are occupied both by T and X atoms. The magnetic measurements of RFeA1 compounds in which R is a heavy rare earth show that they are ferromagnets with a high Curie temperature (Oesterreicher 1977c). Systematic studies were only performed for DyFeA1. Neutron diffraction data indicate a ferrimagnetic structure in which the magnetic moments of the Dy atoms order ferromagnetically and are equal to 7.6(1)/~B/Dy atom. The Fe sublattice orders ferromagnetically with Fe moments equal to #(2a)= 0.8(4)#B and /~(6h)= 0.5(2)/~B. The Fe sublattice is coupled antiferromagnetically to the Dy sublattice. There is a strong reduction of the Dy moment compared to the free-ion value. The magnetic moment lies in the basal plane (Sima et al. 1983). The Lni emission spectra of iron in DyFeA1 give evidence of some charge transfer between 3dFe and 5dDy bands (Slebarski and Zachorowski 1984). The results of M/Sssbauer investigations, which indicate a more complete transfer to the 3d band by transfer of Dy 5d electrons and

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

105

of A1 3p electrons to the iron sites, are in accordance with the observed increase in the intensity of the Lxn spectra. The total magnetic moment localized on the Dy atoms decreases at T = 4.2 K, as a consequence of an opposite polarization of the 5d and 4f bands (Bara et al. 1982, ~lebarski 1987). Also, in the case of the RCoA1 compounds (R = Tb-Er) a ferromagnetic ordering is observed at low temperatures. Magnetic data of these compounds are listed in table 2 (Oesterreicher 1973, 1977a). The neutron diffraction data for ErCoA1 indicate a ferromagnetic ordering at T = 4.2 K with magnetic moments per Er atom equal to p = 7.0#B parallel to the c-axis. No moment is observed for the Co atoms (Oesterreicher et al. 1970). 4.1.6. Compounds with the AlB 2- or Ni2In-type structure Many ternary equiatomic compounds crystallize in the two similar hexagonal structures represented by the A1B2 type with space group P6/mmm (Rieger and Parth6 1969) and the NiEIn type with space group P63/mmc (Iandelli 1983). These two structure types are shown in fig. 6g. In these structures, atoms occupy the following positions: A1 in 0, 0, 0 and B in ½, 2, ½ and 2, ½, ½ for the A1B2 type; and Ni in 2a: 1 2 37, ~, and -~, 1 1 for 0, 0, 0, and 0, 0, ½, and in 2c: 7,17,2~1 and ~,27,2~a and In in 2d: 7, Ni2 in. In the case of RTX compounds, the T and X atoms are statistically distributed in the A1B2-type structure while for Ni2In they are situated in 2c and 2d positions (Mugnoli et al. 1984, Ba£ela et al. 1985b). The difference between the two structural types is due mainly to a doubling of the periodicity along the c-axis, giving in the latter space group an ordered distribution of T and X atoms in ½, 2, ¼ and in ½, 2, ¼, respectively. On the basis of neutron diffraction data, Mugnoli et al. (1984) concluded that LaCuSi exists in two thermal modifications: a low-temperature Ni2 In type and a high-temperature A1B2 type. The magnetic properties of RCuSi (R = Y, Ce, Nd, Sm, Gd or Ho) were investigated by Kido et al. (1983b). The magnetic susceptibilities of YCuSi and SmCuSi are 102 times smaller than those of the other compounds and they show no temperature dependence. In the other compounds, the magnetic susceptibility obeys the CurieWeiss law with effective magnetic moments equal to the free-ion values (see table 2). The magnetic properties of RCuSi with R -- Pr, Gd or Tb were investigated from 4.2 to 150 K in magnetic fields up to 50 kOe. As may be seen in table 2, all these compounds order ferromagnetically (Oesterreicher 1976). The magnetic properties of CeCuSi were studied by neutron diffraction and magnetization measurements. The CeCuSi compound shows a ferromagnetic ordering below Tc -- 15.5 K, with a magnetic moment of 1.25/~B at T--2.5 K, perpendicular to c-axis (Gignoux et al. 1986a). Neutron diffraction studies of TbCuSi indicate a cosinusoidally modulated transverse spin structure below T~ = 16 _+2 K, while DyCuSi and HoCuSi remain paramagnetic down to T-- 4.2 K (Ba~ela et al. 1985b). TmCuSi is a collinear ferromagnet with Tc = 9 K and a magnetic moment #-6.1(2)/~B at T = 2.1 K oriented parallel to c-axis (Allain et al. 1988). GdCuGe is an antiferromagnet with TN----17 K (Oesterreicher 1977c). The RZnSi compounds (R = Ce, Nd, Sin, Gd, Tb or Ho) are paramagnetic in the

106

A. SZYTULA

temperature range between 77 and 300 K. Their effective magnetic moments are in good agreement with the corresponding free-ion values. YZnSi is a Pauli paramagnet. All these compounds are metallic (Kido et al. 1983a). The magnetic properties of pseudoternary RCul _xZn~Si (0 <~x ~< 1) compounds, for R = Gd (Kido et al. 1984b) R = Tb (Ba~ela and Szytuta 1989) and R = Ho (Kido et al. 1985c), were also investigated. For all these systems the paramagnetic Curie temperatures, and for GdCul _xZn~Si the Curie temperatures, have a maximum at the concentration x = 0.4. The values of/~eff are about equal to the free R 3 + ion value in the whole composition range, opening the possibility to describe the magnetic properties of RCul _~Zn~Si by RKKY theory. The magnetic susceptibility of GdTiSi shows Curie-Weiss behaviour with #eee= 7.07#B and 0p = 10.4K (Kido et al. 1984a). The RA1Ga compounds (R = Nd, Tb, Dy, Ho or Er) crystallize in the hexagonal A1Bz-type structure (Martin and Girgis 1983). NdA1Ga is an antiferromagnet with TN= 2.5(3) K and a magnetic structure incommensurate with the crystal lattice in the basal plane. The cycloidal spin structure of the Nd moments rotate in the basal plane. All magnetic moments are perpendicular to the c-axis. The rotation angles are 62.7 ° (Martin et al. 1983). For TbA1Ga and HoA1Ga, two phase transitions are observed (see table 2). The magnetic structure is described by the propagation vector k -- (7,1 7, k~). At low temperatures, kz = 1, which leads to a commensurate structure. In the temperature range Tt < T < TN, incommensurate configurations are found (Girgis and Fischer 1979). The thermal variation of the susceptibility of DyA1Ga in the 4-100 K temperature range exhibits two transitions at Tt = 17 K and at TN = 51.5 K, the latter being the Nrel temperature. Neutron diffraction data at T = 25 K indicate magnetic ordering with a propagation vector k = [½, 7, ~ 3] corresponding to a hexagonal magnetic cell six times larger than the crystallographic cell (am = ax/3, Cm= 2C). In each Dy layer, the magnetic arrangement is triangular (see fig. 7). At T = 4.2K the ordering is collinear and the Dy moments are parallel to the c-axis (Doukour6 et al. 1986). The magnetic cell of ErA1Ga is incommensurate with the crystal lattice in the c-direction, the magnetic structure exhibiting a trigonal spin structure in the basal plane. The spin vectors are perpendicular to the c-axis. All magnetic moments rotate in the basal plane with angles of 120°. The rotation angle is 170° from plane to plane in the c-direction (Martin et al. 1983). Bertaut (1961) discussed the stability of the possible magnetic arrangements in a two-dimensional hexagonal (or triangular) lattice. Writing the exchange energy as E ~ --Y,i,jiiSi.Sj, he took into account the exchange integrals between the first (J~) and the second (J2) nearest neighbours. The magnetic arrangements obtained are represented in fig. 8a. An analogous study can be done in the case of an Isinglike model in which the strong anisotropy forces the magnetic moment to be parallel to the c-axis (Doukour6 and Gignoux 1982). The predicted magnetic arrangements are shown in fig. 8b. RT2_~Si~ and RT2_~Ge~, where R = La, Ce, Nd, Sm, Eu or Gd and T = Fe, Co, Ni or Ag, crystallize in the A1B2-type structure. The magnetic data are summarized

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

17K
107

T<17K

Fig. 7. Magnetic structures of DyAIGa at 25 and 4.2K (Doukour6 et al. 1986).

a)

TbAIGo HoAIGo [1131131 DyAIGo Tt'T,T N DyGa2

ErO°2

'J2

'J2

b)

DyAtGo T-Tt

tt [001

tll J1

[113 1/3]

tt [00]

J1

ErGo2 [0 l / ~ . b q ,

/~

h0] PrGa2 NdGo2

[0 1/2]

Fig. 8. (a) Stability diagram of possible magnetic structures in a two-dimensional triangular (hexagonal) lattice when the moments lie in the basal plane, i.e., c [x, y model discussed by Bertaut (1961)]. (b) Stability diagram of possible magnetic structures in a two-dimensional triangular (hexagonal) lattice when the moments are along the c-axis (Ising-like model). The numbers in the brackets are the propagation vectors in the plane (Doukour6 et al. 1986). in table 2. NdAgSi, NdFeo.67Gel.33 , NdNio.67Sil.33 and EuAgo.67Sit.33 are ferromagnets while EuAgo.67 5il.33 is an antiferromagnet. O t h e r c o m p o u n d s are p a r a m a g nets up to 4.2 K. In these c o m p o u n d s , the R ions are magnetically ordered whereas the T a t o m s are nonmagnetic (Felner et al. 1972, Felner and Schieber 1973).

4.1.7. Compounds with the CaIn2-type structure The R C u S n c o m p o u n d s crystallize in the hexagonal C a I n a - t y p e structure with space g r o u p s y m m e t r y P63/mmc, which is shown in fig. 6f. The R a t o m s occupy the 2b sites (0, 0, ½) and Cu and Sn the 4f sites (½, ½, z), etc. The magnetic susceptibility of CeCuSn obeys the Curie-Weiss law between 40 and 300 K, with #elf = 2.59#B and 0p = + 5 K. The susceptibility has a deviation from the

108

A. SZYTULA

Curie-Weiss law below 40K and a rapid rise below 10K. The magnetic hyperfine splitting in the 119Sn M6ssbauer spectrum is observed at T = 4.2 K, confirming that this compound is ordered magnetically (Adroja et al. 1988a). GdCuSn and GdAuSn compounds are antiferromagnets with N6el temperatures 24 and 35 K, respectively (Oesterreicher 1977c).

4.1.8. Compounds with the LaPtSi-type structure The equiatomic RPtSi, RPtGe and RIrGe compounds with light rare earths (R = La-Gd) crystallize in the tetragonal LaPtSi-type structure with space group I41 md (Klepp and Parth6 1982) which is a variant of the ThSi2-type structure (see fig. 6h). The compounds with R = La are superconductors (Braun 1984). The reciprocal magnetic susceptibility of CePtSi obeys the Curie-Weiss law with an effective magnetic moment #eff 2.56(5)#B. The temperature dependence of the magnetic susceptibility and the specific heat at low temperature show that the compound belongs to the class of heavy fermions (Lee and Shelton 1987, Rebelsky et al. 1988). RPtSi compounds with neodymium (TN = 15 K) and samarium (TN = 4K) show magnetic ordering, those with cerium and praseodymium remain paramagnetic down to 2 K (Braun 1984). =

4.1.9. Compounds with the PbFCl-type structure The tetragonal structure of the PbFC1 type has a space group P4/nmm. In ternary RTX compounds, both the R and X atoms occupy the 2c sites and the T atoms occupy the 2a sites. The crystal structure of the PbFC1 type is shown in fig. 6i. This type of structure is composed of layers perpendicular to the c-axis in the following sequence of planes of the same atoms: R-X-TE-X-R. LaMnSi and GdMnSi are ferromagnets with Curie temperatures Tc of about 295 K, while DyMnSi and HoMnSi are antiferromagnets with TN of about 30K (Nikitin et al. 1987). For the YMnSi sample synthesized at 1000°C, the ferromagnetic ordering exists below Tc = 275 K (Johnson 1974/1976). The different properties are observed for the sample obtained at 1300°C and under pressure of 1.0 GPa. At low temperatures, the sample is an antiferromagnet. With an increase in temperature, in the temperature range of 150-170 K, the transition to the ferromagnetic state is observed. From the 0-2 temperature dependence, the Curie temperature was determined to be 282 K. In the paramagnetic region, the temperature dependence of Zr~1 for YMnSi obeyed the Curie-Weiss law with an effective magnetic moment and a paramagnetic Curie temperature of 2.3#B and 280K, respectively (Kido et al. 1985b). Also, GdCoSi is a ferromagnet with Tc = 250 K (Kido et al. 1982). 4.1.10. Compounds with the TiNiSi-type structure The TiNiSi-type structure belongs to the Prima space group. In this structure, the 4c sites are occupied by four R atoms, four T atoms and four X atoms with different values for the atomic positional parameters. The unit cell of the TiNiSi-type structure is shown in fig. 6j. The magnetic susceptibility of RCoSn, where R = Tb-Lu, in the temperature range

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

109

78-300 K obeys the Curie-Weiss law. The YCoSn compound is a Pauli paramagnet (Skolozdra et al. 1982). Of the RNiSi compounds, the magnetic susceptibility obeys the Curie-Weiss law for compounds with R = Ce-Nd and Tb-Lu. The compounds with R = Y, La, Sm or Lu are all Pauli paramagnets (Gladyshevskii et al. 1977). The CeRhGe compound orders antiferromagnetically below TN= 9.3 K, whereas, in CeIrGe, cerium is in an intermediate valence state and no magnetic transition is observed down to 1.5 K (Rogl et al. 1989). The RAuGa compounds, in which R is Sm or one of the heavy rare-earth elements, crystallize in the TiNiSi-type structure. At high temperatures, the reciprocal susceptibility of all compounds, except for Sm, follow the Curie-Weiss law. The effective magnetic moments are in good agreement with those calculated for free R 3 + ions. The paramagnetic Curie temperatures of the heavy rare-earth compounds do not vary linearly with the de Gennes function. At low-temperatures, only the GdAuGa compound orders antiferromagneticaUy, with a N~el temperature of 6 K. It exhibits also metamagnetic behaviour (Sill and Hitzman 1981). Magnetic susceptibility measurements reveal that CePdSn orders antiferromagnetically with TN= 7.5 K. In the paramagnetic state, between 50-300 K, the susceptibility follows the Curie-Weiss law with 0p -~- - - 6 7 K and ]'Left"= 2.67#B (Adroja et al. 1988a). From magnetic susceptibility measurements of GdPdSn, it is derived that TN= 14.6 K (Adroja et al. 1988a). The magnetic susceptibilities of CePdGa and CePtGa follow the Curie-Weiss law. The observed effective paramagnetic moments are close to those of the free C e 3 + ion in each case. At low temperature, the susceptibility of CePtGa shows considerable deviation from the Curie-Weiss behaviour which may be either due to the effect of a crystalline electric field acting on cerium ions, or due to a hybridization between the Ce 4f electrons and the conduction electrons. The low-temperature specific-heat measurements reveal a peak in both compounds, indicating magnetic ordering. The ordering temperatures are 1.7 K for CePdGa and 3.2 K for CePtGa (Malik et al. 1988). The ternary silicides RRhSi, for R = Y, Gd, Tb, Dy, Ho or Er, crystallize in the TiNiSi type of crystal structure (Chevalier et al. 1982b). The magnetometric data indicate that the Gd, Tb and Dy compounds have a spontaneous magnetization and their magnetic ordering comes probably from a noncollinear arrangement of the moments. HoRhSi and ErRhSi order antiferromagnetically at TN = 8 K and 7.5 K, respectively. At 4.2 K, both compounds undergo a metamagnetic transition at H~ = 6kOe for HoRhSi, and at 12kOe for ErRhSi (Chevalier et al. 1982b). The neutron diffraction data indicate that the magnetic structure of TbRhSi is a double flat spiral below TN = 13 K. The magnetic structure of HoRhSi below TN= 11 K is collinear with a C(+ + - - ) configuration. The magnetic moments of the holmium atoms are parallel to the b-axis. Also, ErRhSi has a magnetic structure consisting of a double flat spiral below TN= 12 K (Ba~ela et al. 1985a, Quezel et al. 1985). TbRhGe crystallizes in the TiNiSi-type structure. Below TN= 15(1) K, the magnetic structure of TbRhGe is incommensurate with the lattice, describable in terms of

110

A. SZYTULA

a modulated transverse spin wave with a propagation vector k = (0, 0.388, 0.236) (Szytuta et al. 1988a).

4.1.11. Compounds with the CeCu2-type structure The CeCu2-type structure is orthorhombic and belongs to the space group Imma (fig. 6k). Rare-earth atoms occupy the 4e cerium sites, while transition metals and X (Si, Ge or Ga) occupy statistically the 8h copper sites (Hovestreydt et al. 1982). The magnetic resistivity and specific-heat measurements reveal a magnetic transition near 3.4 K for CePdGe and CePtGe (Rogl et al. 1989). The neutron diffraction study of a TbNiGa compound indicates an antiferromagnetic ordering with a N6el temperature equal to 23 K. The magnetic propagation vector k = (½, 0, 0) is along the a-axis. The terbium magnetic moment is parallel to the b-axis with a magnetic moment value of 6.8(4)#B (Kotsanidis and Yakinthos 1989). The magnetic characteristic of the series of RAgGa compounds (where R is Pr, Nd, Gd, Tb, Dy, Ho, Er or Tm) were determined in an applied field up to 26 kOe and at temperatures ranging from 3 to 300 K (Sill and Esau 1984). At high temperatures, the reciprocal susceptibilities follow the Curie-Weiss law. The effective paramagnetic moments are in reasonable agreement with those calculated for R 3 ÷ ions. The asymptotic Curie temperatures are relatively small and positive. At low temperatures, the Gd, Ho and Er compounds order ferromagnetically. The Tb compound orders antiferromagnetically, while DyAgGa is metamagnetic. EuTGa and YbTGa (T = Cu, Ag or Au) compounds form the orthorhombic CeCu 2-type structure. 1~1Eu M6ssbauer studies indicate Eu to be divalent in EuTGa. The magnetic susceptibility of these Eu compounds follows the Curie-Weiss law with an effective moment close to that of Eu 2+. Below 10K, EuCuGa orders antiferromagnetically (Malik et al. 1988). Magnetic susceptibility measurements were carried out on YbTGa (T = Cu, Ag or Au) to study the Yb valence. In the susceptibility curve of YbCuGa, a broad maximum, typical for the mixed-valence systems, is observed at about 210K. The susceptibility of YbAgGa and YbAuGa varies slowly with temperature between 50-300 K, which indicates the divalent state of the Yb ion (Malik et al. 1987). 4.2. RTX2 phases The RTX 2 compounds crystallize in different orthorhombic structures: -CeNiSi2 and TbFeSi2 have the same Cmcm space group but they differ in localization of the atoms in the lattice. The orthorhombic CeNiSi2-type crystal is displayed in fig. 9. All types of atoms, i.e., Ce, Ni, SiI and SilI, occupy the 4c site (Bodak and Gladyshevskii 1970). In the two types of structures, all of the R, T and Si atoms are arranged in alternating layers stacked in the sequence: R-T-Si-T-R-Si-Si-R-T-Si-T-R R-Si-Si-R-Si-T-T-Si-R

for the CeNiSi2 type, and for the TbFeSi2 type;

TERNARYINTERMETALLICRARE-EARTHCOMPOUNDS

111

OR O Co ¥

kz

•

Si

Fig. 9. The crystal structure of the CeNiSi2type found in RCoSi2.Coordination polyhedra of Co atoms and their links are also shown.

-RRuB2 crystallizes in the Pnma space group (Ku and Shelton 1981); -RTC2 compounds have Atom2 space group (Jeitschko and Gerss 1986); -RNiA12 compounds (R = Y, Gd-Lu) crystallize in the MgCuAlz-type structure with space group Cmcm (Romaka et al. 1982a). -RNiGaE compounds crystallize in two types of crystal structures: NdNiGa2 for R = L a - G d with the space group Cmmm, and MgCuAI2 for R = Y, Tb-Lu with space group Cmcm (Romaka et al. 1982b). The magnetic properties were investigated for some of the compounds only (Pelizzone et al. 1982). The magnetic properties of RCoSiz compounds were studied by means of magnetic susceptibility measurements between 2 and 250 K. The Ce and Y compounds show an essentially temperature independent Pauli paramagnetism. The compounds with R = Nd, Sm, Gd, Tb, Dy, Ho, Er or Tm are anitferromagnetically ordered below 20 K. The effective rare-earth moments in the paramagnetic state agree well with the free-ion values and, for the heavy rare earths, the N6el temperatures vary with the de Gennes factor. New magnetic and resistivity data indicate that CeCuSi2 has no magnetic or superconducting transition above 1.26 K (Lee and Shelton 1988). CeCul.54Sil.46 crystallizes in the CeNiSiz-type structure. Magnetic, thermal and transport data indicate that the compound is an antiferromagnetic heavy ferrnion system with a N6el temperature TN-----7K (Takabatake et al. 1988). Neutron diffraction data indicate the presence of an antiferromagnetic structure of the G-type (Bertaut 1968) for DyCoSi 2 and HoCoSi2 (Szytuta et al. 1989). In TbCoSi2, a complex spiral structure is observed (Szytuta et al. 1989). The magnitudes of the magnetic moments at 4.2 K localized on the R 3 ÷ ions in RCoSi2 (R = Tb, Dy

112

A. SZYTULA

or Ho) are much smaller than the free-ion values gs J. This may be considered being due to the strong crystalline electric field anisotropy which is probably also responsible for the complex magnetic ordering scheme found in TbCoSia. The RMnSi: compounds (R = La-Sm) and RFeSi2 compounds crystallize in the TbFeSiz-type structure (Yarovetz and Gorelenko 1981). The manganese sublattice of the RMnSiz compounds orders ferromagnetically up to rather high temperatures. The Curie temperatures of the RMnSiz compounds with R between La and Sm increase from 386 to 464 K. At low temperatures, PrMnSi2 and NdMnSia show an additional magnetic transition which corresponds to the ordering of the rare-earth sublattice. PrMnSi2 becomes antiferromagnetic (TN = 35 K), while NdMnSia is still ferromagnetic (To = 40K) (Venturini et al. 1986). Neutron diffraction data at 4.2K indicate that the magnetic structure of PrMnSiz is characterized by ferromagnetic layers of Pr atoms piled up along the b-axis in the + + - - sequence. The Mn layers are ferromagnetically coupled with the adjacent Pr layers, as is usual for 3d moments and light rare-earth moments. The magnetic moment directions of Mn are in the (010) plane (Malaman et al. 1985). The moments of the Mn sublattices in the other RMnSiz compounds are parallel to the b-axis. In NdMnSi2, the Nd and Mn magnetic moments are in the (011) plane. The moment of the Nd sublattice is parallel to the c-axis, while the Mn sublattice is at an angle of 45 ° from the c-direction. In both compounds, large differences of the R moments from the free-ion values are observed, as may be seen from table 3. The moments of the Mn sublattices in the other RMnSi2 compounds (R = La, Ce or Sm) are parallel to the b-axis (Malaman et al. 1988). The magnetic susceptibility of LaFeSia and CeFeSia is temperature independent and CeFeSiz is a mixed-valent system. The compound PrFeSiz is a collinear ferromagnet (Tc = 26 K) with the direction of the moment parallel to the [010] direction, while NdFeSi2 (TN = 6.5 K) exhibits an amplitude-modulated antiferromagnetic structure in which the [010]-axis corresponds to the direction of both the modulation and the magnetic moment. The Fe atoms never have a magnetic moment in RFeSi2 compounds. 57Fe M6ssbauer spectra of PrFeSi2 and NdFeSi2 at T = 4.2 K show only a splitting due to transferred hyperfine fields (Venturini et al. 1986). The RTB z compounds, in which R = Y or Lu, and T is Ru or Os, crystallize in an orthorhombic structure with space group Prima. These compounds are superconductors with critical temperatures of 7.7 K for YRuB2, 1.9 K for YOsB2, 9.9 K for L u R u B 2 and 2.4 K for LuOsB: (Chevalier et al. 1983). TbRuBz is a ferromagnet with Tc = 49(2)K (Weidner et al. 1985). For Tml _xLuxRuBa system, the magnetic susceptibility data allow to determine the magnetic phase diagram (see fig. 10). In the region x = 0.52 and 0.68 a reentrant superconductivity is observed. The initial depression of T, near LuRuBz is caused by the magnetic Tm 3+ ions (Ku and Shelton 1981). The magnetic data for RTC2 compounds indicate that compounds with R = Nd, Gd, Tb, Dy, Er or Tm are all antiferromagnets with ordering temperatures between 7 K for R = Nd and 25 K for R = Tb (Kotsanidis et al. 1989). The neutron diffraction studies of TbNiC2 at T = 16K show a magnetic structure with a wave vector

113

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS TABLE 3 Magnetic properties of RTX 2 compounds. Compound

Crystal structure

CeCuSi2

CeNiSi2 CeNiSi2 CeNiSi2 CeNiSi2 CeNiSi2 CeNiSiz CeNiSi2 CeNiSi2 CeNiSi2 CeNiSi2 TbFeSi2 TbFeSi2 TbFeSi2 TbFeSi2 TbFeSiz TbFeSiz TbFeSi2 LuRuB2 LuRuB2 CeNiC2 CeNiC2 CeNiC2 CeNiC2 CeNiC2 CeNiC2 MgCuA1z MgCuA12 MgCuA12 MgCuA12 MgCuA12 MgCuAI2 MgCuAI2 MgCuAI2 MgCuAI2 NdNiGa2 NdNiGa2 NdNiGa2 NdNiGa2 NdNiGa2 NdNiGa2 MgCuA12 MgCuAI2 MgCuA12 MgCuAI2 MgCuA12 MgCuA12 MgCuA12 MgCuA12

CeCut.548il.46 NdCoSi2 SmCoSi2 GdCoSi2 TbCoSi2 DyCoSi2 HoCoSi2 ErCoSi2 TmCoSi2 LaMnSi2 CeMnSi2 PrMnSi2 NdMnSi2 SmMnSi2 PrFeSi2 NdFeSi2 TbRuB2 TmRuB2 NdNiC2 GdNiC2 TbNiC2 DyNiC2 ErNiC2 TmNiC2 YNiA12 GdNiA12 TbNiA12 DyNiA12 HoNiAI2 ErNiA12 TmNiA12 YbNiA12 LuNiA12 LaNiGa2 CeNiGa2 PrNiGa2 NdNiGa2 SmNiGa2 GdNiGa2 TbNiGa2 DyNiGa 2 HoNiGa2 ErNiGa2 TmNiGa2 YbNiGa2 LuNiGa2 YNiGa2

* References: [1] Lee and Shelton (1988). [-2] Takabatake et al. (1988). [3] Pelizzone et al. (1982). [-4] Szytuta et al. (1989).

Type of magnetic ordering

Tc,N(K)

AF 7 AF 2.5 AF 4.0 AF 7.5 AF 18.5 AF 10.5 AF 6.3 AF 4.5 AF 2.5 F 386 F 398 F, AF 434, 35 F 441 F 464 F 26 AF 6.5 F 49 F 4 AF 7 AF 14 AF 25 AF 10 AF 8 AF 8 Pauli paramagnetic

0p(K)

~eff (lAB)

-47

2.5

-28

3.0

- 8 - 18 - 8 - 6 -17 - 76 395 420 450 460 470 44 41

7.5 9.8 10.7 10.5 9.6 7.8 2.6 2.1 2.1 4.2 3.3 3.5 3.6

8.62 5.74 6.72

2.0 1.9 2.05 2.22

6.8

43 39 25 7 4 18

8.04 10.82 11.75 11.53 10.32 8.09

-40 5.4 15.9

2.64 3.89 3.74

- 3.2 59.9 31.2 24.1 16.2 5.1

8.04 9.86 10.47 10.68 9.29 7.60

Pauli paramagnetic Pauli paramagnetic Pauli paramagnetic

Pauli paramagnetic

Pauli paramagnetic Pauli paramagnetic Pauli paramagnetic [5] [6] [-7] [-8]

~R (~B)

Malaman et al. (1985). Venturini et al. (1986). Weidner et al. (1985). Ku and Shelton (1981).

Ref.*

[1] [2] [3] [3] [3] [-3,4] [-3,4] [3, 4] [-3] [-3] [5, 6] [5, 6] [5, 6] [5, 6] [-5,6] [-6] [6] [7] [-8] [-9] [-9] [9,10] [9] [9] [9] [-I1] [-11] [11] [11 ] [-11] [ l 1] [ 11] [ 11] [11] [12] [12] [12] [-I2] [12] [12] [12] [12] [12] [12] [12] [12] [12] [12]

[-9] Kotsanidis et al. (1989). [10] Yakinthos et al. (1989). [-11] Romaka et al. (1982a). [12] Romaka et al. (1983).

114

A. SZYTULA 15Tm (a/O) 10

lz 2,s , 2,0

]

i

,

o Tc(TcO

.mm(Tc2) TIK)

PARAMAGNETIC

0

i

0.0

I

0.2

i

I

0.4

i

X

I

0.6

ki

si

,

0i

S//"1 t

0.B

i

I

1.0

Fig. 10. Low-temperature magnetic phase diagram for the system Tm~ _xLuxRuB2, determined from AC magnetic susceptibility measurements down to 1.2 K (Ku and Shelton 1981).

t,=(½,'3, 3). The terbium magnetic moment value is # = 6.8#B and it is directed along the c-axis (Yakinthos et al. 1989). The magnetic susceptibility of the RNiAlz compounds, where R = Y, La, Lu or Yb, is temperature independent. For the compounds with R = Gd, Tb, Dy, Ho, Er or Tm the Z-t(T) function obeys the Curie-Weiss law in the temperature range 78-300 K (Romaka et al. 1982b). The magnetic susceptibility was measured also for the RNiGa/compounds in the temperature range 78-300 K. It is independent of the temperature for R = La, Yb, Lu or Y. For the other RNiGa2 compounds, the susceptibility obeys the CurieWeiss law (Romaka et al. 1982a). The values of the magnetic susceptibility, the paramagnetic Curie temperature and the effective magnetic moments are given in table 3.

4.3. RT2X phases The family of compounds with 1 : 2 : 1 stoichiometry crystallizes in two groups of different structure types: in the cubic I2t structure, found also for the Heusler alloys, with general formula X2YZ, and in the orthorhombic Fe3C-type structure. Rare-earth based Heusler alloys exhibit a number of interesting and diverse phenomena such as superconductivity, mixed valence and magnetic phase transitions. The Heusler phases occur with rare earths in the following systems: RAgzIn (Galera et al. 1984), RAuzln (Besnus et al. 1985b), RCuzln (Felner 1985) as well as in some RPd2Sn (Malik et al. 1985b) and RNizSn (Skolozdra and Komarovskaya 1983) systems. Felner (1985) investigated the magnetic behaviour of RCu2In compounds (R = La-Lu) in the temperature range 2-300K. The RCualn (R = Sin, Gd, Tb or Dy) compounds are antiferromagneticaUy ordered at low temperatures (see table 4). LaCu2In is a Pauli paramagnet and LuCu2In is diamagnetic. New data indicate that CeCu 2In is a heavy fermion compound with specific heat

115

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S TABLE 4 Magnetic data for Heusler RT2X compounds. Compound

Type of magnetic ordering

LaCu2In CeCu2 In PrCu2In NdCu 2 In SmCu2 In GdCuz In TbCu2 In DyCu2In ErCu2 In LuCu2In CeAg2In

Pauli paramagnet

PrAg2In NdAg2 In SmAg2 In GdAg2 In TbAg2 In DyAg2 In HoAg2In ErAg2 In TmAg2 In CeAu2 In PrAu 2In NdAu2 In SmAu2In GdAu2 In TbAu2 In DyAu2 In HoAu 2 In ErAu2 In TmAu 2 In YbAuEIn YAu2In TbPd 2 Sn DyPd 2 Sn

TN(K)

AF AF AF AF AF

2.7 2.5 2.5 4.5 10.0 8.8 3.5

No Curie-Weiss behaviour AF 11.5 AF 8.2 AF 6.0 AF 2.6

No Curie-Weiss behaviour Pauli paramagnet AF 9.0 AF 15.0 AF 7.0

HoPd z Sn

2.52 3.53 2.60

- 31 - 33 -21 - 10

7.60 9.70 10.63 9.63

-9 -9 -16 - 24 - 23 - 56 - 29 - 20 -14 - 9.5 - 5.0 - 15 - 5 - 8

8.10 9.62 10.33 10.23 9.47 7.33 2.57 3.55 3.70

- 14 - 7 - 5 - 5 - 4 - 35

8.0 9.7 10.8 10.8 9.63 7,06

- 8.6 - 9.3

4.2 5.0

ErPd z Sn AF AF

1.0 1.0

TmPd 2 Sn YbPd z Sn AF YbNi 2 Sn LuNi 2 Sn

- 30 - 35 - 70

- 6.2 AF AF

0.97 (7) 3.63 3.68

9.95 10.83 10.8 10.67 10.8

[6] [7] [8] [9] [10]

Ref.*

0 - 4.3

7.4 4.34

[4,5]

6.7(5) 4.4(1)

5.7(5)

1.6 4.33

[1] [1] [1] [12 [13 El] [12 [1] El] [23 [3] [2] [22 [2] [2] [2] [2] [2] [2] [2]

[4,5]

5.81 (8) 9,59 9.57

0.23

Pauli paramagnet

/is (/~B)

2.54

- 7.6 - 5.8

- 38

* References: [1] Felner (1985). [2] Galera et al. (1984). [3] Galera et al. (1982b). [4] Besnus et al. (1986). [5] Besnus et al. (1985b).

#~rf (/~B)

El]

No Curie-Weiss behaviour AF 12 AF 6 AF 3 Pauli paramagnet AF AF

0p(K)

[4,5] [4,5] [4,5] [4,5] [4,5] [4,5] [4,5] [4,5] [4,5] [5] [6,7] [6,7] [8] [6] [8] [9] [6] [10] [11] [6] [6]

[12,13] [14]

[14]

Malik et al. (1985b). [11] Stanley et al. (1987). Umarji et al. (1985). [12] Kierstead et al. (1985). Donaberger and Stager (1987). [13] Hodges and Jrhanno (1988). Li et al. (1989). [14] Skolozdra and Komarovskaya Shelton et al. (1986). (1983).

116

A. SZYTULA

coefficient 7 = 1.4 J mol-1 K - 2 (Takayanagi et al. 1988). Investigations by means of 63Cu nuclear magnetic resonance indicate two antiferromagnetic transitions at TN1 = 1.6K and TN2 = 1.1 K (Nakamura et al. 1988a). The RAg2 In compounds (R = Ce, Nd, Sm, Gd, Tb or Dy) order antiferromagnetically at low temperatures. However, no ordering was observed in compounds with R = Pr, Ho, Er or Tm above 2 K (Galera et al. 1984). Neutron diffraction measurements indicated that CeAgzIn is an antiferromagnet with a magnetic Ce moment arrangement of the first type (see fig. 1 la). The moment at T = 4.2 K is found to be # = 0.97(7)pB which is the result of a small CEF splitting (A = 18 K). The neutron diffraction pattern of NdAg2 In at T = 1.8 K exhibits four additional lines that cannot be indexed in a simple manner (Galera et al. 1982b). The compound PrAg2 In remains a Van Vleck type paramagnet down to 1.5 K. In this case, the ground state is the nonmagnetic orbital doublet £3 (Galera et al. 1982a). CeAg2In is a Kondo system in which Ce is trivalent and which orders at TN = 2.7 K. The compound CeCu2In has two N6el temperatures at TN1 = 1.6 K and TN2 = 1.1 K (Nakamura et al. 1988a). In the CeAg2_~Cuxln system, the N6el temperature increases first from 2.7 K for x = 0 to 5.5 K for x = 1.5. It then drops to below 1.5 K with increasing x. CeCu2 In shows incipient valence fluctuations and a large Kondolike resistivity (Liahiouel et al. 1987). The RAu2 In compounds, with R = Gd, Tb, Dy or Ho, order antiferromagnetically at low temperatures (see table 4). Except for GdAu2In, the magnetic moments measured at T = 1.5 K and in fields up to 15 T are reduced compared to the free-ion g j J values. This reduction is manifested mostly at both ends of the series (Besnus et al. 1985a, 1986). The temperature dependence of the magnetic susceptibility of CeAu2 In shows an anomaly at T = 1.2K which may suggest that this marks the N6el temperature (Pleger et al. 1987). In the RPd2 Sn series, the compounds with Tb, Dy, Ho, Er or Yb are all antiferromagnets. The compounds with R = Er, Tm or Yb are found to be superconductors (Malik et al. 1985a,b). Heat capacity, magnetic susceptibility, and resistivity experiments made on ErPd2 Sn indicate that a long-range magnetic order coexist with superconductivity (T~ = 1.17K, TN = 1.0K) (Shelton et al. 1986). DyPd2 Sn and HoPd2 Sn are antiferromagnets of the magnetic MnO-type structure with TN = 15 K and 5 K, respectively. The corresponding magnetic structure (type II)

o1~

q

.0

f ; r"!fl

b)

ToS_ _I:I

• J~,,Q oT_/I y

"'.6/ Fig. 11. Magnetic structures of rare-earth Heusler alloys; (a) first type AF, (b) second type AF (Galera et al. 1982a).

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

117

is shown in fig. 1 lb. The magnetic unit cell doubles along all three crystallographic directions. The magnetic moment is perpendicular to the [1 l l]-axis and, at 1.2K, the moments are 6.7(5)#B for DyPd2 Sn and 4.3(5)#B for HoPd2 Sn (Donaberger and Stager 1987). Supplementary neutron diffraction data for HoPdz Sn reveal that the magnetic moments of the Ho atoms at T = 0.34K are as low as 5.81(8)/~B (Li et al. 1989). 166Er and t7°yb M6ssbauer measurements were made down to 0.05 K for ErPd2 Sn and YbPd2 Sn. They confirm that magnetic ordering occurs at TN= 0.7 K (Er) and 0.26K (Yb). The values of the spontaneous rare-earth magnetic moments have distributions around the mean values of 5.6#B (Er) and 1.8/~B (Yb). For Yb 3 +, the ground state is a Kramer doublet (Hodges and J6hanno 1988). The temperature dependence of the magnetic susceptibility in the temperature range of 78-300 K indicates that LuNi2Sn is a Pauli paramagnet while XN1(T) for YbNi2Sn obeys the Curie-Weiss law with 0p = - 3 8 K and ~eff 4.33ktB (Skolozdra and Komarovskaya 1983). The RPdz Si compounds (R = Gd, Tb, Dy, Ho or Er) and the RPd2 Ge compounds (R = all the lanthanides except for Pm and Yb) crystallize in the orthorhombic Fe 3 Ctype structure (Moreau et al. 1982). This structure belongs to the Pnma space group. It can be built up of trigonal prisms where the corners are occupied by two rareearth atoms (4c site) and four Pd atoms (8d site), while a Si atom is situated in the centre. Resistivity and magnetic measurements performed between 1.7 and 300 K on a polycrystalline sample of CePd2Si indicate that this compound is ferromagnetic below Tc = 2.3 K. The neutron diffraction data show a noncollinear structure with an antiferromagnetic component along the c-axis and a ferromagnetic component along the a-axis (Barandiaran et al. 1986a). Gignoux et al. (1984) investigated the magnetic properties of polycrystalline samples of RPd 2 Si compounds (R = Gd, Tb, Dy, Ho or Er). The Gd and Tb based compounds are antiferromagnetic with a N6el temperature of 13.5 and 21 K, respectively. For both compounds, a metamagnetic transition is observed in low fields. A transition between two different antiferromagnetic phases is observed at 8.5 K in TbPd2Si. The Dy, Ho and Er based compounds are ferromagnetic with Curie temperatures of 9, 3.5 and 2.8 K, respectively. Of the RPd2 Ge compounds, only these with R = Nd, Eu, Gd, Tb, Dy, Ho, Er or Tm order antiferromagnetically (Jorda et al. 1983). The magnetic data for RPd2X (X = Si or Ge) compounds are listed in table 5. =

4.4. RTX3 phases The RTX 3 compounds crystallize in a tetragonal BaNiSn3-type structure (space group I4mmm). This type of crystal structure is similar to the ThCr2 Si2 type (see section 4.5). In these two types of compounds, the rare-earth atoms have different nearest neighbours (see fig.12). The magnetic properties were investigated only for some of the RTX 3 compounds. The obtained data are summarized in table 6. The ternary RFeSi 3 (R = Gd-Tm, Lu

A. SZYTULA

118

TABLE 5 Magnetic properties of RPd2 Si and RPd2 Ge compounds. Compound

Type of magnetic ordering

TNfK)

0F(K)

CePd2 Si GdPd 2Si TbPd 2Si DyPd2Si HoPd2Si ErPd2Si NdPd2Ge EuPd2 Ge GdPd2Ge TbPd2 Ge DyPd2Ge HoPd 2Ge ErPd2Ge TmPd 2Ge

F AF AF F F F

2.3 13.5 21 9 3.5 2.8 1.7 6.5 7.2 9.7 8.1 3.6 3.0 1.2

-11 14 16 6 2 1

AF F (.9) AF F (?) F

#~ff(#B)

/&(/zB)

Ref.*

8.06 9.90 10.61 10.53 9.48

1.1 6.98 5.64 7.38 7.68 6.62

I1] [21 [2-1 I-2] 1-3-1 [2] [33 1-33 [3-1 [3] E33 [3-1 1-33 [33

* References: [1] Barandiaran et al. (1986a). [21 Gignoux et al. (1984). [3] Jorda et al. (1983).

RRhzSi2 0-----~----

I

I

O- - - - - ~ - ~ - ----

{:

I1

o,1

SI~[o 1/2

R

(: 1/2 01 Rhi: 01 1/2

01

LoV 1/2

Fig. 12. Crystal structure of ternary silicides RT2Si2 and RTSi3 (T = Rh) projected along the (100)-axis.

or Y) (Gladyshevskii et al. 1978), RCoSi 3 (R = Ce, Tb or Dy) (Yarovetz 1978) and RNiSi3 ( R = G d - L u or Y) (Yarovetz 1978, Gladyshevskii et al. 1977) compounds are all paramagnets. The RTSi 3 compounds (R = La or Ce; T = Co, Ru, Rh, Ir or Os) crystallize also in BaNiSn3-type structure. LaRhSi 3 and LalrSi a are found to be superconductors with Tc = 2.5K. The temperature dependence of the magnetic susceptibility for CeTSi3 compounds in the temperature range between 1.2 and 293 K indicate that above T = 80 K the Curie-Weiss law is obeyed and that there exists an anomalous Z- 1(T) dependence at low temperatures. The CeCoSi 3 compound has superconducting properties below T~= 1.4 K (Haen et al. 1985).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

119

TABLE 6 Magnetic properties of RTX3 compounds. Compound

GdFeSia TbFeSi3 DyFeSi3 HoFeSi 3 ErFeSi a TmFeSi3 LuFeSi a YFeSia CeCoSi3 TbCoSi3 DyeoSi3 GdNiSi 3 TbNiSi3 DyNiSi3 HoNiSi 3 ErNiSi3 TmNiSi3 YbNiSi3 YNiSia CeRhSi3 CeOsSia CeIrSia GdIrSi3 DyIrSi a GdRhSi3 TbRhSi a

Type of magnetic ordering

TC.N(K)

0p(K)

~eff(~B)

Re~*

+35 +47 +82 +49 +65 +74

7.79 9.36 9.72 9.05 8.09 7.25

--22 +12 -5 --27 --52 --58 +5 --10 --117 +78 -106 -3 -113 --30 +15.7 --13 --18

9.3 10.1 6.87 7.92 9.54 9.03 7.98 6.7 3.9 0.4 2.62

1"1] [1] 1"1] 1"1] [1] [1] 1"1] 1"1] 1"2] 1"3] [3] 1"3,4] 1"3,4-1 1"3, 4] 1"3,4-1

Pauli paramagnet Pauli paramagnet Pauli paramagnet

AF AF

* References: [1] Gladyshevskii et al. (1978). 12] Bodak et al. (1977). 1"31 Yarovetz (1978). 1"4] GladYshevskii et al. (1977).

15.5

7.5

1.03

2.59 8.12 10.41 7.95 9.95

1"3,4] 1"3,4] [3, 4-1 [3, 4"1 1"5] 1"5] 1"5-1 1"6-1 [6-1 [7"1 1.7"1

[5] Haen et al. (1985). [6] Sanehez et al. (1990). [7] Szytuta (1990).

GdIrSi3 and DylrSi3 are antiferromagnets at low temperatures. The values determined for TN in RTX3 are smaller than those obtained in the R T 2 X 2 compounds. This fact indicates that the magnetic interactions depend essentially on the surrounding nearest neighbours (Sanchez et al. 1990).

4.5. RT2X 2 phases The family of c o m p o u n d s with 1 : 2 : 2 stoichiometry contains three groups of different structure types: (1) Ordered variants of the tetragonal BaA14 structure. The c o m p o u n d s crystallize in two variants, in a primitive tetragonal structure space g r o u p P 4 n m m , (CaBe2 GeEtype) or in a body-centred tetragonal structure (space g r o u p I 4 / m m m , ThCr2 Si2-

120

A. SZYTULA ThCr2Si 2

CaBe2Ge2

Y

Y

~Y

T R

0 R

oT

R

oX

Fig. 13. The crystal structure of ThCr2Si 2 (I4/mmm) and CaBe2Ge 2 (P4/nmm). The atomic layers are marked.

type). Both crystal structures are shown in fig. 13. The atomic framework of the ThCr2Si2-type structure can be alternatively displayed as a sequence of planes of the same atoms R - X - T - X - R - X - T - X - R . (2) The second CaBe2 Ge2-type structure consists of atomic layers perpendicular to the c-axis stacked with a sequence R - T - X - T - R - X - T - X - R . The layered crystal structures of these compounds are strongly reflected in their magnetic properties. (3) The RA12Si2 compounds crystallize in the CeA12Si2 structure (space group P3ml). This structure can be derived from a hexagonal close packing of atoms (silicon or X) in which half of the octahedral holes and half of the tetrahedral holes are occupied in an ordered manner by rare earth and by aluminium or the element T, respectively. The differences in chemical bonding between ThCr2 Si2 and CeA12Si2 types were analyzed by Zheng and Hoffmann (1988). For these materials, the heterodesmic (metallic and covalent) character of the chemical bonding is observed (Suski 1985). The majority of the 1 : 2 : 2 phases crystallizes in the ThCr 2 Si2-type crystal structure, which Pearson (1985) has called the most populated of all known structures. For the compounds with X = Si or Ge, a large number of magnetic data were collected by Szytuta and Leciejewicz (1989).

4.5.1. Compounds with the ThCr2Si2-type structure 4.5.1.1. Magnetic properties. The magnetic properties of these compounds are summarized in tables 7-14. In these tables, the data for more than 230 rare-earth compounds can be found. In this section the results of magnetic, neutron diffraction and M6ssbauer effect investigations made for R T 2 X 2 compounds will be briefly discussed. The measurements indicate that the T component has no magnetic moment in most compounds, except for those with Mn. On the other hand, the rareearth moments usually order antiferromagnetically or ferromagnetically at low temperatures. For RT2X2, where R--Y, La or Lu, the magnetic susceptibility is almost temperature independent, suggesting Pauli paramagnetism. For these compounds, also superconducting properties were observed at low temperatures (Braun 1984, Chevalier et al. 1983).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

121

In the R T 2 X 2 series, the Ce-based compounds present unique properties mainly associated with 4f instabilities. The magnetic behaviour of Ce compounds can be dominated by a valence fluctuations between Ce 3 ÷ and Ce 4+ with corresponding moment fluctuations between 2.54#B (4f 1) and 0.0#B/Ce atom (4f°). EXAFS data show a correlation between the valence and the strength of the local Ce-Si overlap for the case in which T represents a 3d or 4d transition metal (Godart et al. 1987). The mixing of the 4f state with conduction-band states can produce various phenomena such as superconductivity, as it was found in CeCu2Si2 (Steglich et al. 1979). The temperature dependence of the specific heat indicates that CeCu2 Si2 is a superconductor below 0.5 K. The electronic specific heat constant, 7 = 1.1 Jmo1-1 K -2, suggests that CeCu2 Siz is a heavy fermion system with an effective mass of approximately 100m0 (Stewart 1984). The band structure of CeCu2 Si 2 and of the isostructural L a C u 2 Si2 was calculated using the self-consistent semirelativistic, linear muffin-tin orbital method (Anderson 1975, Jarlborg and Arbman 1977). The Ce-4f levels are situated mainly above the Fermi energy EF. The density-of-states at EFis large and heavily concentrated around the Ce-4f band (Jarlborg et al. 1983). The susceptibility of CeCuz Sic follows the Curie-Weiss law above 50 K with 0F = - 1 6 4 K and #eff = 2.62#B (Sales and Viswanathan 1976). N M R studies (Nakamura et al. 1988a) of the C e C u z S i 2 superconductor gave a phase diagram (see fig. 14) in which a superconducting region for H < 2.5 T and an antiferromagnetic region for 2.5 T < H < 7 T were observed. Muon spin relaxation measurements on CeCuz.1 Si2 have shown a static magnetic ordering below T'-~0.8K, which coexists with a superconducting state below T, -~ 0.7 K. The observed muon. spin depolarization suggests the existence of a spinglass or an incommensurate spin density wave state, with a small averaged static moment of the order of 0.1#B per formula unit at T ~ 0 K (Uemura et al. 1989). A change from the mixed valence state to trivalent or 'nearly' trivalent cerium occurs for the same number of d-electrons when T represents a 3d or 5d element. By contrast, this behaviour is not found in the 4d series where only trivalent cerium compounds have been identified. The C e T 2 Si 2 compounds, with T = Fe, Co or Ni, are Pauli paramagnets (Ammarguellat et al. 1987). Moment instabilities and magnetic I

'

T[K]

I

I

"--

CeCu2Si2

0.0

,

0

II

2

i

I

4

,

I

B (Testa)

Fig, 14. Temperature versus magnetic field diagram for CeCu2Si2, indicating superconducting (Steglich et al. 1984) and antiferromagnetically ordered regimes as deduced from NMR (Nakamura et al. 1988b) and magnetoresistance (Rauchschwalbe 1987) results on single crystal (0, A) and polycrystalline ((b) samples.

122

A. SZYTULA

ordering are observed in C e T 2 Si 2 with T = Ru (Mignot et al. 1988), T = Rh (Godart et al. 1983) and T = P d , Ag or Au (Murgai et al. 1982). For the compound CeOs2Si2, the valence of Ce is close to + 4 (Horvath and Rogl 1985). Also investigations of solid solutions between various ternary CeT2Si2 systems provide valuable information on the magnetic state. In the CeCu2Si2_xGex system (0 ~<x ~<2), Rambabu and Malik (1987) observed the evolution of a heavy fermion state into an antiferromagnetic state with increasing in Ge content. CeCu2Ge2 is a Kondo lattice system which orders antiferromagnetically below TN= 4.15 K (de Boer et al. 1987). It displays an incommensurate magnetic ordering with a wave vector k = (0.28, 0.28, 0.54) and a small value for the magnetic moment #R = 0.74/~B (Knopp et al. 1989). The magnetic properties of Cel _xR~Ru2Si2 compounds (where R is La or Y) were investigated by Besnus et al. (1987b). When Ce ions are replaced by Y or La ions, the internal pressure changes because of the difference in the atomic radii: r(Ce)= 1.8247 A, r(La) = 1.8791 A, r(Y)= 1.8012 A, respectively. The substitution of La for Ce atoms causes a negative lattice pressure, while Y atoms, when substituted for Ce atoms, produce a positive lattice pressure. Figure 15 shows the results of the investigations of Cel _xR~Ru2 Si2. The change in composition is observed to be accompanied by a change of the electronic and the magnetic properties. In the case of the Cel_~Y~Pd2Si2 system (0 ~<x ~< 1), the results of heat capacity, resistivity and susceptibility measurements (Besnus et al. 1987a) show that a partial substitution of Ce for Y leads to a rapid decrease in the N6el temperature. An evolution from a heavy fermion behaviour to a strong mixed-valence behaviour is observed for the CeCu2_~Ni~Si2 (Sampathkumaran and Vijayaragharan 1986) and CeCu2_~CoxSi2 (Dhar et al. 1987) systems. In EuT2X2 compounds, the Eu ions are divalent or trivalent or they appear in a mixed-valence state (T = Cu, Pd or Ir, X = Si). For compounds with Eu 2÷ ions, a magnetic ordering is observed (Felner and Nowik 1984, 1985). Many compounds with a tetragonal structure and with the general formula 1000

0.1 .3 i

,

,

LoRu2Si2

.5 .7 .9 1 .9 .8 ,

'''

I

,

.5

'

CeRuTSi2

.25 i

.1 0 10 i

J :

YRu2Si2 !

~-a

IOO

-°-

I-

9d/

IO

I

-o% " 0 ~

I )c~

\

j 3 ~ /

0.~ ~I-

o

TK

o

1".

0.01

o (CIT)t~ K

0.1

i 0~99

VIVo

0.98

0.001

Fig. 15. Kondo temperatures (TK), N6el temperatures (TN) and the electronic term of the specific heat at 1.4 K (C/T1.4 K) in the (Ce-La)Ru2 Si2 and (Ce-Y)Ruz Siz systems versus normalized atomic volumes Vo = VeaR.2Si2 (lower scale). The upper scale shows the alloy compositions (Besnus et al. 1987b).

TERNARY I N T E R M E T A L L I C RARE-EARTH C O M P O U N D S

123

YbT2X 2 were prepared and studied. For YbT2X z compounds, where T = Fe, Co, Ni or Cu, and X = Si or Ge, a mixed-valence state exists (Groshev et al. 1987). tv6yb M6ssbauer measurements show that magnetic ordering occurs within the Yb sublattices of YbCozSi2 and YbFe2 Si2 at 1.7 and 0.75 K, respectively. The saturation magnetic moments are 1.4#B and 2.0#a, and they point into directions approximately perpendicular to the local tetragonal symmetry axis (Hodges 1987). The results of the magnetic measurements performed for other ternary silicides and germanides are listed in tables 7-9. Typical examples of the temperature dependence of the magnetic susceptibility are presented in fig. 16 for TbRh2Si2 and GdRh2Si/. The effective paramagnetic moments, #eel, deduced from the high-temperature slope of the ~ 1 = f ( T ) curves are in good agreement with the theoretical values expected for free R 3 + ions (Szytuta et al. 1986a). Magnetic data for single crystals were obtained only for a few compounds. In TbRh2 Si2, the magnetic susceptibility in the temperature range 150-300 K obeys the Curie-Weiss law with the following parameters: #~fe = 10.3#B/Tb atom,

0p = +50(5)K, and

# eaf t =

0~, =

10.5#B/Tb atom,

-- 70(5) K.

TABLE 7 Magnetic data of ternary silicides RT 2 Si2 (T is a 3d element).

Compound

Type of magnetic ordering

TC,N(K)

GdCr 2 Si 2 TbCr2 Si2 DyCr2 Si2 HoCr 2 Si 2 ErCr 2 Si 2 TmCr 2 Si 2 NdFe2 Si2

GdFe: Si 2

TbFe 2 Si 2

DyFe2 Si2

HoFe2 Si2 ErFe2 Si2 YbFe2 Si2

AF AF AF

4.3 2.4 1.5

AF AF AF AF AF AF AF AF AF AF AF AF AF AF AF AF

15.6 14 7 8.4 8 9 6 5.8 10.5 4.2 3.8 3.7 3.8 2.2 2.6,2.9 0.75

0p(K)

+10 -2 - 37 - 5 - 7 + 13 +6

#efe(~B)

#R(PB)

7.95 8.1 9.4 10.3 10.4 9.6 7.8 3.1 (3)

+3

8.18

0

8.20

7.9(1)

7.52(5) 7.4 (5) 7.4(3) 2.0

Re[*

[1] [2] [2] [2] [2] [2] [2] [3] [4] [5] [41 [6] [7] [-1] E4] [7] [-8] [4] [9] [10] [4,11] [-4, 12] [13]

124

A. SZYTULA TABLE 7

7kN(K)

Compound

Type of magnetic ordering

YCo2 Si2

Pauli paramagnetic Pauli paramagnetic AF 30 AF 49 AF 31 AF 30 AF 26 AF 43 AF 44 AF 45 AF 46 AF 46.4 AF 45 AF 8 AF 46 AF 30 AF 46 AF 19.5 AF 21 AF 21 AF 25 AF 21 AF 11.2 AF 15 AF 10 AF 12 AF 13 AF 6 AF 11 AF 6 AF 3 AF 1.7 Pauli paramagnetic AF 18 AF 6.2 AF 14.5 AF 15.5 AF 15 AF 11.6 AF 14 AF 15 AF 14 AF 10 AF 6 AF 7 AF 4.3 AF 4,2, 3.1 AF 3 AF 1.7

C e C o 2 Si 2

PrCoz Si2

NdC% Si2 GdCo2 Si2

TbCo2 Si2

DyCo2Si 2

H o C o 2 Si2

ErCo2Si 2

T m C o 2 Si 2

YbC02 Si2 CeNi2 Si2 PrNi2 Si2 NdNi2 Si2 G d N i 2 Si 2

T b N i 2 Si 2

DyNi]Si2 HoNi 2 Si 2 ErNi 2 Si2 TmNi 2 Si2

(continued) Op(K)

-40

#eff(flB)

u.(u.)

[14] [15] [16]

3.7 3.19 3.19 3.2 3.39

-40 -55 -29 -36 -73 -16

8.3 9.9 8.19 8.22 10.2 9.4

8.9 9.12 8.8 9.2

-27

10.5

-35

10.2

-10 -8

10.5 10.7 10.4 9.85 8.1 10.4

9.4

9.5

-9

-8 --16.5

6.9 4.47

-6 -4 -7 -6 -1

3.67 3.73 8.05 8.0 7.97

Ref.*

10.4

8.7 6.75 6.2 1.4

[17] [18] [19,20] [17] [16] [14] [6,28] [i] [7] [21] [14] [182 [22] [8] [16] [24] [14] [92 [25] [16] [14] [17] [26] [23] [14] [17] [27] [16,24] [13,29]

[3o1

0 16 9

7.9 9.93 10.2

2 -4 0 1.4 4 6.5

10.74 10,7 10.58 9.4 9.58 7.64

2.6 2.6 8.9

8.8 8.1

9.6 6.4 5.6

[31] [32] [32,34] [33] [6,28] [7] [1] [32] [33] [23] [32] [33] [32] [8,33] [32] [32]

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

125

TABLE 7 (continued) Compound

Type of magnetic ordering

LaCu2 Siz

Pauli paramagnetic 164 -140

C e C u 2 Si 2

PrCu2 Si2

NdCu z Si2 SmCu2Si 2 EuCu2Siz GdCu2 Si2

TbCu2 Si2

DyCu2 Si2

HoCu2 Si2 ErCu2 Si2 TmCu2 Si2

0p(K)

TC,N(K)

-

AF AF AF

20.8 15 19

AF 9 Van Vleck paramagnetism AF 14.2 AF 12 AF 10 AF 12 AF 13.5 AF 10 AF 12.5 AF 12.5 AF 12 AF 1l AF 13 AF 11.8 AF 10 AF 11 AF 6.8-10 AF 1.6 AF 7.0, 3.0 3.6

YbCu2 Si2 * References [1] Buschow and de Mooij (1986). [2] Dommann et al. (1988). [3] Pinto and Shaked (1973). [4] Noakes et al. (1983). [5] Felner et al. (1975). [6] L~tka (1989), Czjzek et al. (1989). [7] Nowik et al. (1980). [8] Ba~ela et al. (1988). [9] Nowik et al. (1983). [10] Bour~e-Vigneron et al. (1990). [11] Leciejewicz and Szytuta (1985a). [12] Leciejewicz et al. (1984b). [13] Hodges (1987). [14] Yakinthos et al. (1980). [15] Palstra et al. (1986b). [16] Kolenda et al. (1982). [17] Leciejewicz et al. (1983b). [18] Yakinthos et al. (1984). [19] Shigeoka et al. (1987). [20] Shigeoka et al. (1989b). [21] Leciejewicz et al. (1982). [22] Nguyen et al. (1983).

-2

#,fe(#a)

/tR(#B)

2.62 2.68 2.61 3.41 2.51 2.39 1.12

-21 -10 -20 -14 - 16 -12

7.93 8.03 7.28 7.75 7.95 8.01 9.28 9.35

7.2

8.5 8.6 -4

10.58 10.5

- 3 - 3 - 2

10.4 9.4 7.14

- 90

4.19

8.3 8.2, 6.5

5.1

[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]

Ref.*

[35] [36] [37] [38] [39] [40] [38] [38] [36] [38] [6] [39] [36] [42] [1] [34] [38] [41] [44] [43] [38] [36] [23] [36, 38, 44, 45] [36, 38] [38] [41] [36]

Pinto et al. (1979). Leciejewicz and Szytuta (1983). Pinto et al. (1983). Schobinger-Papamantellos et al. (1983). Yakinthos et al. (1983). Latka et al. (1979). Kolenda and Szytuta (1989). Palstra (1986). Barandiaran et al. (1986b). Barandiaran et al. (1987). Yakinthos and Ikonomou (1980). Barandiaran et al. (1988). Kotsanidis and Yakinthos (1981b). Sales and Viswanathan (1976). Lieke et al. (1982). Schlabitz et al. (1982). Oesterreicher (1976). Szytuta et al. (1983). Allain et al. (1988). Cattano and Wohlleben (1981). Schobinger-Papamantellos et al. (1984). Leciejewicz et al. (1986).

126

A. SZYTULA TABLE 8 Magnetic data of ternary silicides RT2Si2 (T is a 4d or 5d element).

Compound

Type of magnetic ordering

YRu2Si 2 LaRu2 Si 2 CeRu2 Si2 PrRu2Si2 NdRu2 Si2

Pauli paramagnetic Pauli paramagnetic AF 10 F 18 F 17.4 F, AF 26,10 R 18 F, AF 23.5, 10 AF 7 AF 78 AF 31 AF 45 AF 49 AF 44 AF 48 AF 55 AF 58 AF 25 AF 29 AF 29 AF 19 AF 8 AF 5 F 1

SmRuzSi2 EuRu2 Si2 GdRu2 Si2

TbRu2 Si2 DyRu/Si 2 HoRu2 Si2 E r R u 2 Si 2

TmRu2 Si 2 Y b R u 2 Si 2

YRh2Si2 LaRh2Si2 CeRh2 Si2

NdRh2 Si2 S m R h 2 Si 2

EuRh2 Si2 GdRh2 Si/

T b R h 2 Si 2

DyRhzSi 2 HoRh2 Si2 E r R h 2 Si 2

TmRh2Si 2 LuRh2 Si2 CePd2Si2

T¢,N(K )

0p(K)

~eff(~B)

- 18 46.8 29.9 -6

2.46 3.49 3.54 3.56

29 14.4 - 63 54.7 40 57 40 46 I00 10 100 7 12 11.6 - 4 2 65.7 -- 18 No ordered phase down to 1.4K No ordered phase down to 1.3 K AF 36.5 - 81 AF 36 -61 AF 39, 27 AF 37 - 163 AF 37 -72 AF 36 -26 AF 56, 8 - 4 AF 55 7 AF 57 27 AF 46, 8 AF 25 22 AF 132,16 25 AF 101 -7 AF 106, 17 - 6 AF 100 - 13 AF 92, 12 - 26 AF 88 -10 AF 98 AF 94 43 AF 55, 15 7 AF 52, 18 AF 27, 14 3 AF 29, 10 AF 12.8 - 2 AF 4.2 - 28 AF 19.5 - 57 AF 10 -75 AF 8.5 - 55

3.64 0.54 3.95 8.02 8.2 7.51 7,98 8.09 9,65 11,02 10,59 10.98 11A 11,1 10.0 9.48 7.38 3.54

PR(#B)

3.18 3.63

2.9 2.56 2.43 2.9 2.33 4.7 3.59 3.78

5.8

8.8 9.3 9.25 6.6

1.5 2.54

[io]

Ell] [12] [13]

[14]

3.25 3.24

[1,9] [15] [16] [1,9] [1,9] [1,9]

[17] [5]

[18] El, 9]

[17]

8.92 8.5

8.8

[19] [10,16] [1,9] [20] [1,9] [8,19]

4.2

[15] [21]

9.9 9.3 9.45 0.7 2.55 2.55

[i] [i] [2] [1,3] El] [2] [3] [4] [I] [I] [I] [2] [3] [5] [6] [I] [3] [I] [2] [3] [3] [2] [3] [i] [I] [7] [7, 8] [1,9]

7.2 5.6 7.51 8.22 8.2 8.4 10.1 I0.0 10.6

Re[*

[1,9]

[12] 0.62 0.66

Ill]

[22]

TERNARY I N T E R M E T A L L I C RARE-EARTH C O M P O U N D S TABLE 8

#eff (//B)

2 -45.5 -48 - 1

8.8 8.05 8.02 9.8

AF 9.5 AF 10 AF 10 AF 8 Pauli paramagnetic Pauli paramagnetic

- 4 - 5 - 3 - 70 - 36

10.8 10.5 9.5 4.5 2.54

- 30 -18

7.98 7.89

F F AF AF AF AF AF AF AF AF AF F

12.6 2.9 5 26 29 29 42 41 23 19 4.2 1

- 5 53 19 12 27 24 26 100 20 101 6.5 - 16 64 -21

0.23 3.53 3.56 0.47 8.12 8.04 7.96 9.64 10.5 10.36 10.9 9.58 7.34 4.38

Pauli paramagnetic AF 6.6 AF 10.1 AF 10.0

- 2.8 -18

2.54 2.43

Type of magnetic ordering

GdPd2 Si2

AF AF AF AF AF

TbPd2 Si2 DyPd 2 Si 2 HoPd2 Si2 ErPd 2 Si 2 YbPd2 Si 2 CeAg2 Si2 G d A g 2 Si 2 YOs2 Si 2

LaOs2 Si2 CeOs 2 Si 2 PrOs2 Si2 NdOs2 Si2 SmOs2 Si2 G d O s 2 Si 2

TbOs 2 Si 2 DyOs2Si 2 HoOs2Si 2 E r O s 2 Si 2 T m O s 2 Si 2

YbOs2Si 2 LuOs 2 Si 2 CeAu2 Si2 PrAu 2 Si 2 NdAu 2 Si 2 SmAu2 Si 2 EuAu 2 Si 2 G d A u 2 Si 2

TbAu 2 Si 2 DyAu 2 Si 2 HoAu 2 Si 2 E r A u 2 Si 2

(continued) 0p(K)

Compound

AF

AF F AF AF AF AF AF F F

TC,N(K)

13 19 16 20 15 21

15.9 15.5 5.7 13 18 14.8 7.5 14.8 40.0

* References: [1] Hiebl et al. (1983b). [2] Felner and Nowik (1984). [3] Slaski et al. (1984). [4] Chevalier et al. (1985a). [5] L~tka (1989), Czjzek et al. (1989). [6] Buschow and de Mooij (1986). [7] Felner and Nowik (1985). [8] Sekizawa et al. (1987). [9] Felner and Nowik (1983). [10] Quezel et al. (1984). [11] Grier et al. (1984). [12] Palstra et al. (1986b). [13] Godart et al. (1983). [14] Hiebl et al. (1986). [15] Szytuta et al. (1984).

127

#R (~B)

[23]

9.3

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

[5] [63 [233 [24] [23]

7.7

[23,25] [23] [26] [12] [11] [5] [6] [27] [27] [27] [27]

[27]

8.85

[27] [27] [5] [6] [27] [28]

[27] 9.9 8.24

[28]

[28] [27] [27] [27] [29]

1.29

- 9.2 - 6.1 2.5 - 5.0 - 4.9 -35 -25 - 14.8 - 3.6 - 2.1 13.0

Ref.*

3.58 3.62 0.63 6.7 8.7 7.96 7.87 8.9 10.6 10.6 9.0

Szytuta et al. (1986a). Zygmunt and Szytuta (1984). Szytuta (1990). Slaski et al. (1983). Melamud et al. (1984). Yakinthos (1986a). Steeman et al. (1988). Yakinthos and Gamari-Seal (1982). Szytula et al. (1986b). Leciejewicz and Szytuta (1985b). Sampathkumaran et al. (1984). Hiebl et al. (1983a). Kolenda et al. (1985). Felner (1975).

[12] [11] [29] [29]

[29] [29] [29] [5] [6] [29] [29] [29] [29]

128

A. SZYTULA TABLE 9 Magnetic data of ternary germanides RT2 Ge2.

Compound

Type of magnetic ordering

DyCr2G % PrFe2Ge 2 NdFe2G% GdFe 2Ge 2 TbFe2G% DyFe2G% YCo2G% LaCo2G% CeCo2Ge2 PrC02 G%

AF 16 AF 9,14 AF 13 AF 11 AF 7.5 AF 6 Pauli paramagnetic Pauli paramagnetic

NdCo2Ge 2 SmC02 G% EuCo2Ge 2 GdCo2 G% TbCo2Ge 2 DyCo2 G% HoCo2Ge2 ErCo2G% YbCo2Ge 2 LuCo2Ge2 NdNi2Ge 2 GdNi2Ge 2 EuNi2G% TbNi2Ge 2 DyNi2 G% HoNi2Ge2 CeCu2Ge2 PrCu2G% EuCu2 G% GdCu2 Ge2 TbCu2 G% DyCu2 G% HoCu2 Ge2 ErCu2Ge2 TmCu2 Ge2 LaRu2G% CeRu2 Ge 2 PrRu2Ge 2 NdRu 2Ge 2 SmRu2Ge2 EuRu2 Ge 2 GdRu2Ge 2

TbRu 2Ge E DyRu2Ge 2

Tc,N(K)

AF AF AF AF

13, 28 28 26, 5, 30 28

AF AF AF AF AF AF

23 40 30-32 14.5-17 8 4.2

0p (K)

#on (#u)

Pauli paramagnetic F 11 F 18 F, AF 7, 21 F, AF 10, 17 F 10 F 62 AF 32 AF 30 AF 22

Ref.*

[1] 3.44

[2,3,4]

[2, 5] [6]

[3, 7, 8]

--151.9 -8.7 -9 --5.5 -32.5 --43.8 --19 -40 -22--44 -4.7 --10 --8

-91 Pauli paramagnetic AF 20 AF 22 AF 30 AF 9, 16 AF 11 AF 6 AF 4.1 AF 16 AF 13 AF 11-14 AF 13-15 AF 8-10 AF 6-6.5 AF 1.9

.UR(/tB)

--10 --19

2.74 2.87 2.9 4.1

3.34 1.12 6.96 9.3-10.3 10.17 10.0 5.89 4.69 3.69 8.6 7.7

--8

3.98 3.24

8.3 9.5 8.12- 8.69 7.3

3.22

8.0 0.74 2.53 --20 -- 2 0 - --

--21,5 -15 -6 -4.5 --2

30

8.0 8.0 9.7 10.6 10.6 10.7 7.5

8.5-8.6 8.0 6.5 6.0

[1] [9] [9] [9] [9] [10]

[lO] [9] [9] [6] [6,9] [9, 103 [1,8,9] [10,11]

[8, 9, 10] [12] [9] [13] [6] [6] [81 [1] [8]

[14] [2,15] [6] [2,15,16,17] [17,18] [1, 17, 19, 20] [17,18, 19] [17,21] [17]

[22] -70 27 44

62 39 -3 -8

2.3 3.85 3.44

7.53 8.2 10.9-12.1 10.5

0.67 1.82

1.66 3.64 5.0 5.4 9.1

[22] [22] [22] [23, 24] [22] [22] [22] [22,25] [22]

129

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS TABLE 9 Compound

Type of magnetic ordering

HoRu2Gez

AF AF AF AF

ErRuzGez TmRu2 Ge2 YRh2Gez LaRhz Gez CeRhz Gee NdRh2 Ge2 PrRhz Ge2 SmRh2GeE EuRh2Gez GdRh2 Ge2 TbRh2Ge 2 DyRh2Gez HoRh2 Ge2 TbPdzGe2

Tc.N(K)

3 17 20 4

(continued) 0p(K)

~eff (PB)

- 64 57

11.13 10.7 6.6

37 - 6 No ordered phase down to 1.4 K No ordered phase down to 1.4 K AF 15 -3, -25 AF 46, 50 0, 7 AF 47, 42 14, 24 AF 7, 9 3 AF 14, 19 13.20 AF 90, 93 20, 42 AF 77,85 -12,54 AF 44,45 -3,32 AF 40 - 27 AF 4.2

* References: [1] Nowik et al. (1983). [2] Szytuta et al. (1983). [3] Malik et al. (1975). [4] Szytuta et al. (1989). [5] Felner et al. (1975). [6] Felner and Nowik (1978). [7] Ba~ela et al. (1988). [8] Pinto et al. (1985). [9] McCall et al. (1973). [10] Szytuta et al. (1980). [11] Pinto et al. (1982). [12] Kolenda and Szytuta (1989). [13] Szytuta et al. (1988c). [14] Knopp et al. (1989). [15] Oesterreicher (1977c).

#R(#B)

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

9.7 7.1 2.7,2.43 3.82, 3.57 3.9, 3.5 1.5 7.94, 7.0 7.6, 7.3 9.54-10.3 10.64 10.8

2.15 3.02

8.8-9.4 9.27 8.4

Ref.*

[22] [26] [27] [26] [22, 26] [22] [22, 26] [22,28,29] [22, 29] [22, 29] [22, 29] [22, 29] [22, 29] [22,25,29] [22,29] [22] [30]

de Vries et al. (1985). Kotsanidis and Yakinthos (1981a). Schobinger-Papamantellos et al. (1984). Bog~ et al. (1988). Kotsanidis et al. (1984). Yakinthos (1985). Felner and Nowik (1985). Szytuta et al. (1987a). Slaski et al. (1988). Szytuta et al. (1987b). Francois (1986). Yakinthos and Roudaut (1987). Venturini et al. (1989b). Venturini et al. (1989a). Szytula et al. (1988d).

F r o m the values of 0~, the exchange integrals in the plane J"/k = + 8 ( 2 ) K and between the planes JC/k = - 9 ( 2 ) K were determined (Chevalier et al. 1985b). Also, in the cases of PrCo2Si2 (Shigeoka et al. 1989a), NdCo2Si2 (Shigeoka et al. 1988a), CeCo2Ge2 and N d C o 2 G e 2 (Fujii et al. 1988) a strong anisotropy of the susceptibility is observed. F o r N d C o 2 G e 2 , the paramagnetic Curie temperatures along the a- and the c-axis are 0p = - 3 2 K and 0 p - + 2 2 K, respectively. F o r some c o m p o u n d s , a change in the type of the magnetic ordering as a function of the external magnetic field is observed. In figs. 17 and 18 the results for two groups, RRh2Si2 (fig. 17) and RRu2 Si2 (fig. 18), T = 4.2 K are presented. F o r G d R h 2 Si2 and T b R h 2 Si2, the magnetization is linear up to H = 50 kOe. F o r the other c o m p o u n d s , a deviation from linearity is observed in high fields. These nonlinearities observed in a

c

--

130

A. SZYTULA -1

(~) GdRh2Si2 (~) TbRh2Si~

~'10e

-3

/ 12

/

11 200

10

g

10(;

5

¢'/

I.

I

I

100

150

200

I

250 T r K ]

Fig. 16. Temperature dependence of the magnetic susceptibility and reciprocal susceptibility of GdRh 2 Si2 and TbRh2Si 2 (Szytuta et al. 1986a).

(emulg ~...i

//_~"

20

j

!.T7

~o TbRh2Si2 10

20

3,0

40

_ H (T)

Fig. 17. Magnetization curves for RRh2Si2 with R = Gd, Tb, Dy, Ho or Er (Zygmunt and Szytu|a 1984).

high external fields suggest metamagnetic or spin-flop phase transitions (Slaski et al. 1984, Zygmunt and Szytuta 1984). Similar phase transitions are observed in ROs2 Si2 with R = T b or Ho (Kolenda et al. 1985) and in RCo2Si2 with R = Dy or Ho (Kolenda et al. 1982).

TERNARY INTERMETALLICRARE-EARTH COMPOUNDS

131

(emc

0

10

20

30

40

H(kOe

) -'"

Fig. 18. Magnetization curves for RRu2Si 2 with R = Gd, Tb, Dy, Ho or Er as a function of the effective applied field (Slaski et al. 1984). PrFezGe2 shows a particularly complicated magnetization curve at T = 4.2K (fig. 19). It shows two ranges of a rapid growth. The first one, below 1 kOe, provides evidence for a weak anisotropy field. The second range, at about 10 kOe, is probably connected with a metamagnetic phase transition (Leciejewicz et al. 1983a). Such dependencies of the magnetization at T = 4.2K were also observed for P r C o / G e 2 (Kolenda et al. 1982). A magnetic (H, T) phase diagram was determined for GdRu2 Si2 and it is shown in fig. 20. Two antiferromagnetic and one ferrimagnetic phase were observed (L~tka 1989, Czjzek et al. 1989). High-field magnetization measurements were performed on a PrCo2Si2 single crystal at 4.2 K in up to 300 kOe. The magnetization along the c axis increases in four steps at critical fields of Hcl = 12kOe, Hc2 = 38 kOe, He3 = 67 kOe, and He4 = 122 kOe, while the a-axis magnetization is very small and linear against the applied field H. Above He4 = 122 kOe, the c-axis magnetization reaches the saturation value, 3.2/~B/Pr atom (Shigeoka et al. 1989a). In the case of NdCo2Ge2, a similar field dependence of the magnetization was observed (Fujii et al. 1988).

4.5.1.2. Magnetic phase transitions. The temperature dependences of the magnetic susceptibility in some RCo2X2 compounds reveal several anomalies. These occur at 12, 18 and 3 0 K in PrCo2Si z (Kolenda et al. 1982, Shigeoka et al. 1989b), at 15, 24

132

A. SZYTULA

~(~o/g)[?

:°,K . - > 5 ~

/~"/ -T=4"2K

20t

r }JB

il I I

ill~

101 OI

O'g =I{H} H(kOe)

J

0

J_

10

J_

20

.L

30

(ernu/g) 30

40

5'0

PrFe2Gez

20

~

10

J

~

~

~ H =40koe

"-......~H=

20

~o, T(K)

lb

o

2b

4'0

3b

5b

Fig. 19. (Top) Magnetization versus applied field for PrF% G% at different temperatures. (Bottom) Magnetization versus temperature at different applied fields (Leciejewicz et al. 1983a).

Happt. (kOe) 40

I

I

I

I

!

ferri ~I

20

10

\~, af. 2

0

0

p CI rQ m.

t 10

i i 20

30

~"~afjl\\ 40

I 50 T(K)

Fig. 20. Magnetic phase diagram of GdRuzSi 2. Circles and solid lines mark phase boundaries derived from differential magnetization data (L~tka 1989, Czjzek et al. 1989). Diamonds and the broken line mark the antiferromagnetic-to-paramagnetic phase boundary according to results reported by Buschow and de Mooij (1986).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

133

and 32 K in N d C o 2 S i 2 (Shigeoka et al. 1988a) and at 10 and 29.5K in N d C o 2 G e 2 (Kolenda et al. 1982). In the case of N d C o E G e 2 , measurements of the temperature dependences of the specific heat and the resistivity (see figs. 21 and 22) were also made. These measurements, however, show only one phase transition at the N6el temperature (Slaski et al. 1988). Neutron diffraction data show that all compounds at T--4.2 K are antiferromagnets with magnetic structures of the AF I-type (see fig. 23) described by the propagation vector k = (001)2~z/c. With increasing temperature, transitions to modulated magnetic structures are observed, being described by the wave vector k - - [ 0 0 1 - k=]2n/c. The corresponding values of k= are given in table 10. Also, in the P r F e 2 G e 2 compound, there is a transition from a collinear antiferromagnetic structure of the AF II-type (see fig. 23), described by the wave vector k = (00½)2re/c, to an incommensurate structure with wave vector k = (0, 0, 0.476)2n/c at T = 9 K (Szytuta et al. 1990). For all these compounds, the commensurate AF I-type (in P r C o E S i 2 , N d C 0 2 S i 2 and N d C o 2 G e 2) and the AF II-type (in PrFe2 GeE) are observed at low temperatures. An increase in temperature changes the commensurate structure into an incommensurate structure described by the wave vector k = (0, 0, k=). The particular location of the rare-earth atoms in a crystal structure of ThCr2 Si 2type is responsible for the anisotropic character of the magnetic interaction between the magnetic moments of the rare-earth atoms. The anisotropy may be understood in two ways: - t h e magnetic moments are quenched along the c-axis leading to an Ising-like behaviour, ° °°° °°°°•

°.°°°

soE

o° °°-°°°°•

..."" NdCo26e2 °° ° °°•

p

c,

°•° °•• °•°

E 2.13

. . . . ~•..°.-°"•"

.- .-""~

..1"

¢,,2

~-

O~

....

. . . . NdRu2Ge2

~,"°

°, . ° . . . , , °°•-°'"•"•" °" "°°" •°

j'"--"~ .._.....-,"

NdRu2Si2

!~f...~"~ I

"- 1.=.

I

'

1()

~

2(3

'

3(]

'

[i

IL

0 T K] 50-

Fig. 21. Electrical resistivity versus temperature for NdCo2Oe 2, NdRu2Si2 and NdRu2Ge 2 (Slaski et al.

1988).

134

A. SZYTULA 3~

3c ' ~ 25

E

c~ lC 10

20

30

'•4.0

40 T [ K ] ~u

NdRu2Si2

)

'~E3.0 "m 2.0 13. t 3 1.0

10

j

6.0

..b 4JO o

E

..2.13 (,.J

QO

s

1~)

20

30 T [ K ]

NdRu2Ge z

1~

2b

zs

3~" T[K]

Fig. 22. (a) Magnetic heat capacity versus temperature for NdCo2Ge2, (b) for NdRu2Si2, and (c) for NdRu2Ge2 (~laski et al. 1988).

- t h e exchange interaction J0 within the (001) planes is strongly ferromagnetic, whereas the coupling between planes J1, J2 .... , J, is weaker and can be antiferromagnetic. The magnetic behaviour of these compounds is similar to that observed for CeSb (Rossat-Mignod 1979). In this case, the stability of the magnetic structures is discussed on the base of the anisotropic-next-nearest-neighbour Ising (ANNNI) model. In the ANNNI model the interaction between nearest-neighbour layers is positive, J1 > 0, and the interaction between next-nearest neighbour layers is negative, J2 < 0. According to Bak and von Boehm (1980), a mean-field calculation leads to various magnetic structures as a function of the parameter - J 2 / J 1 . The calculation reveals that for Jt > 0 the ground state is ferromagnetic if J2 > - ½J1. However, if J 2 < - ½J1, the ground state is antiferromagnetic. With increasing temperatures a change to modulated periodic structures occurs, characterized by a wave vector k = (0, 0, k~). For IJ2/J11 < 1, the antiferromagnetic ordering is of the AF I-type. A modulated magnetic ordering with a wave vector k given by cosrck= -Ja/4J2 is stable if IJz/Jl[ >¼, and the AFII-type structure is stable if -J2/[Jl[> ½. In the case of TbNi 2 Si2, the temperature dependence of the magnetic susceptibility and resistivity indicate that the N6el transition occurs at TN = 15 K and an additional

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

135

SPIRAL AXIS

...--~-.~-

I

:~l 3 P,' AFI

~-: =,__ ~ 7 I

I I I

I i i

I i I

I

I

i

f - ~ LSW~"

LSW I

I LSW IV

LSW'~I

Fig. 23. The magnetic structure of the R sublattice in various RT2 X2 compounds. TABLE 10 Values of the wave vector k, for

RCo2X

2

compounds.

k,

Compound

Temperature

PrCo2Si 2 [1]

T < 9K 9 K < T < 17K 17K< T<30K

0 0.074 0.223

NdCo2 Si2 [2]

T < 15 K 15K< T<24K 24K< T<32K

0 0.07 0.21

NdCo2Ge2 [3]

T < 12K 12K< T<36K

0 0.261

References:

[I] Shigeoka et al. (1987, 1989a). [2] Shigeoka et al. (1988a). [3] Andr6 et al. (1990).

phase transition at T = 9 K. Neutron diffraction showed that below 9 K the collinear antiferromagnetic structure is of the AF III-type (see fig. 23) and above this temperature an incommensurate structure is present with wave vector k = (½ + z, ½ - z, 0) where z = 0.074 (Barandiaran et al. 1987). The temperature dependence of the magnetic susceptibility of the compounds RRhzSi z and RRh2Ge/, in which R = G d - H o (Felner and Nowik 1984, 1985),

136

A. SZYTULA

indicates that below the Nrel temperature additional phase transitions occur. Neutron diffraction data for DyRh2Si2 revealed that below TN= 52 K the magnetic structure is of the AF I-type with the magnetic moment on Dy 3+ amounting to 9.9(1)#B. It is aligned along the fourfold symmetry axis. However, below 18K it makes an angle of approximately 19° with the tetragonal axis (Melamud et al. 1984). The temperature dependence of the specific heat of HoRh2 Si2 has two peaks, a broad peak at 11 K and a very sharp one at 27K (Sekizawa et al. 1987). Takano et al. (1987b) claim that the temperature dependence of the magnetic specific heat capacity of HoRh2 Si2 can be reproduced relatively well when using three cystal-field parameters and one isotropic exchange constant and adopting appropriate values for these parameters. The lower transition temperature (11 K) is the temperature at which the perpendicular component of the magnetization disappears. At the higher transition point, the component of magnetization parallel to the c-axis disappears (Nrel point). NdRu2Si2 and NdRu2Ge2 exhibit two magnetic transitions: at 10 and 26K for NdRu2Si2 (Felner and Nowik 1984) and at 7 and 21 K for NdRu2Ge2 (Felner and Nowik 1985). Neutron diffraction data indicate that NdRu2 Si2 exhibits a complicated magnetic structure: below TN= 26K it develops a sine-wave modulation k = (0.13, 0.13, 0) of the magnetic moments with an amplitude 3.23#B/Nd atom. A squaring of the magnetic structure occurs at about 15K. At T~< 10K, ferromagnetic ordering takes place with the moments always along the c-axis (Chevalier et al. 1985a). Neutron diffraction studies performed on NdRu2Ge2 showed that in the temperature range from 17 to 10 K this compound exhibits two types of sine-wave modulated magnetic structures, having wave vectors k = (0.19, 0.05, 0.125) and k = (0.12, 0.12, 0), with the amplitude of the magnetic moment along the c-axis. At 10 K, a first-order transition to a ferromagnetic state occurs with a moment of 3.64(13)/~B aligned along the tetragonal axis (Szytuta et al. 1987a). Heat capacity and electrical resistivity studies of NdRu2 Si2 and NdRu2 Ge2 provide evidence of two magnetic phase transitions occurring at 10 and 23 K for NdRu2Si2, and at 10 and 17 K for NdRu2Ge2, respectively (see figs. 21 and 22). The magnitude of the Schottky anomaly due to the nuclear hyperfine splitting (in the low-temperature region, below 1 K) suggests that the magnetic moment in the crystal ground state is about 80% of the free-ion value of Nd 3 ÷ in NdRu2Ge2 and it equals the free-ion value in NdRu2Si2 (Slaski et al. 1988). Neutron diffraction studies have turned out to be particularly revealing, since they made it possible to determine directly the alignment of the magnetic moment in relation to the symmetry of the crystallographic unit cell. Other details at the magnetic structure are also revealed. Modulated and antiphase structures, apart from simple collinear structures were observed, e.g., in rare-earth metals (Koehler 1972). In the case of RT 2X 2 compounds, the neutron diffraction data indicate that the magnetic moments of the rare-earth sublattice exhibit a large variety of ordering schemes (see fig. 23). 4.5.1.3. Magnetic structures.

TERNARY INTERMETALLICRARE-EARTH COMPOUNDS

137

(1) collinear ferromagnetism (F) was found in TbMn2X2, ErMnEX2, NdRu2X 2 (LTP)*, (2) four types of collinear antiferromagnetic structures: - t y p e A F I with wave vector k = ( 0 , 0, 1) was observed in RCo2X 2 ( R = Pr-Tm), R R h 2 X 2 (R = Nd-Tm), TbIr 2 Si2, PrCu 2 X 2 and CeAu 2 Si 2; - type AF II with k = (0, 0, ½) was found in NdFe2 X2, PrFe2 Ge 2 (LTP) and ErFe 2 Si 2; - type AF III described by k - (~, 1 5, 1 0) is adopted by TbNi 2 Si 2 (LTP), CeRh 2 Si 2 and CePd 2 Si 2 ; - t y p e A F I V with k = (½, 0, ½) is exhibited by RCuEX 2 (R = Gd-Er). (3) a number of different noncollinear structures: -sine-modulated longitudinal spin wave L S W I propagating along the c-axis was found in PrCo2Ge2, HoNizGe2, PrNi2Si2, NdNiEX 2, CeRhzGe2, CeA12Ga2, NdCoEX2, PrCo 2 Si 2 and PrFeEGe 2 (HTP); - sine-modulated longitudinal spin waves LSW II propagating along the a-axis occur in RRuzSi 2 (R = Tb-Er), TbRuEGe2, ROs2Si 2 (R = Tb, Ho or Er) and CeAg2Si2, although in TbRu 2 Si 2 and TbRu 2 GeE, at low temperatures, this type of magnetic structure transforms to the square modulated phase: -sine-modulated longitudinal spin waves L S W I I I propagating along the [110] direction were found in NdRu2X 2 (HTP) and TmCu 2 Si2, -LSW IV, being incommensurate structures with two-component wave vectors k = (kx, 0, kz), occur in RFeESi 2 (R = Tb-Ho), RNi2Si 2 (R = Gd, Ho or Er), RPd2Si 2 (R = Tb or Ho) and TbPdzGe2; - m o d u l a t e d magnetic structures are observed in TbNi2Si 2 (HTP), HoRu2Ge 2 with wave vector k=(kx, ky, 0) and CeCu2Ge 2 and TmNiESi 2 with k=(kx, k~, kz).

4.5.1.4. Magnetic properties of solid solutions. Investigations of solid solutions between ternary systems with a ThCr2Si2 type of crystal structure provide valuable information on the interplay of the magnetic interactions between the magnetic moment of rare-earth ions. Sampathkumaran et al. (1987) investigated the influence of various chemical substituents at the Rh site on TN by measurements of the magnetic susceptibility for the series CeRhl.sTo.2Si2 (T = Co, Ni, Cu, Ru, Pd, Os or Au). The results suggested that all these substituents have a general tendency to suppress TN, but the degree of suppression varies from one substituent to the other. The magnetic properties of Ce(Rhl _xRux)2 Si 2 solid solutions was investigated by magnetic and specific heat measurements and by neutron diffraction (Lloret et al. 1987). Magnetic ordering of A F I I I type was observed up to x = 0.4. The magnetic moments were always found to be parallel to the c-axis and their values are strongly depressed when x increases. For instance, # = 1.5#B/Ce atom for x = 0 and # = 0.65#B/Ce atom for x = 0.4. The variation of TN with ruthenium concentration is quite anomalous (see fig. 24). For small concentrations (0 ~<x ~<0.15), a sharp decrease in TN from 36 to 12K is observed whereas for 0.15 < x < 0.4 TN maintains a nearly constant value of about 11 K. *LTP denote low temperature phase, HTP high temperature phase.

138

A. SZYTULA I

i

I

i

1.5

i

% tJ %

30 Z ~=

~

1.0

o\

E

- 0.5

IC--

0

I 0

I 0.2

I

I 0.4

I x

0

Fig. 24. The N6el temperature and the Ce a+ magnetic moment determined by neutron diffraction of Ce(Rhl_xRux)2Si2 (Lloret et al. 1987).

Neutron diffraction studies of the Nd(Rh 1 _xRux)2 Si 2 system at 4.2 K revealed the following magnetic structures: -at x = 0.25, a coexistence of the collinear antiferromagnetic AF I structure and a modulated structure with propagation vector k = (0, 0, 0.838) is observed; - a t x = 0.4, 0.5 and 0.75, modulated structures appear; - at x = 0.9, a coexistence of the ferromagnetic and a modulated structure is seen. For all samples, the observed magnetic moment is the same as the free-ion moment # = 3.27#B (Jaworska et al. 1988). In TbRh2_xTxSi2 (T = Ru or Ir) systems, the magnetic susceptibilities satisfy the Curie-Weiss law at temperature higher than 130 K. Different behaviours were observed in the concentration dependence of the N6el temperature. In the TbRh2_xlr~Si2 system, the N6el temperature decreases from 92 K for x = 0 to 75 K for x = 0.5. For higher concentrations, it remains constant. In the TbRh2_~RuxSi2 system, TN decreases to 15K for x = 0.8 and thereafter it increases to 5 5 K for x = 2 (Jaworska and Szytuta 1987). The results of the neutron diffraction studies of the TbRh2 Ru2 Si2 system indicate that the samples with x ~<0.5 exhibit a simple collinear antiferromagnetic ordering of the AF I type. Neutron diffraction patterns of a sample with x = 0.8 at 4.2 K are characteristic for a spin glass or for mictomagnetic behaviour. A sample with x = 1 has a sine-modulated magnetic structure below 27 K, while the samples with x ~> 1.2 show square modulated structures. The propagation vector k decreases with Ru concentration (Jaworska et al. 1989). The results obtained were described by the classical model, in which interactions between the first and second neighbours are considered. TbRh2Si2 is collinear antiferromagnetic with an A F I type structure implying the following exchange constants between nearest neighbours moments: J"/k = 8(2)K and Jc/k = - 9 ( 2 ) K (Chevalier et al. 1985b) where J" is an exchange constant operating within the (001) planes and jc is an inter-plane constant. TbRu2 Si2 has a collinear square modulated structure with a propagation vector k = (k~, 0, 0). The interaction integrals j a and j,a,, between the first and second neighbour atoms, belonging to the same (001) plane, must be negative.

TERNARYINTERMETALLICRARE-EARTHCOMPOUNDS

139

The substitution of Ru for Rh leads to a change in magnetic interactions and the observed change in the magnetic structure is a result of the frustration of exchange integrals. The exchange integral frustration causes the appearance of spin-glass or mictomagnetic behaviour in compounds with x = 0.8. Such spin-glass or mictomagnetic properties were also observed in the pseudo-binary systems EuSxSe~ _x (Westerholt and Bach 1981) and Gd~_rEuyS (Berton et al. 1981). This behaviour appears in the region intermediate between antiferromagnetism (for x and y equal to 0) and ferromagnetism (for x and y equal to 1).

4.5.1.5. Magnetic properties of RMn2 Si 2 and RMn2 Ge2 compounds. Magnetometric measurements have indicated that the RMn2X 2 compounds have two critical magnetic ordering temperatures (Szytuta and Szott 1981): - a t low temperatures, the magnetic moments localized on Mn and R atoms become ordered; - a t high temperatures, the magnetic moments on Mn atoms become ordered either ferromagnetically or antiferromagnetically. Ferromagnetic ordering is observed in LaMn2 Si2 (Narasimhan et al. 1975) and in the RMn2Ge 2 compounds where R is La, Ce, Pr, Nd or Eu (Narasimhan et al. 1976). For LaMn2Ge2 and PrMnEGe2, measurements of magnetization were made on single-crystal samples. In both cases, the easy axis of magnetization of the Mn sublattice is the [001] axis. For LaMn2 Ge2, the values of the magnetic moment and the anisotropy constant Ks were estimated to be 1.55#R per Mn atom and 2.25 x l06 erg cm-a at 0 K (Shigeoka et al. 1985). For PrMn 2GeE, the magnetization and magnetocrystalline anisotropy constant at OK were estimated to be 5.9/~B/f.u. (f.u. denotes formula unit) and 5.3 x l07 erg/cm a (Iwata et al. 1986a). Other RMn2X 2 compounds are antiferromagnets, as determined from neutron diffraction investigations carried out for a number of RMn 2X 2 systems. In CeMn 2 Si2, the Mn moments, forming an antiferromagnetic sublattice, are stable between 80 and 379 K (the Nrel point) with a magnetic moment value of 2.3pB at 80 K (Sick et al. 1978). The magnetic moments lie along the fourfold axis with the sequence + - + - . No information about the ordering of the Ce moments below 80 K is available. The absence of magnetic ordering in the Pr and Nd sublattices at 1.8 K was established by neutron diffraction studies of PrMn2Si2 and NdMn2Si2 (Siek et al. 1981). By contrast, results of magnetic measurements pointed to a ferromagnetic coupling between the Nd and Mn sublattices (Narasimhan et al. 1975). In PrMn2Si2 and NdMn 2 Si2 as well as in YMn 2 Si2 and YMn 2Ge2, the Mn moments order antiferromagnetically in the same way as in CeMn2 Si2. Interesting results were obtained from magnetic measurements performed on a single-crystal sample of SmMn2Ge 2. In the temperature range between 196 K and the Curie point at 348 K, ferromagnetic properties were found. At temperatures lower than 196K, a collinear antiferromagnetic ordering stabilizes. It disappears at 64 K and reentrant ferromagnetism is observed below this temperature (Fujii et al. 1985). The easy axis of magnetic moments is parallel to the [110] direction below 196K, while at higher temperatures it is parallel to the [100] direction.

140

A. SZYTULA

It should be noted that different values of the phase transition temperatures were published for SmMn2Ge2, as may be seen from table 11 (Duraj et al. 1987, 1988, Gyorgy et al. 1987). Magnetic susceptibility measurements, carried out at pressures up to 1.5 GPa revealed that external pressure changed the magnetic phase transition temperature in SmMn2Ge2. The (p, T) diagram is shown in fig. 25. The Curie temperature decreases slowlywith pressure while the temperature of the ferro-antiferro transition increases for the first phase transition and decreases almost linearly for the second transition. For the antiferromagnetic phases, the Nrel temperature increases with an increasing pressure (Duraj et al. 1987, 1988, Gyorgy et al. 1987). The temperature dependences of the lattice parameters of SmMn2Ge2 at atmospheric pressure indicate that at both temperatures of the phase transitions, i.e., from the ferro- to the antiferromagnetic phase as well as from the antiferro- to the ferromagnetic one, the jump of the value of the a-lattice constant is observed (Aa/ a -~ 0.2%). The lattice parameter c undergoes a small change in the phase transition region (Ac/c "~ 0.02%) (Duraj et al. 1988). Measurements with a differential scanning calorimeter show that the phase transition near 150 K is endothermic with the transition heat L = 0.04(1)calg-1 (Gyorgy et al. 1987). The replacement of Sm atoms by other rare-earth atoms (Nd, Gd or Y) with different atomic radii implies a change in the lattice constant which may cause a change in magnetic properties. The replacements mentioned led to an increase in the lattice constant for the NdxSml_~Mn2Ge2 system and to a decrease for the (Gd, Y)xSml-~ Mn2 Ge2 systems. The change in the lattice constants influences the magnetic properties of these systems: with increasing concentration x the antiferromagnetic ordering disappears for the system Nd~Sm~ _~Mn2Ge2 and the ferromagnetic phases disappear for the (Gd, Y)xSml_xMn2Ge2 systems (Duraj and Szytuta 1989, Duraj et al. 1989a,b). This behaviour is illustrated in fig. 26. Magnetic measurements showed that in EuMn2 Ge2 the Mn moments order ferromagnetically at 330 K but change to antiferromagnetic order when the Eu moments become ferromagnetically ordered at 9 K (Felner and Nowik 1978). In GdMn2 Si2, antiferromagnetic ordering occurs at TN = 453 K (Szytula and Szott 1981) and an additional magnetic transition is observed at Tm= 65 K (L~tka 1987). The value obtained for the spontaneous magnetic moment #s = 4.0#B at low temperatures suggests ferrimagnetic ordering below Tin. Assuming that each Gd atom has its full magnetic moment (7#B), coupled antiparallel to the Mn moments and taking into account that the total moment equals 4.0/tB per f.u., one obtains a value of 1.5#B per Mn atom. The temperature dependence of the magnetic hyperfine field shows that the magnetic ordering in the Gd sublattice disappears at 65 K (Lgtka 1987). Above this temperature, an antiferromagnetic ordering in the Mn sublattice is observed. The field dependence of the magnetization of ErMn 2 Si2 and DyMn2 Si2 suggested that these compounds are ferrimagnets. The magnetization disappears at 34 K for ErMn2Si2 and at 55 K for DyMn2Si 2 (Szytuta and Szott 1981). For DyMnzGe2, the pressure dependence of the Nrel temperature and exchange

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

141

TABLE 11 Magnetic data of ternary silicides RMn2Si 2 and germanides RMn2Ge2. Compound

Type of magnetic ordering

Tc,N(K)

0p(K)

#eff(/~B)

YMn2 Si2

AF AF F AF AF AF F, AF AF F, AF F, AF F, AF F, AF AF F, AF AF AF AF AF F F F F F, AF, F F, AF, F F, AF, F F, AF F, AF F, AF F, AF F, AF F, AF F, AF F, AF F, AF F, AF F, AF AF AF AF

460 516 303-310 379 348 365 32, 380 398 65, 453 60, 485 65, 550 55,473 453 5, 508 498 513 464 395 306-310 316 329-334 334 64, 196, 348 100,150,350 106, 153,341 9, 330 96, 365 33,413 95,414 110,413 47,385 40,438 37,403 4.2, 459 5.1,390 4.2, 475 458 338 453

385

3.5

2, 4

310 330 290 290

4.4-4.8 5.1 5.1 5.1 5.14 3.3 8.4 8.2 9.8 11.0 10.5 10.2 3.7 4.6 4.2 3.8 3.5 3.1 3.9-5.9 6.0

1.54 2.3 2.48 2.57

LaMnz Si2 CeMn2Si2 PrMn2 Si2 NdMn2Si 2 SmMn2Si 2 GdMn 2 Si2 TbMn 2Si2 DyMn2Si 2 HoMn2Si 2 ErMn 2Si2 TmMn2Si 2 YbMn2Si 2 LuMn2Si 2 YMn 2Ge 2 LaMn2 Ge 2 CeMn2Ge 2 PrMn2Ge 2 NdMn2 Ge 2 SmMn 2Ge 2

EuMn 2Ge 2 GdMn 2Ge 2 TbMn2Ge 2

DyMn2Ge 2 HoMn2 Ge 2 ErMn 2Ge 2 TmMnzGe 2 YbMn2Ge 2 LuMn2Ge 2

* References: [1] Szytuta and Szott (1981). [2] Siek et al. (1981). [3] Sampathkumaran et al. (1983). [4] Narasimhan et al. (1975). [5] Siek et al. (1978). [6] Buschow and de Mooij (1986). [7] Shigeoka et al. (1986). [8] Leciejewicz et al. (1984b). [9] Szytuta et al. (1988b).

301

365 270

52 100

8.8 9.6 10.4

100

#R (/~B)

/~Mn(#B)

9.0

1.7

8.9

2.3

2.95 1.55 2.77

1.55

8.0 7.8

1.7 2.3

7.7

2.3

9.9 10.8 8.5

100 100

9.9 9.4 6.2 5.8 3.8

224

[10] [11] [12] [13] [14] [15] [16] [17]

Narasimhan et al. (1976). Shigeoka et al. (1985). Fujii et al. (1985). Gyorgi et al. (1987). Duraj et al. (1988). Felner and Nowik (1978). Shigeoka (1984). Leciejewicz and Szytuta (1984).

Ref.*

[1, 2] [3] [1, 3, 4] [1,5] [I, 2] [1,2] [4] [1] Ill [6] [1, 7] [1] [1] [1,8, 9] [1] [1] [1] [1, 2] [1,10,11] [4, 10] [4,10] [4,10] [ 12] [13] [14] [I 5] [1,4, 10,15] [1] [16] [17] [1,4,10] [16] [1,4,10] [16] [1, 8, 9] [16] [1] [1] [1]

142

A. SZYTULA T[K]j 40O para

300

ferr°~~mMRi

Ge2 20C

/to

antiferro

10C rerr(~i

0.2

i

i

OiS

i 1.0

i

i

1,4 "

P[ GPo ]

Fig. 25. The pressure-temperaturediagram of SmMn2Ge2 showing the paramagnetic, ferromagneticand antiferromagneticregions (Duraj et al. 1987, 1988). TtK],

30( 250 20( 15C

o

para

350

~ ~ ~ ~

~ "

o

~antiferro

100'

I

I

0.2

I

• I 0.4

I

• I 0.6

" I

I

0.8

ferri

I

I

1.0 x

Fig. 26. Magnetic phase diagram for the Sml _xGdxMn2Ge2 systemdetermined on the basis of magnetic measurements (Duraj et al. 1989b). striction was also investigated. The value of dTN/dpis found to be + 2.0 K/kbar. The temperature dependence of the lattice constants indicate that both a and c vary linearly with temperature above TN = 4 2 6 K and drop below TN. The exchange striction of a and c are negative (Kaneko et al. 1988). Detailed magnetic studies were performed on some RMn2Ge2 single-crystal samples (Shigeoka 1984, Shigeoka et al. 1983). The [001] direction (the tetragonal axis) was found to be the easy magnetization axis in (Gd, Tb, Dy, Ho)Mnz Ge2 while in ErMn2Ge2 it was the direction [110] (see fig. 27). The saturation moments per formula unit at 4.2 K are much smaller than the theoretical value expected for free rare-earth ions, indicating ferrimagnetic or noncollinear ordering.

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

i

i

i

143

i

GdMnzGe z 4"

roo13

5

3 m 2 ::t

'tl,Ol

,Ol

4

TbMn2Ge 2

.~q ~/"

=L2

ErMn2Ge2

' ~ 2[-

,;

2'o 3b Lo H (kOe}

so

10

20

30

H (kOe)

40

50

0

[001]

10

20

30 40 H (k0e)

50

10 A

DyMn2Ge 2

HoMnzGe2 CIO0]

2 0

p/

~o

20

~o

H (kOe)

40

[1103

2 ,

1"1003 C110]

so

o

o

~o

zo 30 ~.o H (kOe)

so so

Fig. 27. Magnetization curves along the principal axes of RMn:Ge2 (R = Gd, Tb, Dy, Ho or Er) single crystals at 4.2 K (Shigeoka 1984).

The magnetization curves determined along the easy and hard direction of magnetization for RMn2Ge2 compounds (see fig. 27) suggest that the magnetic anisotropy is large. The anisotropy energy in tetragonal lattices is expressed as EA = K1 sin20 + K2 sin40 + K3 sin+0 sinZ ~bcos2 ~b,

(11)

where Ks is an anisotropy constant of the ith order, and 0 and ~b are the angles between the magnetization vector and the c- and a-axis, respectively. The anisotropy constants K1 and K2 can be determined from the following relation 2K1 4K2 = -7~-2 M M s + ---T, Ms

H e ft

(12)

when the easy axis is parallel to the c-axis, and Heft

M -

2 K1 + 2K2 4K2 M2 ME + ~Ms '

(13)

when the easy axis is perpendicular to the c-axis. Heel is the effective magnetic field, M is the magnetization and Ms is the saturation magnetization. The coefficients K1 and K 2 are listed in table 12 for RMn2Ge2 and TbMn2Si 2 compounds. The large anisotropies observed in these compounds originate mainly from the single-ion anisotropy due to the crystal-field effect. Since the Gd 3 + ion is in the S state, the anisotropy energy in GdMn2 Ge2 is smaller than in the other compounds. The temperature dependence of the magnetization for RMn2Ge 2 where R is Gd,

144

A. SZYTULA TABLE 12 Values of the anisotropy constants KI and K2 for RMn2X 2 compounds.

Compound LaMn2Ge 2 PrMn2Ge 2 GdMn2Ge 2 TbMn 2 Ge 2 DyMn2Ge 2 HoMn2Ge2 ErMnzGe 2 TbMn2 Si2

K1 (erg cm- 3) 2.2 5.3 5.4 8.4 1.3 1.3 -4.2 2.2

x x x x x x x x

K2 (erg em - a)

Direction of magnetic moment

104

[001] [001] E001] [001"] [001] [001] [110"] [001]

106 107 106 107 10s 108 108 10s

3.6 x 106

* References: [1"] Shigeoka et al. (1985). [2] Iwata et al. (1986b).

Ref.* [1] [2] [3] [3] [3] [3"] [3] [4]

[3] Shigeoka (1984). [4] Shigeoka et al. (1986).

Tb or Dy indicates that the magnetic transition at Tmis due to a first-order ferrimagnetic-antiferromagnetic transformation (Shigeoka 1984). The analysis of the temperature dependence of the magnetization at low temperatures carried out in terms of the molecular-field approximation shows that the Gd-Mn interaction is antiferromagnetic (Iwata et al. 1986b). The temperature dependence of the electrical resistivity and the thermal expansion of the RMn2 Ge2 compounds have been measured in order to explain the character of the magnetic transition. As an example, fig. 28 shows the resistivity p versus T curve for GdMnzGe2. As marked by arrows, a sharp jump and a bend appear at the temperatures corresponding to Tm and TN, respectively. A similar behaviour was found for TbMn2 Gez and DyMna Gez (Shigeoka 1984). The temperature dependence of the thermal expansion Al/l of polycrystalline RMnE Ge2 samples is shown in fig. 29. The sharp jumps correspond to the first order transition at Tin. Bends indicate the second order transitions at TN. The magnetic properties of the GdMn/Ge/ compound have been studied by measuring the magnetization of a single crystal in high fields, up to 150kOe. Four

-¢~ GdMnzGe/ 4

i

i

J

TN

i

i

.

~

3

O

200

4 T(K)

0

600

Fig. 28. Temperature dependence of the electrical resistivity for the GdMn2Ge 2 compound (Shigeoka 1984).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

145

RMn2Ge2

Er

1

IS ° / 4 / o

40O

200

600

T(K)

Fig. 29. Temperature dependence of the thermal expansion for several RMn 2Ge2 compounds, R = Gd, Tb, Dy, Ho or Er (Shigeoka 1984).

types of magnetically ordered phases have been observed (see fig. 30). In low magnetic fields collinear antiferromagnetic properties were observed in the range from 96.5 to 365 K. The collinear ferrimagnetic structure becomes stable below 96.5 K where the magnetic moments of the Gd and Mn atoms are antiparallel to each other. Below 96.5 K, the transition from the collinear structure to a canted ferrimagnetic structure occurs in applied magnetic fields perpendicular to the c axis. The Gd moments in this canted ferrimagnet lie in the c plane and the Mn moments turn out of the c plane (Kobayashi et al. 1989). °) 1so

>

\ IV {

100 0 -r

5O

% b)

'

lOO

' £o T(K)

'

~c

3-00

&

--~ -,~ :

I

--o-~ t

÷

~

~

~

~ IU

~ ~

~

---~-- Gd ~ ;" M n

-f

~

--~---~-Mn

~

~

Ill

~

~ Mn

IV

Fig. 30. (a) Magnetic phase diagram of GdMn2G%. The critical fields parallel and perpendicular to the [001 ] direction are indicated by open and closed circles, respectively. (b) Schematic magnetic structure of GdMn2G % in each phase deduced from magnetization measurements (Kobayashi et al. 1989).

146

A. SZYTULA

The magnetic structure in TbMn/Si2 was determined in the course of magnetization and neutron diffraction studies. It was found that the TbMn2Si2 compound exhibits the following magnetic structures: - a collinear ferromagnetic structure of the Tb sublattice and a canted structure of the Mn sublattice at T < 53 K; - two collinear magnetic sublattices: a ferromagnetic Tb sublattice and an antiferromagnetic Mn sublattice at 53 K < T < 65 K; - a collinear Mn antiferromagnetic sublattice at 65 K < T < 550 K (Shigeoka et al. 1986). Also, ThMn2Ge2 exhibits an interesting magnetic structure (Leciejewicz and Szytuta 1984). The neutron diffraction study of ErMnzSi2 and ErMn2Gez (Leciejewicz et al. 1984b) provides the following results: - t h e Mn sublattice orders antiferromagnetically, like in CeMn2 Si2; -the Er sublattice is ferromagnetic with moments perpendicular to the c axis; - t h e Curie temperatures are small: 10+_ 5 K for ErMnESi/ and 8.3 + 3 K for ErMn/Ge2. The specific heat and the resistivity measurements of ErMn2Gea showed a phase transition at 5.1 K corresponding to the disordering temperature of magnetic moments in rare-earth sublattice (Szytuta et al. 1988b). From the temperature dependence of the magnetization and magnetic susceptibility measurements, the T - x phase transition for CeMn2 (Si 1-x Ge~)z was determined (first by Sick and Szytuta 1979 and recently by Liang and Croft 1989). The T - x magnetic phase diagram (fig. 31) has the following regions: - for 0 <~x ~<0.3, the Mn atoms exhibit antiferromagnetic order; - for 0.3 < x < 0.55, the samples undergo a transition from ferromagnetic to antiferromagnetic states via transient state, and two critical temperatures are observed for increasing temperatures, at T1 a transition from ferromagnetic to the transient state, and at T2 a transition from the transient to the antiferromagnetic state; - for 0.55 ~ x ~< 1.0, the samples are ferromagnetic. The following three systems; Lal_xY~MnzSi2 (Sampathkumaran et al. 1983), YMnE(Sil_~Ge~)2 (Kido et al. 1985a) and Y1 _~LaxMnzGe2 (Fujii et al. 1986) show different magnetic structures depending on the concentration parameter x. The magnetic properties of the Cel_xLa~Mn2Si 2 system was investigated by neutron diffraction and magnetic measurements (Szytuta and Sick 1982b). The samples with low La concentration (x ~<0.5) show antiferromagnetic properties. For x = 0.6, the magnetic ordering changes from antiferromagnetic to ferromagnetic with increasing temperature. An increase in the La content leads to ferromagnetism. A collinear magnetic structure was deduced from neutron diffraction data. In all pseudo-ternary systems, the nature of the magnetic ordering in the Mn sublattice depends on the M n - M n distance. The magnetic transition temperature of RMn2X2 compounds are plotted in fig. 32 against the M n - M n distances within the layers, Ra, and between two M n - M n layers, Re. It appears that the respective temperatures follow a curve that is a function of Ra but not a function of Re. It is seen that there is a critical distance of Ra of about

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S

T[K] 40[ -

M PMc

147

a)

30[- N

Tc

200 100 ',I o.o 0.2 TEK]~

.

4001-

0.4 .

.

o[6

X

J.8

~.o

.

TN MC

PM

200'

b)

~!i,T1

10C

AF

T2"~}l" I

I

~

FM I

i

0.0 0,2 0.4 0.6 0.8 1.0 X

Fig. 31. The temperature versus concentration phase diagram of the CeMn2(Si I -xOex)2 system as determined by the magnetic measurements after (a) Szytuta and Siek (1979) and (b) Liang and Croft (1989). The AF, FM and PM labels refer to the antiferromagnetic, ferromagnetic, and paramagnetic phases for the Mn suhlattice order. TN and Tc represent the Neel and Curie ordering temperature. T1 and T2 are temperatures defined in text. MC represents the multicritical point of the magnetic phase transition.

TroTb ~ 500 "Yb T h • "DYGd

RMn2Si 2

• • "Y -Ho

Lu

=._z

Sm

25 ,.15

I.._.~ 500

8 • 300 23

32 11

400

Er" y Th

CeMn~(Si. xGex)2 * Pr "¢~.Pr '= 1 ++ Nd o.N% °La ~' • Let I + ~a / - ~ - - " ~ ( ~ e *

.9

"14 24 12 " 7, ,13 "1619 ".* I'-Z 450 20 -

Ho Rln26e 2 ° Tin" Ho

i

s.20

s..~o

i

i

s.~o c/2t~t ~ s.so

21

~ - ~ 6

1

CeMn2(SixGe I x)2

350

+18

4

3

z._~._--_~

300

.1o

2÷

LaxCel-xMn2Si 2 25O 2,80 200

i

i

3, 5

i

2.85 i

i

i

4 0

i

i

2.90 i

i

i

&O5

i

I

4.10

R I M n - l n }1",~] I

I

I

I

4.15

I

I

4.20

o t~,:]

Fig. 32. The dependence of the N~el or Curie temperature upon interlayer (c-constants) and intralayer (a-constants) distances (Szytuta and Siek 1982b).

148

A. SZYTULA

2.85 A. Antiferromagnetic coupling exists when Ra is less than 2.85 A and ferromagnetic appears for Ra > 2.85 A. Similar critical distances were observed in many alloys with transition metals (Tebble and Craik 1969). Goodenough (1963) suggested that a localization-delocalization effect of the 3d electrons occurs when the critical distance in the Mn compounds is 2.85 A. Magnetic measurements performed on the Ce(Mnl-~Tx)2 Si2 compounds (T = Fe, Co or Cu) were made by Sick and Szytuta (1979) and Szytuta and Sick (1982a). Their data indicate that the compounds of a composition with x ~<0.5 are ordered antiferromagnetically. The N6el temperatures decrease with T concentration. In the Nd(Mn 1-~ Crx)z Si2 system (Obermeyer et al. 1979), an increasing Cr concentration leads to a decrease in the N6el temperatures of the ordered Mn sublattice from 380 K for x = 0 to 260 and 200 K for x = 0.2 and 0.3, respectively. Also, in the case of Ce(Mnl_~Cr~)zSi2, it is observed that there is a strong Mn 3d antiferromagnetism and a decrease in Ty with increasing Cr concentration (Liang et al. 1988). The TN values were found to decrease linearly with x at a rate of ATN/Ax ~- 6.0 K/ (at.%Mn) for the Ce(Mn~Crl_~)zSiz series. The fact that Obermeyer et al. (1979) have observed a very similar linear rate of depression of TN, i.e., 6.3 K/(at.%Mn) in the Nd(Mn~Crl_~)2Si 2 system supports the notion that the rare-earth sublattice plays a minor role in the high-temperature magnetic ordering in these alloys. The electronic structures of the antiferromagnetic YMnzGe2, ferromagnetic LaMnEGez and paramagnetic LaCoEGe2 were calculated by the KKR method (Asano and Yamashita 1972) using the local spin density (LSD) approximation (Ishida et al. 1986). A crystal potential of the muffin-tin type was used. The density of states (DOS) curves of 3d electrons belonging to Mn or Co atoms and of 5d and 4f electrons of Y and La atoms are shown in fig. 33. The results obtained for YMnzGe2 indicate that the s bands of the Ge atoms and also their p states strongly hybridize with Mn d states in the region from 0.2 to 0.7 R~o. The values of the DOS at the Fermi level N(EF) are 20states/(atom spin R~) and 29 states/(atom spin R~o) for antiferromagnetic YMnzGeE and ferromagnetic LaMn2Ge2, respectively. These values satisfy the Stoner condition for ferromagnetism. The threshold value of N(Ev) is expected to be in the range from 15 to 20states/(atom spin R~o) if the Stoner condition is to be fulfilled. In LaCo2Gez, the Co band is below the Fermi level. The value of N(Ev) is 8 states/(atom spin R~). The Stoner condition is thus not fulfilled. Consequently, LaCozGe2 is a paramagnet. The band structure of the majority or spin-up states and the band structure for the minority o r spin-down states in ferromagnetic LaMn2Gez are displayed in fig. 34. The calculated magnetic moment of Mn atom is 1.95#B, which is much larger than the experimental value of 1.55/~B (Shigeoka et al. 1985).

4.5.1.6. Other R T z X 2 compounds. A number of R C o 2 B 2 compounds (R = Y, La, Pr, Nd, Sin, Gd, Tb, Dy, Ho or Er) were synthetized and studied (see table 13) (Felner 1984, Jurczyk et al. 1987, Rupp et al. 1987). The magnetic properties of these alloys were studied in the temperature range 1.5 K < T < 900 K and in the fields up to 10 T. Magnetic susceptibilities of RCo2 B2

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

149

150

Y Mn 2 Ge2

[i

,

a

,,,'

e~

100

o

SO

-0.3

-oJ

o.?

0.3

o.s

0.7

{ Ryd)

b ~o

--5 Mn

~ 3o i oe

13 ~

i

20

10

-0.3

1'J 'I

-0.1

0.1

O.S

O.S

0.7

( Ryd)

Fig. 33. The density of states (DOS) curves of YMn2Ge2. (a) The DOS curves of the d states of Y and Mn are shown by the dotted and broken curves, respectively. The Fermi level is shown by the vertical line. (b) The DOS curves of the s and p states are shown by the solid and broken curves for Y, Mn and Ge (Ishida et al. 1986).

(R = Y or La) are practically temperature independent. The magnetic results for S m C o 2 B 2 (/-telf -- 1.76#B).compare well with the ideal Van Vleck behaviour of Sm 3 + ions with a J = ~ ground state and a low-lying excited first level J = 5. The magnetic susceptibilities of the other compounds satisfy the Curie-Weiss law with values of the effective magnetic moments close to free R 3 + ions at temperatures above T = 200 K. At temperatures below 30 K, antiferromagnetic ordering is found for R = Tb (TN = 13 K), Dy (9.3 K), Ho (8.5 K) and Er (3.3 K), whereas the RCoaB2-borides with R = Pr, Nd or Gd order ferromagnetically at Tc = 19.5 K, 28 K and 26.5 K, respectively (Rupp et al. 1987). From 155 Gd M6ssbauer studies of G d C o 2 B 2 , the hyperfine interaction parameters were determined. The direction of the magnetization was found to be in the basal plane (Felner 1984). Also, CeA12Ga2 crystallizes in ThCr2Siz-type crystal structure. The temperature dependence of the magnetic susceptibility, resistivity and specific heat indicate

150

A. SZYTULA

1

t00

so

.L

-~

o

3

o

sc

~oc -0.2

0.0

0.2

0,/~

o.6 ( R-vd )

Fig. 34. The DOS curves of the d state of Mn and of the d and f states of La are shown for both spin states by the dotted, dashed and broken curves, respectively (Ishida et al. 1986).

TABLE 13 Magnetic data of RCo2B 2 compounds. Compound

Type of magnetic ordering

YCo2 B2 LaCo 2B 2 PrCo2B2

Pauli paramagnetic Pauli paramagnetic F 19.5 F 36 F 28 F 47 F 32 No Curie-Weiss behavionr F 14 F 26.5 F 56 F 26 AF 13 AF 19 AF 9.3 AF 8.5 AF 3.3

NdCozB 2

SmCo2 Bz GdCo2B z

TbCo1,92 B2 TbCol.sB 2 DyCo 2B 2 HoCo1.96B2

ErCozB 2

* References: [1] Rupp et al. (1987). [2] Jnrczyk et al. (1987). [3] Felner (1984).

Tc,N(K)

0p (K)

~eff(#~)

25

3.57

40

3.59

0

3.27

33

7.80

80 76 65 67 28 22

7.22 9.76 9,60 10.87 10.57 9.63

~s (#B)

3.0 2.8 1.26 0.3 7.5 6.42 3.5

Ref.*

[1] [1] [1] [2] [1] [2] [3] [1] [2] [1] [2] [3] [1] [2] [1] [1] [1]

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

151

that this compound is antiferromagnetic with a N6el temperature of 9 K. Neutron diffraction data revealed that it has a long period commensurate collinear structure, with a wave vector k = ( 0 , 0 , kz) and kz=~a, corresponding to a + +-+ + +-+ +-sequence of Ce moments which are oriented perpendicular to the fourfold axis. The magnetic moment is 1.18 + 0.07/~B (Gignoux et al. 1988b, Zerguine 1988). From the anisotropy of the susceptibility at high temperatures, we can deduce the magnitude of the crystalline electric field (CEF) parameters (B° =3.64K, B ° = - 0 . 0 9 K and B~=0.13K) and derive from these parameters that the ground state is the _+½ doublet (Gignoux et al. 1988a). RNi2 P2 (R = Ce, Eu or Yb) compounds also crystallize in the ThCr2 Si2 type. The results of 31p N M R and magnetic susceptibility measurements in the temperature interval 4.2-300 K indicate that all these compounds exhibit nonmagnetic ground states (Nambudripad et al. 1986). LaNizP2 is a Pauli paramagnetic. At temperature above 100K the compounds RNiz P2 with R = Pr, Nd, Gd, Tb, Dy, Ho, Er or Tm show a normal Curie-Weiss behaviour with magnetic moments slightly lower than those of the free R a + ions. The paramagnetic Curie temperatures of these compounds vary between - 5 K and + 12 K (see table 14). GdNi2 P2 is antiferromagnetic with a N6el temperature of TN = 10.5 K. SmNi2P2 shows Van Vleck paramagnetism. CeNi 2 Pz and YbNi2P2 exhibit temperature dependent paramagnetism, which may be explained with a mixed valence of cerium and ytterbium (Jeitschko and Reehuis 1987). The magnetic properties of the RTz P2 compounds (R = La or Eu, T = Fe or Co) were studied by 57Fe and 151Eu M6ssbauer spectroscopy and by magnetic susceptibility measurements. LaFe2 Si2 is a Pauli paramagnet. LaCo2 P2 and E u F e 2 Pz are ferromagnets with a Curie temperature of Tc = 125(3)K and Tc = 27.5(5)K, respectively. E u C o 2 P2 orders antiferromagnetically at the N6el temperature, TN= 66.5(5) K. The results of the M6ssbauer data demonstrate that the iron sublattice does not participate in the magnetic ordering of the europium-containing compound (M6rsen et al. 1988). The ternary RNi2As2 compounds (R = La-Gd) crystallize in two forms: the bodycentred ThCr2Si2 type (L.T. form) and a primitive CaBe2Ge2 type (H.T. form). Electrical and magnetic measurements indicate that these compounds exhibit a metallic conductivity and a magnetic ordering at low temperatures when R = Ce, Pr, Sm or Eu (L.T. form) (Ghadraoui et al. 1988). The magnetic susceptibility in the temperature range between 300 and 1250K determined for RRh2P 2 and RRhzAs2 (R = Ce, Pr or Nd) follows the Curie-Weiss law with a magnetic moment close to the free R a + ion values. No long-range magnetic ordering was observed at 4.5 K in all the above-mentioned compounds (Madar et al. 1985). Ternary RNi2 Sn2 compunds (R = La-Sm) crystallize in T h C r 2 Si z-type structure. The temperature dependence of the magnetic susceptibility indicate that LaNi2Sn2 is a Pauli paramagnet while for the other compounds the Curie-Weiss law is fulfilled in the temperature range 80-300 K, as may be seen from table 14 (Skolozdra et al. 1981).

152

A. SZYTULA TABLE 14 Magnetic data of RT2X2 compounds (X is P, As or Sn).

Tc,N(K)

Compound

Type of magnetic ordering

LaFe2 P2

Pauli paramagnetism F 27 F 125 AF 67 Pauli paramagnetism No Curie-Weiss behaviour

EuFe2P2 LaC02 P2

EuC°2 P2 LaNi2 P2 CeNi2P2

PrNi2 Pz NdNi2 P2

SmNi2P2

AF

10.5

TbNi2P2 DyNi2 P2

HoNizP2 ErNi2 P2 TmNi2 P2 YbNi2P2 LaNi2As2 CeNi2As2 PrNi2 As2 NdNi2As2 SmNizAs2 EuNi2 As2 LaNi2 Sn2 CeNi 2Sn2 Pr2Ni2Sn2 NdNi 2Sn2 SmNi2Si2

Peff(#B)

+ 39 +137 + 20

7.74 2.04 8.10

+12 +10

3.40 3.47 1.50 7.43 7.86 9.61 10.55 10.49 9.38 7.41

Van Vleck paramagnetism

EuNi2P2

GdNi2P2

0p(K)

No Curie-Weiss behaviour LT Pauli paramagnetism HT Pauli paramagnetism LT AF 5.2 HT LT AF 11 HT AF 9.5 LT HT F 9 LT AF 14 Pauli paramagnetism

-124 -5 +5 +5 +1 +4 +3

-10 -6 +3 +8 -8 -12 0.23 -40

Van Vleck paramagnetism

* References: [-1] M6rsen et al. (1988). [2] Jeitschko and Reehuis (1987).

1.89 2.46 3.40 3.37 3.52 1.50 7.41 2.54 3.59 3.73 1.58

Ref.*

[1] [I] [-1] [1] [-2] [-2] [-2] [2] [-2] [-1,2] [2] [2] [2] [2] [2] [2] [2] [3] [-3] [3] [3] 1-33 [3] [3] [-3] [-3] [-4] [-4] I-4] [-4] [-4]

[3] Ghadraoui et al. (1988). [-4] Skolozdra et al. (1981).

The c o m p o u n d CeNi2Sn 2 does not order magnetically above 2 K. The Z-1 (T) curve obeys the Curie-Weiss law with ~off=2.62#a and 0 p = - 5 K . At low temperatures, an increase in heat capacity is observed with a large value of 7 = 250 m J m o l - 1 K -2 ( S a m p a t h k u m a r a n et al. 1988).

4.5.2. Compounds with the CaBe2 Ge2-type structure In this type of crystal structure the ternary RPt2 Si 2 silicides are found. The magnetic properties were determined in the temperature range from 1.5 to l l 0 0 K in the presence of external magnetic fields up to 13 k O e revealing above 200 K the typical paramagnetism of free R 3+ ions (Hiebl and Rogl 1985). The susceptibilities of (Y, La, Lu)Pt2 Si 2 are almost temperature independent. Characteristic m o l a r suscep-

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

153

tibilities at room temperature are collected in table 15. YPt2 Si2, LaPt2 Si2 (Shelton et al. 1984) and LaPtzGe2 (Hull et al. 1981) are superconductors below T~= 1.421.31K, 1.70-1.58K and 0.55K, respectively. The temperature dependence of the magnetic susceptibility of CePt 2 Si 2 resembles the susceptibility of a Kondo lattice and a Fermi liquid system below 2 K (Gignoux et al. 1986b). The magnetic susceptibility versus temperature curves for PrPt2 Si:, NdPt2 Si/and YbPtzSiz follow closely the Curie-Weiss law down to 1.8 K. Magnetic data for S m P t 2 Si 2 (Peff = 0.7#B) show that the Sm ion behaves as an ideal Van Vleck S m 3 + ion with the ground state J = ~ and the low-lying first excited state J = ~. An antiferromagnetic ordering is observed below 10 and 6.5 K in the case of GdPt2Si2 and TbPt2 Si2, respectively (Hiebl and Rogl 1985). DyPt2 Si2 is antiferromagnetic below 7 K (Nowik et al. 1983). Neutron diffraction data for TbPt2 Si2 (Zerguine 1988) indicate that below TN = 8.6 K an incommensurate magnetic structure exists with wave vector k = (k~, kx, ½) where kx = 0.332(2). The magnetic data for the RPt2 Si2 system are summarized in table 15. Ternary RIr2 Si2 silicides have two allotropic forms: the low-temperature modifica-

TABLE 15 Magnetic data of RPt2Si 2 compounds. Compound

Type of magnetic ordering

YPt2 Si 2 LaPt2 Si 2

Pauli paramagnet Pauli paramagnet

Tc,N(K)

CePt2 Si2 PrPt2 Si2 NdPt2 Si2 SmPt2 Si2 GdPt 2 Si2

TbPt2 Siz

DyPt2 Si2 HoPt2 Siz ErPt2 Si2 TmPt/Si2 YbPt2 Si2

LaPt2 Si2

AF 10 AF 9.7 AF 7.2 AF 8 AF 6.5 AF 8.6 F? 3 AF 7 F? 3 No ordered phase down to 2 K F? 3 F? 3

Op(K)

#eff (PB)

-86 -86 7 -4.5 0 -7 -5

2.24 2.65 3.46 3.55 0.7 8.13 8.14

-8 58.5 -27 37

8.10 9.35 9.9 10.59

11

10.56 10.0 9.57 7.32 3.5

26 65 -100

Pauli paramagnetic

* References: [1]Hiebl and Rogl (1985). [2] Gignoux et al. (1986b). [3] Lotka (1989), Czjzek et al. (1989). [4] Nowik et al. (1980).

[5] [6] [7] [8]

Buschow and de Mooij (1986). Zerguine (1988). Nowik et al. (1983). Leciejewicz et al. (1984a).

Ref.*

[1] [1] [1] [2] [1] [1] [1] [1] [3] [4] [5] [1] [6] [-1] [7] [1] 1-8] [1] [1 l 1-1] [1]

154

A. SZYTULA

tion crystallizes in a body-centred ThCr2 Siz-type structure and the high-temperature modification crystallizes in a primitive CaBezGez-type structure. Both forms have different physical properties. The polymorphism and the superconductivity of Lair2 Si2 were studied by Braun et al. (1983). The solid-state transition between P-LaIrzSi2 and I-LaIrzSiz was determined to occur at 1720(10)°C, where P and I mean 'primitive' and 'bodycentred', respectively. P-LaIrzSi2 is a superconductor at 1.58 K, whereas I-LaIr2 Siz does not show any superconductivity down to 1 K. For I-CeIrzSiz, the inverse susceptibility deviates considerably from the CurieWeiss law at temperatures below 200 K and it ceases to depend on the temperature at much lower temperatures. The compound P-CeIr2 Siz exhibits a broad maximum in the )~-1 curve below 700 K, a fact commonly observed in intermediate valence systems (Hiebl et al. 1986). Measurements of the 151Eu M6ssbauer spectra and the magnetic susceptibility show that the 4f configuration of the Eu ion in EuIr 2 Si2 changes continuously with the temperature from 4f 6"2 at 4.2 K to 4f 6"7 at 290 K (Chevalier et al. 1986). Both crystallographic forms of GdIr2 Siz and TbIr2 Si2 are antiferromagnetic with different values of TN and 0p (see table 16). Since the R - R intra- and inter-plane distances are similar in both phases, a change in the density of states at the Fermi level or the location of EF (in the framework of the RKKY-type interaction) could explain the small TN and 0p values observed in the P-form. Only the I-TbIrzSi 2 phase was studied by neutron diffraction (Slaski et al. 1983). A collinear, antiferromagnetic ordering of the AF I-type with the moments aligned along the c axis was discovered. The available magnetic data at Ritz Si2 systems are listed in table 16. In this type of structure, also the RCuzSn2 (R = La-Sm) compounds crystallize. Magnetic data indicate that LaCu2 Sn2 is a Pauli paramagnet. The magnetic susceptibility of other compounds obey the Curie-Weiss law. Effective magnetic moments of RCuz Sn2 compounds (R = Ce, Pr or Nd) are in good agreement with theoretical values for free R 3 + ions, while the moment for SmCu2 Sn2 is 0.74#B (Skolozdra and Komarovskaja 1982). The compounds RCuzSn 2 (R = La, Ce or Sin) were investigated by 119Sn M6ssbauer spectroscopy. Only for SmCuzSn2, a magnetic hyperfine spectrum at liquid helium temperature was found (G6rlich et al. 1989).

4.5.3. Compounds with the CaAlaSia-type structure RAI2 Si2 (R = Y, Pr or Tb-Lu) and RAlaGe 2 (R = Y, L a - N d or Sm-Tm) compounds crystallize in a hexagonal CaA12Si2-type structure (space group P3ml). EuA12 Si2, EuA12Ge2 and GdA12 Si2 order antiferromagnetically below Tn = 35.5 K, 27 K and 22 K, respectively. In the ordered state, a spin-flip transition is observed. Neutron diffraction data showed that EuA12 Si 2 orders antiferromagnetically with the wave vector k--(0, 0, ½), the europium moments being oriented parallel within the (001) planes (Schobinger-Papamantellos and Hulliger 1989). The magnetic data for the RA12X2 system are summarized in table 17.

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

155

TABLE 16 Magnetic data of RIr2 Si2 and RCu2 Sn2 compounds. Compound

Type of magnetic ordering

P-LaIr2Si 2 I-LaIr2Si2 P-CeIr2Si2 I-CeIr2Si2 P-GdIr2Si2 I-GdIr2Si2

No ordered phase down to 1.2 K No ordered phase down to 1.2 K

P-Tblr2Si2 I-Tblr2Si2

TN(K)

AF AF AF AF AF AF AF AF

15 77 81 92 13 80 75 72

#af(#a)

- 360 -116 8.6 8.0 -12.0 -16.0 13 42 -21

1.9 2.05 8.13 8.42 8.05 7.83 9.78 9.97 10.4

--2 +2 +7 --27

10.0 11.1 8.64 6.8

- 1 7 4 10

2.62 3.57 3.63 0.74

-

#R(PB)

Ref.*

[13 [13 [23 [23 [33 [43 [53 [63 [73 [73 [43 [83 [43 [43 [43 [93 El0] [10] [10] [lO3 [10]

8.1

DyIr2Si2 Ho!r2Si 2 ErIr2Si2 LaCu2 Sn2 CeCu 2Sn2

0F(K)

Pauli paramagnet

P r C u 2 Sn 2

NdCu 2 Sn2 SmCu2 Sn2 * References: [1] Braun et al. (1985). [2] Hiebl et al. (1986). [3] Sanchez et al. (1990). [4] Zygmunt and Szytuta (1984). [5] L~tka (1989), Czjzek et al. (1989).

[6] [7] [8] [9] [10]

Buschow and de Mooij (1986). Hirjak et al. (1984). ~laski et al. (1983). Slaski and Szytuta (1982). Skolozdra and Komarovskaya (1983).

TABLE 17 Magnetic data of RAlzX2 compounds, data by Schobinger-Papamantellos and Hulliger (1989). Compound

Type of magnetic ordering

EuA12Si2 EuA12Ge2

AF AF AF

GdA12 Si 2

Tc,N(K)

35.5 27 22

0p(K)

#elf (#B)

#R(#B)

+ 30

7.2

6.0, 5.8

4.6. Other ternary compounds 4.6.1. R2RhSi 3 compounds T e r n a r y silicides R 2 R h S i 3 (R = Y, La, Ge, N d , S m or G d - E r ) crystallize i n a h e x a g o n a l s t r u c t u r e w h i c h is d e r i v e d f r o m the A1B2 type. Si a n d R h a t o m s are p l a c e d i n s i d e d i s t o r t e d t r i g o n a l p r i s m s f o r m e d b y six r a r e - e a r t h a t o m s a n d t h e y are o r d e r e d i n t w o - d i m e n s i o n a l s u b l a t t i c e s p e r p e n d i c u l a r to the c axis. T h e a a n d c p a r a m e t e r s are

156

A. SZYTULA

approximately twice those of the corresponding disilicides R S i 2. YzRhSi3 and La2RhSi3 are diamagnets and nonsuperconducting down to 1.6K. NdzRhSi3 is ferromagnetic at 15 K, GdzRhSi3, Ce2RhSi3 and Tb2RhSi3 are antiferromagnets with metamagnetic phase transitions. Other silicides are paramagnets up to 1.6 K. The results are summarized in table 18. The effective moments deduced from the TABLE 18 Magnetic data of the other ternary compounds. Compound

Crystal structure

Type of magnetic ordering

Y2 RhSia La2 RhSi 3 Ce 2RhSi3 Nd2RhSi3 Gd 2RhSi3 Tb 2RhSia Dy2 RhSi3 HOERhSi a Er 2RhSi 3 Y2NiEAi LazNi2A1 Ce2NiEA1 Pr2Ni2A1 Nd2 Ni2 A1 Sin2 Ni2 AI Gd2Ni2A1 TbzNi2A1 DY2Ni2A1 Ho2Ni2A1 Er2 Ni2 AI TmzNi2A1 Yb2Ni2A1 Lu 2Ni 2A1 Y2Ni2Ga La 2Ni2 Ga Ce 2Ni2 Ga Pr 2Ni2 Ga Nd 2Ni 2Ga Sm 2Ni 2Ga Gd2Ni2Ga Tb2Ni2Ga Dy2Ni2Ga Ho 2Ni 2Ga Er 2Ni 2Ga Tm2Ni2Ga Yb 2Ni2 Ga Lu 2Ni 2Ga

Hexagonal Hexagonal Hexagonal Hexagonal Hexagonal Hexagonal Hexagonal Hexagonal Hexagonal Orthorhombic Orthorhombic Orthorhombic Orth0rhombic Orthorhombic Orthorhombic Or(horhombic Orihorhombic Orthorhombic Orthorhomblc O~horhombic Or,thorhombic O~thorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic Orthorhombic

diamagnetic diamagnetic AF F AF AF

* References: [1] Chevalier et al. (1984). [2] Romaka et al. (1982b).

Tc,N(K)

6 15 14 11

0p(K)

#eff(]~B) ~R(~B) Ref.*

--83 +7 +2 +6 -7 +1 +6

2.40 3.76 7.61 9.7 10.67 10.66 9.36

+41 + 25

3.45 3.5

-20 -2

9.07 10.84

- 11

12.04

-7 +23 + 24

11.24 9.94 8.59

Pauli paramagnet Pauli paramagnet Pauli paramagnet

Pauli paramagnet

Pauli Pauli Pauli Pauli Pauli

[2] [21 [2] [2] [2]

paramagnet paramagnet paramagnet paramagnet paramagnet + 10 0

3.31 3.9

[2] [21 [2]

Pauli paramagnet

Pauli paramagnet Pauli paramagnet

[1] [1] [1] [1] [1] [1] [1] [1] [1] [2] E2] [2] [2] [2] [2] [2] [2] [23 [2] [2] [2]

- 3

9.81

[2]

+14

10.81

[2]

- 3

11.96

[2]

- 1

11.53

[2]

+19 +25

9.68 8.36

[2] [2]

[2] [2]

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

157

high-temperature linear part of the ;(r~1 = f ( T ) curves are in good agreement with the theoretical values for the R 3÷ free ion. The saturation magnetization obtained for Nd2 RhSi3 is dearly smaller than the theoretical value expected for the Nd 3 + free ion (Chevalier et al. 1984).

4.6.2. R2Ni2X compounds The R2Ni2X compounds (R = La-Lu or Y, X = A1 or Ga) crystallize in an orthorhombic structure (space group Imma). The atoms occupy the following positions: 4R atoms in 4(h) sites, 4Ni atoms in 4(f) sites and 2Ga or A1 atoms in 2(a) sites (Gladyshevskii et al. 1981). Magnetic data for these compounds are given basing only on magnetic measurements in the temperature range 78-293 K. The magnetic susceptibility of R 2Ni 2 X compounds with R -- Pr-Tm obeys the Curie-Weiss law with the value of paramagnetic Curie temperature 0p and effective magnetic moments ].leff given in table 18. For the other compounds, the temperature dependence of the magnetic susceptibility is like the Pauli paramagnet dependence (Romaka et al. 1982b). 5. Conclusions

5.1. Magneticmoment The magnetic moments in the ternary compounds considered in this review are almost exclusively due to localized 4f electrons. The values of the effective moments were deduced from the temperature dependence of the magnetic susceptibility (see tables 2-18). The disagreement between the experimental moments and the rare earth's free-ion moments is a result of a strong coupling of the conduction electrons with the localized moments. In this case, in the RKKY theory, the magnetic effective moment is given by the formula: #eel = g j # B ~ I 1

+JsfN(EF)~g---jll,

(14)

where gs is the Lande factor, N(EF) is the conduction electron density of states per atom at the Fermi surface for one spin direction, and Jsf is the effective s-f exchange interaction due to the direct exchange and the s-f mixing. In fig. 35, we have plotted the ratio of experimental effective moments to the free-ion moments as a function of the parameter (gs- 1)/gj. The general trend shows that for RRhESi 2 Jsf is negative, whereas for RRu2Si 2 it is positive. One obtains from fig. 35 that JsfN(EF) is -0.35 and +0.05 for RRhESi 2 and RRu 2 Si2, respectively (Felner and Nowik 1984). Calculations for RCu2 Si 2 (R = Tb-Tm) give negative values of Jsf which do not change with a changing f-element (Budkowski et al. 1987). Analysis of the experimental results of the effective magnetic moments in the GdTESi 2 compounds (T = 3d, 4d or 5d element) shows that these are higher than the theoretical moments. According to eq. (14), this means that Jsf is positive (Lotka 1989). Positive values of Jsf were derived also from ESR data for Gdl _xLaxCu2 Si2 (Kwapulifiska et al. 1988).

158

A. SZYTULA

• - R Rh2Si 2 A- R Ru2Si 2 '~-'+ 1.5

l

1.3 11

0.7 Ho Tb

Nd Ce E~IDY' 6d -0.15 ,I I ,II Ol , III,I ,01~

( ga - t ) / g j

Fig. 35. The ratio of the experimental effectivemoment to the free ion moment as a function of the parameter (gs- 1)/gs(Felner and Nowik 1984). As already mentioned, the excess moment is usually connented with the conduction electron spin polarization. This may be induced by s-f as well as by d - f exchange interactions (Stewart 1972). Taking into account two bands of conduction electrons, one can express the effective moment by #of, =

gs#,~(1

_

+

J sf #2~Zs + - Zd "~

(15)

where Jsf and Jdf are s-f and d - f exchange coupling constants, and Z~ and Zd are the band susceptibilities, respectively. N denotes the total number of atoms. On the basis of the band-structure calculations (Freeman 1972) as well as of experiments (Buschow 1979), it may be concluded that the d band originating from R-5d states contributes to a high density of states in the vicinity of the Fermi energy. The 4f-5d exchange parameter is positive and the polarization of the 5d-band is enhanced by intraband interaction. Thus, the susceptibility of the 5d electrons seems to play a dominant role in the conduction electron polarization in the vicinity of R ion. Then, assuming that IJ~fZs]~ [JdfZdl, from eq. (15) one can obtain the following results: # ° f f = #R4f'~- #R5d, where #4f = g j ~ 1)#B and #RSd=JafZa/#2N. Analysis of the magnetic data for the GdT 2 Si 2 systems, where T = 3d, 4d or 5d element and in which GdRh 2 Si 2 appears to have the largest effective moment, gives value #Go5d= 0.28(3)#B as a maximum (L~tka 1989, Czjzek et al. 1989). In the ternary rare-earth compounds discussed, the magnetic properties are determined by the rare-earth moments. The transition metal atoms T, except for Mn, do not carry magnetic moments. These materials have a metallic character and the interatomic distances between the rare-earth atoms are fairly large. The magnetic interaction between the highly localized 4f electrons is realized by their conduction electrons mediating in an exchange interaction, and by the effects of crystalline electric fields (CEF) acting on the 4f electrons. The influence of these factors on the magnetic properties are discussed below.

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

159

5.2. Exchange interactions

In metallic compounds of rare earths, exchange interactions between rare-earth moments are mediated by the spin polarization of conduction electrons. This leads, in general, to long-range exchange interactions with an oscillatory dependence of the interaction strength on the distance between the moments. In the RKKY theory, the critical temperature of the magnetic ordering Tc, TNis proportional to the de Gennes factor (gs - 1)2j( J + 1), as may be derived from eqs. (4) and (5). The validity of this relation for several groups of RT2 XE compounds is investigated in fig. 36. The following conclusions can be drawn from it: - T h e de Gennes function is not obeyed in RT2X2 compounds containing light rare-earth ions. In many cases, the compounds remain paramagnetic above 1.8 K. - In the case of heavy rare-earth ions, the N6el points follows in principle the de Gennes function. However, large discrepancies are observed when T = Cu, Ru or Os. These observations suggest that various mechanisms of interaction have to be considered when describing the magnetic coupling in RT2 X2 systems with light and heavy rare-earth ions.

• REC02Si 2

~5

o RECo2(]e 2 •

RECu2Si 2

A RECu2Ge2 + RENi2 Si 2

35

x REFe2 Si2

~0 25 2~

t

i

o

Ce PrNdPmSmEu6dTb Dy oEr TmYb

Fig. 36. Observed N~el temperatures in RT2X2 intermetallics and their relation to the de Gennes function (full curves, normalized to R = Gd).

160

A. S Z Y T U L A

In a further step, the variation of the magnetic properties with the filling of transition metal nd-bands Z,d was analyzed. In the TbT2X2 series, the oscillatory character of the N6el temperature is caused by an increase in the number of d-electrons (see fig. 37). Similar effects were observed in the isostructural ErT2 Si2 compounds (Leciejewicz et al. 1984b), and in EuT2Ge2 and GdT2Gez compounds (Felner and Nowik 1978). These results suggest that, while the magnetic interactions may be discussed in terms of the RKKY model, the number of free electrons donated to the conduction band depends on the number of d-electrons. For GdT2Si2, the variation of TN with Z,d (see fig. 38) shows similar trends for the three transition-metal rows with a pronounced maximum for the compounds with Co, Rh or It. For the same column, the lattice parameter a is smaller than for the other compounds. This correlation indicates a dominance of the interactions between Gd moments within the a-b planes (L~tka 1989, Czjzek et al. 1989). In the RFe2 Si2 system, where a local moment on the Fe atom has been found to be absent, the observed transferred 57Fe hyperfine fields at the Fe sites are in reasonable agreement with the conduction electron polarization due to the rareearth moments (Noakes et al. 1983). The difference between the 57Fe transferred field in GdFe2 Si2 in the antiferromagnetic state at 1.2 K measured in zero external field (all Gd moments are parallel to the a-b plane) and that observed in an applied field of 60 kOe at low temperatures indicate anisotropic exchange interactions (L~tka 1989, Czjzek et al. 1989).

100

rbr2Si2 TbT2Ge2

TN(K) 50

x

180

17C

V~O-Inm]' 16C

15C Mn

I

I

I

I

Fe Ru

Co Rh

Ni Pd

Cu Ag

Os

Ir

P~

Au

3d 4d 5d

Fig. 37. The dependence of the Nrel temperatures and the atomic volumes for TbT2X 2 compounds (T = 3d, 4d or 5d transition metal, X = Si or Ge) as a function of the atomic numbers of T elements (Szytuta and Leciejewicz 1989).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS 120

161

G.

8O ~40

•

i

i

i

I

i

I

I

[3,

3-9I Co Ni Ru Rh Pd o---0s Ir ~Pt x ....

• --

Fe

Cu Ag

Au

Fig. 38. Dependence of (a) magnetic ordering TN, and (b) lattice parameter a in GdT2Si2 on the T component, where T = 3d, 4d or 5d transition metal (Czjzek et al. 1989).

A considerable anisotropy of exchange interactions has also been derived from single-crystal magnetization data for TbRh2Si2 (Chevalier et al. 1985b). The neutron diffraction data were discussed in terms of the RKKY theory. In an isotropic RKKY model based on a spherical Fermi surface, the Fermi vector is strongly dependent on the c/a ratio and on the number of free electrons Z per magnetic ion: k F =(6rc2Z/a2c) 1/3. The analysis of the a/c values determined for a large number of RT2 X2 compounds containing heavy rare-earth ions (R = Tb-Tm) shows that when a/c< 0.415 a simple collinear ordering is observed, while in compounds with a/c > 0.415 an oscillatory magnetic structure occurs (Leciejewicz and Szytuta 1987). The stability of the magnetic ordering schemes was discussed in terms of an isotropic RKKY mechanism. Following the RKKY theory, the energy E of a spin system with a screw-like ordering is given by: E = - N ( / ~ 2 )J(k), where N is the total number of magnetic ions in the system, (#2) is an average value of the magnetic moment, and J(k) represents the Fourier transform of the exchange integral J ( R i - Rj) between i and j magnetic ions, with positions given by the vectors Ri and R j, respectively. Assuming that the interaction integral J(k) remains constant, the energy E is proportional directly to a function expressed as: - F ( k ) ~ - [ J ( k ) - J(0)]. A stable situation for a particular magnetic structure means that the function F(k) exhibits a maximum for a non-zero value of the wave vector k of the magnetic structure (Yosida and Watabe 1962). The computation of the F(k) function against k for particular values of kF (or Z) permits the selection of these values of k for which F(k) exhibits a maximum. The Z and k values obtained for a number of RT2X2 compounds are listed in table 19. In the RT2X2 compounds, the observed magnetic ordering scheme requires three free electrons per R 3+ ion. It could indicate that the 6s and 5d electrons of the R 3 + ion are donated to the conduction band. Valence electrons of the other atoms contribute to the chemical bonding. On the other hand, the chemical shift measurements

162

A. SZYTULA TABLE 19 Values of kF and Z obtained for RT2X 2 compounds. Compound

kr

Z

Ref.*

TbRu2Si2

0.233a* 0.22a* 0.2a* 0.235a* 0.312a* 0.295a* 1.0¢* 1.0c* 1.0c* 0.0c* 0.5c*

3.13 3.136 3.16 3.0 3.0 3.02 2.75-3.75 2.77-3.39 2.84-3.2 2.67-3.4 1.4

1-1] [1] [1] 1-2] [3] [3] [4] [4] [5] [4] 1-4]

D y R u 2 Si 2 (Ho, Er)Ru2 Si 2 TbRu2Ge 2 TbOs2Si 2 (Ho, Er)Os2 Si 2

RCo2X2 RRh2Si2 TbRh2Ge2 NdRu2Si2 NdFezSi2 * References: [1] ~laskiet al. (1984). [2] Yakinthos(1986a). [3] Kolenda et al. (1985). I-4] Leciejewiczand Szytuta(1987). [5] Szytutaet al. (1987b).

performed by the X-ray absorption spectroscopy method (XAS) indicate that electrons of all constituents, i.e., of R, T and X atoms, contribute to the conduction band (Darshan et al. 1984). Different values of Z were obtained from the analysis of magnetic data (paramagnetic Curie temperature) of GdT2 Si2 compounds with T = Cu, Ag or Au. Buschow and de Mooij (1986) accepted values of Z equal to 11. Analysis of the values of the paramagnetic Curie temperature 0p and the effective hyperfine fields for GdT2 Si2 compounds, including the negative transferred hyperfine field observed experimentally at the Fe position in GdFe2Si2, was made in the framework of the simple R K K Y model. It offers an explanation of the experimental results when using Z = 13 (Lgtka 1989). The dependence of the Curie or N6el temperatures on the de Gennes factor for several groups of ternary rare-earth intermetallics is presented in fig. 39. In this figure, the data for RFeA1 compounds (with high Curie temperature) and for the Heusler alloys RCuzln, RAg2In and RAu2In (with low N6el temperatures) are shown. The magnetic properties of RCul_xZnxSi compounds with R = Gd (Kido et al. 1984b), Tb (Ba2ela and Szytuta 1989), Dy or Ho (Kido et al. 1985c) were analyzed in terms of R K K Y theory. In these compounds, the paramagnetic Curie temperature plotted as a function of the composition x have a maximum at x = 0.4 (see fig. 40a). Assuming an RKKY type exchange interaction, the paramagnetic Curie temperatures are given by eq. (4). The R atoms occupy crystallographically equivalent positions in the RCul_xZn~Si compounds (A1Bz or Nizln-type structure). The summations in eq. (4) calculated as a function of kF for GdCuSi and GdZnSi are shown in fig. 40b. The results obtained indicate that the change in 0p is primarily due to kF and secondarily due to Ris. Since the 0p values of GdCut _xZn~Si are positive, as is shown in fig. 40a, the sign of the sum functions in eq. (4) has to be negative. This condition

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

163

Tc(KI 250

• RCu2ln A RAg2In * RAu2In

TN(K

200 150 100

10

50

Gd Tb Dy No Er Tm Yb

Fig. 39. The N6el or the Curie temperatures observed for RFeAI, RCu2In, RAg2In and RAu2In compounds and their relation to the de Gennes function.

200

a/X

100

12[ RCuo.eZno,4Si

:t/k )2b

c)

6t R=Gd"xJ//~1

l/ 2k H°--Z/

i

i

0'.2 o.~ o~ o ; 4

2.0 2.2 2.4--/2.6 1.0 1.2~11./,, 1.6 1.8KF(101O m-l)

-4L

I

I

I

010.8 1.0

1.2 1.4 1.6

KF(101om-1 )

Fig. 40. (a) Paramagnetic Curie temperature 0p versus composition x of GdCul _~ZnxSi, (b) dependence of lattice sums for GdCuSi (0) and GdZnSi (©) on the Fermi vector, and (c) dependence of the lattice sums for RCuo.6Zno.4Sion the Fermi wave number (Kido et al. 1984b, 1985c). is satisfied at about k F = 1.25 x 101° and 1.9 x 101° m-1. The corresponding number of conduction electrons per formula unit N was calculated to be 3.7 and 11.5 for kv = 1.25 x 101° and 1.9 x 101° m - 1 , respectively. Consequently, one may conclude that in the GdCua _xZn~Si compounds (0 ~ x ~< 1) N has a value between 3 and 4 when x varies between 0 and 1. The analysis of the interatomic distances in this type of crystal structure indicates that the Cu-Si distance is smaller than the sum of the metallic radii of the elements, which reveals a strong covalent bonding between these atoms (Ba2ela 1987). The Cu and Zn atoms differ in one valence electron. The results obtained show that this electron is probably accomodated in the conduction band. An interesting group of the CeT2X 2 compounds has unique properties associated mainly with 4f instabilities. Some of them are magnetically ordered, while others are Pauli paramagnets. This variety of properties is due to two competing interactions:

164

A. SZYTULA

(1) the indirect magnetic interaction between local moments via conduction electron polarization, the so-called RKKY interaction, whose intensity is proportional to the square of the exchange integral Jse and it can be characterized by a temperature TRKKY ,~

N(EF)j2f;

(16)

(2) another interaction in the system is the Kondo effect which tends to compensate the local moment on moment-bearing ion and, thus, leads to the formation of a nonmagnetic ground state. The Kondo interaction is characterized by a temperature TK which depends exponentially o n Jsf as follows: TK "~' e x p [ - I lN(EF)J,f].

(17)

The schematic dependence of the magnetic transition temperature Tc,N on the normalized Kondo coupling constant J~f/W (fig. 41 a) can be used for the classification of a variety of CeT2X2 compounds. Compounds with high d~f values and TK>> TRKKY should be called nonmagnetic concentrated Kondo systems (CKS), e.g., CeTzSi z compounds (T = 3d metals). The intermediate situation where TK>> TRKKYand TN # 0 corresponds to the magnetic ground state modified essentially by the Kondo compensation of the magnetic moment of rare-earth ions. Figure 41b demonstrates the dependence of the N6el and Kondo temperatures as a function of the unit cell volume for several CeT2X2 compounds. The obtained results indicate that for large volumes

I

i

1

[

11

I

~

TK,TN(K)

I

/~

b}

/o

20

ii /

10

v..vS/" i ~"

IM

I

i II TK

3O

200

/

~, iTN o

o

i

180

,,"160 VEJ3] /'T K /

r¢ #

I--

tY uJ

/

l/

//

IM

/

~ ~ ~

TRKKY

uJ i---

Fig. 41. (a) The classification of concentrated Kondo systems (CKS) by the relation between two characteristic temperatures: TK and TRUly; TN is magnetic transition temperature. (b) Kondo temperatures T~ (©) and magnetic ordering temperatures TN (V) versus the unit cell volume for several CeTzX 2 compounds. The lines are guides to the eye.

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S

165

the RKKY interaction between well-localized f-electrons dominates. And, in the case when the Kondo effect plays a minor role, ordinary magnets are found. For small cell volumes and low temperatures 4f-electrons are weakly localized. It was found that pressure has a considerable influence on the N6el temperature. The results for several compounds are presented in fig. 42a. The weak linear pressure dependence of TN for CeAg2Si 2 and CeAu2Si 2 (dTN/dp = +0.1 and -0.04K/kbar, respectively) confirms on the suggestion that in these materials TK is much smaller than TN. However, the strong nonlinear decrease in TN with pressure in CePd 2 Si2 and CeRhzSi2, dTN/dp = 1.4 and - 5 K / k b a r , respectively, suggests the opposite regime. Changes in TN(p) agree qualitatively with Doniach's phase diagram in which the energy of a Kondo singlet is compared with that of an RKKY-antiferromagnetic ground state (see fig. 42b).

5.3. Crystalline electric field It is well-known nowadays that the crystalline electric field (CEF) at the rare-earth site can strongly effect the magnetic properties of the ternary rare-earth intermetallics. The interaction of the CEF with the multipole moments of the electrons of the R 3 + ion is described by the CEF Hamiltonian [see eq. (6)]. For the ternary rare-earth intermetallics, a systematic study of crystal electric field was performed only for the RT2X2 compounds. The values of the Bm parameters determined for a large number of these compounds are collected in table 20. The B ° parameters seem to be dominant, since the remaining Bm parameters are smaller by an order of magnitude. At a site of the tetragonal point symmetry, the easy axis of magnetization is parallel to the fourfold c axis if B ° is negative, it is perpendicular to the e axis if B2° is positive (Hutchings 1964, Bertaut 1972, Dirken et al. 1989), provided the effect of the second-

X~b)

2.0

o) 1.2

T/W 1.51

I£ ~CePd2Si2

~ \CleRh2Si~ 2

O.8 a_ 0.~ 0.4

1.0 P

-~

0.5

I I

0.~ i I

O.C 0

,

10 P{kbar}

15

0.5

1.0J/W

Fig. 42. (a) The N6el temperature normalized to its value at p = 0 as a function of pressure in CeT2Si 2 (Thompson et al. 1986), (b) Doniach's phase diagram for the one dimensional 'Kondo necklace' model (Doniach 1977),

166

A. SZYTULA TABLE 20 Values of the B,~ crystal electric field parameters in RTzX2 compounds.

Compound

B° (K)

CeCu2 Si2

- 3.0 + 1.0 -3.1 _+ 1.2 - 8.78 -11.4 ± 2 . 6 5 -0.5 + 1.3 + 30.7 -1.08 _ 1.20 + 6.46 - 8.0 -3.99 -1.8 + 0.45 - 0.915 - 1.09 - 1.93 -4.94 - 1.8 - 1.0 - 0.22 + 0.70 +0.241 +2.53 +0.12

CeCuz Ge2 CePd2 Si2 CeAg2Si2 CePt2 Siz CeAu2 Si2 CeAlz Ge2 PrCo2 Siz PrNizSiz NdCo2Ge2 NdMn 2Ge 2 NdRh z Si2 Tb Rh 2 Si2 DyRh 2Siz DyRuzSiz DyFe2 Siz DyCo z Si 2

HoRh2 Siz ErRhz Siz TmFe2Si2 TmCuzSiz

* References: [-1] Horn et al. (1981). [2] Severing et al. (1989). [3] Knopp et al. (1989). [4] Gignoux et al. (1988b). [5] Gignoux et al. (1988a). [6] Shigeoka et al. (1989b). [7] Barandiaran et al. (1986b). [8] Fujii et al. (1988).

B° (K)

B## (K)

-0.4 _+0.1 0.25 _+0.1 +0.41 _+0.12 -6.5 +0.5 - 0.054 + 2.79 -0.0012 -3.25 + 0.7 -0.04 + 0.01 -4.0 + 0.4 + 0.93 + 19.5 + 0.34 ___0.04 -4.6 ± 0.4 - 0.09 + 0.013 - 0.0136 + 0.05 +0.0016 +0.156 0 -0.011 + 0.0057 - 0.020 + 0.189 - 0.02 - 0.0047 - 0.0085 + 0.0043 +0.0063 - 0.0039 -- 0.00 + 0.0011 - 0.002 - 0.0027 + 0.04 -0.00125 -0.00246 -0.017 +0.049 -0.0312 -0.049 [9] [10] [11] [12] [13] [14] [15]

B° (K)

+ 0.0026 +0.00013 -0.00013

B6 (K)

- 0.0024 -0.00032 -0.001

+ 0.000025 + 0.00003

0 -0.00014

+0.002 +0.00126

Ref.* [,1] [-2] [3] [2] [2] [4] [2] [5] [6] [7] [8] [9] [ 10] [ 10] [ 11] [11] [12] [ 12] [ 13] [12] [10] [14] [,15]

Shigeoka et al. (1988a). Takano et al. (1987b). Sanchez et al. (1988). G6rlich (1980). Takano et al. (1987a). Umarji et al. (1984). Stewart and Zukrowski (1982).

o r d e r t e r m i n the crystal field H a m i l t o n i a n is d o m i n a n t . T a b l e 21 c o n t a i n s the v a l u e s of B ° coefficients d e t e r m i n e d e x p e r i m e n t a l l y for a n u m b e r of R T 2 X 2 c o m p o u n d s . These d a t a i n d i c a t e t h a t the signs of the B ° coefficients a n d the c o r r e s p o n d i n g o r i e n t a t i o n of the m a g n e t i c m o m e n t s agree w i t h t h o s e d e d u c e d f r o m n e u t r o n diffract i o n e x p e r i m e n t s . H o w e v e r , it h a s b e e n s h o w n t h a t the sign of B ° d e p e n d s also o n the n u m b e r of 4f a n d n d electrons, b u t the lack of d a t a does n o t p e r m i t us to p l o t a d e t a i l e d d i a g r a m . O n l y i n s o m e c o m p o u n d s , the m o m e n t d i r e c t i o n is i n disa g r e e m e n t w i t h the C E F p r e d i c t i o n . F o r c o m p o u n d s w i t h N i a n d w i t h P d , the v a l u e s of B ° are very s m a l l c o m p a r e d to o t h e r c o m p o u n d s . T h u s , crystal field t e r m s of h i g h e r o r d e r m a y h a v e a s t r o n g effect. I n a d d i t i o n , s m a l l d e v i a t i o n s of s t r u c t u r a l p a r a m e t e r s f r o m t h o s e i n the c o r r e s p o n d i n g RT2 X2 c o m p o u n d s m a y l e a d to a c h a n g e in sign of the B ° coefficients. I n the c o m p o u n d s H o R h 2 Si2 (Slaski et al. 1983), D y R h 2 Si2 ( M e l a m u d et al. 1984),

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS TABLE 21 Values of the B ° coefficients and direction of the magnetic m o m e n t s on RT2Si2 compounds. Compound •C e M n 2 Si 2 PrMn2 Si 2 N d M n 2 Si 2 G d M n 2 Si 2 T b M n 2 Si2 D y M n 2 Si~ H o M n 2 Si2 ErMn2 Si2 T m M n 2 Si2 YbMn2 Si2 CeFe2 Si2 PrFe2 Si2 N d F e 2 Si 2

B°

- 0.7 + 0.45

Direction

Ref.*

rlc ±c 3_ c IIc

[2] [8] [ 13] [ 14] [21] [38] [26]

- 1.35 q~ ±c

- 0.63

±c

[9] [103 [13, 14] [15] [16] [9] [223 [9] [25] [9] [26] [9] [ 15] [27]

IIc

[3] [4, 5]

IIc ±c

GdFe2 Si 2 T b F e 2 Si 2

- 4.07

DyFez Si2

- 1.8

H o F e 2 Si 2

-- 0.6

ErFe2 Si 2

+ 0.67

TmFe2 Si2 YbFe 2 Si 2

+ 2.54 + 10.12

IIc IIc (p ±c

CeCo 2 Si 2 PrC02Si 2 N d C o 2 Si 2

-8.0 - 1.8

[11] /Ic Zc

GdCo2 Si 2 TbCo/Si z

- 2.24

DyC02 Si 2

- 1.0

H o C o 2 Si 2

-- 0.44

ErCo2 Si2

+ 0.44

T m C o z Si 2

+ 1.85

YbCo2 Si 2

+ 5.58

lie IIc

p[c

- 3.99

[4, 17]

±c ±c

[ 15] [4] [ 15] [23] [27]

IIc

[6]

± c ±c

[ 12] [l 3, 14]

±c

CeNi a Si z P r N i 2 Si 2 N d N i 2 Si z GdNi2 Si z

[4] [13, 14] [15] [4,5,17] [21] [23, 24] [ 15]

167

168

A. SZYTULA TABLE 21 Compound TbNi2 Si2

B°

(continued) Direction

- 0.66 I1c

DyNi2 Sia HoNi2Si2

+ 0.17 -0.13

ErNi 2 Si 2

+ 0.14

TmNi2 Si z

+ 0.55

YbNi2 Si2

+ 0.65

CeCu 2 Si 2

-

_l_c _l_c Lc 3.0

PrCu 2Si 2 NdCu 2 Si2 GdCu 2 Si2 TbCu2Si 2

1]c

+0.8, +1.3

DyCu2 Si2

+ 0.57

HoCua Si2

+ 0.175

ErCu 2 Si2 TmCuz Si2 YbCu 2 Si2

- 0.2 - 0.79 - 3.23

I c ±c lc Zc

CeRu2 Si 2 NdRu2 Si 2 GdRu2 Si2 TbRu 2 Si 2

- 8.33

DyRuz Sia

- 4.94

HoRu

--

IIc q~

II c II c 2 Si 2

1.64 IIc

ErRu2Si 2

+ 1.78

TmRuz Si2

+ 6.89

CeRh2 Si2 NdRh z Siz

- 0.9

Zc I c [kc _Lc

GdRh2 Si2 TbRhg Si 2

- 3.3

DyRh28i 2

-- 1.9

HoRh2 Si2

- 0.64

ErRh2 Si2

+ 0.7

TmRh2 Si 2

+ 0.69

II c ~o q~ ±c ic

Ref,* [ 15] [12, 17] [21 ] [15] [12] [ 15] [12] [15] E12] [15] E1] [7] [ 13,14] [15, 18] [19,20] [21] [24] [18] [19,20] E18] E18] E15] [30] [ 13,14] [15] [30] [15] [30] [ 15] [30] [15] [30] E15] [28] [31 ] [32] [13, 14] [15] E28, 33] E15] [33] E15] [33] [15] [32] [ 15] E37]

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S TABLE 21 Compound

B2°

CePd2 Si2

- 11.4

NdPd2 Si2 GdPd2 Si2 TbPd 2 Siz

- 0.18

DyPd 2 Si2 HoPdz Si2

- 0.11 + 0.04

ErPd 2 Si 2 TmPd2 Si2

+ 0.04 + 0.15

CeOs2 Si2 NdOsz Si2 GdOs 2 Si 2 TbOs2 Si2

- 8.32

DyOs2 Siz HoOs 2 Si~

- 4.93 - 1.64

ErOs2 Si2 TmOs2 Si2

+ 1.78 + 0.88

Celr2 Si2 NdIr2 Si2 Gdlr2 Si 2 TbIr 2 Si2

- 3.9

DyIr2 Si2 HoIr2 Si2 Erlr2 Si2 Tmlr 2 Si 2

- 2.32 - 0.77 + 0.84 + 3.24

(continued) Direction

Ref.*

±c

[37] [29]

_1_c l c

±c

~o IIc

I]c _1_c

±c [Ic

* References: [1] Horn et al. (1981). [2] Iwata et al. (1986b). [3] Shigeoka et al. (1988b). [4] Leciejewicz et al. (1983b). [5] Yakinthos et al. (1984). [6] Barandiaran et al. (1986b). [7] Szytu~a et al. (1983). [8] Shigeoka et al. (1988a). [9] Noakes et al. (1983). [10] Pinto and Shaked (1973). Ell] Fujii et al. (1988). [12] Barandiaran et al. (1987). [13] Dirken et al. (1989). [14] Czjzek et al. (1989). [15] L~tka (1989). [16] Szytuta et al. (1987a). [17] Nguyen et al. (1983). [18] Budkowski et al. (1987). [19] Leciejewicz et al. (1986).

[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]

[ 13,14] [ 15] [34] [ 15] [ 15] [36] [ 15] [15]

E13, 14] [15] [35] E15] [ 15] [35] [35] [ 15]

[13, 14] E15] [33] [ 15] [15] [15] [15]

Pinto et al. (1985). G6rlich et al. (1989). Bourre-Vigneron et al. (1990). Leciejewicz and Szytuta (1983). Pinto et al. (1983). Leciejewicz and Szytuta (1985a). Leciejewicz et al. (1984b). Hodges (1987). Quezel et al. (1984). Steeman et al. (1988). Slaski et al. (1984). Takano et al. (1987b). Szytuta et al. (1984). ~laski et al. (1983). Szytuta et al. (1986b). Kolenda et al. (1985). Leciejewicz and Szytuia (1985b). Severing et al. (1989). Leciejewicz et al. (1990).

169

170

A. SZYTULA

TmRh2 Si2 (Yakinthos 1986b) and for HoFe2 Si2 (Leciejewicz and Szytula 1985a), the moment directions have been reported to be neither parallel nor perpendicular to the fourfold c axis. Such canting points to a strong influence of higher-order crystal field terms. Apart from its influence on the easy direction of magnetization, the CEF has also considerable influence on the magnetic transition temperatures. Taking only the second-order CEF term into account, the large deviations of TN from that predicted by the de Gennes rule can be understood (Noakes and Shenoy 1982). The observed values of the magnetic transition temperatures of RCu2 Siz compounds do not follow the de Gennes rule (see fig. 43). However, if a CEF Hamiltonian, Hof is added to the exchange Hamiltonian, the agreement with the de Gennes function improves considerably (Noakes and Shenoy 1982). Using H = -2y(g

s -

1)2Jz<Jz> + B20 [3Jz2 -- J ( J

+

1)],

(18)

the magnetic ordering temperature is given by TN = 2 J ( O ,

-

1)2 ~' Jz2 exp(s=

o Fz

3B z Jz/TN)

L J=

exp(-- 3B2 J ~ / T N )

•

_1

(19)

The values deduced for B ° are as follows: 0.8 K for Tb, 0.5 K for Dy, 0.175 K for Ho, - 0 . 1 9 9 K for Er and - 0 . 7 8 9 K for Tm (Budkowski et al. 1987).

TN[K] 15

\\ lc

•

•"\\

•\

•\

•

i \\\\\ ~I \

\

i

\\

"\~/,, GId

l'lb

Dy

HO

Er

Tm

RE

Fig. 43. Comparison of experimental(solid triangles) and calculated magnetic transition temperatures TN for RCu2Si2 compounds. The broken smooth line represents the de Gennes rule. The dotted line is for trends obtained on the basis of the molecular field model (Noakes and Shenoy 1982) including CEF effects. The solid line (open circles) represents TNpredicted by the B° model with A° as for GdCu2Si2 (L~tka et al. 1979). The dotted line (open squares) represents calculations made with the full CEF Hamiltonian using the five B,~ parameters of Stewart and Zukrowski (1982), the symbols [] represent data of Koztowski (1986),the symbol (3 refer to data of Budkowski et al. (1987).

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

171

All these results show that the crystal electric field has a significant effect on the magnetic properties of the RT2 X2 compounds. Of other ternary intermetallics, the CEF parameters were determined only in some cases.

In CeCuSi, the Ce a+ ions occupy positions with point symmetry 3m. For a hexagonal symmetry, 3m, the CEF Hamiltonian is given by eq. (9). The values determined for the B," parameters in CeCuSi are: B ° = 9.14 K, B ° = -0.035 K, B43= 6.56 K. The magnetic moment of the Ce atoms lies in the basal plane, which is in agreement with the sign of B °. Under these conditions, the multiplet J = ~ is split into three doublets which are mainly _+ [M s ) states (Ms = ½, ~ or ~), with a small mixing between -t- [½) _+ [~) states due to the B~ term. For the above B," parameters, the ground state in the paramagnetic regime is found to be the doublet + [½), well separated (A = 90 K) from the first excited level + J~). In the ordered state, the basal plane is then favoured as the easy magnetization direction, with an associated magnetic moment of 1.2#B at 0 K. This value is quite consistent with the experimental data (#R = 1.25/~B) (Gignoux et al. 1986a). In the rare-earth Heusler intermetallic compounds, the ordering temperatures are low and the associated magnetic energies are small. The crystalline electric field (CEF) effects, therefore, play an essential role in determining the magnetic properties. The values of the rare-earth magnetic moments determined experimentally for R T 2 X cubic compounds are smaller than the free R 3+ ion values. This result indicates the strong influence of crystal field effects. In these compounds the rare-earth ions occupy a site of cubic point symmetry, and the crystalline electric field will then lift the (2J + 1)-fold degeneracy of the freeion state. The CEF interactions are commonly described by the parametrization of Lea et al. (1962), Wx o + 504) + W ( 1 - X) (oO H,f = B4(O ° + 50~) + B6(O ° + 21064) = --~-(04 F~

210~),

(20) where W is an energy scale factor and x represents the relative weight of the fourthand sixth-order terms. The quantities F4 and F6 are numerical factors (Lea et al. 1962). The CEF parameters B,", W and x for several members in the RPd2 Sn series are listed in table 22. The results obtained indicate that the compounds with R = Dy, TABLE 22 Crystalline electric field parameters for various rare-earth ions in RPd2 Sn compounds. R Tb Dy Ho Er Tm Yb

B° [-1] (10-ZK) B° [1] (10-*K) -0.61 0.32 -0.39 -0.104 0.13

0.38 0.41 -0.60 1.48 -33.0

W(meV) I-2] x [2] +0.053 -0.036 +0.0287 -0.0450 +0.076 -0.530

-0.785 -0.509 +0.325 +0.3022 -0.513 -0.722

OES [2] 10.71 11.8 17.56 20.32 11.98 13.43

GSS [-2] M/NM M M M M/NM M

OES = overall energy splitting, GSS = ground state status, M = magnetic, NM = nonmagnetic, [11 Malik et al. (1985b), [-2] Li et al. (1989).

172

A. SZYTULA

Ho, Er or Yb have a crystal-field split ground state that is magnetic and, therefore, a magnetic ordering in these systems is expected at low temperatures. The results are in agreement with experimental data. For R = Tb or Tm (both have J = 6) the scaling values of x are located in the region of the LLW diagram (Lea et al. 1962) where the F3 and F5x energy levels are crossing, so that the separation energies between the ground state and the first excited state are small: 0.7 and 0.3 meV for R = Tb and Tm, respectively (Li et al. 1989).

Acknowledgements I am grateful to Professor J. Leciejewicz, Drs H. Hrynkiewicz and K. L~tka who spent much time in discussing many details of the manuscript. Special thanks are due to Miss G. Domoslawska for the preparation of the graphical part of this work.

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Umarji, A.M., S.K. Malik and G.K. Shenoy, 1985, Solid State Commun. 53, 1029. Venturini, G., B. Malaman, M. Meot-Meyer, D. Fruchart, G. le Caer, D. Malterre and B. Roques, 1986, Rev. Chim. Miner. 23, 162. Venturini, G., B. Malaman, L. Pontonnier, M. Bacmann and D. Fruchart, 1989a, Solid State Commun. 66, 597. Venturini, G., B. Malaman, L. Pontonnier and D. Fruchart, 1989b, Solid State Commun. 67, 193. Weidner, P., R. Sandra, L. Appl and R.N. Shelton, 1985, Solid State Commun. 53, 115. Westerholt, K., and H. Bach, 1981, Phys. Rev. Lett. 47, 1925. Yakinthos, J.K., 1985, J. Magn. & Magn. Mater. 46, 300. Yakinthos, J.K., 1986a, J. Phys. 47, 1239. Yakinthos, LK., 1986b, J. Phys. 47, 673. Yakinthos, J.K., and H. Gamari-Seale, 1982, Z. Phys. B 48, 251. Yakinthos, J.K., and P.F. Ikonomou, 1980, Solid State Commun. 34, 777. Yakinthos, J.K., and E. Roudaut, 1987, J. Magn. & Magn. Mater. 68, 90. Yakinthos, J.K., Ch. Routsi and P.F. Ikonomou, 1980, J. Less-Common Met. 72, 205. Yakinthos, J.K., Ch. Routsi and P. SchobingerPapamantellos, 1983, J. Magn. & Magn. Mater. 30, 355. Yakinthos, J.K., Ch. Routsi and P. SchobingerPapamantellos, 1984, J. Phys.-Chem. Solids 45, 689. Yakinthos, J.K., P.A. Kotsanidis, W. Schfifer and G. Will, 1989, J. Magn. & Magn. Mater. 81, 163. Yarovetz, V.I., 1978, Autoreferat Dis. Kand. Khim., abstract of the thesis, Russian (Nauk, Lvov) p. 24. Yarovetz, V.I., and Yu.K. Gorelenko, 1981, Vestn. Lvov Univ. Ser. Khim. 23, 20. Yosida, K., 1957, Phys. Rev. 106, 893. Yosida, K., and A. Watabe, 1962, Progr. Theor. Phys. 28, 361. Zerguine, M., 1988, Thesis, Grenoble. Zheng, Ch., and R. Hoffmann, 1988, J. Solid State Chem. 72, 58. Zygmunt, A., and A. Szytula, 1984, Acta Magnetica, Suppl. 84, 193.

chapter 3 COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

O. BECKMAN and L. LUNDGREN Department of Technology Uppsala University Box 534, S-751 21, Uppsala, Sweden

Handbook of Magnetic Materials, Vol. 6 Edited by K.H.J. Buschow © Elsevier Science Publishers B.V., 1991 181

CONTENTS 1. I n t r c d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. T X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 X: g r o u p ]lI; B . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. M n B , F e B , C o B . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. P s e u d o b i n a r y m o n o b o r i d e s . . . . . . . . . . . . . . . . . . . 2.2. X: g r o u p IV; Si, G e , Sn . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. C u b i c F e S i 0320) s t r u c t u r e . . . . . . . . . . . . . . . . . . . . 2.2.1.1. M n S i . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1.2. F e G e , c u b i c B20 . . . . . . . . . . . . . . . . . . . . 2.2.1.3. F e l - t C o t S i . . . . . . . . . . . . . . . . . . . . . .

186 187 187 187 188 188 189 189 191 191

2.2.1.4. M n l _ t C o t S i . . . . . . . . . . . . . . . . . . . . . 2.2.1.5. C r l _ t M n t G e . . . . . . . . . . . . . . . . . . . . . 2.2.1.6. C r l _ t F e t G e . . . . . . . . . . . . . . . . . . . . . . 2.2.1.7. C r G e 1 _=Six . . . . . . . . . . . . . . . . . . . . . . 2.2.2. U C x a g o n a l C o S n (B35) s t I u c t u r e . . . . . . . . . . . . . . . . . 2.2.2.1. F e C e , hexagol~al B35 . . . . . . . . . . . . . . . . . . 22.2.2. F e S n . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. M o n c c l i n i c C o G e ~,t~ucture . . . . . . . . . . . . . . . . . . . X: g r o u p V; P, As, 5b, Bi . . . . . . . . . . . . . . . . . . . . . . 2.3.1. P17osphides . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.1. M n P . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.2. F e P . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.3. P s e u d o b i n a r y p h o s p h i d e s . . . . . . . . . . . . . . . . .

192 193 193 193 193 193 194 195 195 198 198 202 202

2.3.1.4. M n l - t C r t P . . . . . . . . . . . . . . . . . . . . . 2.3.1.5. M n l - t F e t P . . . . . . . . . . . . . . . . . . . . . 2.3.1.6. M n l _ t N i t P . . . . . . . . . . . . . . . . . . . . . 2.3.2. A r s c n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.1. C r A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.2. M n A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.3. F e A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.3. F s e u d o b i n a r y a r s e n i d e s . . . . . . . . . . . . . . . . . . . . 2.3.3.1. (V, Cr)As, (Ti, Cr)•s . . . . . . . . . . . . . . . . . . 2.3.32. M n x _ t C r t A s . . . . . . . . . . . . . . . . . . . . 2.33.3. M n l _ t T i ~ A s . . . . . . . . . . . . . . . . . . . . 2.3.3.4. M n x _ t F e t A s . . . . . . . . . . . . . . . . . . . . 2.3.4. P s e u d o b i n a r y c o m p o u n d s w i t h a e o r r m e n c a t i c n . . . . . . . . . 2.3.4.1. C r A s l _:,Ix . . . . . . . . . . . . . . . . . . . . .

202 203 203 203 203 203 206 206 206 207 208 208 208 208

2.3.

182

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COMPOUNDS 2.3.4.2. 2.3.4.3. 2.3.4.4.

OF TRANSITION

ELEMENTS

WITH NONMETALS

MnAsl_xPx . . . . . . . . . . . . . . . . . . . . . . FeAsl_~Px . . . . . . . . . . . . . . . . . . . . . . Mnl-tCrtAsl-xP~ . . . . . . . . . . . . . . . . . . .

2.3.4.5. C r A s l _ x S b x . . . . . . . . . . . . . . . . . . . . . Antimonides, including MnBi . . . . . . . . . . . . . . . . . . 2.3.5.1. C r S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.2. M n S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.3. F e l + t S b . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.4. C o S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.5. M n B i . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6. P s e u d o b i n a r y a n t i m o n i d e s . . . . . . . . . . . . . . . . . . . . 2.3.6.1. M n l _ t T i t S b . . . . . . . . . . . . . . . . . . . . . 2.3.6.2. C r 1 _ t C o t S b . . . . . . . . . . . . . . . . . . . . . . 2.3.6.3. M n 1 _ t C r t S b . . . . . . . . . . . . . . . . . . . . . 2.4. X: g r o u p VI; S, Se, Te . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. CrS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. C r S e . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. C r 1 tTe . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4. M n S . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5. M n T e . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.6. V1 tCr~Se . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.7. C r A s l _ x S e x . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.8. C r T e l _ ~ S e x . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.9. C r T e l x S b x . . . . . . . . . . . . . . . . . . . . . . . . . 3. T 2 X - a n d T T ' X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . 3.1. X: g r o u p III; B . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. ( F e l _ t C o t ) 2 B . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. ( F e l _ t M n t ) 2 B . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. (Nia tTt)zB . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. X: g r o u p IV; Si, G e , Sn . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. M n C o S i . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. M n N i G e . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. M n ( C o l _tNit)Si . . . . . . . . . . . . . . . . . . . . . . . 3.2.4. M n C o ( S i l _ ~ G e x ) . . . . . . . . . . . . . . . . . . . . . . . 3.2.5. M n ( C o l _ ~ N i ~ ) G e . . . . . . . . . . . . . . . . . . . . . . . 3.2.6. M n N i ( S i l _ x G e x ) . . . . . . . . . . . . . . . . . . . . . . . 3.2.7. M n R h S i . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8. C o m p o u n d s w i t h h e x a g o n a l N i z l n - t y p e s t r u c t u r e . . . . . . . . . . . 3.2.9. M n C o S n . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. X: g r o u p V; P, As, Sb . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. P h o s p h i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1. F e 2 P . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2. F e z - t P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.3. ( C r l _ t F e ~ ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.4. C r F e P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.5. ( M n l _ t F e t ) / P . . . . . . . . . . . . . . . . . . . . . 3.3.1.6. M n F e P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.7. M n 2 P . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.8. ( F e l _ t C o t ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.9. ( F e l _ t N i t ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.10. ( C r a _ ~ N i t ) z P . . . . . . . . . . . . . . . . . . . . . 3.3.1.11. ( M n l _ r C o ~ ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.2. A r s e n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2.1. C r z A s . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.

183 208 209 209 209 210 210 210 211 211 211 212 212 212 212 212 212 212 213 214 214 214 214 215 215 215 215 217 218 218 218 219 221 221 222 222 223 223 223 224 224 225 225 231 232 232 232 233 233 233 234 234 235 237 237

184

O. BECKMAN

a n d L. L U N D G R E N

. . . .

237 239 239 239 240 240 241 241 241 242 243

3.3.3.1. F e 2 ( P l _ ~ A s x ) . . . . . . . . . . . . . . . . . . . . . 3.3.3.2. M n F e ( P ~ _ ~ A s x ) . . . . . . . . . . . . . . . . . . . . 3.3.3.3. M n C o ( P l _ x A s x ) . . . . . . . . . . . . . . . . . . . . 3.3.4. A n t i m o n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4.1. M n / S b . . . . . . . . . . . . . . . . . . . . . . . 3.3.4.2. M n 2 _ t C r t S b . . . . . . . . . . . . . . . . . . . . . 3.3.4.3. O t h e r m o d i f i e d M n 2 S b c o m p o u n d s . . . . . . . . . . . . . 3.3.4.4. M n z S b x _ x A s x . . . . . . . . . . . . . . . . . . . . . 3.4. T T ' X c o m p o u n d s w i t h a 4 d e l e m e n t . . . . . . . . . . . . . . . . . . . 3.4.1. F e R u P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. F e R h P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3. M n R u P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4. M n R h P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.5. M n R u A s . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.6. M n R h A s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.7. ( C r x _ r P d t ) 2 A s . . . . . . . . . . . . . . . . . . . . . . . . 4. T X 2 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. C r B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. V l - t C r t B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. M n B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. F e G e 2 , F e S n / , M n S n 2 . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. F e G e / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. F e S n / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3. M n S n / . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. C r S b 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. C r t F e l _ t S b 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7. M n S 2 , M n S e 2 , M n T e 2 . . . . . . . . . . . . . . . . . . . . . . . 4.7.1. M n S 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2. M n S e / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.3. M n T e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8. C o S / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9. C o S e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10. T e r n a r y s y s t e m s . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.1 NiSz_~Se~ . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.2. C o P x S 2 _ x , C o A s x S 2 _ x , C o S e x S 2 _ ~ . . . . . . . . . . . . . . . . 5. T 2 X 3 , T 3 X 4 , T s X 6 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . 5.1. C r z S 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Cr2Se3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. C r 2 T % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. C r z S a _ x T e x . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. C r 2 S e 3 _ ~ T e x . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. F e / T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7. C r t F e 2 _ t T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . .

243 243 245 245 245 246 247 248 249 250 250 250 250 251 251 252 252 252 254 254 254 254 254 255 256 256 257 257 257 258 258 259 259 259 259 259 259 260 260 262 262 262 262

3.3.3.

3.3.2.2. M n 2 A s . . . . . . . . . . 3.3.2.3. F e z A s . . . . . . . . . . . 3.3.2.4. C o z A s . . . . . . . . . . 3.3.2.5. ( C r l _ ~ M n t ) 2 A s . . . . . . . 3.3.2.6. V M n A s . . . . . . . . . . 3.3.2.7. ( M n l _ t F e t ) / A s . . . . . . . 3.3.2.8. ( F e l _ t C o t ) 2 A s . . . . . . . . 3.3.2.9. ( M n l _ t C o t ) 2 A s . . . . . . . 3.3.2.10. M n ( F e , C o ) A s a n d M n ( C o , Ni)As 3.3.2.11. ( C r l _ t N i t ) z A s . . . . . . . . Arseno-phosphides . . . . . . . . .

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. . . . . . . .

COMPOUNDS

OF TRANSITION

ELEMENTS

WITH NONMETALS

5.8. C r 3 S 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9. C r 3 S e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10. C r 3 T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11. Cr3Se4_xTe~, . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12. C r s S 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13. C r s T e 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. T 3 X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. M n 3 S i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. M n 3 G e , M n 3 S n . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. M n ~ G e , t e t r a g o n a l p h a s e . . . . . . . . . . . . . . . . . . . . . . 6.4. F % Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. F e 3 _ t T t S i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. F % G e , h e x a g o n a l D019 . . . . . . . . . . . . . . . . . . . . . . . 6.7. F % G e , c u b i c L12 . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. ( F e l - t V t ) 3 G e . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9. ( F e l _ t N i t ) 3 G e . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10. F % S n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11. M n 3 P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12. F e 3 P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. T s X 3 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. F e s P B z a n d F e s S i B 2 . . . . . . . . . . . . . . . . . . . . . . . . 7.2. M n s P B 2 a n d M n s S i B z . . . . . . . . . . . . . . . . . . . . . . . 7.3. M n s S i ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. M n s G e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. M n s ( G e l _ x S i x ) 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6. F % G % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7. ( F e t M n l _ t ) s G % . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8. ( F e t T l _ t ) s G e 3 , T = N i o r C o . . . . . . . . . . . . . . . . . . . . . 7.9. F % S i 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10. M n s S n 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.11. F e s S n 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.12. (Fe, T ) s S n 3 , T = N i o r C o . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185 262 262 262 263 263 264 264 264 265 266 267 268 268 268 269 269 269 269 269 270 272 272 273 273 273 274 274 275 275 275 276 276 276

1. Introduction The ferromagnetism of transition metal interrnetallic compounds has been covered by Booth (1988) in volume IV of this series. The present chapter is a supplement to Booth's chapter, since it deals with compounds of transition metals with nonmetallic and semimetallic elements. In order to keep the size of this chapter within reasonable limits, we have excluded carbides, nitrides, oxides and halides. The chapter then closely covers the scope of the combined physics and chemistry conference series International Conference of Solid Compounds of Transition Elements. However, sulfides are only treated when there is a direct connection to related selenides and tellurides. The present compilation does not exclusively deal with ferromagnetic compounds. The intention has been to cover all types of ordered magnetic structures, i.e., ferromagnetism as well as ferri-, antiferro- and helimagnetism. However, disordered magnetic systems such as spin glass and amorphous magnetism are excluded. The compounds are listed according to the stoichiometric composition. The first two sections are devoted to the large groups TX and T2X, TT'X, where T is a transition element and X a nonmetal element. Then follow sections on various Tr, Xn compounds. Within each section, the compounds are arranged according to the nonmetallic elements of the third, fourth, fifth and sixth group of the periodic table. In the chemical formulas, we have arranged the elements according to increasing atomic number. The magnetic phase diagrams are presented according to the same rule. Each section (subsection) starts with a survey of the relevant crystallographic structures. Sometimes there is an ambiguity in the literature as regards crystal settings. In those cases, we have followed Hahn (1983). In a separate table we have given a summary of lattice parameters and basic magnetic data in order to give the reader a schematic overview. Our intention has also been to present the overwhelmingly large piece of information in the literature in simplified magnetic phase diagrams compiled from several scientific papers. For more detailed information, the reader should consult the references quoted. The magnetic moment is usually given as the low-temperature saturated moment ~ts and expressed in Bohr magnetons, /~B. The paramagnetic moment, which is calculated from the slope of a 1/g versus Tcurve, is expressed as #off and occasionally as #p (= 2S). A g-factor of g = 2 is then assumed.

186

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

187

2. TX compounds 2.1. X : group III; B 2.1.1. MnB, FeB, CoB

These monoborides crystallize in the orthorhombic FeB (B27) structure; space group Prima, No. 62 (table 1). As an example, fig. 1 shows the ac projection of the FeB structure, where both iron and boron occupy the 4(c) sites (x, 1, z) with x = 0.180, z = 0.125 for Fe, and x = 0.031, z = 0.620 for B (Kiessling 1950). MnB and FeB show ferromagnetic ordering, and data by Lundqvist et al. (1962) and Cadeville (1965) on these compounds are given in table 2. Besides To, the paramagnetic Curie temperature, 0p, the effective number of Bohr magnetons ]~eff with #p = 2S, and the saturation moment #s are given. CoB exhibits diamagnetic properties. CoB was reported to be ferromagnetic by Lundqvist et al. (1962), probably because of contamination by Co2 B (Cadeville 1965). TABLE 1 Crystallographic parameters for some TB compounds. Compound

a (/~)

b (A)

c (/~)

Ref.

MnB FeB CoB

5.560 5.506 5.253

2.977 2.952 3.043

4.145 4.061 3.956

Kiessling (1950) Aronsson (1961) Aronsson (1961)

Fe

B

O ~

° 3 !4

Fig. 1. Crystal structure of FeB (orthorhombic), as projected on the

ac

plane in the Pnma setting.

TABLE 2 Magnetically ordered monoborides. Compound MnB FeB

Tc (K)

0p (K)

fleff(#B)

pp = 2S

Ps (~B)

578 572 598 582

575 600 625 646

2.71 2.70 1.84 2.43

1.89 1.88 1.09 1.63

1.92 1.84 1.12 1.12

Ref. Lundqvist et al. (1962) Cadeville (1965) Lundqvist et al. (1962) Cadeville (1965)

188

O. BECKMANand L. LUNDGREN

From M6ssbauer measurements, Bunzel et al. (1974) find an internal field of 11.8 T for FeB. They conclude that the spins lie close to the ab plane in the Pbnm setting, i.e., the ac plane in Pnma as shown in fig. 1. The M6ssbauer data indicate that the spins deviate about 20 [] from the a axis; the same angle as the Fe-Fe bonds form with the a axis. The structure should be described as canted ferromagnetism. Li and Wang (1989) performed linearized augmented plane-wave band calculations for FeB. The boron 2s a n d 2p bands, well below the Fermi surface, hybridize and form covalent B-B bonds. There is no electron transfer to iron. 2.1.2. Pseudobinary monoborides Cadeville and Meyer (1962) and Cadeville (1965) studied several pseudobinary monoborides (fig.2). (Mn, Fe)B shows a maximum Curie temperature of 789 K at Mno.sFeo.sB. The saturation magnetization decreases linearly from MnB to FeB with 0.8#s per d-electron. In (Fe, Co)B, the Curie temperature and saturation magnetization decreases linearly with 1.12#B per d-electron aiming at Tc = OK for Feo.09Co0.91B. A similar behaviour was observed for (Mn, Co)B. The saturation magnetization decreased linearly to zero for CoB with a slope of 0.96#B per d-electron. Substitution of chromium decreases Tc as well as #s (fig. 2). The latter has a slope of 3,u b per d-electron, a value that also applies to vanadium substitution. 2.2. X: group IV," Si, Ge, Sn Only a few TX compounds with group IV elements are magnetically ordered. Since the type of magnetic order is closely related to the crystal structure, it is convenient to arrange the material according to the structures presented in table 3. Table 4 gives a survey of the magnetically ordered stoichiometric TX compounds of group IV. FeGe exists in three different polymorphs (Richardson 1967a,b). The low-temperature B20 polymorph transforms at about 630°C to the B35 modification, which in

T c (K)

~t s (rt B)

1000.

. 2

500

0

0

CrB

MnB o Curie temp Tc

FeB []

CoB

Sat. morn. ~-s

Fig. 2. Curie temperatureand saturationmomentof pseudobinarymonoborides.

189

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS TABLE 3 TX (X is a group IV element) crystal structures. Compound

Structure

Space-group

FeSi CoSn CoGe

Cubic B20 Hex. B35 Monocl.

P213 P6/mmm C2/m

No 198 No 191 No 12

M=4 M=3 M=8

TABLE 4 Magnetically ordered TX (X is a group IV element) compounds. Compound

Magn. order*

Struct.

a (A)

MnSi (Fe, Co)Si FeGe

H H H AF AF AF

B20 B20 B20 Monocl. B35 B35

4.558

FeSn

b (/~)

c (A)

fl (deg)

TN (K)

Tt (K)

29.5

#s Ref.t (PB) 0.4 [a]

See text 4.700 11.838 5.002 5.300

3.937

4.9336 4.055 4.449

279 103.514 340 411 368

120

1.0 [b] I-c,d] 1.7 I-d] 1.7 l-e]

* Magnetic order: H = helix, AF = antiferromagnetism. References are only given to structural parameters. For other data, see text. "~References: [a] Shirane et al. (1983). [b] Richardson (1967b). [el Different magnetic moments for different lattice sites (Felcher et al. 1983). [d] Richardson (1967a). I-el Nial (1947).

turn transforms at 740°C to the monoclinic CoGe structure. This structure decomposes at 750°C. 2.2.1. Cubic FeSi (B20) structure The cubic FeSi (B20) structure is lacking inversion symmetry, and is, therefore, a good candidate for a long-range magnetic superstructure called a Dzyaloshinskii spiral (Dzyaloshinskii 1964). Nakanishi et al. (1980) and Bak and Jensen (1980) analyzed the cubic FeSi structure and found that a helical spin density wave along the [-100] or [111] direction will appear if the anisotropy energy is small. A helical spin structure, in fact, exists in both MnSi and cubic FeGe, as well as in some ternary (Fe, Co)Si compounds. 2.2.1.1. MnSi. The manganese and silicon atoms occupy the 4(a) site (x, x, x) with x -- 0.138 for Mn and x = 0.845 for Si (Ishikawa et al. 1977a) (fig. 3). Williams et al. (1966) and Wernick et al. (1972) reported MnSi to order magnetically at 30 K. At 1.4 K, the magnetization increases linearly with field up to a saturation value of 0.4#B at 0.62 T. This is significantly smaller than the moment of 1.4#B obtained from/~eff = 2.19#B in the paramagnetic region. Fawcett et al. (1970) measured the thermal expansion and specific heat of MnSi, and found the transition to be of second order with a change in magnetic entropy of Sm = 0.385 J/K tool (however, note the correc-

190

O. BECKMAN and L. LUNDGREN

Mn

0 Fe

Si

• Ge

Fig. 3. Crystal structure of MnSi and FeGe (cubic B20).

tion in the paper by Ishikawa et al. 1977a). From renormalization group theory, Bak and Jensen (1980) predicted the transition to be of first order in the P213 space group. As mentioned above, a theoretical analysis shows that MnSi should have a helical spin structure. This has been confirmed by ESR (Date et al. 1977), by N M R (Motoya et al. 1976, 1978a) and by neutron diffraction experiments. By means of small-angle neutron diffractometry, Ishikawa et al. (1976, 1977a,b) have shown that MnSi has a spiral magnetic structure with a long period of 180 A in the (111> direction below TN=29.5 +0.5 K. In a magnetic field larger than 0.15 T, a conical structure is stabilized with the cone angle close to ferromagnetic alignment at 0.62 T at 1.4 K. Because of the small anisotropy energy, the spiral axis will be aligned parallel to an applied magnetic field for fields larger than 0.4 T. A magnetic phase diagram has been deduced by Kusaka et al. (1976) from ultrasonic attenuation studies and by Ishikawa and Arai (1984) from small-angle neutron scattering (fig. 4). Using polarized

1

B(T)

MnSi para (induced ferro) 0.5 conical para helix 0

1'0

10

"

' T(K) 30

Fig. 4. Magnetic phase diagram of MnSi from Kusaka et al. (1976) and Ishikawa and Arai (1984). Region A is a paramagnetic (or nearly paramagnetic) phase, which penetrates into the ordered phase.

COMPOUNDS OF TRANSITIONELEMENTS WITH NONMETALS

191

neutrons, Shirane et al. (1983) have studied the helicity of the helical spin density wave. In two consecutive papers Tanaka et al. (1985) and Ishida et al. (1985) report investigations of single-crystal MnSi as regards the crystal chirality by convergent-beam electron diffraction, and the helicity of the helical spin density wave by polarized-neutron diffraction. They found a left-handed helical spin density wave in left-handed single crystals indicating a negative sign of the DzyaloshinskiiMoriya interaction. The band structure of ferromagnetic MnSi was calculated by Taillefer et al. (1986), showing good agreement with de Haas-van Alphen (DHVA) measurements. They noted very high cyclotron masses (~ 15too). Conventional Stoner theory gave a very high ordering temperature, which, however, was drastically reduced to a value close to the experimental value when the strong spin fluctuations, characteristic of MnSi, were taken into consideration. Zero-field positive muon spin relaxation (Matsuzaki et al. 1987) and thermoelectric power (Sakurai et al. 1988) studies have been performed on MnSi. 2.2.1.2. FeGe, cubic B20. The cubic polymorph of FeGe shows great similarities with MnSi as regards both crystal and magnetic structure. Iron and germanium occupy the 4(a) site (x, x, x) with x = 0.1352 and 0.8414 for Fe and Ge, respectively (Richardson 1967a), fig. 3. Lundgren et al. (1968, 1970) made magnetization measurements on powder and single crystals of FeGe. They found TN = 280 K. Data in the paramagnetic region gave #eef=2.1#R and a paramagnetic Curie temperature of 295 K. From magnetization and torsion measurements, they proposed a helical spin structure propagating in the [111] direction in zero field. Because of the small anisotropy energy, the helical axis turns parallel to an applied field already at some tens of a millitesla. With increasing magnetic field, the spins align ferromagnetically at about 0.2 T with a saturation moment of 1.0#B. W~ippling and Hfiggstr6m (1968) and Ericsson et al. (1981) confirmed from M6ssbauer measurements a spin structure directed along the [111] direction, in agreement with ESR measurements in the frequency range 3-35 GHz by Haraldson et al. (1978). A Dzyaloshinskii-type magnetic structure was observed by Wilkinson et al. (1976) in small-angle neutron diffraction experiments on powder samples, giving a repeat distance of 700 A. A magnetic field of 0.33 T made the helical spin structure collapse with the spins parallel to the field. Extended small-angle neutron diffraction by Lebech et al. (1989) have confirmed the helical spin ordering according to the theory of Bak and Jensen (1980). Lebech et al. found that cubic FeGe orders magnetically at 278.7 K into a long-range spiral with a period ~ 700 A, which is nearly independent of temperature. The propagating direction is along the [100-1 axis just below TN but changes to [111] with a pronounced hysteresis in the interval 211-245 K. In table 5, we give specific heat data for some B20 compounds, i.e., the coefficient of the linear electron term ~, the coefficient of the Debye T 3 law/~, and the Debye temperature 0 (Marklund et al. 1974). 2.2.1.3. Fe1-tCotSi. The pseudobinary compounds Fel_tCotSi with a cubic B20 structure (fig. 3) form disordered solutions in the whole concentration range. CoSi is

192

O. BECKMAN and L. LUNDGREN TABLE 5 Specific heat data for some TX, B20 compounds. Compound

7 (mJ/mol K 2)

fl (ktJ/mol K 4)

0 (K)

1.37 1.1 10.3

14.2 16.9 62.1

515 487 315

FeSi CoSi FeGe

a diamagnetic semimetal, while FeSi is a semiconductor with a small bandgap (0.05 eV). FeSi is paramagnetic with a broad maximum in susceptibility around 500 K (Jaccarino et al. 1967). The anomaly in susceptibility has been explained by Takahashi and Moriya (1979) and Gel'd et al. (1985) by taking into account the effect of spin fluctuations. As regards the pseudobinary compounds, Beille et al. (1981, 1983) have shown that Fel_tCotSi has a long-period helimagnetic structure in the region 0.05 < t < 0.80 similar to the one in MnSi and FeGe. However, in contradiction to MnSi, a right-handed helix of left-handed chirality was found in a single crystal (Tanaka et al. 1985, Ishida et al. 1985). The saturation magnetic moment and the N6el temperature show a maximum around t = 0.35 (fig. 5). Helical spin resonance and magnetization measurements by Watanabe et al. (1985) show similarities with the results obtained by Date et al. (1977) on MnSi. Motokawa et al. (1987) have made pulsed high-field magnetization measurements, but did not observe any remarkable change in magnetization. Right- or left-handed spin structures have been investigated by Ishimoto et al. (1986) by means of polarized neutrons.

2.2.1.4. Mnl_tCotSi.

Mnl_tCotSi also shows a long-period helimagnetic structure (Beille et al. 1983) for small Co concentrations. The N6el temperature decreases rapidly with increasing cobalt content. N M R and magnetization measurements have been reported by Motoya et al. (1978b).

Tc (K)

ktS (]-tB) -

50 ~

0.3 0.2 0.1

O'

D

0

i

0

FeSi

0'.5

O Curietemp.Tc

t

[] Sat.morn.P~S

CoSi

Fig. 5. Curie temperature and saturation moment of pseudobinary (Fe, Co)Si compounds.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

193

2.2.1.5. Crl_tMntGe. CrGe is paramagnetic with an anomalous peak in the magnetic susceptibility at 45 K (Sato and Sakata 1983), indicating a nearly ferromagnetic metal. Substitution with manganese gives ferromagnetism for t/> 0.09, followed by a mixing with a spin-glass phase for t ~>0.17. For 0.24 ~
)Fe

•

Ge

Fig. 6. Magnetic structure of hexagonal FeGe (B35). At low temperatures, the spins leave the c axis and form a double cone structure as indicated. FeSn has the same type of anitiferromagnetic structure, but the spins are confined to the c planes.

194

o. BECKMANand L. LUNDGREN

at 4.2 K. Within the c planes, the spins are ferromagnetically coupled because of strong positive exchange coupling (Jo = 255 K). Weaker antiferromagnetic coupling between c planes (J1 - - 4 0 K, J2 = -11 K) favours a conical screw structure with a turn angle close to 180° for the c-plane spin components. For the magnetic field parallel to the c axis, pulsed field measurements showed a spin-flip transition at 7.1 T (4.2 K), slightly increasing with temperature. At 4.2 K, the critical field changes with field orientation to 1.4 T for the field perpendicular to the c axis. An additional fieldinduced transition was observed at 4.8 T by magnetoresistance measurements (Stenstr6m and Sundstr6m 1972). Magnetic torque measurements by G/ifvert et al. (1977) showed that the change in anisotropy energy with temperature causes the spins to leave the c axis below 40-50 K. Nazareno et al. (1971) calculated the band structure of FeGe by the nonrelativistic APW method, and Sundstr6m (1972) deduced the Fermi surface. The nesting of the Fermi surface indicated the existence of several spin density wave vectors close to zc = re~c, explaining the conical screw type structure (Beckman et al. 1973). A M6ssbauer study by H/iggstr6m et al. (1975b) gave a hyperfine field of 15.5T at 77 K. The temperature variation of the hyperfine field partly follows the Brillouin functions for S = ½ and S = 1. Close to the N6el temperature, a critical exponent fl = 0.328 was obtained. Forsyth et al. (1978) reported single-crystal neutron-diffraction measurements confirming the double-cone structure below 30K and a cone half angle of 16° at 4.2K. The iron magnetic moment was found to be 1.7#a, in good agreement with the value obtained by Watanabe and Kunitomi (1966). Extended neutron-diffraction studies have been reported by Bernhard et al. (1984, 1988). In zero magnetic field, the collinear c-axis structure changes to the doublecone structure at about 60 K. The cone half angle increases gradually with temperature to 14° at 4.2 K, although there is a pronounced kink at 30 K. The interlayer turn angle of the c-plane spin component, which is almost independent of temperature and magnetic field, is 165.6° corresponding to a repeat distance of ,~ 100 A along the c axis. Based on symmetry analysis, Lebech et al. (1987) predicted a clockwise or anticlockwise triangular ordering of the c-plane spin components as an alternative to the ferromagnetic ordering mentioned above. However, the presently available experimental data do not permit a choice between the different structures. Neutron diffraction in a magnetic field perpendicular to the c axis confirmed the transitions at 1.4 and 4.8 T (4.2 K) (Bernhard et al. 1988). The critical fields decrease with increasing temperature and no field induced transitions were observed above 30 K. At 4.2 K, the cone structure was found to persist up to the maximum available field, 9.4 T. FeSn. Yamaguchi and Watanabe (1967) reported antiferromagnetic ordering below TN= 373 K with the magnetic cell doubled along the c axis and with iron moments of 1.5#a (77K) in the basal plane either in the [100] or in the [210] direction (fig. 6). As in hexagonal FeGe, there is a strong ferromagnetic exchange coupling within the c planes and a weaker antiferromagnetic coupling between the c planes. From STFe M6ssbauer experiments, Trumpy et al. (1970) reported super-

2.2.2.2.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

195

position of two six-line spectra in the ratio 2:1 with hyperfine fields Bhf(Fe) equal to 16.7T and 13.9T (77K). The crystal structure has two Sn positions; one singlefold and one two-fold. The 119Sn measurements gave Bhf(Sn)= 4.9 T (77 K) for the single-fold site and zero field for the two-fold site, TN = 368 K. M6ssbauer and neutron diffraction experiments by Ligenza (1971) indicated a doubling of the magnetic cell also in one a direction. Below TN the spin direction along 1-210] should flip to [100] at 70K. From extensive M6ssbauer measurements, H/iggstr6m et al. (1975a) found that a minimum of six six-line spectra are needed in order to make a fit to the experimental curves. This implies spin directions intermediate between [100] and [210] and a doubling of the magnetic cell along the a axis. However, a more probable solution is to retain the smaller magnetic cell, and assume that the spins have a fan-like distribution in the hexagonal planes (Hfiggstr6m 1989). Muon spin precession in FeSn has been reported by Hartmann and W/ippling (1987). Finally, we give in table 6 specific heat data for some B35 compounds, i.e., the coefficient of the linear electron term 7, the coefficient of the Debye T a law fl, and the Debye temperature 0 (Larsson et al. 1974).

2.2.3. Monoclinic CoGe structure FeGe has three non-equivalent iron sites in the unit cell at the 4(i), 2(a) and 2(c) crystallographic positions. From M6ssbauer experiments, W/ippling et al. (1970) report magnetic ordering at TN = 335 K for the four-fold site and for one of the twofold sites. At 110 K, also the last iron site shows a hyperfine field splitting (fig. 7). Magnetization and M6ssbauer measurements by Malaman et al. (1973) and Max et al. (1974) gave T N = 3 4 2 K and the lower transition at Tt= 122K. Neutrondiffraction data by Felcher et al. (1983) give the following magnetic moments and hyperfine fields at 20K: #i=1.85#R, #a=0.98#B, #c=0.8#B and Bi=20.2T, B, = 12.3 T, Bc = 8.3 T. 2.3. X: group V; P, As, Sb, Bi Among the 3d-transition element compounds with group V nonmetals two crystallographic structures dominate, i.e., the hexagonal NiAs (B81) structure and the closely related orthorhombic MnP (B31) structure (table 7). In the M n P structure both the metal and the nonmetal occupy the four-fold site 4(c) (x, ¼, z) in the Pnma setting. The NiAs structure is shown in fig. 8, and the close relation between the two structures TABLE 6 Specific heat data for some TX, B35 compounds. Compound FeGe FeSn CoSn

y (mJ/molK2)

fl (gJ/molK4)

0 (K)

8.46 10.95 4.57

62 99 73

341 303 299

196

O. B E C K M A N and L. L U N D G R E N B(T)

FeGe, monocl.

20-

...............:::i::i~iiii~i!~!i~i:

0

0

100

200

300

T(K)

400

Fig. 7. The hyperfine fields of iron sites 4(i), 2(a) and 2(c) in monoclinic FeGe as a function of temperature. At low temperatures the M6ssbauer patterns for the 2(a) and 2(c) site show a broadening, indicating a distribution of hyperfine fields (after Felcher et al. 1983 and W/ippling 1990). TABLE 7 TX (X is a g r o u p V element) crystal structures. Structure NiAs MnP

Space-group

Hex. B81 Ortho. B31

P63/mmc Prima

No 194 No 62

M = 2 M = 4

0 Ni •

As

Fig. 8. Crystal structure of the hexagonal NiAs (B81) phase.

is d e m o n s t r a t e d in fig. 9. The NiAs structure is obtained for metal p a r a m e t e r s x = 0, z = ¼ and n o n m e t a l p a r a m e t e r s x = ¼, z = ~z in Prima. C o m p a r e with data for M n A s at r o o m temperature, Mn: x = 0.005, z = 0.22; As: x = 0.22, z = 0.58 (Zieba et al. 1978). We have a d o p t e d the P n m a setting ( H a h n 1983). O t h e r settings are sometimes used in the literature. Generally, the binary T X c o m p o u n d s show a high degree of m u t u a l internal solubility, and a great n u m b e r of ternary and q u a t e r n a r y solid solutions have been

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

CMnP

,o / . . . o / ,

/

•

Mn

o

As

o]

#

-./

197

o~

•

/

°MnP Pnma

0

a

C)

•

3a4

Fig. 9. Relationship between the hexagonal NiAs structure and the orthorhombic MnP structure (dashed lines). The a axis coordinates are given for Mu and As in the Pnma setting. The lattice parameters are related according to: aMnp= CNiAs,bMnv= aNiAs, CMnP= aNiAs~f~.

investigated. Thus, there is an overwhelmingly large amount of papers in the literature, which influences the organization of this section. First, we summarize the magnetically interesting compounds in table 8 with their characteristic data. The compounds are then described under the headings phosphides, arsenides and antiTABLE 8 Magnetically ordered TX (X is a group V element) compounds. Compound

Magn. order?

Struct.

a (A)

b (A)

c (A)

Tc (K)

MnP FeP

F,H H

MnP MnP

5.258 5.191

3.172 3.099

5.918 5.792

291

CrAs MnAs FeAs

H F,H H

MnP MnP(RT) MnP

5.649 5.72 5.442

3.461 3.676 3.373

6.208 6.379 6.028

CrSb MnSb FeSbl ÷x

AF F AF

NiAs NiAs NiAs

4.103 5.463 4.139 5.754 Nonstoichiometric, see text

580

MnBi

F

NiAs

4.285

628

6.113

TN (K) 125

Tt (K)

/~s Comment* (#B)

50 1.3 [a] 0.4 [a]

272 317

1.7 [b,c] <160 3.3 [d,e] 77 0.5 If]

710 ~200

3 [g] 520 3.5 [hi 0.9 [i] 4.0 [ j ]

? Magnetic order: F = ferro, H = helix, AF = antiferro. References are only given to structural parameters. For other data, see text. * Comments: [a] Rundqvist (1962b). [b] Selte et al. (1971), NiAs structure above 1180 K, Ido (1987). [c] First-order transition at TN with 11 K hysteresis. [d] MnP structure data by Wilson and Kasper (1964); NiAs structure at high and low temperatures. [e] First-order transition at Tc with 10 K hysteresis, change to helix at lower temperature with large hysteresis. [f] Selte et aL (1972). [g] Kallel et al. (1974). [hi Pearson (1967). [i] Nonstoichiometric with excess iron, TN dependent on composition. [ j ] Chen (1974).

198

O. B E C K M A N and L. L U N D G R E N

monides. Each subsection starts with the magnetically ordered stoichiometric binary compounds, followed by the pseudobinary mixed-cation compounds. The chapter ends with pseudobinary compounds with mixed anions, grouped according to the cation.

2.3.1. Phosphides Among the monophosphides of the 3d metals, VP crystallizes in the NiAs structure, while CrP, MnP, FeP, and CoP adopt the MnP structure (Rundqvist and Nawapong 1965). TiP and NiP crystallize in separate structures, related to the NiAs structure. Only MnP and FeP have ordered magnetic structures, i.e., low-temperature helical spin ordering, which changes to ferromagnetic order in MnP at higher temperatures. 2.3.1.1. MnP. Figure 10 shows the ac-plane projection of the crystal structure in the Pnma setting. Zero magnetic field. The manganese monophosphide MnP has attracted much interest because of its intricate magnetic behaviour. MnP is ferromagnetic below Tc = 291.5 K (Huber Jr. and Ridgley 1964), with b as the easy axis and c as the hard magnetic axis. The saturation moment was found to be 1.29#B per Mn atom. With the magnetic field in the easy b direction, Terui et al. (1975) determined the critical exponents at Tc = 290.59 K to be/~ = 0.34 _ 0.02, V= 1.29 ___0.05 and 6 = 4.89 _ 0.1. Early neutron-diffraction measurements by Forsyth et al. (1966) and by Felcher (1966) revealed a magnetic phase transition at Tt = 47 K to a helical spin structure, where the spins rotate in the ab plane with a propagation vector of 0.117(2zc/c) in the hard c direction. Fjellvgtg et al. (1984a) reported Tt = 53 -t- 3 K, the propagation

40 @ O

20

@

@ O

'o Mm

b

C

p

Fig. 10. Crystal structure of M n P in Pnma setting projected on the a c plane. The atoms are situated at the levels ¼b and ¼b as indicated above. The structure applies to FeP, CrAs and FeAs as well. The numbers refer to the helical structure in fig. 11.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

199

vector zc=0.116(2rc/c) and ~/helix= 1.45#B at 10K (fig. 11). The spin structure is a double helix with the following phase angles: q~="1,2 =aa,4 = + 20° and ~2,3 = ~4,1 = 0°. The helix is characterized by the phase ¢ and the propagation vector zc. MnP, FeP, CrAs and FeAs have similar crystal structures and double helices. Data are summarized in table 9. Neutron spin wave scattering studies by Tajima et al. (1980) indicate that the ferro-helix transition is a result of small changes in the exchange parameters. Smit (1983) has pointed out that these small changes in connection with the actual values of anisotropy constants give rise to a first-order ferro-helix transition. Polarized neutron experiments by Moon (1982) confirm the magnitude of the saturation magnetic moment, but give a ratio ].,lb/].,l a = 1.091 between the two orthogonal magnetic moments of the helix. This result could be interpreted either as an elliptical spiral or in terms of a distorted circular spiral with a bunching of the moments along the easy b axis. H~ggstrrm et al. (1987) have studied the magnetic structure using the Mrssbauer technique, substituting manganese by 1 at.% 57Fe, whereby the Curie temperature slightly decreased to 285 K. In the helical phase, the Mrssbauer spectrum at 11 K indicated a small hyperfine field modulation in the ab plane in agreement with N M R results by Nagai et al. (1970) on 5s Mn. The hyperfine field is not a priori proportional to the magnetic moment, but the results indicate a distortion of the helix.

|

tl

i

v

~

---_)c

$c

b Fig. 11. Magnetic structure of M n P with a double-helix propagating in the c direction. A similar helical structure exists in FeP, CrAs and FeAs. D a t a for the structures are listed in table 9.

TABLE 9 D a t a for the helix structure in some MnP-type crystals. Compound MnP FeP CrAs FeAs

¢ = a1,2 = a3,4

a2,3 = ~ 4 , 1

z
#s (laB)

+ 20 ° + 176 ° -121° + 154 °

0° -- 140 ° + 184 ° - 86 °

0.116 0.20 0.353 0.375

1.3 0.4 1.7 0.5

200

O. BECKMAN and L. LUNDGREN

A self-consistent APW spin-polarized band calculation was made by Yanase and Hasegawa (1980) and gave a spin moment of 1.2/~B per Mn atom. Magnetic field parallel to the easy b-axis. Huber Jr. and Ridgley (1964) measured the magnetic behaviour in a field along the easy b axis (Pnma). There is a fieldinduced first-order transition from the screw phase to the ferromagnetic phase. The transition field decreases from 0.23 T at liquid helium temperatures to zero at T~= 47K. Field parallel to the intermediate a-axis. Neutron diffraction and magnetization measurements have revealed several transitions between different magnetic structures for the magnetic field parallel to the (magnetically intermediate) a axis in the Pnma setting (Ishikawa et al. 1969, Komatsubara et al. 1969, 1970, and Obara et al. 1980) (fig. 12). At low temperatures, the helix turns to a fan at 0.60T in a first-order transition. The fan transforms to the paramagnetic state at 4.0 T with a saturation moment of 1.33#B per Mn atom. Hiyamizu and Nagamiya (1972) theoretically analyzed the magnetization and the torque measurements by Komatsubara et al. (1965) in terms of second- and fourth-order anisotropy energies and anisotropic exchange energies, ignoring magnetostrictive effects. Shapira et al. (1981) have made extensive studies of the phase diagram, concentrating on the upper triple point, where the fan, ferro and para phases meet with a common tangent. This point is interpreted (Hornreich 1980) as a Lifshitz point (LP) at 121 ___1 K and 1.65 T (fig. 12). The ferro-fan transition is of first order while the ferro-para and fan-para transitions are of second order. Along the modulated fan part of this second-order line, the wave vector q should vary continuously and vanish at the Lifshitz point. This was confirmed by Moon et al. (1981) through neutron diffraction. They observed that the modulation vector q vanished with an exponent fig = 0.49 _ 0.03 approaching the Lifshitz point, which is consistent with the theoretical value of fig = 0.54 (Hornreich et al. 1975). Softening of the spin waves in inelastic B(T) MnP

4

3 ~

1_

para

/

0

~. 0

ferro i 100

• 200

T(K) 300

Fig. 12. Magnetic phase diagram of MnP with the magnetic field parallel to the magnetically intermediate a axis (Prima). LP is a Lifshitz point, see text (after Shapira et al. 1981).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

201

neutron scattering has been studied by Yoshizawa et al. (1985) with further confirmation of a Lifshitz point• From susceptibility measurements, Bindilatti et al. (1989) have determined the critical specific heat exponent ~ to lie between 0.4 and 0.5. A theoretical interpretation of the occurrence of the Lifshitz point has been presented by Yokoi et al. (1984)• Kamigaichi et al. (1968) noted that hydrostatic pressure up to 5 kbar lowered the ferromagnetic transition temperature Tc by 1.5 K/kbar. The effect of uniaxial pressure on Tc and Tt was investigated by Matsumara et al. (1975). Field parallel to the hard c-axis. Figure 13 shows the magnetic phase diagram with the magnetic field parallel to the magnetically hard c axis according to Shapira et al. (1984)• At low temperatures, the magnetic field most probably turns the helix to a cone with the propagation vector parallel to the c axis. At higher fields, the cone is assumed to transform to a fan with the propagation vector still parallel to the c axis. The spins are then oscillating in the bc plane• The cone, fan and ferromagnetic phases meet at a triple point at T ~ 60 K and an applied field of 4.1 T. The fan, ferro- and paramagnetic phases meet at a triple point at T = 121 K and 5.1 T. Most probably, this point is a Lifshitz point in analogy with the configuration of the magnetic field parallel to the intemediate a axis (Shapira et al. 1984). Takase et al. (1979) have reported low-temperature specific heat measurements in a magnetic field for the ferromagnetic, screw and fan phases of MnP. Analysis of the electronic part of the specific heat shows that the d-electrons form fairly narrow B(T) 8

MnP

para

4

2

0 100

200

T(K)

300

Fig. 13. Magnetic phase diagram of MnP with the magnetic field parallel to the hard c axis. LP is a probable Lifshitz point (after Shapira et al. 1984).

202

O. B E C K M A N and L. L U N D G R E N

bands at the Fermi surface. A de Haas-van Alphen effect in MnP has been reported by Ohbayashi et al. (1976).

2.3.1.2. FeP.

Stein and Walmsley (1966) report VP, CrP, FeP, and CoP to be weakly paramagnetic down to 4.2 K. However, using crystals of higher purity, Bellavance et al. (1969) noticed a transition to a helical spin structure around 120 K in FeP. In a neutron-diffraction study, Felcher et al. (1971) found that FeP is magnetically ordered below 125K in a double helix parallel to the c axis (Pnma) similar to MnP with a period at 4.2 K of 29.2 A, ~c = 0.20(2n/c) and #n = 0.4#s (table 9). KalM et al. (1974) have discussed the exchange integrals in a Heisenberg model using a matrix model by Bertaut (1961a,b). The magnetic structure is interpreted in terms of a linear chain model by Westerstrandh et al. (1977) from magnetization and thermal expansion measurements.

2.3.1.3. Pseudobinary phosphides.

Fjellvhg et al. (1984c) have studied polycrystalline samples of M n l - t T t P with T = V, Cr, Fe or Co by magnetic susceptibility and neutron diffraction measurements. In general, the ferromagnetic transition at 291 K for MnP decreases by substitution of other 3d elements for Mn. Helimagnetism is observed at lower temperatures. In some cases, spin-glass regions occur at higher t values, probably due to disordered metal sublattices. Substitution of Mo and W for Mn also decreases the ferromagnetic transition temperature (Fjellv~tg and Kjekshus 1985b). The para-, ferro- and helimagnetic phases then seem to meet in a triple point at t ~ 0.08,

2.3.1.4. Mnl-~CrtP.

Magnetization measurements by Iwata et al. (1979) as well as neutron diffraction and magnetization measurements by Fjellvgtg et al. (1984c, 1985) show that the low-temperature helical phase exists for t ~<0.1, while the high-temperature ferromagnetic phase exists up to t ~ 0.55 with decreasing transition temperature (fig. 14). For t = 0.40, the transition temperature has decreased to 142_ 10 K. The magnetic moment is parallel to the b axis (Pnma) with #s = 0.93/zB.

T(K) 300

p a/

/ oo

200

100 f

helix, h c

hc i

t

CrP

0.5

i

0

MnP

0.5

t

FeP

Fig. 14. Magnetic phase diagram of the ternary c o m p o u n d s C r P - M n P - F e P and Fjellv~g et al. 1984a,c, 1986b).

(after S6nateur et al. 1969

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

203

2.3.1.5. Mnl_~Fe~P. According to Bonnerot et al. (1968), there is a continuous solid solution phase in this pseudobinary system with the MnP structure. The magnetic phase diagram according to S6nateur et al. (1969) is shown in fig. 14. FjellvSg et al. (1984b) find that the para-, ferro- and helimagnetic phases of MnP meet in a triple point slightly above 200K at t ~ 0.12. In the helimagnetic phase, the propagation vector increases and the magnetic moment decreases for increasing iron content. 2.3.1.6. Mnl_~NitP. The MnP-type structure prevails up to t ~ 0.65 (Fjellvgtg and Kjekshus 1984). The Curie temperature of the ferromagnetic phase decreases from Tc = 291 K for MnP to Tc = 234 + 5 K for t = 0.10 with ~ts = 1.01#B. The transition temperature drops towards zero before t = 0.20. The helical hc phase covers only a very narrow range, t < 0.015. 2.3.2. Arsenides As seen in table 8, only CrAs, MnAs and FeAs have ordered magnetic structures. 2.3.2.1. CrAs. CrAs crystallizes in the MnP structure, but undergoes a secondorder phase transition to the NiAs structure at 1180 K (Ido 1987). With decreasing temperature, CrAs shows a first-order transition to a helimagnetic double spiral structure of the MnP type at TN = 261 K with an appreciable change in cell volume (AV/V= 0.021) (Kazama and Watanabe 1971b). The hysteresis region is A T = l l K with TN=272K for increasing temperature (Selte et al. 1971). The double helix of hc type has a magnetic moment of 1.7/~B per Cr atom and a propagation vector of 0.353(2zr/c) in the c direction (table 9). Selte et al. (1971) reports a weak ferromagnetic moment below 250 K. In the paramagnetic region, CrAs follows the Curie-Weiss law only in the highspin configuration in the NiAs phase with np = 2S g 3#B (Ido 1987). In the MnP phase, there is a gradual change with increasing temperature from a low-spin to a high-spin configuration. The band structure of CrAs has been calculated by Podloucky (1984a). 2.3.2.2. MnAs. The NiAs structure dominates at both high and low temperatures, while the MnP structure exists in a limited temperature region from 307-317 to 393 K. The M n P and NiAs structures are energetically very close to each other. The hightemperature MnP-NiAs transition at TD = 394 K in the paramagnetic region is of second order (Zieba et al. 1982), while the low-temperature N i A s - M n P transition is of first order accompanied by a ferro-paramagnetic transition with large hysteresis: decreasing temperature gives Tc,d = 307 K and increasing temperature Tc.i = 317 K (Zieba et al. 1982). Neutron diffraction studies by Zieba et al. (1978) show that the NiAs-type ferromagnetic phase is retained down to 4.2 K, with #~n = 3.31#B at 4.2 K and 2.46#B at 298 K. The magnetization extrapolates above Tc with a Brillouin function for S = 23-to zero at Tc,extr.= 360 K (Zieba et al. 1978) (fig. 15). The situation is complicated by the fact that the magnetic moment per Mn atom of MnAs varies between the low-spin value of S = 1 and the high-spin value of

204

O. BECKMAN and L. LUNDGREN

MnAs o

II~/

I

0

I

100

200 NiAs

300

400

II MnP I

500 T(K) NiAs

Fig. ! 5. Magnetization and inverse susceptibility of MnAs, showing the temperature regions of different NiAs and MnP crystal structures.

S = 2 as a function of pressure, temperature and magnetic field. Mn seems always to take the high-spin value in the NiAs structure, while a low spin or varying spin is characteristic for the MnP structure. In the paramagnetic region of the NiAs phase, i.e., above TD= 394 K, the Curie-Weiss law is obeyed with #e~f= 4.45#B and 0p = 285 K (Pytlik and Zieba 1985), which corresponds to 2S ~ 3.6. Ido (1985) reported a slightly bent 1/Z versus T curve with 2S varying between 3.6 and 3.8. In the ferromagnetic NiAs structure, the magnetic saturation at low temperatures gives a Mn moment of 3.31#B (Zieba et al. 1978) and 3.45#B (Ido 1985) (fig. 15). From NMR studies, Pinjare and Rama Rao (1982) claim the existence of a phase transition at ~ 220 K in connection with either canting of the spins or lowering of the local symmetry. Self-consistent APW band calculations have been reported by Katoh et al. (1986). The small energy difference between the NiAs and MnP structures leads to an intricate interplay as regards the influence of temperature, magnetic field and pressure. Further, the substitution of both anions and cations has a similar effect as the application of hydrostatic pressure. In the following, the effect of magnetic field and pressure on the binary compound MnAs will be discussed. The additional complication of ion substitution will be described under the heading of pseudobinary compounds. Influence of magnetic field and pressure. Figure 16 shows the influence of both magnetic field and pressure on the structural and magnetic phases of MnAs, according to Menyuk et al. (1969) and Zieba et al. (1987). Obviously, the pressure tends to stabilize the MnP-type structure in the low-spin state, while the magnetic field stabilizes the NiAs-type high-spin structure (Date et al. 1983). A dominating feature of the pressure diagram is the very broad hysteresis region between the two structures at low temperatures. In zero applied pressure, the NiAs ferromagnetic structure is retained to the lowest temperatures (Zieba et al. 1978), but an applied pressure induces an irreversible transition to the MnP structure, which prevails also after releasing the pressure (Andresen et al. 1984). The NiAs structure can then only be restored after heating the sample above 160 K. At pressures higher than ~4.3 kbar, the MnP structure dominates below room temperature. There is a transition from

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

205

T(K)

~

500 NiAs,para

nAs

MnP, para 300 NiAs,ferro 200

-

) Hysteresisr e g i ~

100

MnP,ha ~

-

~ i

I

l0 5 B(T)

0

MnP, ha

I

I

I

|

1

2

3

4

I

I

5 6 7 pressure(kbar)

Fig. 16. Influence of magnetic field and pressure on the magnetic and crystal structures of MnAs (after Menyuk et al. 1969 and Zieba et al. 1987). To indicates the phase transition between NiAs and MnP structures in the paramagnetic region and TN the N6el temperature. Ts is a transition between two different helical structures.

paramagnetism to a helical structure TN~ 230 K. The helical structure is of the double spiral type ha, similar to the structure observed in MnP, with the propagation vector z = 0.125(2~a*) at 12.6kbar along the orthorhombic a axis (Andresen et al. 1984). At lower temperatures (Ts~80 to 140K), there is a change in the spiral structure in analogy with the effect of phosphorus substitution (Zieba et al. 1987). A chemical substitution simulates the same effect as an applied hydrostatic pressure, which is clearly demonstrated for MnAs. Within the 3d element series there is a gradual reduction in the metallic radius from Ti to Ni. In MnAs thus Ti, V, and Cr are expected to produce a negative pressure effect. However, only Ti substitution simulates a negative pressure with stabilization of the NiAs structure. A positive pressure effect with stabilization of the MnP structure is noticed for substitution by V, Cr, Fe, Co, and Ni (Selte et al. 1977). Anion substitution acts in the expected way. Thus, P increases the chemical pressure, stabilizing the MnP structure, while Sb stabilizes the NiAs structure through negative chemical pressure (Fjellv~g et al. 1986a). As shown in fig. 16, a magnetic field stabilizes the NiAs structure, thus simulating a negative chemical pressure. Zieba et al. (1982) and Pytlik and Zieba (1985) report a limited region of the orthorhombic, paramagnetic, phase in the (T, B) phase diagram. The region has a phase boundary of second-order transition from To (B = 0) to a tricritical point at 370 _ 10 K and 9 _ 0.1 T. From this point, the phase boundary is a first-order transition line down to zero field at Tc = 307 and 317 K.

206

O. BECKMAN and L. LUNDGREN

2.3.2.3. FeAs. FeAs has essentially an MnP-type structure. Below a N6el temperature of 77 + 1 K, there is a double-helix magnetic structure with the axis parallel to the c axis and a propagation vector of 0.375(2r~c*) similar to MnP (table 9). The magnetic moment is 0.5 ___0.1/~B per Fe-atom at 12 K (Selte et al. 1972). The band structure of FeAs has been calculated by Podloucky (1984a).

2.3.3. Pseudobinary arsenides Figure 17 shows the magnetic structures of the arsenides VAs-CrAs-MnAs-FeAs, including pseudobinary compounds.

2.3.3.1. (V,, Cr)As, (Ti, Cr)As.

VAs and CrAs are completely soluble in each other with the MnP-type structure (Selte et al. 1975a). The CrAs-rich samples undergo a transition to the NiAs structure at high temperatures, like CrAs. The helimagnetic phase, he, of CrAs with TN= 261 K (on cooling) extends only to 5 at.% VAs where TN= 240 K (on cooling). The transition is of first order with a pronounced hysteresis. The propagation vector of the double helix stays almost constant; rc = 0.360(2nc*) for 5 at.% VAs compared to zc = 0.353(2rcc*) for CrAs at 80 K. Fjellvgtg and Kjekshus (1985a) report a similar behaviour for the (Ti, Cr)As system. The helimagnetic structure disappears at 10 at.% TiAs. Then the propagation vector has increased slightly to ~ = 0.396(2nc*), and the magnetic moment of the Cr atom has decreased to #s = 1.21#B. The transition temperature To in the paramagnetic region between the NiAs- and MnP-type structures decreases rapidly from 1180 K for CrAs approaching zero for 50 at.% Ti.

T(K)

\ 1000.

\

NiAs para I I ! I I I I I I I /two

P 500

\

MnP para

I I phases t I

MnP 0 VAs

CrAs

,4 hi jhc MnAs

"~

bc

FeAs

Fig. 17. Phase diagram of the pseudobinary compounds VAs-CrAs-MnAs-FeAs. For CrAs-MnAs, see also fig. 18.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

207

2.3.3.2. Mnl_tCrtAs. The complicated phase diagram of these pseudobinary compounds is shown in figs. 17 and 18. The high-temperature NiAs structure transforms to the MnP structure at temperatures ranging from 1180 K (CrAs) to 393 K (MnAs) (Ido 1987, Kazama and Watanabe 1971a). The Curie-Weiss law is obeyed only in the NiAs structure with a magnetic moment that corresponds to the average spin of Cr and Mn atoms (Ido 1987). An anomalous susceptibility behaviour in the MnP structure is caused by a continuous high-spin to low-spin transition (Kazama and Watanabe 1971a, Wrhl and B/irner 1980). Ordered magnetic structures of high complexity appearing at lower temperatures are sketched in fig. 18 as reported by Fjellv~g and Kjekshus (1985c). The details of the diagram will be given below for Mnl _tCrtAs. (i) NiAs, ferromagnetic phase. The first-order NiAs (ferro) to MnP (paramagnetic) transition with a temperature hysteresis of 10K extends up to t = 0.08, while the NiAs, ferromagnetic region, extends to t = 0.05 at about 220 K. The region returns to t = 0 at 160 K; see MnAs. (ii) MnP, helix, h a to MnP, paramagnetic transition. In the composition range, 0.05 ~ 0.88 because of the first-order character of the transition, and ends at TN= 261K and 272K for CrAs (t = 1). (iv) MnP (helix, h,) to MnP (ho) transition. This first-order transition is accompanied by a hysteresis, ending at zero temperature for t ~ 0.385. This phase boundary is a continuous extension of the phase boundary under (ii), while the second-order T(K)

~NiAs I 400 -

par~ MaP,para

300 - ~ R

NiAs ferro

l"

200 100 0 CrAs

....

! .... 0.5 t MnAs

Fig. 18. Phase diagram of Cr~Mn1-tAs (after Fjellv~g and Kjekshus 1985c).

208

O. BECKMANand L. LUNDGREN

boundary, (iii), between hc and paramagnetism meets under an angle at the triple point M. The composition Mno.6aCro.aTAS has been subject to detailed thermal, magnetic and structural studies by Komada et al. (1987) and Fjellv~tg et al. (1988a). A temperature sweep includes the M n P structure with paramagnetism, ha and hc helices as well as the high-temperature NiAs phase. For T = 160 K, they find zc = 0.243(2nc*), ~bl.2=-147 °, # h = 1.30#B, and for T = 130K; za=O.O67(2na*), t~1,2=45 °, flu = 1.30#a. The pressure-induced transition from a helix to a ferromagnet in Mno.615 Cro.aas As has been studied by neutron diffraction (Andresen e t al. 1986b).

2.3.3.3. Mn~_tTi~As. Magnetization measurements by Ido et al. (1983) and Ido (1985) show that the temperature interval of the orthorhombic MnP type region in MnAs decreases for increasing titanium substitution ending at T = 345 K for t = 0.2. The ferromagnetic transition temperature has a minimum of Tc = 345 K for t = 0.2. Tc then decreases towards Tc ~ 120K at t---0.7. The transition is of first order for t ~<0.1. 2.3.3.4. Mn~_~FetAs. According to Selte et al. (1974a), the ferromagnetic NiAs structure exists only in a narrow region close to MnAs. The Mn-rich phase (0.01 < t < 0.12) has the M n P structure with a helimagnetic ordering below the N6el temperature, which varies from TN = 180 +_ 3 K for t = 0.03 to 206 ___1 K for t = 0.10 (fig. 17). On the Fe-rich side, the double-helix magnetic ordering in pure FeAs extends only to t ~ 0.98. In the range 0.65 ~
COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

209

T(K) 500

[ MnAs 1-xPx

NiAs,para

400 MnP, para

300

200 ~

MnP,ha - -

100t

~

0

0.05

M

n

X

P

,

0.10

ferro

0.15

Fig. 19. Phase diagram of the pseudobinary compounds MnAsl-xP~ on the MnAs-rich side. TDindicates the crystallographic transition from the MnP to the NiAs phase, Tci and Ted the first-order transition from the paramagnetic MnP phase to the ferromagnetic NiAs phase.

between the spirals (compare figs. 10 and 11 for a helix parallel to the c axis). The low temperature h'a structure has the following data: z~ = 0.087(2na*) with /th = 1.50 ___10#B and a phase difference ~bl,4 = 39 + 8 degrees between the spirals. The intermediate ferromagnetic phase has #f = 1.37 _+ 0.08#B with the spins parallel to the b axis. Labban et al. (1987) measured the specific heat for the composition t = 0.12. Strong contributions are observed from the TN and To transitions as well as from a dilational effect coupled to the low- to high-spin conversion between these transitions. The magnetic Tsl and TS2 transitions gave only small contributions, however. The low- to high-spin anomaly has been studied by measurements of the heat capacity and in the paramagnetic range by diffuse neutron scattering (Fjellvfig et al. 1987, Andresen et al. 1986a).

2.3.4.3. FeAs~_xP~. Selte et al. (1974b) reported complete solubility. Helimagnetism was observed only close to FeP. For x = 0.90, the N6el temperature is TN = 96 + 5 K. Other parameters at 4.2K are: #Fe = 0.42 _+ 0.02/~B, Zc= 0.254(2rCC*) and q51,2 = 155 + 5°. The absence of helimagnetism for the other compositions is assumed to be coupled to the relative size of the different exchange parameters in the structure.

2.3.4.4. Mn~_tCrtAsl_xP~,.

Fjellv~g et al. (1988b) have made extensive structural and magnetic studies of this complex pseudobinary system with a discussion of low- to high-spin conversion.

2.3.4.5. CrAs~_xSbx.

CrAs has a double helix in the MnP crystal structure and CrSb an antiferromagnetic structure with the NiAs structure. The pseudobinary system has been investigated by Kallel et al. (1974) and by Suzuki and Ido (1986) as

210

O. B E C K M A N and L. L U N D G R E N

1000

T(K)

~

CrAs 1-xSb x TD

500

MnP

\

\

para

IN//"

>-% MnP,h c

0

~ 0

CrAs

,

~ x

\ ~

/Tt ! . . . . 0.5

CrSb

Fig. 20. Phase diagram of the pseudobinary c o m p o u n d s CrAsl _~Sbx according to Suzuki and Ido (1986). TD indicates the phase transition between the NiAs and the M n P crystal structures in the paramagnetic state. T~ is the transition to a helical structure in the M n P phase and on the CrSb side to an antiferromagnetic phase. Tt indicates a first-order transition within the magnetically ordered states, observed for the compositions x = 0.6 and 0.7.

is sketched in fig. 20. Magnetic properties on the CrAs-rich side have been investigated by Kamigaki et al. (1987). Pressure effects have been studied by Kaneko et al. (1977) and by Yoshida et al. (1980).

2.3.5. Antimonides, including MnBi Kjekshus and Walseth (1969) have studied the nonstoichiometry (T1 +tSb) of the antimonides of Cr, Fe, Co and Ni, which all crystallize in the NiAs structure, fig. 8. For the Co and Ni compounds, the NiAs phase exists for both positive and negative t values, while FeSb shows a single phase for positive t only. 2.3.5.1. CrSb. CrSb is a collinear antiferromagnet with a N6el temperature of 713 K (Hirone et al. 1956). Neutron-diffraction measurements by Snow (1952) indicated that the spins are parallel to the c axis with an antiferromagnetic coupling between neighbouring ferromagnetic c planes. The magnetic moment was determined to be 3.0#B per Cr atom at zero temperature, indicating Cr 3+ ions (S = 2) (Takei et al. 1963). The temperature dependence of the magnetization does not follow the Brillouin function of S = ~, however, and the zero temperature powder susceptibility is unusually low. There is also an anomaly in the magnetic specific heat close to the transition. Abe et al. (1984) discussed these observations on the basis of the molecular-field theory by taking into account an anisotropic strain dependence of the exchange interactions as an extension of the theory by Bean and Rodbell (1962). 2.3.5.2. MnSb. MnSb is a ferromagnet with Tc = 588 K (Kjekshus and Pearson 1964). From magnetization measurements, Ido (1985) reported a linear Curie-Weiss behaviour from Tc up to about 850 K, which gives 0p = 592 K and a magnetic moment per Mn atom of/tMn = 3.18pB. Above the melting point of about 1050 K, 0v = - 2 6 3 K

COMPOUNDS OF TRANSITION ELEMENTSWITH NONMETALS

211

and #~n = 4.00#3 as expected for the high-spin state of Mn a ÷ (3d4). The saturation moment in the ferromagnetic regime is ~3.5#B at 77K with the magnetization perpendicular to the c axis (Takei et al. 1963). The spins are parallel to the c axis just below the Curie point, but turn to the c plane at 520 K. Markandeyulu and Rama Rao (1987) measured the magnetocrystalline anisotropy above 300 K in single crystals using FMR. At 300K, they find K~ = - 1 3 0 k J m -3 and K2 = 7 5 k J m -a. Both anisotropy constants pass through zero and change sign at the spin-flip transition of 520K. At 564K, the values are K1 = 9.8kJm -a and K2 = - 4 . 4 k J m -a. In a study of the pseudobinary system (Cr, Mn)Sb, Reimers et al. (1982) report Tc = 573 K for MnSb with a saturation moment of 3.5#B at zero kelvin. Neutron-diffraction studies of Mnl +tSb with excess Mn content have been reported by Watanabe et al. (1972). Podloucky (1984b) calculated the electronic structure of MnSb for the NiAs structure as well as a fictitious B31 (MnP) structure. Katoh et al. (1986) have performed self-consistent APW band calculations of MnSb.

2.3.5.3. Fel+tSb. Stoichiometric FeSb has not one single phase. Alloys quenched from 800°C show the NiAs structure for (0.08 ~
212

O. BECKMANand L. LUNDGREN

Neutron-diffraction measurements by Andresen et al. (1967) on the LTP show a large hysteresis in the first-order transition with 633 and 613 K for increasing and decreasing temperature, respectively. The Mn atom magnetic moment is 4.5 _ 0.2#B at 4.2 K in the ferromagnetic structure. Coehoorn and de Groot (1985) have made self-consistent spin-polarized band structure calculations of the low-temperature phase. The ferromagnetic properties of MnBi are of great practical interest (Wohlfarth 1959, 1985). A large uniaxial anisotropy at room temperature with a large fine particle coercivity is of interest for permanent magnets. A large magneto-optic coefficient makes MnBi attractive as a recording medium. The magnetic c axis anisotropy at higher temperatures decreases with temperature and changes sign at 90 K, whereby the spins turn to a direction in the hexagonal plane (Stutius et al. 1974).

2.3.6. Pseudobinary antimonides 2.3.6.1. Mnl_tTitSb. Mnl_tTitSb has a NiAs structure. Tc decreases from 580K for MnSb towards 150 K at t = 0.7, the highest titanium concentration with magnetic ordering (Ido 1985). The saturation moment of 3.5#B per manganese atom at 77 K stays approximately constant. 2.3.6.2. Crl_tCotSb. The N6el temperature of 713K for CrSb decreases slowly with increasing Co content with a possible change in spin arrangement around t ,,~ 0.5. CoSb is paramagnetic (Ido 1985). 2.3.6.3. Mn1_tCrtSb. CrSb is a c-axis antiferromagnet and MnSb a ferromagnet with spins perpendicular to the c axis below 520 K. The complicated phase diagram has been studied by Takei et al. (1963) and by Reimers et al. (1982). Several ordered magnetic phases are found, some of which are sketched in fig. 21. The different phases meet in critical points, which are discussed by Fishman and Aharony (1979). 2.4. X: group VI; S, Se, Te Only chromium and manganese compounds show magnetic ordering as is listed in table 10.

2.4.1. CrS Neutron diffraction experiments indicate antiferromagnetic ordering with TN= 460 K and a magnetic moment of 3.4/~B at 85 K (Sparks and Komoto 1964). 2.4.2. CrSe In the paramagnetic region, Lotgering and Gorter (1957) determined #off= 4.50 _+0.06#B. From neutron-diffraction measurements, Corliss et al. (1961) coneluded that the three spins in each basal plane form an 'umbrella' like array (fig. 22). Individual moments alternate in sign along lines parallel to the c axis. The magnetic cell is three times the crystallographic cell with a = aox/3 and c = Co. The component of the chromium moment perpendicular to the c axis is 2.90#B. With an assumed

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

213

600

T(K)

M n l_tCrtSb

400U

Y

0 MnSb

"--"

0.5

t

CrSb

Fig. 21. Phase diagram of the pseudobinary compounds Mnl _tCrtSb according to Takei et al. (1963) and Reimers et al. (1982). Vertical arrows indicate a spin direction parallel to the c axis, horizontal arrows indicate spins perpendicular to the c axis. A similar phase diagram is found for pseudobinary compounds between ferromagnetic CrTe and antiferromagnetic CrSb (Takei et al. 1966). TABLE 10 Magnetically ordered TX (X is a group VI element) compounds. Comp.

Magn. order*

Struct.

CrS CrSe CrTe MnS MnSe MnTe

AF AF F AF AF AF

Monocl. NiAs NiAs NaC1 NiAs

a (A)

b (A)

c (A)

3.826 5.913 6.089 3.699 6.072 Nonstoichiometric See text 4.148

6.710

fl (deg)

Tc (K)

101.6

TN (K)

#~ (PB)

Commentt

460 280

3.4 3.6

la] [-b] l-c]

~ 330 173 307

I-d] [e]

* Magnetic order: F = ferro, AF = antiferro. References are only given to structural parameters. For other data, see text. t Comments: [a] Jellinek (1957). [b] Kjekshus and Jamison (1971). [c] Deficient in Cr, Chevreton et al. (1963a), see section 5, Cr2Te 3 etc. l-d] Hulliger (1968). [e] Pearson (1967), NaC1 structure above 1353 K. ' s p i n - o n l y ' v a l u e of 4/~B, the spins are tilted ~ 4 5 ° f r o m the c axis. M a k o v e t s k i i a n d S h a k h l e v i c h (1980) a n d Y u r i et al. (1987) r e p o r t e d T N = 2 8 0 K a n d a c h r o m i u m m o m e n t of 3.6 ___0.1#a.

2.4.3. Crl_tTe S t o i c h i o m e t r i c C r T e does n o t exist in e q u i l i b r i u m at r o o m t e m p e r a t u r e ( A n d r e s e n 1970). D e p e n d i n g o n the p r e p a r a t i o n , C r v a c a n c i e s will be either r a n d o m l y d i s t r i b u t e d i n a N i A s - t y p e s t r u c t u r e o r o r d e r e d i n s u p e r s t r u c t u r e s of different s y m m e t r i e s

214

O. BECKMAN and L. LUNDGREN

C) Cr

• Se

Fig. 22. Magnetic structure of CrSe according to Corliss et al. (1961). The chemical cell is drawn with heavy lines. The magnetic cell containing six formula units is marked with dashed lines in the c planes. In order to simplifythe figure, spins are only indicated for the six chromium atoms in the magnetic cell. Selenium atoms are marked in the chemical cell only.

(Chevreton 1964). A large variation in Curie temperatures (327 to 360 K) reported in the literature (Lotgering and Gorter 1957) is probably dependent on the chemical composition. See further section 5, where the stoichiometric compounds CrzTe3, Cr3Te4, CrsTe6 are treated.

2.4.4. MnS MnS has been studied by Corliss et al. (1956) using neutron diffraction. There are three polymorphic forms: a cubic NaC1 structure, a cubic zinc-blende structure and a hexagonal wurtzite structure. They are antiferromagnets with the N6el temperature in the region 75-150 K. 2.4.5. MnTe The structure of this antiferromagnet consists of ferromagnetic sheets in c planes with antiferromagnetic coupling along the c axis. The N6el temperature of TN = 307 K increases with pressure at a rate of 2.6 K / k b a r (Ozawa et al. 1966). 2.4.6. Vl_tCrtSe Yuri et al. (1987) reported a magnetic susceptibility for V1-,CrtSe, which is similar to CrSe for 0.05 ~< t ~<0.83. The magnetic transition temperature decreases from TN = 280 K (CrSe) to TN ,~ 205 K for t = 0.10. 2.4.7. CrAsl_xSex Kjekshus and Jamison (1971) discussed the transition from the M n P structure of CrAs to the NiAs structure of CrSe. The M n P structure prevails in the region 0 ~<x ~< 0.4, with a smooth transition to the NiAs structure, which exists for 0.5 ~<x ~< 1. There is an indication of an increase in N6el temperature towards the centre of the pseudobinary region, although the transition is uncertain around x ,,~ 0.5.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

215

In the paramagnetic region, #efe shows a minimum of 3.7#B at x = 0.5 compared to #elf = 3.9#B for x = 0.2 and #elf = 4.3#B for CrSe.

2.4.8. CrTel_xSe~ Lotgering and Gorter (1957) reported a linear decrease in Curie temperature with x from Tc = 320 K for CrTe towards Tc ~ 180 K for x = 0.5. Transition to the antiferromagnetic structure of CrSe is not reported. 2.4.9. CrTej_xSbx CrTe is a ferromagnet and CrSb an antiferromagnet. As pointed out by Takei et al. (1966), the pseudobinary system then shows great similarities as regards the magnetic structure with the (Mn, Cr)Sb ternary system (fig. 21), which also crystallizes in the NiAs structure. The appearance of canted spins is in good agreement with a double exchange model by de Gennes (1960). 3.

T 2X

and TT'X compounds

3.1. X: group III," B Magnetically ordered T2B and TT'B compounds exhibit ferromagnetic properties. They crystallize in the tetragonal CuAlz-type structure, with space group Prima. The chemical unit cell contains four formula units. In this structure, the B-B distances exceed 2.1 A and the B atoms are classified as 'isolated'. As shown in fig. 23, the B atoms have eight close T or T' neighbours forming an Archimedian antiprism and straight boron chains run through these antiprisms. Based on single-crystal

@

•

©

• O

•

@

B:

c 3c 4.4

Fe:

0

Fe:

Fig. 23. Crystal structure of Fe2B (tetragonal CuA12 type) as projected on the tetragonal c plane. The unit cell contains four formula units.

216

0. BECKMAN and L. LUNDGREN

refinements, Aronsson et al. (1968) have reported the interatomic distances for several borides with the CuAl2-type structure. Crystallographic and magnetic data for T2 B compounds (Cadeville 1965) are given in table 11. The variation of Tc and #s with electron concentration in (TI-tT~)2B compounds is shown in fig. 24. Results from the extensive magnetic measurements on TI_tT~B (Lundqvist et al. 1962) and (T1-tT~)2 B compounds (Cadeville and Meyer 1962, Cadeville 1965, Cadeville and Daniel 1966) revealed a great similarity between the magnetic m o m e n t versus electron concentration curves for these borides and the Slater-Pauling curve for the same transition metal alloys. This similarity led to the assumption that the boron atoms can be regarded as interstitial atoms, dissolved in a metallic lattice, and TABLE 11 Crystallographic and magnetic data for T 2 B compounds. Compound Cr2B Mn2B Fe2B Co2B Ni2 B

a (A)

c (A)

5.180 5.148 5.109 5.016 4.990

4.310 4.208 4.249 4.220 4.245

Tc (K)

#s (#B/f.u.)

0p (K)

#orr

Zg (at 295 K)

(#Blf.u.)

(cgs)*

1013 428

3.84 1.56

1068 459

4.36 3.32

6.6 x

10 - 6

0.87 x 10-6

*Z [SI] = 4~p Zg[cgs], where p is given in cgs units.

~2

M.-~ /

...... 7 - - - - - ~ k \

,

,o_N,\ \

0

1000

Ti-Fe

cr-Fo 7 /

v.o 7

,.

/

0 M n 2B

....

, Fe 2 B

\ \ Fo_~,

\ Co 2B

Ni2B

Fig. 24. Saturation magnetic moment (#s) and Curie temperature (Tc) versus electron concentration for (T, T')2B compounds (after Cadeville 1965).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

217

one boron atom transfers 1.7-1.8 electrons to the metal 3d band. This accounts for the observed shift of the Slater-Pauling curve as a whole to lower electron concentration for the borides. This idea found support in low-temperature specific heat measurements (Kuentzler and Meyer 1968, Kuentzler 1970a,b, Hanson et al. 1971). Highresolution bremsstrahlung measurements by Kohm and Merz (1974) also implied charge transfer to the metal in T2 B compounds. Recently, Li and Wang (1989) calculated the energy bands and the density of states for Fe2 B and FeB. Contrary to the previous assumption, the B 2s and 2p states are well below the Fermi energy and no electron transfer was found to occur between Fe and B atoms in these compounds. The calculated density of states agrees with photoelectron spectroscopy measurements (Joyner and Willis 1981), and Li and Wang also infer that their results are in agreement with the X-ray and neutrondiffraction investigation on charge and spin distribution by Brown and Cox (1971) and Perkins and Brown (1974), although these authors interpret their results differently. It was also found by Li and Wang that the Fe 3d states in Fe2B are similar to that in metallic Fe.

3.1.1. (Fel-tCot)2B The Fe-B crystallographic phase diagram has recently been re-examined by Kneller and Khan (1987). Fe2B is a simple ferromagnet with Tc = 1013 K and #s = 3.84#B per formula unit. Early M6ssbauer spectroscopy measurements by Shinjo et al. (1964b) gave a hyperfine field of 24.2 T, in good agreement with later investigations. Torque measurements on single crystals by Iga et al. (1966) showed that the easy axis of magnetization lies in the basal plane for T < 518K and is directed along the c axis for T > 524K. In the temperature range 518-524 K there is a gradual rotation of the direction of the easy axis. The iron sites in Fez B are crystallographically equivalent. The sites are also magnetically equivalent if the easy axis of magnetization is parallel to the e axis, but non-equivalent if the easy axis is perpendicular to the c axis. Due to the anisotropic hyperfine interactions, the M6ssbauer spectrum reflects the direction of the easy axis, and measurements by Murphy and Hershkowitz (1973) verified the occurrence of a spin rotation with temperature in Fez B. From M6ssbauer studies by Takfics et al. (1975), the concentration and temperature dependencies of the direction of the easy magnetization axis were determined for the system Fe2 B-Co2 B and shown in fig. 25. The result for Co2B, i.e., that the spins are located in the basal plane, is at variance with N M R results by Kasaya et al. (1973) and torque data by Iga (1966). A discrepancy which may be attributed to the details of the sample preparation in combination with a weak anisotropy. Combining M6ssbauer (Vincze et al. 1974, Takfics et al. 1975) and N M R (Cadeville and Vincze 1975) measurements, a marked change of the Co moment in (Fel -~Cot)2 B with t was observed. The Co moment changes from 0.8#a in pure Co2B to about 1.3#B on the iron-rich side, whereas the Fe magnetic moment stays nearly constant for all values of t. The experiments implied that the electron states at the iron sites are well localized.

218

O. BECKMAN and L. LUNDGREN Tc (K) 1000 800 600 400 200 o Fe2B

Co2B

Fig. 25. Magnetic phase diagram of the system Fe2B-Co2B, showing the direction of the easy axis of magnetization (after Tak~icset al. 1975).

3.1.2. (Fe1_tMn,)eB M6ssbauer and magnetic measurements on (Fel_tMnr)2B compounds have been reported by Schaafsma et al. (1980). Assuming a proportionality between the iron hyperfine field and iron magnetic moment, it was found that the Mn moment is small. Ferromagnetism in this system disappears at t ~ 0.6. 3.1.3. (Nil_tTt)eB Iga (1970) has investigated the magnetocrystalline anisotropy in (Fel _tNit)zB compounds. Cadeville et al. (1967) have investigated the electric and magnetic properties of (Nil -tTt)2 B borides. The magnetic properties of transition-metal borides have been reviewed by Buschow (1977). 3.2. X: group 1V; Si, Ge, Sn Magnetically ordered TT'X compounds with group IV nonmetals commonly crystallize in the two related crystal structures given in table 12. TT'X (X = Si or Ge) compounds, especially those with T = Mn, show interesting magnetic properties. These compounds have the orthorhombic TiNiSi-type structure at room temperature, but generally transforms to the hexagonal ordered Ni2 In-type structure at higher temperatures. This crystallographic transformation, which is TABLE 12 Crystal structure of TT'X (X is a group IV element)compounds. Structure TiNiSi-type Ni2In-type

Orth. C23 Hex. B82

Space group Pnma P63/mmc

No 62 No 194

M=4 M=2

C O M P O U N D S O F TRANSITION ELEMENTS WITH NONMETALS

219

characterized as diffusionless, is of first order and the transition shows large thermal hysteresis. The transition is found to be strongly dependent on the details of the sample preparation. The TiNiSi structure is analogous to ordered Co2 P and belongs to the space group Pnma, with the atoms ordered on three inequivalent 4(c) positions. The T atom with fewer d-electrons generally occupies a pyramidal site and the other T atom a tetrahedral site (see section 3.3, X: group V). As pointed out by Fjellv~g and Andresen (1985), the TiNiSi structure can be considered to be formed from the MnP-type structure by filling the bipyramidal holes in this structure. The phase transformations hexagonal Nizln to orthorhombic TiNiSi and hexagonal NiAs to orthorhombic MnP have been discussed in the literature (see, e.g., Jeitschko 1975). The great similarity between the crystal structures of these compounds is also reflected in similarities in magnetic structures. Several of these phases exhibit a complicated antiferromagnetic structure at low temperatures and have an antiferro-ferromagnetic transition at elevated temperatures; e.g., MnP, Mn(As, P), high-pressure MnAs, compositions close to MnCoP and MnRhAs. A common observation is that the magnetic transition is sensitive to details of the sample preparation and the specific ordering of the metal atoms may have a profound influence on the long-range antiferromagnetic screw structures. Figure 26 shows the magnetic phase diagrams for several quarternary silicide and germanide systems. Crystallographic (room temperature) and magnetic data are given in table 13. 3.2.1. MnCoSi

The magnetic properties of MnCoSi are sensitive to details of the sample preparation, and reported crystallographic data differs, especially as regards the length of the a axis. X-ray, magnetization and specific heat measurements by Johnson and Frederick

500 "1-

\~ I

400 -

I I I I

300 2O0

I

i~l

F

iF + AF

p

~

p

I

v'x

j

TiNiSi

omplex ~ AF

F

I

100 0 MnNiSi

MnNiGe

MnCoGe

MnCoSi

MnNiSi

Fig. 26. Magnetic phase diagrams for some quaternary silicide and germanide systems.

220

O. BECKMAN and L. LUNDGREN TABLE 13 Magnetically ordered TT'X compounds; X = Si, Ge or Sn.

Compound

MnCoSi MnNiSi MnCoGe MnNiGe MnRhSi MnFeGe FeNiGe FeCoGe MnCoSn FeNiSn FeCoSn CoNiSn

Struct.

TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi Ni2In Niz In Ni2 In NizIn Nizln Niz In Ni2In

a (A) 5.857 5.901 5.954 6.048 6.193 4.112 4.039 4.002 4.280 4.134 4.175 4.120

b (A) 3.688 3.606 3.816 3.753 3.797

c (A) 6.856 6.902 7.055 7.094 7.145 5.242 5.103 5.035 5.394 5.190 5.278 5.208

TN (K)

Tc (K)

360 622 337 356 367 228 770 370

~s

Mn

T'

2.6 2.6 2.9 2.3

0.4 0 0.9 0

2.3

1.1 0.70* 2.50* 2.21" 1.37'

2.07* 0.70*

*p~ is given in #B/f.u.

(1973) on a sample with lattice parameters a = 5.8498(12)A, b = 3.6894(20)A and c = 6.8513(8)A revealed a noncollinear antiferromagnetic structure with TN= 381 K. Neutron diffraction and magnetization measurements by Binczycka et al. (1976) [on a sample with lattice parameters a = 5.819(7)A, b = 3.691(4)A and c = 6.853(9)A] indicated a first-order antiferro-ferromagnetic transition at Tt = 207 K and a Curie temperature of Tc ~ 400 K. At r o o m temperature, the magnetic moments were determined to be 2.2#B (Mn) and 0.3/~B (Co) and to form a collinear ferromagnetic structure in which the moments are parallel to the b axis. At 80 K, the moments form a complex helical structure, with the screw axis parallel to the c axis. In a subsequent investigation by Niziol et al. (1978), the large sensitivity of the magnetic structure to sample preparation was emphasized. Magnetization and neutron diffraction measurements on a sample with lattice parameters a = 5.8571A, b = 3.6881A and c = 6.8556 A gave, below 360 K, a double-spiral magnetic structure of M n P type with the (temperature dependent) wave vector propagating along the c axis. At 4.2 K, the moments were found to be 2.6#B (Mn) and 0.4#B (Co). Above 360 K, the authors suggested ferromagnetic order up to 390 K, implied by a strong field dependence of the magnetization. However, this could not be conclusively verified by the neutrondiffraction measurements. The existence of a temperature range where ferromagnetism occurs in pure MnCoSi is, therefore, doubtful, but ferromagnetism is readily induced by small amounts of alloying substitutions and presumably also by pressure. High-field magnetization measurements by Niziol et al. (1979, 1980) indicated a field-induced transition from a helix (H) to an intermediate antiferromagnetic structure, IAr, (denoted fan structure by the authors) at temperatures below about 250 K. At 4.2 K, the second-order H-IAv transition occurs at about 4 T and the first-order IAF -- ferromagnetic transition is estimated to occur at 20-25 T. At temperatures above 250 K, the helix transforms directly to a ferromagnetic structure with applied fields.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

221

The crystallographic transformation from the TiNiSi-type to the Ni2In-type structure occurs at about 1180 K, with a thermal hysteresis of about 25 K. 3.2.2. MnNiGe Magnetization and neutron-diffraction measurements by Szytula et al. (1976), Bazela et al. (1976) and Niziol et al. (1982) gave a spiral magnetic structure below TN= 346K. At 293 K, the spiral axis lies along the a axis [simple spiral; z = 0.230(5) x 2na*] and the magnetic moments were determined to be 2.34(5)#B (Mn) and 0#B (Ni). From the observation of a change of the intensity of the 000 + sattelite reflections at Tt = 185 K, and a minor jump of the propagation vector close to that temperature, the authors suggest a change in the spiral structure from a simple spiral above Tt to a cycloidal spiral below Tt, where the spiral axis lies in the bc plane making an angle of 45 ° with the b axis. In a later neutron-diffraction study by Fjellvgtg and Andresen (1985), a spiral magnetic structure with propagation vector = 0.228(5) x 2ha* was found below TN= 356 K. Fjellv~g and Andresen also found an abrupt change in the intensity of the 000+__ sattelite, but at Tt = 260K. In contradiction to the earlier reports, this was attributed to the formation of a double spiral structure, but with no change in the propagation vector. The intensity decrease of the 000___ sattelite below Tt was explained by introducing a phase angle of 50° between two sets of spirals running through the four Mn atoms of the unit cell of the MnNiGe structure. At 12 K, • = 0.185 x 2ha* and #(Mn)= 2.3#B. This structure is similar to the ha-type double spiral structure found in MnP-type compounds (see section 2.3; X: group V). The discrepancy with the previous neutron-diffraction investigation was attributed to differences in sample preparation, which easily affects the details of the long-range screw structures. The influence of hydrostatic pressure on the magnetic and crystallographic transitions have been investigated by Anzai and Ozawa (1978). As shown in fig. 27, the first-order crystallographic TiNiSi-Ni2In transition temperature To decreases with increasing pressure, whereas the magnetic helix-paramagnetic transition temperature TN increases with pressure. To and TN coincide in a tricritical point T~ritat a pressure of about Pcrit 3 kbar, somewhat dependent on heating and cooling cycles (indicated by the shaded area in the figure). At pressures above Petit, the two transitions coincide and the temperature of the first-order transitions decreases with increasing pressure. This demonstrates a collaborating phase transition in which two distinctly different physical properties can cause either a simultaneous transition or two separate ones. The authors interpreted these transitions in MnNiGe within a phenomenological picture, based on a Landau-like free-energy theory. The crystal and magnetic properties of (Mnl_tTit)NiGe have been studied by Bazela and Szytula (1981) using X-ray, neutron-diffraction and magnetic susceptibility measurements. The TiNiSi-type crystal structure is retained for all t. For t < 0.1, a helical structure is found. For 0.15 < t < 0.65, a noncollinear magnetic structure is observed. TiNiGe is a Pauli paramagnet. -=-

3.2.3. Mn(COl_tNit)Si Magnetization measurements by Johnson and Frederick (1973) showed that MnNiSi is a simple ferromagnet with Tc = 622 K and with an average moment per formula

222

O. BECKMAN and L. LUNDGREN Tc (K) 40O

380

360

340

320 0

2

4 p (kbar)

6

8

Fig. 27. Change of the magnetic and crystallographic transition temperatures TN and TD with hydrostatic pressure for MnNiGe (after Anzai and Ozawa 1978). The shaded area indicates the region of thermal hysteresis.

unit of 2.62/~B. Tc decreases and the average magnetic moment increases as Co is substituted for Ni. At about 90% Co, antiferromagnetic properties are found at temperatures below about 150 K (see the magnetic phase diagram in fig. 26). Extrapolation of magnetization data indicate an average moment of 3.2#B for MnCoSi, in close agreement with 3.0/zB found from neutron-diffraction measurements (see MnCoSi). Neutron-diffraction measurement by Niziol et al. (1980) on MnNiSi gave #s = 2.7(3)#R with the moments parallel to the b axis.

3.2.4. MnCo(Sil_xGex) The magnetic properties of the MnCoSi 1_xGex solid solution have been investigated by Niziol et al. (1980) (see the magnetic phase diagram in fig. 26). For x < 0.4, complex antiferromagnetic structures exist at low temperatures with a transition to a collinear ferromagnetic structure at higher temperatures. For x > 0.5, only ferromagnetic properties are found. The average magnetic moment per formula unit increases from about 3#B for MnCoSi to 4/~B for MnCoGe. Neutron diffraction measurements by Niziol et al. (1982) gave 2.9#B (Mn) and 0.9/~B (Co) for MnCoGe. The pressure dependence of the magnetic transition temperatures of the MnCo(Ge, Si) system have been investigated by Niziol et al. (1989) using ACsusceptibility measurements. 3.2.5. Mn(Col_,NitJ Ge The crystallographic and magnetic properties of Mn(COl _tNit)Ge have been investigated by Niziol et al. (1981, 1982). These compounds have the orthorhombic TiNiSitype structure at low temperature and transform at 400-500K to the NizIn-type structure. Neutron-diffraction measurements show a preference in site occupancy. The Mn atoms occupy pyramidal sites, whereas the Co and Ni atoms are randomly

COMPOUNDS OF TRANSITIONELEMENTSWITH NONMETALS

223

arranged within their sublattice. For compounds with t > 0.5, a variety of helical and ferromagnetic cone structures are proposed (schematically represented by complex AF in fig. 26). For t < 0.5, collinear ferromagnetic structures are found. In these compounds, only the Mn and Co atoms carry a magnetic moment. The influence of hydrostatic pressure on the crystallographic and magnetic transitions have been investigated by Niziol et al. (1983) and Zach et al. (1984). The results are similar to those obtained by Anzai and Ozawa (1978) on MnNiGe (see above), but compounds with t = 0.3, 0.5 and 0.6 exhibit a second tricritical point, where a decoupling of the magnetic and crystallographic phase transitions occur. The nature of the triple points are discussed within a Landau-type theory.

3.2.6. MnNi(Si l_xGe:,) The magnetic properties of MnNi(Si l_xGe~) compounds have been investigated by Szytula et al. (1980) and Bazela et al. (1981a) (see the magnetic phase diagram in fig. 26). For x >0.3, complex antiferromagnetic structures are reported. For 0.5 ~<x ~<0.7, a ferromagnetic component is observed. In the case of x = 0.5, the magnetic moment components of Mn are #~ = 3.0(2)ktB, #z = 0.7(4)#R and ~total 3.07(23)#B. For 0 ~<x ~<0.4, ferromagnetism is found. For MnNiSi, the Mn moment is # = 2.7(3)#B and directed parallel to the b axis. The pressure dependence of the magnetic transitions of MnNi(Si, Ge) compounds have been investigated by Duraj et al. (1988). =

3.2.7. MnRhSi Johnson and Frederick (1973) reported antiferromagnetism with TN = 367K for MnRho.9s Si. The Mn atoms occupy the pyramidal site. 3.2.8. Compounds with hexagonal Ni2 In-type structure In table 13, crystallographic and magnetic data for compounds with the hexagonal Ni 2 In-type crystal structure at all temperatures are summarized. The room-temperature crystallographic data and the values of saturation magnetic moment per formula unit (at 4.2 K and a field of 1.8 T) are (except for MnFeGe) from Buschow et al. (1983), who investigated the magneto-optical properties of metallic ferromagnetic materials. The Curie temperatures for FeNiGe and FeCoGe are from Castelliz (1953). Szytula et al. (1981) investigated the crystallographic and magnetic properties of MnCoGe, FeCoGe, MnFeGe and MnNiGe using X-ray, neutron-diffraction, magnetometric and M6ssbauer-effect methods. It was found that MnCoGe and FeCoGe have collinear ferromagnetic structures while MnFeGe has a complex, noncollinear structure. The magnetic moments are localized on Mn and Fe atoms and lie in the basal plane. For MnFeGe, the values of the magnetic moments are 2.3#B (Mn) and 1.1#B (Fe). The authors reported a Curie temperature of Tc = 228 K, whereas Castelliz (1953) found Tc = 390K. The M6ssbauer spectra for MnFeGe indicate more than two Zeeman splittings which implies the presence of vacancies. The values of the magnetic moments and effective magnetic fields are close to those observed in the

224

O. B E C K M A N and L. L U N D G R E N

closely related T5 X3 compounds. The weak moment for FeNiGe possibly indicates the absence of magnetic ordering. 3.2.9. MnCoSn Neutron diffraction, magnetization and M6ssbauer effect measurements have been performed by Bazela et al. (1981b). Below Tc = 145 K, a canted spin arrangement is found, where the moments make an angle of 34 ° with the c axis. 3.3. X: group V; P, As, Sb TT'X compounds containing phosphides and arsenides represent a class of compounds with unusually interesting magnetic properties. These compounds crystallize almost exclusively in the three different forms given in table 14. The structural aspects of the metal-rich phosphides and arsenides have been described in detail by Fruchart (1982). As emphasized by Fruchart, the basic building block common to these structures is the rhombohedral TT'X subcell shown in fig. 28. These subcells are stacked on top of each other, forming channels lined along the tetragonal a axis, the hexagonal c axis or the orthorhombic b axis. One of the metal atoms, T~, occupies a tetrahedral site and the other atom, T~, a pyramidal site. It is generally found that the T atom with fewer 3d electrons preferentially occupies the pyramidal site. With increasing atomic number of the T atom and/or decreasing atomic number of the X atom, the crystal structure generally changes in the sequence tetragonal(T)-hexagonal(H)-orthorhombic(O). The magnetic moment of the TH atom is always larger than the moment of the T~ atom. The Mn~i moment is large, ranging from about 2.5#a to 4#B, whereas the moments of the Co and Ni atoms are small, or zero. Figure 29 shows the magnetic moment per formula unit for the T2 X and TT'X compounds with group V metalloids. The solid lines are data for the corresponding (TI-tT;)2X systems with the same crystal structure. Only arsenide compounds crystallize in the tetragonal structure. These compounds are always antiferromagnetic and a maximum of the magnetic moment occurs at electron concentrations equal to that of Mn2As. Noteworthy in fig. 29 is the occurrence of weak magnetic ordering at compositions close to CrNiAs (CrNiP) and at CrFeAs (CrFeP, Mn2 P). Band structure calculations have recently been performed on T2P and TT'P compounds (Ishida et al. 1987, Eriksson et al. 1988, S. Fujii et al. 1988), and the calculated values of the magnetic moments are found to be in good agreement with experimental data. It is also observed that the P atoms transfer electrons to the TABLE 14 Crystal structures for TT'X compounds; X = P, As or Sb. Structure Fe2As-type Fe2P-type Co2 P-type

Tetr. C38 Hex. C22 Orth. C23

Space group P4/nmm P~2m Pnma

N o 129 No 189 No 62

M = 2 M = 3 M = 4

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

225

a Fe2P

0

FeoI

Fe II

Po

2

Co 2 P

a

Fe2As a

cIb 3b

T

el

Co I 0

COlI 0-,.-

P

•

0_..

•

o

0

Fe I

Fe II

As

0

0-,-

o

2

Fig. 28. Crystal structures of hexagonal Fez P, orthorhombic Co2 P and tetragonal Fe2 As. Top left comer shows the rhombohedral TT'X subcell, which is the basic building block common to these structures.

T atoms and the electron transfer is larger to the T~ atom, due to a stronger mixing between the p bands of the P atom with the d bands of the T~ atom. These calculations are not in agreement with the energy band scheme for transition-metal pnictides as proposed early by Goodenough (1973). In this scheme, it is assumed that the X atom p bands are filled up by electron transfer from the T atom 4s bands (which are empty) and 3d bands.

3.3.1. Phosphides Crystallographic and magnetic data for T2P and TT'P compounds are given in table 15.

3.3.1.1. Fe2P. The crystal structure of FezP was determined by Rundqvist and Jellinek (1959) and accurately refined by Carlsson et al. (1973). At 297 K, the unitcell dimensions are: a = 5.8675(2)A, e = 3.4581(2)/~.

226

O. BECKMANand L. LUNDGREN ~t 0xB/f.u. )

xMn2 As

6

I

x

I 5

Te~agonal

•

Hexagonal

[]

Orthorhombic

t I

4

A

A MnFeAs

CrMnA~r/ MnFe(P,As) @ ~'X Fe2As

3VMnAs/

//

MnFeP []

A /~nCoP

2 ~,s Cr 2As 1

Mn P 2Q

CrFeAs0 0

CrFeP rl

Cr 2

Mn2

/ / ]

/. ~

•

~eNiP

ECrNiP~ V I

Fe 2

~

"N~ I

C°2

"

Ni2

Fig. 29. Saturation magnetic moment (#s) versus electron concentrationfor T2X and TT'X compounds (X = P or As). Solid lines represent data for (TI-,T;)2X compounds having the same crystal structure.

Fez P displays rich magnetic properties. A critical balance between ferro- and antiferromagnetic interactions in this compound results in a great sensitivity of the magnetic properties to the external parameters pressure, concentration of alloying additions, temperature and magnetic field. Fea P is basically ferromagnetic but, due to the extreme sensitivity of the phase transition to the presence of vacancies and impurity atoms, early reports showed large discrepancies as regards transition temperature and the nature of the transition. Furthermore, the large magnetocrystalline anisotropy precluded an accurate determination of the saturation moment from measurements on polycrystalline samples. The saturation moment is otherwise not sensitive to small deviations from the ideal Fez P formula. The main properties of pure FezP of ideal stoichiometry can be summarized as is done in the following paragraphs. Mrssbauer spectroscopic studies (Wiippling et al. 1974, 1975) as well as magnetic measurements on single crystals (Fujii et al. 1977, Lundgren et al. 1978, Andersson et al. 1978) showed a first-order ferro-paramagnetic transition at 216K, with a thermal hysteresis of the transition of about 0.7 K. At the transition, the hyperfine fields drop from about half of their saturation values (11.4 T for Fel and 18.0 T for Fen) to zero. The transition is accompanied by a discontinuous change in the dimensions of the hexagonal unit cell with a decrease in the a-axis of 0.06-0.07% and an increase of the c-axis of 0.08% for increasing temperatures (i.e., a volume change of AV/V= -0.05%). The temperature dependence of the lattice parameters is shown in fig. 30, indicating large magnetoelastic effects. As indicated by the curves in the figure, the

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

227

TABLE 15 Crystallographic (after Fruchart 1982) and magnetic data for T2 P and TT'P compounds. Comp.

Struct.

a (h)

b (/~)

c (/~)

Cr2P CrMnP CrFeP CrCoP CrNiP Mn2 P

Hd Hd O O O H

6.332 6.200 5.826 5.765 5.789 6.08

10.399 10.473 3.565 3.552 3.532

3.299 6.693 6.650 6.682 6.807 3.459

MnFeP

O

5.953

3.567

6.739

MnCoP

O

5.947

3.503

6.725

MnNiP Fe2 P

H H

5.937 5.865

FeCoP FeNiP Co2P CoNiP Ni2 P

O H O H H

5.749 5.843 5.646 5.833 5.865

3.524 3.456 3.534 3.513

6.597 3.433 6.608 3.347 3.387

#s (PB)

0.01" 0.83* Mn~ Mnil 0 ~ 0.84 Fel Mnii 0.5 2.6 Coi Mnlt 0.65 2.55

Fel 1

TN (K)

Tc (K)

265 146

Ref.? Para Para 1-1] Para [2, 3, 4]

103

[5,6]

265

[7, 8]

Fen 2 1.85" 1.0"

583

I-2,9]

570

1-1o]

216 430 95

See text I-2] 1-2,11] Para Para Para

* Ps is given in #B/f.u., H = hexagonal, Hd = pseudohexagonal, O = orthorhombic. t References: [1] H~iggstr6m et al. (1986a); M6ssbauer spectroscopy. [2] Fruchart et al. (1969); magnetic susceptibility, M6ssbauer spectroscopy. 1-3] Iwata et al. (1981); magnetic susceptibility. [4] Nylund et al. (1972); magnetic susceptibility. 1-5] Yessik (1968); neutron scattering. 1-6] Grandjean et al. (1977); specific heat. [7] Suzuki et al. (1973); neutron scattering, 125 K. 1-8] Sj6str6m et al. (1987); M6ssbauer spectroscopy. [9] Radhakrishna et al. (1987); neutron scattering. 1-10] Okamoto et al. (1981); magnetic susceptibility on single crystals. [11] Fujii et al. (1978); magnetic susceptibility on single crystals.

magnetoelastic effects are suppressed if sufficient amount of Ni or Mn are substituted in Fe2P. Substitution of Ni results in 'stable' ferromagnetic properties, whereas substitution of Mn gives antiferromagnetism at low temperature. The pressure (p) dependence of the transition is AT/Ap = - 5 K/kbar (see below). The transition changes from first to second order in applied fields (B) above 0.07 T and increases by about AT/AB = 25 K/T in fields up to 4 T. Specific heat measurements (fig. 31; Beckman et al. 1982) gave an entropy change at the transition of AS = 0.02R, which is in agreement with Clapeyrons equation: AT/Ap = AV/AS. The very small entropy change at the transition as well as no indication of magnetic excitations in the specific heat are characteristic for delocalized d-electrons and an itinerant electron model should be used (see, e.g., Moriya and Usami 1977, Moriya 1985, Wohlfarth 1979, 1986).

228

O. BECKMAN and L. LUNDGREN

T.

©

~

~

Fe2P

©

©

©

> ~t "-d

0

I

I

I

I

100

200

300

400

I

L

500 T(K)

Fig. 30. Temperature dependence of the a and c parameters for FezP as well as of the a parameter for Fe2P compounds with substitutions of Ni or Mn (after Lundgren 1977, 1978).

C (J/mole K)

I

lOO

(a)

8o

6o 40 /

20

// /

.100

260

C (J/mote K)

,-,.

100 ; 80

,,,," _-

215

.- "'_'.-

216

300 T(K)

l

..........

217

Co)

;

FezP \ "'_.'_--

218

.....

219

-

2:20 T-(K)

Fig. 31. (a) Temperature dependence of the specific heat of Fe2P. (b) Enlarged plot of the specific heat around Tc. Chain curve: estimated background (after Beckman et al. 1982).

COMPOUNDS OF TRANSITIONELEMENTS WITH NONMETALS

229

Magnetization measurements on single crystals (Fujii et al. 1977, Lundgren et al. 1978) show that the spins are directed along the hexagonal c-axis with an exceedingly high uniaxial anisotropy. The saturation moment is 2.92#B per formula unit and the anisotropy field 6.5 T, equivalent to a uniaxial anisotropy energy of 2.5 x 106 J m -3 Neutron-diffraction results on powdered samples at 77 K (Scheerlinck and Legrand 1978) gave moments of 0.69/~B and 2.31/~n for Fez and Fen, respectively. In contrast, a single-crystal polarized neutron-diffraction study (Fujii et al. 1979a), at the same temperature, gave 0.92#B and 1.70#B. The magnetic form factor of Fei was found to be close to that of a free iron atom, while that of Feii was found to be close to that of Fe 4 + ion. The total magnetic moment determined from this single-crystal measurement is about 10% smaller than the value obtained from magnetization measurements. The electronic structure of T2 P (T = Mn, Fe or Ni) has been calculated by Ishida et al. (1987) using KKR and LMTO methods within the framework of the LSD approximation. The calculations indicate that Fe2 P is ferromagnetic and the values of the magnetic moment for Fez, Fen, P~ and Pn found to be 0.89#B, 2.24#B, -0.07#B and -0.06/~B by the KKR method and 0.76#B, 2.3 l pB, -0.09#B and -0.08#R by the LMTO method. These results agree well with self-consistent spin-polarized electronic structure calculations by Eriksson et al. (1988), using the LMTO-method, where 0.92#B and 2.03#B are found for the two iron sites. Fe2P has an orthorhombic structure at high temperatures (900°C, 80kbar; Srnateur et al. 1976). Electronic structure calculations of orthorhombic ferromagnetic Fe2P by S. Fujii et al. (1988) gave 3.02pB per formula unit and 0.86#B, 2.19#B and -0.03#B for Fei, Fen and P, respectively. At temperatures above Tc, the susceptibility deviates markedly from a CurieWeiss behaviour and high-temperature measurements (Krumbiigel-Nylund 1974, Krumbfigel-Nylund et al. 1974, W/ippling et al. 1985, Chenevier et al. 1989) gave a paramagnetic Curie temperature of about 470 K, i.e., more than twice the value of the transition temperature, which implies strong short-range order above Tc. Komura et al. (1980, 1983) have studied the magnetic excitations at temperatures above 77 K. They found that the spin wave energies of magnons propagating along (001) are much larger than those in the basal plane. It was inferred that one-dimensional ferromagnetic chains along (001) persist well above the transition temperature. From elastic and inelastic neutron scattering (H. Fujii et al. 1988), it was shown that giant short-range order exists at temperatures up to T ~ 3Tc. Polarized neutron scattering investigations by Wilkinson et al. (1989) revealed spin correlations up to a distance of 12/~ at temperatures up to at least T ~ 3.7Tc. However, from transverse field #SR measurements (W/ippling et al. 1985) no magnetic correlations could be found at a life time longer than 10 -1° s. Effects of pressure and substitutions of B, Si and As. The magnetic properties of Fe2 P are sensitive to pressure, with pronounced anisotropy. The transition temperature Tc decreases with hydrostatic pressure, but bifurcates at about 5 kbar as shown in fig. 32. In the temperature regime indicated by the shaded area in the figure, the magnetization curves (Kadomatsu et al. 1985) show double metamagnetic transitions. In the limit of zero pressure, AT/Ap has been reported to be - 3 . 5 K/kbar (Fujii

230

O. B E C K M A N a n d L. L U N D G R E N

T (K) 300

(a) 200

T (K) 300

T (K) 300

200

200

100

100

Fe2P Tc

T

100

(c) (Mnl_tFet)2P] % _

! 0 20

15 10 5 Pressure (kbar)

0

0 0.06

0.04

t

0.02

0

0 0.94

I 0.96

t

I 0.98

Fig. 32. (a) (T, p) d i a g r a m for F e 2 P (after K a d o m a t s u et al. 1985). (b) (T, t) d i a g r a m for F e 2 _ t P (after L u n d g r e n et al. 1978). (c) (T, t) d i a g r a m for ( M n l - t F e t ) 2 P (after Fujii et al. 1982).

et al. 1977), - 4 . 0 K / k b a r (Goodenough et al. 1973) and - 5 . 4 K / k b a r (Fujiwara et al. 1980). Due to an anisotropic compressibility [Aa/a=-2.5 x 10 -4 and Ac/c = -1.5 × 10 -4 per kbar at room temperature (Rundqvist 1980)] the c/a ratio increases with hydrostatic pressure. Uniaxial stress experiments by Fujiwara et al. (1982) revealed anisotropic effects. Pressure applied along the a axis gives AT/Ap=-6.4K/kbar, whereas pressure applied along the c axis gives AT/Ap = 7.8 K/kbar, which is in accordance with results by Lundgren (1977, 1978), who found that a tensile stress of 108 N/m 2 along the c axis decreases the transition temperature with 8 K. Small substitutions of B, Si or As result in an increase of the a parameter and a decrease of the c parameter. The transition temperature increases rapidly with nonmetal substitution. Some crystallographic and magnetic data are summarized in table 16. A crystallographic hexagonal-orthorhombic transformation occurs for both Si and As substitutions (Jernberg et al. 1984, Lundgren 1977, 1978). The pressure effects have been discussed on the basis of a pair-interaction model (see, e.g., Kadomatsu et al. 1985). It was argued that the exchange interactions between the iron sites I and I, sites I and II, and sites II and II are strongly antiferromagnetic, strongly ferromagnetic and weakly antiferromagnetic, respectively. With an increase of the c/a ratio, the antiferromagnetic I - I interaction in the basal plane becomes stronger than the ferromagnetic I - I I interaction, which runs zigzag along the c-axis. This results in a decrease of Tc, in agreement with pressure data. From a somewhat modified viewpoint (Lundgren et al. 1980), it appears that an increase of the a parameter and/or a decrease of the c parameter gives rise to an increase of Tc. A larger emphasis is put on the variation of the a parameter since both the a parameter and the volume show a similar change at the transition. It is found that the variation of Tc with pressure, stress and nonmetal substitutions is well correlated to the parameter (Aa/a - Ac/2c). This is shown in fig. 33, where the pressure axis has been scaled using room temperature compressibility data. The good correlation between Tc and lattice parameters indicate that the change in electron concentration with X atom substitutions only has a minor influence on the ordering temperature.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

231

TABLE 16 Crystallographic and magnetic data for some Fe2(P, X) compounds. Compound Fe2P Fe2Po.gAsoA Fe2Po.sAso. 2 Fez Po.7Aso.a Fe2 Po.4Aso.6* Fe2 Po.96Bo.o4 Fe2 Po.92Bo.o8 Fez Po.9Sio.1 (Eeo.97Cuo.o3)2P

a (A)

c (A)

Tc (K)

#s (~B/f.u.)

5.8675 5.928 5.976 6.020 6.125 5.8974 5.9163 5.9212 5.8778

3.4581 3.438 3.425 3.418 3.418 3.4099 3.3695 3.4226 3.4517

217 358 411 443 470 350 450 370 265

2.94 2.99 3.03 3.07 3.05 3.04 3.14

Ref.* [1,2] [3,4,5] [3,4,5] [3,4,5] [3,4,5] [5,6] [5,6] [7] [8]

* This compound is orthorhombic below 220 K. "~References: [1] Fujii et al. (1977). [5] Lundgren (1977, 1978). [2] Lundgren et al. (1978). [6] Chandra et al. (1980). [3] Roger (1970). [7] Jernberg et al. (1984). [4] Catalano et al. (1973). [8] Andersson et al. (1978).

Tc(K)

8%B n

400

Para

300

~ ~ o B F e 2 P ~ ~k / ~ 3%Cu

200

100 AF1 0

1

Ferrrro I

0 ~ 0' 20~ 10

0

~

s

10%Si

i

0.1 Aa/a-0.5Ac/c (%)

I

0.2

p(kbar)

Fig. 33. Magnetic ordering temperature versus the parameter (Aa/a- 0.5Ac/c) for some Fez(P, X) compounds, where Aa and Ac are the differences from the a and c values of pure Fez P. Included is also the pressure dependence of the ordering temperature for Fe2P, where the pressure axis has been scaled using room-temperature compressibility data (after Lundgren et al. 1980, Kadomatsu et al. 1985).

3.3.1.2. Fee-tP. Accurately defined nonstoichiometric Fe 2 P in polycrystalline form can only be obtained by rapid quenching from high temperatures (Carlsson et al. 1973). The lattice contracts uniformly with vacancies and with a relative change in volume of about 0.1% for At = 0.01. M6ssbauer spectroscopic studies by W/ippling et al. (1975) show that the vacancies are predominantly found on site II. Initially, the transition temperature decreases with 1 K for At = 0.001, and for t > 0.03 the ordered magnetic state seems to change into a metamagnetic state, which is indicated by the shaded area in fig. 32. The local deformations of the crystal lattice caused by the vacancies result in large hysteresis effects of the magnetization curves. Zvada et al. (1988) have also studied the magnetic properties on nonstoichiometric samples.

232

O. BECKMAN and L. LUNDGREN

The great similarity between the magnetic phase diagrams for 'pressure on Fe2P', 'nonstoichiometric Fe2 P' and 'Mn substitutions in Fe2 P' is emphasized.

3.3.1.3. (Cr~-~Fet)eP. Only minute substitutions of Cr in Fe2P impose antiferromagnetism. M6ssbauer and magnetic susceptibility measurements by Dolia et al. (1988) show that only 1% Cr induces antiferromagnetism with a reduction of the transition temperature to 150 from 216 K in pure Fe2 P. Further substitutions of Cr reduces the transition temperature at a much slower rate. 3.3.1.4. CrFeP. M6ssbauer spectroscopic studies (H/iggstr6m et al. 1986a) indicated antiferromagnetic behaviour with a Nrel temperature of 265 K. The saturation magnetic hyperfine field at the Fe nuclei is only 1.0 T. 3.3.1.5. (Mnl-tFet)2P. This system has been studied extensively (Fruchart et al. 1969, Roger 1970, Nagase et al. 1973, Fujii et al. 1982, Srivastava et al. 1987, Chenevier et al. 1987, 1989). The main magnetic phase diagram is shown in fig. 34. According to Srivastava et al. (1987), the system crystallizes with the hexagonal structure for t~>0.76 and t~<0.30 and with the orthorhombic structure for 0.32 < t < 0.74. Manganese substitutes preferentially for iron on site II in both structures. Depending on thermal treatment it is, however, possible to synthesize compounds in the compositional range 0.35 ~
Hex

Orth

Hex

Orth P

4O0

-P

P

200

TN AF 0 Mn2P

~,

AF

AF

F I Fe2P

I

0 Co 2 P

Fig. 34. Magnetic phase diagrams of the systems Mn2P-Fe2P and Fe2P-Co2P (after Fruchart et al. 1969, Srivastava et al. 1987).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

233

authors for a t = 0.97 compound at 77 K indicated an incommensurate screw antiferromagnet propagating along the (110) direction in the reciprocal lattice with a period of 79 A. For t < 0.97, antiferromagnetic properties are found. The Hall resistivity of (Mnl-tFe02P mixed crystals has been measured by Fieber et al. (1988) for temperatures 4.2K ~< T~< 300K and magnetic fields B ~<7T. Using magnetization data, the normal and anomalous contributions could be separated. Anisotropic skew scattering is proposed to be the main source of the anomalous contribution and two kinds of free carriers n, p contribute to the normal Hall effect. Tc and electron concentration appeared to be correlated and suggested the presence of a positive magnetic coupling via the conduction electrons.

3.3.1.6. MnFeP. This compound has the orthorhombic Co2P-type structure at room temperature, but transforms to the hexagonal Fe2P structure above 1473 K (Chenevier et al. 1987). Neutron diffraction measurements by Suzuki et al. (1973) on the orthorhombic phase gave an antiferromagnetic structure with magnetic moments 0.5#B (Fei) and 2.6#B (Mnn) at 125 K. M6ssbauer spectroscopy studies (Sjrstrrm et al. 1987) indicated magnetic ordering below 265(5)K. Below 170 K, the 57Fe spectra revealed a remarkable distribution of hyperfine fields. It was inferred that this distribution may arise from a helical type magnetic structure with a modulation of the spins. 3.3.1.7. MneP. Neutron diffraction measurements by Yessik (1968) indicated that the magnetic structure can be described as a spin modulation commensurate with the lattice below the ordering temperature TN= 103 K. The Mn~ atoms were found to have no significant moment and z-3 of the Mnn atoms have a magnetic moment of 0.84#B. Mrssbauer spectroscopy studies by H/iggstrrm et al. (1986b) show that 57Fe substitutes for Mn~ in Mn2 P. The magnetic moment for all the Fe atoms are the same and are estimated to be 0.63#B. A magnetic triangular substructure for Mn~ was proposed. In a recent neutron diffraction investigation by Bacmann et al. (1990), all moments were found to be located in the hexagonal c-plane. The same spin configuration for the Mnn moments as proposed by Yessik (1968) was obtained, but with a value of the magnetic moment three times larger. It was also found that the Mni moments form a triangular configuration, in accordance with the results from Mrssbauer studies by H/iggstrrm et al. (1986b). No value of the Mn~ moment was reported. The specific heat has been determined by Grandjean et al. (1977) from 5 to 350 K. A small peak in the specific heat correlated with antiferromagnetic ordering was found at 102.5(5) K. The magnetic entropy was calculated to be 9.4 J K - 1tool- 1 and the electronic specific heat constant 7 = 24 mJ K - 2 mol- 1 3.3.1.8. (Fe1-,Cot)eP. This system has a hexagonal structure for t < 0.16 and an orthorhombic structure for t > 0.16. As shown in fig. 34 (data from Fruchart et al. 1969), Tc increases rapidly with t to about 440 K at t = 0.16. The saturation moment

234

O. BECKMAN and L. LUNDGREN

decreases simultaneously to about 2.75#a. Across the hexagonal-orthorhombic transition, the saturation moment drops to 1.8#B, whereas Tc is only reduced to 407 K.

3.3.1.9. (Fel-~Nit)eP.

The hexagonal FezP-type structure is retained in the whole system. M6ssbauer experiments (Maeda and Takashima 1973) revealed that the Ni atoms preferentially occupy site I in the composition range t ~<0.3 and site II for t > 0.7. As shown in fig. 35, the ferromagnetic Curie temperature Tc increases with t to about 330K at t=0.1 and then decreases. For t>0.8, the system is a Pauli paramagnet. From magnetization and resistivity measurements (Fujii et al. 1978), it was found that the first-order transition in Fe2P changes into a second-order transition by substitution of only 8% Ni. The variation of the Curie-Weiss temperature 0 is included in the figure, showing the pronounced difference between Tc and 0 for Fe2 P. This implies giant short-range order in the paramagnetic state which is mentioned in section 3.3.1.1. The saturation magnetic moment (Lundgren 1977, 1978) decreases linearly with t, with A#s = -0.36#B for At = 0.1 (at least up to t = 0.4). The anisotropy constant (K) decreases with Ni substitutions in Fe 2 P (Fujii et al. 1978). The magnetoelastic effects also decreases, which is apparent from the temperature dependencies of the a parameter for some (Fel_tNit)EP compounds as shown in fig. 30. Defining Aa*/a as the difference from the temperature dependence of the a parameter for the t = 0.4 sample, K is plotted versus ½(Aa*/a)2 in fig. 36, implying a close relation between the anisotropy and lattice deformation. The slope of the line in fig. 36 gives Young's modulus in the basal plane, E ~ 4 x l0 n N/m 3, in reasonable agreement with room-temperature compressibility data. Further measurements (e.g., magnetostriction, anisotropy in the paramagnetic region.) would be valuable to elucidate the origin of the profound anisotropy.

3.3.1.10. (Crl_tNi~)eP.

The magnetic properties of this system has been studied by Roger (1970) and Iwata et al. (1981). The system has the orthorhombic Co2PT (K) 400

I

I

~

Hex

300 200

100

h Pauli. Para

p T Ferro I

0 Fe 2 p

Ni 2 P

Fig. 35. Magnetic phase diagram for the system FezP-NizP (after Fruchart et al. 1969, Fujii et al. 1978, Lundgren 1977, 1978).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

235

(Fel_t Ni t)2 P ~3

t= 0

~2 v

0.10

I 2

0

I 4

I 6

I 8

(xl0 -6)

0.5(Aa*/a) 2 Fig. 36. Uniaxial anisotropy constant K (after Fujii et al. 1978) plotted versus elastic strain for some (Fel-tNit)2P compounds at zero kelvin. Aa*/ais the magnetoelastic contribution as calculated from the temperature dependence of the a parameter with the t = 0.4 sample as reference (fig. 30). The slope of the line gives a Young modulus in the basal plane, E ~ 4 x 10x1N m-a.

type structure for 0.35 < t < 0.50 and the hexagonal Fe2P-type structure for t > 0.55. As shown in fig. 37, in the orthorhombic phase, the compounds have a narrow ferromagnetic domain (0.43 < t < 0.50). The value of Tc (and saturation moment) show a maximum of 146 K (and 0.83pB) for CrNiP (t = 0.5) and drops rapidly with increasing Cr content. In this system, it has been proposed that the Ni atoms are nonmagnetic (Goodenough 1973), but the spontaneous moment appears from Cr-Ni-Cr interactions.

3.3.1.11. (Mnl-tCot)eP.

The magnetic properties of this system have been studied extensively by magnetization measurements (Fruchart et al. 1969, Roger 1970, Okamoto et al. 1981) and by neutron scattering (Fujii et al. 1979b, Fruchart et al. 1979, 1980, 1985, Radhakrishna et al. 1987, 1990, Puertolas et al. 1988). As shown in fig. 38, antiferromagnetism occurs in the hexagonal phase (t ~<0.2). In the orthorhombic phase (t > 0.2), a large ferromagnetic domain exists with a maximum Tc value of about 570 K for MnCoP (t = 0.5). T(K)

i

I

Orth

150

,,

of,,

100

Hex

Pauli Para

,,

50

0 Cr2P

//

[

0.3

,//,, 0.4

0.5

[

0.6

/ p----

Ni2P

Fig. 37. Magnetic phase diagram of the system C r 2 P - N i 2 P (after Iwata et al. 1981).

236

O. BECKMANand L. LUNDGREN T(K) I Hex

Orth

600 F500 ~400

-

~

Op

~1-S (~B]f-U.)

-

i 300 i 200 100 ~

o

i AF

I

Mn2P

Co 2P

Fig. 38. Magnetic phase diagram of the system Mn2P-Co2P (after Fruchart et al. 1969, Okamoto et al. 1981).

The site occupancy is (Fruchart et al. 1969) given by (Co2tMnl_2t)MnnP

for t < 0.5,

Cox(Cozt-lMn2-2t)nP for t>0.5. In MnCoP, the Co atoms occupy site I and Mn atoms site II. There is some ambiguity as to the magnetic structure determined from neutron-diffraction measurements. Polarized neutron-diffraction experiments on single crystals by Fujii et al. (1979b) gave the magnetic moments 0.06#B (CoI) and 2.66#B (Mnn) at room temperature, whereas a later study by some of these authors (Radhakrishna et al. 1987) implied that the Co atoms have magnetic moments of 0.65#B alternating in sign while the Mn atoms have moments of 2.55#B that are aligned ferromagnetically. From a subsequent polarized neutron-diffraction study by Radhakrishna et al. (1990), the occurrence of antiferromagnetic-like domains associated with canting of the Co moments was proposed. Electronic band structure calculations by S. Fujii et al. (1988) gave 3.14#B per formula unit and 0.0@B, 3.13#B and --0.05#B for Co, Mn, and P, respectively. The very small Co moment, obtained in these calculations, does not fully agree with the neutron-diffraction data by Radhakrishna et al. (1987, 1990). Magnetization measurements on single crystals (Okamoto et al. 1981, Radhakrishna et al. 1990) showed that the b axis is the easy axis of magnetization and the c axis the hard axis. For t > 0.5, the Co atoms gradually occupy site II which results in a decrease of both Tc and saturation moment with increasing Co content. For 0.2 < t < 0.4, an antiferromagnetic phase occurs at low temperatures. Neutron-diffraction measurements by Puertolas et al. (1988) on samples in this concentration regime gave a 'double-helix' magnetic structure, similar to that observed in the binary phosphides and arsenides as well as in the ternary silicides and germanides. For a t = 0.25 sample, Puertolas et al. (1988) also found weak ferromagnetism existing up to 400K. This

COMPOUNDS OF TRANSITIONELEMENTS WITH NONMETALS

237

possibly indicates a more complex magnetic phase diagram than found from the magnetization measurements. The pressure dependence of Tc for compounds in the compositional range 0.3 ~
238

O. BECKMAN and L. LUNDGREN TABLE 17 Crystallographic (after Fruchart 1982) and magnetic data for T2As and TT'As compounds.

Comp. Cr2As

Struct. T

a

b

c

#~

TN

(A)

(A)

(A)

(#B)

(K)

3.594

6.346

CrMnAs CrFeAs

T H

3.760 6.096

6.259 3.651

CrCoAs CrNiAs

H H

6.068 6.111

3.657 3.656

Cq 0.40

Crn 1.34

0.83

2.97

~0.2"

Nil

Tc (K)

393 440 408 405 Para 45 Para

[1,2] [33 [4] [4, 5] [3] [4] [4]

Crll

0.65

MnzAs

T

3.761

6.265

0.55 1.10' 1.19" Mnl Mnn 2.2 4.1 3.7 3.5

182 188

T

3.745

MnCoAs

O

6.212

MnNiAs Fe2As

H T

6.195 3.638

FeCoAs FeNiAs Co2As CoNiAs

H H H H

6.065 6.070 6.066 6.079

6.076

3.722

Fel 0.2

7.007 3.726 5.986

3.577 3.581 3.557 3.467

Mna 3.6

463 450

3.16" 2.89*

350 345 ~175

Fe I 1.28

Fen 2.05

353 367

2.24*

301 220

0.1'

*/zs is given in #B/f.u. t References: [1] Y. Yamaguchi et al. (1972); neutron scattering, 130K. [2] Yuzuri (1960); magnetic susceptibility. [3] Hollan (1966); magnetic susceptibility. [4] Krumbfigel-Nylund (1974); magnetic susceptibility. [5] Fruchart et al. (1982); neutron scattering, 77 K. [6] Grandjean et al. (1972); M6ssbauer spectroscopy. [7] Iwata et al. (1980); magnetic susceptibility of single crystals. [8] Sirota and Ryzhkovskii (1975); neutron scattering, 77 K. [9] Austin et al. (1962); neutron scattering, 293 K. [10] Yuzuri and Yamada (1960); magnetic susceptibility. [11] Kanomata et al. (1977); magnetic susceptibility and thermal expansion. [12] Yoshii and Katsuraki (1966, 1967); neutron scattering, 293 K. [13] Katsuraki and Achiwa (1966); neutron scattering, extrapolated to 0 K.

[5] [4] [73 [8] [9] [3, lO, 11] [4]

573 544 MnFeAs

Ref.t

30

I-3, 12] [11] [4] [11] [4] [4, 11, 13] [3, 6] [4] [4] [4]

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

239

)-

)-

site I O II

J

5i

,a

Cr2As

Mn 2 As

Fe2As

Fig. 39. Magnetic structures of the tetragonal compounds Cr2As, Mn2As and Fe2As.

3.3.2.3. Fe2As.

Neutron-diffraction measurements on FezAs by Katsuraki (1964a), Katsuraki and Suzuki (1965) and Katsuraki and Achiwa (1966) gave the antiferromagnetic structure (TN= 353K) shown in fig. 39. As for MnzAs the moments form ferromagnetic c plane layers, but have a + + - - - + + arrangement along the c axis. Thus, ferromagnetic alignment exists in the Feu-FerFeH unit. The magnetic moments on sites I and II were found to be 1.28#B and 2.05#B, respectively. Torque measurements by Achiwa et al. (1967) showed that the moments are located in the (100) direction and the magnetic anisotropy was estimated to be K ~ 500 J m-3 at 77K. From M6ssbauer spectroscopy measurements by Grandjean et al. (1972), it was inferred that the quadrupole splitting changes through the antiferro-paramagnetic phase transition (TN = 367 K) and, in contradiction to the conclusions drawn from the neutron diffraction and torque data, it was inferred that the spins are not perpendicular to the c axis. These conclusions were rejected by Krumbfigel-Nylund (1974) from M6ssbauer measurements on single crystals. At 293 K, the hyperfine fields were determined by Krumbfigel-Nylund to be 11.0(1)T and 9.4(1)T at Fe~ and Fei, respectively. TN was found to be 354K. A N6el temperature of 368 K was determined from susceptibility measurements by Hollan (1966).

3.3.2.4. CocAs.

Co2 As exists in two different modifications where the low temperature (< 725 K) crystallographic phase, generally denoted 0~-Co2As, has hexagonal symmetry. Magnetic susceptibility measurements by Kjekshus and Skaug (1972) indicated a ferrimagnetic transition at Tcg 60 K and the same effective Bohr magneton number #eff = 2.25#R per Co atom was found for both the low- and hightemperature phases of paramagnetic CozAs. Magnetization measurements by Krumbfigel-Nylund (1974) on a sample with composition Coa.95As implied magnetic ordering at 30 K, but the magnetic moment was reported to be very weak (0.1/~a).

3.3.2.5. (Crl_tMnt)2As.

All compounds in this system crystallize in the tetragonal Fez As structure. They exhibit antiferromagnetic properties. Neutron-diffraction measurements by Yamaguchi and Watanabe (1978) showed that the magnetic structures for (Crl_tMnt)zAs compounds can be divided in three regions. In the first region

240

O. BECKMAN and L. LUNDGREN

(0 ~ t ~ 0.24), the magnetic structure is the same as that for Cr2As. A new magnetic structure, intermediate between the Cr2As and the Mn2As structures, was observed in the second region (0.24 ~< t ~<0.65). In the third region, the magnetic ordering is of the Mn2 As type (see the magnetic phase diagram in fig. 40). In a later neutrondiffraction measurement on CrMnAs by Fruchart et al. (1982), it was shown that the Mn atoms occupy 79% of site II. It was proposed that the moments on site II (where Mn is dominant) are coupled like in Mn2As and the moments at site I (where Cr is dominant) couples like in Cr2As. At 77 K, the moments were determined to be 2.97(5)#a (site II) and 0.83#B (site I), in reasonable agreement with 3.14(17)#B (site II) and 0.41(30)#a (site I) reported by Yamaguchi and Watanabe (1978).

3.3.2.6. VMnAs. In VMnAs (TN = 447 K), the metal atoms are perfectly ordered with the Mn atoms in site II and the V atoms in site I. Neutron diffraction measurements by Fruchart et al. (1982) gave the moments 3.12(10)#B (Mnn) and 0.02(10)#B (V~) at 77 K. The magnetic structure is similar to that of CrMnAs (see above). 3.3.2.7. (Mn1_tFet)eAs. This system has complete solid solubility (Hollan 1966) and crystallizes in the tetragonal F%As-type structure. M6ssbauer spectroscopy studies by Grandjean and Gerard (1975) show that the Mn atoms preferentially occupy site II and the Fe atoms site I, analogous with the corresponding phosphorous system. The magnetic phase diagram was studied by Rosenberg et al. (1967, 1969) and Kanomata et al. (1977). As shown in fig. 40, there is a narrow range of ferrimagnetism for 0.24 < t < 0.35 and the ferri-antiferromagnetic phase transition is of first order with a discontinuous change of lattice parameters. Neutron-diffraction measurements have been performed by Yoshii and Katsuraki (1966, 1967) on the ternary compound MnFeAs. Based on the same magnetic structure as Mn2As the magnetic moments were determined to be 0.2#B (Fel) and 3.6#B (Mnii) at room temperature. The total moment at 0 K can be estimated to be 4.5#B.

T(K)

400

200

Hex

Tetr

6OO

(gB/f.u.) 3

~S~

\ /I. IAF

I AF I CrMnAs II I "type III Ur2Asl

tYpe It

t

I ,

0 i

Cr2As

Mn As 2 type

~ [

type

Fil I

Mn 2As

AF Fe 2As type F/i

I

I

Fe2As

I

o

Co2As

Fig. 40. Magnetic phase diagrams of the systems Cr2As-Mn zAs, Mn2As-F%As and F%As-C02 As.

COMPOUNDS OF TRANSITIONELEMENTS WITH NONMETALS

241

The assumption that MnFeAs and Mn2As have the same magnetic structure has been questioned. From M6ssbauer spectroscopy measurements by Grandjean and Gerard (1975), it was argued that there exist three types of hyperfine structures, probably connected to three types of magnetic structures: for 0 ~
3.3.2.8. (Fel-tCot)eAs. Compounds in this system have the tetragonal Fe2Astype structure for t<0.3, and the hexagonal Fe2P-type structure for t>0.37 (Krumbfigel-Nylund 1974). As shown in fig. 40, only 5% of Co-substitution in Fe2 As induces a ferromagnetic component at low temperatures. The ferri-antiferromagnetic and antiferro-paramagnetic transitions are both of second order. In the hexagonal phase, both Tc and the saturation moment decrease monotonously with increasing Co content, in analogy with the corresponding phosphorous system. Going from Mn2As to CozAs, the total magnetic moment at OK decreases as follows: 6.3#B (Mn2As), 4.5#B (MnFeAs), 3.3/~B (FezAs), 2.2pB (FeCoAs) and 0/~B (CozAs).

3.3.2.9. (Mnl-tCot)2As.

Compounds in this system exhibit tetragonal, hexagonal and orthorhombic phases. The magnetic phase diagram is shown in fig. 41 (Krumbfigel-Nylund 1974). In the tetragonal phase (t < 0.25), the system is antiferromagnetic and TN decreases slowly with increasing t. An hexagonal phase exists in the narrow compositional range 0.375 < t < 0.385 and magnetic ordering takes place at around 220 K. At 4.2 K, an external field of 13 T is insufficient to obtain saturation, implying significant antiferromagnetic interactions. Ferromagnetism is found in the orthorhombic phase in the compositional range 0.45 < t < 0.57 with the highest values of Tc = 348 K and saturation moment #s = 3.16/~B for t = 0.5 (MnCoAs). In the hexagonal phase (0.6 < t < 0.95), both Tc and ps decrease with t.

3.3.2.10. Mn(Fe, Co)As and Mn(Co, Ni)As.

In the series MnFeAs-MnCoAsMnNiAs, the most interesting magnetic properties occur at compositions close to MnCoAs, which is ferromagnetic. Substitution of 20% Fe as well as 50-60% Ni in

242

O. BECKMAN and L. LUNDGREN ~s

T(K) Hex Orth

Hex

t (gB/f'u')

-II

400

iTci 300 200

1

100

0

"///'/////A~~ I

Mn 2As

c~ 0

i

Co 2 As

Fig. 41. Magnetic phase diagram of the system MnzAs-Co2As (after Krumb/igel-Nylund 1974).

MnCoAs impose metamagnetism at low temperatures. The magnetic phase diagram is shown in fig. 42 (Krumbfigel-Nylund 1974).

3.3.2.11. (Crl-tNit)eAs. Magnetization measurements on single crystals by Iwata et al. (1980) showed that (Crl_tNi,)2As compounds are antiferromagnetic for 0.4 < t ~< 0.45 and ferromagnetic for 0.45 < t ~< 0.7 (see the magnetic phase diagram of fig. 43). The critical fields for the antiferromagneti c compounds are very small. In the ferromagnetic regime, maxima occur at t = 0.5 for the saturation moment (/~s = 1.19#~), the Curie temperature (Tc = 188K) and the uniaxial anisotropy constant (K = 146kJm-a). The moments are directed along the c axis. Neutron diffraction measurements (Fruchart et al. 1982) show that the metal atoms are ordered with Cr at site II and Ni at site I. The data on CrNiAs indicated that Cr and Ni have weak ferrimagnetically coupled moments, directed along the c axis. At 77 K, the moments are 0.55(15)#n (Cr) and 0.65(15)#B (Ni). T(K) ?etr (gB/f.u.)

600, 500 400 300 -

5 TN

4 3

AF

200 -

2

100

1

0 MnFeAs

MnCoAs

0 MnNiAs

Fig. 42. Magnetic phase diagram of the systems MnFeAs-MnCoAs and MnCoAs-MnNiAs (after Krfimbugel-Nylund 1974).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS T(K)

243

Orth

200

Tc

% 100

0 -II Cr2As

TN!

'

0.3

..~

i

,

,

0.4 0.5 0.6 0.7

I/_ Ni2As

Fig. 43. Magneticphase diagram of the systemCrzAs-NizAs (after Iwata et al. 1980). Krumbfigel-Nylund (1974) has examined the systems Cr(T1 _tNi0As (T = Mn, Fe or Co), (Crt_~Mn0NiAs and also (Crt_tNit)As. It is found that both the variation of Tc and Ps scales with the electron concentration in these systems.

3.3.3. Arseno-phosphides 3.3.3.1. Fee (P~-xAsx). Compounds in this system crystallize basically in the Fe 2 Ptype structure for x ~<0.65 and in the FezAs type structure for 0.65 < x <~ 1 (Fruchart et al. 1969, Roger 1970, Catalano et al. 1973). However, for 0.35 ~<x ~<0.65 (Lundgren 1977, 1978), a distortion to an orthorhombic phase occurs at low temperatures. This transition is of first order and results in a small (~ 1%) decrease of the total magnetic moment. Figure 44 shows the temperature dependence of the axial ratio c/a in the hexagonal phase (or c/~fh-~3 in the orthorhombic phase) for various compositions. As can be seen, this ratio becomes closely the same in the (low-temperature) orthorhombic phase. The crystallographic distortion is similar to that which occurs in the system Fe2(P, Si) (Jernberg et al. 1984). As shown in table 16, small substitutions of As in Fe2 P results in a drastic increase of Tc, whereas the saturation magnetic moment only increases slightly. The large magnetocrystalline anisotropy energy of Fe2 P remains almost constant for x ~<0.1, but drops rapidly with x for x > 0.1 (Lundgren 1977, 1978).

3.3.3.2. MnFe(Pl_xAs~).

The magnetic phase diagram in fig. 45 is based on data by Krumbfigel-Nylund (1974) and Lundgren (1977, 1978). In the hexagonal phase (0.15 ~<x ~<0.65), antiferromagnetism occurs below about 180 K for 0.15 ~<x ~<0.275, and a first-order transition to a reentrant ferromagnetic phase at 130 K is observed for a sample with x = 0.275. This ferromagnetic phase is different from that found in samples with x ~>0.30. Magnetization measurements at 20K show an anisotropy field of 3 T for the x = 0.275 sample, whereas the anisotropy field for samples with

244

O. BECKMAN and L. LUNDGREN

c/a

Fe2Pl_xASx

0.57

X=0.3 ..__--, 0.4

0.5

0.56

I

0.6

[ I I

I I I

Hex

I I I

0.55 Orth 0.54

I

0

100

I

200

I

I

I

300 T(K)

Fig. 44. Temperature dependence of the axial ratio c/a for some F%P1-xAsx compounds. In the lowtemperature orthorhombic phase, the axial ratio is defined as c / ~ (after Lundgren 1977, 1978).

T(K)'

gs (p~f.u.)

400

4

300

3

200

2

100

1

0 MnFeP

0 MnFeAs

Fig. 45. Magnetic phase diagram of the system MnFeP-MnFeAs (after Krumbiigel-Nylund 1974, Lundgren 1977, 1978).

x >~0.30 is small (~<0.2T). For x ~>0.30, the ferro-paramagnetic transitions are of first order and are accompanied by a discontinuous change in lattice parameters, without any change in the hexagonal symmetry. Figure 46 shows the temperature dependence of the axial ratio c/a for samples with various compositions. For the sample with x = 0.30, the discontinuous change in the lattice parameters are Aa/a = --0.90% and Ac/c = 1.74% with increasing temperature, i.e., a volume decrease of only 0.07%. There is some ambiguity whether this transition is to an antiferromagnetic or to a paramagnetic state. For the sample with x = 0.275, the magnetic phase transitions at 130 and 180 K do not give rise to any significant change in the lattice parameters. It was found by Zach et al. (1988) that the transition temperatures increase with the application of pressure. This observation implies that the effect of external pressure and the effect of chemical pressure are different, which emphasizes the importance of anisotropy effects.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS c/a 0.58

245

MnFePl-xAs x X=0.275

~

0.30 040

0.57

I

#

i i

I I

0.56

,

!

0'550 4' 100

I

I

, 200

0.60

t

, 300

i

, T(K) 400

Fig. 46. Temperature dependence of the axial ratio c/a for some hexagonal MnFeP1-xASx compounds (after Krumbfigel-Nylund1974, Lundgren 1977, 1978). The average magnetic moment is 4.1#B in the hexagonal phase, independent of composition. The first-order transitions in MnFe(P, As) are presumably of the same origin as the occurrence of a crystallographic transition in the Fe2Pl-xAsx system (0.35 ~<x ~<0.65). 3.3.3.3. MnCo(P1-xAsx). The system MnCo(Pl_xAsx) has the orthorhombic Co2 P-type structure for all x. Tc and the average magnetic moment changes linearly with x having Tc = 583 K and #s = 3.03/~B for MnCoP, and Tc = 350K and ps = 3.16/~ for MnCoAs (Krumbfigel-Nylund 1974, Krumbfigel-Nylund et al. 1974). 3.3.4. Antimonides Several magnetically ordered TT'Sb compounds crystallize in the cubic Clb structure, which is strongly related to the cubic L21 structure. These compounds are denoted 'Heusler compounds' and have been treated by Booth (1988) in volume IV of this series. The only TT'Sb compound dealt with in this chapter is Mn2 Sb and its close modifications. Mn2 Sb crystallizes in the tetragonal Fez As-type structure (table 14, fig. 28). 3.3.4.1. Mn2Sb. From magnetization measurements, Guillaud (1943) predicted that the Mn 2 Sb compound is ferrimagnetic below 550 K, and the ferrimagnetic moment was determined to be 0.936/~B per Mn atom. Later, single crystal measurements by Guillaud et al. (1949) showed that the ferrimagnetic moment was located in the ab plane at temperatures below 240 K and along the ¢ axis in the temperature range 240 K < T < 550 K. The magnetic structure proposed by Guillaud et al. is shown in fig. 47, and was later verified by Wilkinson et al. (1957) from neutron-scattering experiments. The magnetic cell is the same as the chemical cell. At low temperatures, the moments at site I and at site II were determined to be 2.13(20)/~B and 3.87(40)#B,

246

O. BECKMAN and L. LUNDGREN

site I ©

II [] e

l.a

/ Ja

Mn 2 Sb

Cr-modified Mn 2 Sb

Fig. 47. Magnetic structure of Mn2Sb (after Guillaud et al. 1949, Wilkinson et al. 1957) and the lowtemperature ferrimagnetic structure of Cr-modified MnzSb (after Cloud et al. 1960, 1961). For the temperature dependence of the direction of the easy axis of magnetization, see fig. 48. The low-temperature magnetic structure of Cr-modified Mn2Sb is the same as the structure of Mn2As (see fig. 39).

respectively. This gives a net ferrimagnetic moment of 0.87(22)/~B per Mn atom, in fair agreement with that found by GuiUaud et al. (1949). Using polarized neutrons, Alperin et al. (1963) studied the spatial distribution of the unpaired electrons about the Mn atoms in single crystals at room temperature. It was found that the electron distribution associated with each atom is aspherical and compact. A small fraction of the density seems to reside in bonds or otherwise exist between atoms. At low temperatures, the magnetic moments determined by Alperin et al. were 1.77#B (site I) and 3.55#B (site II), extrapolated from roomtemperature data. Sirota and Ryzhkovskii (1975) studied the solid solution Mn2 As~ Sb 1-~ by neutron scattering (see below). The reported values of the magnetic moments of Mn2 Sb are in good agreement with the earlier studies.

3.3.4.2. Mne-tCrtSb.

Swoboda et al. (1960) observed that substitution of Cr in Mnz Sb results in a magnetic transition from a ferrimagnetic to an antiferromagnetic state with decreasing temperature. This transition is of first order and is accompanied by a discontinuous change in lattice parameters without any change in crystal symmetry. Depending on the Cr content, the transition occurs at temperatures in the range 140-400K. The transition may be interpreted in terms of the exchange inversion model by Kittel (1960). This model assumes that the exchange energies depend on the interatomic separation and a critical balance between exchange and elastic energies may cause a sudden change in spin directions (and lattice parameters) at a specific temperature. The Cr substitution gives rise to that critical situation. The occurrence of an antiferromagnetic state in Cr-modified Mn2 Sb at low temperatures was verified by neutron scattering experiments by Cloud et al. (1960, 1961). The magnetic structure is shown in fig. 47. The basic magnetic sublattice of Mn2 Sb is the three-layered set of adjacent Mn(II)-Mn(I)-Mn(II) planes having the ferrimagnetic moment [#(Mnn)-#(Mn0[. Ferromagnetic ordering of these sublattices gives the magnetic structure of Mn2 Sb. Antiferromagnetic ordering of these sublattices gives the low-temperature magnetic structure of Mnz_tCrtSb which also results in a

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

247

doubling of the magnetic cell along the c direction. The direction of easy magnetization depends on temperature and Cr content (see fig. 48). An intermediate antiferromagnetic state between the ferri- and antiferromagnetic states was revealed by Bither et al. (1962a) for Mn2_tCrtSb with t<0.03. The transitions between the different states are all of first order. From neutron-diffraction measurements (Austin et al. 1963), it was found that the magnetic unit cell of this structure has a c axis three times that of the chemical cell and that the spins are located in the basal plane. Extensive X-ray and magnetic studies on single crystals has been performed by Darnell et al. (1963). Torque and magnetization measurements show that for both the ferri- and antiferromagnetic states a change from positive to negative uniaxial anisotropy occurs with decreasing temperatures. The magnetic phase diagram of fig. 48 is from Darnell et al. The thermodynamic equations describing the exchange inversion transition of Crmodified Mn2 Sb was derived by Doerner and Flippen (1965). The transport properties near the ferri-antiferromagnetic transition was investigated by Sato et al. (1984). They found that, for Mnl.ssCro.lzSb, the thermal conductivity near the transition increased 11% in an applied field of 1.5 T at 297.5 K. The exchange inversion entropy AS at zero field and 1.5 T were estimated to be 1.4 and 2.0 J/mol K, respectively. The authors indicate the possible use of these compounds for magnetic cooling. The prospects for applications of the (Mn, Cr)2Sb compounds as permanent magnets or recording media were investigated by Perry (1977).

3.3.4.3. Other modified MneSb compounds. It was soon discovered that transformations from ferri- to antiferromagnetic ordering with decreasing temperature could be obtained by other substitutions than Cr. Bither et al. (1962b) found that this transformation also occurs for substitutions with V, Co, Cu, Zn as well as with Ge and As. Kanomata and Ido (1984) studied the exchange inversion for substitutions with Ti, V, Cr, Fe and Co. The results were discussed in a molecular-field theory. In a simplified theory (Shirakawa and Ido 1976, Kanomata et al. 1977), the relative stability of the ferri- and antiferromagnetic states depends on the quantities Jb(Su) and 3Ja(S~) (see notations in fig. 47). If the former quantity is larger (smaller) than T(K) 6OO

400

Mn2.tCrtSb ~

P

Ferri //c

300

200 2 C - ~ 100 0

/

AF .l.C

/ ~ / f f . . . .Intermediate ._ AF ' I I 0.05 0.10

I 0.15

t Fig. 48. Magnetic phase diagram of Mn z _tCrtSb compounds. The direction of the magnetic moments is indicated. The solid lines represent first-order transitions and the dotted lines second-order transitions (after Darnell et al. 1963).

248

O. BECKMAN and L. LUNDGREN

the latter quantity the ferrimagnetic state is qualitatively more (less) stable than the antiferromagnetic state. The magnetic phase diagrams obtained by Kanomata and Ido (1984) and Bither et al. (1962b) are schematically represented in fig. 49. Blaauw et al. (1977) studied the system Mn 2_tFetSb (t ~<0.2) using 57Fe M6ssbauer spectroscopy. The spin-flip transition at T~, where the easy axis of magnetization changes from perpendicular to c to parallel to c, was observed through the T dependence of the quadrupole interaction. It was observed that the corresponding change in the hyperfine magnetic field was 4.96 T at T < T~to 7.94 T at T > T~, which was attributed to crystalline anisotropy. T~ increases with increasing values of t.

3.3.4.4. MneSbl_xAsx. The magnetic moments of Mnl and MnH in this solid solution were determined from neutron diffraction data at 297 and 78 K by Sirota and Ryzhkovskii (1975). As can be seen in fig. 50a, both magnetic moments decrease monotonously with increasing Sb concentration in the range 0.4 ~<x ~< 1. Increasing the As concentration to 15% in a solid solution based on Mn2Sb reduces the Mn, moment at 297K from 3#B for Mn2Sb to 2.7#B for Mn2Aso.~sSbo.85, and at 78K from 3.8/~Bto 3,4#B, respectively. Simultaneously, the Mn~ moment initially decreases with increasing As content from 1.7/~Bfor Mn2Sb to 1.55#B for an As content of 5%, passes through a minimum, and then increases with a subsequent increase of the As content to 1.9/~B for Mn 2Sbo.85Aso.15 at 297 K. The existence of a minimum as well as the insignificant temperature dependence of the Mn~ moment in this concentration range may be coupled to the possibility of four ordered magnetic structures as inferred by Cloud (1968) from X-ray and magnetization measurements on Mn2Sbl_xAs~ with x = 0.10 and 0.15. According to Cloud, first-order transitions take place in the sequence ferrimagnetic (F) -~ intermediate antiferromagnetic (IAF) --~ intermediate ferrimagnetic (IF)--~ antiferromagnetic (AF) Mn 2_tTt Sb T(K) 600

T=Ti

T=V 600

----Z__ 400

-----L__ 400

200 '

0

'

0.1 0.2 t

0

I

0

P 400

400

Ferri

/AF

200 ,

0.1 0.2 t

0

~

Ferri

200 1 ,' " ,

0

T=Cu 600

---L..

Feral

200

T=Co 600

400

Ferri

0

T=Fe 600 -

0.1 0.2 t

0

It

0

AF I

,

200 / A F ,

,

0.1 0.2 0 . . 3 04 t

0

I

I

0.1 0.2 t

Fig. 49. Magnetic phase diagrams of some Mn2_~TtSb compounds, T = Ti, V, Fe, Co or Cu (after Kanomata and Ido 1984, Bither et al. 1962b).

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

Mn2Sbl_xASX

4.5 4.0

(a)

T(K) 600

MnII

,,-., 3.5

•

~:~ 3.0

249

Mn2Sbl_xASX (b)

.----.<.

40(

Ferri

2.5 Mn I

20(

2,0

"AF+Ferri

1.5 I

I 0.2

I 0.4

I X

I 0,6

I

I 0.8

I

I

I

0.12

1.0

014

X

Fig. 50. (a) Magnetic moment (#3) versus x for Mn2 Sbl _~As~ compounds. Solid symbols are data at 78 K and open symbols data at 297 K. Circles represent ferrimagnetic and squares antiferromagnetic structures (after Sirota and Ryzhkovskii 1975). (b) Magnetic phase diagram of the system MnzSbl_xAs~. The direction of the magnetic moments is indicated (after Ryzhkovskii 1978).

upon cooling. The magnetic structures are collinear layered structures. In terms of the tetragonal c axis of the chemical unit cell, it was proposed that the magnetic unit cells of the various structures have tetragonal axes of c (F), 6c (IAF), 3C (IF) and

2c(AF). The neutron diffraction study by Sirota and Ryzhkovskii (1975) was supplemented with magnetization and resistivity measurements by Ryzhkovskii (1978), who proposed the magnetic phase diagram of fig. 50b. In the region 0.1 < x < 0.2, there is some ambiguity as regards the location of the magnetic moments. 3.4. T F ' X

compounds with a 4d element

Magnetically ordered TT'X compounds where T is a 3d element and T' is a 4d element generally crystallize in the structures given in table 14. Crystallographic and magnetic data for these compounds are given in table 18. TABLE 18 Crystallographic (after Fruchart 1982) and magnetic data for TT'P and TT'As compounds with T' = Ru or Rh. Comp.

Struct.

a (A)

b (A)

c (A)

#s (#B/f.u.)

TN (K)

FeRuP FeRhP MnRuP

O O H

5.796 3.622 6.268

3.723 17.34

6.731 5.908 3.533

~2 1.72 ~2.1

150

MnRhP MnRuAs MnRhAs

H H H

6.227 6.615 6.481

3.58 l 3.614 3.715

3.06 3.94 3.7

Tc (K) 350 269 401 521 190

Tt (K)

176 116

157

250

O. BECKMAN and L. LUNDGREN

3.4.1. FeRuP This compound has the orthorhombic Co2 P-type structure. Antiferromagnetic ordering takes place at around 150 K. M6ssbauer and DPAC measurements (Bostr6m et al. 1971) show that the hyperfine fields acting on Fe and Ru are closely similar. At low temperatures, the hyperfine fields were found to be 4.2 T (Fei), 4.0 T (Ru~), 16.6T (Fe~i) and 15.5T (Run). About ¼ of the Fe atoms occupy site I. 3.4.2. FeRhP Crystallographic data by Chenevier et al. (1988) show that the system (FetRh 1-t)2P with 0.4 ~< t ~<0.6 is isotypic with NbCoB (Krypyakevich et al. 1971), which can be built up with elements of the Fe2P and Co2P structures. Partial metal ordering is observed with Fe atoms favouring site I. Magnetization and M6ssbauer measurements (Chaudouet et al. 1982, Chaudouet 1983) show that FeRhP is ferromagnetic below 350 K. The saturation moment is 1.72#B per formula unit. The moment at the Rh atom is weak. The value of the saturation moment is closely the same as that for the isoelectronic compound FeCoP. 3.4.3. MnRuP Magnetic AC susceptibility, specific heat and neutron diffraction data have been presented by Bartolom6 et al. (1986a). It is observed that below the ordering temperature, TN = 269(1) K, an incommensurate spiral structure appears. A first-order transition to a different incommensurate phase takes place at 176 K, and at 116 K a further reorientation of the magnetic moments is found. Only weak anomalies at the transitions were detected in the specific heat. In the ordered phases, complex incommensurate spiral structures were found. Three different localized magnetic moments at the Mn atoms in the layers were observed, ranging in site 1 from 1.44#B to 1.02#B and in sites 2 and 3 from 3.12#B to 2.20ktB. The paramagnetic susceptibility deviates from a Curie-Weiss behaviour at temperatures up to T ,~ 3 To. 3.4.4. MnRhP This compound has the Fe2 P type crystal structure. The Rh atoms are located at site II and the Mn atoms at site I. Magnetization measurements (Chaudouet 1983) show that this compound is ferromagnetic below Tc = 401 K. Saturation magnetization is obtained at a magnetic field of 2-3 T and the saturation moment is 3.06/~B, closely the same as for MnCoP (and MnCoAs). The ratio between Tc and 0p is found to be Tc/Op = 0.86. Neutron diffraction experiments (Chenevier et al. 1985) at room temperature show that the Rh atoms carry no significant moment and that the magnetic structure consists of a stack of ferromagnetic (001) planes, with an easy direction making an angle of 26 ° with the c axis. The moment on the Mn atoms are 3.08(10)#B. Assuming a rhodium polarization (Kouvel 1966, Felner and Nowik 1980), a refinement of the neutron scattering data show that the Rh atoms carry a magnetic moment of 0.32# B parallel to the c axis, directed opposite to the Mn moments.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

251

3.4.5. M n R u A s

This compound exhibits ferromagnetic properties with Tc = 521 K (Chenevier et al. 1985). At 4.2K, the saturation moment is 3.94/~B. The paramagnetic Curie temperature 0p is high with Tc/O v = 0.76. Neutron-diffraction data implies that the magnetic moments are parallel making an angle of 71 ° with the c axis. At 300 K, the value of the magnetic moment was determined to be 3.42(10)~B. No moment on the Ru atoms was detected. 3.4.6. MnRhAs

The ternary arsenide MnRhAs has the hexagonal Fez P-type structure. The Rh atoms occupy site I and the Mn atoms site II. Magnetization measurements (Chenevier et al. 1984) show that this compound is antiferromagnetic at low temperatures, but exhibits a first-order transition from the AF state to a ferrimagnetic state (F + AF) at Tt = 158 K. The Curie temperature was determined to be Tc = 200K. Neutron scattering experiments (Bacmann et al. 1986) indicate no significant moment on the Rh site. The moments of the Mn atoms order with a magnetic structure consisting of a stack of ferromagnetic (001) planes. For T < Tt, two different structures may be possible as indicated by the magnetic phase diagram of fig. 51. At T = 6 K, #z = 1.2/.tB and #xr = 3.45#~. For Tt < T < Tc the components #z, and #xy are ferro- and antiferromagnetically coupled, respectively, with those of the adjacent layers. At 178 K,/xz = 1.2#B and/~xr = 2#n. A weak moment (0.2#~) at the Rh site also appears. Below Tt, metamagnetic behaviour is found. Magnetization measurements and neutron-diffraction data show that the ferrimagnetic phase can be induced by a magnetic field. Kanomata et al. (1987) have studied the effect of hydrostatic pressure on the magnetic transitions. The pressure dependences of Tt and Tc were determined to be ATt/Ap ~ 1.0 K/kbar and ATc/A p ~ 0.7 K/kbar, respectively. The data by Kanomata et al. (1987) have been included in the schematic magnetic phase diagram of fig. 51. Specific heat and AC susceptibility measurements by Garcia et al. (1985) and Bartolom6 et al. (1986b) gave anomalies also at 58 and 241 K. From crystallographic

T(K)

~f

Tc 2__00 Tt-100

/C

C w I

0 B(T

I

10

5

0

10

I

20 p(kbar)

Fig. 51. (T, B, p) magnetic phase diagram of MnRhAs. At low temperatures, two possible structures are indicated (after Bacmann et al. 1986, Kanomata et al. 1987).

252

O. B E C K M A N and L. L U N D G R E N

measurements, Kanomata et al. (1988) report a discontinuous change in the lattice parameters at 223 K. The origin of these anomalies is not yet clear. 3.4.7. (Crl_tPdt)2As These compounds have the tetragonal Fe2As-type structure for 0 ~i 0.9. In the antiferromagnetic range 0.4 ~
4.

TX 2

compounds

A vast number of transition-element binary compounds of composition TX 2 are known, mainly crystallizing in the structures given in table 19. Only a few compounds show magnetic ordering. They are listed in table 20 with some characteristic data. 4.1. CrBe

The crystal structure of CrB2 is of the hexagonal B32 (A1B2) type (fig. 52). From N M R measurements on 11B, Barnes and Creel (1969) found itinerant-type antiferromagnetic ordering with a Nrel temperature of TN= 88 + 2 K. Magnetic susceptibility measurements have given TN= 88 K (Tanaka et al. 1976) and TN= 86K (Castaing et al. 1969). Funahashi et al. (1977) have performed neutron-diffraction measurements on single-crystal CrB2 and found a helical magnetic structure of cycloidal type. The propagation vector was determined to be z=0.285Zllo where zll o = 2rc/(½a) is the reciprocal lattice vector of [110]. The magnetic moments of 0.5 + 0.1#B turn in the ac plane. The band structure of CrB2 has been calculated by Liu et al. (1975). Castaing et al. (1969, 1971) have made extensive specific heat measurements on several diborides, including CrB2. Some low-temperature specific heat parameters are collected in table 21, i.e., the coefficient of the linear electron term 7, the coefficient of the Debye T 3 law fl and the Debye temperature 0.

TABLE 19 Crystal structures of TX 2 compounds. Structure Pyrite Marcasite CuAl2-type A1B2-type

Cubic, C2 Ortho. C18 Tetr. C16 Hex. C32

Space-group Pa3 Pnnm I4/mcm P6/mmm

No No No No

205 58 140 191

M M M M

= = = =

4 2 4 1

COMPOUNDS O F TRANSITION ELEMENTS WITH NONMETALS

253

TABLE 20 Magnetically ordered TX2-compounds. Comp.

Magn. order*

Struct.

CrB2 MnB 2 FeGe2 FeSn2 MnSn2 CrSb2 MnS2 MnSe z MnTe2 CoSz CoSe2

H F AF AF AF AF AF AF AF F AF

C32 C32 C16 C16 C16 C18 C2 C2 C2 C2 C2

a (A) 2.969 3.01 5.908 6.535 6.659 6.028 6.097 6.417 6.943 5.523 5.857

b (A)

c (A)

6.874

3.066 3.04 4.955 5.32 5.447 3.272

Tc (K)

T~ (K)

Tt (K)

86 g150 289 378 325 273 48 53 86.6

263 93 73

#s (PB)

Ref.t

0.5 0.2 1.2 1.6 2.33 1.94

[a] [b] [c] [d] [e] If] [g] [g] [g] [a] [a]

48.5

124

0.84 93

* Magnetic order: F = ferro, AF = antiferro, H = helix. References are only given to structural parameters. For other data, see text. "~References: Ia] Pearson (1967). [e] Le Caer et al. (1982). [1o] Cadeville (1966). [f] Holseth et al. (1970). [c] Corliss et al. (1985). [g] Hastings et al. (1959). I-d] Trumpy et al. (1970).

TABLE 21 Specific heat data for some TB 2 compounds. Compound ScB2 TiB2 VB2 CrB2 MnB2

y (mJ/mol K 2)

fl (~tJ/mol K ' )

0 (K)

2.2 1.08 4.84 13.6 2.8

1.175 0.345 0.32 1.2 1.25

550 820 850 545 540

c

(D Cr Mn

OB

Fig. 52. The unit cell of the hexagonal B32 structure of CrB 2 and MnB2.

254

O. BECKMANand L. LUNDGREN

4.2. Vl_tCrtB e Castaing et al. (1972) studied the magnetic susceptibility and specific heat for this ternary system. The large electronic specific heat of CrB2 increased with substitution of vanadium with a maximum at t ~ 0.8. The Nrel temperature TN= 86 K for CrBz was found to decrease linearly towards zero for t = 0.77.

4.3. MnBe MnBz crystallizes in the hexagonal C32 (A1Ba) structure (fig. 52). Magnetization measurements by Cadeville (1966) give a ferromagnetic transition at 157K with a saturation moment of #s = 0.25ktB per manganese atom. In the paramagnetic state, the Curie-Weiss behaviour gives #elf = 2.30/~B and 0p = 148 + 5 K. Andersson et al. (1966) find the transition temperature Tc = 143 K and a saturation moment of 0.19#B. In the paramagnetic state, ~eff = l'55/['tB"

4.4. FeGee, FeSne, MnSne These compounds, which crystallize in the tetragonal CuA12-type structure (C16), show large similarities in their magnetic structures.

4.4.1. FeGe2 Early neutron-diffraction measurements (Krrn and Szab6 1964, Satya Murthy et al. 1965, Forsyth et al. 1964) have given a Nrel temperature in the vicinity of 300 K. There was some ambiguity as regards collinear or noncollinear spin structures. Corliss et al. (1985) made extensive neutron-diffraction and heat capacity measurements revealing two distinct magnetic transitions. At the N~el temperature, TN = 289 K, a basal plane spiral structure propagating along [100] is formed. The propagation vector changes gradually, and at a lower transition temperature, Tt = 263 K, a simple collinear structure appears with ferromagnetic coupling within the (100) planes and antiferromagnetic coupling along [100]. The spins are confined to the basal plane with magnitude 1.2#B (Forsyth et al. 1964) (fig. 53). Corliss et al. (1985) observed that the spiral propagation vector decreases continuously to zero in the intermediate temperature range according to a power law with an exponent of 0.407 ___0.005. They have further made heat capacity measurements in the temperature range 1.5-300 K. The electronic contribution has the coefficient = 4.3 mJ/mol K 2. The magnetic contribution was found to exhibit two 2-like anomalies at 264.0 and 285.0K with a temperature coefficient of ~ = 0 . 1 5 9 - 0.001. Both transitions are considered to be of second order. Neutron-diffraction measurements by Menshikov et al. (1988) confirm the two transitions at 290 and 263 K. However, a small hysteresis (~0.5K) at the 263K transition indicates a first-order phase transition. 4.4.2. FeSne Nicholson and Friedman (1963) reported the antiferromagnetic Nrel temperature TN = 378 K and a zero kelvin magnetic moment of 1.6#B. Early neutron diffraction

C O M P O U N D S O F TRANSITION ELEMENTS WITH N O N M E T A L S

255

a

@

Fe

•

Ge

Fig. 53. The unit cell of FeGe2 showing relative spin orientations in the collinear structure below Tt = 263 K. The structure also applies to FeSn 2 above the transition temperature at 93 K.

studies by Iyengar et al. (1962) revealed ferromagnetic coupling within the (100) planes. Trumpy et al. (1970) studied the Mrssbauer effect in iron-tin alloys and found the following hyperfine fields at 77K: Boff(Fe)= 15.2 ___0.2T and Beef(Sn)= 3.3 _ 0.2 T. Venturini et al. (1985) made extended neutron diffraction and Mrssbauer experiments. They confirmed the transition at 378 K to a collinear magnetic structure of ferromagnetic (100) planes, which are antiferromagnetically coupled along [100] (fig. 53). The spin direction lies in the (001) plane. Below Tt = 93 K, they report a noncollinear antiferromagnetic structure with the iron moments forming a canted structure along the c axis. The angle between the two spin directions is 18°. The iron moment is (1.64+__0.05)#B at 5K. Mrssbauer measurements on 57Fe shows no indication of the low-temperature transition at Tt = 93 K. However, two different 1195n spectra are observed at low temperatures; an additional second site appears below 93 K. The Sn Mrssbauer spectra indicate that the spin direction is close to [100] at room temperature. With decreasing temperature, they slowly leave [100] forming an angle of ,~15 ° at 100K. The new Mrssbauer component below 93K indicates that the spins are canted along the [110] direction.

4.4.3. MnSne Corliss and Hastings (1963, 1964, 1968) performed neutron-diffraction measurements, indicating a simple antiferromagnetic structure below TN= 325 K consisting of ferromagnetic (110) sheets, coupled antiferromagnetically to each other. The spin direction is perpendicular to the sheets. A low-temperature transition at 73 K with accompanying hysteresis reported by Kouvel and Hartelius (1961) is interpreted as a change from alternating ferromagnetic sheets, state I (+ - + - ) to the sequence (+ + - - ) in state II (fig. 54). The Mn moment is 2.33#B at the transition, remaining practically constant down to 4.2 K. In the vicinity of 90 K neutron-diffraction studies further indicated a slight modulation of 0.5#B of the manganese moments with a wavelength of 31 A in the [110] direction.

256

O. BECKMAN and L. LUNDGREN

II i¢

Fig. 54. Antiferromagnetic ordering in the basal plane of tetragonal MnSn2. State I (+ - + -) exists from TN= 325 K to about 90K. Below Tt = 73 K, state II (+ + - -) prevails. Between 90K and Tt, neutron diffraction indicates a sinusoidal modulation of the spins (Le Caer et al. 1982).

Pulsed field measurements at 4.2K by Kouvel and Jacobs (1968) show a steep increase in magnetization indicating a II to I transition at 12 T. Le Caer et al. (1982) report 119 Sn M r s s b a u e r experiments on MnSn2. A broadening in the spectra above the lower transition suggests that the modulated spin component, observed in neutron diffraction, is perpendicular to the antiferromagnetic axis with a modulation amplitude of A#/# = 0.27 _ 0.02 at 72 K.

4.5. CrSbe CrSb 2 seems to be the only marcasite type TX 2 compound which shows magnetic order (Kjekshus et al. 1979). Heat capacity measurements give an antiferromagnetic transition at TN = 274.1 K (Alles et al. 1978). Neutron-diffraction studies by Holseth et al. (1970) indicate a simple uniaxial antiferromagnetic structure with the magnetic cell doubled along the b and c axes (fig. 55) and TN = 273 _ 2 K. The direction of the magnetic m o m e n t of 1.94#B is perpendicular to the (101) planes. The measured magnetic m o m e n t follows approximately a Brillouin function for S = 1.

4.6. CrtFel_tSb 2 This ternary compound has the same antiferromagnetic structure as CrSb2 (Kjekshus et al. 1979). The Curie point decreases linearly with temperature approaching zero for t = 0.5.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

ct

aJ

257

-

Fig. 55. Antiferromagneticstructure of CrSb2 with the magnetic cell doubled along the b and c axes according to Holseth et al. (1970). The relativespin directionsare marked by plus and minus signs. The spins are perpendicular to the diagonal (101) plane, which is shaded. For clarity, the antimony atoms are omitted. 4.7. MnSe, MnSee, MnTee These compounds crystallize in the cubic pyrite structure. They all show antiferromagnetic ordering. Hastings et al. (1959) performed magnetic susceptibility measurements down to 76 K and neutron diffraction experiments at 4.2 K. The susceptibility measurements give #eff = 6.30#B, 5.93#B, and 6.22#B for MnS2, MnSe2, and MnTe2, respectively, corresponding to a S = ~ spin state. The Curie-Weiss temperatures are 0p = 592, 483, and 528 K. Nrel temperatures are not given. The pyrite structure is a NaCl-like arrangement of T and X2 pairs with the pair axes parallel to various body diagonals. According to Hastings et al. (1959), MnS2 order with the type-III antiferromagnetic structure, with the magnetic cell twice as large as the chemical cell. MnSe2 shows a complicated ordering with the magnetic cell three times the size of the chemical cell. MnTe2 has the simple type-I ordering, with the magnetic cell equal to the chemical cell (fig. 56). The systematic change in spin structure among the three compounds has been discussed by Hirai (1987). 4.7.1. MnSe From low-temperature susceptibility measurements, Lin and Hacker Jr. (1968) report the Nrel temperature TN = 48.2 K and #eff = 6.16/~B. The antiferromagnetic structure has been confirmed in neutron-diffraction measurements by Hastings and Corliss (1976), who found the transition to be of first order with a hysteresis of 0.5K. Chattopadhyay et al. (1984) found no hysteresis. The magnetization follows a S = Brillouin function with a sharp drop at TN = 47.7 K, thus confirming the first-order transition. The Mn magnetic moments are parallel to the direction of the doubling of the chemical cell. 4.7.2. MnSee As regards MnSe 2, Dimmock (1963) has pointed out that the MnSe2 magnetic structure as given by Hastings et al. (1959) cannot exist in the immediate vicinity of

258

O. BECKMAN and L. LUNDGREN

MnS 2

MnSe 2

MnTe 2 Fig. 56. Antiferromagneticstructures of MnS2, MnSe2 and MnT% according to Hastings et al. (1959). Only the manganese atoms are indicated, with relative spin directionsmarked by filled and open circles. Spin directions are indicated for MnS2 and MnTe2. Later, neutron-diffractionmeasurements have in some cases revealed sinusoidal modulation structures.

a second-order transition to the paramagnetic state. He suggested a sinusoidally modulated structure close to TN. From neutron-diffraction measurements, Plumier and Sougi (1987) have shown the existence of a first-order transition at Tt = 48.5 K from the previously reported structure to two independent sinusoidally modulated magnetic structures of comparable amplitudes and propagation vectors along [100]. The first-order transition has also been reported by Chattopadhyay et al. (1987). They also made a small correction to the magnetic ordering earlier proposed by Hastings et al.'(1959).

4.7.3. MnTee MnTe2 has been studied by ~25Te M6ssbauer technique by Pasternak and Spijkervet (1969). An inconsistency between these results and earlier neutron-diffraction studies was resolved by a generalization of the magnetic ordering (Hastings et al. 1970). The critical behaviour at TN = 86.55 K has been analyzed through neutron-diffraction experiments b y Hastings et al. (1986) according to a 3d Ising model.

4.8. CoSe This ferromagnet has been studied by Adachi et al. (1968), who found Tc = 124K, slightly higher than Tc values of 110 and l 1 6 K reported by Benoit (1955) and

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

259

Heidelberg et al. (1966), respectively. Measurements of FMR and EPR have been made by Miyadai and Manabe (1980), of electrical resistivity by Yomo (1983) and of magneto-optical properties by Sato and Teranishi (1983).

4.9. CoSec Adachi et al. (1968) report TN= 93 K for this antiferromagnet.

4.10. Ternary systems 4.10.1. NiSe_xSe~ Stoichiometric and nonstoichiometric NiS2 with antiferromagnetic transitions in the region 40-50 K has been studied by Czjzek et al. (1974), Gautier et al. (1972, 1973) and Kikuchi et al. (1980). Magnetic measurements of the ternary nickel sulphurselenium system have been reported by Miyadai et al. (1983), by Mrri and Takahashi (1983) and by Sudo and Miyadai (1985). 4.10.2. CoPxSe-x, CoAsxSe_~, CoSe~Se_~ These ternary compounds are all ferromagnetic with a Curie temperature decreasing linearly from 122K for CoS2 to approximately 55K for x = 0 . 2 (Nahigian et al. 1974). 5. T 2 X 3 , T 3 X 4 ,

TsX6 compounds

The chromium dichalcogenides show several stoichiometric compositions with crystal structures that in general are derived from the NiAs structure (Jellinek 1957). On rapid cooling, the structure may be described with a NiAs-type cell with randomly distributed chromium vacancies. By slow cooling, the vacancies order, thus giving rise to several superstructures (Chevreton 1964, Andresen 1970). These structures show magnetic spin ordering, usually with antiferro- and ferrimagnetism. In table 22 the crystallographic structures (including NiAs) are listed that are found among the magnetically ordered T2 X3 compounds (table 23).

5.1. CreS3 There exists two forms, both of which are ferrimagnetic; rhombohedral C r 2 S 3 with Tc= 120K and trigonal C r 2 S 3 with Tc = l l 0 K (van Bruggen and Jellinek 1967). TABLE 22 Crystal structures of T2X 3 and T3X 4 compounds. Structure NiAs Cr2 $3 Cr2S a Cr3 $4

Hex. B81 Rhomb. Trig. Monocl.

Space group P63/mmc R3 P31c C2/m

No No No No

194 148 163 12

M= M= M= M=

2 2 4 2

260

O. BECKMAN and L. LUNDGREN TABLE 23 Magnetically ordered T2X3, T3X4 and TsX5 compounds.

Comp.

Magn. order

Struct.

a (A)

b (A)

c (/~)

fl

Cr2S3 Cr2S3 CrzSe3 Cr2Te3 Fe2Te3

Ferri Ferri AF F F(?)

Rhomb. Trig. Rhomb. Trig. Hex.

5.937 5.941 12.509 6.814 3.816

Cr3S4 Cr3Se4 Cr3Te4

AF AF F, AF

Monocl.* Monocl.* Monocl.*

5.964 6.32 6.89

3.428 3.62 3.94

11.272 91.6 11.77 91.4 12.35 91.2

Crs $6 CrsTe 6

AF, ferri F, AF

Trig. Monocl.*

5.982 6.913

3.970

11.509 12.44

16.698 11.182 34.765 12.073 5.6548

Tc (K)

TN (K)

122 110 43 180 10(?)

90.68

Commentt [a,b] [a, c] [-d] [e,c] If]

325

280 80 85

[a] [g] [g]

303 327

168 102

[a, c] [e]

* Lattice parameters given in the unconventional I2/m setting. t Comments: [a] Jellinek (1957). [b] Hexagonal descr, M = 6. [c] Hexagonal descr, related to NiAs unit cell by a = a'~/3, c = 2c'. [d] Wehmeier et al. (1970). [el Andresen (1970). If] Pearson (1967), data for the NiAs cell. [g] Bertaut et al. (1964). F r o m neutron-diffraction measurements, Bertaut et al. (1968) find three magnetic sublattices in the r h o m b o h e d r a l structure; in the hexagonal description lattice positions 3(a) and 3(b) are parallel and 6(c) antiparallel (fig. 57). The different thermal variation in sublattice magnetization gives rise to a weak ferrimagnetism, which increases from zero at 0 K, goes through a m a x i m u m at 80 K and disappears at Tc = 122 K. N e u t r o n diffraction m e a s u r e m e n t s by van L a a r (1967a) on trigonal Cr2S3 give magnetic m o m e n t s of ~ 2#B on lattice sites 2(b), 2(c) and 4(f). The magnetic structure is a spiral with a periodicity of twice the crystallographic c axis. The average ferromagnetic c o m p o n e n t is estimated to only 0.01/~ B per Cr ion. Yuzuri et al. (1987) have determined the pressure effect on the Curie temperature to be + 1.0 K / k b a r . They also measured the change in lattice p a r a m e t e r s (NiAs structure) with temperature.

5.2. CreSe 3 Chevreton et al. (1963b) reported a r h o m b o h e d r a l structure, which is i s o m o r p h with CrzS 3. M e a s u r e m e n t of the electrical conductivity shows semiconductivity with a b a n d gap of 0.156eV. The c o m p o u n d is reported to be antiferromagnetic with TN = 43 K (Yuzuri 1973).

5.3. CreTe3 Chevreton et al. (1963a) found a trigonal structure, i s o m o r p h o u s with the trigonal Cr2S 3. This trigonal form shows ferromagnetic ordering with T c = 1 8 2 _ 2 K

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

261

b~

aE (~) 3(a), 3(b)

~

6(c)

Fig. 57. Hexagonal unit cell with the magnetic structure of rhombohedral Cr2 $3 after Bertaut et al. (1968). Spins in lattice position 6(c) are antiparallel to spins in 3(a) and 3(b). (Andresen 1970). Fully o c c u p i e d c h r o m i u m layers have spins parallel to the c axis with #s = 2.56#B. T h e c h r o m i u m ions, in layers c o n t a i n i n g vacancies, h a v e negligible m o m e n t s (fig. 58). T h e pressure effect o n the Curie t e m p e r a t u r e is - 1 . 7 8 K / k b a r (Yuzuri et al. 1987).

•

Cr I

+ Crli

[ ] Vac

Fig. 58. Hexagonal unit cell of ferromagnetic Cr2Te3 after Andresen (1970). Nonmagnetic Cq in 2(c): _+(½, ~, ¼); magnetic Cql in 4(b): -+ (7, a 7, 2 z), __+(7, 1 7, 2 ~1 - z) (z ~ 0) and vacancies in 2(a): + (0, 0, ¼) and 2(d): +(~,~,~). 2 i i

262

O. BECKMAN and L. LUNDGREN

5.4. CreS3_xTe x

Yuzuri and Yusuki (1986) have investigated the magnetic properties of this ternary system. They find a transition from the ferrimagnetism of CrzSa to the ferromagnetism of Cr2Te3 at x = 0.6, and an anomaly at x = 2.7. The crystal structures are treated as NiAs structures with ordered vacancies. 5.5. CreSe3_x Tex

From magnetization measurements, Yuzuri and Segi (1977) found that the transition from antiferro- to ferromagnetism takes place at x = 2.5. This transition is also noticed in the measurements of the lattice parameters. Measurements in the paramagnetic region gave #off = 3.8/~B for all x giving S = ~ for the chromium ions (g = 2). 5.6. FeeTe3

Hermon et al. (1974) measured the magnetization and Mtssbauer effect between liquid-helium temperature and 300 K. There is an indication of a transition to weak ferromagnetism at 10K. An internal field of 1.1T was observed at the lowest temperatures. 5.7. CrtFee_tTe 3

This ternary system has been studied by Terzieff (1983) by magnetization measurements in the paramagnetic region between 100 and 1100 K. The paramagnetic Curie temperature decreases from slightly above 200K for CrzTe3 to zero at t = 1.28, indicating a gradual decrease in the ferromagnetic coupling between the c planes when chromium is replaced by iron. 5.8. Cr3S 4

Cr3 $4 has a pseudohexagonal monoclinic structure of the NiAs-type, and is antiferromagnetic with TN = 280 K (Bertaut et al. 1964). Alternating ferromagnetic (101) planes have spins parallel to [10T]. The Curie-Weiss temperature 0p = - 5 4 7 K. 5.9. Cr3Se4

Bertaut et al. (1964) found the same spin configuration as in Cr 3 84 with TN = 80 K. Yuzuri (1973) reported antiferromagnetism with TN = 82 K. 5.10. Cr3Te 4

Bertaut et al. (1964) reported ferromagnetism with Tc = 329 K. Below 80 K, they find a weak superimposed antiferromagnetic component, explaining a decrease in the magnetization at low temperatures. Andresen (1970) reported a total spin value of

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

263

S = 1.68 and S = 1.50 for the two chromium sites, respectively. The spins are nearly parallel and form g 30 ° angles with the a axis. Tc = 325 + 2 K. The average ferromagnetic moment is 2.54ktB (g = 2). There is also a weak antiferromagnetic moment below T = 85 K. From magnetization measurements Yamaguchi and Hashimoto (1972) find Tc = 316K and a saturation moment of 1.79#B per Cr atom at 4.2K.

5.11. Cr3Se4_~Te~ Yuzuri and Segi (1977) studied these ternary compounds and found a transition from antiferro- to ferromagnetism at x = 0.8.

5.12. CrsS 6 The structure is given by Jellinek (1957) as a trigonal with space group P31c. The structure can be considered as the NiAs structure with every sixth chromium atom removed by ordered vacancies. The compound is antiferromagnetic below 168 K and ferrimagnetic between 168K and To= 303K, with the spins in the basal plane (Jellinek 1957, Kamigaichi 1960). Neutron diffraction experiments by van Laar (1967b) indicate an antiferromagnetic screw-type spiral with the propagation vector along the c axis and a periodicity of ~ 50 A. All four chromium sites, 2(a), 2(b), 2(c) and 4(f), have moments slightly below 3#B. In the ferrimagnetic region, sites 2(b) and 2(c) are antiparaUel to 2(a) and 4(f) (fig. 59). The net total moment is 0.2#B per unit cell containing ten chromium ions. Popma et al. (1971) have done ferrimagnetic resonance experiments at 35 GHz and Konno and Yuzuri (1988) at 9.3 GHz. Both groups find unusually low resonance fields, which Popma et al. ascribed to magnetic anisotropy. This effect could be ruled out by Konno and Yuzuri, who find extremely

Cr - ~ " 2(a) . ~ r " 4(f) 2(b) ~

Vac [] 2(d)

2(c)

Fig. 59. Ferrimagnetic spin arrangement in trigonal Cr5S6 according to van Laar (1967b).

264

O. B E C K M A N and L. L U N D G R E N

large g values with a maximum of g = 20 at 250 K. From magnetization measurements, they obtained a maximum net magnetic moment of 1.3#B at 208 K.

5.13. CrsTe 6 This compound has a monoclinic structure (C2/m) and Tc = 327 _ 2 K. From neutron diffraction measurements, an average magnetic moment of 2.40#B (g = 2) along the a axis is observed. Below TN= 1 0 2 + 2 K , there is an antiferromagnetic ordering leading to a doubling of the unit cell in the a and c directions (Andresen 1970). 6. T3X

compounds

Among the Ta X compounds, ordered magnetic structures are only found for phosphides and elements belonging to the fourth group. The phosphides crystallize in the tetragonal system, while the group four compounds have cubic or hexagonal structures. The cubic compounds are related to the Heusler alloys. Here, we only deal with the proper T 3X compounds, however. The relevant crystal structures are listed in table 24 and table 25 gives a list of the magnetically ordered compounds.

6.1. Mn3Si The structure, which is shown in fig. 60, has four crystallographic sites (A, B, C, D). There are two non-equivalent manganese positions. Mn~ atoms in B sites have eight nearest neighbour Mnn atoms, and Mnn atoms in A, C sites have four Mn~ atoms and four Si atoms as nearest neighbours. Si occupies the D sites. M n 3 Si is an itinerant antiferromagnet with a Nrel temperature of TN= 25.8 K (Tomiyoshi and Watanabe 1975). The incommensurate spin structure is described either as a proper screw or as a transversal sinusoidal structure. From neutron-diffraction measurements, Tomiyoshi et al. (1987a,b) found that the magnetic satellites give a propagation vector q = 0.425a'11 parallel to (111). The satellites appear near a Brillouin zone boundary in pairs along a [111] direction. The magnetic moment is 1.7#B for Mni and only 0.19/~B for Mnu. Already a small substitution of iron for manganese turns the incommensurate spin structure into a commensurate structure (Tomiyoshi et al. 1987a). Thus, Mn2.8 Feo.2Si is a commensurate antiferromagnet with the magnetic cell twice the chemical unit

TABLE 24 Crystal structures of TaX compounds. Structure BiF a AuCu3 NiaSn A13Ti NiaP

Cubic D0 a Cubic L12 Hex. D019 Tetr. D022 Tetr. DOe

Space group Fm3m Pm3m P6a/mmc I4/mmm I4

No No No No No

225 221 194 139 82

M M M M M

= = = = =

4 1 2 2 8

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

265

TABLE 25 Magnetically ordered TaX compounds. Comp.

Magn. order

Struct.

Mn3 Si Mn3Ge MnaGe Mn3Sn

AF AF Ferri AF

D03

F%Si Fe3Ge FesGe Fe3Sn

F F F F

D03

D019

5.646 5.161 3.668 5.458

MnsP F%P

AF F

D0o D0,

9.181 9.107

D019 D022 D019 D019 L12

a (A)

c (A)

5.722 5.347 3.816 5.665

4.374 7.261 4.531

Tc (K)

TN (K)

Tt (K)

#s (PB)

26 365

[a] [b] [c] [d]

920 420

4.361

810 640 740 743

4.568 4.460

716

4.207

~230 380

Comment*

2.03 2.21 2.27

[e] [lo] I-f] [g]

1.84

I-fl [h]

115

* References are only given to structural parameters. For other data, see text. [a] Aronsson (1960). [b] Lecocq et al. (1963). [c] Kg&ir and Kr6n (1971), Tc estimated value. [d] Tomiyoshi (1982). [e] Lecocq and Michel (1964). If] Pearson (1967). [g] Trumpy et al. (1970). [hi Rundqvist (1962a). m

v

x

•

Mn I (B)

w

0

Si (D)

O Mnli (A;C) Fig. 60. The cubic D03 structure of Mn3 Si. There are four crystallographic sites, A, B, C, D with two nonequivalent manganese positions, Mn~ and Mnn. F% Si crystallizes in the same structure. cell. T h e N6el t e m p e r a t u r e of 23 K is a little lower t h a n for Mn3 Si. It varies s m o o t h l y with c o m p o s i t i o n .

6.2. Mn3Ge, Mn3Sn F i g u r e 61 shows the h e x a g o n a l D019 structure p r o j e c t e d o n a c plane. T h e c o m p o u n d s are usually r e p o r t e d as n o n s t o i c h i o m e t r i c with a n excess a m o u n t of m a n g a n e s e .

266

O. BECKMANand L. LUNDGREN

0

0

0

O

%.°/0 O/oO%Oo

@

O

O

O

Mn, O Fe

~

Ge, 0 ~ Sn

® 3c

4 Fig. 61. The hexagonal D019 structure of MnsGe, MnaSn, FeaGe and Fe3Sn projected on the c plane. The atoms are situated at the levels¼c and ¼c in the c direction as indicated above. From a neutron-diffraction study of Mn3.4Ge, K~tdfir and Krrn (1971) reported a triangular spin configuration with magnetic moments of 2.4#a per Mn atom and TN = 395 ___10 K. Magnetic, X-ray and neutron-diffraction measurements of Mna.a Sn showed the same type of triangular spin structure with TN = 420 K (Zimmer and Krrn 1972, 1973). In both compounds, the spins are confined to the c plane. The triangular spin configuration with weak ferromagnetism in Mn3Ge and Mn3Sn were studied by polarized neutron diffraction by Nagamiya et al. (1982). With the same technique, Tomiyoshi et al. (1983) studied Mn 3Ge. The magnetic form factor of the Mn atoms was found to agree quite well with that expected for Mn z +. The magnetic moment of the Mn atoms was 1.93#B at 77K. Tomiyoshi and Yamaguchi (1982) showed that the triangular spin structure of Mn3Sn is stabilized by the Dzyaloshinskii-Moriya interaction (Dzyaloshinskii 1958, Moriya 1960). The symmetry of the anisotropy energy does not agree with the spin symmetry. The spin triangle is deformed, resulting in an observed weak ferromagnetic moment in the c plane with a maximum of ~ 0.006#B per unit cell of Mn3.2 Sn (Tomiyoshi et al. 1987c) (fig. 62). For Mn3 Sn, this deformation disappears in a first-order transition at Tt = 230K with a temperature hysteresis of about 15K (Ohmori et al. 1987). At low temperatures, the spin structure transforms into a periodic triangle-helix structure. The propagation vector is parallel to the c axis with a period of 12c. The manganese moment is 2.75#B at 7 K and 2.55#B at 100 K to compare with the room-temperature value of 1.78#B given by Tomiyoshi (1982), which could be extrapolated to zero temperature by a S = 1 Brillouin function giving 2.1/tB. The Dzyaloshinskii antisymmetric spin interaction in these compounds have been discussed by Kataoka et al. (1984) and Sticht et al. (1989).

6.3. Mn3Ge, tetragonal phase Kfidfir and Krrn (1971) investigated the D022 phase by neutron diffraction. This phase is stable at low temperatures and transforms to the hexagonal D019 phase at

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

267

(~(~B)

0.01 t/

L Mn 3.2Sn

IIC

o

, , , T(K) 0 160 200 300 400 500 Fig. 62. Spontaneous magnetization parallel and perpendicular to the c axis in nonstoichiometric Mn3Sn according to Tomiyoshi et al. (1987c). Between the two transition temperatures, Tt=230K and TN= 420 K, a small magnetic moment appears in the c plane. about 860 K. The magnetic structure is ferrimagnetic with the spins along the c axis (fig. 63). A net magnetization of 0.9#B per unit cell was measured. Two combinations of manganese moments are consistent with the resultant magnetization, i.e., either #1 = 3.4 ___0.3#B and #n = 1.9 _ 0.2#B or #i = 3.8 ___0.4#B and #n = 1.7 + 0.2#B. Tc lies above the tetragonal-hexagonal transformation, but is estimated to be about 920 K.

6.4. Fe3Si The crystal structure (cubic D0a) is the same as for Mn3Si (fig. 60). There are four crystallographic sites (A, B, C, D). Iron occupies two non-equivalent positions: Fei (B site), which is surrounded by eight Fe atoms and Fen (A and C sites), which

OjJ7

)e( $ Mn

•

Ge

Fig. 63. Magnetic structure of ferrimagnetic MnaGe in the tetragonal D0z2 phase.

268

O. BECKMANand L. LUNDGREN

have four Fez and four Si atoms (D sites) as nearest neighbours. Fe 3Si is a ferromagnet with Tc = 808 K and a net magnetic moment of 1.50#B per Fe (Lecocq and Michel 1964). Shinjo et al. (1964a,b) found Tc = 823 K and a saturation magnetization of 1.67#B per Fe with 2.15#B for Fe~ and 1.15#B for Fen. From M6ssbauer measurements, they give hyperfine fields of 32 T at Fei and 20.5 T at Fen at 77 K. Hines et al. (1976) find a saturation moment of 4.83#B, consistent with magnetic moments of +2.20#B, + 1.35#B and --0.07#B for Fei, Fen and Si sites, respectively. The magnetocrystaUine anisotropy constant K 1 in quenched and annealed Fe 3Si has been measured by Goto and Kamimori (1983). Extrapolation to zero temperature gives K1 = +10.8kJ/m 3 and K1 = - 1 1 . 4 k J / m 3 for ordered (annealed) and disordered F%Si, respectively. The anisotropy energy decreases in absolute value with temperature to + 5.4 and - 5.8 kJ/m 3 at 300 K.

6.5. Fe3_tTtSi Transition elements substituted in Fe3 Si show a selective site occupation. This has been demonstrated by NMR (Burch et al. 1974, 1981), neutron diffraction (Pickart et al. 1975) and Mrssbauer effect (Blaauw et al. 1977). The results for 3d transition elements are summarized in a review paper by Niculescu et al. (1983). The elements to the left of Fe in the periodic system (Ti, V, Cr, Mn) show a preference for Fei (B) sites, while the elements to the right (Ni, Co) prefer Fe n (A, C) sites. For the description of hyperfine fields and atomic moments a model is presented, which takes into account two main contributions. One contribution is linearly dependent on the site moment and the other on the average moment of the first nearest neighbours. By spin-echo NMR, Burch et al. (1981) analysed 3d, 4d and 5d metal substitutions in the Fe3 Si system. Of the 4d elements, Ru, Rh and Pd enter into the Fen (A, C) sites with t < 0.15 to 0.25. The 5d elements Re, Os and Pt also enter the same sites with a maximum t value of 0.1 to 0.25.

6.6. Fe3Ge, hexagonal D019 Fe3 Ge exists in two close-packed structures (compare Mn3 Ge). The high-temperature hexagonal phase (fig. 61), is stable above 970 K (Kanematsu and Ohoyama 1965a,b), but can be retained at low temperatures. From magnetization and Mrssbauer measurements, Drijver et al. (1976) find Tc = 640K for the hexagonal phase. The spins are then parallel to the c axis. At Tt = 380 K, there is a second-order spin-flip transition to the c plane. Extrapolation to zero temperature gives a magnetic moment of 2.0#B per iron atom and a hyperfine field of 26 T.

6.7. Fe3Ge, cubic L12 Drijver et al. (1976) found great similarities in the ferromagnetic properties of the two Fe3 Ge phases. The cubic phase has a larger saturation magnetization of 2.20/~B (T = 0 K) than the hexagonal phase, and also a slightly larger Curie temperature, namely Tc = 740K. The preferred spin direction is (100) with a large anisotropic

COMPOUNDS OF TRANSITIONELEMENTSWITH NONMETALS

269

hyperfine field (1.8 T), mainly caused by an anisotropic g-factor. The hyperfine field is 25 T.

6.8. (Fe~_tVt)sGe A M6ssbauer study of this ternary system is reported by Haggstrrm et al. (1985). The hexagonal D019 structure of Fe3Ge is stable for t ~<0.10. For 0.17 ~
6.9. (Fel-tNit)sGe Kanematsu and Takahashi (1984) have done magnetization and X-ray studies on this ternary system. The hexagonal D019 structure of FeaGe prevails for t ~<0.05. With increasing nickel content, a two-phase region appears, followed by the D03 (or Heusler-type L21) structure within the region 0.15 ~ 0.6. The ferromagnetism disappears for t ~>0.8. The Curie temperature stays approximately constant at ~ 600 K for t ~<0.12, increases abruptly to 740 K for t = 0.13 and gradually decreases for increasing nickel content.

6.10. FesSn Trumpy et al. (1970) found from Mrssbauer experiments a Curie temperature of Tc = 743 K for this ferromagnet with the spins parallel to the c axis. The saturation moment is 2.27 + 0.02#B per Fe atom. Hyperfine fields of 26.8 and 10.3 T are obtained for the Fe and Sn positions, respectively.

6.11. MnsP Gambino et al. (1967), in a study of transition-metal phosphides, reported MnaP as an antiferromagnet with TN = 115 K. From susceptibility measurements in the paramagnetic region they find #p = (2S)= 1.68#B.

6.12. FesP Magnetization measurements by Meyer and Cadeville (1962) indicated a Curie temperature of Tc = 716 K and a saturation magnetization of 1.84#B per iron atom at zero kelvin. The material is magnetically very hard with the spins in the basal plane. The anisotropy energy constants are K1 = - 5 3 0 k J / m 3 and K2 = +240kJ/ m 3. Mrssbauer measurements on FeaP have been reported by Wfippling et al. (1971) and M6ssbauer, magnetization and neutron-diffraction experiments by Lisher et al.

270

O. BECKMAN and L. LUNDGREN

gO

® @

©e

Fe I

@

0 ®

•0 @

0

ol

® @

e~

O~

Fei10

• o

@

G

@

®

®

o

0

O

C

0

FeriI E)~

#

~

PO0

• _ c2

®3~4

Fig. 64. Basal plane projection of the atomic positions in Fe3P (tetragonal D0e) with eight formula units per cell. The atoms are situated at the approximate levels 0, ¼c, ½c and ¼c in the c direction, as indicated above.

(1974). Magnetization measurements gave a saturation moment of 1.70 ___0.06#B at room temperature and 1.84 ___0.06#B at 4.2 K. The anisotropy energy in the basal plane is ,,~2kJ/m 3. The coercive field is ~<160A/m at room temperature and ~<320 A/m at 4.2 K. The crystallographic cell contains eight Fe3P units with three different iron sites (fig. 64). Room-temperature neutron diffraction gave the magnetic moments 2.12 ___0.04pB, 1.25 ___0.04pB and 1.83 ___0.04#B for the iron sites Fe], Fel~ and Fern, respectively. The M6ssbauer spectra indicate a splitting of the magnetic moments of ,-~0.1#B for the atoms on each iron site. The hyperfine fields are 28.4 and 27.3T for Fe,, 17.3 and 17.5T for Fell and 23.0 and 25.0T for Feiii at room temperature. N M R measurements by Koster and Turrell (1971) give hyperfine fields which are in good agreement with the M6ssbauer data.

7. T s X 3 compounds Magnetically ordered T s X 3 compounds generally crystallize in the structures given in table 26. The Ni2 In-type crystal structure is shown in fig. 65. Crystallographic and magnetic data of T s X 3 compounds are given in table 27. TABLE 26 Crystal structures of magnetically ordered T 5X 3 compounds. Structure Cr s B 3-type Tetr. D81 MnsSia-type Hex. D88 Ni2In-type Hex. B82 (partially filled)

Space group I4/mcm P63/mcm P63/mmc

No 140 No 193 No 194

M=4 M=2 M= 2

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

271

Ni2In

2(a) C) (000),(00 1) Ni

2(d) •

In

(2 1 3

o

Fig. 65. Crystal structure of hexagonal Ni2In (B82). TABLE 27 Crystallographic and magnetic data for TsX 3 compounds. Compound

Structure

a (A)

c (A)

FesPBz Fe5SiB2 MnsPB2 Mn5SiB2

D81 D81 D81 D8a

5.482 5.550 5.54 5.61

10.332 10.332 10.49 10.44

MnsSi 3 MnsGe 3 Fe5 Si3

D8 s D8 s D8s

6.916 7.195 6.755

4.824 5.032 4.717

Tc (K)

TN (K)

628 784 411 312

16(1)

4(c)

1.6 1.9

2.2 2.6 1.6' 1.1'

68 296 373

#s (#B)

4(d)

6(g)

0.4 1:85

1.2 2.9 1.2"

2(a) Fez Gea Mn 5Sn 3 Fes Sn3

B82 B82 B82

4.020 4.39 4.22

5.024 5.51 5.22

485 263 600

2(d)

1.4

1.8 1.2"

2.1"

* ps is given in tiE/transition element. T h e t e r n a r y c o m p o u n d s T s X B 2 , with T = F e o r M n a n d X = Si o r P, are isostrucrural a n d b e l o n g to the t e t r a g o n a l C r 5 B 3 t y p e structure. T h e space g r o u p is I 4 / m c m , with 16 T~ in 16(1), 4 Tn in 4(c), 8 B in 8(h) a n d 4 X in 4(a). The m a g n e t i c m o m e n t s as well as the Curie t e m p e r a t u r e s of the Ts SiB2 c o m p o u n d s are generally f o u n d to be larger t h a n in the c o r r e s p o n d i n g Ts PB2 c o m p o u n d s . T h e c o m p o u n d s have small ranges of h o m o g e n e i t y , p r e s u m a b l y a s s o c i a t e d with s u b s t i t u t i o n of B a t o m s for X a t o m s in the 4(a) position. This results in a n e n h a n c e d m o m e n t of the TI a t o m s with a perturbed near environment.

272

O. BECKMANand L. LUNDGREN

7.1. FesPBe and FesSiB 2 X-ray investigations of the ternary system F e - P - B by Rundqvist (1962a) revealed that the ternary compound FesPB2 has the tetragonal structure of the Cr5B3 type, with a = 5.48 A and c = 10.33 A. Magnetization measurements by Blanc et al. (1967) gave simple ferromagnetic behaviour with Tc varying between 615 and 639 K, depending on the composition. Tc for the stoichiometric compound was reported to be 628 K and the average magnetic moment per iron atom 1.73#B, extrapolated to 0 K. Mrssbauer and X-ray studies by H/iggstrrm et al. (1975c) indicated simple ferromagnetism with the tetragonal axis as the easy direction. At 80 K, the hyperfine fields were found to be 16.5 T at Fel and 22.2 T at Fen, which roughly correspond to 1.6#B and 2.2#B, respectively. It was observed that in the nonstoichiometric compounds a third, low-intensity, component in the spectrum was present. From crystallographic data, which indicated that phosphorous positions are the only sites of defects in the structure, it was inferred that the third component in the Mrssbauer spectrum emanates from Fei with a perturbed environment, where the phosphorous position is occupied by boron atoms. The magnetic hyperfine field at this perturbed site is 20% higher than at the unperturbed sites. The intensity of this component increases with increased B/P atomic ratio. These results are in accordance with the result of boron excess in Fe3P and Fe2P (W~ippling et al. 1971). Mrssbauer spectroscopy investigations (W~ippling et al. 1975, Ericsson et al. 1978) on Fe5 SiB2 showed simple ferromagnetism in the temperature range from 140 K up to the Curie temperature Tc = 784 K, with the spins parallel to the c axis. At lower temperatures, there were indications that the spins are located in or close to the ab plane and that the pure ferromagnetic coupling is partly destroyed. At 80 K, the magnetic hyperfine fields were reported to be 19.2 T at Fe~ and 25.9 T at Fen, which roughly correspond to 1.9#B and 2.6#B, respectively. The ratio between the magnetic hyperfine fields is approximately 1.35, closely the same as for FesPB2. 7.2. MnsPBe and MnsSiBe From magnetic and N M R measurements on MnsPB2 and MnsSiB2 by Kasaya (1975) it was proposed that these compounds are simple ferromagnets with the easy axis of magnetization along the c axis. The Curie temperatures are 411 and 312K, and the average magnetic moments 1.6#B and 1.1#B, respectively. Kasaya only observed one intense line in the 55Mn N M R spectra, interpreted to arise from the Mn atoms at the 16(1) site, and the structures of the spectra were assumed to be due to resonances at the domain walls. The absence of any 55Mn signal from the Mn atoms at the 4(c) site was left as an open question. In an alternative analysis of these data, W/ippling et al. (1976) identified the signals from both the manganese sites and the average magnetic hyperfine field at the manganese nuclei was estimated to be 18.2 and 16.5T for MnsSiB2 and MnsPB2, respectively. It was noted that the hyperfine field, and thus the magnetic moment, is smaller on the 4(c) position than on the 16(1) position for MnsSiB2, contrary to the other compounds.

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273

7.3. Mn5Si 3 This compound is prototype (Aronsson 1960) of the hexagonal D88-type crystal structure. The space group is P63/mcm with the atomic positions: 4 Mn~ in 4(d), 6 Mnii in 6(g) and 6 Si in 6(g). Neutron-diffraction measurements by Lander et al. (1967) on single crystals gave a magnetic ordering temperature of 68K with a complicated antiferromagnetic structure. The model proposed consists of a modulated noncollinear spin structure propagated through the crystal in three hexagonally related directions. The average magnetic moment was found to be 0.4(1)#B for Mn~ and 1.2(1)#a for Mnn, and the moments lie in the basal plane. From measurements of the field and temperature dependences of the magnetization in different crystallographic directions, Sudakova et al. (1975) questioned the proposal that all moments are located in the basal plane. The magnetic phase transition at 68 K is also revealed as anomalies in the linear thermal expansion and specific heat (Gel'd et al. 1972) and thermal and electrical conductivities (Meizer et al. 1974). In these measurements, a second transition at 99 K is observed, the origin of which is not yet clear. It was found by S6nateur and Fruchart (1966) and S6nateur et al. (1967) that small substitutions of carbon in the Mn5 Si3 lattice induce ferromagnetism. Tc increases rapidly up to the limiting value 152 K for Mn5 SiaCo.22 and with an average value of the magnetic moment #s = 1.27#B per manganese atom, extrapolated to 0 K. 7.4. Mn5Ge3 This compound is isostructural with MnsSi3. Early results from magnetization measurements implied simple ferromagnetism with Tc around 300 K and with a mean saturation moment ranging from 2.35#B to 2.5#B, and measurements by Kappel et al. (1973) led to a moment of 2.60(2)#B per Mn atom at 4 K. Magnetic anisotropy measurements on a single crystal by Tawara and Sato (1963) showed that the easy axis of magnetization is parallel to the c axis. The uniaxial anisotropy constant is K = 4.2 x 105 J/m a at 77 K and K = 3.0 x 104 J/m a at 300 K. Polarized neutron scattering experiments on single crystals by Forsyth and Brown (1965) gave a moment of 1.7(1)#B for the 4 Mnx atoms on the 4(d) position and 2.7(1)#B for the 6 Mnn atoms on the 6(g) position, and the moments are aligned along the c direction. By combining zero-field NMR techniques with specific heat measurements below 1 K, Jackson et al. (1965) uniquely determined the effective nuclear fields at the two Mn sites as 19.5 and 39.9 T on the 4(d) and 6(g) sites, respectively. This observation of a larger moment on the 6(g) site is at variance with the early proposed scheme by Kanematsu (1962) which predicts a larger moment on the 4(d) site. 7.5. Mns(Gel-xSix)3 X-ray and magnetization measurements by Kappel et al. (1976) showed that a continuous series of solid solutions can be obtained over the complete concentration range. The system is ferromagnetic in the range 0 ~<x ~<0.75. The Curie temperature

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o. BECKMANand L. LUNDGREN

decreases from 296 K (x = 0) to 151 K (x = 0.75) and the average magnetic moment decreases slowly from 2.60/~B to 2.15#B. For x = 0.8, it becomes antiferromagnetic, but the magnetic structure goes over into a ferromagnetic arrangement in a field of about 4 T at 4.2 K. Neutron-diffraction studies by Sheinker et al. (1977) implied that antiferro- and ferromagnetic reflections coexist well below this concentration. From N M R studies by Pannisod et al. (1983), it was shown that the transition from ferromagnetic Mn5 Gea to antiferromagnetic Mn5 Si3 takes place inhomogeneously. Manganese atoms with at least two Si neighbours have much smaller moments than the others. They recover their full moment under an applied field, which results (at a local scale) in the metamagnetic transition observed for x = 0.8. For x > 0.8, antiferromagnetism occurs on the bulk scale. 7.6. Fe5Ge3

This compound has the hexagonal crystal structure of the B8 2 type (see fig. 65). The space group is P63/mmc. There is some ambiguity as to the vacancy distribution. It was early proposed by Kanematsu and Ohoyama (1965a) that the unit cell formula is Fez+zxGezAe_zx , with 2 Ge atoms at the 2(c) sites, 2 Fe atoms at the 2(a) sites, and 2x Fe atoms and (2 - 2x) vancancies (A) at the 2(d) sites. This atomic distribution is supported by some X-ray and M6ssbauer effect measurements (e.g., Hall et al. 1977, Raj et al. 1978, Bara et al. 1981), although alternative models have been suggested (e.g., Daniels et al. 1975, Bhargava and Iyengar 1976). The M6ssbauer spectrum can be divided into three components, where one Zeeman sextet is assigned to 2(a) sites and the two others to 2(d) sites. At 78 K, Bara et al. (1981) found that the hyperfine fields are 13.5T at the (2a) site and 20.5 and 17.0T a t the 2(d) site. Measurements on oriented particles in external fields up to 5 T by Hall et al. (1977) indicated a collinear magnetic structure. A large anisotropy in the hyperfine magnetic field was reported. Magnetization measurements by Yasukochi et al. (1961) showed that FesGe3 is a simple ferromagnet with Tc = 485 K and a mean magnetic moment of 1.59#B per Fe atom. Measurements of magnetocrystalline anisotropy and magnetostriction by Tawara (1966) showed that the moments are located in the basal plane and the uniaxial anisotropy constant K = - 5 . 1 × 105J/m 3 at 300K and K = - 8 . 4 × 105 J/m 3 at 77K. A weak (roughly 10J/m 3) basal plane anisotropy could be detected. A neutron diffraction study by Forsyth and Brown (1965) gave a magnetic moment of 1.4(1)#B at the 2(a) site and 1.9(1)#B at the 2(d) site, in good agreement with the average moment found from magnetization measurements by Yasukochi et al. (1961). The result from this neutron diffraction study differs from the results obtained by Adelson and Austin (1965), Austin (1969) and Katsuraki (1964b), where a larger moment was reported for the iron atoms at the 2(a) site and a canting of the moments was suggested. 7.7. (FetMnl_~)sGe3

Compounds of this system have the hexagonal D88-type structure for t < 0.2 and the hexagonal B82 type for t > 0.6. The magnetic properties have been studied in

COMPOUNDS OF TRANSITION ELEMENTSWITH NONMETALS

275

several investigations (Suzuoka et al. 1968, Austin 1969, Reiff et al. 1972, Bara et al. 1981). X-ray, neutron diffraction, magnetization and M6ssbauer effect measurements by Bara et al. (1981) showed that all compounds are ferromagnetic with collinear magnetic ordering of the spins. Substitution of Mn in FesGe3 almost exclusively takes place at the 2(a) position. The magnetic moments and Curie temperatures decrease with Mn substitution. Substitution of Fe in MnsGe3 occurs at the 4(d) position. The magnetic structure of Mn4FeGe3 is analogous to Mn5Gea. The magnetic moments at 4(d) and 6(g) sites are 1.55(15)/~B and 2.45(15)/~B, respectively. The moments are oriented parallel to the c axis. In FesGe3, the moments are located in the basal plane. 7.8. ( F e t T l _ t ) 5 G e 3, T = Ni or Co

Cos G% and NisG % show Pauli paramagnetism. Magnetization measurements by Kanematsu et al. (1962, 1963) showed that substitution of Ni atoms in CosGe3 fills up the d-band in an analogous way as the s-electrons of Cu fill the d-band in CuNi alloys. Substitution of Fe in CosGe3 results in an increase of the paramagnetic moment (#elf) and in a decrease of the Pauli susceptibility (Xo). Ferromagnetism occurs for t > 0.25. M6ssbauer effect studies by Bhargava and Iyengar (1976) showed that the Co atoms preferentially occupy the 2(a) sites for t > 0.55. Substitution of Fe in Ni5 G% initially results in an increase of Zo while #af is small. With increasing Fe substitution, )~o decreases and ~teff increases. 7.9. FesSi3

This compound has been reported by Weill (1943) to have the hexagonal Mn5 Si3(D88) type structure with a = 6 . 7 5 5 A and c=4.717/k. From magnetization and M6ssbauer spectroscopy measurements, Shinjo et al. (1964a) reported simple ferromagnetism with an average moment per iron atom #s = 1.2#~ and Tc = 373 K. The low-temperature hyperfine fields at Fel and Fen were tentatively determined to be 23.5 and 13.5 T, respectively. 7.10. MnsSn~

On the basis of crystal-structure determination, Nowotny and Schubert (1946) identified three binary Mn-Sn compounds; Mnll Sn3 of hexagonal Ni3Sn type, Mn2Sn of hexagonal Ni2In type and MnSn2 of tetragonal CuAlz type. Mn2Sn has a wide homogeneity range, Mn2.o5 Sn-Mnl.v7 Sn. The magnetic properties of Mnl.wSn (denoted MnsSn3 in table 27) have been investigated by Yasukochi and Kanematsu (1961). It was found that the magnetic properties depend strongly on sample preparation. A variation of Tc between 226 and 263 K with a corresponding change in average magnetic moment between 1.23#B and 0.92pB was reported.

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7.11. FesSn3 This compound as well as several other iron-tin compounds have been studied by magnetization (Jannin et al. 1963) and M6ssbauer spectroscopy measurements (Yamamoto 1966, Dj6ga-Mariadassou et al. 1970, Trumpy et al. 1970, 1971). The B82 compound Fes Sn3 has a small homogeneity range and shows several structural changes where the two limits are the 73 and 72 forms. Crystallographic and M6ssbauer effect measurements on 73 reveal a random distribution of iron vacancies in ¼ and ¼ planes while for 72 order appears in the vacancy distribution. Fe5 Sn3 is ferromagnetic with an average magnetic moment of 2.10/~B per iron atom. The Curie temperatures are Tc = 632 K for 73 and Tc = 588 K for 72. The M6ssbauer spectra can be divided into three components. Analogies with FesGe3 has been emphasized by Bhargava and Iyengar (1976). 7.12. (Fe, T)sSn3, T = Ni or Co

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Yamaguchi, M., and T. Hashimoto, 1972, J. Phys. Soc. Jpn. 32, 635. Yamaguchi, Y., and H. Watanabe, 1978, J. Phys. Soc. Jpn. 44, 1782. Yamaguchi, Y., H. Watanabe, H. Yamaguchi and S. Tomiyoshi, 1972, J. Phys. Soc. Jpn. 32, 958. Yamaguchi, Y., AT Goldman, K. Ishimoto and M. Ohashi, 1987, J. Magn. & Magn. Mater. 70, 197. Yamamoto, H., 1966, J. Phys. Soc. Jpn. 21, 1058. Yanase, A., and A. Hasegawa, 1980, J. Phys. C 13, 1989. Yashiro, T., Y. Yamaguchi, S. Tomiyoshi, N. Kazama and H. Watanabe, 1973, J. Phys. Soc. Jpn. 34, 58. Yasukochi, K., and K. Kanematsu, 1961, J. Phys. Soc. Jpn. 16, 1123. Yasukochi, K., K. Kanematsu and T. Ohoyama, 1961, J. Phys. Soc. Jpn. 16, 429. Yessik, M., 1968, Philos. Mag. 17, 623. Yokoi, C.S.O., M.D. Coutino-Filho and S.R. Salinas, 1984, Phys. Rev. B 29, 6341. Yomo, S., 1983, J. Magn. & Magn. Mater. 31-34, 331. Yoshida, H., T. Kaneko, M. Shono, S. Abe and M. Ohashi, 1980, J. Magn. & Magn. Mater. 15-18, 1147. Yoshii, S., and H. Katsuraki, 1966, J. Phys. Soc. Jpn. 21, 205. Yoshii, S., and H. Katsuraki, 1967, J. Phys. Soc. Jpn. 22, 674. Yoshizawa, H., S.M. Shapiro and T. Komatsubara, 1985, J. Phys. Soc. Jpn. 54, 3084. Yuri, S., S. Ohta, S. Anzai, M. Aikawa and K. Hatakeyama, 1987, J. Magn. & Magn. Mater. 70, 215. Yuzuri, M., 1960, J. Phys. Soc. Jpn. 15, 2007. Yuzuri, M., 1973, J. Phys. Soc. Jpn. 35, 1252. Yuzuri, M., and K. Segi, 1977, Physica B 86-88, 891. Yuzuri, M., and M. Yamada, 1960, J. Phys. Soc. Jpn. 15, 1845. Yuzuri, M., and T. Yusuki, 1986, J. Magn. & Magn. Mater. $4-57, 923. Yuzuri, M., T. Kanomata and T. Kaneko, 1987, J. Magn. & Magn. Mater. 70, 223. Zach, R., R. Duraj and A. Szytula, 1984, Phys. Status Solidi A 84, 229. Zach, R., R. Fruchart, P. Chadouet, B. Chenevier, M. Bacmann and D. Fruchart, 1988, 9th Int. Conf. on Solid Compounds and Transition Elements, Oxford 1988. Zieba, A., K. Selte, A. Kjekshus and A.F. Andresen, 1978, Acta Chem. Scand. A 32, 173.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS Zieba, A., Y. Shapira and S. Foner, 1982, Phys. Lett. A 91, 243. Zieba, A., R. Zach, H. Fjellvgtg and A. Kjekshus, 1987, J. Phys. Chem. Solids 48, 79. Zimmer, G.J., and E. Kr6n, 1972, AIP Conf. Proc. 5, 513.

287

Zimmer, G.J., and E. Kr6n, 1973, AIP Conf. Proc. 10, 1379. Zvada, S.S., L.I. Medvedeva, A.P. Sivachenko and S.I. Khartsev, 1988, J. Magn. & Magn. Mater. 72, 349.

chapter 4 MAGNETIC AMORPHOUS ALLOYS

P. HANSEN Philips GmbH Forschungslaboratorium Aachen D-5100 Aachen, Germany

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991 289

CONTENTS I. Ir t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. P r e p a r a t i o n m e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. L i q u : d q u e n c h i n g . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Vapor q u e n c h i n g . . . . . . . . . . . . . . . . . . . . . . . . . 3. Structure of a m o r p h o u s allo) s . . . . . . . . . . . . . . . . . . . . . . . 3.1. C o m p o s i t i o n a n d h o m o g e n e i t y . . . . . . . . . . . . . . . . . . . . 3.2. D e r sity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. M i c r o s t r u c t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. A l o m i c structure . . . . . . . . . . . . . . . . . . . . . . . . . 4. S | a b i l i t y c f a m o r p h o u s al:oys . . . . . . . . . . . . . . . . . . . . . . . 4.1. C r y s t a l l i z a t i o n t e m p e r a t u r e s . . . . . . . . . . . . . . . . . . . . . 4.2. S t r t c t u r a l r e l a x a t i o n . . . . . . . . . . . . . . . . . . . . . . . . 5. M a g n e t ! c properties . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. M a g n e t i c structures . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Influence of p r e p a r a t i o n c o n d i t i o n s . . . . . . . . . . . . . . . . . . . 5.3. L o w - t e m p e r a t u r e m a g n e l i c m o m e n t s . . . . . . . . . . . . . . . . . . 5.3.1. O n e - s u b n e t w o r k alloys . . . . . . . . . . . . . . . . . . . . . 5.3.1.1. Transition-metal-ba~,ed alloys . . . . . . . . . . . . . . . . 5.3.1.2. R a r e - e a r t h - b a s c d alloys . . . . . . . . . . . . . . . . . . 5.3.2. T w o - s u b n e t w o r k alloys . . . . . . . . . . . . . . . . . . . . . 5.4. T e m p e r a t u r e c'epcndence c f l i e m a g n e t i z a t i o n . . . . . . . . . . . . . . . 5.4.1. M o d e l s . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1.1. Mean-field t h e o l y . . . . . . . . . . . . . . . . . . . . 5.4.1.2. d - b a n d m o d e l with r a n d o m axial a n i s o t r o p y . . . . . . . . . . 5.4.1.3. O t h e r c c n c e p t s . . . . . . . . . . . . . . . . . . . . . 5.4.2. O n e - s u b n e t w o r k alloys . . . . . . . . . . . . . . . . . . . . . 5.42.1. Transitfon-metal-ba,,ed alloys . . . . . . . . . . . . . . . . 5.42.2. R a r e - e a r t h - b a s e d alloys . . . . . . . . . . . . . . . . . . 5.4.3. T w c - s u b n e f w o l k alloys . . . . . . . . . . . . . . . . . . . . . 5.5. Critical ~)pex~erts . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. U n i a x i a l m a g n e t i c an:'sctropy . . . . . . . . . . . . . . . . . . . . . 5.7. M a g n e t o s t r i c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 5.8. C o e r c i v i l y . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9. M a g n e t i c e x c i l ~ t i e r s . . . . . . . . . . . . . . . . . . . . . . . . 5.10. A n t ealing effects . . . . . . . . . . . . . . . . . . . . . . . . . 6. M a g n e t o - c p t i c a l p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Phenomeno~ogical t h e o r y . . . . . . . . . . . . . . . . . . . . . . 290

292 293 293 295 297 297 298 301 303 307 307 313 315 315 319 320 320 320 333 339 344 344 344 347 348 349 349 354 356 369 373 379 385 392 395 398 398

MAGNETIC 6.2.

AMORPHOUS

ALLOYS

Microscopic models . . . . . . . . . . . . . . . . . . . . . . . . 62.1. ]nlerbal~d t r a n s i t i o n s . . . . . . . . . . . . . . . . . . . . . 62.2. Tntraband t i a n s i t i o r s . . . . . . . . . . . . . . . . . . . . . 6.3. O n e - s u b n e t w c r k alloys . . . . . . . . . . . . . . . . . . . . . . . 6.4. T w o - s u b n e t w o r k alloys . . . . . . . . . . . . . . . . . . . . . . . 7. Tran,,port p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Resistivity a n d m a g n e l o r e s i s t a n c e . . . . . . . . . . . . . . . . . . . . 7.2. H a l l ~ffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. T e c h n o l o g i c a l a p p l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . 8.1. M~tallic glasses . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. M a g n e t o - c p t i c a l r e c o r d i n g . . . . . . . . . . . . . . . . . . . . . . 8.2.1. Storage ~ri~ciple . . . . . . . . . . . . . . . . . . . . . . . 8.2.2. M a t e r i a l ~,e?ection . . . . . . . . . . . . . . . . . . . . . . . 8.2.3. T h e r m c m a g n e t i c ~witching process . . . . . . . . . . . . . . . . . 8.2.4. M a g n e t o - o p t i c a l d!sk . . . . . . . . . . . . . . . . . . . . . 8.2.5. Recorder r e q u i r e m e n t s . . . . . . . . . . . . . . . . . . . . . 9. S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291 399 399 401 402 405 413 413 420 423 423 425 425 428 429 432 432 435 436

1. Introduction

Amorphous alloys, sometimes called metallic glasses or glassy metals, have received much attention in the last decade due to their interesting properties and their applicability for new devices. These metallic alloys are characterized by a structural disorder where each atom constitutes a structural unit. This leads to different behavior with respect to their electronic and magnetic properties as compared to their crystalline counterparts where the lattice periodicity and the crystal symmetry are the dominant elements controlling the basic features. In particular, the magnetic properties of amorphous alloys are strongly affected by the bond and chemical disorder causing a distribution in the magnetic moments and exchange interactions. Also, the random electrostatic fields create local anisotropies via spin-orbit coupling, giving rise to a varying orientation of the magnetic moments. The structural disorder introduces new magnetic structures such as speromagnetism, asperomagnetism and sperimagnetism which posesses a noncollinear arrangement of the magnetic moments. The existence of competing positive and negative exchange coupling leads to spinglass behavior in many alloys. Also, the transport properties differ considerably from those of the corresponding crystalline materials, which becomes clear from the large extraordinary Hall effect. The new effects and phenomena associated with amorphous alloys have led to new theoretical concepts and a tremendous amount of experimental work in this field which gave new insights in the understanding of disordered systems with respect to both structure and magnetism. Further, the investigation and development of the preparation techniques have led to very homogeneous and ultra-thin films and have opened a new field in research on interface physics and multilayer effects. The interesting properties of the amorphous alloys have been tailored for various technical applications. Alloys with low coercivity can be used for cores in distribution transformers or alloys with a high permeability for magnetic shielding. Alloys for magnetic power controllers, force transducer and magnetic sensors have been investigated. Amorphous rare-earth-transition-metal alloys show suitable magnetic and magneto-optical properties and have been developed as a medium for erasable, optical data storage and recording. The class of amorphous alloys include a large variety of different materials ranging from nonmagnetic alloys via spin glasses and transition-metal-metalloid glasses to rare-earth-transition-metal alloys. Therefore, it appears to be almost impossible to present a complete survey of the tremendous amount of data, effects and ideas reported in the past decade. In this chapter, we 292

MAGNETIC AMORPHOUSALLOYS

293

will focus on the magnetic amorphous alloys with special attention of the rare-earthtransition-metal alloys which have been recently investigated in more detail. It will be attempted to present a selection of data and theoretical concepts that are relevant with respect to the influence of the structural disorder on the magnetic properties of these alloys. Further extensive information can be found in the reviews on the structure and the magnetic properties (Cahn 1980, Chen 1980a, Handrich and Kobe 1980, Luborsky 1980, Cargill III 1981a,b, Mizoguchi 1981, Buschow 1984a, Egami 1984, Moorjani and Coey 1984, O'Handley 1987a). Data of amorphous alloys are compiled by different authors (Ferchmin and Kobe 1983, Buschow 1984a, Hansen 1988a). This contribution on amorphous alloys is organized as follows: The section following this introduction deals with a brief description of the most common preparation methods involving the liquid-quenching and vapor-quenching methods. In the next section, some basic aspects of the structure of amorphous alloys are treated in terms of the radial distribution function leading to information on the local atomic arrangement. In section 4, some models describing the stability of the amorphous alloys are introduced. The activation energies associated with a thermally activated rate process are related to the crystallization temperatures. Also, the structural degradation and effects of oxidation are discussed. A survey on the magnetic properties is given in section 5. Various experimental data on the composition and temperature dependence of the magnetic moment, the anisotropy or coercivity are presented, which demonstrate the strong influence of the structural disorder. The experimental data are compared with theoretical results inferred from calculations based o n the mean-field theory. The magneto-optical properties are presented in section 6. The spectral dependences are interpreted in terms of the relevant band transitions, and typical dependences of the Faraday rotation on composition and temperature are discussed. The Kerr rotation plays a special role in the case of the rare-earth-transition-metal alloys used for optical data storage and recording. Section 7 deals with the transport properties of amorphous alloys, which are completely different as compared with their crystalline counterparts. The high resistivity and the large extraordinary Hall effect reflect the high scattering probability of the conduction electrons. Some technical applications of amorphous alloys are considered in section 8. The strong interest in the field of optical recording was taken into account by presenting a more extended discussion of the particular material properties, the thermomagnetic switching process and typical disk configurations with a high signal-to-noise ratio. A summary of the most relevant properties and results in the field of amorphous alloys is given in section 9.

2. Preparation methods

2.1. Liquid quenching A common method to produce amorphous alloys is based on the fast quenching of a liquid. This can be reached with a moving chill block that extracts heat from the liquid and thus solidifies it. A high thermal conductivity of the chill block is necessary

294

P. HANSEN

to obtain high cooling rates in order to prevent any crystallization process. The heat transfer from the melt layer to the metal determines the quenching rate and is important for the maximum thickness of the amorphous layer that can be achieved by this process. Various techniques (Pond et al. 1974, Chen 1980a) were developed. The liquid-quenching method cannot be applied to elements that are immiscible in a liquid as, e.g., Fe and Ag or Fe and Ge. The splat cooling technique is one of the easiest possibilities to prepare amorphous samples by liquid quenching. In this case, a drop of liquid is caught against a fixed anvil by a rapidly moving piston. This leads to disc-shaped samples of typically 1 cm diameter and 20 to 60 gm thickness. The melt-spinning (Bedell 1975) is a widely used technique to produce amorphous alloys. It permits a much better control of the preparation conditions as compared with the splat cooling and provides a large-scale production. The melt-spinning apparatus is sketched in fig. la. The rf-melted alloy is contained in a quartz or alumina vessel. The melt is sprayed through a narrow orifice onto the surface of a

'";'}er di.'

bon

cr

\ rf heating

(a)

pressure

•//Aargon o~rf

heating

w h e e l ~ (b) Fig. 1. Schematic representation of (a) the apparatus for melt-spinning and (b) crucible melt extraction.

MAGNETIC AMORPHOUS ALLOYS

295

spinning wheel that is preferentially made out of copper to provide a high heat conductivity. Additionally, watercooling of the wheel can be used. The ejection velocity of the melt is controlled by the pressure of an inert gas like argon. This method permits the production of thin ribbons of 10-40 ~tm thickness at velocities of 10-50 m/s. The quality of the ribbon is determined by various parameters (Liebermann and Graham Jr. 1976, Ray 1978, Kavesh 1978, Liebermann 1983). In particular, the melt jet velocity and the speed of the rotating wheel primarily control the dimensions of the amorphous ribbon. Alloys such as rare-earth-transition-metal alloys need process conditions preventing any oxidation. Another modification of the chill-block method is the crucible melt extraction technique. In this case, the heat-extracting rotating disc is in contact with the surface of the melt (Maringer and Mobley 1974, 1978), as sketched in fig. lb. As in the case of melt-spinning, a continuous ribbon can be obtained. Debris on the disc are removed by a wiper. The shape of the ribbon depends on the profile of the rotating disc. Their thickness is less than in the case of melt-spinning due to the substantial low cooling rates caused by the short time of contact between the liquid and the rotating disc. The roller quenching is a further technique that uses two counter-rotating rollers (Chert and Miller 1970, Babi6 et al. 1970, Lewis et al. 1977). In this case, the melt jet is quenched between two rollers leading to a better contact than in the case of other methods. However, the contact time is small and, thus, the total heat transfer cannot be significantly improved. The dimensions of the amorphous ribbons are determined by the roller pressure or the gap between the rollers. However, this requires an extremely precise control of the experimental arrangement.

2.2. Vapor quenching The vapor-quenching method bypasses the liquid state. Thus, many amorphous alloys that cannot be made by liquid quenching can be well prepared by this method. Also, a much wider range of alloy concentrations can be realized. The vapor deposition has to be performed in a protective atmosphere to prevent reactions with oxygen or nitrogen. The vapor-quenching methods are mostly restricted to the preparation of amorphous films. The thermal evaporation is a well-established method to produce multicomponent alloys. In this process, the metal source is heated by resistance, electron beam or by laser heating. From the melted material, the atoms are released into the vacuum where the vapor pressure has to be sufficiently high to obtain a reasonable deposition rate on the substrate. Most alloys do not evaporate congruently. Therefore, it is advantageous to use a multiple source system that permits to heat each component of the alloy separately and to control the partial vapor pressures independently. This can be realized by electron-beam multiple source evaporation (Glang 1970) as sketched in fig. 2 for the case of three sources. An electron beam generated by an e-gun melts the metal in the crucible. The path of the electron beam is controlled by means of an electric and magnetic field. It is scanned over the metal surface to avoid any hole burning. The vapor pressure of each constituent is controlled by a quartz oscillator via a feedback to the e-gun. To avoid lateral inhomogeneities of the amorphous film, rotation of the substrate is required. The deposition

296

P. HANSEN C~

-substrate

-quartz

oscillator

e-beam

e-gun

Fig. 2. Schematic arrangement of a multiple e-gun evaporation system.

rates are of the order of 10-50nm/s. High film quality can be reached for film thicknesses below 0.3 Ixm. Thicker films tend to vary in composition with thickness because it is difficult to keep the deposition conditions constant over a longer time period. The sputtering technique (Glang 1970, Vossen and Kern 1978) is also a wellknown deposition technique where the target is bombarded with ions of a rare gas. Different sputtering arrangements such as DC, rf and magnetron sputtering have been investigated. In all cases, a plasma is generated by a potential difference which also accelerates the rare-gas ions. They transfer their kinetic energy to the surface of the target releasing atoms of the different constituents which form an amorphous film on the substrate. A schematic representation of the magnetron sputtering system is shown in fig. 3. Typically, argon is used as sputter gas and a voltage of some hundred volts is applied to generate the plasma. A magnetic field induced by a magnet fixed below the target confines the plasma, leading to higher sputter rates (Huggins and Guvitch 1983) as compared to DC and rf sputtering where the substrate serves as anode and, thus, the plasma is spread over the entire volume between the target and substrate. This anode-cathode configuration for DC and rf sputtering is

vacuum

Fig. 3. Principle of a magnetron sputtering system.

MAGNETIC AMORPHOUS ALLOYS

297

associated with a high electron bombardment of the substrate requiring a substrate cooling which is not the case for magnetron sputtering. Also, very dense and homogeneous films at low argon pressures can be produced by magnetron sputtering at high deposition rates. Thereby, the product of the sputter gas pressure and the distance between target and substrate is an essential parameter controlling the film quality (Thornton 1974, Hoffmann and Thornton 1980, Somekh 1984). These advantages make the magnetron sputtering process very attractive for the production of thin amorphous films such as rare-earth-transition-metal films for optical recording. Disadvantages of the sputter techniques are the presence of the sputter gas which is partly incorporated into the film, very expensive alloy targets and a low variability concerning compositional variations. The latter can be avoided using a multipletarget co-sputtering system.

3. Structure of amorphous alloys 3.1. Composition and homogeneity The interpretation of the electric and magnetic phenomena of amorphous alloys requires a reliable knowledge about their chemical composition. In particular, ferrimagnetic alloys exhibit a very sensitive variation of some magnetic properties on composition. Different nondestructive methods such as X-ray fluorescence or the outcoming characteristic radiation induced by ion or electron bombardment can be used. The latter method involves a complex technique and a complicated analysis of the measured data. However, it was demonstrated that the electron probe microanalysis (EPMA) is a powerful method (Willich and Obertop 1982) that can be applied universally to thin and thick films of complex composition. This technique also permits to determine the film thickness. The penetration of oxygen into films deposited by evaporation or sputtering can be well analyzed by secondary-ion mass spectroscopy (SIMS) which provides essential information concerning the film quality. The homogeneity of amorphous alloys depends on the preparation method, the control of the deposition parameters or structural fluctuations on either atomic or larger scale. In the latter case, small-angle X-ray scattering can be applied to resolve small atomic clusters of the order of 1-2 nm (Nold et al. 1980, Osamura et al. 1981), but also columnar structures of the order of 5-25 nm (Leamy and Dirks 1977) which have been observed in various rare-earth-transition-metal alloys prepared by evaporation and sputtering (Leamy et al. 1980, Yasugi et al. 1981). The variation of the deposition parameters during the formation of amorphous films causes significant changes in composition. Variations in depth can be investigated by SIMS and Auger depth profiles. The depth profile of a B1-xFex amorphous film is shown in fig. 4 (Moorjani and Coey 1984). Variations of the iron content by more than 1 at.% occur. In ferrimagnetic alloys, this can be sufficient to cause drastic changes in the position of the magnetic compensation temperature and, thus, in the coercive field. Also, the approach to magnetic saturation (Kronmfiller 1981c, Malozemoff 1983, Garoche and Malozemoff 1984, Chudnovsky 1989), dynamic magnetic

298

P. HANSEN 0.53

Bl_xFex 0.52 x

0.51

0.50 I 0.4

I 0.6

i 0,8

Depth

1 1.0

I 1.2

~ 1.4

from surface

t 1.6

i 1.8

[/zm)

Fig. 4. Variation of the iron content with depth in a sputtered amorphous B-Fe film (Moorjani and Coey 1984).

processes (magnetic resonance, domain-wall motion) or transport properties can be strongly affected by structural irregularities.

3.2. Density Amorphous alloys of composition Mt -xTx with T = Fe, Co or Ni, and M = B or P can be prepared with high densities. These transition-metal-metalloid alloys have densities within 2% of the corresponding crystalline counterparts (Luborsky 1980). The density p decreases with increasing metalloid content, as shown in fig. 5. Calculated densities based on a dense random-packed structure agree for many compositions within 5% with the measured densities. Some measured densities and calculated packing fractions q = ~rcrapo are compiled in table 1 where r and Po are the atomic

9.0 8.8q

Co(fcc)

8.6 8.4 E

~"" " " & 4,,,,,£,,q,,

C Ol-x B ×

8.2 8.0

--& 7.8 7.6

Fel_ x B x °°°°o%

7.4

o

7.2 7.0

I

I

0.10

0.20

o

o

I

0.30

Fig. 5. The mass density versus boron content for amorphous B-Fe and B-Co alloys. The solid circles represent partially crystalline samples (Hasegawa and Ray 1979).

MAGNETIC AMORPHOUS ALLOYS

299

TABLE 1 Measured densities and calculated packing fraction q=~nr3po for some amorphous transitionmetal-metalloid alloys (Luborsky 1980). r represents either the Goldschmidt radius for transition-metal atoms or the tetrahedral covalent radius for the metalloid atoms. P0 denotes the average density. Alloy

Composition x

p (g/cm3)

Po (at./nm3)

q

PxNil-~

0.186 0.211 0.228 0.240 0.262

8.00 _ 0.04 7.93 7.80 7.79 7.73

90.0 90.4 89.7 90.2 90.5

0.678 0.676 0.667 0.668 0.665

[1]

PxCo1_~

0.150 0.190 0.203 0.220 0.236

7.9 7.97 _ 0.04 7.94 7.89 7.90

86.9 89.5 89.8 90.0 90.9

0.677 0.668 0.687 0.685 0.688

[2, 3]

PxFel -x

0.145 0.160 0.184 0.216

7.252 + 0.04 7.205 7.128 7.025

83.6 83.7 83.7 83.8

0.681 0.678 0.672 0.665

[4]

(FexNil -~)o.soBo.2o

0.25 0.375 0.50 0.625 0.75 0.875 1.0

7.94 7.83 7.72 7.65 7.53 7.46 7.39

98.5 97.7 96.9 96.6 95.7 95.3 95.0

0.697 0.697 0.697 0.701 0.700 0.703 0.707

[5]

(FexCo1_x)o.soBo.2o

0 0.125 0.25 0.375 0.50 0.625 0.75

8.22 8.06 7.93 7.84 7.70 7.59 7.52

104 99.1 98.1 97.6 96.5 95.7 95.4

0.714 0.709 0.706 0.706 0.702 0.700 0.702

[5]

*

References: [1] Cargill III (1970). [2] Davis (1976). [3] Cargill III and Cochrane (1974).

Ref.*

[4] Logan (1975). [5] O'Handley et al. (1976a).

radius a n d the average density, respectively. The calculations are based o n a twelvefold c o o r d i n a t i o n a n d use the G o l d s c h m i d t atomic radii for the metal a t o m s a n d the tetrahedral covalent radii for the metalloid a t o m s (Cargill III 1975a, Gaskell 1983). O t h e r alloys prepared by sputtering a n d e v a p o r a t i o n exhibit lower densities due to the presence of a less dense m i c r o s t r u c t u r e or due to the i n c o r p o r a t i o n of oxygen, n i t r o g e n or the sputter gas. Then, 5 - 1 5 % lower densities are observed as c o m p a r e d to the c o r r e s p o n d i n g crystalline alloys. F o r r a r e - e a r t h - t r a n s i t i o n - m e t a l alloys, the difference in density depends also o n the rare earth as s h o w n in fig. 6 ( F u k a m i c h i et al. 1987b). Some m e a s u r e d densities a n d calculated p a c k i n g fractions are compiled

300

P. HANSEN 12 10

Fe2R

o

Y

tl

La

i

t

CePrNd

Sm Gd TbDyHoEr

t f t tt ~

tt It t rt t it

Lu

i

.0 4.5 5.0 5.5 6.0 6.7 7,0 7.5 8.0 8,5 9.0 9.5 10.0

Density of Rare Earth Hetals

(g/cm3)

Fig. 6. Room-temperature density of amorphous and crystalline alloys of composition RFe 2 versus the density of rare-earth metals (Fukamichi et al. 1987b).

in table 2. The influence of the preparation conditions is demonstrated in fig. 7, showing the density versus argon pressure for sputtered GdTb-Fe films (Klahn et al. 1990a). Low argon pressure leads to films with a high density, while those prepared at high argon pressures or by evaporation show a much lower density. This behavior can be attributed to the different energy of the atoms forming the film. In the first case, high-energetic atoms are present giving rise to local rearrangements of the atoms at the film surface which results in dense films. In the second case, the atoms are thermalized by the argon gas or by the evaporation process. Their energy is too low to induce a sufficient atomic mobility at the film surface to produce an energeti• cally favorable atomic arrangement. This leads to a less-compact microstructure and thus to less-dense films. These different conditions for the film growth are determined by the substrate temperature (Movchan and Demchishin 1969), the mobility of the adatoms, the initial energy of the sputtered atoms, the sputter gas atoms and the product of the sputter-gas pressure and the distance between target and substrate (Thornton 1974, Somekh 1984). Dense films, e.g., can be obtained by magnetron sputtering using a pressure-distance product of less than 60 Pa mm.

TABLE 2 Measured densities and calculated packing fraction r/= 4nr3po for some rare-earth-transition-metal alloys. r and Po represent the Goldschmidt atomic radius (twelve-fold coordination) and the average density, respectively. Alloy

Composition x

p (g/cm 3)

Po (at./nm 3)

~/

Reference

Tbl _~Fex

0.67

8.3

55.6

0.75

Rhyne et al. (1974a,b)

Gdl _xCO~

0.85 0.79 0.67 0.54

8.8 8.7 8.5 8.4

71.1 65.5 56.0 48.5

0.76 0.76 0.76 0.76

Tao et al. (1974)

MAGNETIC AMORPHOUS ALLOYS

8.5

-~'-'/Oer y stattine

301

GdTb-Fe

t~

E o

~8.0

o 1 ctt%Tb

N

~"Pevaporoted

7.5

I

0

0.5

I

I

1 1.5 PAr (Pal

I

2

2.5

Fig. 7. Room-temperature density of amorphous GdTb-Fe alloys prepared by magnetron sputtering versus argon pressure (Klahn et al. 1990a).

3.3. Microstructure

Amorphous alloys are expected to behave isotropic with respect to their structure and properties. However, thin films prepared by evaporation and sputtering show a columnar structure (Dirks and Leamy 1977, Leamy and Dirks 1978, Leamy et al. 1980, Yasugi et al. 1981). This structure was investigated by various techniques such as microfractography, transmission electron microscopy or small-angle electron and X-ray scattering. The structure is composed of rod-like columns of 5-25 nm diameter. They are surrounded by less dense material of 1-25nm thickness, reducing the average material density. A typical columnar structure of a G d - C o film is shown in fig. 8a, obtained by microphotography (Leamy and Dirks 1978). The microstructure of an evaporated GdTb-Fe film observed by transmission electron microscopy (Klahn et al. 1990a) is presented in fig. 8c. The column orientation in vapor-deposited films is related to the vapor incidence (Nieuwenhuizen and Haanstra 1966, Fiedler and Schirmer 1988) and can be explained in terms of self-shadowing. A computer simulation based on hard spheres (Henderson et al. 1974) maximizing tetrahedral packing yields an amorphous structure with columnar structure. This microstructure originates from a low atomic mobility during film formation, in agreement with results obtained from the occurrance of microstructure as a function of the preparation conditions (Klahn et al. 1990a, Klahn 1990). Computer simulation based on hard disks (atoms) and different mobilities of the adatoms (Brett 1989) leads to columnar structures as shown in figs. 8d and e for low and high surface mobilities, respectively. The calculations yield a substantial density increase, a decrease in dislocations and voids inside the columns and an increase in average coordination number with increasing adatom mobility in agreement with experimental results for films prepared with decreasing pressure-distance product (Klahn 1990). Resputtering effects (Gambino and Cuomo 1978, Okamine et al. 1985) and the incorporation of the sputter gas into the film (Heitmann et al. 1987a,b, Klahn

302

P. HANSEN

Fig. 8. Columnar structure: Transmission electron micrograph of (a) a carbon replica of the fractured edge of an amorphous Gd0.22Coo.78 film prepared by evaporation and (b) the phase contrast of the microstructure of a 50nm thick sputtered Gdo.zsCoo.76 film, left: underfocussed, right: overfocussed. The low-angle region of the diffraction pattern of the film in (b) is given in the inset (Leamy and Dirks 1978). (c).Transmission electron micrograph of an amorphous GdTb-Fe film prepared by evaporation (Klahn et al. 1990a). (d) and (e) computer simulation of columnar structures for low and high adatom surface mobility, respectively (Brett 1989).

1990) also gives rise to a strong influence on the microstructure. F u r t h e r , c o n c u r r e n t ion b o m b a r d m e n t leads to significant m o d i f i c a t i o n s of the m i c r o s t r u c t u r e of v a p o r d e p o s i t e d films (M/iller 1987, Rossnagel a n d C u o m o 1989).

MAGNETIC AMORPHOUS ALLOYS

303

3.4. Atomic structure

The atomic structure in single-crystalline materials is defined by the crystal symmetry. The knowledge of a few atomic positions in the unit cell is sufficient to describe the crystal. Further, a three-dimensional close-packed structure like the fcc lattice can be built only from tetrahedra and octahedra while the bcc lattice is made of octahedra alone. In amorphous alloys, the symmetry is absent and principally each atom constitutes a structural unit. However, their high density and the magnitude of magnetic moments and other properties being close to those of crystalline compounds suggest that the short-range order and thus also local structures are very similar to those in crystalline materials with high coordination numbers. This is due to the presence of a short-range order which extends over a range of some neighbor shells of atoms up to a distance of about 1 nm. There is no long-range order like in microcrystalline materials. However, there is a continuous transition from amorphous via 'nearly crystalline' (O'Handley 1987a) involving nanocrystals (Li and Smith 1989) to the microcrystalline structure depending on composition, preparation process and the conditions for local atomic ordering. Computer simulation in terms of the dense random-packed hard-sphere (DRPHS) model using different polyhedra (Bernal 1960) indeed lead to an amorphous structure that involves bond and topological disorder. Both play probably an essential role in the formation of an amorphous structure and are illustrated in fig. 9 for a binary alloy by a two-dimensional network (Moorjani and Coey 1984). The bond disorder (fig. 9b,e) is caused by a nonsymmetric arrangement of the atoms while topological disorder (fig. 9c, f) involves a different number of bonds and/or a different number of ions on a closed path. In addition, amorphous alloys exhibit chemical disorder which also can be present in crystalline alloys as, e.g., in the fcc PtCo, where the Pt and Co atoms are distributed at random as indicated in fig. 8d. Various further structure models were built (Finney 1970, Bennett 1972, Henderson et al. 1974, Ichikawa 1975), but still result in a packing density of less than 0.66 which is significantly lower than the measured data. These structures involve a predominance of tetrahedral interstices. A more satisfactory solution was obtained with a soft-sphere model using the Lennard-Jones type potentials and a

bond order

bond

disorder

topologica[

order

chemical order ct

b

d

e

chemicctt disorder f

Fig. 9. Types of disorder on two-dimensional binary lattices (Moorjani and Coey 1984).

304

P. HANSEN

relaxed DRPHS structure (Weaire et al. 1971, Barker et al. 1975, von Heimendahl 1975). This model reaches a packing fraction of 0.74 which is almost equal to that of an fcc lattice and is due to a much lower void content. Experimentally, the amorphous structure can be studied by means of X-ray, electron and neutron diffraction as well as by extended X-ray absorption fine structure (EXAFS) measurements (Cargill III 1975b). An X-ray diffraction diagram for an Zro.66Coo.34 alloy before and after crystallization is presented in fig. 10. The amorphous structures do not show any sharp diffraction peaks due to the absence of longrange periodicity. The crystallized sample shows the typical X-ray pattern of the CuA12 structure (Buschow 1984a). As any symmetry is absent in amorphous alloys, only statistical information and averaged data can be determined. The average distribution of atoms can be described by the radial-distribution function (RDF) 4nr2p(r) and represents the number of atoms, N = 4~

f: p(r)r 2 dr,

(1)

1

between rl and r 2. It is convenient to use the reduced radial-distribution function,

G(r) = 4nr[p(r) - P0 ],

(2)

because it is directly related to the Fourier transformation of the interference function S(q) which represents the diffraction intensity divided by the square of the scattering factor. P0 denotes the average density and q is the defraction vector. For monoatomic solids, S(q) is related to G(r) by

G(r) = ½n

fooq[S(q) -

1] sin(qr)dq.

(3)

C

o C

O4

[

.

.

.

.

~O'~

I

I |j[

I

.

.

.

.

.

C~ I Q4 |

.

4.2 40 38 36 3/* 32 30 28 26 2/* 22 20 18 16 1/* (3 (deg)

Fig. 10. X-ray diffraction pattern of melt-spun Zr0.66Co0.34before crystallization (upper curve) and after crystallization (bottom curve). The indexing of the bottom curve corresponds to the tetragonal CuA12 structure (Busctlow 1984a).

MAGNETICAMORPHOUSALLOYS

305

For polyatomic solids, p(r) is composed of the partial distribution functions (Faber and Ziman 1965, Wagner 1972, 1978, Cargill III 1975a, Waseda 1980). The Fourier transform for a binary alloy of composition A1 -xBx takes the form .

fB(q)

o

, ,

SA(q) = (1 -- X)2(f(q))fA(q) SAA(q)-t- X2(f(q)) ~AB~q)"

(4)

SAA and SAB are the compositionally resolved structure factors for A-A and A-B pairs, respectively, fg(q) is the scattering factor of atom A and fB(q) of atom B. ( f ( q ) ) denotes to compositionally averaged factor. SB(q) can be expressed accordingly. The total radial distribution function thus is composed of the averaged partial distribution functions of the different types of atoms. In the case of binary alloys, at least three independent sets of data are necessary to determine the three partial distribution functions. This can be achieved using different diffraction methods (X-ray, electron, neutron diffraction), different isotopes with different neutron-scattering factors (Mizoguchi et al. 1978, Kudo et al. 1978) or by the substitution of elements of similar size and chemical affinity but different scattering power (Chipman et al. 1978, Williams 1982). Also, different kinds of radiation were applied to determine the partial distribution functions (Waseda and Tamaki 1976). A comparison of experimentally determined and calculated reduced radial distribution functions was made for various transition-metal-metalloid alloys (Cargill III 1975b). For many alloys, a good agreement between experimental and calculated data was achieved. This is demonstrated in fig. 11a for amorphous Po.14Bo.o6Feo.4oNio.4o. The curve represents G(r) deduced from dispersive X-ray diffraction and the histogram is the reduced G(r) of amorphous Fe calculated from the soft-sphere model (Egami 1978a). The good agreement of the G(r) of amorphous iron with the experimental data in respect to both the entire radial dependence and the individual peak heights reveals the dominance of the transition-metal ion or the much lower X-ray scattering power of the metalloid. Therefore, pronounced changes in G(r) only occur for alloys with metalloid atoms differing significantly in their atomic radius. This is demonstrated in fig. llb for amorphous Bo.25Feo.v5 and SioA5Bo.loFeo.75, the latter representing the case that a larger metalloid is involved (Aur et al. 1982). The second peak is shifted towards larger distance by 0.025nm, reflecting the difference in the atomic radii of about 0.02 nm between Si (0.11 nm) and B (0.091 nm). Further, the study of the G(r) reveals a strong short-range order which means that there is a strong preference of the metalloid atoms to have dissimilar atoms as nearest neighbors. Also, the apparent radius of the metalloid atom in the alloys is significantly smaller than the radius of the free atom. The rare-earth (R)-transition-metal (T) alloys play a special role within the amorphous materials with respect to the substantial difference in their atomic radii and scattering power. The structure can be well accounted for by the binary dense random-packing model (Cochrane et al. 1974, 1978a,b, Cargill III and Kirkpatrick 1976, Williams 1981, Cargill III 1975a,b, 1983) achieving packing densities of 0.76 (see table 2). The difference in their atomic radii leads to a split of the first peak of G(r) into subpeaks according to the three contributions from the partial distribution

306

P. HANSEN

Po.lz.B o.o6F eo.z.o N io.~o

6

/,

2

't

0

0.5

1.0

1.5

r(nm)

..... Si0.15Bo.lo Feo.7s . . . . . . Bo.25Feo.75

/..0

"C

2.0

(D

0.0

-2.0

,,v,y (b) F

0,16

I

]

0.32

I

I

0,/.8

I

I

0.6/.

]

0.80

r(nrn)

Fig. 11. Reduced radial-distribution functions for amorphous PB-FeNi determined by the energy dispersive X-ray diffraction. The histogram represents G(r) (a) for amorphous Fe calculated from the soft-sphere model (Egami 1978a) and (b) for amorphous B Fe and BSi-Fe ribbons. The shift of the second peak reflects the difference in the radius between Si (0.11 nm) and B (0.091 nm) (Aur et al. 1982).

functions PRR(r), PRT(r) and PTT(r). This also applies to Lal_xFex alloys where the three correlations for Fe-Fe, Fe-La and La-La are well distinguishable (Matsuura et al. 1988), as shown in fig. 12. The arrows indicate the positions of the peaks correlated to the different interatomic distances. The extracted nearest-neighbor distances and coordination numbers are listed in table 3. The split of the first peak of G(r) for amorphous Gdo.36 Feo.64 is shown in fig. 13. The broken lines represent Gaussian fits of the three possible neighbor-pair peaks (Cargill III 1975a,b). Therefore, in this case, one diffraction experiment is sufficient to deduce the nearest neighbor distances rij and coordination numbers N u based on eqs. (1)-(4). The radial dependence of G(r) for amorphous Tbo.33Feo.67 is shown in fig. 14. Again, the first peak is split and the maxima of the partial distribution functions are indicated by the arrows. The structure of the second peak originates from the indicated atomic clusters

MAGNETIC AMORPHOUS ALLOYS

/ [

307

Lo.1-xFe× OFe

Im~'~

"L"

=~_

0

.

.

.

.

.

xj -2 0.2

I

I

i

t

0,/~

0.6

0,8

1.0

1.2

r(nm}

Fig. 12. Reduced radial distribution function for amorphous La-Fe alloys (Matsuura et al. 1988). The arrows indicate the positions of the interatomic distances corresponding to the sketched types of atomic arrangements.

(Rhyne 1974). Average distances of nearest-neighbor atoms and coordination numbers are compiled in table 3. The compositional short-range order (CSRO) is less pronounced in the rare-earthtransition-metal alloys as compared to the transition-metal-metalloid alloys. The CSRO was discussed in terms of the heat of mixing (Buschow and van Engen 1981a, Buschow and van der Kraan 1981). A negative heat of mixing implies the attraction of dissimilar atoms and a positive value the opposite behavior. Therefore, the heat of mixing can be used as an additional parameter to improve the dense random packing model.

4. Stability of amorphous alloys 4.1. Crystallization temperatures Amorphous alloys are in a metastable state and tend to transform into stable crystalline phases. At temperatures below the crystallization temperature, structural relaxation effects take place and are caused by atomic rearrangements. The crystallization is associated with nucleation and growth processes (Avrami 1939, 1940, 1941). The transition to the crystalline state is accompanied by an exothermic heat effect giving rise to a sharp peak in the temperature dependence of the exothermic heat. Therefore, differential scanning calorimetry is a widely used technique to study thermally induced transformations in amorphous alloys and to determine the crystallization temperature, T~. The magnitude of T~ is very different for amorphous materials and depends strongly on composition. The activation energy ranges typically between 2 and 6 eV. Amorphous metals (Fe, Co, Ni) with a very low impurity content exhibit crystallization temperatures below 70 K (Felsch 1969, 1970a,b, Wright

308

P. H A N S E N

TABLE 3 Average distances (ru) of nearest-neighbor atoms and coordination numbers (Nu) for amorphous and crystalline rare-earth-transition-metal alloys. Partials

Amorphous rq(nm)

Crystalline Nu

Gd-Gd Gd-Fe Fe-Fe

Gdo.36 Feo.64 0,347 ±_ 0.005 6.0 ± 1 0.304 4- 0,005 6.5 4- 0.6 0,254 _ 0.005 6.5 + 0.5

Gd-Gd Gd-Co

Gdo.18Coo.82 0.34 3 4- 1 0,297 ___0.0005 12 + 1

Co-Co

0,247 ±_ 0.005

Tb-Tb Fe-Tb Fe-Fe

0.35 0.30 0.26

Ho-Ho Ho-Co Co-Ho Co-Co

0.352 0.298

La-La La-Fe Fe-Fe

0.360 0.315 0.252

ru(nm)

Nu

[i]

GdFez 0.320 0.306 0.261

4 12 6

[1]

GdCos 0.287 0.318 0.245 0.249

7.2 ± 0.7

Tbo.33 Feo.67

6 12 4,8 2.4 TbFe2

6.4 6.3

0.318 0,304 0.254

-

-

5.3 3.3 6.1

-

Hoo.3oCoo.7o

0.251

Ref. t

-

[1,2]

4 12 6 6

[3] [4]

-

[5]

HoC%

Lao.35 Feo.6s

LaFe2 *

* The intermetallic c o m p o u n d has not yet been synthesized. t References: [1] Cargill III (1975a,b). [4] Cochrane et al. (1978a). [2] Rhyne et al. (1974a). [5] M a t s u u r a et al. (1988). [3] Nagy ct al. (1977).

Gd°'36F%'6~~ I

I

I

10 -E £D

./K/

0.2

i\

0.3 r(nrn)

\

"\ ',

0.4

Fig. 13. The first peak in the reduced radial distribution function for a m o r p h o u s G d - F e . The broken lines represent the three possible neighbor peaks (Cargill III 1975a,b).

MAGNETIC AMORPHOUS ALLOYS

309

2~

v I/!'!".. oo,

DO0

0

0.2

L,/ o°o •

orb

•

0.4

0.6

0.8

1.0

r(nm) Fig. 14. The reduced radial distribution function for amorphous T h - F e at T = 433 K . The arrows indicate

the contributions of respective atomic clusters (Rhyne 1974).

1976), which rapidly increase if the impurity content is raised. Thus, alloys of composition M1-xT~ with T = Fe, Co or Ni need a very low M concentration of typically x < 0.15 to establish the amorphous state with T~ above room temperature (Fujimori et al. 1984, Fukamichi and Hiroyoshi 1985). For example, the crystallization temperatures for amorphous Zrl_~Fex with 0.88 ~<x ~<0.93 range between 882 and 806K (Ryan et al. 1987b). The compositional dependence of T~ for amorphous transition-metal-metalloid alloys (Naka et al. 1976, Luborsky and Walter 1977a) is shown in fig. 15. Although these alloys exhibit a pronounced dependence of T~ on

i

I

750

P°'13C°°'°7 Fe°'8°-x M x i'4=Cr 0 Feo.80-xNix

700

650

~

P°'lZ'B°'°6 F e°'e°-x Ni '

..,x

60c

X/ PO.lZ,BO.O6Feo.so-xNix

55 0

i 0,20

I 0.40

I 0.60

0.80

x Fig. 15. Crystallization temperatures for amorphous P-CoFeM alloys (open symbols) measured with a heating rate of 5 K/min (Naka et al. 1976) and BP-FeNi, B-FeNi (solid symbols) measured with a heating rate of 40 K/rain (full line) and two hours anneals (broken line) (Luborsky and Walter 1977a).

310

P. HANSEN

composition, the overall T~ values remain high. This applies to most of the alloys containing glass formers, leading to a high stability of these alloys in the roomtemperature range, which is of importance for technical applications. At the M-rich side of M - T alloys, T~ again decreases as shown for amorphous Snl _~T~ alloys (Geny et al. 1982). The T~ values for many rare-earth-transition-metal alloys range between 400 and 800K as obvious from table 4. The strong dependence of T~ on composition is demonstrated in fig. 16a for R-T alloys with R = Gd or Tb and M = Fe or Co (Klahn 1990) and in fig. 16b for amorphous N d - F e (Suzuki 1985) and Tb-Co (Buschow 1980a,c). T~ increases with increasing atomic number of the rare-earthelement (Buschow 1980b, Buschow and Beekmans 1980). In the case of Tb-Co, T~ interferes with the Curie temperature which restricts the investigation of the magnetic properties in the amorphous state. This limitation occurs for all rare-earth-cobalt

TABLE 4 Crystallization temperatures for amorphous rare-earth-transition-metal (R-T) alloys. Preparation methods used are liquid-quenching (lq), and vapour-quenching (vq). Further T~ data are compiled in previous reviews (Luborsky 1980, Buschow 1984a, Hansen 1988a). R1 -xT~ Smi _xFex Gd 1 _xFe x Tbl _xF% Dyl - x F% Hol_xFe x Erl_~F%

Tm 1_xF% Ndl _~Cox Sml_~Co~ Gd l_~Co~ Tb 1 - ~Cox

Hol _~Co~ Er 1 _xCo x Pr~ _~Nix Nd 1 - xNix Gd 1 _~Ni~

Tbl -~Nix Dy i _xNi~ Er i - x Ni~

x

T~ (K)

0.40 0.40 0.40 0.31 0.31 0.25 0.31 0.40 0.31 0.31 0.31 0.31 0.25 0.31 0.40 0.60 0.31 0.31 0.31 0.31 0.31 0.40 0.31 0.31 0.31

618 410 590 603 608 433 631 628 648 460 516 550 528 570 573 528 408 633 449 489 553 538 587 591 620

* References: [1] Buschow (1981a). [2] Buschow and van der Kraan (1981). [3] Buschow (1984a).

Preparation method

Ref.*

lq, vq lq lq lq lq lq lq lq lq lq, vq lq lq lq lq lq lq lq lq lq lq vq lq lq lq lq

[1, 2]

[4] Buschow and Beekmans (1980). [5] Buschow (1980a). 1-6] Buschow (1980b).

[-3] [1,2]

[4, 5]

[6]

MAGNETIC AMORPHOUS ALLOYS

311

1000

R 1-x

800

Fex

600

400

200

(o) I

I

I

I

I

I

I

I

0.50

I

1.00

X

800

Ndl_x Fex om Tb 1 x Cox oe

700

,

600

,

~

----2(\

500

400

3OO 200

[b)l 0.3 0.4

ITc~ i i I "~'4 0.5 0.6 0.7 0.8 0.9 1.0 X

D,

Fig. 16. (a) Crystallization temperature versus composition for amorphous R-T alloys (Ktahn 1990): (©) Buschow (1980a, 1985), (A) Campbell (1972), (E]) Felsch (1970b), (O) Felsch (1969), (A) Buschow (1985). (b) Crystallization temperature and Curie temperature versus composition for amorphous Nd-Fe (Suzuki 1985) andTb-Co (Buschow 1980a,c, Hansen et al. 1989) alloys.

alloys and is even more pronounced for amorphous Fe, Co and Ni with their very low T~. The dependence of T~ on the heating rate s = dT/dt can be used to determine the activation energy of crystallization (Luborsky and Liebermann 1978). Considering the fraction x of amorphous material transformed into the crystalline state in time t and at temperature T, one obtains for the first-order rate process (Kissinger 1957, Boswell 1980),

ex) =/,(1 - x).

(5)

312

P. HANSEN

For a thermally activated process, the rate constant k obeys an Arrhenius type of equation

where ko is a constant and AE is the activation energy. Combining eqs. (5) and (6) and using dx = (~x/&)r dt + (~?x/~T)t d r with (Ox/Or) dt ~ O, one obtains dXdt k o ( 1 - x ) e x p - ~ - ~ .

(7)

At the peak of the exothermic heat, the change of the reaction rate dZx/dt 2 is equal to zero, yielding with T = T~, ko exp -

=

s.

(8)

From the measured data of s and T~, the activation energy can be deduced from the slope of a plot of ln(T)/s) versus TZ 1. This is shown in fig. 17a for amorphous Yo.33Feo.67 and Yo.2sFe0.75, leading respectively to activation energies of 2.5 and 3.2 eV (Croat 1982) and in fig. 17b for an amorphous GdTb-Fe film with an activation energy of 2.6 eV (Klahn et al. 1987). A similar method based on eq. (5) is the isothermal annealing, leading to almost the same AE values. The stability of amorphous materials was studied in terms of the DRPHS models (Polk 1972). The significance of the chemical bonds was investigated (Chen 1980b) and a stability criterion based on a nearly free electron approach was proposed (Nagel and Tauc 1975). However, problems arise for these models concerning the interpretation of the various alloy systems. The kinetic approach to thermal stability based on a diffusion-controlled rate of transformation (Uhlmann 1972, Davies 1976, Takayama 1976) leads to the relation T~ = eE,

(9)

where e is a constant and E is a measure of the potential-energy barrier for cooperative atomic transitions. Assuming E to be proportional to the formation enthalpy, AHh, of a hole corresponding to the size of the smaller type of atom in a binary alloy A l_xBx (Buschow and Beekmans 1979a, Buschow 1981b), a relation of the form

T~ = flAHh

(10)

was proposed where fl is again a constant. Unfortunately, the values of AHh cannot be determined experimentally. However, these hole enthalpies can be calculated using a semiempirical approach to describe energy effects in metals (Miedema et al. 1980) by expressing AHh in terms of the formation enthalpies AHA and AHR of a monovacancy in a pure A and B metal by the relation AH~ = cAN B +

(1

-

-

c)(VB/VA)5/6~HA,

(11)

MAGNETIC AMORPHOUS ALLOYS

313

/*'01 yo.25Feo,75 / A E=3.2eV

~ 2.0

3F %.67

1.0[ /

/

1,0

1.1

AE=2,5eV

1.2 Txl(10-3K-1)

1.3

-13 .ic

E" -14 "7 ¢_" -15

~ 7 0 0

800 900

' N ~

T(K)

-, ~ & E=2.6eV Gdo.'r75Tbo.ossF e°.78 ~ , ~

-16 -17 (b) I 1.00

~

1.04

I

I

I

I

1.08 1.12 T~{10-3Kq)

I

I

1.16

Fig.17.Plot of log (T~/s) v e r s u s Tx- 1 for (a) amorphous Y - F e alloys (Croat 1982), and (b) amorphous GdTb-Fe(Klahn et al. 1987) alloys. Tx and s represent the crystallization temperature and the heating rate, respectively.

where c is the effective concentration, xV2/3 c = xV2/3 +

(1 -- x ) V2/3"

(12)

VA and lib represent the molar volumes. Using the values listed for most metallic elements (Miedema 1979), Tx can be calculated from eqs. (10) to (12). The result is presented in fig. 18 and shows an excellent agreement between eq. (10) and the measured T~ values for a large number of alloys (Buschow 1982a). 4.2. Structural relaxation

The structure of amorphous alloys is temperature dependent due to its metastable state. Therefore, temperature treatments tend to change the atomic arrangement.

314

P. HANSEN

1500 _n Sn~_x Co x o Sn1_ x F e x • Sn1_ x Nix

.,,Te%,sslro.z,s • Til_x COx /.., . 0 U- T ~/~Do ssir0 zs 1000 -4' Tl~"lX_x~e x .,¢.,~TCto.ssRh o.ls * Wl x Fex d - + ' N~o__.Rh_ ._ +T.o.:_x Tx ' ~ * < > ~;os7 Vo~ .... :_x *Tl,.xNlx , ~ . / ~ . • 500

,~oo~

-

// 0

Pi

I

I

I

I

I

I

I

I

I

I

I

I

I

I

i

I

I

100 AHh (kJ/rnol)

I

]

I

200

Fig. 18. Experimental crystallization temperatures versus calculated hole formation enthalpies (Buschow 1982a,b, 1984a). T represents transition metals.

Annealing at temperatures below the glass or crystallization temperature is thus associated with a change of various properties which depends on that particular annealing time and temperature (Egami 1978b, 1981, 1983a,b, 1984). Reversible relaxation phenomena are associated with different effects and properties such as the field-induced anisotropy, isochronal changes in the Curie temperature, electrical resistivity, elastic constant, etc. The reversible relaxation effects occur even at very low temperatures, while the irreversible processes take place at higher temperatures as compared to the glass or crystallization temperature. Generally, three typical effects are observed: (i) reversibility, (ii) 'crossover' effects involving a crossover of the changes of a property versus annealing time, ta, for two different annealing temperatures and (iii)the presence of 'ln t,' kinetics. First approaches to account for these effects utilize an activation energy being linearly related to the instantaneous magnitude of the measured property (Egami 1978a) or an discrete spectrum of activation energies (Woldt and Neuh/iuser 1980). However, difficulties arise using these models to explain all phenomena simultaneously. This has led to a new approach based on a continuous spectrum of relaxation processes (Gibbs and Evetts 1982, Gibbs et al. 1983, Fish 1985). Then, the total measured change of a property can be expressed by (Gibbs et al. 1983, Fish 1985) (' (13a) AP(t) = J~ c(E)q(E, T~, ta) dE, where q(E, T., &) in the case of first-order kinetics is of the form

q(E, T~,ta)=qo(E, Ta) {1 - e x p [ - Vtaexp(-- ~T~)]},

(13b)

provided each process is thermally activated, c(E) is the measured property change if only one such process having an activation energy E is thermally activated per unit volume of the material, q(E, T~, ta) is the number density of processes of the

MAGNETIC AMORPHOUSALLOYS

315

activation energy E which have contributed to the relaxation after annealing time ta. c(E)q(E, Ta, ta) thus is the property change related to relaxation processes having activation energies in the range E to E + dE. The parameter v appearing in eq. (13b) is the frequency factor. In the case of one isothermal annealing experiment and where q(E, T,, ta) is approximated by a step function (Primak 1955) with q(E, T,, ta) = 0 for E < Eo, the property change is given by

AP = co(E)qo(Eo, T~)kTa ln(vta),

(14a)

where Eo = kT, ln(vta)

(14b)

representing the typical 'ln ta' kinetics. Irreversible changes are associated with a reduction in volume (Chen 1978a,b) where the kinetics of the variation in linear dimensions were investigated (Kursumovic et al. 1980a,b). These changes in volume involve changes in the radial distribution function and, thus, can be studies by diffraction methods. Also, diffusivity and viscosity changes with annealing temperature (Anderson and Lord 1980, Taub and Schaepen 1980). Any structural relaxation affects the local electron density and thus gives rise to changes in the magnetic properties. Their variation with thermal annealing will be discussed in section 5.10.

5. Magnetic properties 5.1. Magnetic structures The magnetic properties and rules in crystalline materials are governed by the crystal symmetry. The possible magnetic structures are defined by the magnetic space groups. In the case of collinear arrangements of magnetic moments, this leads to the familiar forms of magnetic order like ferromagnetism, antiferromagnetism and ferrimagnetism, and, in the case of noncollinear structures, to helimagnetism or canted spin structures. The presence of chemical and structural (bond and topological) disorder in amorphous materials produces an inequivalency of sites that leads to a distribution (i) in magnitude of magnetic moments, (ii) in exchange interactions and (iii) induces large randomly varying electrostatic fields giving rise to locally varying single-site anisotropy. Although magnetic order depends sensitively on distances and local environments, the structural disorder does not prevent the existence of collective magnetic order. When the local anisotropies are negligible as compared to the exchange interactions, the possible collinear arrangements of magnetic moments in amorphous materials are sketched in fig. 19 for the common types of magnetic order (Coey 1978). It has been assumed that each atom carries a time-independent moment but any local fluctuation of its magnitude is not represented by the length of the arrows. The ferromagnetic structure shown in fig. 19a is observed for many materials as, e.g., Gdl-xM~ alloys with M = Ag, Au, A1 or Cu and transition-metal-metalloid alloys like Tl-xMx with T = Fe, Co or Ni and M - - B , P or C. The existence of an amorphous antiferromagnet is still questionable because a consistent subdivision of

316

P. HANSEN (a) ferromagnet

magnetization

I~1 , 0

(b) a n t i f e r r o ma g n e t

~:0 ~ = -~=

(c) ferrimagnet

~,o ~ > -~

Fig. 19. Collinear magnetic structures in amorphous materials (Coey 1978).

a random structure into two sublattices is impossible (Simpson 1974). In crystalline materials, antiferromagnetism is defined by symmetry and requires equivalent atoms on equivalent sites. Both requirements cannot be fulfilled in an amorphous structure. The collinear ferrimagnetic structure shown in fig. 19c is observed for Gdl_xRx alloys with T = Fe, Co or Ni and thus represents a two-subnetwork structure containing two distinguishable groups of atoms. In this sense, e.g., FeNi or FeCo will not be discussed under the topic of the two-subnetwork alloys. In addition to these familiar types of magnetic order, noncollinear structures with 0 < S~Sj < IS~IISjI like speromagnetic, asperomagnetic and sperimagnetic order occur in amorphous alloys as illustrated in fig. 20. These structures involve a competing random anisotropy and exchange interaction where the local anisotropy aligns the magnetic moments along the locally varying crystalline field axis. All these structures represent arrangements of magnetic moments which are frozen at a sufficiently low temperature. The speromagnet can be considered as a random antiferromagnet and the asperomagnet as a random ferromagnet. Both represent one-subnetwork mag(a) a s p e r o m a g n e t

magnetization

~1 ¢ 0

(b) s p e r o m a g n e t

~1 = 0

(c) sperimagnet

~1 , 0

Fig. 20. Noncollinear magnetic structures in amorphous materials (Coey 1978).

MAGNETIC AMORPHOUS ALLOYS

317

netic structures. The speromagnetism was observed for Yl-xFex and Fo.75Feo.25 while anisotropy-dominated asperomagnetism was found for D y o . z l N i o . 7 9 . Other spin structures, where the ferromagnetic alignment is limited to domains of some nanometers, are discussed for amorphous Zr-Fe alloys (Rhyne and Fish 1985, Ryan et al. 1987b). Sperimagnetism occurs in two-subnetwork structures like rare-earth-transitionmetal alloys of composition Rt _xT~ where the large spin-orbit coupling of the nonS-state rare earths give rise to large local anisotropies. Two classes of alloys can be distinguished containing heavy and light rare earths. In the first case, the R and T moments are coupled antiparaUel and in the second case parallel according to Hund's rule and the exchange coupling between the spins of the R and T atoms involving negative coupling of the 5d rare-earth electrons and the 3d transition-metal electrons (Campbell 1972). The first case, representing the antiparallel alignment of the moments, is illustrated in fig. 20c and fig. 21a for a collinear T sublattice which is representative for Co-based alloys due to the strong ferromagnetic coupling of the Co sublattice. For light rare earths with a parallel alignment of R and T moments, the situation is shown in fig. 2lb. In Fe-based alloys also a distribution of the Fe moments can occur as shown in fig. 21c,d. The strength of the R - T exchange coupling depends on the R element (Beloritzky et al. 1987) and is related to the variation of the 4f-5d interaction which is larger for light rare earths because the spatial extent of the 4f and 5d electrons is reduced. The distribution of moments induced by local anisotropies is not uniquely associated with disordered structures. Rare-earth-iron garnets also show a distribution of rare-earth moments due to the high single-ion anisotropy at low temperatures (Clark and Callen 1968, Englich et al. 1985). Another possibility is the presence of an exchange interaction of both signs which Sperimognetic

a) Dy-Co

structures

b) Nd-Co

._---~ c) D y - F e

- __~ d) Nd-Fe

r a r e e a r t h moment t r a n s i t i o n meta[ moment

• . . . . . -~

Fig. 21. Sperimagnetic structures in amorphous rare-earth-transition-metal alloys containing heavy rare earths (Dy, Tb, etc.) and light rare earths (Nd, Pr, etc.) (Taylor et al. 1978). The configurations sketched in (a) and (b) represent an asperomagnetic R suhlattice and a collinear T sublattice, while in the configurations (c) and (d) both sublattices exhibit a noncollinear structure.

318

P. HANSEN

is associated with the spin-glass behavior. These materials possess a typical spinfreezing temperature defined experimentally by a sharp peak in the low-field susceptibility as shown in fig. 22a for amorphous Sbo.s0Feo.5o (Xiao and Chien 1985). The magnetic phase diagram of Sb-Fe alloys shown in fig. 22b indicates the ranges of composition and temperature where spin-glass behavior is observed. However, also speromagnets, exhibiting a random distribution of moments due to the random local anisotropy, show a spin-freezing temperature associated with the typical cusp in the low-field susceptibility and thus might be considered as a spin glass. A large variety of compositions of either crystalline and amorphous materials show spin-glass behavior (Moorjani and Coey 1984). There is a principal difference between amorphous Fe-based and Co-based alloys with respect to the magnetic structure. The former tend to spin-glass behavior or speromagnetic structures (Xiao and Chien 1987, Ryan et al. 1987a,b, 1988, Fukamichi et al. 1988, Wakabayashi et al. 1987, 1990, Kakehashi 1990a,b) while the latter in general exhibit good ferromagnetic order. This is associ10

>,

5

0

(o)

i

i

20

~0

60

T(K} 300 Sb1_ x F e x

200

/ para

o

F-

100

fe spin

o

g t a ~ s / Ie

I ,l 0,30

0.40

0.50

0,60

0.70

x

Fig. 22. (a) Low-field susceptibility (2.4 kA/m) versus temperature exhibiting the typical cusp at the spinfreezing temperature Tf for amorphous Sbo.soFeo.so and (b) the magnetic phase diagram for amorphous Sb-Fe alloys (Xiao and Chien 1985).

MAGNETICAMORPHOUSALLOYS

319

ated with the different bonding character of these alloys as it is shown by X-ray photoelectron spectroscopy (XPS) valence-band spectra (Amamou 1980, Amamou and Krill 1979, 1980) and the much higher exchange interaction of the Co alloys.

5.2. Influence of preparation conditions The structure of amorphous alloys represents no ideal statistical arrangement of atoms but depends on the particular preparation conditions leading to differences in the local atomic environments and nearest-neighbor distances, the occurrence of a typical microstructure or the incorporation of gas atoms. This gives rise to variations in the magnetic properties. The magnetic moment is less sensitive to structural differences while the Curie temperature, the coercivity, the uniaxial anisotropy and the compensation temperature occurring in ferrimagnets are strongly affected by structural changes and thus depend on the preparation parameters. The compositional variation of the specific magnetization and the Curie temperature for evaporated (Miyazaki et al. 1987a) and liquid quenched (Miyazaki et al. 1986) amorphous Sml-xFex alloys are shown in fig. 23. The magnetization data are independent of the preparation technique and agree with those of crystalline compounds indicated by the squares. The corresponding Tc variation reveals a completely different behavior for the two amorphous alloys, probably due to the higher amorphicity of the evaporated films. In the case of amorphous films prepared by sputtering, the deposition parameters are of significant importance (Niihara et al. 1985, Hashimoto et al. 1987, Heitmann et al. 1987a,b) as demonstrated in fig. 24 for the uniaxial anisotropy constant, Ku. The influence of the sputter atmosphere on Ku for magnetron sputtered Gdo.24Tbo.o4Feo.72 films (Heitmann et al. 1987a) is shown in fig. 24a, while the influence of the argon gas pressure on K~ for diode sputtered [-(Gd, Tb)l _xCox] 1_yAry films (Heitmann et al. 1987b) is shown in fig. 24b for different bias voltages. In the first case, an increasing oxidation of the rare earths causes a reduction of K~ and in the second case a change of the microstructure and resputtering effects at the growing film surface lead to the observed Ku variations. In these cases, also the compensation temperature, the Curie temperature and the coercivity are strongly affected. A very important parameter controlling the structural disorder is the effective cooling rate that can be influenced via the substrate temperature of vapor-quenched films. This is demonstrated in fig. 25, showing the variation of the coercive field, He, versus the substrate temperature, T~, of sputtered Sm~_ ~Cox films (Munakata et al. 1984). Films prepared at T~~<500K exhibit an amorphous structure and reveal low coercivities. The films prepared at higher substrate temperatures are characterized by an increased amount of crystalline particles causing an increase of He. For these substrate temperatures, the effective cooling rate is too low to maintain good amorphicity. These few examples taken out of a great number of investigations may demonstrate the relevance of deposition conditions on the magnitude and sign of magnetic properties. Therefore, a meaningful comparison of amorphous alloys with the same composition concerning their structurally sensitive properties can only be made when

320

P. HANSEN

200 Srnl. x Fe x 160

E <

120

°°

b

80

oQ

40

0 0

0.20

0./,0

0.60

0.80

1.00

x Sin1. x Fe×

80O 700

Sm Fe 2.

600

Sm2 F e T ~

Sm F e a ~ Sm F e s ~ X ' ~ v

50O

I.-

400 .... 2 ' "17

300 200 (b) 100

I

0.20

I

I

0.40

0.80

I

0.80

1.00

x

Fig. 23. Concentration dependence of (a) the specific magnetization at H = 1.2 x 106A/m and T = 0 K and (b) the Curie temperature for amorphous Sm-Fe alloys prepared (0) by evaporation (Miyazaki et al. 1987a)and (©) by liquid quenching (Miyazaki et al. 1986).The squares represent crystalline compounds (Miyazaki et al. 1987b).

the preparation parameters and the knowledge of their influence on the structure are available.

5.3. Low-temperature magnetic moments 5.3.1. One-subnetwork alloys 5.3.1.1. Transition-metal-based alloys.

Models of moment variation. The average magnetization is based on the exchange coupled magnetic m o m e n t s which are

M A G N E T I C A M O R P H O U S ALLOYS

321

15 %.

(Gd 0.2t,T bo.oz,F e0.72) l_y Ay

atmosphere ~. "~

~E o

a ArlN 2 • Ar/O 2

~_

5

-5

0

0.02

0.0/, 0.06 YN'Yo (at %)

0.08

{Gd,Tb)l_x C°×]l-y Ary 10

O Vb=0V fi

~.~--

V b =-50V zx V b =-100V

o

~

°,+//I -5

Fig. 24. Dependence of the uniaxial anisotropy constant at room temperature on (a) the nitrogen A = N and oxygen A = O content in amorphous Gdo.2+Tbo.o+Feo.72 films prepared by magnetron sputtering (Heitmann et al. 1987a) and (b) on the argon pressure for amorphous (Gd, Tb)l _~Co~ films prepared by diode sputtering at different substrate bias voltages (Heitmann et al. 1978b).

correlated to the sum of spin-up and spin-down d electrons outside the last filled shell. The magnitude of the magnetic moment per atom and its temperature dependence have been discussed in terms of two extreme pictures of fully localized electrons (Heisenberg model) and fully itinerant electrons (Stoner model). The localized model cannot account for the fractional values of the observed moments and leads to a much too low Curie temperature, while the itinerant model gives rise to a Curie temperature which is an order of magnitude too high and also the moments in the paramagnetic state are completely destroyed. Thus, various approaches have been made to improve or combine these theories. An essential element of the disordered local moment theories (Hubbard 1979a,b, 1981a,b, Hasegawa 1979, 1980a,b, 1983, 1984, Oguchi et al. 1983, Moruzzi et al. 1986, Moruzzi and Marcus 1988) and the local band theories (Capellmann 1974, Prange and Korenman 1975, 1976, 1979a,b, Korenman et al. 1977a,b,c, Korenman 1985) is the introduction of a fluctuating mean

322

P. HANSEN

Sml.xCO x

1.4 o x [] A

1.2 1.0

d= d= d= d=

g4Onm 13/.Onrn 6gOnm 230nm

o


L

0.6 0.4 0.2 0

~ 300

1

! 500

i 700

go0

1100

T~ {K) Fig. 25. Coercive field versus substate temperature for Sm-Co alloys prepared by diode sputtering (Munakata et al. 1984). The argon pressure was 0.076Torr for the 940nm thick film and 0.063 Tort for the other films.

field, which means that a local mean field is introduced, whose direction may vary in space and time. In the disordered local moment theories the mean fields are assumed on lattice sites with no correlation among them, while for the local band theories it is assumed that the excitations maintain sufficient short-range magnetic order even above Tc. The real difference between these two viewpoints is not the absolute scale of short-range magnetic order, but in whether or not local ordering plays a significant role in the energetics of creating local magnetic strength (Korenman 1985). Although these theories account for various basic features of ferromagnetism of 3d metals (Williams et al. 1982, 1983a,b), there remain still some unsolved problems. Therefore, a basic theory for amorphous alloys with 3d metals which involves the additional problem of structural disorder is not yet available. Different models were developed to interpret the trends in magnetic property variation with alloy content. The first two models discussed focus on the valence per atom or the splitting of bands for alloys but take no account of the particular atomic structure and nearest-neighbor environments. The bond model is based on the local symmetry or coordination and the chemical bonding and was applied to explain primarily the magnetic moment variation of transition-metal-metalloid crystalline and glassy alloys (Corb et al. 1982, 1983, Corb 1985). The environment model considers only the influence of the local coordination of the disordered structure but does not account of any band features. First attempts to interpret the moment variation of Slater-Pauling plots representing the moment versus composition or electron concentration (fig. 26a) were based on a charge-transfer model (Mizoguchi et al. 1973a,b). However, the better understanding of compositional effects in terms of bonding and experimental XPS (X-ray photoelectron spectroscopy) and UPS (ultra-violet photoelectron spectroscopy) work have formed a more realistic picture of the influence of valence band structure and bonding on the moment variation of

MAGNETIC AMORPHOUS ALLOYS

323

alloys. In M - T alloys, (sp)-d bonding dominates where the hybridization between metalloid sp states and metal d states reduces the degree of localization of d electrons tending to broaden the d band into a more free-electron-like configuration (O'Handley 1987a). The metal-metalloid (sp)-d hybridization feature is much more significant for M - F e alloys than for M - C o alloys as shown by XPS measurements (Amamou and Krill 1979, 1980). This is consistent with the higher degree of d state localization in Co and Ni compared to Fe. Co and Ni, therefore, are expected to be less sensitive to their environment than Fe. The magnetic properties are primarily affected by p - d hybridization while s-d interaction is less significant. The strong p d covalent hybridization for C is expected to suppress the Fe moment as observed for carbon additions in B-Fe glasses (Mitera et al. 1978, Kazama et al. 1978a,b). This demonstrates the general trend that chemical bonding weakens magnetism (O'Handley 1987a). For R - T alloys, the situation is slightly different due to the highly localized nature of the 4f electrons. Band-gap theory. The moment variation with the average number of electrons (Slater-Pauling curve) was first discussed in the concept of virtual bond states (Friedel 1958, Mott 1964). This model has been extended and reinterpreted (Terakura and Kanamori 1971, Terakura 1976, 1977) and expressed in a more generalized form referred as band-gap theory (Malozemoff et al. 1983, 1984, Williams et al. 1983a,b). The atom-averaged magnetic moment in alloys of composition Ml-xTx with T = Fe, Co or Ni and M the solute can be expressed in terms of the atom-averaged number of spin-up and spin-down electrons, fix = #a( NT -- N~)•

(15)

The average atomic valence Z is related to N T and N ~ by Z = N ~+ N 1.

(16)

Combining eqs. (15) and (16), one obtains f,~ = # . ( 2 N ~

-

Z).

(17)

Thereby, the total number of spin-up electrons consists of d and sp electrons and, thus,

N ~ = N~ + N~p.

(18)

In the alloy, Z has to be considered as an averaged number of the T and M atoms, Z = (1 - X)ZM + xZx,

(19)

and thus/~x can be expressed in the form (Malozemoff et al. 1984) /ix(x) = #. [(1 - x)(2N~M -- ZM) + x(2N~T -- ZT) + 2N~p],

(20)

where 2NTT = 10 for iron and elements to its right and 2N~r = 0 for elements to its left. For #o = #.(2N~ T _ ZT)+ 2#.N~p and 2NTd. = 0, eq. (20) reduces to the form (Friedel 1958) fiT(X) = #o _ (1 -- x)(10 + ZM -- Zx)#..

(21)

324

P. HANSEN

This relation predicts a linear reduction of the average transition-metal moment with increasing M concentration, 1 - x, where #o is the T moment in the pure metal. Some typical averaged moments fiT per transition-metal atom at T = 4.2K are compiled in tables 5 and 10. It is seen that fiT is decreased with the presence of nonmagnetic elements as expected from eqs. (20) and (21). A typical Slater-Pauling curve for amorphous alloys is shown in fig. 26a. This plot of/~T versus average atomic valence reveals a shift of fiT for amorphous alloys towards smaller values of Z as compared to that of crystalline alloys without metalloids (dotted lines). Figure 26b shows the Fe moment variation for amorphous B-FeNi and BP-FeNi alloys (Kaul 1981a). A plot of fiT expressed in the form = Zm + 2/v p,

(22)

and expressed versus the average 'magnetic valence' Z m = ( I - - x ) ( 2 N ~ T - Z T ) + x(2N~M-Z~) and N~p = 0.3 (full line) is presented in fig. 27 for amorphous B-Co alloys (Malozemoff et al. 1984). The experimental data lie above the calculated line [eq. (22)], indicating strong magnetism. This feature is confirmed by the continuous moment and Tc variation across the phase change from crystalline to amorphous for various Co- and Ni-based alloys (Egami 1984, Stein and Dietz 1989) while for many Fe-based alloys a discontinuity was observed (Sumiyama et al. 1983, Stein and Dietz 1989). Various crystalline (Williams et al. 1983a,b) and amorphous (Malozemoff et al. 1983, 1984) alloys were interpreted in terms of this generalized Slater-Pauling TABLE 5 Average transition-metal moment at T = 4.2 K for amorphous alloys of composition M1 _~T~ with x ~ 0.8. Composition

#(#B)

Reference

Bo.2oFeo.8o Po.2oFeo.so Sio.2oFeo.8o Geo.2oFeo.8o Zro.2oFeo.8o Hfo.2Feo.8o Yo.zoFeo.so Lao.24Feo.76

1.99 2.1 2.23 2.2 1.65 1.45 1.89 1.53

Hasegawa et al. (1976) O'Handley et al. (1977) Felsch (1969, 1970a) Kazama et al. (1978b). Buschow and Smit (1981) Buschow (1984b) Coey et al. (1981) Heiman and Lee (1976)

Bo.2oC0o.8o Po.22 C0o.78 Mgo.2oCoo.8o Zro.2oCoo.so MOo.2oCOo.8o Hfo.2oCOo.so Nbo.2o COo.so Yo.2oCoo.8o Lao.2oCoo.8o

1.28 1.18 1.23 0.83 0.48 1.75 1.35 1.65 1.3

O'Handley et al. (1977) Cargill III and Cochrane (1974) Buschow (1984b)

Yo.lvNio.sa Lao.2oNio.so

0.04 0.04

McGuire and Gambino (1978) Buschow (1984b)

Buschow (1982b) Buschow et al. (1977) Heiman and Kazama (1978a)

MAGNETIC AMORPHOUS ALLOYS i

i

i

I

.../Fe-Co ;ff:Z...~.,~ g e - Ni

(o) ¢o

x

i

;

HI.xT x

\, ".. ,\ a6\\x

+

+ I

325

I

I

[]

I

%'~

I

7(Mn) 8(Fe) 9(Co) 10(Ni) 11(Cu) Avero.ge number of 3d electrons

2.75

*~'O'c~

BO.2o(F e× Nil-x )o.8o

"w, %..~

2.50

w... ",,,~

,--g :& ,,= 2,25

°%,Ji ]k.

v

"_'+, +,~

"q o'%

2.00

Po lt.Bo 06(Fex Nil-x )0.80 • • (b)

1.75 0

I

0.25

I

I

0.50

0.75

.%

•

'El,, I

1.00

X

Fig. 26. (a) Slater-Pauling plot for amorphous M 1-xT~ alloys (e) Bo.2o(Fe, Co)o.so, (&) Bo.2o(Fe, Nio.so), (m) Bo.2o(Co, Ni)o.so (O'Handley et al. 1976a,b); (©) Po.2o(Fe, Co)o.so, (~) Po.2o(Fe, Ni)o.so, (D) Po.2o(Co, Ni)o.so (O'Handley et al. 1977); (+) Bo.ls(Fe, Cr)o.ss (Dey et al. 1980); (x) Bo.2o(Fe, Mo)o.so (Sostarich et al. 1982). (b) Compositional variation of the Fe moment for amorphous FeNi-B and BP-FeNi alloys [B-FeNi: (©) Kaul (1981a), (e) Becket et al. (1977), (A) O'Handley et al. (1976a); PB-FeNi: (D) Kaul (1981a), (m) Beeker et al. (1977)]. The broken lines represent the linear relations ~ro = 2.00 + 0.80(1 - x ) and #F, = 1.85 + 0.80(1 - x ) for B-FeNi and PB-FeNi, respectively (Kaul 1981a).

model. It was pointed out that Slater-Pauling-like behavior can be attributed to a gap or minimum in the conduction-band density of states. Such a gap tends to conserve the number of conduction electrons in an alloy series leading to a straight line of #a- versus Zm- Although the systematics and rationalizing in the moment variation was improved, various alloys show significant deviations from the predicted linear dependence. This can be attributed to the limitations of the model that takes insufficient account of the atomic structure, nearest-neighbor environments and chemical disorder. The deviation from linearity is also obvious from the comparison of the concentration dependence for amorphous alloys of composition M l - x C o x with M = Mg, Zr or Mo (Buschow 1984b) and M = La, Y, HI', Zr, Ti, Ta, Nb, W or Mo (Shiba et al. 1986) as shown in fig. 28a,b. The full lines in fig. 28a represent the

326

P. HANSEN

2.5!

I

S

s'/

B1-x Cox SS J

2.0

SJ S SSJS

1.5 1.0 0.5

°_2

I

I

-1

S~ SST L~ I

0

x

I

I

1

I

2

Zm

Fig. 27. Generalized Slater-Pauling plot for amorphous Bl-=Cox alloys (Malozemoff et al. 1984). (x, ©) Hasegawa and Ray (1979), (@) McGuire et al. (1980a), (A) Watanabe et al. (1978).

compositional variation predicted by eq. (21). Good agreement between the calculated and measured data is achieved for Z r - C o alloys indicating the presence of a strong ferromagnetism, while for M g - C o alloys a strong deviation from a linear concentration dependence occurs. Almost all Co-based alloys are good ferromagnets for x > xc where xc represents the critical concentration for the appearance of collective magnetic order. Some amorphous alloys still exhibit ferromagnetism where their crystalline counterparts are already Pauli paramagnets, which applies, e.g., for Sn-Co (Marchal et al. 1980), Ce-Co (Malterre et al. 1988) or M - C o alloys with M = Hf, Nb or Ta (Buschow 1982b). This was attributed to the number of neighboring Co atoms which are necessary for a Co atom to develop a moment. Various Fe-based alloys are less strong magnets as compared to the corresponding Co alloys which can be ascribed to the much higher sensitivity of the F e - F e exchange interaction on structural and chemical disorder due to a higher degree of d state delocalization. For bond lengths below 0.25nm, even antiferromagnetic coupling occurs (Masumoto et al. 1980, Coey et al. 1981, Maeda et al. 1981, Yamauchi et al. 1984, Fukamichi et al. 1989b). The behavior of Fe alloys is demonstrated in fig. 29 for compositions M1-xFex with M = B (Fukamichi et al. 1978, Mitera et al. 1978, Hasegawa and Ray 1978, Chien et al. 1979, Buschow and van Engen 1981a, Chien and Unruh 1982, Stobiecki and Stobiecki 1983), M = P (Durand and Yung 1977, Mitera et al. 1978, Fukamichi et al. 1978), M = Zr (Masumoto et al. 1980, Buschow and Smit 1981, Fujimori et al. 1982, Shirakawa et al. 1983, Coey et al. 1984, Ryan et al. 1987b), M = Y (Chappert et al. 1981, Coey et al. 1981, Buschow 1982b, Gignoux et al. 1982) and M = Sc (Fukamichi et al. 1986a). In the case of B-Fe or P - F e shown in fig. 29a, the extrapolation to x ~ 1 leads to #Fe ~ 2.3#B which is in good agreement with the iron moment of crystalline iron. The moment variation in fig. 29b reveals a critical concentration, x~, where the average Fe moment disappears. The magnitude of x~ reflects the structural and chemical environment of the transition-metal atom. In the range x > xc, B-Fe, P - F e and various other Fe-based alloys are ferromagnets in contrast to Z r - F e alloys where /TFe passes through a maximum followed by a sharp decline and approaching #Fe = 0 at a second critical concentration x~ = 0.95

MAGNETIC AMORPHOUS ALLOYS

327

~1_xCOx

M= g

o

I

o

•

M=

0

(al 0

0.2

0.4

0.6

• Lo

1500

0.8

1.0

Ml-xC°x

Zr

[] y

11

• Hf

Nb Hf

To--'7 ] ~ "

o Zr ® Ti

tOo~o

• To 1000 E

A Nb • W

° • . D4 ~•

vMo

<

_~

A

Ti~ n

°a•

o ~

A

O

I"

A

[]

vA

o•®

500

mOA A [] 0"--0

I

0.50

0.60

@ V

@I

0.70

I

i

0.80

0.90

1.00

X

Fig. 28. Concentration dependence of the average Co moment at T = 4.2K (Buschow 1984b) and (b) the room-temperature magnetization (Shiba et al. 1986) for different amorphous alloys. The full line in (a) represents Friedel's model [eq. (21)]. The arrows in (b) indicate the metal concentration necessary to obtain amorphous films (Fujimori et al. 1984).

(Read et al. 1989). Compositions with x > 0.94 even reveal asperomagnetic order (Ryan et al. 1987b). This is confirmed by amorphous Ce-Fe (Fukamichi et al. 1988), La-Fe (Wakabayashi et al. 1987, 1989) and Hf-Fe (Hiroyoshi et al. 1985, Ryan et al. 1987a) alloys. The magnetic phase diagram for Cel-xFex alloys is displayed in fig. 30, demonstrating the limited compositional range for the existence of ferromagnetism. At high x and low temperatures, a speromagnetic or spin-glass-like state is present. In this figure, the phase boundaries are determined by the concentration dependence of the Curie temperature at high temperature and by the spin-freezing temperature at the low-temperature side with two tricritical points (Tc = Tf) at the Fe-rich and the M-rich side. The tricritical point compositions for amorphous Fe-

328

P. HANSEN

Ml-x Fex

I

A

M

'

2.0

'~" 1,5

a) 1.00

F

I

0.95

0.90

I

I

0.85

0.80

0.75

X

2.5 M 1-xF ex

2.0

._~ 1.5 1.0

0.5

(b) 0 0.20

0.40

0,60

0.80

1,00

X

Fig. 29. Concentration dependence of the average iron moment for amorphous (a) B-Fe and P-Fe alloys (Durand and Yung 1977) and (b) B-Fe (Chien and Unruh 1982), Y-Fe (Chappert et al. 1981, Coey et al. 1981) and Zr-Fe (Masumoto et al. 1980, Buschow and Smit 1981, Fujimori et al. 1982, Coey et al. 1984) alloys.

rich M - F e alloys with M = Zr, Hf, Ce or La were found to be 0.065, 0.07, 0.1 and 0.1, respectively. The corresponding Tc values are 150, ,-450, 120 and l l 0 K . The noncollinear structures associated with these low Curie temperatures for many Febased alloys are due to antiferromagnetic exchange requiring high magnetic fields to align the iron moments completely. Large single-ion anisotropy as present in R-T alloys can be ruled out as an origin for the noncollinear structure because the spinorbit coupling is significantly lower for the T elements than for rare-earth elements. In the case of Zr-Fe, M6ssbauer experiments indicate that below Tf only the transverse spin components freeze (Ryan et al. 1987b). A less dramatic moment reduction for x ~ 1 was also observed for Sc-Fe alloys (Felsch 1970b) or for rareearth-iron alloys discussed in section 5.3.2. An intermediate situation occurs for amorphous Y-Fe alloys which also reveal a noncollinear magnetic structure (Chappert et al. 1981). This can be well studied by M6ssbauer spectroscopy because the influence of the local environment on the iron moment is directly reflected in the hyperfine field distribution P(Hw)(Rodmarcq et al. 1980, Chappert et al. 1981, Chien and Unruh 1982). The M6ssbauer spectrum of amorphous Yl-xFex alloys at T = 1.6K (Chappert et al. 1981) is shown in fig. 31. In this case, the moment variation can be directly derived from the hyperfine-fleld distribution because the proportional-

MAGNETIC AMORPHOUS ALLOYS

329

250 Cel. x Fex

200 para 150

i

i

100

ferro

,

J

50 spin glass 0 0.50

I

I

I

I

0,60

0.70

0.80

0.90

1.00

X

Fig. 30. Magnetic phase diagram for amorphous Ce-Fe alloys (Fukamichi et al. 1988).

> t~

>

o~

E c

"1-

-6

-3

0

v(mm/s)

6

k

0

I

1

I

2

I

3

Hhf (107A/m)

Fig. 31. Mrssbauer spectra of amorphous Y-Fe alloys at T = 1.6K. The corresponding hyperfine-field distributions are shown on the right-hand side of the figure, indicating a relatively increasing fraction of nonmagnetic iron (shaded area) with a decreasing iron content (Chappert et al. 1981).

330

P. H A N S E N

ity between hyperfine field and magnetic moment was established from crystalline Y-Fe alloys (Gubbens et al. 1974). The hyperfine-field distribution is shown on the right-hand side of fig. 31 and the shaded area indicates the relatively increasing fraction of nonmagnetic iron with decreasing x. The analysis of the spectra reveal an asperomagnetic order in the entire range of concentrations x > xc as demonstrated in fig. 32. This random ferromagnetism again can be attributed to a broad distribution of Fe-Fe exchange interactions including a significant fraction of antiferromagnetic bonds. The moment variation for amorphous La-Ni and Hf-Ni alloys (Buschow 1984b) is presented in fig. 33. Very similar results have been found for amorphous Y-Ni and Ce-Ni alloys (Fr6my et al. 1984). These alloys are ferromagnetic, but the onset of magnetic order takes place at much higher concentrations as compared to the corresponding Fe or Co alloys. Split bands. Valence bands of Ml-xTx alloys split into two resolvable parts at different energies when the difference in atomic number is greater or equal to two (Beebey 1964, Velicky et al. 1968). The split-band character is a consequence of polar d-d bonding and was experimentally confirmed for various amorphous alloys (Oelhafen et al. 1979, 1980). The concept of split bands, originally applied to crystal-

Yl-xFex

x=0.32 0.57

0.71

0.82

Fig. 32. Schematic representation of speromagnetic structures in amorphous Y-Fe alloys (Chappert et al. 1981).

0.6

Ml_xNix

/

"-b O.Z, ,:& 0.2 0

0.7

j ~ 0.8

M=Hf 0.9

1.0

x

Fig. 33. Concentration dependence of the average Ni moment in amorphous Hf-Ni and La-Ni alloys at T = 4.2 K (Buschow 1984b).

MAGNETIC AMORPHOUSALLOYS

331

line alloys (Berger 1977, Berger and Bergmann 1980), was extended to amorphous alloys (O'Handley and Berger 1978). The interpretation of magnetostriction (O'Handley 1978a, O'Handley and Berger 1978) and Hall effect (O'Handley 1978b) measurements for amorphous Bo.2o(FeCoNi)o.8 o alloys indicate that Fe and Ni indeed contribute to the valence-band density of states at different energies and thus a minimum in the density of states is present. This model was shown to account well for the compositional variation of the magnetostriction and spontaneous Hall effect in these alloys. Coordination bond model. This model was derived from valence-bond theory to account for the magnetic moment variation of crystalline and glassy transitionmetal-metalloid (M-T) alloys (Corb et al. 1982, 1983, Corb 1985). It assumes that the average T moment is suppressed according to the number of M neighbors and the strength of the M - T bonds. The model is based on a strong p - d bonding, causing a T moment reduction of one fifth of its moment for each 3d electron participating in the nonmagnetic covalent T - M bond. This leads to an average T moment suppressing for M1 -xTx alloys of the form fiT(X) = #° [1 -- (1 + ~--~-~)(1 -- 1)1,

(23)

representing a linear decrease of fiT with the metalloid concentration 1 - x. Z~ is the number of T atoms surrounding an M atom. This model accounts for the moment variation for various M - T alloys (Corb et al. 1982, 1983, Corb 1985, O'Handley 1987a, Stein and Dietz 1989), however, the band-gap model appears to be able to explain more general trends in a wider class of alloys (O'Handley 1987a). Although these models are contradictory in their basic origin, both lead to a linear decrease of 17 according to the relation fix(X) = #°1-1 - p(1 - x)], where the slope p differs according to the assumptions made in these models. Environment model. The third picture to interpret the moment variation is based on the structural disorder and accounts for the different environments of a transition metal (Jaccarino and Walker 1965). The probability of a T atom to have j nearest T neighbors out of a maximum number n is given by n!

P(x, k,n) - k!(n - k)!"

(24)

Assuming a minimum number j of nearest T neighbors to be necessary for a T atom to carry a moment #1 and for less than j T neighbors a moment #2, then fi(x) can be expressed in the form fi(x) = #1Pj(x) + #2 [1 - P~(x)], where Pj(x) = ~ P(x, k, n). k=j

(25)

332

P. HANSEN

In the case #1,/~2 ~ 0, no critical concentration is expected. For #2 = 0, a critical concentration can be calculated from the tangent of the turning point of/i(x) at x = xt by xc = xo/P}(xt) where xt is determined by Pj'(xt)= 0. The comparison between experimental data for amorphous Y - F e (Chappert et al. 1981, Coey et al. 1981), Y - C o (Buschow et al. 1977) and S n - C o (Teirlinck 1981) and the environment model is shown in fig. 34. The full lines represent the calculated result with j = 7 for Fe, j = 8 for Co in Y and j = 9 for Co in Sn assuming #2 = 0. This means that at least seven nearest Fe neighbors and eight or nine nearest Co 2.5 Y1-x mx

2.0

1.5

m

1.0

0.5

0

0

0.2

0.4

0.6

0.8

1.0

X

Snl_ x Co x

150

•

100 E

<

50

Ib) 0 0.2

0.4

0.6

0.8

1.0

X

Fig. 34. Concentration dependence of (a) the average transition-metal moment for amorphous Y-Fe, (El) Chappert et al. (1981), ( I ) Coey et al. (1981); Y-Co, (O) Buschow et al. (1977) and (b) the specific magnetization for amorphous S n - C o alloys (Teirlinck 1981) at T = 4.2K. The full lines were calculated from the environment model I-eq. (24)] with #2 = 0 and j = 7 for Fe, j = 8 for Co in Y and j = 9 for Co in Sn. In the latter case, the density variation was not taken into account.

MAGNETIC AMORPHOUSALLOYS

333

neighbors are necessary to carry a magnetic moment for a Fe or Co atom, respectively. Nuclear magnetic resonance experiments for amorphous Y-Co alloys reveal already a disappearance of the Co moment for j = 6 (Alameda et al. 1985). Ni atoms require an even higher number of nearest neighbors to develop a moment, which is obvious from their higher xc values because xc increases with increasing ]. The models so far discussed can account for the moment variation for various alloys, but there are also various counter examples where/~(x) cannot be explained in terms of one of these models. This is associated with the extreme assumptions that are made in the case of the band-gap model disregarding certain influences of structure and local environment and in the case of the coordination bond or environment model where particular band features are ignored. The appearance of magnetism at xc reflects the influence of chemical environment and structural disorder. A significant fraction of transition-metal atoms in amorphous alloys experience a larger number of nearest-neighbor T atoms as compared to the corresponding crystalline alloys leading to higher xc values. Also, compositional short-range order plays a prominent role and from the heat of formation it can be concluded that its influence increases from Mg to Zr, leading to an increase of M neighbors that tends to increase x¢. Various xo values for M-rich amorphous alloys are compiled in table 6. They are deduced from the compositional variation of the saturation magnetization, the Curie temperatures or hyperfine fields. Many alloys show spin-glass behavior for M-rich compositions close to xo as, e.g., for M = Sn (Piecuch et al. 1983) or M = Sb (Xiao and Chien 1985). In that case, the smaller value in the brackets in table 6 indicates the onset of spin-glass behavior and the larger value in the brackets represents the tricritical point (Tc = Tf) where long-range magnetic order appears. The x~ values calculated from the band-gap theory are given in the last column. These values roughly reproduce the observed trends of an increasing x~ from Fe- to Ni-based alloys and for alloys containing elements from group II to group V. This confirms the importance of the chemical environment and disorder for the onset of collective magnetic order and the magnitude of the transitionmetal moment as it is already well-known for crystalline alloys as, e.g., for PtCo (Sanchez et al. 1989). The models and experimental results suggest that magnetic order in one-subnetwork T-based alloys is favored by (O'Handley 1987a,b) (i) a strongly positive heat of formation for like-atom clustering, (ii) minimum p - d hybridization, (iii) more negative average alloy valence and hence more positive magnetic valence and moment and (iv) a small interatomic spacing for Co-rich alloys but a larger spacing for Ferich alloys (negative exchange coupling at small Fe-Fe distances). Many other amorphous alloys not discussed in this section have been studied intensively and the data were compiled in different reviews (Buschow 1984a, Moorjani and Coey 1984, Coey and Ryan 1984, Egami 1984, Hansen 1988a).

5.3.1.2. Rare-earth-based alloys. The alloys of composition Rl-xMx, where R represents the rare earths carrying a magnetic moment, form a second class of magnetic one-subnetwork alloys. The magnetism is controlled by the localized 4f electrons and the 5d conduction electrons. However, in contrast to the transition-metal-based

334

P. HANSEN

TABLE 6 Critical concentrations for amorphous alloys of composition M1 -xTx with T = Fe, Co or Ni. The values in the last column have been calculated from the band-gap theory (Malozemoff et al. 1983, 1984). The values in the brackets represent tricritical points (Tc = Tf) where the Curie temperature equals the spinfreezing temperature. Group

M

Fe xc

Ref.*

II

Mg

-

III

B Y La

0.3,0.4 0.4 -

Si Ge Sn Ti Zr Mo Hf Th

0.4 0.3,0.4 0.4(0.25) 0.45,0.5 0.4,0.95 0.5 0.4 0.4

[4] [1,4] [1,7,8] [9,10,25] [11,24] [12] [13] [14]

P Sb Nb Ta

0.45 0.5(0.4) 0.65 0.6

[151 [16] [17] [12]

IV

V

Co xc <0.2

[1] [5,6]

* References: [1] Buschow and van Engen (1981a). [2] Buschow and van Engen (1981b). [3] Buschow and van Engen (1981c). [4] Teirlinck (1981). [5] Chappert et al. (1981). [6] Buschow (1982b). [7] Teirlinck et al. (1981). [8] Piecuch et al. (1983). [9] Sumiyama et al. (1983). [10] Liou and Chien (1984). [11] Heiman and Kazama (1979). [12] Xiao and Chien (1987). [13] Buschow (1984b).

Ni Ref.*

xc

Ref.*

Fe

Co

Ni

[2]

0.7

[6]

0.35

0.47

0.70

0.8 0.8

0.48

0.60

0.80

[22] [13] 0.57

0.68

0.85

0.63

0.73

0.88

~0.6 [18] 0.5 [19] 0.45 [13] 0.5 0.5 0.7 0.65 0.65 0.5 0.7 0.6 0.7

xc (Theory)

[3] [4] [20] [13] [13] [6]

[211 [6] [6] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

0.8 0.85 0.8 -

[22] [13]

[231

Buschow et al. (1978). Coey and Ryan (1984). Xiao and Chien (1985) Chien et al. (1983), Chien and Unruh (1982). Hasegawa and Ray (1979). Heiman and Kazama (1978a). Aboaf and Klokholm (1981). Pan and Yurnbull (1974). Moorjani and Coey (1984). Berrada et al. (1977). Read et al. (1989). Sumiyama et al. (1990).

alloys, t h e t y p e o f m a g n e t i c o r d e r is d e t e r m i n e d b y the e x c h a n g e i n t e r a c t i o n a n d the s t r o n g s i n g l e - i o n a n i s o t r o p y . T h e l a t t e r d o m i n a t e s for m o s t r a r e earths, e x c e p t for S-state G d w i t h a s m a l l a n i s o t r o p y . T h e q u a n t u m n u m b e r s , i o n i c r a d i i a n d the de G e n n e s f a c t o r for the r a r e e a r t h s in t h e i r m o s t c o m m o n c o n f i g u r a t i o n s are g i v e n in t a b l e 7. The Hamiltonian describing the exchange interaction between two atoms with spins Si a n d Sj g e n e r a l l y is o f the f o r m = -

~ J~S~Sj, i>j

(26)

MAGNETIC AMORPHOUS ALLOYS

335

TABLE 7 Quantum numbers, ionic radii and de Gennes factors for the rare-earth elements in their most common configurations (Moorjani and Coey 1984). Valence Y La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

3+ 3+ 4+ 3+ 3+ 3+ 2+ 3+ 3+ 3+ 3+ 3+ 3+ 3+ 3+

4f"

0 0 2 3 4 7 7 8 9 10 l1 12 13 14

Radius (nm) ionic

metallic

0.092 0.114 0.094 0.106 0.104 0.100 0.109 0.094 0.093 0.092 0.091 0.089 0.087 0.086 0.085

0.180 0.183 0.171 0.183 0.182 0.180 0.204 0.180 0.178 0.177 0.177 0.176 0.175 0.173 0.173

L

S

J

0 0 5 6 5 0 0 3 5 6 6 5 3 0

0 0 1 ~ ~ ~} 7 3 ~ 2 ~ 1 ½ 0

0 0 4 9 ~ ~ 7 6 ~-15 8 ~-15 6 ~ 0

g

gJ

(g -- 1)2J(J + 1)

4 Tr8 z7 2 2 3_ 2 _43 ~ _6s 7 -~

3.20 3.27 0.71 7.00 7.00 9.00 10.00 10.00 9.00 7.00 4.00

0.80 1.84 4.46 15.75 15.75 10.50 7.08 4.50 2.55 1.17 0.32

and can proceed either t h r o u g h a positive intra-atomic 4 f - 5 d exchange combined with a direct positive interatomic 5 d - 5 d exchange (Campbell 1972) leading to ferromagnetic order or indirectly via spin-polarized conduction electrons where b o t h ferromagnetic and antiferromagnetic order can occur. The latter interaction is k n o w n as R K K Y ( R u d e r m a n n - K i t t e l - K a s u y a - Y o s i d a ) interaction ( R u d e r m a n n and Kittel 1954, K a s u y a 1956, Yosida 1957). The exchange coupling constant for disordered alloys can be expressed by (de Gennes 1962a,b) Jij ~ j2fF(¢u) e-'i~/z, where ¢ij cos ~i~ - sin ~ij =

Jsf is the rare-earth conduction-electron interaction, 2 is the electron m e a n free path and ~ij = 2 k F r i j where kF is the Fermi m o m e n t u m and r~j = tri - rjl. The structural disorder leads to a distribution of rij and thus to a distribution of exchange coupling constants. These can be positive or negative because F(~ij) is an oscillating function. A p r e d o m i n a n t l y positive distribution results in a ferromagnetic coupling. W h e n the distribution is almost zero, then spin-glass behavior is expected involving b o t h positive and negative exchange constants. The first case is realized for Gd-rich alloys while the second was observed for m a n y diluted systems (Moorjani and C o e y 1984). The locally varying electrostatic fields and the strong s p i n - o r b i t coupling of the non-S-state rare earths give rise to a strong locally changing anisotropy inducing a varying orientation of magnetic moments. The electrostatic field H a m i l t o n i a n can

336

P. HANSEN

be expressed generally in terms of tensor operators O~,, oetoe= ~

k k B.O.,

(27)

k,n

which are directly related to the angular momentum operators (Stevens 1952). The sum over n is restricted to even terms and to n ~<4 for d electrons and n <~6 for f electrons. The general case of structurally disordered alloys cannot be solved. Therefore, it has been assumed that the atomic site retains a high degree of local symmetry but the local axes of the crystal field will vary at random from one site to another. For an axial symmetry only even order terms occur. Choosing the local axis at site i along the direction n~ of the lowest energy of the moment, then ~ ) reduces to the simple form (28)

~f(i) = __ Di(n i . ji)2,

where D = - 3 B ° and D > 0. The distribution of second-order electrostatic fields correspondingly leads to a distribution of energy level splitting controlling the local anisotropy (Cochrane et al. 1974, Cochrane et al. 1978a, Fert and Campbell 1978, Czjzek et al. 1981). The influence of exchange interaction and a random axial anisotropy on the average magnetic moment can now be studied using the Hamiltonian (Harris et al. 1973), = -

Z J~jJi" J~ - ~ Di(n~" g~) - g#B ~, H . J~, i>j

"

(29)

i

where the third term on the right-hand side represents the field energy due to an externally applied field. In the classical limit, the energy at T -- 0 K can be expressed by Ei = - # o ( H + Hex~h)COSOi -- D cos2(~bi - 0~),

(30)

where the exchange interaction was treated in the molecular field approximation. It was assumed that D~ has the same value at each site. 0i and ~b~represent the angles between the direction of the magnetic field and the magnetic moment and the local easy axis, respectively. From the condition dEi/dO~ = 0 and the spherical average nl2

#=

I

cos Oi sin q~id~bi,

do

the reduced magnetic moment m---#/#o = ( J z ) / J can be calculated (Callen et al. 1977). In the absence of any magnetic field, a speromagnetic order is expected. The presence of a magnetic field tends to align all magnetic moments, forming a random hemisphere around the positive field direction giving rise to an asperomagnetic order where the cone angle decreases with increasing field. Experimental studies show, however, that significant barriers are present to rotate the moments in the field direction and in certain cases large fields are necessary to reach the asperomagnetic state. Various features of this random axial anisotropy model have been studied (Callen

M A G N E T I C A M O R P H O U S ALLOYS

337

et al. 1977, Chi and Alben 1977, Patterson et al. 1978, Chi and Egami 1979, Harris 1980, Fibich 1990). The field dependence of the reduced magnetization resulting from this simplified model (Coey 1978) is shown in fig. 35. The curve for J = ~ corresponds to the classical limit. With increasing field, the fanning angle of the asperomagnetic structure reduces and saturation can only be reached when the applied field exceeds the local anisotropy field significantly. However, it turns out that for most amorphous alloys of composition Rl-xMx, this limit cannot be reached even in fields up to 2.5 × 10 7 A/m as demonstrated in fig. 36 showing the reduced magnetization at T = 4.2K for M = Ag and x = 0.5 (Boucher 1976, 1977, Pappa 1979). The broken lines represent the random anisotropy model reproducing the experimental data quite

1.00

J=8

0.80 E 0.60 I

0.40 0.20 0

I

I

I

1

2 g/.ZBH/DJ

3

Fig. 35. Relative magnetization curves for an array of magnetic ions with random easy axis anisotropy at T = OK (Coey 1978).

1.0 f

~

//"

_': ":'_

"

~.

--

"

R= Gd

oot.?:/./,--E

trf ¢

R0,0Ag0,0

H(10/A/m)

Fig. 36. Reduced magnetization for amorphous Ro.soAgo.so alloys at T = 4 . 2 K versus magnetic field (Boucher 1976, 1977, Pappa 1979). The broken lines are fits based on the random anisotropy model.

338

P. HANSEN

well in fields greater than 8 x 10 6 A/m which is the field needed to establish the asperomagnetic state. Magnetic saturation can be achieved only for Gd-based alloys. In this case, the local anisotropy is small and the next-nearest-neighbor exchange coupling leads to ferromagnetic order. The compositional variation of the saturation magnetization for amorphous Gdl -x Gex alloys at T = 4.2 K (Gambino and McGuire 1983) is shown in fig. 37. A critical composition for the disappearance of ferromagnetism can be estimated from the fall-off of Ms yielding xc --- 0.55. Similar results were observedfor Gd-A1 (Mizoguchi et al. 1977a,b, McGuire et al. 1978), Gd-Ag (Hauser 1975, Boucher 1976, Pappa 1979), Gd-Au (Poon and Durand 1977a, Gambino et al. 1981), Gd-Cu (Heiman and Lee 1976, Heiman and Kazama 1978b, McGuire et al. 1978), and Gd-Si (Simonnin et al. 1986), revealing xc values between 0.2 and 0.4. For x < x~, the nearest-neighbor coupling is no longer dominant and an intermediate range occur where a significant portion of antiferromagnetic interaction is present. With increasing dilution, the cluster glass region and the dilute spin-glass region (x < 0.01) appears. The magnetic properties of alloys containing non-S-state rare earths are controlled by the large random anisotropy and negative exchange interactions. Different systems have been investigated in more detail such as R-Au (Poon and Durand 1977a,b, 1978, McGuire and Gambino 1979, Berrada et al. 1979, Friedt et al. 1980, Hadjipanayis et al. 1981), R-Ag (Boucher 1977, Pappa 1979), R-Si (Hauser 1986, Simonnin et al. 1986), R-Cu (Heiman and Kazama 1978b, McGuire and Gambino 1979). Various alloys have been discussed in terms of the random anisotropy model (Ferrer et al. 1978) and good agreement with the experimental data was found for the highfield region while disagreement occurs in the low-field region which can be attributed either to hysteresis and magnetic after-effects. The predictions of this theory are inadequate to account for the magnetic properties of the light rare earths. Lowtemperature magnetic moments are compiled in table 8 for some R-M compositions.

2

Gdl_xGex

.<

0

0

0.25

0,50 x

1 Xc

I 0,75

1.00

Fig. 37. Compositional variation of the saturation magnetization for amorphous Gd-Ge alloys at T = 4.2K (Gambino and McGuire 1983).

MAGNETIC AMORPHOUS ALLOYS

339

TABLE 8 Curie temperature and low-temperature magnetic moment for amorphous R - M alloys with nonmagnetic M elements. The numbers in the brackets represent Curie or N~el temperatures of the corresponding crystalline compounds. R~M~_~ Euo.ToMgo.3o Euo.75Zno.25 Euo.7oZno.3o Euo.81 Ago.19 Euo.75 Ago.25 Euo.Ts Cdo.z5 Gdo.60Mno.40

Gdo.76Cu0.24 Gdo.voCuo.ao Gdo.ss Gao.ls Gdo.s5 Ruo.15 Gdo.7o Ruo.3o Gdo.6o Ruo.4o Gdo.sz Rho.18 Gdo.54Ago.46 Gdo.83 Pto.17 Gdo.aoAuo.2o Tbo. 50Ago,50 Dyo.soAgo.5o Hoo.~oAgo.5o Ero. 50Ago.50

Tc(K)

~R(#B)

131 134 133 70 37 134 230 142 144 148 78 77 57 111 122(138) 150 149 64(106) 18(59) 11(33) 6(20)

6.85 6.8 6.85 3.8 7.39 6.8 5.3 6.4 6.6 5.8 6.1 7.1 6.0 5.6 6.7 6.5 7.0 5.0 4.8 5.7 4.9

Re~rences Maurer and Friedt (1983)

Buschow and van der Hoogenhof (1979) Maurer and Friedt (1983) Buschow et al. (1980)

Boucher (1976) Buschow et al. (1980) Poon and Durand (1977b) Boucher (1977)

5.3.2. Two-subnetwork alloys In rare-earth-transition-metal alloys R 1 xTx, both the R and T atoms contribute to the magnetic properties. Their spins are coupled antiparallel via a strong exchange coupling between the 3d electrons of the transition metal and the 5d electrons of the rare earth where the latter are polarized by the 4f shell (Campbell 1972). This leads to a parallel alignment of the T and R moments for light rare earths (J = L - S) and to an antiparallel alignment for the heavy rare earths (J = L + S). Thus, for Gd-based alloys a collinear order is present leading to ferrimagnetism. However, as in the case of one-subnetwork alloys the presence of non-S-state rare earths involves local random electrostatic fields giving rise to large local anisotropies competing with the exchange interaction. This leads to spero-, aspero- or sperimagnetic order as illustrated in fig. 21. Some typical data for the rare earth ions are compiled in table 7. The average magnetic moment of an R1 _xTx alloy is given by ]~av = 1(1 -- X)IAR ~ XfiTI,

(31)

where + and - refer to light and heavy rare earths, respectively. The average rareearth moment,/~R, is controlled by the localized 4f electrons. The average transitionmetal moment,/~a-, is determined by the structural and chemical environment and by hybridization and mixing effects. Data for/Tav of some amorphous and crystalline alloys are listed in table 9. The kTavfor many amorphous alloys are lower than for

340

P. HANSEN

TABLE 9 Averaged magnetic moments/7~ = (1 -X)~R- x/Tr at T = 4.2 K for amorphous and crystalline R-Fe and R-Co alloys (Cochrane et al. 1978a). Amorphous alloy

x

/~av( # B )

Gdl _~Co~

0.67 0.75 0.78 0.79 0.83 0.67 0.67 0.75 0.83 0.79 0.67 0.77 0.67 0.75 0.67 0.75 0.77 0.74

1.4 0.7 0.47 0.27 0 1.57 1.43 0.63 0.4 0.4 1.5 0.53 0.67 0.70 1.6 1.08 0.79 0.48

Tbl _xFe~ Tbl _xCo~ Dya _xFe~ Dyl _xCo~ Ho 1_xFex Hol _~Co~ Era _~Cox

* References: 1-1] Lee and Heiman (1975). 1-2] Jouve et al. (1976).

Comparable crystalline compound

#~ (/~B)

GdCo2 GdCoa Gd 2Co7

1.67 0.55 0.27

GdCo5 TbFe z TbCoz TbCo 3 TbCos

0.2 1.57 2.23 0.85 0.08

DyFez

1.83

HoFe 2 HoFe3 HoCo2 HoCo3

1.83 1.15 2.6 1.4

Ref.*

[1] [2] [1] 1-3] [1] [4] [3] 1-2] [1]

[2]

I-3] Rhyne et al. (1974b). [4] Rebouillat et al. (1977).

the crystalline counterparts. The compositional variation of the saturation magnetization Ms = IM, - Mx[,

(32)

and the transition-metal spin value ST = ~T/gx#B at T = 4 . 2 K (Hansen et al. 1989) are shown in fig. 38. Ms is simply related to/Tav by the n u m b e r of atoms N per unit volume V (Ms = N(qv/V expressed in e m u / c m 3 corresponds to 1 k A / m in SI units). gT denotes the g-factor of the T atoms and Ma- and MR are the T and R sublattice magnetizations, respectively. The ferrimagnetic order of these alloys leads to a compositional compensation at X¢omp where Ms = 0 and g-rSr=gRSR. Xcomp is a sensitive function of composition. The MR sublattice dominates for x < Xcompand the MT sublattice for x > Xcomp. The triangles in fig. 38a represent single crystalline Ms data reduced by 5% to a c c o u n t for the lower density of the evaporated films. The data for Sa- displayed in fig. 38b are calculated from eq. (31) assuming SGd = 7 and gGd = 2. The full lines in fig. 38b are calculated from the environment model (Jaccarino and Walker 1965) w i t h j = 5 a n d j = 7 for the G d - F e and G d - C o alloys, respectively. Thus, less nearest T neighbors are necessary for the onset of magnetism as c o m p a r e d to the one-subnetwork alloys like Y - F e and Y - C o . The dotted lines indicate the critical composition for the appearance of a magnetic m o m e n t at the T a t o m yielding xo ~ 0.4 for T = Fe and T = Co, respectively. These slightly lower x~ and j values

M A G N E T I C A M O R P H O U S ALLOYS

341

2000

/Gdl.xCox

1500

I

Gdl.xFex/ 100(

500 (a) l

i

l

t

I

0.2 0.4 0.6 0.8 1.0 X

1.00

o°O°°

Gdl_xFex, ~ ~ ,0.75

/

~

,.n0.50 0.25 00

0.2 0.4 0.6 0.8 1.0 X

Fig. 38. Compositional variation of (a) the saturation magnetization and (b) the spin value for amorphous G d - F e and G d - C o alloys at T = 4.2 K (Hansen et al. 1989). The full squares in (a) were taken from the work of Taylor (1976). The full lines in (b) were calculated from the environment model.

with respect to the one-subnetwork alloys (see table 6) can be attributed to the additional R T exchange coupling but also reflects the dominance of the strong TT exchange coupling. The variation of Ms and the average transition-metal moment at T = 4 . 2 K for amorphous Gdl_~T x alloys with T = F e , Co or Ni and

342

P. HANSEN

Gdl-x(FeyCot-r)=, Gdl-=(F%Nil-y)~ and Gdl_=(CorNil_y)x alloys with 0.17 ~<x ~<0.22 and y ranging from 0.19 to 0.94 (Taylor and Gangulee 1980) are presented in fig. 39. The variation of the average transition-metal moment with the averaged number of 3d electrons corresponds to the Slater-Pauling curve of the onesubnetwork alloys (see fig. 26), but the moments are slightly shifted towards a higher number of 3d electrons except for the Gd-FeNi alloys. This shift can be attributed to the additional R - T exchange interaction. From the binary alloys, the moments for Fe, Co and Ni can be calculated yielding fiFe ~-" 2.09#B,/iCo = 1.45#B and ]~Ni ~0.31#B. Amorphous Gdl_~Mn~ alloys were also found to exhibit ferrimagnetic order 800 O n o A

600 A

<

400

Gd-T Gd-FeCo Gd-CoNi Gd-FeNi

o° / o/ /

:~ 200 i

&

[]

A

0 -200

(a) I

6{Fe)

8{Ni)

7(Co) Averag e number of 3d electrons 2.5 a, Gd-T • Gd-FeCo o Gd-CoNi x Gd-FeNi

~o e

2.0

• × A

1.5

A

,:t

8

x

o

1.0

o o o o o o

0.5

×

(b) 0

I

I

I

6(Fe} 7[Co) 8(Ni) Average number of 3d electrons

Fig. 39. (a) Difference of sublattice magnetization and (b) transition-metal moment versus average number of 3d electrons for amorphous G d - T alloys with T = Fe, Co or Ni and G d - F e C o , G d - F e N i and G d - C o N i alloys at T = 4.2K (Taylor and Gangulee 1980).

M A G N E T I C A M O R P H O U S ALLOYS

343

(McGuire and Taylor 1979) as opposed to the ferromagnetic order in crystalline alloys (Kirchmayr and Steiner 1971). The Mn moment depends on composition going from 2#B to 0.5#B per Mn for 0.8 <~ x ~< 0.2. The magnetic moment behavior of Mn in G d - M n is similar to that found in crystalline alloys where a well-developed moment occurs only when the transition-metal atoms are isolated from one another. The moment variation for amorphous iron alloys of light rare-earth elements (Dai et al. 1985, 1986, Miyazaki et al. 1987a, 1988) and for cobalt alloys (Dai et al. 1985, Takahashi et al. 1988a,b) is shown in fig. 40. The moments were deduced from magnetization measurements in fields ~<1.4 x 106 A/m and were extrapolated to T = 0 K from temperature-dependent measurements between 77 and 450 K, yielding the /i T data /iPr = 0.35#B, ~Nd=0.26#B, fiSm= 0. These values were determined from eq. (31), assuming compositionally independent moments for the R atoms. The broken lines in fig. 40a,b were inferred from fig. 38. The much higher/iFe for N d - F e alloys can be attributed to the very low Nd moment used to evaluate these data. A higher fiNa (Taylor et al. 1978, Dai et al. 1985) reduces the #tEe data to those for the Pr-Fe 3.0

Rl-x Fe×

o

2.0 -%

t~ 1.0

0.20

0.40

0.60

0.80

1.00

X

2.0 RI xCox

1.5

R=Pr

-%

Nd

s"

•3 1.0 I::&

0.5 b) I

0.20

I

O.Z,O

0.60

I

0.80

1.00

X

Fig. 40. Compositional variation of (a) #F~ (Miyazaki et al. 1987a, 1988) and (b) #co (Takahashi et al. 1988a,b) for amorphous R-Fe and R-Co alloys with R = Nd, Pr or Sm at T = 0 K.

344

P. HANSEN 200 Prl_ x F e x

x:O.90

160

~ 120

~ 80 40

I

I

I

0.2

0.4 H{107 A/m)

0.6

0.8

Fig. 41. Field dependence of the specific magnetization for amorphous Pr-Fe alloys at T = 20 K (Croat 1981a).

alloys. A fit of low-field magnetization data for N d - F e alloys leads to a good agreement between experiment and calculated data using eq. (23) with/~vel = 2. I#B, #ve2 = 1.2/~a, find = 1.13#B andj = 6 (Dai et al. 1985). Generally, however, the compositional variation of fiFe differs from that of the G d - T alloy in particular in the rare-earth-rich regime. This can be associated with the difficulty to determine accurate moments per atom for non-S-state rare-earth alloys due to noncollinear subnetworks. Very high fields are necessary to align the R moments as demonstrated for the specific magnetization o- (a = Ms/p expressed in emu/g corresponds to Am2/kg in SI units, where p is the density) in fig. 41 for amorphous Prl-xFex alloys (Croat 1981a). Therefore, at low fields, the contribution of the almost speromagnetic Pr (Croat 1981a, Wan et al. 1990) and Nd (Croat 1981b, Taylor et al. 1978, Siratori et al. 1990) subnetwork to the net magnetization at low temperatures is quite small. This is not in agreement with the random anisotropy model predicting a remanence of the relative magnetization of about 0.5 at T = 0 K and H = 0. An additional complication arises in R-Fe alloys from the Fe subnetwork for compositions approaching the critical concentration xe. In this range of compositions, an increasing portion of the Fe subnetwork exhibits an asperomagnetic behavior inducing an additional effective dependence on composition when transition-metal moments are evaluated from lowfield magnetization data.

5.4. Temperature dependence of the magnetization 5.4.1. Models 5.4.1.1. Mean-field theory. The lack of a general analytic expression to predict the temperature dependence of M s had led to the use of simple approximations allowing at least a qualitative interpretation of the experimental data. The mean-field theory is widely used to describe the concentration and temperature dependence of Ms and

MAGNETIC AMORPHOUSALLOYS

345

to determine the subnetwork magnetizations in ferrimagnetic alloys (Hasegawa 1975, Gangulee and Kobliska 1978b, Hansen and Urner-Wille 1979, Mansuripur and Ruane 1986, Hansen et al. 1989, Hajjar and Mansuripur 1989). The mean-field theory is based on the Heisenberg model assigning an i atom a magnetic moment, #i(T) = #i(0)(m~),

(33)

where pi(0) = gi#BJi and (mi) = (Ji)/Ji. gi and Ji are, respectively, the gyromagnetic factor and the total angular momentum of an i atom where the latter is composed of the spin and orbital angular momenta. (m~) represents the time-averaged projection of the total angular momentum along the quantization axis and is defined by +Ji

miexp(-E,/kBT) (mi) = m,=+-S, Ji

(34)

exp(-E,/k.r)

mi = -- J i

where E~ = - #~(0)(H + H~'~)ch)m,.

(35)

ka denotes the Boltzmann constant. In the molecular-field approximation the exchange field can be written in the form

~o - EJ gigj#B ~ #j(T), Hexch(T)-

(36)

where the Jii represent the exchange constants and the summation in eq. (36) can be performed leading to the Brillouin function

where

#i(O)" H

Zi

= k-~

u~O

+ **exch).

(38)

Assuming all moments of the same atomic species to be equal, the sublattice magnetization Mi(T) is defined by

mi(T) = Nxi#i(T).

(39)

N is the total number of magnetic atoms per unit volume and xi is the fraction of the ith species in the alloy. The saturation magnetization is given by

Ms(T) = ,=~ M,(T) , where r is the number of subnetworks.

(40)

346

P. HANSEN

Structural disorder causes fluctuations (Handrich 1969, J/iger 1977) of the exchange interaction. Restricting to nearest-neighbor exchange, eq. (36) can be rewritten as

q) _ 2 ~ n~J(J~J) (1 + Aij)Mj(T). Hexch(T)- Ngi#a j=l gjPB

(41)

i and j now denote the subnetworks and n o are the number of nearest neighbors. Assuming the exchange fluctuation A~j to be small (A~j~ 1), the Brillouin function can be expanded in a Taylor series yielding in the absence of an external field for a one-subnetwork alloy (Handrich 1969, Kaneyoshi 1986),

Ms(T) = ½Ms(O){Bs[z(1 + A)3 + Bs[z(1 - A)]},

(42)

and, for a two-subnetwork (J/iger 1977), M~ (T) = ¼M~(0){Bj, [2~ M~ (T) + 272M2(T)] + Bs~E21-~M~ (T) + 272M2(T)] + Bj~ [2~~M~ (T) + 2i-2M2(T)] + Bj, [2~-~M d T ) + 2~-2M2(T)]}, (43) where

2i~ - N~g#f3 g ' j (dij)(1 + Aii ).

(44)

A corresponding equation applies to M2(T). The average values 3ij are obtained from (A21A22) =AxlA22. -2 -2 The mixed terms ( A l l A 2 2 ) vanish because the fluctuations of Jll and Jz2 are independent. For 3~ = 0, these equations correspond to the molecular-field equations applied to crystalline ferrimagnets. In this case (J~j--0), the Curie temperature can be expressed in terms of the 2~j by Tc = ½{Tll + T22 + x / ( T l l - T22) 2 + 47"12Tz~ },

(45a)

where the T~j are related to the 2o by

Tit = N(Ji + 1)#i(O)2xi 3kB 2ij.

(45b)

The relations given in eqs. (42) and (43) were used to calculate the sublattice magnetizations regarding the exchange constants as adjustable parameters. The calculations reveal an increasing flattening of the temperature dependence of M s with increasing exchange fluctuation parameter 3 (Handrich 1969) and a pronounced shift of the compensation temperature towards lower temperatures (Kaneyoshi 1986, 1987). The mean-field theory does not account for spin-wave excitations at low temperatures and does not account for the exchange fluctuation in the range of the Curie temperature. The comparison of mean-field calculations with experimental results will be discussed in section 5.4.2.

M A G N E T I C A M O R P H O U S ALLOYS

347

5.4.1.2. d-band model with random axial anisotropy. The mean-field theory based on the localized-electron picture as outlined in the preceeding section omits the itinerant character of the d electrons. A model that accounts for the d-band features was developed for crystalline compounds (Bloch and Lemaire 1970, Bloch et al. 1975) and was applied to different amorphous Rl-xTx alloys (Jouve et al. 1976, Bhattacharjee et al. 1977a,b). This model treats the T atoms in terms of itinerant d-electron magnetism and the R atoms with localized 4f electrons interacting via the polarized d band by a local exchange interaction. The corresponding Hamiltonian can be expressed by = .~ hjc+cj, + I ~ n]ni ~- Jexcn ~ J , ' a j - D ~, ~j. t,j

i

j

(46)

j

The first two terms on the right-hand side describe the kinetic energy and correlation in the d band (Hubbard 1963), ci,+ and cj~ are the creation and annihilation operators for a d-band electron of spin a at site i and j, respectively, ni ~ and ni ~ are, respectively, the particle number operators for spin-up and spin-down electrons, tij is the d-band transfer matrix and I is the strength of the on-site Coulomb interaction. These two quantities represent the properties of the average d band. The third term describes the exchange interaction between the R and T atoms where Jexch is the exchange coupling constant and tri is the Pauli spin matrix for the d band. The last term represents the random anisotropy. Using the molecular-field approximation and the z-direction parallel to the molecular field, the Hamiltonian of eq. (46) can be written in the form

= ~, ('~k-- ltTA)e~reka -- 2 (JexchtrzJzJ + D~j), k

(47)

j

where A=

I+

~.

ek is the Fourier transform of t~j, x is the transition metal concentration and A represents the molecular field of the d electrons. ~z = n T - n * is the polarization of the d-band electrons that is related to the Fermi function f(e) and the total number of d electrons N = n T+ n * inside the d band. ¢7~ and N are correlated by the selfconsistent equations,

#~ = ~ [f(~k -- ½A) --f(ek + ½A)],

(48a)

k

N = ~ [f(ek -- ½A) +f(ek + ½A)]. k

(48b)

From these relations, the net magnetization M~ (T) = #B [ x ~ + (1 - x)gJ z ] / V

(49)

can be determined assuming the d-band to correspond to a free electron band. This requires the knowledge of the electron density of states N F at the Fermi level. The

348

P. HANSEN

numerical calculation then can be performed treating I, J0xCh,D and NF as adjustable parameters.

5.4.1.3. Other concepts. The treatment of a spin cluster in an effective field was analyzed in terms of the BPW (Bethe-Peierls-Weiss) approximation (Bethe 1935, Peierls 1936, Weiss 1948, Moorjani and Ghatak 1977). The relevant Hamiltonian is of the form N

~'=-2

~" J o i S o ' S i - g # a H ' S o - g # , H 1 /=1

~., Si.

(50)

/=1

So represents the spin operator interacting with the nearest and next-nearest neighbors limiting the exchange coupling constants to Jol and Jo2. N is the number of the atoms in the cluster and H is the applied magnetic field.//1 denotes the sum of H and an internal field representing the interaction of the spins in the cluster and with the rest of the medium. This approach applies to the high-temperature range where the effect of clustering is important for the transition from the magnetically ordered state to the paramagnetic regime. The Curie temperature is determined by the condition that the internal field vanishes, leading to the equation 2 [Ll(zl) + L2(z2)] - x(n - 1~'

(51)

where L;=cothz~-z; -1 is the Langevin function and zi=2S(S+ 1)Joi/kBT. The critical concentration for the onset of ferromagnetism also can be calculated from eq. (51) yielding (Handrich 1972) xc = ( n - 1) -1 (Ising model) and xc = 3 ( n - 1) -1 (Heisenberg model) where n denotes the number of nearest neighbors. The interaction between two neighboring atoms represents another molecularfield approach and was discussed in the pair approximation (Smart 1966, Kobe and Handrich 1972). The coherent potential approximation (CPA) offers a further approach to calculate the concentration and temperature dependence of magnetic properties in amorphous alloys (Elliott et al. 1974, Tahir-Kheli 1976, Foo and Wu 1972). The application of this concept to disordered alloys involves the introduction of a coherent exchange interaction. In the weak-coupling limit the CPA results agree with those derived from the mean-field theory while in the strong-coupling limit the CPA goes beyond the mean-field theory and is capable to predict critical concentrations. The magnetization and the Curie temperature usually are calculated using the Green function method. This leads to the equations Gij(2 ) = Gij Jv Z Jek [Gij(Z) -- Gkj(Z)], k

and 1 -mm

1 f +_f [ ~N

exp

(52)

(mk__~T)]-1 -- 1

Trim(z) dz,

(53)

where z = E/m and m = (Sz)/S. From the second equation, the relative magnetization

MAGNETIC AMORPHOUSALLOYS

349

m is determined self-consistently. The coherent exchange interaction .l~k is related via T-matrices to the exchange coupling constants Jll, Jlz and Jzz as reported for binary alloys (Foo et al. 1971). The Curie temperature can be determined from a cubic equation and the critical concentration in CPA is xc = 2/n (Tahir-Kheli 1972a,b,c, Jones and Yates 1975). The mean-field theories do not account for local magnetic excitations and thus cannot provide an accurate description of the low-temperature behavior of the magnetic properties. This problem can be solved by the spin-wave theory that is based on the exchange Hamiltonian given in eq. (25). In the quasicrystalline approximation and the long-wavelength limit, the spin-wave energy can be expressed by (Keffer 1966) E k = E o -t- Dk 2 + Fk 4 -I- "",

(54)

where k is the wave vector of the spin wave and D and F are the spin-wave stiffness constants. The presence of spin waves gives rise to a reduction of the average magnetization, leading to a temperature dependence of the form Ms(T) = Ms(0)[1 -- B T 3/2 -t- C T 5/2 + -..].

(55)

The coefficients B and C are related to the spin-wave stiffness constant D by 3

g#B ,

and C _ 3 x l r 2 \ r t 5 ~ ( g#R "~ ( kB y/2

((2a-) = 2.612 and ( ( I ) = 1.341 are the zeta functions and (r 2) represents the average mean-square range of the exchange interaction. D is directly proportional to the exchange constants. With increasing exchange strength, the slope of Ms(T) versus T 3/2 decreases as expected from experimental results of alloys with increasing Tc. 5.4.2. One-subnetwork alloys 5.4.2.1. Transition-metal-based alloys. The temperature dependence and the Curie temperature reflect the strength of the exchange coupling. The structural disorder in amorphous alloys induces an exchange fluctuation that causes a pronounced flattening of the Ms(T) curves. This is demonstrated in fig. 42 showing the reduced hyperfine fields versus reduced temperature for amorphous and crystalline FeF2 alloys (Litterst 1975). The temperature curve for the amorphous alloy lies substantially below that for the crystalline compound. This reduction of Ms was explained in terms of the mean,field theory [eq. (42)] using an exchange fluctuation parameter A=

AJij

.~. Jij,

(56a)

l,J

which is defined according to the Aij introduced in eq. (41) and adapts values in the

350

P. HANSEN

1.0

ysta|[ine

0.8 0.6

FeF2

e ~

0.4 0.2 I

0.2

t

0.4

t

0.6 T/Tc

I

0.8

1.0

Fig. 42. Normalized hyperfine fields versus reduced temperature for crystalline and amorphous F0.67Fe0.33 (Litterst 1975).

range 0.4 ~
1-

,

(56b)

the discrepancy between theory and experiment could be removed as it was shown for amorphous B-FeCo (Prasad et al. 1980) and BSi-CoFe (Bhatnagar et al. 1982, 1984) alloys. The low-temperature data can be described in terms of the spin-wave theory [eq. (55)] as reported for P - C o (Cargill III and Cochrane 1974, Hfiller and Dietz 1985) and PB-FeNi (Chien and Hasegawa 1977, Kaul 1981b) and other Feand Co-based alloys (Fernandez-Baca et al. 1987, Liniers et al. 1989). Some results are reproduced in fig. 45. Deviations from the calculated line occur for T ~>0.2Tc to 0.4Tc due to the neglect of critical fluctuations or the temperature dependence of the spin-wave stiffness constant. In the corresponding crystalline compounds, deviations from the T 3/2 law occur already for T >~0.15Tc. However, not all amorphous ferromagnets obey the T 3/2 dependence. In the case of Ni-based alloys, the weak itinerant ferromagnetism leads to a temperature dependence of Ms given by

M2(T) =

M2(O)[1 -- (T/Tc)"].

(57)

MAGNETIC AMORPHOUS ALLOYS

351

1.0 &=O 0.5 0.6

0.8

0.7

-

0.8 0.6

E 0./,

o Zro.2~ Feo.Ts

~,k~

0.2 I

I

I

I

0.2

0.4

0.6

0.8

1.0

T/Tc

1.0

A=0 0.8

000 0 = 0.6 E O.A

Po.~l,B o.oeFeo,4oNio.~.o

~'l

0.2

0

(b) i

i

0.2

i

i

0.4

i

i

0.6

i

i

0.8

i

1.0

T/Tc

Fig. 43. Relativesaturation magnetization m, = M,(T)/Ms(O) versus reduced temperature for (a) amorphous Zr-Fe and La-Fe alloys (Heiman and Kazama 1979)and (b) an amorphous PB-FeNi alloy (Kaul 198lb). The full lines represent mean-field calculations [eq. (42)] for different exchange fluctuation parameters. In the case that spin-wave excitations are neglected, the band theory yields t / = 2. If collective spin fluctuations are taken into account the theory predicts values for t/ smaller than 2 (Murata and Doniach 1972, Moriya and K a w a b a t a 1973a,b). Amorphous Y t - x N i x alloys obey relation (57) with t / = 2 for 0.93 <~x <~ 0.97 while for x < 0.93 q decreases with decreasing x reaching ~/= 1 for x = 0.833 (Li6nard and Rebouillat 1978). A corresponding behavior was found for amorphous Cet_xNix alloys (Fr6my et al. 1984) revealing 1.4 ~
352

P. HANSEN

JLa=/~=0 0.5 0.8 0.6

Y 0.4

i

0.2 I

O0

I

I

0.2

I

I

I

0.4

I

0.6

I

I

0.8

I

~'

1.0

T/Tc Fig. 44. Relative saturation magnetization ms = a,(T)/as(O) versus reduced temperature for an amorphous P-Co alloy (Pan and Turnbull 1974). The full lines represent mean-field calculations [eq. (42)] for different exchange fluctuation parameters.

coupling constant leads to an increase of Tc provided the ferromagnetic coupling is maintained. This applies to Co-based alloys which are strong ferromagnets and exhibit larger Tc values as compared to the corresponding crystalline counterparts as demonstrated in fig. 46a for amorphous and crystalline Y-Co alloys (Fukamichi et al. 1987a). The Tc values for x > 0.70 represent estimated data because Tc interferes with the crystallization temperatures. The opposite situation occurs for Fe-based alloys where both the moment and the average exchange coupling constant either are equal or smaller than in the crystalline compounds and thus a corresponding behavior is observed for the Curie temperatures as shown in fig. 46b for amorphous and crystalline B-Fe alloys (Stobiecki and Stobiecki 1983). This can be attributed to the sensitive dependence of the Fe-Fe exchange on the atomic distances that can even change sign for distances below 0.254nm. The competing positive and negative exchange constants are also the reason for the turndown of Tc in the limit of Fe-rich alloys as shown in figs. 46b and 47a. In the case of amorphous M - F e alloys with M = Zr, Hf, Ce, La or Lu, the magnetic phase diagrams (see fig. 30 for Ce-Fe) indicate a transition to an asperomagnetic or spin-glass-like state (Fukamichi et al. 1989a, Kakehashi 1990a, Krey et al. 1990). However, many other Fe-based alloys behave similar to the Co-based alloys and exhibit a monotonous rapid fall of Tc with increasing solute concentration as, e.g., observed for amorphous Ti-Fe alloys (Liou and Chien 1984, Xiao and Chien 1987). The variation of Tc for amorphous FeNi alloys (Kaul 1981a) is presented in fig. 48. The full lines were calculated in terms of the coherent potential approximation. Variations in the metalloid composition produces changes in Tc from 500 to 700 K for Fe-rich alloys (Luborsky 1978, 1980). Amorphous alloys containing Co exhibit significantly higher Tc values due to the stronger Fe-Co exchange as compared to

MAGNETIC

AMORPHOUS

ALLOYS

353

1.000

~ 0.975

x=0'76/

/~

(o) 0.950

x=0.81 / x=0.78

\ i 4.00

0

i t 800 1200 T~(K~)

i 1600

1800

1.00 0.95 ~ o a 4 B o . o s

Feo.l,oNio.~.o

o.9o 0.85 0.80 (b) 0.75

0.0

=

0.1

i

i

0.2 0.3 (T/Tc )3'2

i

0.4

0,5

Fig. 45. The change of relative saturation magnetization ms = M,(T)/M,(O) versus reduced temperature (a) for amorphous P1 _=Cox alloys (Cargill III and Cochrane 1974) and (b) for an amorphous P B - F e N i alloy (Kaul 1981b). The full lines were calculated from the spin-wave theory [eq. (55)].

the Fe-Fe exchange. Curie temperatures and low-temperature magnetic moments for some transition-metal one-subnetwork alloys are compiled in table 10. The critical concentration Xc decreases in 3d based alloys in the sequence Ni, Co, Fe from roughly 0.8 to 0.4, in agreement with magnetic moment and hyperfine-field measurements. The xc values reflect the different number of nearest TM neighbors necessary to establish magnetic order according to the environment model. Critical concentrations are collected in table 6 for various amorphous alloys. It should be noted that the

354

P. HANSEN 1500

j

o! / 1000

/'/ amorpho

500-

crysta[tine

0.50

0.60

0.70

0.80

1.00

-Fel

BFe2 ~,=

1000

,,~BFe 3

800 + 0

~

0.90

x

BFe~"

600

~x

o

+x

~+

0

O 0°

400 +

Bl-x Fex

200 (b)

+ 0

0

1

0.20

++1

0.40

I

0.60

I

0.80

1.00

X

Fig. 46. Concentration dependence of the Curie temperature for (a) amorphous (Fukamichi et al. 1987a) and crystalline (Buschow 1980c) Y-Co alloys and (b) for amorphous B-Fe films [(O) magnetization (Stobiecki and Stobiecki 1983), (O) anomalous Hall effect (Stobiecki 1982), (4-) M6ssbauer (Chien and Unruh 1981), (x) ribbons (Hasegawa and Ray 1978), (11) crystalline B-Fe compounds (Vincze et al. 1979)].

pronounced sensitivity of the exchange interaction on the structural disorder gives rise to a dependence of Tc on the preparation conditions. In particular for liquidand vapor-quenched amorphous alloys large Tc differences were observed as shown in fig. 23b.

5.4.2.2. Rare-earth-based alloys. The temperature dependence of the magnetization of amorphous alloys with the rare earths as the only magnetic component are

MAGNETIC AMORPHOUS ALLOYS

355

350 MI_x Fex 300 M=Sc 25£ 200 150 100 5O

(a) 0 0.40

0.60

0.80

1,00

X

30O

Til-x Fe x

200

10[

{b) I

I

0.20

0./.,0

0.60

0.80

1.00

X

Fig. 47. Concentration dependence of the Curie temperature for (a) amorphous M1 -xFex alloys with M = Sc, Hf or Zr (Fukamichi et al. 1986a) and (b) for amorphous [(0) Liou and Chien (1984)] and crystalline [([]) Fukamichi et al. (1982)] Ti-Fe alloys.

controlled by the RKKY exchange interaction and the random anisotropy. In Gdbased alloys, the latter is small and the temperature behavior is governed by the relatively weak RKKY interaction. The structural disorder gives rise to the characteristic flattening of the Ms curves as already discussed for the TM-based alloys. A typical example is shown in fig. 49a for amorphous Gd-Au (Durand and Poon 1977). The full lines represent the mean-field theory for different values of the exchange fluctuation parameter [eq. (56a)]. The best fit was obtained for A = 0.4 and a spin value of S = 7 for the Gd atom. Thus, the magnitude of A corresponds to those found for alloys containing TM elements. The low-temperature magnetization obeys the T 3/2 law derived from the spin-wave theory I-eq. (55)] as shown in fig. 49b (Durand

356

P. HANSEN 800 700 600 500 400 3OO 200

//V•

Bo.20(Fey Nil_y )o.eo Bo.19 Si o.01(Fey Ni 1-y )0.80

100 0 0

.Zt T °" 0.25

0.50 Y

0.75

1,00

Fig. 48. Concentration dependence of the Curie temperature for amorphous B-FeNi [(~7) Kaul (1981a), (!?) Becker et al. (1977)], BSi-FeNi [(A) Kaul (1981a)] and BP-FeNi [((3) Kaul (1981a), (@) Becker et al. (1977), (D) Chien et al. (1977), (111)Krause et al. (1980)] alloys. The full lines were calculated from the coherent potential approximation (CPA).

and Poon 1977). However, the agreement of the exchange values evaluated from the spin-wave theory and the Curie temperature is not satisfactory. The Curie temperature of Gdl _xMx alloys is shown in fig. 50, displaying a strong increase of Tc with increasing x (Heiman and Kazama 1978b). The full line was calculated from a statistical nearest-neighbor model yielding (Oguchi 1971) [ - I / -' ] X~ n

- 1

where n is the coordination number. If n is taken to be 12, the critical concentration xc = 4/n is found to be ½, in good agreement with the experimental results.

The RKKY interaction is expected to be sensitive to fluctuations in nearestneighbor distances. This tends to reduce Tc in amorphous alloys as compared to the crystalline counterparts as observed for various compositions. A few examples are listed in table 8. The numbers in the brackets are the Curie temperature of the corresponding crystalline compounds. Tc values and low-temperature magnetic moments for some R - M alloys are also listed in table 8. It should be noted that the random anisotropy for non-S-state rare earths is rather high and thus very high magnetic fields are required for magnetic saturation. Discrepancies in magnetic moments, therefore, in many cases can be ascribed to insufficient saturation. 5.4.3. Two-subnetwork alloys

The temperature dependence and the Curie temperature in amorphous R1 -xTx alloys is determined by the spin and angular momentum of the R and T atoms and their

MAGNETIC AMORPHOUS ALLOYS

357

TABLE 10 Transition-metal moment at T= 4.2K and Curie temperature for some amorphous one-subnetwork alloys. MI-~Tx Bo.zoFeo.8o Po.125Co.o75Feo.so Sco.25Feo.75 Tio.zsFeo.75 Zro.a5Feo.T5 Yo.52Feo.48

kit (#B)

Tc(K)

References

651 586 277 238 283 18 70 108 330 190 230 ~765 512 450 195 > 600 20 118 327 390 164 11

Becker et al. (1977) Tsuei et al. (1968) Fukamichi et al. (1986a)

Y0.32Feo.68 Yo.2oFeo.so Lao.24Feo.76 Ceo.2oFeo.8o Geo.53Feo.47 Bo.2oCoo.so Po.24COo.76 Yo.sTCoo.43 Yo.4oCoo.6o Yo.2oCoo.8o Yo.2~Nio.75 Yo.13Nio.s7 Yo.o~Nio.95 Yo.oaNio.97 Co.ogNio.91 Co.lsNio.85

1.55 1.68 1.13 0.65 0.95 0.86 1.69 1.89 1.53 0.80 0.90 1.02 0.88 0.20 0.60 1.65 0.03 0.12 0.36 0.41 0.21 0.034

Bo.2oFeo.4oNio.4o Bo.2oFeo.40Coo.4o

1.03 1.43

662 > 800

O'Handley et al. (1976a)

Coey et al. (1981) Kazama et al. (1980) Buschow and van Engen (1980) Suran et al. (1976) O'Handley et al. (1976a) Pan and Turnbull (1974) Heiman and Lee (1975) Fukamichi et al. (1986b) Buschow et al. (1977) Li6nard and Rebouillat (1978)

Fr6my et al. (1984)

exchange coupling parameters JR--R, JR--T and JT-T. The direct exchange between the 3d electrons of the T atoms leads to a ferromagnetic coupling. The much weaker R K K Y interaction between the rare-earth atoms also gives rise to a parallel alignment of their moments, but JR-R ~ JT--T" The exchange between the 3d transition-metal electrons and the 5d rare-earth electrons induce a negative JR-T producing a parallel alignment of T and R moments for light rare earths and an antiparaUel alignment for heavy rare earths. Collinear structures are expected at low fields only for alloys containing S-state rare earths and for x values sufficiently above the critical concentration. Alloys exhibiting speromagnetic or sperimagnetic order (see figs. 20 and 21) require very high magnetic fields to reach magnetic saturation due to the random anisotropy discussed in section 5.3.1.2. Both the transition-metal spin value and the exchange coupling constants are sensitive functions on composition. Most attention has been focussed on evaporated and sputtered (Gd, Tb)l _~Fex and T b l _~(Fe, Co)~ alloys with 0.6 < x < 0.8. They are suitable candidates for magneto-optical recording (see section 8.1). The temperature dependence of amorphous G d t _~F% alloys (Hansen et al. 1989) is shown in fig. 51. The strong variation of the low-temperature magnetization with x is associated with ferrimagnetic order (see also fig. 38a) and leads to a variety of different magnetization curves. The appearance of magnetic compensation (Ms = 0) is limited to a very narrow range of compositions.

358

P. HANSEN

~,, A=O

0.8

0.4

0.6

0.6

0.4

• Gdo.eoAuo.2o

0.2

• crystalLine

n

la)

I 0.2

t 0.&

~

t 0.6

I 0.8

1.0

[ 20K 215 ~

o Gdo.6s Nio.32

195 ~

• Gdo.8o Auo.2o

~£~ 155 135 115 {b} g5

• i 500

t 1000 T3/2 (K 3/2)

t 1500

Fig. 49. (a) Relative saturation magnetization ms = Ms(T)/Ms(4.2 K) versus reduced temperature for amorphous Gd-Au and (b) temperature dependence of Ms versus temperature for amorphous Gd-Au and Gd-Ni alloys (Durand and Pooh 1977). The arrows indicate deviations from the T 3/2 law.

The full lines were calculated from the mean-field theory using eq. (43) for A = 0. The good agreement between experimental and calculated results was confirmed for various other Gd-Fe-based and R-Fe-based alloys (Heiman et al. 1976b, Taylor and Gangulee 1976, Gangulee and Taylor 1978, Mimura et al. 1978, Hansen and UrnerWille 1979, Hartmann et al. 1984b, Hansen and Hartmann 1986, Mansuripur and Ruane 1986, Hansen et al. 1989), but it should be noticed that now three exchange parameters were used to adjust the theory to the experimental data when compared to one-subnetwork alloys. The better fit thus obtained is no indication for a higher accuracy of the extracted values for the exchange constants. They should only be regarded as empirical parameters. However, they are well suited to calculate the sublattice magnetizations and to model the temperature dependence of other magnetic properties which can be expressed in terms of the sublattice magnetizations.

MAGNETIC AMORPHOUS ALLOYS

359

300 crystalline Gd

200

Gdx tl_x

/ H=A~ ;rNi Cu

100

~

AI

Nio/ 0 0

0.20

0.40

0.60

0.80

1.00

X

Fig. 50. Concentration dependence of the Curie temperature for amorphous Gd-M alloys with M = A1, Au, Cu or Ni. (O) Heiman and Kazama (1978b); (O) Lee and Heiman (1975), Boucher (1977), Durand and Poon (1977), Mizoguchi et al. (1977a). The full line represents a statistical nearest-neighbor theory [eq. (57)].

150C . "

~

Gdl-xFex --calculated ~x=0.37

. ~ ~ 0 . 4 7 I00C •

0.80

100

200

300

400

500

T(K) Fig. 51. Temperature dependence of the saturation magnetization for amorphous Gd-Fe alloys prepared by evaporation (Hansen et al. 1989). The full lines were calculated from the mean-field theory I-eq.(43), with Z = 0].

360

P. HANSEN

Expressions for the compositional dependence of the exchange constants Jik extracted from the mean-field analysis are compiled in table 11 for some R - T alloys. Their validity is restricted to a limited concentration range. A plot of the sublattice magnetizations versus temperature is given in fig. 52 for a composition exhibiting a compensation temperature T~ompat 295 K. These curves are based on experimental data and correspond to one of the curves shown in fig. 51. The temperature variation of the spontaneous moment per formula unit for crystalline and amorphous TbFe2 (Rhyne et al. 1974b) is presented in fig. 53. It demonstrates the strong reduction in moment and Curie temperature in the amorphous state that applies to all R-Fe alloys. Part of the moment reduction can be attributed to the asperomagnetic order of both sublattices as indicated by the arrows. This problem arises for all low-field magnetization data of R-Fe alloys containing non-S-state rare earths (Taylor et al. 1978, Croat 1981a,b, Mansuripur and Ruane 1986, Hansen and Witter 1988). Amorphous R-Co alloys are characterized by significantly higher exchange interactions inducing a collinear Co sublattice and producing much higher Tc values for Co-rich alloys. The temperature dependence of Ms is shown in figs. 54, 55 and 56 for some R-Co alloys (Jouve et al. 1976, Honda and Yoshiyama 1988a, Hansen et al. 1989). The large Tc for alloys with x > 0.7 interferes with the crystallization temperatures which prevent Ms and Tc measurements for T > T~. The full lines in figs. 54 and 55 were obtained from mean-field calculations based on eq. (43) with A = 0. Choosing A to be of the order of 0.5 as found for the one-subnetwork alloys, the exchange coupling constants used to fit the experimental data have to be slightly modified to account for the shift in Teompinduced by A. The dependence of Jik o n x used for the theoretical lines shown in fig. 55 are given in table 11. The mean field analysis reveals a strong rise of JCo-Cofor x > xo in contrast to JFe-Fe passing through a maximum around x ~ 0.5 due to the increasing portion of negative exchange for Fe-rich R - F e alloys. It should be noticed that in the case of N d - T alloys (fig. 55c) no T~ompoccurs due to the parallel alignment of the sublattice magnetizations which holds for all alloys containing light rare earths (Dai et al. 1986, Takahashi et al. 1987, Yang and Miyazaki 1988, Yang et al. 1988). A model that accounts for the itinerant d-electron ferromagnetism of the Co sublattice was described in section 5.4.1.2. It was used to calculate the temperature variation o f Ms for different R - C o alloys (Jouve et al. 1976, Bhattacharjee et al. !977b). The comparison of experimental and calculated results is shown in fig. 56. In the range of the broken lines the formation of crystalline phases takes place. The theory was treated in terms of the molecularfield approximation. Thus, both mean-field models based on the localized and d-band approach account for the measured temperature variation of Ms. A comparison of the extracted parameters with data obtained from independent measurements will decide which of the two models represent the better approximation. Generally, the comparison between theoretical and experimental results suffer from the lack of data in the high-temperature regime for Co-rich alloys. Various other mean-field results were reported for G d - C o based and R - C o alloys (Hasegawa 1975, Hasegawa et al. 1975a,b, Taylor and Gangulee 1976, Roberts et al. 1977, Gangulee and Kobliska 1978a,b, Honda and Yoshiyama 1988a,b).

MAGNETIC AMORPHOUS ALLOYS

~

....

E

E

A~

c~ C~

r__, ~ i.~

r~

~"O "O

r"-i r-'l

]

I

I

I

I

I

~~ ~ooo .

t

~V

--~

VWW~ ~

v~

I

"O

t_.~ t . . ~ L . . I

361

362

P. H A N S E N 1000

~

800

.....

6d

~.~

600 ~-~

Gdo.25s Fe 0.7t.s

%

400 Z

x

200

oF

,

.

0

100

IT'°: ° 200

300

,

. 3

400

500

T(K) Fig. 52. Temperature dependence of the saturation magnetization and the sublattice magnetization for an amorphous Gd-Fe alloy exhibiting a compensation temperature. The Ms curve corresponds to that shown in fig. 51 for x = 0.745.

i

~

bFe2 staHine

0 0

i 100

I 200

I 300

b

i

400 500 T(K)

i

600

i~

700

800

Fig. 53. Temperature dependence of the spontaneous moment per formula unit for crystalline and amorphous TbFe2 (Rhyne et al. 1974b).

The room-temperature concentration dependence of Ms is shown in fig. 57 for some amorphous R-Fe and R-Co alloys prepared by evaporation (Orehotsky and Schr6der 1972, Roberts et al. 1977, Hansen et al. 1989). The full lines in fig. 57b represent mean-field theory results. Ms = 0 at low transition-metal concentrations refer to alloys with Tc equal to room temperature. The corresponding x value is higher for Co-based alloys because their x c value is higher as compared to the Febased alloys. The magnitude of Ms at the maximum is determined by the sublattice moments and the exchange coupling constants and reflects the position of xo and

MAGNETIC AMORPHOUS ALLOYS

1500 ~q.

Gdl-x Cox - - catcutctted

a~=0.436

1000

363

0.538 ~k

500

\ o.839~

._.

( p ~ 4 ~ ~-

O~- --w''''-"''~ 100 200 ' '

~ 3'00 T{K)

400 '

UlO 50

Fig. 54. Temperature dependence of the saturation magnetization for amorphous Od-Co alloys prepared by evaporation (Hansen et al. 1989). The full lines were calculated from the mean-field theory [eq. (43), with zT= 0].

Tc. The magnetic compensation is defined by MR(x¢omp, T~omp)-- Mx(x¢omp, T~omp)= 0,

(59)

where X¢omp and T~omp are the compensation composition and the compensation temperature, respectively. For amorphous Gd-Fe, e.g., Xcomp= 0.77, Tcomp = 4.2 K and Xcomp= 0.745, T~omo= 295 K were found. The room temperature T~omp values for most alloys prepared under the same conditions appear in range 0.7 < X~omp< 0.8 (fig. 57a,b) except for Er-T alloys exhibiting Toompvalues below room temperature (Dirks et al. 1977). The variation of T~ompwith composition is presented in fig. 58 for some binary and ternary amorphous alloys (Hansen et al. 1989). The plots yield a Tcomp shift of 40K/at.% for T b - T alloys and 100K/at.% for G d - F e alloys which demonstrates the high sensitivity of TcompOn composition. The compositional variation of T~ompfor Dy- and Ho-based alloys yields smaller shifts of the order of 20 K/ at.% (Hansen et al. 1991). Therefore, any changes on the R or T moment and the exchange interaction by small additions of nonmagnetic atoms, the presence of impurities, oxidation effects, thermal treatments or structural changes lead to drastic variations in Tcomp(Katayama et al. 1977, Mfiller et al. 1977, Biesterbos et al. 1979, Tsunashima et al. 1980, Schelleng et al. 1984, Heitmann et al. 1987a,b). Compensation temperatures for some amorphous alloys are listed in table 12. The reduced Fe moment and the sensitivity of the iron exchange on the structural disorder produces lower Tc in amorphous R-Fe alloys than in the corresponding crystalline phases. This is obvious from the Tc data given in table 12 and those for crystalline (Buschow 1977) and amorphous (Heiman et al. 1976b) RFe2 alloys which are presented in fig. 59a showing the trends across the series. The downwards trend

364

P. HANSEN 1400

Tbl-xCox --calculated

1200 I000

x=O.g2 <

800 6OO 0,85 400 200 100

300

500

T(K)

700

1400]

?oOoOoE 800 .<

E

600

Dyl-xCox --calculated

~

=0.92

z~

400

0.82

200 0

}

I ~t*fr

100

l

I~l'~'r- 7

300

I "%

500

I

700

I

900

T(K)

1400 1200 ~ - - . ~

Ndl_× Cox - - catculctted

o

1000

x=O.g2

-~ 800 <

~--- 600

~

0.78

400 ~ 0 (c)

200

(

100

.

6

4

300

500

700

go0

T(K) Fig. 55. Temperature dependence of the saturation magnetization for amorphous (a) Tb-Co, (b) Dy-Co and (c) Nd-Co alloys prepared by diode sputtering (Honda and Yoshiyama 1988a). The full lines were calculated from the mean-field theory [eq. (43) with z/= 0].

MAGNETIC AMORPHOUS ALLOYS

365

E r 0.225 C00,77s

3

.765

:& 2 :&

v

\\\

//-Dyo,,, Coo,,,

I

2O0

&O0

600

800

1000

T(K)

Fig. 56. Temperature dependence of the average spontaneous magnetic moment per formula unit for amorphous R-Co alloys (Jouve et al. 1976). The full lines were calculated from the d-band model [eqs. (48) and (49)]. The Curie temperature was estimated from partially crystallized samples.

of Tc towards La and Lu is associated with the increasing portion of negative FeFe interaction and a decrease in average Fe moment (Buschow and van der Kraan 1981). The crosses represent the Tc values of the pure crystalline rare-earth elements revealing almost the same turndown of Tc which indicates the importance of the RR exchange for low and medium Fe concentrations. In this case, Tc is expected to vary according to the de Gennes factor (g - 1)2J(J + 1) listed in table 6. This variation indeed was verified for these alloys (Rhyne 1976) and for amorphous R1 _~Co~ alloys with x=0.31 (Buschow 1980b), x=0.40, 0.50 (Yang et al. 1990) and RI_~Ni~ (Buschow 1980a) alloys with x = 0.31. In these cases, the T concentration is below xc and thus the Co or Ni atoms carry no magnetic moment. Therefore, the Co and Ni atoms just dilute the R matrix and Tc is determined only by the R-R exchange interaction that can be expressed in terms of the de Gennes factor. This variation is shown in fig. 59b for amorphous Ro.69Co0.31 alloys (Buschow 1980b). The amorphous R~ _~Co~ alloys with x > xo are characterized by a strong cobalt subnetwork exchange that causes a collinear Co subnetwork and gives rise to large Curie temperatures. These are larger than the Tc values of the crystalline counterparts (see table 12) and for x > 0.7 even exceed the crystallization temperatures in contrast to the R-Fe alloys. This difference in Fe- and Co-based alloys is demonstrated by the plot of Tc versus x shown in fig. 60 for amorphous R-Fe and R-Co alloys with R = Gd, Tb, Dy or Ho (Buschow and van der Kraan 1981, Hansen et al. 1989, 1991) and in fig. 61 for amorphous R-Co alloys (Takahashi et al. 1988a,b). All R-Fe alloys exhibit a maximum of Tc around x --- 0.7 followed by a strong turndown. However, the compositional range 0.9 ~<x ~< 1.00 has not been investigated in detail for R-Fe alloys and the existence of a tricritical point has not yet been documented. The initial decrease of Tc for Gd-rich Gd-Co-based alloys with increasing x in fig. 60 reflects the nonmagnetic behavior of the Co atoms and, therefore, the Tc variation agrees

366

P. HANSEN 1000

<

Gdl-× Fex

500

Gdl-×Cox|11

z

{a) 0

I¢

0.4

X

0.6

0.8

500 Rl-xC°x

/ /

,oo

Dy ~300 <

~2oo 100 0 0,55 0.60 0.65 0.70 0.75 0.80 0,85 0.90 X

Fig. 57. Compositional variation of the room-temperature saturation magnetization for amorphous R1 -=Tx films prepared by evaporation: (a) R = Gd or Tb, T = Fe or Co (Hansen et al. 1989) and (b) R = Ho or Dy, T = Co (Roberts et al. 1977). The full symbols in (a) refer to Ms data taken from different investigators [Gd-Fe: Taylor (1976), Mimura et al. (1978), Lee et al. (1986); Gd-Co: Taylor and Gangulee (1976); Tb-Co (dotted line): Choe et al. (1987)]. with t h a t of diluted o n e - s u b n e t w o r k r a r e - e a r t h alloys as s h o w n b y the chain line representing a m o r p h o u s G d - C u alloys ( H e i m a n a n d K a z a m a , 1978b). F o r x n e a r xc, the increasing R - C o exchange leads to a n increase of Tc a n d for x > x , the s t r o n g C o - C o exchange causes the d r a m a t i c rise of Tc. F i g u r e 61 shows the c o m p o s i t i o n a l v a r i a t i o n of Tc for different R - C o alloys revealing Tc to be a l m o s t i n d e p e n d e n t of

M A G N E T I C A M O R P H O U S ALLOYS

367

6OO 500 -- -- I : - - ~

-- ~ ..Zc ........~.

~Gd1-xFex~dl-xC°x

400 300

I'-°

.\ --.Tcomp/ \

200

~

i m

tO0 . 0 0.70

~

\

0,75 X 0.80

0.85

500 ......-~. . . . . ~ . ~ . . , ~ T b1-×Fex 400 Tc \o\" -"~" co.

300 Tb1-x(Fe 1×y,o.21,

&

\

~...Tb1_xMX

o,.

200 100

[b) (~6

o

I 0.7

Foe

~

X

I 0.8

0.9

Fig. 58. Compositional variation of the compensation temperature for amorphous R 1 -xTx alloys prepared by evaporation (Hansen et al. 1989). (a) R = Gd; T = Fe or Co and (b) R = Tb or GdTb, T = Fe, Co or FeCo. The full symbols in (a) and (b) refer to T~omp data taken from different investigators [Gd-Fe: Heiman et al. (1976b), Taylor (1976), Mimura et al. (1978), Biesterbos et al. (1979); G d - C o : Tao et al. (1974), Taylor and Gangulee (1976), Biesterbos et al. (1979); Tb-Fe: Mimura et al. (1976a,b, 1978), Takayama et al. (1987); Tb-Co: Biesterbos et al. (1979), Heitmann et al. (1985), Choe et al. (1987)]. The dotted line in (b) represents sputtered G d T b - C o films (Kryder et al. t987).

368

P. HANSEN TABLE 12 Curie temperatures Tc and compensation temperatures Teompof crystalline and amorphous R1 _~T~ alloys with T = Fe, Co or Ni. + denotes no compensation, the magnetization is dominated by the indicated element (Lee and Heiman 1975, ArreseBoggiano et al. 1976, Alperin et al. 1976, Heiman et al. 1976a,b, Rhyne 1976). R~ _~T~

Tc (K)

Crystalline Gdo.s7 Feo.43 Gdo.4oFeo.6o GdFe z GdFe 3 Gd6 Fe23 GdCo 2 GdCo 3 GdzCo 7 GdCo 5 GdNi z TbFe2 TbFe3 Tb6 Fe23 Tb2 Felt TbCoz TbCo3 TbCos DyFe2 DyFe3 Dy 6 Fe23 DyCo 3 DyNi3 Hoo.4o Feo.60 HoFe z HoFe 3 Ho 6Fe23 Hoo.45 Coo.ss Hoo .40Coo .60 HoCo/ HoCo3 HoCo5 Ho2Ni17 HoNi2 HoNi5 Ho6Mn23 ErFe2 TmFe2

785 728 659 409 612 775 1008 85 711 648 547 409 256 506 980 638 600 524 450 69 612 567 501

85 418 1000 162 22 10 434 575 565

Amorphous 350 > 500 490 460 420 550 750 > 500 > 500 38 390 405 387 365 > 600 > 600 > 600 287 333, 350 351 > 900 47 250 260 290 300 375 600 > 600 > 600 > 600 > 400 15 400 Not magn. 105 < 50

T=omp(K) Amorphous

Crystalline

Gd + Tb + Tb + Tb +

Gd + Gd + 450 150 ~ 100 510 400 300 80 Gd + Tb + Tb + Tb +

Tb + Tb + 100 Dy + Dy +

500 250 Co + Dy + Dy +

Gd +

Gd + Gd + 410

230

Ho + 350 80

180 120 50 Fe + Ho + 325 270 150 Co +

Er + Tm+

Er + Tm +

Ho + 400 40

the rare earth except for Er-Co alloys. This can be attributed to the dominance of the Co-Co exchange for medium and high Co content. It should be noticed that the magnitude of Tc strongly depends on the preparation conditions affecting the structural disorder and thus the exchange coupling constants. In particular strong differences in Tc are observed for vapor-quenched and liquid-quenched alloys (Miyazaki et al. 1987a, Takahashi et al. 1988a,b), shown in fig. 23.

MAGNETIC AMORPHOUS ALLOYS

369

1000 RFe 2 800

600

400

. ~ -

orphous

200

a) 0 i ~ P t t t t i t ~ ~ ~ t La Ce Pr Nd P m S m Eu Gd Tb Dy Ho Er Tm Yb Lu R

200 Ro.69 C 00.31

150

100

50

0

0

De/ a Ce Pr N d P m S m Eu Gd Tb Dy Ho Er Tm Yb l u R

Fig. 59. Curie temperature for (a) crystalline(Buschow 1977)and amorphous (Heimanet al. 1976b)RFe2 alloys and (b) amorphous Ro.69Co0.31 alloys (Buschow 1980b).

5.5. Critical exponents Magnetically ordered systems undergo a second-order phase transition when passing the critical temperature. The magnetization represents the order parameter that is controlled by the reduced temperature e = (T/Tc) - 1 and the external magnetic field. The critical phenomena are discussed in terms of the static hypothesis (Domb and Hunter 1965, Widom 1965, Wilson 1974a,b), which can be expressed in the general form

I~lp +, where the signs + and - refer to T < Tc and T > To respectively. # and 6 are the critical exponents which refer respectively to the temperature dependence of M below

370

P. HANSEN

~0

0.2

0.4

x

0.6

0.8

1.0

Fig. 60. Compositional variation of the Curie temperature for amorphous R-T alloys prepared by evaporation (Hansen et al. 1989). The full symbols refer to Tc data taken from different investigators [Tb-Fe: Alperin et al. (1976), Heiman et al. (1976b), Busehow and van der Kraan (1981), Takayama et al. (1987); Tb-Co: Lee and Heiman (1975), Buschow (1980a), Busehow et al. (1980); Gd-Cu: Heiman and Kazama (1978b)]. The full lines for Dy-Fe and Ho-Fe were taken from Hansen et al. (1991).

1000 Rl-x COx oR=Sm •

p~

% ' f

• Er []z, Nd D y e /

500

O0

/m Id

i

0.20

i

0.40

i

x

i

0.60 0.80 1.00

Fig. 61. Compositional variation of the Curie temperature for amorphous R-Co alloys prepared by evaporation (Takahishi et al. 1988a,b).

MAGNETIC AMORPHOUS ALLOYS

371

Tc and the field variation of M at Tc according to the relations M ~ ( - e ) p ( H = 0 , T < Tc),

(61a)

( T = To, H--*0).

(61b)

M~H

1/~

The critical exponent 7 associated with the susceptibility above Tc is defined by the expression X-1 ~

(T>~ Tc).

(61c)

The critical exponent ~ is associated with the specific heat and is defined by Cn ~ e-"

(T ~> rc).

(62)

The static hypothesis, eq. (60), leads to the equalities 7 =/~(6 - 1), = 2(1 -/~) - 7.

(63a) 63b)

A comparison of the micromagnetic theory of phase transitions (Kronmfiller and F~ihnle 1980, F~ihnle and Kronmiiller 1980, F~hnle 1980, Herzer et al. 1980, 1981, Meyer and Kronmfiller 1982) with experimental data reveal that exchange fluctuations are the primary origin of the differences of the critical exponents between amorphous and crystalline materials. The examination of the critical behavior requires materials which possess values of Tc well below their crystallization temperatures. The critical exponents were determined from different representations such as Kouvel-Fisher plots, modified Arrott plots or scaling plots (Reisser et al. 1988), leading to slightly different results. Typical values of the critical exponents for some crystalline metals (Fe, Ni, Co, Gd) and amorphous alloys are compiled in table 13. The critical exponents predicted by the three-dimensional Heisenberg model are also listed in table 13. They are in reasonable agreement with the experimental data of many amorphous alloys. Also, the scaling laws are satisfied for many alloys. This can be ascribed to the longwavelength dependence of the critical fluctuations near Tc and, thus, the critical behavior is independent of the local atomic structure. This is confirmed by theoretical investigations (Harris 1974) predicting no influence of the structural disorder on the critical exponents. However, outside the critical region strong differences between amorphous and crystalline materials occur. This is obvious from the temperature dependence of the susceptibility and the effective exponent y(T) defined by (Kouvel and Fisher 1964) 7(T)-

dlnx -~ dine "

(64)

For amorphous alloys 7(T) typically shows a maximum in the temperature dependence as shown in fig. 62 for amorphous Zr-Fe (Reisser et al. 1988) in contrast to crystalline compounds where 7(T) decreases monotonically with temperature (F/ihnle

372

P. HANSEN

o

_,.- ~ o "-r. ~

izl 0

r~

"a

8 o

o

"-r. -,=,

,~ ~

~ o

~.~

~

~

~ .~ o

~f o o ~ o o I I + I +

o o o o o o o o I I I I I I I

o I

I

o o +1

+1 +1 ~

+1 +1 +1 +1

+1

,,-,1

S o'-'a ~t

4-1

I~

+1 4-1

+1 +1 r.--

4-1 +1

4-1

,,~

~ ~1 +1

~ ~ +1+1~

0 ~ ~1 ~ +1+1 +1

~1 ~

o

,-fi °

8

~1=o

"I. c~ d

"I, "I,

,-~

MAGNETICAMORPHOUSALLOYS

373

1.70 0

0

0

0

0

1.60

0

0

0

o

o

o

1,50

/

0

o 0 0 0

I.&0 Z ro.lO F eo.@o

1.30 200

i 250

i 300

i

350

&00

T(K]

Fig. 62. Temperature dependenceof the effectiveexponent7(T) for amorphous Fe-Zr with Tc= 207.5K (Reisser et al. 1988).

et al. 1983). A similar behavior for 7(T) was reported for disordered Po.25Feo.75 and Pdo.75Feo.zs alloys satisfying also the scaling laws (Seeger and Kronmiiller 1989).

5.6. Uniaxial magnetic anisotropy Amorphous magnetic alloys are expected to behave magnetically isotropic or to exhibit a low anisotropy in the case of thin films where the deposition on a substrate induces intrinsic stresses (d'Heude and Harper 1989) which may cause a stressinduced anisotropy. However, for most alloys a uniaxial anisotropy energy, E, = Ku sin 2 0,

(65)

was found with values of the uniaxial anisotropy constant, Ku, ranging between some hundred J m -a for field-induced anisotropies in metal-metalloid alloys and some hundred kJ m-3 for rare-earth-transition-metal films. 0 represents the angle between the preferred axis and the direction of magnetization. Significant larger K~ values occur for amorphous transition-metal-based alloys when the alloy is formed of two different magnetic atoms or for Co-based alloys (Ounadjela et al. 1989). The strong uniaxial anisotropies occurring in R-T films are due to the deposition process (evaporation, sputtering) causing locally an anisotropic atomic arrangement that leads to a preferred axis parallel to the film normal (K, > 0) or to an easy plane (K, < 0) of magnetization. The magnitude of K, depends on the degree of shortrange order and the magnitude of the magnetic anisotropy per atom. The former is primarily controlled by the energy of the atoms at the growing surface and the latter by spin-orbit coupling leading to high anisotropies for R-T alloys with non-S-state rare earths like Tb or Dy. Different origins were discussed to account for the observed anisotropies such as structural inhomogeneities (Graczyk 1978, Herd 1977, 1978, 1979, Katayama et al. 1977, Leamy and Dirks 1979, Mizoguchi and Cargill III 1979,

374

P. HANSEN

Yasugi et al. 1981, Kusuda et al. 1982a,b), incorporation of oxygen (Brunsch and Schneider 1978, Dirks and Leamy 1978, Leamy and Dirks 1979, Biesterbos et al. 1979, Tsunashima et al. 1980, Hoshi et al. 1982, van Dover et al. 1986, Heitmann et al. 1987a,b, Klahn et al. 1988), columnar microstructures (Suzuki 1983), stress-induced anisotropies (Tsunashima et al. 1978, Leamy and Dirks 1979, Takagi et al. 1979, Togami 1981, Labrune et al. 1982), dipolar interactions (Chaudhari and Cronemeyer 1975, Mizoguchi and Cargill III 1979, Wang and Leng 1990), pair ordering (Gambino et al. 1974, Taylor and Gangulee 1976, 1977), anisotropic exchange (Meiklejohn et al. 1987), bond orientation and anelastic deformation (Egami et al. 1987, Hirscher et al. 1990, Y. Suzuki et al. 1987). In one-subnetwork 3d-based alloys, usually low anisotropies are found originating primarily from the magnetostriction coupling the magnetization to the internal stresses (Egami et al. 1975, O'Handley 1975) or pair ordering (Luborsky 1977, Miyazaki and Takahashi 1978). The anisotropy constant of amorphous SiB-FeCo alloys in the as-quenched and field-annealed state (Miyazaki and Takahashi 1978) is shown in fig. 63. The observed anisotropies were associated with pair ordering. Typically Ku values up to 6 x 10 2 J m -3 were reached by field annealing (Luborsky 1978, Fujimori et al. 1984, Maehata et al. 1986) which is shown in fig. 64 for amorphous B-FeNi alloys. These anisotropies are associated with short-range pair ordering and interstitial or monoatomic ordering of the metalloids. However, also large anisotropies have been found in rare-earth-based one-subnetwork alloys prepared by liquid quenching as reported for Gd-Cu alloys (Algra et al. 1980). The uniaxial anisotropy in vapor-deposited rare-earth-transition-metal films strongly depends on the composition, the R and T component and the deposition parameters. The presence of oxygen leads to a selective oxidation of the R component and reduces

°'4/(a) '~

i~

0.2

Si°'lO B°'13 (Fel-× Cox)o.77

4

~ ~,

0/0

•

•

,

0.2

•

.

• ~---¢"0.4

0.6

0.8

1.0

0,6

0.8

1.0

X

O.lO

:z

0.05

0

I

I

0,2

0,4 X

Fig. 63. Compositional dependence of the room-temperature uniaxial anisotropy constant for amorphous (a) as-quenched and (b) annealed (T~ = 573K and H = 184kA/m) SiB-FeCo alloys prepared by melt quenching (Miyazaki and Takahashi 1978).

MAGNETIC AMORPHOUS ALLOYS

6

375

]

Bo.2o(Vex Nil->,)o.8o / ~

7o:===oo~ ' / ~ . . ~ - ' k ' k " , / = j .~_ . _ , _ L Z/'06.. ..... _'x.~\~, ... / 7°

.,

32s~...", ~ ~ . k . \ ~ . - ' t # 1i...:j ..... ...., . . . . . ".M / lillS'O.IOBo.12(FexC01-x)0.78.-#, : " ~ ~ ; ~ ,

15.oi.4" i.." {

~'. -~

/Po.,
b: 0,2

O.A

./

%~

/300 / x

0.6

" 0,8

1.0

Fig. 64. Compositional dependence of the magnetically induced uniaxial anisotropy (Luborsky 1978) in B-FeNi (open symbols)(Luborsky and Walter 1977a), PB-FeNi (solid symbols) (Luborsky and Walter 1977b), and SiB-FeCo (crossed symbols)(Fujimori et al. 1977). Ku (Shen et al. 1981, van Dover et al. 1986, Klahn et al. 1988). Columnar structure appears to be less significant and also stress-induced effects via magnetostriction are not dominant as concluded from films before and after removal of the substrate (Hoshi et al. 1982, Y. Suzuki et al. 1987). Pair ordering and dipolar interaction lead to a relation between Ku and the sublattice magnetizations that can be expressed in the form K u = ~ CikMiMk.

(66)

i g:k

Using the sublattice magnetizations inferred from the mean-field analysis, the dependences of Ku on composition and temperature can be calculated. The comparison with experimental data revealed a good agreement for various alloy compositions (Taylor and Gangulee 1976, 1977, Taylor et al. 1978, Hansen and Hartmann 1986, Mansuripur and Ruane 1986, Hansen and Witter 1988, Hansen et al. 1989, 1991). The compositional variation of K~ at room temperature is shown in fig. 65 for amorphous G d - F e (Hansen et al. 1989) and G d - C o (Taylor and Gangulee 1976) alloys prepared by evaporation. The full lines were calculated from eq. (66). Although a good fit of the experimental data was achieved, the reliability of the evaluated coefficients appears to be limited due to the high sensitivity of Ku with respect to small structural variations or to additions of other elements like Si, Ge, Sn or Au, giving rise to even negative K, (Hartmann et al. 1985b). These dependencies demonstrate the strong influence of composition on sign and magnitude of Ku which also applies to sputtered films where the sputter gas, pressure-distance product, bias voltage or substrate temperature are relevant parameters affecting Ku. The influence of the substrate temperature on Ku is demonstrated in fig. 66a for magnetron sputtered T b - F e alloys (van Dover et al. 1985), reflecting the reduction in mobility of the adatoms on the film surface which decreasing substrate temperature T~. The increase of Ku with T~ was confirmed for N d - F e (T. Suzuki et al. 1987) and T b - F e

376

P. HANSEN 0.4

0.2

E "o

0 -~--~

,

,

,

,

l,

~0

2

-0.2 [a)

o

-u

-0.4

0.4

0.2 OO

Gdl_xCo x --

calculated

E o

-0.

2 -0. o

~

-0.6

(b) -0.8 ~ 0.95

0.85

0,75

0.65

X

Fig. 65. Compositional dependence of the uniaxial constant of (a) Gd-Fe (Hansen et al. 1989) and (b) Gd-Co (Taylor and Gangulee 1976) alloys prepared by evaporation. The full lines were calculated from eq. (66) where the sublattice magnetizations were inferred from mean-field calculations.

(Kobayashi et al. 1983, Takeno et al. 1986) alloys. The anisotropy of amorphous T b Fe alloys is larger by more than one order of magnitude as compared to the Gdbased alloys which is associated with the high single-ion contribution of the Tb. In that case, a linear increase of Ku with the R content is expected and indeed can be

MAGNETIC AMORPHOUS ALLOYS

377

Tbl-x Fex

o

2

0.5

0.6

0.7

0,8

0,9

1.0

X

o

/

6 •

~

o

b,.x(Gd,Fe}x Tb,_xlFe,,Co~x /

el

23

o

,! 2 1

•

i

¢

b) O(

!

]

0.1

I

0.2 1-x

i

0.3

0.4

Fig. 66. Compositional dependence of the uniaxial anisotropy constant at room temperature (a) for magnetron sputtered Tb-Fe alloys at two substrate temperatures T~ (van Dover et al. 1985) and (b) evaporated GdTb-Fe and Tb-Fe alloys (Hansen and Witter 1988, Hansen et al. 1989). Circles and triangles in fig. (a) represent vibrating sample magnetometer and torque magnetometer measurements, respectively.

observed (Sato et al. 1985, Hansen et al. 1989) as shown in fig. 66b. The slope depends on the deposition parameters (Klahn et al. 1990b). The variation of the roomtemperature Ku as a function of the R element (Y. Suzuki et al. 1987) is shown in fig. 67 for (Gdo.75Ro.2s)o.19Coo.81 alloys. A clear maximum of Ku appears around Tb and Dy. The two curves in fig. 67a represent the measured Ku before (open circles)

378

P. HANSEN

(Gdo.75 R 1.25)0.19Co 0.81 6

5 g" E

/+ 3

o

2

2 1

-1 -2

{a) I

I

I

I

I

I

I

I

I

I

[

I

I

Pr Nd PmSm Eu Gd Tb Dy Ho Er Tm Yb Lu R

La Ce

iI"

o amorphous + crystatline

/theory

i

1,~ <3_ 1 -2 -3 o

-5 -(b) I

f

I

I

I

I

I

I

I

I

"~"

[

LaCe Pr Nd PmSmEu Gd Tb DyHo Er TrnYb Lu R

Fig. 67. (a) Uniaxial anisotropy constant for amorphous GdR-Co alloys, prepared by sputtering before (open circles) and after (solid circles) removal of the substrate, versus rare-earth element and (b) uniaxial anisotropy per rare-earth atom versus R element for G d R - C o alloys (Y. Suzuki et al. 1987). The crosses in fig. (b) refer to crystalline compounds (Tajima 1971) and the full line was calculated from the single-ion model [eq. (68)].

and after (solid circles) removal of the substrate, indicating that the stress-induced contribution, K~ = - ~-o-2=,

(67)

does not play the dominant role, but in Tb-Fe-based films it was found responsible up to 40 percent of the total anisotropy (Cheng et al. 1989). a and 2= denote the stress- and saturation-magnetostriction constant, respectively. The single-ion contribution of the S-state Gd is zero. The K, value of the G d - C o alloy thus can be considered as a reference. Subtracting its K, from the stress-free data (solid circles), the variation of the single-ion contribution is obtained leading to the variation shown

MAGNETIC AMORPHOUSALLOYS

379

in fig. 67b. The crosses refer to crystalline materials (Tajima 1971). The full line was calculated from the equation (Y. Suzuki et al. 1987) Ku -

( l']e2q(r2)6 3 esJ J - 2] a 3 x,

10

(68)

where J is the total angular momentum of the R atom and as is the second-order Stevens factor (Stevens 1952). e, q, a and x are the electron charge, the valency of the neighboring ion, the average distance between nearest neighbors and the R concentration, respectively. 6 is the local strain of the atomic environment produced by inelastic deformation and (r 2) represents the average distribution of the 4f wave function. Corresponding results were obtained for evaporated R-Co and R-Fe alloys (Miyazaki et al. 1988, Takahashi et al. 1988a,b). The temperature dependence of Ku strongly depends on composition. For many alloys, the dipole equation [eq. (66)] accounts well for the measured results. This is shown in fig. 68a for amorphous G d - F e and G d - C o alloys. The temperature variation for some Tb-containing alloys is given in fig. 68b, indicating a steeper slope of K, in the high-temperature range (Hansen et al. 1989). However, also a sign change can occur as it is observed for H o - C o alloys (Hansen et al. 1991). This is shown in fig. 69 and can be discussed in terms of eq. (66) assuming different signs for the coefficients. The temperature variation of Ku for ferromagnetically coupled N d - F e and N d - C o alloys (Miyazaki et al. 1987a,b) is presented in fig. 70.

5.7. Magnetostriction The magnetostrictive effects in amorphous alloys originate from the magnetoelastic interactions associated with the local anisotropies and the local strains controlling the local direction of the magnetic moments. The origin of the local strains was discussed in terms of the single-ion model with random local axis (Cochrane et al. 1974, Ffihnle and Egami 1982, Suzuki and Egami 1983, Lachowicz and Szymczak 1984, O'Handley and Grant 1985, Furthmfiller et al. 1986, 1987a,b, Szymczak 1987, F/ihnle and Furthmfiller 1988, 1989, Pawellek et al. 1988, Suzuki and Ohta 1988). The macroscopic magnetostriction representing the relative changes in length and volume is related to the macroscopic magnetoelastic constants which have to be considered as an average over the local elastic contribution. The linear magnetostriction can be expressed by 2 = 32s(cos20- ½),

(69)

where 0 is the angle between the magnetization and the strain, 2s represents the saturation magnetostriction constant 2s = ~(211 -- 2±),

(70a)

where 2 LIand 2± refer to the relative changes in length parallel and perpendicular to the direction of magnetization. The spontaneous volume magnetostriction cos can be

380

P. H A N S E N

O!

-0.2

~

,

,

TIK) 300 ,

L+O0 ~

500

j

O.70,~.,..o,.~

-1.2

£

200

x=O.70 ° 9 , , , ~ " ~ " - f - jv 1~"'~'

~:~, -0.6

12 ~ 10

100

(o)

m

~

F~&~o

6

~,

Tbo.21Feo.sz,C°0.15

2 !

O0

(b)

I

100

200

300 T(K)

&00

500

600

Fig. 68. Temperature dependence of the uniaxial anisotropy constant for (a) amorphous Gd-Fe and G d Co alloys and (b) amorphous T b - F e , T b - F e C o and G d T b - F e alloys (Hansen et al. 1989) prepared by evaporation. The full and broken lines in (a) were calculated from eq. (66) where the sublattice magnetiza-

tions were inferred from mean-field calculations.

written as cos = 211 + 22±.

(70b)

Some typical values for amorphous transition-metal-metalloid alloys are compiled in table 14 and fig. 71. Fe-rich alloys exhibit a large positive saturation magnetostriction in contrast to polycrystalline iron. Many Co-rich alloys exhibit a small negative 2s, in agreement with that of crystalline cobalt, but with increasing Co content, 2~ becomes positive. The different sign of 2~ in these alloys has led to the development of zero-magnetostriction alloys which are of interest for different applications (Boll et al. 1983, Tag0 et al. 1985). Low magnetostrietion can easily be reached using Cobased alloys with some additives (Sherwood et al. 1975, O'Handley et al. 1976c, Gyorgy 1978, O'Handley 1978a, O'Handley and Sullivan 1981, Fujimori et al. 1984,

MAGNETIC AMORPHOUS ALLOYS

381

800

/" I

H°°2° C°°'8° 600 Ku

E

£ 2

2

400

Ms 200

0

0

0

200

400

600

T(K)

Fig. 69. Temperature dependence of the uniaxial anisotropy constant and saturation magnetization for an amorphous Ho-Co alloy prepared by evaporation (Hansen et al. 1991). Chen and Rao 1986, Shiba et al. 1986, Jergel et al. 1989). The presence of a compositional point for 2s and o~s is also demonstrated in fig. 72 for amorphous B CoFe alloys (Jergel et al. 1989). In particular a negative 2s was reported for amorphous M - C o with M = B, Nb, Ta or W, and a positive 2s for M = Ti, Hf or Zr (Fujimori et al. 1984, Shiba et al. 1986). The room-temperature magnetostriction constant was shown to scale with a 2 for various amorphous alloys (du Tr6molet de Lacheisserie 1982), which is shown in fig. 73. However, many Co-based alloys do not follow this dependence. The temperature dependence of 2, can be well described in terms of the single-ion model for uniaxial symmetry predicting the relation (Callen and Callen 1965) 2s(T) = 2 s(0)[s/2 (x),

(71)

where [5/z(X) is the reduced Bessel function, 3 3 [5/2(x) = 1 + ~5 - x c°thx, and x is related to the relative magnetization, ms(T) = M~(T)/Ms(O), by 1

ms(T) = - - + coth x. x

(72)

The temperature variation of the reduced linear saturation magnetostriction versus reduced saturation magnetization is displayed fig. 74 for different amorphous alloys (O'Handley 1978a, du Tr6molet de Lacheisserie 1982). The data follow well the line calculated from eq. (71), confirming the dominance of single-ion contributions in

382

P. HANSEN

1.0

x=0.63 ~£/'~ .53

0.8

NdlxFex

\IE 0.6

e~

v

0.4 0.2 (a)

100 200 300 400 T(K)

7

65 x=O~ E o

4

0.69"~

3

0,85

Ndl-xC°x

2

Ib) 0.52 _"

0

I

100

I

200 T(K)

I

300

I

400

Fig. 70. Temperature dependence of the uniaxial anisotropy constant for amorphous (a) Nd-Fe (Miyazaki et al. 1987a,b) and (b) Nd-Co alloys (Takahashi et al. 1988a,b) prepared by evaporation.

these alloys. Co- and CoFe-based alloys again deviate from the pure single-ion behavior and their temperature dependence suggests the presence of two-ion contributions (O'Handley 1978a, Hernando et al. 1984, Chen and Rao 1986) which are proportional to m2(T) (Callen and Callen 1965). Then, 2s can be expressed by

)~s(T) = 21 [5/2(x) + 22m2(T),

(73)

with 21 < 0, 2 z > 0 and x defined by eq. (72). The occurrence of a compositional and temperature compensation of 2s in CoFe-based alloys confirms the presence of these two mechanisms contributing to 2s. However, also the competition between two single-ion contributions was discussed to cause 2~ = 0 in B-CoMn alloys (du Tr6molet

MAGNETIC AMORPHOUS ALLOYS

383

TABLE 14 Room-temperature saturation magnetostriction for amorphous metal-metalloid alloys and rare-earthtransition-metal alloys. Alloy

2s(x 106)

Bo.zoFeo.so Po. 13Co.ovFeo.so Po.14Bo.06 Feo.40Nio.4o Bo.2oFeo.3oNio.so Po.o9Coo.ga Bo.2oCoo.so Bo.loSio.15Coo.75 Bo.2oFeo.o6Coo.v4 Bo.2oNo.4oCoo.4o Pro.2o Feo.so Smo.zoFeo.so Gdo.33 Feo.67 Tbo.2o Feo.so Tbo.33 Feo.67 DYo.aa Feo.67 Gdo.3oCoo.7o Gdo.23 C0o.77

(1)At H = 1600kA/m. (2)At H = 2000kA/m. * References: [1] O'Handley (1977b). [-2] Tsuya et al. (1975). [3] O'Handley (1976). [4] O'Handley (1978a). [5] Simpson and Brambley (1971).

31.0 31.0 11.0 8 -4.3 -4 -3 ~0 - 7 96 tl) 140~a) 20 220 ~1) 310~z) 38t2) 5 33

Refs.* [1] I-23 [3] [4] [5] [-4] [-6] I-7] [4] [8] [-8] [9] [8] [10] [10] [11] [11]

[6] Arai et al. (1976). [7] Jergel et al. (1989). [-8] Ishio (1988a). [-9] Moorjani and Coey (1984). [10] Clark (1980). [11] Twarowski and Lachowicz (1979).

de Lacheisserie and Yavari 1988). The magnetostriction arising from a disorder caused by randomly oriented easy axes follows a power law 2s(T) = 2s(0)m,(T)" with n < 3 (Cullen and del Moral 1990). The magnetostriction in amorphous rare-earth-transition-metal alloys is composed of an R and a T contribution where in the case of non-S-state rare earths 2s is primarily controlled by the strong single-ion contribution of the R atoms (Suzuki et al. 1988, del Moral and Arnaudas 1989) in accordance with the anisotropy. Alloys containing S-state rare earths are characterized by a magnetostriction which is comparable in magnitude with that of the T-based alloys. This is demonstrated in fig. 75, showing 2s versus x at T = 80 K for amorphous Y - T and G d - T alloys with T = Fe or Co (Yoshino and Masuda 1988). In the case of Y-Fe and G d - F e (fig. 75a), the variation of 2s reflects the behavior of Ms and Tc versus x. The value of 2s for G d - F e is higher than that of Y - F e alloys due to the positive Gd contribution. At the R-rich side, 2~ approaches zero for Y - F e or approaches the 2~ value for Gd in the case of G d - F e alloys because the Fe contribution vanishes at low x. At the Ferich side, 2s decreases due to the noncollinear structure of the Fe sublattice. Amorphous Y - C o and G d - C o alloys (fig. 75b) show a corresponding behavior at the

384

P. HANSEN

Bo.2o(COl_xF ex)o.eo i./~"~A\

P0.13C0.o71COl_xF ex}o.75 ,,/

g

,"•

lO

0

•

t

/..Y

2.--

S /"

/;~

/

\

"-

SIo.15Bo.lo( C%xFex)o.7s

'<~

I

I

I

I

0.2

0.4.

0.6

0.8

1.0

X

Fig. 71. Compositional dependence of the saturation Illagnetostriction for various amorphous metalmetalloid alloys (Luborsky 1978): PBA1-FeCo (Brooks 1976), PC-FeNi (Arai et al. 1976), B-FeNi (O'Handley 1977c, Luborsky 1978), PB-FeNi (Luborsky 1978), PC-FeCo, SiB-FeCo (Fujimori et al. 1976), and B-FeCo (O'Handley 1977c).

0

0.04 0.08

0,12

0.16 0.20

×

Fig. 72. Compositional variation of the saturation linear magnetostriction (solid symbols) and the spontaneous volume magnetostriction (open circles) for amorphous B-FeCo and B-CoNi alloys (Jergel et al. 1989).

R-rich side. The additional minimum of 2 S occurring at x --- 0.4 can be attributed to the vanishing Co moment at the critical concentration xc ~ 0.5. The decrease of 2s at small x is associated with the negative 2s for Co-rich alloys. Some magnetostriction data for amorphous R - T alloys are compiled in table 14. Amorphous alloys with non-S-state rare earths exhibit magnetostrictive effects higher by more than one order of magnitude as it is demonstrated in fig. 76a. The measurements were performed in fields up to 1.6 x 106 A/m (Ishio 1988a, Ishio and Miyazaki 1988). At temperatures below Trio (R = Dy or Tb), the coercive field strongly

MAGNETIC AMORPHOUS ALLOYS

385

0

30 O

~<~ 20 %

10

0

-10

J /

1

~

t

i

3 I I -z.o.-2(A2m~/kg2) 2

i

Fig. 73. Room-temperature saturation magnetostriction versus the square of relative saturation magnetization for different amorphous transition-metal-metalloid alloys (du Tr6molet de Lacheisserie 1982): (O) B-Fe (Narita et al. 1979), (A, V) B-FeNi, ( i ) PB-FeNi (O'Handley 1977c), ([]) B-FeNi (O'Handley 1978a), (©) Fe-based alloys (Itoh et al. 1980).

increases due to the presence of a compensation temperature preventing correct ,~ measurements. The sign of 2 corresponds to that found in the corresponding crystalline counterparts (Clark 1980). The variation of 2 in the series Ro.2oFeo.8o is presented in fig. 76b and was explained in terms of the single-ion theory (Ishio 1988a, Suzuki et al. 1988, Ishio et al. 1990). However, the data shown in fig. 76 are measured in a nonsaturated state. Magnetic saturation can only be reached at much larger magnetic fields as already discussed in section 5.3. The field dependence is displayed in fig. 77, revealing an increase of 2 in fields up to 2 × 106 A/m (Clark 1980) which are known to be much too low to achieve magnetic saturation due to the high locally varying anisotropy fields. The high R contribution to 2s can be used to enhance or suppress the magnetostriction, e.g., in amorphous B-Fe-based alloys (Kazama and Fujimori 1982, Gr6ssinger et al. 1988). The large forced volume magnetostriction O~o/OH reveals comparable magnitudes and dependencies on composition for R-Fe and Y-Fe, B-Fe alloys and thus appears to be primarily controlled by the iron (Ishio 1988b). The magnetostrictive effects originate from the local strains which correlate 2s and a~s to the local atomic arrangement. This leads to a strong dependence of these properties on the deposition parameters (Itoh et al. 1983).

5.8. Coercivity The coercive field and the losses are controlled by the process of magnetization reversal and thus depend on magnetic nucleation, rotation of magnetic moments and

386

P. HANSEN 1.0

0,8 o ~ .~ 0.6 ,.<

o.z,

0.2 0

I

I

0.8

I

I

I

I

0,6 0./+ ms(T)

I

I

0.2

0

Fig. 74. Reduced saturation magnetostriction versus reduced specific saturation magnetization for various amorphous transition-metal-metalloid alloys (O'Handley 1978a, du Tr6molet de Lacheisserie 1982). The full line represents the single-ion model [eq. (71)]. (O) Bo.2oF%.so (O'Handley 1977a), (©) Bo.t4Feo.s6 (O'Handley et al. 1979), (A) Bo.2oNio.5oFeo.3o, ( , ) Bo.EoCOo.4oNio.#o (O'Handley 1978a), (~) Co.toPo.lsFeo.75 (Berry and Pritchet 1978).

30

Gdl_xFex ,~20 10

30

20

Gdl-xC°x'~

10

0 cbl 0.20 ,-'-'o,-"~,0.40 ", 0.60 ,~ x Fig. 75. Compositional variation of the saturation magnetostriction at T = 80 K for (a) amorphous Y-Fe and Gd-Fe alloys and (b) Y-Co and Gd-Co alloys (Yoshino and Masuda 1988).

M A G N E T I C A M O R P H O U S ALLOYS

387

R°'2°Fe°'8°

600 400

200

-200 -400 (a)

l

100

I

,

200

300

400

T(K)

8OO ~

6OO

R°'2°Feo.so

4OO K

20O

=o

V

-200 -400 -600

(b) I I I I I I I I 1 I I I I La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb

R Fig. 76. (a) Temperature dependence of the magnetostriction at H = 1.6 x 106 A/m and (b) variation of the magnetostriction at T = 77 K and H = 1.6 x 106 A/m as a function of the rare-earth element for amorphous R - F e alloys (Ishio 1988a). At temperatures below THoin fig. (a), the coercivity strongly increases preventing correct X measurements. The full line in fig. (b) represents the single-ion theory.

domain-wall motion. The losses additionally increase with frequency due to the presence of eddy currents. The rotation of magnetization and domain-wall motion are associated with the anisotropy, strain, exchange interaction, demagnetizing effects and the presence of structural and surface inhomogeneities where the latter in amorphous materials are sensitive functions of the preparation conditions and annealing treatments. There exists two extreme pictures to describe the magnetization reversal: (i) coher-

388

P. HANSEN

300

,-< 200 ~o

~

6

7

/7

Tb°.l° DY°.23Fe°.67

100 f 0 ~

DYo.33Feo.67 t 1.0 1.5 H(10SA/m)

0.5

i 2.0

Fig. 77. Field dependence of the room-temperaturemagnetostriction of amorphous Tb-Fe, Dy-Fe and TbDy-Fe alloys (Clark 1980).

ent rotation (Brown Jr 1945, Stoner and Wolhfarth 1948, Aharony 1962) involving a simultaneous rotation of all magnetic moments and (ii) domain-wall motion. The former process yields a coercive field determined by the nucleation field, 2K Hc- -#oMs

Neff Ms,

(74)

where K is the anisotropy constant and Neff the effective demagnetizing factor. The latter process involves local nucleation and domain expansion controlled by the presence of defects, local material inhomogeneities, surface roughness or intrinsic magnetic fluctuations caused by structural disorder (Dekker 1976, Gyorgy 1978, Kronmfiller 1981 a,b, Kronm/iller and Gr6ger 1981, Mansuripur 1982, Ramesh and Srikrishna 1988). The coercive field arising from these irregularities can be calculated in terms of a statistical theory (Pfeffer 1967, Kronmfiller 1970, 1973) _

1

q

dx/~

,

(75a)

where q = (p/2F)In(teL~25) and the wall is assumed to move along the x axis. F, p and L are the domain-wall area, the density of pinning centers and the domain width, respectively. E denotes the energy fluctuation according to the present irregularities. The brackets indicate the averaging over the statistical parameter. The domain wall thickness, 5 = ~/-A/K, is determined by the micromagnetic exchange stiffness constant A and the anisotropy constant K. The coercive field originating from domain wall motion thus can be calculated from eq. (74) yielding Hc -

qp6"

#oMs'

(75b)

where p and n comprises the particular features of the material irregularity. Anisotropy and exchange fluctuations give rise to n = - ½ and n -- - {, respectively (Kron-

MAGNETIC AMORPHOUS ALLOYS

389

mfiller 1981a,b). Surface roughness leads to n = 1 (Gyorgy 1978, Kronmfiller 1981b) and in this case the magnitude of Hc estimated from eq. (75) is of the order of 0.7 A/m and thus represents one of the limiting factors for the coercivity of magnetic glasses. Much higher coercivities arise from elastic stress centers because they represent much stronger obstacles for domain movement through the magnetostrictive coupling. This contribution resulting from dislocation dipoles gives rise to n = - 1 (Grrger and Kronmfiller 1981) and p is proportional to the saturation magnetostriction constant and the shear modulus. This contribution implies the dependence of Hc ~ K1/4and was found to control H~ in Fe-based glasses which is demonstrated in fig. 78a. In low-magnetostrictive Co-based alloys, surface irregularities and relaxation effects are the relevant factors governing He. In these soft-magnetic materials, the defect-controlled domain-wall motion accounts well for the observed coercivity. The other extreme where no free domain-wall displacement takes place is represented by hard-magnetic materials used for permanent magnets. In particular

1.75 1.50 o

~

1.25

/

Po.lzBo.o , sFeo.~.oNio.z,o

I

I

B°'2°Fe°'I'i/

1.00

0.75

I

5

I

6

5'OOI(b)

I

I

7

Kl/t. (j/m3)1/z.

I

8

"S

1.00

:~ ~,, 0"50I

o~

I-

0

0.051-

• ~.

0.o1

'

.

"Tb-Fec°

'

- -

'5'.o'"1'o.o

K.ulloSj/rn31 Fig. 78. Room-temperature coercive energy versus uniaxial anisotropy constant (a) for amorphous B-Fe, B-FeNi and PB-FeNi alloys (Gr6ger and Kronmfiller 1981)and (b) for various sputtered and evaporated amorphous Gd-Fe, GdTb-Fe and Tb-FeCo alloys (Klahn et al. 1990a,b).

390

P. HANSEN

polycrystalline N d - F e - B and Sm-Co are well-known as suitable materials for permanent-magnet applications. In this case, the grain size is a further relevant parameter determining Ho while in amorphous alloys the local structure controlled by the deposition parameters is of primary importance. In this case, the coercive field and its temperature dependence were discussed in terms of a generalized form of the nucleation field (Kronmfiller et al. 1988, Givord et al. 1990) 2K Hc = c t - #o Ms

(76)

Nef f M s ,

where ~ represents a microstructural parameter and Nef f a n averaged local demagnetizing factor. The temperature dependence of He for many crystalline hard-magnetic materials can be well described in terms of eq. (76), treating ~ and Neff as adjustable parameters (Hirosawa et al. 1986, Hirosawa and Sagawa 1988, Hirosawa 1989, Givord et al. 1990). Another approach to calculate He for hard-magnetic materials with a uniaxial anisotropy constant K, > 0 is based on the solution of the differential equations for the case that the domain wall passes a planar barrier with different material properties, yielding (Friedberg and Paul 1975, Hilzinger 1977, Paul 1976, 1982)

Ho-

1.21A ( A K , _ Kb']

\

J"

(77)

A denotes the thickness of the barrier. A b and K b a r e the exchange stiffness constant and the anisotropy constant inside the barrier, respectively. Equation (76) is restricted to barriers satisfying A ~ 6. For many magnetic materials, however, both local rotation controlled by the nucleation field in a small volume and domain-wall propagation are responsible for the observed He. The activation volume depends on temperature and thus the temperature dependence of He is also determined by thermal activation processes (Rio et al. 1987, Givord et al. 1988, Labrune et al. 1989, Givord et al. 1990). Rareearth-transition-metal alloys are characterized by rather high coercivities except for those containing only S-state rare earths. Domains imaged in amorphous Tb-Fe alloys indicate the importance of nucleation processes. In this case, Ku is related linearly to the Tb content as demonstrated in fig. 66b. According to eqs. (75)-(77), the coercivity is expected to increase with K,~ where n is determined by the mechanism controlling H c. The linear increase of K, with the R content in amorphous R - T alloys was well established and a plot of ~oMsHe versus Ku presented in fig. 78b for Tb-containing alloys yields n - 1.3 (Klahn and Hansen 1991). These data thus support neither a pure nucleation process (He ~ Ku), nor just domain wall motion. In the latter case, the calculated Ho values for exchange fluctuations (H e KSu/4) are much too low to account for the observed coercivities and surface roughness, pinning through anisotropy fluctuations, clustering or stresses on an atomic scale give rise to a much weaker Ku (n < 1) dependence (Kronmfiller 1973, 1981b, Kronmiiller and Gr6ger 1981). However, the local stresses may be quite large as compared to the average macroscopic magnetoelastic interaction and, thus, ~

MAGNETIC AMORPHOUS ALLOYS

391

might also be important for the interaction with thin domain walls in particular in Tb-containing alloys. The direct relation between Hc and Ku and the single-ion origin of Ku varying with 2jd 2 [eq. (68)] for amorphous R-T alloys suggests Hc to vary with the same factor which indeed was well confirmed experimentally for the heavy rare-earth-transition-metal alloys (Komatsu and Fukamichi 1989, Komatsu et al. 1989). Also, the Ku variation of Ho predicted for the domain-wall pinning through a planar barrier (H¢ ~ K 3/2) is in reasonable agreement with the observed dependence (fig. 78b). The presence of a compensation temperature is a factor giving rise to severe changes of the magnitude and the temperature profile of Ho. This is demonstrated in fig. 79 for different amorphous alloys of composition (Gd, Tb)l_xFex with x around 0.7 (Hansen and Witter 1988). The total T~ompshift corresponds to a change in x of the order of 0.03. In the vicinity of T~omp,the energy of #oMsH¢ is almost constant because Hc varies as M~-1 leading to a singularity of Hc at T~omp.The resulting profile can be utilized to tailor these films for magneto-optical data storage as discussed in section 8.2. In this case, also the Hc versus T characteristic in the switching range near Tc is of significant importance. This is shown in fig. 79 for GdTb-Fe and Tb-FeCo alloys with different Tb content and compensation temperatures. The strong anisotropy of Tb leads to a very steep temperature dependence of H¢ near Tc and the position of T~omvaffects the curvature of He. The interpretation of H~ data for alloys of almost identical composition requires a detailed knowledge about the preparation conditions due to the high sensitivity of H~ on structural disorder. Annealing of the alloys lead to a drastic reduction of Hc due to structural relaxation and oxidation processes. 400

x=0.664 x=0.710 x=0.738 x=0.729 x=0.689 ¢=0.111 y=~66 y=0.169 y=0.181 y=0.163

300

----t

..,,. .<

~_yb}l_, , ' \ ~ Tbl_×(gel_yCoy)×

q:~

::= 20C

,~o,76 '~ 100

x= 0,760 ~ y= 0.333 I

~00

350

~ 'K'

I

400 T(K)

450

500

Fig. 79. Temperature dependence of the coercive field for evaporated amorphous GdTb-Fe and Tb-FeCo alloys with different compensation temperatures [(~7) T~omp=170K, (O) T~omp=181K, (D) Tcomp= 395 K, (A) T~o,.p= 466 K] (Hansen and Witter 1988).

392

P. HANSEN

Most transition-metal-metalloid glasses are soft ferromagnets exhibiting technically interesting properties. In this respect, three groups of ribbons can be distinguished (Warlimont and Boll 1982): (i) Fe-based alloys with high Ms and low power loss, (ii) FeNi-based alloys combining good soft-magnetic properties with intermediate Ms and (iii) Co-based alloys with low Ms, 2s and excellent soft-magnetic properties. Typical coercive fields range from 0.24 to 8 A/m for BSi-CoNiFe and B-Fe alloys. Typical Hc values for B-CoFe glasses (Gyorgy 1978) are displayed in fig. 80. Hc is at a miminum when 2s passes through zero, indicating the importance of stresses. 5.9. M a g n e t i c e x c i t a t i o n s

Single-particle and collective-particle excitations contribute to the excitation spectrum of magnetic materials. The spin waves or magnons are the excitations of lowest energy and involve a deviation of the moment from the parallel or antiparallel alignment of the ground state. This requires an exchange energy D k 2 according to eq. (54) where D is the spin-wave stiffness constant which is related to the exchange constants and k is the wave vector of the spin wave. D is a function of temperature and can be expressed by D ( T ) = D(O)

1- a

(78)

,

where n = ~ for an ideal Heisenberg ferromagnet (Dyson 1956, Izuyama and Kubo 1964) while the band theory predicts n = 2 (Izuyama and Kubo 1964, Mathon and Wohlfarth 1968). Typical values for D(0) are compiled in table 15. D(0) is expected to scale with Tc. This indeed was found for many Co-based alloys (Suran et al. 1981, H/iller 1986) and is demonstrated in fig. 81. Different slopes were found for Cometalloid alloys and Co-transition-metal alloys, which probably can be attributed to the different bonding responsible for the alloy formation. For Fe-based alloys, the D(0) also increase with Tc but the data do not follow straight lines (H/iller 1986) 8

25

E

B°'2°Fes"e°'xCOx

20

H¢

15

5 0

0i 0.50

i

l

i

0.60

i

0.70

I

-5

0.80

X

Fig. 80. Compositional variation of the room-temperature coercivity and saturation magnetostriction of amorphous B-FeCo alloys (O'Handley et al. 1976c).

MAGNETIC AMORPHOUS ALLOYS

393

TABLE 15 Spin-wave stiffness constant at T = 0 K and Curie temperature for amorphous alloys and crystalline iron, cobalt and nickel. Alloy

Tc (K)

D(0) (10 - 23 eV m 2 )

Fe(cryst.) Co(cryst.) Ni(cryst.) Bo.l,~Feo.86 Bo.18Feo.s2 Po.26 Feo.74 Bo.t3Sio.o9Feo.78 Bo.17Wo.o5 Feo.75 Bo.EsFeo.4oNio.35 Co.ovCro.loPo.13Feo.7o Po.16Bo.o6Alo.o3Feo.75 PoA6Bo.o6Alo.o3Feo.37Nio.38 Po.25 Coo.7s Bo.25Sio.o5Coo.7o Bo.llSio.llFeo.osCoo.7o Tio.229Coo.771 Po.aoNio.9o Yo.33Coo.67 (Gdo.26Coo.74)o.95Moo.o5

1040 1400 630 556 617 580 710 450 637 360 630 482 480 539 738 550 280 470 -

311 580 359 118 167 115 156 59 120 60 134 91 105 115 221 164 140 480 470

References Aldred and Froehle (1972) Pauthenet (1982a,b) Aldred (1975) Ishikawa et al. (1981) Rhyne et al. (1982) Hfiller and Dietz (1985) Yu et al. (1988) Kaul and Mohan Babu (1989) Kaul and Mohan Babu (1989) Xianyu et al. (1982) Birgenau et al. (1978) Birgenau et al. (1978) Hfiller and Dietz (1985) Maskiewicz (1982) Swierczek and Szymura (1988) Suran et al. (1981) Hfiller and Dietz (1985) Fukamichi et al. (1986b) Macsymowicz et al. (1985)

40(3 Ml_xCox

~'E 30C 200 I00

~

"~°~¢° t

0

500

1000 Tc(K)

Fig. 81. Spin-wave stiffness constant at T = 0 K versus Curie temperature for various amorphous alloys (Luborsky 1980, H/iller 1986). (+) M = W (Hfiller et al. 1985), ( . ) M = Ti (Suran et al. 1981), (C]) M = Bi (Maeda et al. 1976), ( 0 ) M = P (Hiiller and Dietz 1985), ((3) M = BSi (Maskiewicz 1982).

which is probably associated with the noncollinear magnetic structure for Fe-rich alloys and those with compositions near xc. D(T) is correlated to the coefficient B of the T 3/2 term [eq. (55)] governing the low-temperature variation of the saturation magnetization. D(T) can be determined from the spin-wave excitations using standing spin waves in thin films, from Brillouin scattering, magnetization data or neutronscattering experiments. The spin-wave resonance condition for the resonance field

394

P. HANSEN

applied normal to the film plane reads

D (n~z~2] c°=?IH"--4~Ms +gltB \ h J j"

(79)

h is the film thickness and H, the resonant field of the nth spin-wave mode. The temperature dependence of D(T) obeys the T 5/2 law for some amorphous alloys such as B-Fe (Rhyne et al. 1982) or G d - C o M o (Macsymowicz et al. 1985), while for other alloys D(T) deviates from this relation. The strong temperature dependence of D(T) measured by inelastic neutron scattering is presented in fig. 82 for an amorphous BSi-Fe alloy (Yu et al. 1988). D(T) is related to the micromagnetic exchange stiffness constant A(T) by

A(T)-

MdT) ....

2 ~ B t)(l),

(80a)

where g#B = 7h and 7 denotes the gyromagnetic ratio. A(T) is related to the domain wall energy aw of a 180° Bloch wall by aw = 4A,,/-~. Thus, D(T) also can be estimated from wall energy measurements. A(T) can be expressed in terms of the exchange constants (Gangulee and Kobliska 1978b)

A(T) = { ~ N,S,(T) Z "]iJZur2Sj(T)'

(80b)

J

where Ni, z u and rij are the number of i atoms per unit volume, the number of nearest neighbors and the atomic distance between the atoms i and j, respectively. Combinations of eqs. (80a) and (80b) yields a relation between D(T) and the sublattice magnetizations in ferrimagnets. The temperature dependence of A(T) obtained from standing spin-wave spectra in an amorphous G d - F e film (Vittoria et al. 1978) is displayed in fig. 83. The presence of non-S-state rare earths gives rise to a strong coupling between

150 Bo,13 Sio.o9 F

E 100

eo.Ta~~

o

'o I.-

50 I

200 I

I

h00 T(K) I

I

600 I

800 I

Fig. 82. Temperature dependence ofthe spin-wave stiffness constant for amorphous BSi-Femeasured by inelastic neutron scattering (Yu et a1.1988).

MAGNETIC AMORPHOUS ALLOYS

395

2

\ 0

I

I

I

I

100

200

300

400

\ 500

T{K]

Fig. 83. Temperature dependence of the micromagnetic exchange stiffness constant for an amorphous Gd-Fe alloy evaluated from standing spin-wave spectra (Vittoria et al. 1978).

the spin system and the lattice via spin-orbit coupling yielding high linewidth in the resonance spectra (Lubitz et al. 1976) which prevents the determination of D(T). It should be noted that strong differences were observed for D(0) values evaluated from magnetization and neutron-diffraction experiments. This discrepancy was attributed to additional low-lying magnetic excitations (Fernandez-Baca et al. 1987).

5.10. Annealing effects The amorphous structure represents a metastable state and thus any thermal treatment causes a continuous change of the atomic arrangement. Different processes can be distinguished: (i) corrosion and oxidation, (ii) structural relaxation and (iii) crystallization. The latter describes the transition to the crystalline state and this process requires an activation energy of the order of 2.5 eV. This is briefly discussed in section 4.1. The first two processes affect the structural, magnetic and electrical properties in a specific way (Egami 1984). The structurally sensitive properties like the compensation temperature, the uniaxial anisotropy, the coercivity or the conductivity thus are suitable parameters to investigate the time and temperature dependence of these processes. The oxidation and structural relaxation of magnetic glasses is less important because they exhibit an even higher corrosion resistance than the corresponding crystalline alloys (Waseda and Aust 1981). However, annealing in a magnetic field leads to strong changes in the magnetic properties (Luborsky 1978, 1980, Egami 1984) (see fig. 64). The evaporated or sputtered rare-earth-transition-metal films exhibit a low resistivity against corrosion and oxidation due to the high oxygen affinity of the rare earths (Saito et al. 1986). The degradation by oxidation and structural relaxation was investigated for different amorphous R - T alloys (Luborsky et al. 1985, van Dover et al. 1986, Hartmann et al. 1987, Klahn et al. 1987, Greidanus and Klahn 1989, Klahn 1990). The time dependence of the reduced coercive field for a GdTb-Fe film with and without protection layers is shown in fig. 84. The bare

396

P. HANSEN 1.0

o,,,

• .

GdTb-Fe

i-\ 0.8

• mn

•

o.7 •

0.6

ibJ i

°%,

•

n Intalal

I

I102 1hour

I lUlltll

I

I Ilnlnnl

1031 1day

i

, nlnllll

I10 S 1week 1month

I

, nttnhnl

I10 1year

t(min}

Fig. 84. Degradation of the reduced coercive field for amorphous GdTb-Fe films (Greidanus and Klahn

1989). (O) Structural relaxation, (mm)trilayer in dry atmosphere, (A) oxidation of the bare film. The inset illustrates the typical trilayer stack used for optical recording: (a) glass substrate, (b) dielectric layer, (c) GdTb-Fe layer, (d) metal reflector, (e) organic protection layer. film (triangles) shows a drastic reduction of H c due to the selective oxidation of the rare earths. A typical trilayer configuration (insert of fig. 84) used for magneto-optical recording protects the magnetic film and leads to a significantly higher stability (squares). The circles represent the degradation of Hc due to structural relaxation. In this case, the G d T b - F e film was coated with an 50 nm aluminium layer to avoid any oxidation effects (Klahn et al. 1987). The structural relaxation process can be described by a spectrum of activation energies (Gibbs et al. 1983, Fish 1985) according to the various atomic rearrangements possible in an amorphous material (see section 4.2). However, the structural degradation causes only small changes in the magnetic and electronic properties as compared to the oxidation process that is associated with a very low activation energy. Electrical conductivity measurements performed on evaporated and sputtered R-Fe, R-Co, G d T b - F e , Tb-FeCo, D y - F e C o , with R = Gd, Tb, Dy or Ho, films reveal activation energies ranging from 0.18 to 0.31 eV (Allen and Connell 1982, Klahn et al. 1988, Klahn 1990). The variation of the normalized conductivity with annealing time for bare evaporated R - F e and R - C o alloys is presented in fig. 85a. The Fe-based alloys clearly indicate a much stronger structural degradation. Arrhenius plots for in-situ measured uncoated films are shown in fig. 85b. Oxygen depth profiles indicate that an oxide layer grows into the film leading to three different layers (van Dover et al. 1986, Aeschlimann et al. 1988): (i) a 10nm thick surface layer where both R and T atoms are completely oxidized, (ii) a layer where mainly the R atoms are oxidized and (iii) the bulk layer. The presence of oxidation processes, therefore, are very important in the interpretation of the properties of thin films. The resistivity of thin R - T films against corrosion and oxidation can be improved using dense films obtained by magnetron sputtering (Hong et al. 1986) and by small additions of Ti, Nb, Ta, Cr (Imamura et al. 1985, Niihara et al. 1988), Hf, Mo (Kobayashi et al. 1988), In (Iijima 1987, 1988) or Pt (Hatwar and Majumdar 1988).

MAGNETIC AMORPHOUS ALLOYS

397

1.0

/Dy-Co 0.9

Tb-Co

"6 0.8 b 0.7

(a) I

0.6

I

I

f

20

I

40

i

I

60

I

80

I

100

ta(h}

160 I

110 90 I

I

T (C°) 65 25 I

,~A

(b)

=0.31eV

-5 Tbo.22 Feo.3t, Co o.t,,~

:O,23eV

-4

I

-3

-2

3 110-3 K 1

Fig. 85. (a) Variation of the normalized conductivity with annealing time for bare amorphous R-T alloys prepared by evaporation (Klahn 1990). (b) Arrhenius plot of in-situ measured conductivities for three days for amorphous 80 nm thick Tb-FeCo films prepared by rf diode sputtering (open circles) and evaporation (solid circles) (Klahn et al. 1988). Annealing of the R-T alloys in fig. (a) was performed in dry nitrogen-oxygen atmosphere at 383 K.

398

P. HANSEN

6. Magneto-optical properties 6.1. Phenomenological theory

The interaction of polarized light with a magnetic material leads to a change in the state of polarization depending on the direction of magnetization. The magnetooptical effects originating from these light-induced electronic transitions associated with the spin-orbit coupling can be observed either in transmission (Faraday effect) or in reflection (Kerr effect). In both cases, the incident linearly polarized light interacting with the magnetic material is transformed into elliptically polarized light. This can be described phenomenologically in terms of a complex rotation ~b(M)= - ~ b ( - M ) resulting from different velocities v+_ =c/N+_ of right and left circularly polarized light in the magnetic medium. N÷ and N_ are the complex refrective indexes N_+ =n_+ -ik_+,

(81)

where k+ and k_ are the extinction coefficients which are related to the optical absorption by k+_ = (2/4n)a+. + and - refer to right and left circularly polarized light, respectively. The specific Faraday rotation and ellipticity, and Kerr rotation and ellipticity then are defined by 1 OF= ~ Re(q~v),

1 OF = ~ Im(~bF),

(82a)

OK= Re(qSK),

~K = Im(CkK),

82b)

where

fD ~bF= 2c (N_ -- N+ ), ~bi~=

(83a)

i(N_ - N+ )

(83b)

N+N_ - 1

The complex refrective index is related to the dielectric tensor e(M) or the optical conductivity tensor tr(M) which are correlated by the expression ~(M) = 1 - 4~i ~(M).

(84)

(D

For M II z, the conductivity tensor reduces to the form \

trxx tTxy 0 \ ,r(M) =

-- axy 0

ff xx

0 ).

0

azz

(85)

MAGNETIC

AMORPHOUS

ALLOYS

399

From MaxweU's equations, one obtains N~ = 1 - 4z~(iaxx + a~,). co

(86)

Combining eqs. (81)-(86) and using the real and imaginary parts of the complex ..(1).T ia!z) with i, k = x, y, z, the rotations and ellipticities tensor components a,k = "~k are given by the expressions 2n

OF =

O,

(1)

c(n2 "-}-k2 ) (na~ r

(2)

- kaxr ),

(87a)

, 2 . - 2 , ( k a ~ ) + na~)),

(87b)

2re

ctn + K )

and OK =

4 ~ k ( - k 2 + 3 n 2 - 1 ~ a (1)+n(n 2 3k 2 --_(2) _ _ ' xy 0o~y co n2(n 2 3k 2 1)2+k2(k 2 - 3 n 2 - 1 ) 2 ' -

- -,.,(2)

47rn(n 2 - 3k 2 - 1)a(x~) - k ( - k 2 + 3n 2 - l),.xy ~ti(=

co

n2(n 2 -- 3k 2 -

1) 2 + k 2 ( k 2 -

3 n 2 _ 1) 2

(88a) (88b)

,

where n = ½ (n + + n_ ) and k = ½(k + + k_ ). Sign, magnitude and spectral dependence of the Faraday and Kerr rotation and ellipticity thus are controlled by the offdiagonal components of g which are determined either by interband or intraband transitions and by the optical constants. These band transitions in crystalline metals and alloys give rise to broad 0F or OK spectra (Krinchik and Artem'ev 1968, Erskine 1975, Katayama and Hasegawa 1982, van Engelen and Buschow 1986), in contrast to oxides as, e.g., bismuth-substituted garnets (Hansen and Krumme 1984) or lanthanides and chalcogenides (Reim and Schoenes 1990). This is demonstrated in figs. 86 and 87 showing the spectral dependence of coOxy-(2)(Krinchik and Artem'ev 1968) and OK(Weller et al. 1988b). The major features of these spectra are even less pronounced for structurally disordered metals (Prinz et al. 1981). Experimentally, the tensor elements or complex rotations can be obtained from ellipsometric measurements (Clemens and Jaumann 1963, Prinz et al. 1981, Allen and Connell 1982). Ov data have the advantage to represent the bulk properties. However, the high optical absorption restricts Ov measurements to thin films and also corrections due to multiple reflections have to be taken into account. OK data are affected by the surface properties and for film thicknesses below 100 nm also by the optical constants of the substrate. In this case, significantly enhanced OK values can be measured (Weller and Reim 1989b). 6.2. M i c r o s c o p i c models 6.2.1. Interband transitions

The magneto-optical properties for energies above 1 eV are mainly governed by (1) and ~,xr ,,(2) can be expressed in terms interband transitions. Their contributions to axr

400

P. H A N S E N

•...

Ni

.':

3 2~

,,zCo

." I

\X~J "

/ - 1

ti-! 0

\.~', ~

/Fe

..Jr...... .\../.,....

"U..

"J

1

2

3

4

5

Photon energy (eV) Fig. 86. Absorptive component of the magneto-optical conductivity of Ni, Co and Fe versus photon energy (Krinchik and Artem'ev 1968). The vertical scale is correct for Ni. The scale for Co and Fe have to be multiplied by a factor of five. The chain line represents the contribution from intraband transitions.

-0, COl- x F e x

-05 A

-(?.2

d

x*x

=0.s2 Z

t:r..,,,,x~,~,Jm,~

n~J

,- ×=oT

~ -o.4 -O.i

%.." -O,i

-0.7

I

1

1

1

I

2 3 4 Photon energy (eV)

I

5

6

Fig. 87. Room-temperature Kerr rotation for different polycrystalline Co 1_xFe~ films (Weller et al. 1988b).

of the absorption rates for left and right circularly polarized light by (Bennett and Stern 1965) (1) cr~y

7~e2 -

m2- - Me+

~ ...-5---75.2, 2 h o g m 2 V s ~,~, ¢O~p - - 09

(89a)

MAGNETICAMORPHOUSALLOYS 7~e 2

(2)

a~r =

~ (M z_ - MZ+)a(co,~- co),

2hcom 2 V~ ,,p

401

(89b)

where M+ = (//In+ I~> and the operators rt+ = rt~ _+i~r are linear combinations of the electron kinetic momentum operator defined by h n = p + 8-~5mc z [s x gV(r)].

(90)

V, is the sample volume and VV(r) is the electric field controlling the motion of the electron with spins s and momentum p. [e> and [fl> are linear combinations of wave functions with spin-up and spin-down states and the summation in eq. (89) extends over the occupied and unoccupied states. The second term in eq. (90) represents the spin-orbit contribution. Different approaches for the calculation of-'") ~ ( 2 ) were reported (Wang and ~'ik and t~ik Callaway 1973, Erskine and Stern 1973a, Singh et al. 1975, Laurent et al. 1979, Misemer 1988). In addition to the many features of the band structure, the magnitude of the spin-orbit coupling and the spin polarization are the significant parameters determining the magneto-optical effects. Some features of the measured spectra were reproduced by the theory for the crystalline metals (Fe, Ni, Co, Gd), however, parts of the spectra show a less satisfactory agreement between theory and experiment. Also relativistic band structure calculations were performed yielding only minor changes with respect to the nonrelativistic results (Ebert et al. 1988). 6.2.2. Intraband transitions

Normal electron scattering and skew scattering processes are responsible for the intraband transitions (Erskine and Stern 1973a,b, Voloshinskaya and Fedorov 1973, Voloshinskaya and Bolotin 1974, Reim et al. 1984). They contribute to the lowenergy part of the magneto-optical spectra. The frequency dependence originating from these processes yield (Erskine and Stern 1973a). cog f Q ax,=-g(a,>~f~+t/k

Fico(Y + i@-]~ ~j jj,

(91)

where f(co) = g22 + (y + ico)2. co2 = &re2N/m , and are the plasma frequency and the spin polarization, respectively. N and m* denote the concentration and the effective mass of conduction electrons, respectively. O denotes the skew scattering frequency and ~ = 1/7 is the normal scattering lifetime, t/ is proportional to the strength of the spin-orbit coupling. In the high-frequency limit, defined by (2)> 7 and (2)>>g2, eq. (91) yields t- '-rx( 1y ) - -

--

~/']

(92a)

(A) 2

~xrn (2) -- - ~ ~/(a= > 7(2)

(92b)

402

P. HANSEN

These expressions indicate that the skew scattering process is negligible at high photon energies. The normal scattering process is proportional to the spin-orbit coupling and the spin polarization. Therefore, the contribution of d electrons is more significant than that of p electrons due to the large exchange spitting of the d-electron bands and their relatively large spin-orbit splitting. At high energies, the contribution of this process to axy is expected to be small and, in particular, coa~Zy) is independent of ~o (chain line in fig. 86) in contrast to interband transitions.

6.3. One-subnetwork alloys The crystalline metals Fe, Co, Ni are characterized by a negative Kerr rotation and a positive Faraday rotation (Clemens and Jaumann 1963, Krinchik and Artem'ev 1968, Buschow et al. 1983, Buschow 1988, Weller et al. 1988b), except for Ni, exhibiting a sign change below 1 eV and above 4 eV. In all cases, the typical features of the spectra are determined by two minima (maxima) of OK (0v) located between 1 and 2eV and 4 and 5eV as shown in fig. 87 for Fe, Co and Feo.szCoo.48 (Weller et al. 1988b). Intra 3d alloys like Col-xFex reveal an increase of the magnetooptical effects reaching a maximum around x = 0.5. This strong variation of 0,: with x indicates a significant change of the spin polarization which is in accordance with the Slater-Pauling curve (fig. 26) showing a maximum of the magnetic moment around x ~ 0.65. Also, a shift of the OK minimum towards higher energies was observed which might be attributed to a change in the majority d-state excitations (Weller et al. 1988b). The magneto-optical properties of crystalline alloys and intermetallics which have been discussed in a recent review (Buschow 1988) reveal a reduction of the main peak between 1 and 2 eV as compared to the pure elements and the typical features of the spectra are less pronounced (van Engelen and Buschow 1986, Buschow et al. 1983, Buschow 1988). Some s or p metals like A1, Ga and Sn affect primarily the high-energy side of the spectrum for Co-based alloys. Pt and Pd enhance also the magneto-optical effects at high energies which was attributed to spin polarized 4d and 5d electrons for Pd and Pt, respectively. The larger effect of the Pt was associated with the spin-orbit coupling of the Pt being higher than that of Pd (Buschow et al. 1983, Buschow 1988). High magneto-optical effects were found in some Mn-based alloys such as MnBi (Chen et al. 1973), MnSb (Sawatzky and Street 1971, Buschow et al. 1983) and PtMnSb (van Engen et al. 1983, Inukai et al. 1986, Ohnuma et al. 1988). The latter reaches a OK value of --1.27 ° at 1.72 eV (720 nm) and room temperature. This large Kerr rotation was assigned to the unusual band structure of this half-metallic ferromagnet (de Groot et al. 1983, 1984, de Groot and Buschow 1986). However, for most other compositions, an interpretation of the magneto-optical spectra in terms of band calculations was not yet available. Amorphous alloys principally show a similar spectral dependence of OK and OF as compared to their crystalline counterparts. However, for many alloys, the rotation is reduced and the structure of the spectra is much less pronounced due to the influence of the structural disorder on the spin-up and spin-down bands and on the magnetic order. The former influence was interpreted in terms of a change

MAGNETIC AMORPHOUS ALLOYS

403

of the balance between spin-up and spin-down transitions due to the loss of the k-selection rule of vertical transitions (Weller and Reim 1988). This causes a reduction of the rotation and a broadening of the transitions. The latter effect was shown to play an important role for various Fe-rich alloys where competing positive and negative exchange interactions lead to a drastic reduction of Ms and Tc with increasing Fe content. One-subnetwork amorphous alloys were not investigated very intensively in contrast to R - T alloys. The Kerr rotation for B-Fe glasses are shown in fig. 88 for airincident (curve B) and substrate-incident (curve A) light (Buschow and van Engen 1981a). The two rotations are related via the substrate refractive index. The OKvalues for the amorphous alloys appear to be slightly below the crystalline data (solid circles). The decrease of OK for the Fe-rich alloys that is not observed from the magnetization of B-Fe glasses possibly indicate a small deviation from the collinear structure. This effect was shown to occur more pronounced for Zr-Fe (fig. 29b), CeFe (fig. 30) or Y-Fe (fig. 31) alloys with respect to the magnetic properties and, therefore, these alloys are expected to exhibit much lower rotations as compared to their crystalline counterparts. The compositional and spectral variation of OKfor M Fe compounds (Buschow et al. 1983) and the corresponding amorphous alloys (Buschow and van Engen 1981a) behave similar for M = Si, Ge or Sn and follow the trend observed for Ms. This was also observed for amorphous F - F e (Sugawara et al. 1989). The opposite behavior where OK is larger in the amorphous state than in the crystalline state was reported for Si-Fe (Afonso et al. 1980). The magneto-optical behavior for Co-based alloys reflects the compositional and temperature dependencies of M s which are based on a strong ferromagnetic coupling. The room temperature Kerr rotation is shown in fig. 89a for B-Co glasses at 2 = 633 nm (1.95 eV) and 830 nm (1.49 eV). The full line represents the corresponding Ms variation. The values for Si-Co were found to agree with the B-Co data within -0.6 -0.5

-0.4 0J

-0.3

-0.2 -0.1

°0 4

I

I

I

0.6

I

0.8

I

1.0

X

Fig. 88. Compositional variation of the room temperature Kerr rotation at 2 = 633nm (1.95eV) for amorphous B-Fe alloys prepared by vapor quenching (Buschow and van Engen 1981a). Curve (a) represents 0~ data measured for substrate-incident light and curve (b) for air-incident light. The solid circles indicate OK values for crystalline materials.

404

P. HANSEN

-0.5 150 -0.4 100 A

-0.3 -0.2

50

-0.1

< b

0

(a) I

0.1

I

o16

I

I

o18

x

1.0

-0,5 -O.L

Ti 1-xCox

o° o f

~ -0.3 (I~ -0.2 -0.1 0

I

I

400

I

I

I

I

800 1200 [v~(kA/m)

I

I

1600

-0.5 -0.4

Zrl-x Cox

o°3°o~O

"~ -0.3 (~ -0.2 -0.1 i 4001 I 8001 J 12100 I 16100 Ms(kA/m) Fig. 89. (a) Compositional variation of the room temperature Kerr rotation at 2 = 633 nm (1.95eV) (open circles) and ~.= 830nm (1.49eV) (solid circles) for amorphous B-Co alloys prepared by evaporation (Buschow and van Engen 1981a).The data were measured at the substrate interface. (b) Room temperature Kerr rotation at 2=780nm (1.59eV) versus saturation magnetization for amorphous Ti-Co and (c) Zr-Co alloys prepared by sputtering (Honda and Yoshiyama 1988b). The data were measured at the air-film interface.

experimental error (Buschow and van Engen 1981c). This behavior is confirmed for a m o r p h o u s T i - C o and Z r - C o alloys ( H o n d a and Yoshiyama 1988b). These results are displayed in figs. 89b and c, demonstrating that the r o o m temperature OK at 2 = 780 n m (159 eV) scales well with Ms. In the vicinity of zero magnetization, a deviation from linearity is expected since the reduction of b o t h Ms and Tc cause a decrease of 0i~. Also, OK data for a m o r p h o u s Y - C o alloys (Choe et al. 1987) fit into the OK versus

MAGNETIC AMORPHOUS ALLOYS

405

x variation shown in fig. 89a. Crystalline Cr-Co alloys exhibit also a linear variation with Ms (Tsutsumi et al. 1983, Honda and Yoshiyama 1988b). The magneto-optical behavior of the Co-based alloys thus can be interpreted in terms of a weakly structured spectral dependence typically like that reported for amorphous Y-Co alloys (Choe et al. 1987). The nonmagnetic diluting elements primarily tend to decrease the spin polarization and the strength of the exchange coupling resulting in a linear decrease of Or: with x or Ms except for temperatures close to Tc. Deviations between the compositional dependence of 0~: and Ms were reported for Mg-Co (Buschow and van Engen 1981b).

6.4. Two-subnetwork alloys The magneto-optical activity of rare-earth (R)-transition-metal (T) alloys originates from the R and T contributions. The heavy rare earths reveal strong transitions between 4 and 5 eV which is shown in fig. 90 for crystalline RFe2 compounds (Katayama and Hasegawa 1982). Gd exhibits a positive Kerr rotation in the entire spectral range investigated, with a peak around 295 nm (4.2 eV) due to interband p d transitions (Erskine and Stern 1973a). Tb, Dy, Ho and Er exhibit a strong negative peak around 280nm (4.4eV). This feature is much less pronounced for the corresponding amorphous alloys (Togami et al. 1983, Y. Suzuki et al. 1987). These transitions were assigned to interband 4 f ~ 5d transitions (Erskine and Stern 1973a). The ferrimagnetic order of the heavy R-T alloys leads to a sign change of OKexcept for Gd where the Gd and T contributions add due to the opposite sign of the Gd sublattice rotation. This implies that the R and T contribution can be roughly considered as independent, provided no common bands are formed between the 4f,

5.0 4.0 I

0.2

Photon energy (eV) 3.0 2.4 2,0

I

I

.~

I

/GdFe 2

/ \

(I~ -0,2

\ ~ ,/~ ~HoFe2 , \ // ~ D y F e 2

-0.4

~ Z b F e 2

20(

I

I

300

400

I

500 ~k(nm}

1.8

I

f

~.~-.:~

I

I

600

700

800

Fig. 90. Wavelength dependence of the room-temperature Kerr rotation for crystalline RFe2 compounds (Katayama and Hasegawa /982).

406

P. HANSEN

5d R electrons and the 3d T electrons. This was confirmed for amorphous G d - F e and G d - C o alloys where the sublattice rotations were estimated from the Kerr rotation of amorphous Gd-Ni, Y-Fe and Y-Co alloys (Tsunashima et al. 1989). The spectral dependence of amorphous R - T alloys with R = Gd or Tb and T = Fe, Co or FeCo is shown in fig. 91. The magnitude of the room temperature 10KI for Gd0.e4Feo.a7Coo.39 is almost reduced by a factor of two (fig. 91a) as compared to the data for crystalline Feo.50Coo.50 (Weller et al. 1988a,b). Part of this reduction is due to the reduced Fe and Co moment and the lower Tc in the R - T alloys, but the remaining reduction in 10KI originates from the influence of the structural disorder on the spin-up and spin-down transitions. The comparison of the amorphous binaries G d - F e and G d - C o (Hansen et al. 1989) (fig. 91b) with the crystalline pure elements (fig. 87) indicate a lower reduction in 10KI. In fig. 91b, the absolute value was plotted to eliminate the influence of the magnetic compensation on the sign of 0K. This figure also shows the influence of the temperature on 0K which is much more pronounced for the R-Co alloys than for the R-Fe alloys due to the much stronger shift of Tc with the Co content. The light R - T alloys behave differently concerning two aspects: (i) their moments are aligned parallel to the T moment and (ii) their wavelength dependence is different with respect to sign and spectral variation (Suzuki and Katayama 1986, Choe et al. 1987, 1988, Gambino et al. 1986, McGuire and Gambino 1987b, McGuire et al. 1987, Y. Suzuki et al. 1987, Takahashi et al. 1987, Honda and Yoshiyama 1988a, Weller et al. 1988a, Tsunashima et al. 1989). The different signs occurring for 0K and 0V in R - T alloys are summarized in table 16 using the common sign convention (Kahn et al. 1969). This leads to a positive Faraday (Kerr) rotation for the magnetization parallel to the propagation of the transmitted (reflected) light when the displacement vector D turns counter clockwise for an observer facing the light. It should be noticed that the presence of a compensation composition or temperature leads to a sign change in OK or 0F due to the reversal of the net magnetization in the presence of an external field. Therefore, this sign change represents no intrinsic material property but is important when 0K or OF data of the ferrimagnetically ordered alloys are compared. The room temperature spectral dependence of amorphous N d - C o alloys is displayed in fig. 92a. The Nd contributes to 0K via f ~ d interband transitions (Weller et al. 1988a) leading to an increase of 10KI in the short-wavelengths range (Choe et al. 1989). The low-energy peak of 10KI, originating from Co, decreases continuously with increasing Nd content due to a reduced Co content and spin polarization. A further rise of the Nd content causes a strong reduction of Tc resulting in a strong overall reduction of Tc and the room-temperature spectrum vanishes for x - 0.38 (Tc = 295 K) (Honda and Yoshiyama 1988a,b). A corresponding influence of Nd and Pr was observed for Fe-based alloys (Suzuki et al. 1988). Their spectral variation together with that of other alloys is shown in fig. 92b. A comparison of the other various spectra reveals that the highest rotations in the visible and ultraviolet region can be reached with amorphous N d - F e C o and Pr-FeCo alloys which is of interest for magneto-optical recording operating at short wavelengths. However, the (1) and other rare earths, except for Eu, give rise to very small contributions to axr a~2) x y in the visible due to the large binding energies of the 4f electrons. Also, the

MAGNETIC AMORPHOUS ALLOYS

Photon energy (eV) 1 2 3 L

407

5

-0.1 Tb°'22F e ° ' 6 ~ -0.2

do,2z,Feo.37Co 0.39 -0.3

d -0.4

-0•5

(al I

-0.6

[

1500 700 500 ~k(nm)

0,8

Gdl_xTx T= LOK

x=xO~ ..~ ~"~

..... T= 295K Z 5 8 4

0.6

I

300

)

xJ 0.L

0.2

T=Co (b) 0

5•0

10~0 (nm)

15100

Fig. 91. Wavelength dependence of (a) the room-temperature Kerr rotation for crystalline FeCo and amorphous Tb-FeCo and Gd-FeCo alloys (Weller et al. 1988a,b) and (b) the Kerr rotation for amorphous G d - F e and G d - C o alloys at two temperatures (Hansen et al. 1989).

optical constants are large limiting the attainable Kerr rotation in amorphous R - T alloys (Weller and Reim 1989a). The compositional variation of the Faraday rotation at 2 = 633 nm (1.95 eV) for amorphous R - T alloys with R = Gd or Tb and T = Fe or Co is presented in fig. 93

408

P. HANSEN

TABLE 16 The sign of the Faraday rotation and the polar Kerr rotation in the visible and infrared, assuming the direction of the net magnetization parallel to the applied field. The sublattice magnetizations are aligned antiparalM in the case of heavy rare earths (Gd, Tb, Dy) and parallel for light rare earths (Nd, Pr) as indicated by the arrows. R~ -xT~

R('i~) Gd Tb,Dy

T(T) Fe,Co Fe,Co

R

T

Nd,Pr

Fe,Co

Or

OK

x= 0 Xeomp~ X~ 1 X< Xeomp ~ + 6]" "D~ + "i) + 0~" - / + "ff$

X= 0 Xcomp~ X~ 1 X< Xeomp + 'i) o]" + ~'~ -"D O~" +/-- @~

x~0 +

x=l Q~

+

~

0<x
x=0 -

x=l ~

-

1"

0<x
(Hansen et al. 1989). The compositional compensation [Ms(xcomp)=0] for the different alloys is indicated by the arrows. The low-temperature OF data given in fig. 93a reveal a dilution of the G d contribution for x < 0.5. In this range of compositions, the Co carries no magnetic m o m e n t and the Fe m o m e n t and exchange is small and, therefore, both behave like nonmagnetic elements like Cu or A1, indicated by the crossed symbols. For x > 0.5, the spin polarization and the exchange coupling strongly increases and the rotations from the R and T elements add, giving rise to a strong rise of OF. This supports the picture of two independent sublattice contributions which approximately is valid for this wavelength that is between, and just sufficiently away from, the centers of the R and T transitions. The strong temperature dependence of the magnetic and magneto-optical properties gives rise to a significant change of the compositional variation of OF and OK at high temperature which is shown in fig. 93b. At the R-rich side, the Curie temperatures passing the roomtemperature limit the rotation. For the Fe-rich alloys, the strong turndown of 0v is caused by the low Tc of the possibly speromagnetically ordered Fe-rich R - F e alloys causing the typical m a x i m u m of IOF[ and IOKIaround x ~ 0.75 (Hansen 1987, Hansen et al. 1987, 1989). A similar variation of OK and OF occurs for alloys with R = Dy or Ho and T = Fe or Co (Hansen et al. 1991). The m a x i m u m disappears when Co is added, which raises Tc due to the high C o - F e exchange coupling. A comparison of the high- and low-temperature data suggest that the R contribution is of minor importance at high temperatures. This is confirmed for various amorphous R - C o alloys where the room temperature OK at 2 = 633 nm (1.95eV) was shown to scale well with the Co sublattice magnetization inferred from mean-field results (Honda and Yoshiyama 1988b). These results are displayed in fig. 94 for R -- G d or Dy. A plot of 0K versus x for R = Y, Gd, Tb or Ce also reveals an almost R-independent room-temperature rotation (Choe et al. 1987). The temperature dependence of the Faraday and Kerr rotation is determined by eqs. (87) and (88) where axy (1) and oxr _(2) are proportional to the spin polarization (az) for both interband and intraband transitions. For G d - T alloys, the magneto-optical transitions from the G d and the transition metal can be assumed to be independent because of the 4f and 5d G d electrons and the 3d T electrons form no common band. Then, ( a z ) is proportional to the sublattice magnetization and the combination of

MAGNETIC AMORPHOUS ALLOYS

4~'u+u ~ ~'=~++~ ~_+++++ 0

-0.1

409

Ndl-x Cox

"~:F+I-

/

x=0.66

!

°°°%°Oo.......~0.75

~p

-0,2 oJ

;;; -'. Z / •

-0.3

o

../

-0.4

(o) I

-0.5

I

I

I

I

2 3 4 Photon energy (eV)

1

5

0.1 0 -0.1 ~

~

-0.2

-

.......

~DY

. . . . ~-.~.~---~'='~ ~Tbo.15

;,~--"~-. . . . . . . . . . . . . . . . . . . . . qc~

-0.3

~.-..~ . . . . . .

"

;

'\

•

-0.4 -0.5

-~.~Tbo.22 Feo.Te . . . .

....

__

" ~ . ~

.,I'./

=

--.,~Tb0.,~ Nd0.,0(FeCol

,,,,,~

,,,,,,.,,,,"

~

j ~.I

'Its"/

_

"~."~,~.

\

0.22FeoTa

Tbo.15 Nd020 FeoJ,5sCo 0.195 Ndo.15 Fe0.595Co 0.105

Ndo.z,oFeosl Coo.og Tbo.ts (FeCo)o.Bs

.~Pr o.~,oFeo6o Ndol.o • Coo15Feoz=5

f

./

-0.6

".~..~-'I"

:b) -0.7

I

I

I

I

300

500

700

900

7, (nm)

Fig. 92. Room-temperature Kerr rotation for (a) amorphous N d - F e alloys versus photon energy (Weller et al. 1988a) and (b) for various amorphous R - T alloys versus wavelength (Suzuki et al. 1988).

eqs. (87), (88) with eqs. (89) or (91) yields Ov = AMod(T) + BMTM(T),

(93)

and a corresponding equation for OK. The magneto-optical coefficients A and B in principle are determined by eqs. (87)-(91), but this requires an evaluation of the

410

P. HANSEN

T=Z,.2K

/,

A

E

-o 3 %

co,

~.Z~,.

•

Xeomp

• ".

I

I

I

0,5

I

I

"",

1.0

I

3.5

(b) 3.0

o

T=295K

•

2.5

"E~ 2.0

Gdl-x Fex"-~..~..l~,.-" Tbl_x F e x , ~ ( I~

,o

;// / #

/

I i 0.3

I

I

~

I

I

/ 0.5

II

/'Tb,_xCo,

I'l

/" 0.L

~;~

x°o,,,

I!

II

/TbFe--. /TbCo II 0.6

x

0.7

0.8

0.9

1.0

Fig. 93. Compositional variation of the Faraday rotation/or binary R - T alloys with R = Gd or Tb and T = Fe or Co at (a) T = 4.2 K and (b) T = 295 K (Hansen et al. 1989). (©) Gd-Co, ([]) Od-Fe (Hansen et al. 1989), (0) Gd-Co (Gambino and McGuire 1986), (n) Gd-Fe (Gambino et al. 1986), (1) Tb-Co (McGuire and Hartmann 1985) ( ~ Gd-Cu, (z~) Gd-A1 (McGuire and Gambino 1987a) in fig. (a); in fig. (b), (©) Gd-Co, ([]) Gd-Fe (Hansen et al. 1989), (0) Tb-Fe (Urner-Wille 1981), (1) Tb-Co (Heitmann et al. 1985). The arrows indicate the compensation composition [eq. (59)] of the respective alloys.

MAGNETIC AMORPHOUS ALLOYS 0.5

411

(a)

Gd-Co

0.4

o

"~ 0,3 n~

O__~0.2

0.1 0

I

I

I

400 0.5

I

oZ

I

I

I

800 1200 Mco (kA/rn)

i

1600

(b)

0.4

0,3

0.2

0.1

0

I

0

400

i

I

I

800 1200 Mco (kA/rn)

I

I

1600

Fig. 94. Room-temperature Kerr rotation at 2 = 780rim (1.59eV) versus cobalt sublattice magnetization Mc, for amorphous Gd-Co and Dy-Co alloys (Honda and Yoshiyama 1988b). Me, was inferred from the fit of the mean-fieldtheory to the measured saturation magnetization. respective matrix elements. This problem has not yet been solved and thus A and B have to be regarded as adjustable parameters. The measured temperature dependence of OF at 2 ----633 nm (1.95 eV) was investigated for different amorphous G d - T alloys (Hansen and Urner-Wille 1979, McGuire and Hartmann 1985, Hansen and Hartmann 1985, Hansen et al. 1989) and is shown in fig. 95 for amorphous G d - F e and G d - C o alloys. Both systems exhibit a sign change of Ovat Xoomp,resulting in a different sign of Ovfor Gd-rich and T-rich alloys. The full lines were calculated from eq. (93), where the sublattice magnetizations were inferred from the fit of the measured saturation magnetizations. The good agreement achieved between measured and calculated rotations with temperature-independent magneto-optical coefficients suggests again that the assumption of independent sublattice rotations is a reasonable approach for these alloys. The evaluated sublattice rotations confirm the dominance of the Fe and Co sublattice magnetization at this wavelength and for high temperatures. At low temperatures, the Gd contribution is essential and dominates for Gd-rich alloys as is obvious from fig. 93a. The noncollinear moment distribution of the non-S-state rare earths leads to a reduced sublattice rotation as reported for amorphous T b - C o alloys (McGuire and Hartmann 1986). Various attempts were made to improve the magneto-optical properties by small additions of further elements. The influence of rare earths and transition metals on

412

P. HANSEN

3

~

8

[]

0

Gdl-x Fex - - ca[culoA-ed

5

[]

I

/

[]

I

100

I

I |

200 T(K, 3 ~

II

400

500

_11_

2 Gdl_xCOx - - colcutated T(K) 100 200 300 400 500 600 700

o

I

-2

i

i

i

I

I

I

"0.75 (b)

Fig. 95. Temperature dependence of the Faraday rotation at 2 = 633 nm (1.95 eV) for amorphous (a) G d Fe and (b) G d - C o alloys (Hansen et al. 1989). The full lines were calculated in terms of the sublattice magnetizations [eq. (93)] inferred from mean-field results.

the room temperature OK at 2 = 633nm (1.55eV) is demonstrated in fig. 96 for amorphous Tb-Fe-based alloys (Imamura et al. 1985). The influence of the R additions can be attributed to changes of Tc except for Nd or Pr, giving rise to additional contributions via f ~ d transitions. Many transition metals, such as Ti, V, Cr, Mn and Cu, and metals (A1 and Au) tend to decrease Tc and the spin polarization resulting in a low OK and 0r (Tsujimoto et al. 1983, Aratani et al. 1985, Imamura et al. 1985, McGuire and Hartmann 1985, Hansen and Hartmann 1986) while Co raises Tc and affects the band structure (figs. 60 and 87). Other elements, like Bi, Pb, Sn

MAGNETIC A M O R P H O U S ALLOYS

413

0,30 Tb,Fe)l_x Rx

+

R=Gd

0.25 ~ 0.20

.8 0.15 0.10 0.05 0

Ill)

I

I

r

I

0.30 0.25

,

"-~ 0.20

v

.dc u

.8 ~:~ 0.15 0.10 0.05

(b)

p

,

0.02

0.04

I

I

0.06

0.08

0.1o

X

Fig. 96. Room-temperature Kerr rotation at 2 = 633 nm (1.95 eV) for amorphous Tb-Fe-based alloys with small additions of (a) rare earths and (b) transition metals (Imamura et al. 1985).

(Hansen and Urner-Wille 1979, Urner-Wille et al. 1980, Hartmann et al. 1984b, Masui et al. 1984) or In (Iijima et al. 1989) give rise to a small increase of the magneto-optical properties. Also Ni, Pt (Imamura et al. 1985) and U (Dillon Jr et al. 1987) were studied with respect to their magnetic and magneto-optical properties. The influence on the structural disorder and composition by the preparation parameters gives rise to significant changes of OK and 0V (Sato and Togami 1983, Tsujimoto et al. 1984, Shieh and Kryder 1985, Heitmann et al. 1987b), as expected from the corresponding influence on the magnetic properties.

7. Transport properties 7.1. Resistivity and magnetoresistance Structurally disordered alloys exhibit much larger resistivities than crystalline materials due to different scattering processes reducing the conduction-electron mean free path. The resistivity values for amorphous alloys range typically from 100 to 300 g~ cm. Data for some M-T, R - M and R T alloys with M = Cu or Au and T = Fe, Co or Ni are compiled in tables 17-19. Experimental and theoretical work was discussed in different reviews (Campbell and Fert 1982, Buschow 1984a). The resistivity tensor p couples the components of the electric field E and the

414

P. HANSEN TABLE 17 Resistivity of some amorphous alloys.

Alloy

Magnetic order

Sio.2oPdo.so Lao.76Gao.24 8no.21Feo.79 Sno.59Feo.41* Bio.14Feo.s6 Gdo.26Feo.74 Sno.szCoo.48* Gdo.67Coo.33 Po.26Nio.v6 Tio.52Nio.4s* Yo.oTNio.93 Sno.6oNio.4o Gdo,68Nio.32 Gdo.55Auo.4s GdsoAuo.2o

Diam. Diam. Ferrom. Ferrom. Ferrom. Ferrim. Ferrom. Ferrim. Param. Param. Ferrom. Param. Ferrom. Ferrom. Ferrom.

T(K)

p(gf~ cm)

4.2 4.2 4.2 200 4.2 4.2 200 4.2 4.2 4.2 4.2 200 4.2 4.2 4.2

76 219 120 235 227 274 265 280 162 325 86 140 197 288 312

References K/ister et al. (1980) Shull et al. (1978) McGuire and Hartmann (1985) Geny et al. (1982) McGuire and Hartman (1985) McGuire and Hartman (1985) Geny et al. (1982) Durand and Poon (1977) Cote (1976) Buschow (1983) Cochrane and Str6m-Olsen (1978) Geny et al. (1982) Durand and Poon (1977) McGuire and Hartmann (1985) Cote (1976), Durand and Poon (1977)

* Composition at maximum resistivity.

TABLE 18 Curie temperature Tc, saturation magnetization M s at T = 4.2 K, electrical resistivity, p and Hall resistivity Pn at T = 4.2K for amorphous R Au and R-Cu alloys (McGuire and Gambino 1979, McGuire et al. 1980a). Alloy

Pro .47Auo.s3 Ndo,385Auo.615 Smo,43Auo.57 Euo.2oAuo.so Gdo.537 Auo.463 Tbo.47 Auo.53 Dyo,46 Auo.s4 Hoo.4.,Auo.56 Ero.s8 Auo.42 Tmo.62Auo.38 Pro .4oCuo .6o Ndo.44 Cuo. 56 Gdo.42 Cuo.58

Tbo.503Cu0.497 Dyo,4s Cuo.55 HooA.4Cuo.56 Ero.s2 Cuo.49 Tmo.61 Cuo.39

Tc

Ms

(K)

(kA/m)

T = 4.2 K

T = 297 K

< 4.2 10

127 159 48 302 401 748 812 74 787 636 183 238 1180 621 1020 939 668 812

167 230 173 213 205 190 132 93 191 194 86 114 176 147 141

168 234 177 198 210 197 138 95 199 207 82 116 175 151 145 220 178 159

< 4.2 99 > 4.2 15 11 9.5 < 4.2 < 4.2 77 23 16 8 < 4.2

p(p~ cm)

176 149

PH (gf~ cm) 0.96 2.24 0.83 0.30 - 5.66 - 1.27 - 0.40 -0.30 - 0.03 --0.09 0.43 2.07 - 1.96 - 0.26 0.15 0.45 0.52 0.31

MAGNETIC AMORPHOUS ALLOYS

415

TABLE 19 Electrical resistivity and Hall resistivity Pn for amorphous R-T alloys.

Y1 - xFex Y~ _xCox Yz _~Nix Gd 1_xFe~

(Gdo.26 Feo. 74)0.89 BioA1 Gd t _~,Co:,

x

T (K)

p (g~ cm)

0.71 0.75 0.67 0.936 0.83 0.74 0.79 0.734

77 77 77 4.2 4.2 4.2 77 77 4.2 77 77 77 77 77 4.2 4.2 4.2 4.2 295 77

226

0.84 0.82 0.79

GdoA45 Coo.72MooA] Gdo.19Coo.7oAuoAo Gda _xNi~

0.84 0.64 0.59 0.40 0.75 0.67

Tba _xFex Hol _xCox

* References: [1] yon Molnar et al. (1981). 1-2] Asomoza et al. (1977b). [3] McGuire and Gambino (1978). [4] McGuire and Hartmann (1985).

244 140 90 274 195 211 400 141 162 250 172 138 152 400 197 245 200

P, (gfl cm) 4.22 4.4 3.3 -1.42 -0.33 - 11.5 11.25 - 11.6 -22.0 4.1 -4.6 -5 -1.4 -4.3 0.88 0.37 -0.19 -2.28 11.0 -3.2

Ref.* [1] [2] [1] 1-3] [3] [4] [1] [1] 1-4] [1] [1] 1-5] I-1] [1] I-6] 1-6] [6] 1-6] [7] [2]

[5] Shirakawa et al. (1976). 1-6] McGuire and Gambino (1978). 1-7] Malmh/ill (1983).

current density J by E = par. The components of p depend on B = # o ( H + M) due to the Lorentz force and scattering mechanisms. For an isotropic medium in a magnetic field applied to the z direction, p can be expressed in the form

P=

H

Pi

0

0

Pll

,

(94)

where P ll and p± are the resistivities for the electrical current applied parallel and perpendicular to the direction of magnetization. Both can be split into a spontaneous or extraordinary part and an ordinary part. The off-diagonal element PH is the spontaneous or extraordinary Hall resistivity. The average resistivity for an disordered material than is given by j0 = ~Pll-t1 ~z p ± ,

(95)

where iS(T, 0) = p(T). The magnetoresistance describes the change of the resistivity by the applied m a g -

416

P. HANSEN

netic field. The isotropic and anisotropic part of the magnetoresistance thus can be expressed by Api(T,/-/) = ~(T, H) - ¢5(T,0),

(96)

Apa(T, H) = [Pll (T, H) - p±(T, H)].

(97)

Apart from the high resistivity, some further characteristic features of amorphous alloys were observed. A very low temperature dependence of p at H = 0 was found with Ap/p(O)= [ p ( T ) - p(O)]/p(O) below 10% for 0 ~ T ~<300 K. Many alloys exhibit a low-temperature resistivity minimum with a large logarithmic upturn as shown in fig. 97a for PBA1-Fe and PBA1-FeNi glasses (Rapp et al. 1978). This temperature behavior was also found for FeNi-based alloys (Babi6 et al. 1978, Steward and Phillips 1978, Rao et al. 1979), Co-based alloys (Cochrane et al. 1975, Marzwell 1977, Rao et al. 1979) or Ni-based alloys (Cochrane et al. 1975, Berrada et al. 1978, Cochrane et al. 1978a,b). It is very similar to that observed for Kondo systems involving spin-flip scattering of the conduction electrons on localized magnetic inpurities as demonstrated for amorphous Pd-Si alloys containing Cr, Mn, Fe or Co impurities (Hasegawa and Tsuei 1971a,b). However, the presence of this upturn in nonmagnetic amorphous alloys like La0.66Alo.34 (Mueller et al. 1980) and the field independence of the logarithmic resistivity found for many alloys suggest that this behavior originates from a nonmagnetic mechanism. A model treating the electron scattering in terms of a two-level system (Cochrane et al. 1975, Tsuei 1978) or by tunneling (Anderson et al. 1972) leads to a temperature dependence of p of the form p(T) = p(O) + c In 1 +

,

(98)

where A is the mean value of the energy separation between the two levels. This logarithmic temperature dependence predicted by eq. (98) is confirmed in several amorphous alloys such as La-A1 (Mueller et al. 1980), P-Co, P-Ni (Cochrane et al. 1975, Cochrane and Str6m-Olsen 1977, Berrada et al. 1978), Y-Ni (Cochrane et al. 1978a,b) and Tb- or Pb-based alloys (Cornelison and Sellmyer 1983), while the agreement with experimental results with other theoretical treatments (Kondo 1976, Black and Gyorffy 1978) yielding a (ln T) 2 dependence is less satisfactory. For amorphous G d - C o alloys, only the low-temperature range can be described by eq. (98) (Okuno et al. 1981). A further feature is a maximum of the resistivity and a minimum of the temperature coefficient c~= (1/p)dp/dT occurring in the compositional variation. This is shown in fig. 97b for amorphous Sn-Fe (Geny et al. 1982) and was also reported for Sn-Cu (Korn et al. 1972), Sn-T with T = Fe, Co or Ni (Geny et al. 1982), Sn-Au (Blasberg et al. 1979), Ti-Ni (Buschow 1983) and Hf-Ni (Buschow and Beekmans 1979b). In many alloys, the maximum cannot be observed due to the limited glass-forming range. These concentration dependencies of p and c~are commonly encountered in liquid alloys suggesting that there exists a close similarity in the resistivity behavior between amorphous and liquid alloys (Gfintherodt et al. 1978, Geny et al. 1982). These results

M A G N E T I C A M O R P H O U S ALLOYS /Po z~ ~xa'-~axa '16 Bo '06 A[O '03 Feo,75

417

A z~

144,4 00(300000 O0

1/,/*.3

" •14.4.2

162.1

A

A

0000 Az~

162.0

z~

O~Oo ,xA

",

oo

161.9 "~

:& o

o.. 1/.4,1

%

161.8

o

j Oo

2I

Po.15 B 0.oe A[o.o3 Feo, 60 Ni0.1s S I

14/*.0

o

g- 161.7

o

o oo %~6

(a) I

1/.3,9 0,01

o.,

0.1

I

I

1.0 T(K)

10

' 161.6 100

40

250 p

20

20C

02"-

15C

,,? o

o, 100

50

-20

J

-40

(b) I

0.5 X

-60 1.0

Fig. 97. (a) Resistivity versus T (logarithmic scale) for amorphous PBA1-Fe and PBA1-FeNi alloys (Rapp et al. 1978). (b) Compositional dependence of the average resistivity and the resistivity coefficient at T = 200 K for S n - F e alloys (Geny et al. 1982).

suggest that the theoretical model for liquid metals (Ziman 1961, Faber and Ziman 1965) based on the nearly free electron model and the Boltzmann transport equation should be extendable to the amorphous alloys (Cote 1976, Nagel 1977, Cote and Meisel 1977, Esposito et al. 1978). This theory relates p to the resistivity structure factor which relates its maximum at q = ~ 2kF where q is the electron scattering vector and kF the Fermi wave vector. This maximum of the structure factor also determines that of p and the minimum of a. These theoretical considerations are in

418

P. HANSEN

qualitatively agreement with the experimental results and accounts for the different resistivity behavior of related alloys. The compositional variation of the resistivity for R-Feo.50Coo.o5 alloys (Weller and Reim 1989) is presented in fig. 98. A significant anisotropy of the resistivity was reported for amorphous Au-T alloys with T = Fe, Ni or Co (Bergmann and Marquardt 1978) and Co-based alloys (Shiba et al. 1986). Another reason for the occurrence of a temperature resistivity minimum was associated with the onset of magnetic ordering and was ascribed to coherent exchange scattering by the rare-earth spins (Asomoza et al. 1977a,b, Fert et al. 1977). This model predicts a resistivity CJpm [ 1

(99)

P = J + 1 L + cm(2kF)],

where Pm is the maximum resistivity and c the concentration of magnetic atoms. m(2kF) is the spin correlation function. The first term on the right-hand side represents the contribution from the scattering of each atom. The second term is proportional to the number of pairs and arises from coherent exchange scattering. In amorphous alloys, only the spin correlations between neighbor sites contribute to m(2kF) and, thus, the resistivity resulting from this process is controlled by the local magnetic order. In this case where the magnetic order is of longer range than the structural order, m(2kF) can be expressed by (Fert and Asomoza 1979) m(2kF) = [a(2kF)- 1]j 2,

(100)

250 []

o

[3

200

E

150

o C:~

[]

o_ 100 •

Tb

+

Tm

.: \

50

hi 0,20

I

0.4.0

I

!

0.60

0.80

1,00

x

Fig. 98. Room-temperature resistivity versus composition for amorphous R-FeCo alloys prepared by sputtering (Weller and Reim 1989a).

MAGNETIC AMORPHOUS ALLOYS

419

where j2 = (Ji" Jk )/j2 describes the local magnetic order and a(2kv) is the structure factor. The low-temperature resistivity upturn and thus the occurring minimum of p is caused by the competition between elastic exchange scattering and inelastic spinflip processes. A resistivity minimum due to magnetic ordering was observed, e.g., for amorphous R-Ni alloys (Fert et al. 1977, Asomoza et al. 1977a, Fert and Asomoza 1979) or U T alloys with T = Fe, Ni, Gd, Tb or Yb (Freitas et al. 1988). As an example, the results for amorphous Dy-Ni (Asomoza et al. 1979a, Fert and Asomoza 1979) are shown in fig. 99. The resistivity upturn at low temperatures thus can be explained assuming m(2kv) to be positive, i.e., a(2kv)> 1. The isotropic part of the magnetoresistance is displayed in fig. 100 for amorphous Dy-Ni and turns out to be positive in accordance with eq. (100) for a(2kv) > 1 and j > 0. The much smaller anisotropic part of the magnetoresistance is presented in fig. 100b. This anisotropy was ascribed to the quadrapole moment of the rare earth (Fert and Asomoza 1979, Asomoza et al. 1979a). The magnetoresistance was found to be positive for Dy-Ni, Ho-Ni (Asomoza et al. 1979b) and Ce-Co (Felsch et al. 1982) and negative for Er-Ni (Asomoza et al. 1979b) and DyGd-Ni (Amaral et al. 1988). Amorphous R - U with R = Gd or Tb reveal a sign change of Ap with temperature (Freitas et al. 1988). Below the spin-freezing temperature, an increasing portion of antiferromagnetic interactions become important, leading to a negative magnetoresistance according to eq. (100) with (Ji',lrk) < 0 in contrast to amorphous U - F e with collinear or random ferromagnetism where Ap > 0 due to a positive <Ji. Jk>. The latter is in agreement with results for amorphous Si-Fe (Shimada and Kojima 1978). Also, a negative magnetoresistance was observed in the spin-glass-like amorphous D y - U and N d - U systems (Freitas et al. 1988).

297 296

o

Dy0.2s N i 0 . 7 / /

29/. 295 ~

~ ~ 6

:zl. ~o.. 293 292

~0 kA/m

"et~z/"'-. ~ '2/.00 kA/m •" ~'H= 0 kA/m

~,.+'

291 "" Tc /

290

~ 0

q 20

i /*0

T(K}

t 60

i 80

100

Fig. 99. Temperaturedependenceof the resistivityfor amorphous Dy-Ni at differentmagneticfields(Fert et al. 1977, Asomozaet al. 1977a,b, 1979b).

420

P. HANSEN 2.5

(a} Dyo.25 Nio.75

2.0 /H=2400 kA/m 1600 k A / m 640 k A / m

1.5 C~

~1.0

0.5

I

20

10

30

40

T(K) (b)

T=I.2K 4.2 7.0 10.0

D Yo.25Nio.75 3.0

15.0 <~2.0 o

".4"

•

•

~,

25.0

•

1.0

30.0 40.0

'

0

0.5

r

1.0

1.5 H(106A/m)

I

I

2.0

2.5

Fig. 100. (a) Isotropic magnetoresistance versus temperature for amorphous Dy-Ni at different magnetic fields and (b) anisotropy of the magnetoresistance for different temperatures for amorphous Dy-Ni (Asomoza et al. 1979a,b, Fert and Asomoza 1979).

7.2. Hall effect The Hall resistivity is determined by the off-diagonal elements of the resistivity tensor and is composed of the ordinary and the spontaneous or extraordinary part. PH thus can be expressed by PH = #o(RoH + RsMs).

(101)

Ro is the ordinary and Rs the spontaneous Hall coefficient. The ordinary Hall effect arises from the Lorentz force acting on the moving electrons, and the spontaneous Hall effect is caused by asymmetric scattering of the conduction electrons by the magnetic atoms via skew scattering (Smit 1955, 1958, Fert and Friedrich 1976) or side jumb scattering (Berger 1970, 1972, 1973) with contributions proportional to p

M A G N E T I C A M O R P H O U S ALLOYS

421

and p2, respectively. Thus, Rs can be expressed by (Majumdar and Berger 1973) (102)

Rs = ap + bp 2,

where a and b are constants. The spontaneous contribution usually dominates in amorphous alloys. Typical values for Gd, evaluated from amorphous G d - M alloys with M = Cu, Au (McGuire and Gambino 1979, Gambino et al. 1981, McGuire and Gambino 1987a) or M = Ge (Gambino and McGuire 1983) are Ro = -0.03 I~)cm/T and Rs = 5 ~f)cm/T. For alloys with Ro ~ R~, the Hall resistivity is proportional to the saturation magnetization, which implies the presence of a Hall hysteresis corresponding to magnetization or magneto-optical measurements. This is displayed in fig. 101 for amorphous Gd-Au and G d - F e alloys (McGuire et al. 1977), demonstrating that pn is negative for the Gd spin parallel aligned to the applied field. The study of amorphous R-Cu and R-Au alloys reveals a positive PH for light rare earths and a negative PH for the heavy rare earths, which is shown in fig. 102. This suggests that the spontaneous Hall effect is correlated to the rare-earth spin. In the case of the heavy rare earths, the spin and orbital moments are parallel aligned to the applied magnetic field while for the light rare earths the spin moment is oppositely aligned to the magnetic field due to their antiparallel coupling. This is in accordance with the side jumb scattering process which is proportional to the conduction electron polarization caused by the rare-earth spin. Amorphous Fe-based (Shimada and Kojima 1978, Stobiecki and Kowalski 1984, McGuire and Hartmann 1985), Co-based (Asomoza et al. 1977b, McGuire et al. 1980a, Shiba et al. 1986) and Ni-based (McGuire and Gambino 1978, McGuire and Taylor 1979) alloys exhibit a positive spontaneous Hall effect. This is in agreement with T-rich G d - T alloys as reported for G d - F e (McGuire et al. 1980a, Stobiecki and Kowalski 1984, Honda et al. 1985), Gd-Co (Ogawa et al. 1975, Asomoza et al. 1977b, Okuno et al. 1981, Stobiecki and Kowalski 1984) and Gd-Ni (Mimura et al. 1976a, McGuire and Gambino 1978, McGuire and Taylor 1979, Asomoza et

-£ O

0

-2

-4

-8

-1,s -1'.o -o'.s

015 H (106A/m]

1.~0

1.5

Fig. 101. Hall resistivity at T = 4.2 K as a function of applied magnetic field for amorphous G d - A u and G d - F e alloys (McGuire et al. 1977).

422

P. H A N S E N 12 10 8

f\

6

°52

R-Cu

0 -2 -4 -6 Ce Pr Nd PmSm Eu Gd Tb Dy Ho Er Tm Yb R Fig. 102. Tangent of the Hall angle at T = 4.2 K and H = 1.6 × 106 A/m for a m o r p h o u s R - C u and R - A u alloys (McGuire and G a m b i n o 1979).

al. 1979b). The results for some of the one-subnetwork alloys identify the side jumb scattering as the dominant mechanism controlling the spontaneous Hall effect. This is demonstrated in fig. 103 displaying the room-temperature spontaneous Hall coefficient as a function of resistivity for various amorphous M-Co alloys. The logarithmic plot reveals a p 2 dependence of Rs (Shiba et al. 1986, Jen and Yang 1988), as predicted by the side jumb process. Similar results are obtained for amorphous GdAu alloys (Gambino et al. 1981). For two-subnetwork R-T alloys, the resistivity dependence of Rs indicates that the skew scattering mechanism is also of importance (Fert and Friedrich 1976, 1977, Lachowicz 1984). Heavy rare-earth-transition-metal alloys exhibit a magnetic compensation. Thus, compositions with x < Xcomv show a sign of change of Pn as compared to those with x > Xcompdue to the reversed direction of the sublattice magnetizations which also applies when passing through the temperature compensation. These results suggest that the spontaneous Hall effect can be composed in analogy to the magneto-optical properties by an R and T contribution leading to the equation Pn = fro(Roll + RsT MT + RsR MR).

(103)

Combining eqs. (10 l) and (103) yields for the spontaneous Hall coefficient of binary alloys R~ =

R~T MT + R~R M R ,

(104)

[M R -- MT[

which indicates that R~ undergoes a singular behavior at the compositional or temperature compensation and is observed for different R-T alloys, and shown for

MAGNETIC AMORPHOUS ALLOYS

5

m

M1-xC°x 3 1 E 0.5 :& 0.3

423

/,,

¢

t3

[] •

/

0'1~o 0.05

/

/

/'~

o

•

/

A

:

M=Y

Hf Zr Ta

Nb

0'03 F 10

I

I

[

30 50 100 p (/.l,~ cm)

I

300

Fig. 103. Logarithmic plot of the spontaneous Hall coefficient as a function of the resistivity at room temperature for various amorphous Co-based alloys (Shiba et al. 1986). The full line represents a p2 dependence.

amorphous Gd-Co alloys in fig. 104. The spontaneous Hall effect of R-T alloys thus can be considered as the sum of the R and T contribution, because in the case of heavy rare earths the positive T contribution and the negative R contribution add due to the antiparallel alignment of the R and T sublattice and in the case of light rare earths both R and T contribution are positive and are also additive due to the parallel alignment of the sublattices. This behavior corresponds to that of the Faraday sublattice rotations. This aspect was discussed for various R-T alloys (McGuire and Hartmann 1985, McGuire et al. 1986, McGuire and Gambino 1987a,b). The linear relation between 0v and the Hall angle OH= arctan(pn/p) is presented in fig. 105 for amorphous R - M alloys with M = A1, Cu or Au (McGuire and Gambino 1987a). 8. Technological applications

8.1. Metallic glasses The class of amorphous M - T alloys with M = B, P, C, A1 or Si and T = Fe, Co or Ni have received much attention with respect to their favorable properties concerning various commercial applications such as power supplies, transformers, magnetic sensors and transducers, magnetic heads, magnetic shielding or magnetometers (Luborsky et al. 1978, Boll et al. 1983, Mohri 1984, Moorjani and Coey 1984, Hilzinger 1985, Fish and Smith 1986, O'Handley 1987a, Hilzinger 1990). Generally, these alloys are characterized by a high electrical resistivity, high mechanical strength,

424

P. HANSEN

60 Gdl_xCOx

40

°o oo

o

20

:&

o

0

-20 -40 -60 /

-80 0.60

I

I

0,70

I

Xcomp

I~

0.80

I

i

0.90

t

1.00

X Fig. 104. Compositional dependence of the spontaneous Hall coefficient at T = 295K for amorphous G d - C o alloys (McGuire et al. 1980a). 4

3

R°'6°M°'40

R=N..~d /

er......_/E~ 2

E

Z

Dy~/8° I

0

-2

Tb...~

-1

0

1

OH(deg} Fig. 105. Faraday rotation at 2 = 633nm and T = 1.6K as a function of the Hall angle for amorphous R - M alloys with M = A1, Cu or Au (McGuire and Gambino 1987a).

good corrosion resistance, the absence of crystalline anisotropy, structural defects and grain boundaries due to the noncrystalline state. The magnetic properties such as saturation flux density, Curie temperature, magnetostriction and induced anisotropy can be controlled by the alloy composition and a subsequent temperature

MAGNETIC AMORPHOUSALLOYS

425

treatment. The Fe-rich alloys exhibit the highest saturation flux density and the Cobased alloys are characterized by low magnetostriction, very high permeabilities and low magnetic losses (Yagi et al. 1988). The high electrical resistivity and the small thickness of the melt-quenched ribbons lead to low eddy current losses. In combination with the low hysteresis losses, this results in very low core losses which is of interest for power electronics at high frequencies (Pfeifer and Kunz 1982, Boll and Hilzinger 1983, Lupi 1988). Magnetic core materials for transformers operating at frequencies above 20 kHz require low power losses and a high flux density to achieve a high output power (Grfitzer 1978). Disadvantages arise from the lower attainable induction of metallic glasses (Luborsky and Johnson 1981) as compared to the grain-oriented Si-Fe and from the lower packing factor of the core material. Metallic glasses were also utilized in particle accelerators (Birx et al. 1983, Raskine and Smith 1983) and for pulse compression systems to obtain high-power pulses (Chu et al. 1982, Pacala et al. 1984, Smith 1988). Materials for magnetic heads need a high saturation flux density, a high magnetic permeability, thermal stability and a good resistance to wear and corrosion. Amorphous Co-based alloys are attractive candidates for this application (Takahashi et al. 1983) and are used to manufacture audio heads for tape recorders. Another field of application for amorphous alloys are sensors and transducers (Mohri 1984) utilizing primarily the low coercivity of nonmagnetostrictive alloys for magnetometer applications or the stress dependence of the hysteresis loop in magnetoelastic sensors for displacement, stress or torque measurements. The small eddy current losses of the ribbons permit to operate the magnetometers at frequencies above 100kHz, leading to designs with small coils, low power consumption and a quick response (Mohri 1983). The combination of favorable mechanical and magnetic properties of metallic glasses has led to the development of magnetoelastic transducers. The stress-induced anisotropy K~ = -~-o-2s gives rise to a strong influence on the permeability and the hysteresis. This can be used to design force and displacement transducers using a single amorphous core multivibrator with a DC output (Mohri and Sudoh 1981). Other transducer designs provide a high linearity (Meydan and Overshott 1982), magnetic torque transducers offer the possibility of a rapid and contactless response and low magnetostriction amorphous alloys permit the development of high-frequency transducers. Metallic glasses are also suitable soft-magnetic materials for magnetic shielding due to their high permeability which applies primarily for Co-based alloys like (MoSiB)o.aoFe0.04Coo.66 (Boll and Borek 1980, Warlimont and Boll 1982). Such alloys are insensitive to strain and shock and reveal better shielding factors at low fields than crystalline materials.

8.2. Magneto-optical recording 8.2.1. Storage principle The structural disorder in magnetic alloys has generated a number of interesting features which can be tailored for different applications. The amorphous rare-earth-

426

P. HANSEN

transition-metal films deposited by magnetron sputtering represent a suitable class of materials for magneto-optical information storage and, therefore, these materials have received much attention in the past decade. The magneto-optical recording represents one of the most advanced storage techniques (Hartmann et al. 1984a, Imamura et al. 1985, Kryder 1985, Meiklejohn 1986, Connell 1986, Hansen and Heitmann 1989, Hansen 1990, Klahn et al. 1990b). It combines the merits of magnetic and optical techniques. The optical disk systems offer the unlimited cyclability of the magnetic media, contactless write, erase and read operations, high storage capacity and removability of the optical disk. This has led to strong efforts concerning the tailoring of the amorphous R-T alloys and with respect to the development of optical recorder with polarization sensitive detection. At present, amorphous R-T alloys of general composition GdTb-Fe, Tb-FeCo and Dy-FeCo are the most promising candidates for magneto-optical storage. They fulfill all requirements concerning the magnetic and magneto-optical properties and with respect to those imposed by the recording system. The thermomagnetic switching process is based on a few simple principles. The write/erase process utilizes the temperature characteristics of the magnetic properties where the temperature profile of the coercivity plays a dominant role. A typical temperature variation of the coercive field Hc is sketched in fig. 106 (Hansen 1987, Hansen and Witter 1988, Craseman et al. 1989). In the room-temperature range, the high Ho fixes any domain configuration, while at temperatures above T~ the material becomes magnetically soft permitting to orient the direction of magnetization parallel to that of an applied magnetic field Hs. This different behavior at room temperature and at high temperatures is reflected by the corresponding magnetic hysteresis loops

T=295K

300

30 . . . . . . . . .

J.......

29s

_N~-ILls ÷H s l \

t t5~o &To

T(K)

Fig. 106. Schematic representation of the temperature variation of the coercive field for an amorphous rare-earth-transition-metal alloy. The material changes from a magnetically 'hard' state around room temperature to a magnetically 'soft' state at high temperatures where the direction of magnetization can be reversed by weak switching field H s as indicated by the hysteresis loops.

M A G N E T I C A M O R P H O U S ALLOYS

427

also shown in fig. 106. The temperature rise can be achieved with a laser beam heating the film locally as sketched in fig. 107. The maximum temperature reached in the magneto-optical film is determined by the thermal constants of the total film stack and the laser pulse energy. The indicated asymmetry of the temperature profile results from the disk velocity. The writing process is performed either by laser modulation at constant magnetic field or by field modulation at constant laser power. The latter permits direct overwrite but is limited in the switching frequency to the range <10 MHz due to the operation margins of the coil generating the magnetic field. The information thus obtained is stored by magnetic domains. Their size is determined by the temperature profile and is typically of the order of 1 ~tm. The written domains can be imaged by Lorentz microscopy (Suits et al. 1986, Rugar et al. 1987, Suits et al. 1987, 1988, Ichihara et al. 1988a,b, Greidanus et al. 1989a,b,c, Zeper et al. 1989a,b), scanning electron microscopy (Aeschlimann et al. 1990) or by magnetic force microscopy (den Boef 1990, Rugar et al. 1990) which is shown in fig. 108 for domains written by laser modulation and field modulation. The domains in fig. 108c (left) indicate the accurrance of subdomains. Reading of the stored information is performed utilizing the magneto-optical Kerr effect that represents the rotation of the plane of polarization of linearly polarized light as a function of the direction of magnetization when reflected at the surface of a magnetic material. Thus, the written information can be read using polarization optics detecting the difference in polarization of the reflected light for the two possible directions of magnetization in a uniaxial material with respect to the film normal. Some further aspects are discussed in section 8.2.5 in connection with the optical recorder.

objective

~ ~ t

,e o+

,/n li

(

.O-,oye

II

d°moir~-~+l I ~reftective watt H,~--.~ I- -I - - I - -I---,~.---.~ foyer I'~++/I ~ I I l~,~l .F~'+++..J J i i t l . / " ' - J

coit/r-~--l-]

~-1~m-~:

',/3', position Fig. 107. Principle of thermomagnetic writing or erasure. The magneto-optical layer is locally irradiated by a laser beam reducing the coercivity in the heated volume according to fig. 106, and the magnetization can be switched by an external magnetic field.

428

P. HANSEN

(Ct)

'

' 5,u,m

(b)

(c} '

(d)

'

" 5/~m

J 1.5 ,u,m

....

5,u,m

Fig. 108. (a), (b) Magnetic domains in amorphous GdTb-Fe films imaged by Lorentz microscopy (Greidanus et al. 1989a,b). The domains in (a) were written by laser modulation at different magnetic fields. The laser power was 6.8mW and the linear disk velocity 2.1 m/s. The pulse frequency was 1 MHz and the pulse time 400 ns. The domains in (b) were written by field modulation at different frequencies: The laser power was 3.7 roW, the linear disk velocity 0.5 m/s and the applied field 24.7 kA/m. (c) The domains in the Tb-FeCo films were imaged by magnetic force microscopy (den Boer 1990). The domains were written by laser modulation. (d) Domains in a Co/Pt multilayer imaged by Lorentz microscopy (Greidanus et al. 1989c, Zeper et al. 1989a,b).

8.2.2. Material selection The write a n d r e a d processes are b a s e d on a n u m b e r of magnetic, m a g n e t o - o p t i c a l a n d o p t i c a l p r o p e r t i e s which have to be well c o n t r o l l e d to meet the r e q u i r e m e n t s i m p o s e d o n the m a g n e t o - o p t i c a l material: of a uniaxial m a g n e t i c a n i s o t r o p y with a positive a n i s o t r o p y constant, Ku, with Ku > ~1 t o M s ,2 . large r o o m - t e m p e r a t u r e coercivity to p r o v i d e a high d o m a i n stability a n d s t o r a g e density; a Curie t e m p e r a t u r e r a n g i n g between 400 K <~ T < 550 K; - p r e s e n c e

-

-

MAGNETIC AMORPHOUSALLOYS

429

-squareness of the hysteresis loop in the high-temperature range to guarantee perfect switching characteristics; -high optical absorption, ~, to produce a sufficiently high local temperature rise; - high figure of merit RO 2 (R = reflectivity); - long-term stability. There are many magnetic materials fulfilling some of these requirements but at present there are only the amorphous R-T alloys and to some extent also a few magnetic oxides (Abe and Gomi 1987) and Pt-Co multilayers (Zeper et al. 1989a,b, Greidanus et al. 1989c, Hashimoto and Ochiai 1990) satisfying all these requirements together with some additional conditions inferred from the recording system. As discussed in sections 5 and 6, the magnetic and magneto-optical properties can be well controlled by the composition and the deposition parameters. A high uniaxial anisotropy can be obtained in Tb-containing alloys (fig. 66b). The presence of Tb induces also a sufficiently high coercivity (fig. 78b) and the films are characterized by a good squareness of the hysteresis loops. The Curie temperature for Co-rich alloys is too high (fig. 57) while that for Tb-Fe alloys is too low. However, in the latter case, small additions of Co can be used to control Tc where Tc is increased by roughly 7 to 10 K per at.% Co depending on the R-Fe alloy. The presence of a compensation temperature used to optimize the temperature profile of Hc can be adjusted for R1-xTx alloys by the ratio (1 -x)/x. The optical absorption in metals is very high and, thus, the local heating using a laser leads to no principal problems. The optical Kerr rotation is not large but the figure of merit R02 is sufficient to reach good read-out characteristics. An optimal set of magnetic and magneto-optical parameters thus can be achieved for ternary GdTb-Fe, Tb-FeCo or Dy-FeCo alloys. The high corrosivity of these alloys requires a protection against air and can be achieved by suitable coatings as outlined in section 8.2.4.

8.2.3. Thermomagnetic switching process The storage of information in amorphous alloys is based on thermomagnetic writing and erasure. They are primarily controlled by the laser-induced temperature profile, the radial and time dependence of the magnetic properties and the domain nucleation and domain-wall motion (Heitmann et al. 1985, Kryder 1985, Imamura et al. 1985, Connell 1986, Hansen and Heitmann 1989, Hansen 1990). The understanding of the thermomagnetic switching process involves the treatment of three basic problems: (i) the solution of the equations of heat conduction for a multilayer structure leading to the temperature distribution in the magneto-optic films; (ii) the calculation of the temperature and radial dependence of the relevant magnetic parameters for ternary or quarternary alloys; and (iii) the investigation of the conditions for domain-wall stability (Huth 1974, Mansuripur and Connell 1983, 1984, Mansuripur 1987, Hansen 1987, 1988b, McDaniel and Mansuripur 1987, Nagato et al. 1988, Takahashi et al. 1988, Sato et al. 1988a,b, Suits et al. 1988). The basic requirement for thermomagnetic switching is the presence of a uniaxial anisotropy with Ku >~poMs 1 2 and of sufficiently high coercivity to guarantee high stability of any magnetization configuration at room temperature. Only then two

430

P. HANSEN

stable directions of M, parallel and antiparallel to the film normal, occur which is necessary to represent the two logical states '0' and '1'. The formation of a magnetic domain in the presence of an applied field then is possible at temperatures close to Tc where Hc is low (figs. 80 and 106). The size and shape of the domain is controlled by the driving force F = -~E/~R, where E is the total energy and R the position of the domain wall. F can be expressed in the form F -- IF~ + FD + Fwl - Fno,

(105)

where Fn, FD, Fw, Fn~ are the forces associated with the field energy, demagnetizing energy, domain-wall energy and the coercive energy. The forces are functions of the radial profile and thus depend on the temperature. They can be expressed for the case of cylindrical symmetry by (Huth 1974, Hansen 1987, 1988b)

Fn = -T- 4rcohRHoMs(R),

(106a)

Fno = 4ZC#ohRHc (R)Ms(R),

(106b)

Fw = 2nh[aw(R) + R~aw(R)/~R],

(106c)

FD

=

- -

47r/2ohRMs (R)/Td(R).

(106d)

Hd(R) is the z-averaged demagnetizing field and in general requires numerical computation (Huth 1974, Suits et al. 1988). An analytical expression for/Td(R ) can be obtained using a rough approximation where the radial dependence of Ms(R) is replaced by its average value M(R) (Hansen 1987, 1988b). The Ha(R) can be written in the form /qd(R)= ffls(R)f(R, rwoomp, h) where f(R, rr . . . . , h) can be expressed in terms of elliptic integrals. Ho, h, R, r and rTcom p a r e the applied magnetic field, the film thickness, the domain radius, the radial coordinate and the compensation temperature radius [Ms(rrcomp)=O], respectively, r r . . . . appears explicitly in f(R, rrcomp, h) only for films with T~omp above ambient temperature, T~. The - and + sign in eq. (106a) refer to writing and erasing, respectively. Domain expansion occurs for Fn + FD + Fw < 0 and domain contraction for Fn + FD + Fw > 0, provided F > 0. The laser-induced temperature profile T(r) causes a strong radial dependence of M s, K,, He and aw and thus also with respect to the force balance. The general problem of the calculation of the temperature distribution in a stack of layers can be solved numerically (Mansuripur et al. 1982, Bartholomeusz 1989, Holtslag 1989). However, for R-T-coated films also an approximation can be used treating layers with similar thermal behavior as one effective layer. This model yields the relation (Holstslag 1989)

r(r) = T~ + A(t) exp(-- r2/r2), (107) where t is the pulse duration, rt = ~ o + x t, ro the radius of the laser beam and the diffusivity of the effective layer. From eqs. (106) and (107), the radial dependence of the forces acting on the domain wall can be calculated where the radial dependence of aw can be obtained combining eqs. (105), (106) and (107) and using the sublattice magnetization inferred from mean field results. A typical variation of the forces as a function of the wall position is shown in fig. 109 for a GdTb-Fe alloy with T~omp

MAGNETIC AMORPHOUS ALLOYS

Sf '-

1.0

O. 5

// E o

431

J'0.2

/t fJ R{,~m) / O.Z,

0.6~

0.8

~.

~ f eff

o

R=r./cr ~% ~ o,5

1.0

\

.

\

.

.

/

.

J

"• ~"' fH ~fHe !

Fig. 109. Radial dependence of the reduced forces f = F/4~h 2 acting on the domain wall, where h is the film thickness. The written domain radius R is determined by the coercive radius rno obtained from the

condition feff (r//°) = ff/c (rH¢) where feff =ftt + fo + fw.

above room temperature. The laser beam diameter is 1 ~tm and the maximum temperature in the spot center is slightly higher than the Curie temperature. Thus, the material is paramagnetic for radii smaller than the radis rrc where the Curie temperature is reached. The forces represented in fig. 109 are normalized according to f - F/4~h 2. During writing, the stable domain radius is reached at the coercive radius R = r~c defined by F(rnc) = 0. At this radius, the effective force Feff = Fn + FD + Fw driving the domain wall is balanced by the coercive force F~o. For a rotating disk the domain length can be approximated by

L = 2rno + vt,

(108)

where v is the linear disk velocity of typically 5 m s 1 and t is the pulse duration of 30 to 50ns. This leads to a domain length of 1 gm for the case presented in fig. 109. When the laser is switched off, the heated spot cools down very rapidly and the domain is frozen due to the increasing coercivity. The magnetization in the unheated region remains undisturbed. The erase process can be considered as the reversed writing process with the opposite direction of the applied magnetic field. The optimum write/erase conditions are mainly determined by the magnetic field, the compensation temperature and the Curie temperature where the latter has to be adapted to the available laser power. Strong deviations from this ideal switching behavior can result from different sources such as local material inhomogeneities, effects on submicron scale, fluctuations of the focussing and tracking system, laser-induced thermal fluctuations, etc. In particular, the occurrence of subdomains as shown in fig. 108c or irregular shaped domains as reported for Tb-Fe and Tb-FeCo films (Suits et al. 1987, 1988, Greidanus et al. 1989b) require a different model of domain formation in terms of the nucleation field present (Suits et al. 1987, 1988).

432

P. HANSEN

8.2.4. Magneto-optical disk The amorphous R - T films are preferentially prepared by magnetron sputtering, yielding dense films at high sputtering rates without substrate cooling (Klahn et al. 1990a). However, the bare films are not sufficiently stable in air and thus need a protection which can be achieved by a suitable coating. A typical film stack is sketched in fig. 110. It consists of a pregrooved PC or glass substrate, an antireflective dielectric layer (80 nm), the magneto-optical layer (45 nm), a reflective metal layer (30 nm) and finally a protective polymer layer (some I~m). The pregroove structure serves for tracking. From accelerated life tests with disks of this type of multilayer structure, life times of more than 10 years were extrapolated (Klahn et al. 1987). However, the multilayer structure serves also for an enhancement of the carrier-tonoise ratio which requires a proper adjustment of the thicknesses of the intermediate antireflective and the magneto-optical layer. Finally, the switching sensitivity depends on the thermal constants of the different films and thus the stack additionally has to be optimized in this respect. Therefore, deposition processes for the different layers have to be well controlled to reach optimum switching characteristics and to keep the raw byte error rate below 10 .4 to 10 -5. The error correction codes and interleaving reduce the byte error rate to a level of 10 -16 to 10 -17. Direct overwrite capability is a further requirement for many storage applications. Magnetic field modulation is one possibility (Tanaka et al. 1987, Nakao et al. 1987, Ando et al. 1988, Miyamoto et al. 1989) to solve this problem. However, the switching power and a suitable spacing between disk and coil limits the modulation frequencies below 10 MHz. Therefore, direct overwrite methods operating without a modulated magnetic field are of interest. Different techniques have been reported (Osato et al. 1987, Schultz and Kryder 1989, Schultz and Kryder 1990), but further development seems to be necessary to fulfill the present recording requirements. 8.2.5. Recorder requirements A magneto-optic recorder is very similar to other optical disk systems as, e.g., a digital audio compact disc unit (Carasso et al. 1982, Deguchi et al. 1984). However, laser beam

magr Fig. 110. Cross section of a magneto-optical disk with a pregrooved substrate.

MAGNETIC AMORPHOUS ALLOYS

433

in the read-out light path, polarizing optical elements have to be added. Furthermore, in a magneto-optic recorder differential detection of the polarization direction has to be applied (Hartmann et al. 1985a), as sketched in fig. 111. The light emitted from a laser, L, is collimated to a parallel beam which passes two neutral beam splitters, NBS, and is focussed onto the disk, Di, by an objective lens of numerical aperture, NA = 0,5. The light reflected from the disk is deflected by the beam splitters to the detection arrangement and to the tracking and focussing circuitry, Tr, Fo. The detection arrangement consists of a polarizing beam splitter, PBS, which splits the light into two perpendicularly polarized components that are detected by PIN photodiodes, D1 and D2. Their output is connected to a differential amplifier. The 2/2 waveplate is used to adjust the bias level of the differential detection circuit to a minimum by setting the azimuth of the polarization plane to 45 ° with respect to the characteristic beam splitter axes (see insert). The modulation of the azimuth due to the Kerr rotation _+OK produces amplitude variations between A~ and Ai- and A + and A2 at the diodes D1 and D2, respectively. The coil, C, provides magnetic fields for thermomagnetic switching. To compete with other magnetic recording systems, the magneto-optical system has to fulfill the following requirements: -high storage density; -low access time; -high write and erase sensitivity; - l o w switching field; -high carrier-to-noise ratio; - l o w bit error rate; -direct overwrite capability. The tailoring of these recording parameters, improvement of the bit error characteristics (Yamamoto and Yamada 1988) and the understanding of their relation to the magnetic and magneto-optical properties are key aspects in the sussessful develop-

/x;:i [ T,Fo II/I

D

Di

Fig. 111. Differential detection arrangement for magneto-optical recording (Hartmann et al. 1984a). (L) laser, (Di) magneto-optical disk, (D1) and (D2) PIN photodiodes, (C) coil, (NBS) beam splitter, (PBS) polarizing beam splitter, (Tr), (Fo) tracking and focussing. The modulation of the azimuth due to the Kerr rotation produces amplitude variations between A 1,2 + and A~2 at the diodes Dx and D2, respectively.

434

P. HANSEN

ment of the magneto-optical system. Recorder measurements performed for various disks based on GdTb-Fe and Tb-FeCo films reveal a characteristic dependence on the magnetic parameters (Crasemann et al. 1989, Crasemann and Hansen 1989) which can be interpreted in terms of the switching model outlined in one of the previous sections. An example is displayed in fig. 112 showing the decrease of the domain length, L, with increasing Tc at constant laser power. The full line was calculated from eqs. (105) and (106) using an average radial coercivity profile. The scatter in the data primarily has to be associated with the different T~ompvalues of the films. Some typical data for a magneto-optical disk are compiled in table 20. With these material data, the magneto-optical technology offers a wide field for applications such as the data storage, digital audio recording or video recording. Also, the magneto-optic system is expected to be a good candidate as a multipurpose recording system due to its large storage density and relatively short access time.

1'65[ L • 1,4~-~

• •

oOo" " .o

i:2t 400

o Tb-FeCo • GdTb-Fe ~theory

o ,

420

440

/.60 Tc[K)

ooO

, 480

,\ 500

520

Fig. 112. Domain length as a function of Curie temperature at a writing field of 16kA/m and writing energy of 0.6nJ/pulse (Crasemann et al. 1989, Crasemann and Hansen 1989).

TABLE 20 Typical performance data of a magneto-optical disk (Hansen 1990). Alloy Write power (50 ns pulse) Erase power (CW) Read power Write/erase field Archival life CNR Bit size (recording density) Track width (track density) Speed Capacity (5¼ inch, per side) Access time (average latency) Transfer rate

Tb-FeCo, GdTb-Fe, Dy-FeCo <10mW <10mW ~<1mW 16-32 kA/m >10 years >50dB (1 MHz, 30kHz bandwidth) 1.0-1.5 pm ( ~ 25000 bpi) 1.6 pm ( ~ 17000 tpi) 220 rpm 500 MByte (3 x 10v bit/cm2) 44ms (14ms) 1.1 MByte

MAGNETIC AMORPHOUS ALLOYS

435

9. Summary The structural disorder of magnetic M-T, M - R and R - T alloys (T: magnetic transition metals, R: rare earths, M: not T and R) gives rise to significant changes of the mechanical, electrical, magnetic and magneto-optical properties as compared to the crystalline counterparts. Although it is not yet possible to explain many properties in terms of the relevant band structure of amorphous alloys, many new concepts and theories were generated and an overwhelming amount of experimental work was performed, leading to new physical insights concerning the atomic structure and short-range order, the relation between chemical bonding and magnetism, magnetic structures, anisotropic magnetic properties and transport properties on the one hand and the development of materials with a unique combination of properties on the other hand which makes these alloys attractive for a variety of applications. Generally, amorphous Fe-based alloys behave differently from Co- and Ni-based alloys due to their stronger (sp)-d hybridization and weaker covalent p - d bonding, resulting in broader valence bands. Also, they exhibit a sensitive dependence of the exchange coupling on the atomic distance, leading even to antiferromagnetic bonds for Fe-Fe distances below 0.25 nm. The distribution of atomic distances inferred from the radial distribution function suggests the presence of a concentration-dependent portion of negative exchange interactions. Thus, various amorphous M1-xFex alloys show noncollinear magnetic structures, and for M = Zr, Hf, Y, La, Ce or Lu even speromagnetic or spin-glass-like behavior occurs with a tricritical point for x ~>0.9 and Curie temperatures ranging between 100 and 200K. In amorphous M - C o alloys, small Co-Co distances are favorable for the magnetic moment formation and tend to increase the exchange interaction and thus Tc. Therefore, amorphous Co-based alloys are predominantly strong ferromagnets, although significant differences in the magnetic properties are observed for Co-based alloys containing metalloids or other elements. The magnetic moment variation was interpreted in terms of the magnetic valence model or the environment model. In both cases, the experimental data were well described for certain classes of alloys. Most transition-metal-metalloid alloys exhibit good corrosion resistance, high electrical resistivity, good mechanical properties and are soft-magnetic materials. Ferich alloys exhibit the highest saturation flux density, and the Co-based alloys show low magnetostriction, high permeabilities and very low magnetic losses. These properties make various magnetic glasses attractive candidates for commercial applications such as power supplies, transformers, sensors, transducers, magnetic heads, magnetic shielding or magnetometers. Amorphous rare-earth-transition-metal alloys reveal pronounced differences in their magnetic properties as compared to M - T alloys due to the different electronic structure of the rare earths and the presence of two magnetic sublattices formed from elements of different groups. The negative exchange coupling between the 5d rareearth electrons and the 3d transition-metal electrons leads to a parallel alignment of the R and T moments for the light rare earths and an antiparallel alignment for the heavy rare earths. A further difference in the amorphous R - T alloys with respect to M - T alloys is the strong influence of the structural disorder on the local direction

436

P. HANSEN

of the R moments which are coupled via the strong spin-orbit coupling to the randomly varying axes of the electrostatic field. This leads to sperimagnetic structures except for the Gd (S-state) based alloys exhibiting ferrimagnetic order. Amorphous R-Fe and R-Co alloys reveal the same differences as observed for M - F e and M Co alloys. Fe-rich R-Fe alloys exhibit a very low Tc, below 200 K, due to competing positive and negative exchange interactions. Therefore, all Rl_~Fex alloys show a maximum in the concentration dependence of Tc around x ~ 0.7, followed by a strong turndown of Tc at large x, in contrast to R-Co alloys revealing a steep increase of Tc for alloy compositions with x above the critical composition. Amorphous R-T alloys containing non-S-state rare earths are characterized by strong uniaxial anisotropies and high coercivities but low magnetizations in the case of sperimagnetic order. The presence of a compensation temperature for the antiferromagnetically coupled alloys gives rise to strong influences on the temperature and the concentration dependence of the magnetic, magneto-optical and transport properties. Amorphous R-T alloys also show a large extraordinary Hall effect arising from side jumb and skew scattering processes. The favorable magnetic and magneto-optical properties have led to the development of GdTb-Fe, Tb-FeCo or Dy-FeCo alloys for magneto-optical data storage. References Abe, M., and M. Gomi, 1987, J. Magn. Soc. Jpn. 11, Suppl., p. 299. Aboaf, J.A., and E. Klokholm, 1981, J. Appl. Phys. 52, 1844. Aeschlimann, M., G.L. Bona, F. Meier, M. Stamponi, A. Vaterlaus, H.C. Siegmann, E.E. Marinero and H. Notarys, 1988, IEEE Trans. Magn. MAG-24, 3180. Aeschlimann, M., M. Scheinfein, J. Unguris, F.J.A.M. Greidanus and S. Klahn, 1990, J. Appl. Phys. 68, 4710. Aharony, A., 1962, Rev. Mod. Phys. 34, 227. Alameda, J.M., Y. Berthier, F. Briones, M.C. Contreras, D. Givord, A. Li6nard and H. Rubio, 1985, J. Magn. & Magn. Mater. 54-57, 233. Aldred, A.T., 1975, Phys. Rev. B 11, 2597. Aldred, A.T., and P.H. Froehle, 1972, Int. J. Magn. 2, 195. Alfonso, C.N., A.R. Lagunas, F. Briones and S. Gir6n, 1980, J. Magn. & Magn. Mater. 15-18, 833. Algra, H.A., K.H.J. Buschow and R.A. Henskens, 1980, J. Physique 41, Suppl. C8-646. Allen, R., and G.A.N. Connell, 1982, J. Appl. Phys. 53, 2353. Alperin, H.A., J.R. Cullen and A.E. Clark, 1976, AIP Conf. Proc. 29, 186.

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chapter 5 MAGNETISM AND QUASICRYSTALS

R. C. O'HANDLEY, R. A. DUNLAP* and M. E. McHENRYt Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139, U.S.A.

*Permanent address: Department of Physics, Dalhousie University, Halifax, Novia Scotia, Canada B3H3J5. tMST-6, Los Alamos National Lab, Los Alamos, NM 87545 U.S.A. Permanent address: Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213 U.S.A.

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991 453

CONTENTS 1. ] r t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. G e r e r a l b a c k g r o u n d . . . . . . . . . . . . . . . . . . . . . . . . 1.2. H i s l o r i c a l b a c k g r o u n d . . . . . . . . . . . . . . . . . . . . . . . 2. ~[heoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. C l u s t e r t e c h n i q r es . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. P o i n t - g r o u p s y m m e t r y c c n s l d e r a t i o n s . . . . . . . . . . . . . . . . 2.1.2. s - p r r e t a l cluslers . . . . . . . . . . . . . . . . . . . . . . . 2.1.3. T r a n s i t i o n - m e t a l clusters . . . . . . . . . . . . . . . . . . . . 22. Polytope techniques . . . . . . . . . . . . . . . . . . . . . . . . 2.3. H a m i l t o n i a n t e c h n i q u e s o n q u a s i l a t t i c e s . . . . . . . . . . . . . . . . . 24. Global manifestatiors of icosahedral s3mmetry . . . . . . . . . . . . . . . 3. Al-lzased q u a s i c r y s t a l s . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. A 1 - M g - Z n a n d A 1 - C u - L i q t a s i c r y s t a l s . . . . . . . . . . . . . . . . . 3.1.1. A t o m f c s t l u c t u r e . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. E l e c t r o n i c s t I u c t u r e . . . . . . . . . . . . . . . . . . . . . . 3.2. S l r u c t u l e o f A l - t r a n s i t i o n - m e t a l q u a s i c r 3 s t a l s . . . . . . . . . . . . . . . 3.3. F a r a m a g n e t ! c q u a s i c r 3 s t a l s . . . . . . . . . . . . . . . . . . . . . . 3.3.1. A 1 - T . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. A 1 - T - S i . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2.1. A 1 - M n - S i . . . . . . . . . . . . . . . . . . . . . . 3.3.2.2. A I - ( M n , V ) - S i . . . . . . . . . . . . . . . . . . . . . 3.3.2.3. A I - ( M n , £ r ) - S i . . . . . . . . . . . . . . . . . . . . . 3.3.2.4. A I - ( M n , F e ) - S i . . . . . . . . . . . . . . . . . . . . . 3.3.3. A I - ( M n , C r ) - G e . . . . . . . . . . . . . . . . . . . . . . . 3.3.4. A 1 - T 1 - T 2 . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4.1. A 1 - C u - F e . . . . . . . . . . . . . . . . . . . . . . 3.3.4.2. A 1 - M o - F e . . . . . . . . . . . . . . . . . . . . . . 3.3.4.3. A 1 - T a - F e . . . . . . . . . . . . . . . . . . . . . . . 3.4. F e n o m a g n e t i c q u a s i c r y s t a l s . . . . . . . . . . . . . . . . . . . . . . 3.4.1. A 1 - M n - S i alloys . . . . . . . . . . . . . . . . . . . . . . . 3 . 4 2 . A 1 - M n - G e a r d r e l a t e d alloys - . . . . . . . . . . . . . . . . . 3.4.3. A 1 - F e - C e a l l o ) s . . . . . . . . . . . . . . . . . . . . . . . 4. Q u a s i c r y s t a l s n o t b a s e d c n A1 . . . . . . . . . . . . . . . . . . . . . . . 4.1. T i - N i b a s e d qua~,:'¢rystals . . . . . . . . . . . . . . . . . . . . . . 42. Other quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . 5. C o n c l u s i o n s a n d o u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

454

455 455 456 459 460 461 462 465 467 467 470 472 472 472 472 475 476 476 479 479 481 482 4~4 485 487 487 488 4c~0 4c~2 4~c2 496 5(0 .'01 501 5(3 5£4 5£6

1. Introduction

1.1. General background Quasicrystals (QCs) are a new phase of condensed matter whose structures differ from those of either crystals or glasses (Shechtman et al. 1984, Nelson 1985, Steinhardt 1987). QCs exhibit long-range orientation order that is incompatible (e.g., five-fold) with periodic crystallographic packing in three dimensions (three-dimensional packing admits of two-fold, three-fold, four-fold and six-fold rotations). This nonclassical orientation order can only be accomodated in three dimensions by allowing for two sets of reciprocal lattice vectors of incommensurate length (Levine and Steinhardt 1984). The ratio of the lengths of these vectors for icosahedral QCs (five-fold symmetry) is given by the golden ratio • = ½(1 + 5l/z) = 1.618 .... an irrational number. These reciprocal lattice vectors, or the basic structural units they define, occur in the structure in a quasiperiodic sequence determined according to certain matching rules. Reviews of the structure of QCs can be found in the articles by Henley (1986a), Janot and Dubois (1988a,b) and Egami and Pooh (1988). Three-dimensional QCs have been discovered which exhibit five-fold symmetry (icosahedral QCs) (Shechtman et al. 1984) and two-dimensional QCs with eight-fold (octahedral QCs) (Wang et al. 1987) and ten-fold (decagonal QCs) (Bendersky 1985, Chattopadhyay et al. 1985, Fung et al. 1986) orientational order have been observed. Other orientational orders are possible. What is important about icosahedral structures from a magnetic point of view is that they allow for more symmetry operations than do cubic structures. This has been shown to have important implications for crystal-field effects and moment formation on a local scale and for domain-wall symmetries on a long-range scale. With the discovery of icosahedral quasicrystals [i-QCs] in A186Mn14(Shechtman et al. 1984), Pd6oU2oSizo (Poon et al. 1985), A1-Cu-Li (Knapp and Follstaedt 1985), Ti-Ni-Si (Zhang et al. 1985) and many other nonmagnetic or weakly magnetic alloys systems, a torrent of studies aimed at elucidating the structure and properties of quasiperiodic materials has appeared. For the most part, these new QC structures are metastable phases that are generally produced by rapid solidification or by some other nonequilibrium processing methods such as energetic particle-beam bombardment (Budai and Aziz 1986), solid-state reaction (Follstaedt and Knapp 1986, Knapp and Follstaedt 1986), and, in some cases, thermal transformation from an amorphous precursor (Lilienfeld et al. 1985), and mechanical alloying (Eckert et al. 1989). Upon 455

456

R.C. O ' H A N D L E Y ET AL.

further heating, metastable QCs transform to stable crystalline phases. Figure 1 schematically illustrates that the free energy of a given alloy composition decreases through a series of stable or metastable phases as the order increases from a shortrange orientational order in amorphous metallic phases via a long-range orientational order and quasiperiodic translational order in quasicrystals and finally to a longrange orientational and translational order in crystalline alloys. Experimental evidence exists for many quasicrystals which confirms the free energy relationship Gcrys < GQC< Gglass. It is now possible to make quasicrystals in the A16 Lia Cu (Dubost et al. 1986), GaMg2.1Zn3 (Ohashi and Spaepen 1987) and A1-Cu-Fe (Tsai et al. 1987) systems which are absolutely stable, i.e., GQc < Gcrys.

1.2. Historical background Before the discovery of quasicrystals, the influence of icosahedral symmetry on material properties was not often considered, due to the perceived incompatability of long-range icosahedral order and space filling. This tenet of classical crystallography did not, however, diminish the interest in (distorted) icosahedral units as important constituents in the structure of many metallic alloys. As early as 1952, Frank calculated the total energy of an icosahedral arrangement of atoms (see fig. 2), interacting through a Lennard-Jones pair potential, and found (Frank 1952) it to be lower than either fcc or hcp 13-atom configurations. It is through the notable structural stability of icosahedral units that Frank and Kasper (1958) have sought to understand the details of many complex alloy structures, particularly those of rareearth-transition-metal intermetallics. The frequency of occurrence of icosahedral arrangements in these Frank-Kasper phases appears to be related to the lower

t O~ c

~crysta~' • "

~

/ Crystal

Order

Fig. 1. Schematic of the free energy of the amorphous, quasicrystalline and crystalline states as a function of increasing order. Some quasicrystals (broken line) are absolutely stable relative to the crystalline state.

Fig. 2. Icosahedral cluster of spherical atoms at the vertices of an icosahedron.

MAGNETISM AND QUASICRYSTALS

457

energy of this configuration and to the fact that, since the coordinating atoms are equidistant from the central atom at a distance slightly larger than the vertex-tovertex distance, they may more easily deform radially to comply with the coordination requirements of peripheral atoms (Samson 1965). The latter reason is also a manifestation of the larger number of symmetry-lowering distortions available for this highsymmetry group. The lower energy found by Frank (1952) for icosahedral units supported his assertion that icosahedral coordination might prevail in densely packed liquid phases and that the stability of these icosahedral arrangements may indeed account for the large amount of supercooling possible in many transition-metal liquids. This demonstrated local stability of the icosahedron and its presumed importance in liquidmetallic phases leads naturally to the suggestion of icosahedral short-range order existing in amorphous metallic phases. There is a rich amount of recent literature in which evidence of local icosahedral order in amorphous phases has been inferred from the results of molecular-dynamic simulations. In 1978, Briant and Burton proposed a model of the amorphous state as containing a large proportion of 13atom icosahedral units (Briant and Burton 1978). Before this model, the two general models advanced to explain the structure of the amorphous state were the dense random packing of hard spheres (Bernal 1965) and the microcrystalline model of Wagner (1969). The choice of Briant and Burton of icosahedral units was in part motivated by Frank's observations, but was also due to the strong similarity of calculated interference functions for icosahedral microclusters and those experimentally derived for many amorphous metallic alloys. Hoare (1978) summarized the state of affairs in soft-sphere, dynamic models of packing and structural specificity. In his work, he describes the results of dynamical simulations of simple atomic systems using pair potentials in either molecular dynamics or Monte Carlo simulations. Application of these models to slow cooling of isolated clusters of atoms, modelling liquid droplets, reveal interesting structural motifs based on larger icosahedral units which are dubbed amorphons. Many of these motifs are either superstructures or substructures of the 54-atom Mackay icosahedron (Mackay 1952). This structure is built up from the icosahedral cluster (fig. 2) by adding one atom over (radially outward from) each of the twelve icosahedral (vertex) atoms and placing 30 atoms directly over each of the 30 icosahedral edges. The Mackay icosahedron has also found utility in describing the local structure of the ~-A1-Mn-Si phase which has been suggested as a possible precursor of the quasicrystalline phase in A1-Mn and A1-Mn-Si (Guyot and Audier 1985, Henley 1985), see section 3.2. The results of Briant and Burton (1978) were amplified by Steinhardt et al. (1981), whose molecular-dynamics simulations of supercooled liquids revealed long-range, orientational order but no translational order. Haymet (1983), who has used these results in a mean-field theory of freezing, suggested that glass formation in simple substances may be due to supercooling of the liquid into a region where the diffusion constant is so small that thermal fluctuations cannot disturb aligned regions of local icosahedral symmetry. Haymet also offered the additional interesting result that for any purely repulsive potential of the form U(r)= ea"r-", where r denotes the inter-

458

R.C. O'HANDLEYET AL.

atomic distance and e and a are empirical parameters, the icosahedral 13-atom cluster always provides the lowest total energy compared with the 13-atom fcc and hcp clusters. This important generalization of Frank's proof for the Lennard-Jones potential to a more general class of potentials further substantiates the stability of icosahedral units. In recent years, various icosahedral clusters have been examined to understand the structure of metallic glasses. It was also of interest to reconcile the apparent incompatibility of local icosahedral units with periodic or other space-filling schemes. It has been shown by Sadoc and Mosseri (1984) that a four-dimensional space can be tiled perfectly by regular tetrahedra while maintaining Ih symmetry. Several schemes for projecting out of this four-dimensional space into three dimensions while maintaining local icosahedral packing units have been proposed. These schemes have had noticeable success both in yielding densities similar to those observed in metallic glasses and in reproducing significant features in the interference functions for metallic glasses. Sachdev and Nelson (1985) have developed a Landau description of shortrange icosahedral order in metallic glasses based on a projection from this ideal curved space icosahedral crystal. The projection introduces frustration in the resulting three-dimensional structure due to the incompatibility of the curved-space crystal with the flat-space into which it is projected. The disorder which this projection induces has been described in terms of tangled arrays of Frank-Kasper disclination lines. The resulting density correlation function provided an excellent fit to experimental values determined for vapor-deposited amorphous metals. Another interesting parallel path for the study of icosahedral symmetry has been in the study of boron and carbon chemistry. The early work of Longuet-Higgins and de Roberts (1955) identified symmetrized linear combinations of atomic s and p orbitals for an uncentered icosahedron. Their calculations revealed that this configuration offered particular stability if 12 covalent bonds were formed between the icosahedron and its neighboring atoms and 26 valence electrons were left to fill the bonding molecular orbitals inside the icosahedron [this is the origin of the famous 2N + 2 rules for icosahedral stability (Eberhardt et al. 1954)]. This result was used to interpret the crystal structure of elemental boron, in which B12 icosahedra are known to pack in a large rhombohedral unit cell, as well as the B4C structure in which these icosahedra are again important structural units. The importance of this work was not only in establishing a valence-electron concentration criterion for the stability of the icosahedral configuration, but also in establishing how icosahedral units can pack to form an extended solid (albeit not maintaining global icosahedral symmetry). The work of Longuet-Higgins and de Roberts (1955) was preceded by that of Eberhardt et al. (1954), who considered the stability of many of the hydrides of boron including the icosahedral B12H11 configuration. Subsequent work by Hoffman and Lipscomb (1962) and Hoffman and Gouterman (1962) involved factorization of the secular equation and crystal fields in polyhedral molecules including those in icosahedral or dodecahedral configurations. In a more recent work, the stability of icosahedral gold clusters has been examined by Mingos (1976) using molecular-orbital calculations. The prediction of stable Au13 clusters has been experimentally confirmed in Au complexes by Briant et al. (1981).

MAGNETISM AND QUASICRYSTALS

459

A stable Sc13 cluster has been suggested by results of ESR measurements of Scx in neon matrices by Knight et al. (1983), and theoretically by the self-consistent-fieldscattered wave [SCF-SW] calculations by Salahub (1986). The stability oficosahedral alkali metal clusters was predicted by Fripiat et al. (1975), who used the SCF-SW method to calculate the electronic structure. The experiments of Shechtman et al. (1984), demonstrating long-range icosahedral symmetry in rapidly solidified Ala6Mn14, brought a new interest in icosahedral symmetry and produced a torrent of studies aimed at elucidating the structure and properties of quasiperiodic materials. Clearly, there has been an expansion in the range of compositions through which the QC state is accessible and progress in understanding the atomic (section 3.2) and electronic structures (section 2) of these new phases. At the same time, a rapid growth in the varieties of magnetic behavior which they exhibit has occurred: Curie paramagnetism, temperature-independent paramagnetism and paramagnetism with positive or negative linear dependence of susceptibility on temperature (Pauli-like), diamagnetism, spin-glass behavior (section 3.3), and ferromagnetism (secion 3.4). The ferromagnetism observed in QCs so far is remarkable for its small magnetization, its large high-field susceptibility and the comparatively high Curie temperatures observed in some QC compositions given their small transition-metal content. In some respects, the young history of magnetic QCs parallels that of the early development of amorphous (a) metallic alloys (O'Handley 1987). The first materials to be made in these new structures were generally only weakly magnetic: a-Au-Si, a-Pd-Si, vis-a-vis i-A1-Mn(-Si). Then came a period of exploration of dilute transition metal (T) substitutions to study virtual-bound states and local moment formation: a-Pdso_xFex-Si2o vis-a-vis i-Als6Mn~4_xT~. Finally, with the ineluctable growth in understanding of phase formation and processing, ferromagnetic phases were produced: a-Fe-P-C, a-Co-P and a-Fe-B vis-a-vis i-A15sMn2oSi25, i-A1-FeCe and i-A1-Mn-Cu-Ge. At this juncture, QC phases do not yet have the same attractive mechanical and technical magnetic properties that sustained the scientific interest in metallic glasses. What they lack presently in technical potential, they make up for in unusual magnetic behavior and scientific challenge. Whether or not magnetic QCs move beyond this point remains to be seen. 2. Theoretical studies

The theoretical study of the electronic structure of quasicrystals has to a certain extent been limited by inadequate knowledge of the structure at an atomic level. Further, the absence of traditional Bloch periodicity in these materials rules out the use of some of the most powerful theoretical techniques in elucidating solid-state electronic structure. Nevertheless, progress has been made using several techniques which probe features of the electronic structure which result directly from local icosahedral symmetry. These techniques include a variety of cluster methods and effective medium calculations. Another general avenue used to understand the electronic structure of quasicrystals has been the construction of simple Hamiltonians

460

R.C. O'HANDLEYET AL.

which exploit quasiperiodic tilings of one, two and three dimensions by the Fibonacci two- and three-dimensional Penrose lattices, respectively. The methods employed have been of necessity schematic, e.g., tight-binding Hamiltonians for noninteracting electrons, the philosophy being to identify topologically induced features in the electronic structure which are expected to persist qualitatively (even in higher spatial dimensions) when more realistic computational techniques are used. Various important issues relating to the electronic structure of quasicrystals have been addressed, including: (1) stability of various atomic configurations; (2) the density of electronic states, in particular the density of states at the Fermi level D(EF) and its connection with transport and magnetic properties; (3) localization of states by local symmetries and/or by nonperiodic lattices and potentials; (4) resonant scattering, especially by transition metals in the structure as well as the connection between these resonant states and local moment formation; (5) topological features in the chemical bonding induced by the icosahedral symmetry; (6) magnetic moment formation and its dependence on the local symmetry. In the next sections, we explore the status of these issues grouping the review and discussion according to techniques which address the influence of icosahedral symmetry on local properties, such as cluster and effective medium techniques, and those which consider quasiperiodicity and lattice properties and their influence on electronic structure. A final section discusses the influence of global icosahedral symmetry on collective magnetic and superconducting properties.

2.1. Cluster techniques While a comprehensive characterization of the electronic structure of a three-dimensional quasicrystal comparable to state-of-the-art band structure calculations is not yet feasible, inroads have, nevertheless, been made by considering features in the electronic structure resulting directly from local icosahedral symmetry. Among the more common methods used to address the influence of icosahedral symmetry on the electronic structure has been cluster calculations using a variety of techniques for solving the Hamiltonian. Examination of clusters of various symmetries allows for comparison of the relative stability of these arrangements. These calculations directly address the influence of icosahedral symmetry on the local stability of configurations which model fragments of the solid state. Features of the real-space chemical bonding can be assessed as well as gross features of the density of states. These calculations offer the merits of computational simplicity as well as the ability to model noncrystallographic arrangements of atoms. When clusters are used to infer properties of extended systems, it is extremely important to assess the convergence of these properties with cluster size. Further, the influence of the free-surface boundary conditions on inferred properties needs also to be examined.

MAGNETISM AND QUASICRYSTALS

461

2.1.1. Point-group symmetry considerations A very basic understanding of the implications of icosahedral symmetry on electronic structure comes from a cursory discussion of icosahedral group theory and its implications for state splittings or degeneracies and crystal-field effects. McHenry et al. (1986a), and McHenry and O'Handley (1988) have discussed the ramifications of potentials with icosahedral symmetry on the splitting of atomic-like states. Unlike any of the crystallographic point groups, the icosahedral group has irreducible representations of dimension greater than three, namely the four-dimensional gu and five-dimensional hg representations. As shown in fig. 3, these higher-dimensional representations carry important implications for the splitting of spherical harmonics associated with d and f orbitals in an icosahedral crystal field. This figure shows the progressive lifting of the degeneracy of d and f states upon reduction of the crystalfield symmetry. Notable is the fact that the five-dimensional hg representation has as its basis the five d orbital spherical harmonics, meaning that d orbital degeneracy is not lifted by icosahedral symmetry. Further, the f level degeneracy is split into the four-fold gu and the three-fold tzu representations which again is unlike any crystallographic splittings. It is also worth noting that in Frank-Kasper phases, e.g., icosahedral coordination is a likely configuration for transition metals. On the other hand, larger rare-earth metal ions are rarely seen to be icosahedrally coordinated. Several effects of icosahedral site symmetry which are of specific importance to a consideration of magnetic properties, which include the following. (1) Reduced crystal-field splitting may leave the d and f levels more closely spaced in energy and, hence, gives rise to sharper peaks and deeper valleys in the density of states, D(E). (2) As a consequence of (1), the d and f levels would be more spatially localized than in conventional crystalline materials. (3) Magnetic anisotropy is a result of a local moment sensing, via a spin-orbit or spin-spin interaction, the crystal field of its environment (Kanamori 1963). This local anisotropy is balanced against the exchange interaction to determine whether the relevant symmetry in determining the anisotropy is the long-range (quasi)crystallographic symmetry or the local site symmetry (Imry and Ma 1975, Albert et al. 1978a,b, Callen et al. 1977). We expect local effects such as spin-orbit interaction to be enhanced for atoms in an Ih symmetry. This in turn will affect magnetic anisotropy. (4) The presence of sharp peaks in D(E) means that the Fermi energy can lie in a region of much enhanced state density (i.e., near a sharp peak) or in a region of much SYMMETRY sphericot icosahedra[ cubic atomic level

(T} . . . . .

(4} . . : 2 ~ _ <--

tetragona[ [2) t2)

t~

{21. . . . . . (5)

~5~.--'"

...... .....

Ill {11 {21

Fig. 3. Effect of lowering symmetry(spherical, icosahedral, cubic, tetragonal) on the five-folddegenerate d state and the seven-folddegenerate f state. Degeneraciesof states are given in parentheses.

462

R.C. O'HANDLEY ET AL.

depleted state density (i.e., near a deep valley). Thus, the value of D(EF) is a sensitive function of the chemical composition of alloy. The Stoner criterion is the well-known condition for local moment formation,

I(EF)D(EF) > 1,

(1)

where I(Ev) is the Stoner exchange integral evaluated at EF. This implies that local moment fluctuations at an icosahedral site could be either stabilized (>11) or destabilized (~<1) depending on the value of D(EF). It is worth noting that the above-mentioned consequences (1)-(4) of large degeneracies in an icosahedral crystal field apply not only to icosahedral QCs, but also to crystalline alloys with appreciable fractions of icosahedral sites. Further, these effects are a result of using the icosahedral point-group symmetry to block diagonalize solutions to the Schr6dinger equation. On the other hand, if the icosahedral double group is employed, both p and d orbitals can be split due to spin-orbit interactions (Ramos et al. 1987) as follows, p(tlu)-~ Pl/2 (e2u) + P3/2(qu),

(2)

d(hg) --~ d3/2 (qg) + ds/2(Ig),

where the representations on the left-hand side are from the Ih point group and those on the right are for the Ih double group. The p, d subscripts for the double group representation reflect the j quantum numbers for the irreducible representation and imply splitting of the d states by spin-orbit interactions. Ramos et al. 0987) have also obtained Ih-symmetrized molecular-orbital solutions of the relativistic, selfconsistent field direct scattered wave method for an Au13 cluster. For this cluster with large spin-orbit interactions, a 2.2 eV splitting of the two d-subbands was calculated. These results are of importance in that the calculated D(E) was directly compared with those obtained by photoemission studies for icosahedral Au clusters, on various substrates, and shown to reproduce many experimental spectral features.

2.1.2. s-p metal clusters The electronic structures and wave function topologies of cluster eigenstates have been calculated for A113, A133, MnA112, and MnA132 clusters in icosahedral symmetry (McHenry et al. 1986a), using the self-consistent field, scattered-wave technique [SCFX~-SW] with the X~ local density functional (Johnson 1975). These particular clusters were chosen to represent the local icosahedral symmetry of extended A1 and A1-Mn alloys. The premise for such calculations is that the important features of the electronic structure are determined primarily by the local environment and, therefore, are modelled to a good approximation by calculations on locally occurring units with representative symmetries. It is possible that cluster calculations do not overemphasize the importance of icosahedral site symmetry because only one atom in each cluster experiences such symmetry. The Alia and A133 clusters are comprised of a single A1 atom coordinated by icosahedral arrangements out to first and second nearest neighbors, respectively. These clusters exhibit several important features.

M A G N E T I S M A N D QUASICRYSTALS

463

(1) An energetically favorable shift is calculated for the manifold of electronic states for Ih Al13 as compared with similar octahedral clusters (Salahub and Messmer 1977) (fig. 4). The entire In manifold of occupied states is shown to be shifted by ~0.06R~ below those of the Oh cluster. (2) The envelope of the state density follows D(E), which is proportional to E" for an icosahedral cluster. As shown in fig. 5, D(E) shows a larger average value than the n = ½ dependence observed for the free-electron-like fcc A1 clusters. (3) More structure (peaks and valleys) in the D(E) is seen in Ih clusters as compared to the uniform E 1/2 behavior, (i) calculated for octahedral A1 clusters (Salahub and Messmer 1977) (ii) calculated for band structure of fcc A1 (Moruzzi et al. 1978) and (iii) observed for fcc A1 by photoemission studies (Steiner et al. 1980). (4) A large density of states at the Fermi level of pure A1 clusters is also observed as compared with similarly sized octahedral clusters, due mainly to the existence of states at Er with large degeneracies (g and h). The Fermi energy is a sensitive function of electron concentration, so that a wide range of D(Ev) values is possible with alloying. Topological features of the molecular-orbital wave functions were also characterized. Figure 6a shows the highest occupied molecular orbital (HOMO) 4Hg for the A133cluster. The orbital manifests ten-fold symmetry, characteristic of the In group, Oh CLUSTER

0.0

0.1

•A2u,~

0.2

Aig

0.3

Tig

I CLUSTER

T zg,. ffiffi ffi m ~ffi'~,.......~

~:

______

.......

A G

0.4

Tm 0.5

........

Az u 0.6 I

H

Tlu

__- _-_-~_--_~----.r-. . . .

T2u Eg

....

TpG T2

0.7 H

0.8

Tm 0.9

TI 1.0 1.1

Aig

-

-

A 1.2 Fig. 4. Molecular-orbital eigenvalues (orbital electronegativities) calculated for icosahedral (Ih) and cubic (Oh) clusters of 13 A1 atoms (after McHenry et al. 1986a).

464

R.C. O'HANDLEY ET AL. i

i

~,,,I

I

I

ALl3

I

AL33

I

D(E) (ARB)

I

-I .2

-0.8

o.o

-0.4

1.2

-0.8

-0.4

ENERGYIRy

ENERGY(Ry)

oo

)

Fig. 5. Density of states D(E) obtained by Gaussian broadening of All~ and A133 cluster eigenvalues. The broken line illustrates the extent to which the envelope of D(E) increases more than linearly in E.

~ A t

L ~ / A t .;:.~. . . . i~------~. ;,. . . .

a:_%'

,:',z"

' -',,

I/ . . . . ~ " ,

\

Jill,

(a)

// /

/

t. j

~

-

,,,

"". ~,^

X

,"

;

"t ~ %

./

,

,~ ,

.

(

,,

/

/ /

(b) Fig. 6. (a) Highest occupied molecular orbital (HOMO) 4 h for the I~ A13a cluster cut through the equatorial plane in fig. 2, showing characteristic ten-fold symmetry. (b) Localized 4Hg HOMO for I~ MnAI3~ cluster.

as well as radially extended p bonding orbitals which are characteristic of p bonding in many aluminium configurations (Johnson and Messmer 1983, Sermon 1987). Casula et al. (1986) have used a tight-binding Hamiltonian to investigate the energetics of 13, 55, and 147 atom icosahedral and cuboctahedral A1 clusters. These clusters allow both for the direct comparison of similarly sized clusters of the two

MAGNETISM AND QUASICRYSTALS

465

symmetries as well as for examination of the importance of cluster size effects on the calculated electronic structure. Comparisons of their cuboctahedral and icosahedral clusters reveal the latter to be characterized by a slightly increased band width, a downward shift of the center of gravity of the occupied levels, and an increased density of states at the Fermi level. These features were shown to persist in clusters of all sizes. A weak site dependence of the local density of states was observed, even in the largest clusters, and was attributed to the delocalized character of the electronic states of aluminium. The localization of states and opening of gaps noted by McHenry et al. (1986a) were not observed to be as important in the larger clusters of this study. 2.1.3. Transition-metal clusters The Mn-centered clusters, MnAltz and MnA13z, also exhibit several characteristic features, namely: (1) a large density of Mn d states, nearly resonant with the A1 Fermi level, pointing to either a structural instability of such a configuration or to a magnetic instability, fig. 7; (2) strong antibonding interactions between Mn and the A1 host which manifest themselves in extremely localized Mn d states. Figure 6b illustrates the radially localized HOMO for the MnA132 cluster. This hg orbital illustrates the extremely localized Mn d states which have an antibonding interaction with A1 s-p states on the periphery of the cluster. This orbital illustrates well the nearly atomic-like nature of the Mn d states in this cluster. In the previously mentioned work of Ramos et al. (1987), it was found that, to a large extent, the central Au atom in their Aut3 cluster (i.e., the site with Ih symmetry) contributed charge density only to pure atomic spinors, i.e., it was not hybridized with the outer shells; consistent with the observations for Mn in A1. However, for the lowersymmetry peripheral sites, significant sp-d hybridization was observed. Further, because of relativistic effects, increased s-d overlap was observed leading to appreciable s-d hybridization. Calculations on Mn-centered icosahedral A1 clusters were extended by McHenry et al. (1988a) to address magnetic properties and local moment formation. It was shown that for Mn atoms in fcc A1 hosts, A1 and Mn form directional p-d hybrid bonds (fig. 8), which serve to move much of the Mn d character below the Fermi I

I

I

i

I

I

I

i

I

I

I

i

D(E) (orb)

-1.2

-0.8

-0.4

f,

0 -1.2 Energy (Ry)

,

-0.8

-0.4

Fig. 7. Cluster density of states (Gaussian broadened) for icosahedral MnA112 and MnA132 clusters (after McHenry et al. 1986a).

466

R.C. O'HANDLEY ET AL.

0

;"£": • "\l

f, .-.',i o) )

"'--222-_-2:t,

2t2g (AI18Mn)

3e9 (AI18Mn)

Fig. 8. Highest orbital molecular orbitals for an Oh Mn-centeredcluster. (Left)tZg orbital and (right) 3% orbital showing Mn bonding to first and secondnearest neighbors,respectively(McHenryand O'Handley 1988).These bonding orbitals in cubic symmetryare to be contrasted with the lack of bonding in a similar cluster with icosahedral symmetry(fig.6b). level E F. Thus, for Mn in an Oh environment, as modelled by an AllsMn cluster,

the local moment calculated was small (~IyB) and consistent with a single electron moment associated with the odd number of d electrons in atomic Mn (Bagayoko et al. 1987). On the other hand, this p - d bonding interaction is frustrated by the higher symmetry about an icosahedrally coordinated Mn atom (fig. 6b). Thus, Mn d states, whose atomic eigenvalues roughly coincide with the A1 Fermi energy, are unaltered by crystal-field effects or by strong directional bonding because of the high symmetry of the icosahedral site. A large Mn D(EF) is thus maintained for the icosahedral configuration providing the driving force for moment formation. For the MnA132 cluster, a moment of 3.6yB was calculated on the Mn site, which was partially compensated for by an antiferromagnetic coupling to the A1 free-electron gas. A total cluster moment of 3#B was observed. Further, a nearly 8 eV exchange splitting was observed for the Mn d states, comparable to that observed for atomic Mn. The large local moment calculated for Mn at an icosahedral site in an A1 host is unprecedented and suggests that one possible explanation for the large moment observed for Mn in quasicrystals (see section 3.3) may be partial occupancy of icosahedral sites by Mn atoms (McHenry et al. 1988b). Several calculations on icosahedral transition-metal clusters have also been performed. Elsasser et al. (1987) have compared the total energies of 13 atom fcc, hcp and icosahedral clusters of Cu, Ni and Au using a semi-empirical H a r t r e e - F o c k approach. These calculations employed a H a r t r e e - F o c k Hamiltonian, using intermediate neglect of differential overlap and for all clusters determined the energy minimum as a function of the nearest neighbor distance. Results of their study indicated the icosahedral arrangement to be the minimum-energy arrangement of these small assemblies of atoms for all three elements. Further, it was noted that the difference in energy between the icosahedral and fcc configurations was ~ 8% of the fcc binding energies in all cases and that this energy corresponded roughly to ~ kB Tm (where Tm denotes the melting temperature), which is the thermal energy at the melting point. This correlation is suggestive of the importance of the icosahedral units in the liquid phase.

MAGNETISM AND QUASICRYSTALS

467

Besides the calculations for Nil3, by Elsasser et al. (1987), calculations on a Scla cluster have been performed by Salahub (1986) using the SCF-SW method, motivated, as previously mentioned, by the suggestion of an Sc13 molecule of exceptional stability by Knight et al. (1983). Calculations of Demuynck et al. (1981), using ab initio SCF calculations, have also demonstrated the stability of a Cula icosahedral cluster as compared with a similar 13-atom cuboctahedral cluster. A calculation on a Co13 cluster (McHenry et al. 1986b) again revealed the stability of an Ih 13-atom configuration as compared with an Oh 13-atom cluster. The magnetic properties, including the magnetic moment, were essentially similar for the two structures, with only a slight moment enhancement for the icosahedral cluster. Harris and McMaster (1986) used the Vosko-Wilk-Nusair parameterization for exchange-correlation to study electronic structure, stability and magnetic properties in icosahedral and cuboctahedral Fe~a clusters. In both structures, they found enhanced moments (2.8#B per Fe atom) on 'surface' atoms and stability was enhanced by moment formation.

2.2. Polytope techniques One of the earliest electronic-structure calculations which considered the influence of icosahedral symmetry was that of Nelson and Widom (1984). This work was motivated by models of glassy alloys having icosahedral short-range order. Using a tight-binding Hamiltonian, they calculated the density of states for a system of polytope {3,3,5} having 120 particles whose three-dimensional positions were projected from a space-filling configuration on the surface of a four-dimensional sphere. They found a discontinuous D(E), which reflected unsplit clusters of eigenvalues corresponding to states of various classes of the icosahedral point group. The envelope of these states increased at faster than the free-electron-like energy dependence. The clustering of states was suggestive of a D(E) with many peaks and gaps present. The symmetry-required absence of d level splitting at the Brillouin zone center was a distinguishing feature of the electronic structure of an icosahedrally ordered transition-metal glass phase modelled by Widom (1985). Using a one-orbital (d-orbital) tight-binding analysis, he calculated the D(E) for the 120-vertex polytope {3,3,5} which was used as a model for the amorphous state. Using a Stoner criterion, he concluded that ferromagnetism was likely to be enhanced for Fe, but reduced for Ni in the amorphous state as compared with their fcc crystalline phases. Phillips and Carlsson (1988) also have used a polytope model (polytope {3,3,5}) as well as a 147-atom extension of the Mackay icosahedron as environments for single d electron tight-binding calculations. Site energies for the polytope and the central site energy for the Mackay icosahedron were compared to those of the fcc structure in order to infer stability of the icosahedral units. It was concluded that the icosahedral arrangements were preferred only over a limited range of d band fillings between two and five d electrons per atom.

2.3. Hamiltonian techniques on quasilattices One of the simplest manifestations of quasiperiodicity is the one-dimensional Fibonacci lattice in which lattice points are constructed from the sequence

468

R.C. O'HANDLEYET AL.

F,=F,_I + F , - 2 (Fo =F1 = 1) and ~=limF,+l/F, is the golden ratio ½(1 + x//5). Kohmoto and Banavar (1986) have explored the density of states for such a onedimensional tiling, using a tight-binding Hamiltonian, in which they found selfsimilar structures in the wave functions and a D(E) spectrum consisting of many localized states within gaps. Manifestations of the one-dimensional quasiperiodicity have been addressed by several other groups as well, including Luck and Petritutis (1986) and Nori and Rodrigues (1986), who also used tight-binding schemes, Niu and Nori (1986), who used a real-space, renormalization group approach, and Ostlund et al. (1983), Kohmoto et al. (1983), and Fujita and Machida (1986). An interesting experimental result on one-dimensional quasiperiodic lattices was the synthesis of such in GaAs-A1As heterostructures by Merlin et al. (1985) and the study of their vibrational modes by Raman spectroscopy. Choy (1985) solved a tight-binding Hamiltonian on a two-dimensional Penrose lattice (Penrose 1974) and found a continuous, symmetric distribution of electronic states about a sharp central peak which he identified as a van Hove singularity, i.e., caused by dispersionless states induced only by the lattice structure. In later, more accurate calculations of a similar nature, Kohmoto and Sutherland (1986) showed that the central peak was isolated from the rest of the band by gaps, and was not strictly a van Hove singularity but was of zero width and caused by localized states. This suggests that Ia symmetry may inhibit some atomic states from hybridizing with those of neighboring atoms. They also identified five-fold symmetry in the wave function amplitude about the origin of their two-dimensional Penrose lattice. Such a wave function is a two-dimensional precursor to the three-dimensional highest occupied orbital about an icosahedral site shown in cross section in fig. 6a. Kohmoto and Sutherland (1986) concluded that the ground state of the two-dimensional tiling displays the self-similarity in the D(E) displayed in the one-dimensional Fibonacci lattice, as well as interesting scaling properties to the wave functions. Tsunetsuga et al. (1986), in studying the two-dimensional Penrose lattice have examined the eigenstates and have concluded that most are critical (can be described by a Cantor function), i.e., neither extended nor localized. Kumar and Ananthakrishna (1987) used a tight-binding model to study the electronic structure in a quasiperiodic superlattice comprised of two types of slabs. Among other interesting results they find extended states in the quasiperiodic direction when the slabs contain more than one layer and van Hove singularities corresponding to the underlying periodicity. Doria and Satija (1988) described the effects of quasiperiodic coupling strengths 2 on long-range magnetic order in a one-dimensional quasiperiodic quantum Ising model. They assume two values 2 and 2 ' = r2 in the quasiperiodic sequence 2(j). Long-range magnetic order appears above a critical coupling strength 2c. A new result of their calculations is the nonharmonic variation of magnetization from site to site at criticality. To describe this variation, they define a new order parameter, w, the difference between the maximum and minimum magnetization, which depends on coupling strength 2 and on r = 4'/2. For an infinite system, they find 2 approaches zero exponentially for 2 > 2c. One of the important experimental observations of quasicrystal properties has

MAGNETISM AND QUASICRYSTALS

469

been the large resistivities (comparable to those of metallic glasses), and, therefore, the inferred short mean free paths [~1 A] in quasicrystals (Fukamichi et al. 1987). Sokoloff (1986) has considered the question of electron localization in quasicrystals (A1-Mn) by considering scattering from almost periodic potentials. In this work, weak pseudopotential theory and the Ziman method (Ziman 1961) are used to calculate scattering rates for a three-dimensional Penrose lattice. It was shown that the almost-periodic Penrose lattice proposed for quasicrystals did not contribute to the resistivity in any order of time-dependent perturbation theory. Thus, like perfect periodic crystals, the resistance at T = 0 K is not increased by the quasiperiodicity. Structural defects and/or large s-d resonant scattering matrix elements due to the Mn impurity states, must be introduced into the Penrose tiling to account for the large, nearly temperature-independent resistivity that characterizes QCs (Fukamichi et al. 1987). Smith and Ashcroft (1987) have used a nearly free-electron (NFE) model and an A1 pseudopotential to calculate the electronic structure for atoms on a Penrose lattice. The electronic structure exhibited band gaps associated with each reciprocal lattice vector of the QC structure which led to notable singularities in the density of states (fig. 9). The largest band gap observed was near EF, suggesting that stable icosahedral phases may be due in part to a Hume-Rothery instability like that suggested by Bancel and Heiney (1986). This nearly free-electron result with many gaps superposed on D(E)~ E 1/2 should be applicable to the A1 states in Al-based quasicrystals. Indeed the Smith-Ashcroft NFE D(E) resembles a large cluster limit of that generated by local density functional theory on A1 icosahedral clusters, see fig. 5 (McHenry et al. 1986a). Marcus (1986) has calculated the density of states for two- and three-dimensional Penrose lattices with atoms at vertex sites for the two rhombi which generate the tilings. A one-orbital tight-binding Hamiltonian was employed. A D(E) with many peaks and gaps was observed for the two-dimensional tiling, in agreement with several previous calculations (Choy 1985, Kohmoto and Sutherland 1986). However, the three-dimensional tiling was shown to yield a smooth, relatively featureless density of states in which all of the states remained delocalized. Marcus concluded that, in the three-dimensional case, there should be little signature of the QC lattice I

i

Quasiperiodic---b~ ~

1.0

0.5

!itY o

EF . . . .

o

5

, , ,

10

1,5

E (eV) Fig. 9. Density of states calculated for a nearly free-electron model of A1 atoms on a Penrose lattice. The broken line is a result for a periodic AI lattice (from Smith and Ashcroft 1987).

470

R.C. O'HANDLEY ET AL.

in the electronic structure. This conclusion is not expected for a tight-binding calculation where bonding effects are weak to begin with. A similar result (little difference in electronic structure between Ih and Oh symmetry) was obtained using local density functional theory on icosahedral Co clusters (McHenry et al. 1986b). Redfield and Zangwill (1987) have performed total energy calculations using an effective medium technique to investigate the icosahedral phase stability in A1-T binary alloys. Using a pair potential and embedding function, the total energy is calculated for various A1-T alloys. This approach views the alloy as a collection of atoms with a particular nearest-neighbor configuration, embedded in a potential reflecting the average local background electron density. These calculations are very successful in predicting various optimum stoichiometries for QC formation in AI-T systems, such as AI-Mn, A1-Cr and AI-V (Lawther et al. 1990). It is also worth mentioning the several empirical techniques which have been used to try to understand the chemical tendencies for quasicrystal formation. Bancel and Heiney (1986) have suggested the use of Hume-Rothery rules to understand the formation of quasicrystals in AI-T alloys. In this model, optimum quasicrystal compositions are determined by the conduction-electron density which allows the Fermi level to lie in a minimum in the density of states as determined by the structure factor. Another semi-empirical technique employed to understand the chemical trends in quasicrystal formation has been the use of quantum structural diagrams by Villars et al. (1986). This technique considers average valence-electron numbers and s-p orbital radii differences as coordinates to determine regions of this parameter space in which certain known alloys form stable or metastable QCs. Out of this space, new alloy systems can be projected. The technique has been used to predict new ternary alloy phases in which quasicrystals may be found with higher probability than by geometrical methods of prediction. None of the quasicrystals discussed in this chapter, except those already known in 1986 (AI-Li-Cu and A1-Mg-Zn), is among those listed by Villars et al. (1986) as possible new quasicrystals. That is not to say that their generalized coordinates would not place these new QCs in the field of likely candidates.

2.4. Global manifestations of icosahedral symmetry Up to this point, we have considered the implications of an icosahedral environment on local moment formation. We turn now to the second consequence for magnetism of icosahedral symmetry, that on a global scale. The interaction between atomic moments and the crystalline anisotropy is governed by the relative importance of the local anisotropy represented by D and the exchange energy, J (Imry and Ma 1975, SeUmyer and Naris 1985). In the case where D/J > 1, as may be the case for 4f moments (if L # 0), the local anisotropy dominates and dispersed moment structures are possible (Alben et al. 1978a) if the local anisotropy is randomly oriented (Coey et al. 1976, Coey 1978). On the other hand, if D/J < 1, as is the ease for 3d moments, then the effects of long-range exchange interactions dominate, the magnetization direction is uniform over larger distances, and it is the long-range anisotropy (or symmetry) which is more important than the local anisotropy (or symmetry). Since in known quasicrystalline materials it is 3d magnetic moments, predominantly on

MAGNETISM AND QUASICRYSTALS

471

Mn, that determine the magnetic behavior, then it is the long-range symmetry of the system that is of relevance. These effects of long-range icosahedral symmetry are, therefore, limited to icosahedral QCs and will not be observed in crystalline materials with only local icosahedral coordination, unlike the consequences of local icosahedral symmetry (section 2.2), which may be seen in icosahedral crystals. The anisotropy energy, EA, can be expanded in spherical harmonics, Y~",with l ~>6 and coefficients Kz. Lower-order terms vanish by symmetry. The leading term in this expansion for icosahedral symmetry is given as EA = K6 yO _ (~) 1/2(y65 _ Y651,

(3)

or

EA = (~5K6) [231 cos 6 0 -- 315 cos 4 0 + 105 cos 2 0 -- 5 + 42 cos 0 sin s 0 cos(5~b)], where 0 and q~ are the usual spherical coordinates. The anisotropy energy calculated along principal quaiscrystallographic directions has been calculated according to eq. (3) and is given in table 1 (McHenry and O'Handley 1987). If we assume K 6 < 0, then the twelve vertex directions (see fig. 10), given by permutations of [100000] are clearly easy directions for the magnetization. The angular proximity of the principal axes, compared with the case of, e.g., a cubic crystal, results in a larger number of possible domain-wall orientations. Further, the small anisotropy energy barrier expected between adjacent domain orientations (because of the vanishing of the lower-order anisotropy terms), could render these materials very soft magnetically. TABLE 1 Calculated anisotropy energy for principal directions in icosahedral symmetry (see fig. 2). Principal directions

0

E /K 6

(rad)

Vertex (V) Edge center (E) Face center (F)

0 0.5536 0.6524

1 -0.3125 --0.5556

V

Fig. 10. Icosahedron showing angular relations between twelve vertex (V) directions, 30 edge (E) directions and 20 face (F) directions.

472

R.C. O'HANDLEYET AL.

If, on the other hand, K6 > 0, then the twenty permutations of the [-111000] direction become the easy axes and again magnetic softness is implied.

3. AI-based quasicrystals 3.1. Al-Mg-Zn and A1-Cu-Li quasicrystals 3.1.1. Atomic structure Quasicrystals in the A1-Mg-Zn and A1-Cu-Li systems are of great interest for several reasons. The similarity of the local structure in the A1-Mg-Zn quasicrystalline phase and the (A1, Zn)49Mg32 crystalline Frank-Kasper phase has been noted by Henley and Elser (1986). The local crystalline symmetry is interesting in that it contains icosahedral units with central sites occupied and the decoration beyond the icosahedral first nearest-neighbor polyhedron is by second nearest neighbors located above the faces. Both of these features differ from the Mackay icosahedron (basis of ~-A1MnSi), which had been used as a structural model for i-A1MnSi QCs (section 3.2). Icosahedral packing is preserved to n coordination shells in (A1, Zn)49 Mg32 (Samson 1965, Pauling 1988). The A1-Mg-Zn quasicrystals are interesting in that the components all have s and p electrons as their important valence electrons with presumably little influence of the d electrons of Zn on the electronic structure, especially near the Fermi energy. Therefore, analysis of experiments which examine the electronic structure are relatively unencumbered by considerations of d states, and local moments are also unimportant in these materials. The A1-Li-Cu quasicrystals are believed to be structurally similar to the A1-MgZn system. Further, the icosahedral phase A16Li3 Cul appears to be thermodynamically stable (Cassada et al. 1986). Recently, however, transmission electron microscopy on small A1-Li-Cu precipitates have revealed that their electron diffraction patterns could be explained in terms of multiple twinning of a bcc phase with a large unit cell (Ball and Lloyd 1985). This experiment has called into question the putative stability of quasicrystalline A1-Li-Cu (Vecchio and Williams 1988). 3.1.2. Electronic structure Baxter et al. (1987) have examined the electrical resistivity of A1-Mg-Zn quasicrystals exploiting the fact that these alloys do not possess local moments and, therefore, the intrinsic quasicrystal resistivity could be explored. Single-phase icosahedral Mg3z(Al~-xZilx)49alloys were examined for x = 0.5 and 0.69. Their resistance and magnetoresistance behavior were well explained by application of quantum corrections to a model of conduction in disordered alloys. In particular, the low-temperature field-dependent resistivity was characterized by weak (defect-related) localization and enhanced electron-electron interactions. Most interesting was a strong dependence of the resistivity and the valence-electron susceptibility on composition. The Pauli susceptibility was observed to vary dramatically with small compositional changes, indicating structure in the density of states at the Fermi level. This compositional dependence could not be explained by a nearly free-electron model and was, therefore, taken to imply a more complicated structure to the D(E), i.e., a structure more peaked

MAGNETISM AND QUASICRYSTALS

473

and gapped like that observed in several calculations cited above. Room temperature resistivities of the two alloys were 59 and 90 Ixf~cm, respectively, a factor of 2-4 times lower than typical values observed in the QCs with local moments (e.g., A1-Mn-Si). Wong et al. (1987) have examined transport as well as superconducting properties of icosahedral (I) and Frank-Kasper (FK) phases of A15z.5Cu12.6 Mg3s. The icosahedral phase was reported to have a resistivity of 60 g~ cm at room temperature while that of the Frank-Kasper phase was ,,~37 gf~ cm. The I phase exhibited a relatively flat temperature dependence [p(4.2)= 58 gf~cm], while the FK phase had a small positive slope [p(4.2) = 23 g~ cm]. Both phases showed superconducting behavior at low temperatures. The superconducting transition temperature was found to be 0.81 K for the I phase and 0.73 K for the FK phase. From measurements of H~2, it was determined that D(Ev)= 0.52 state/eV atom for the I phase and 0.89 state/eV atom for the FK phase. The lower resistivities in these alloys as compared with A1-MnSi alloys were attributed to the absence of resonant d scattering. The higher resistivity of the I phase as compared in the crystalline FK phase as well as its field dependence were explained by localization theory. The D(EF) values derived for the I phase were consistent with a free-electron model, while those for the FK phase were nearly a factor of two larger (based on its significantly smaller normal state resistance). Inasmuch as the I phase resistivity in the normal state is strongly influenced by localization effects and defect scattering, it may not reflect an intrinsic resistivity. On the other hand, the crystalline FK phase has a D(Ev) nearly 50% of that of the freeelectron value and that of pure fcc A1 or bcc Mg. This is interesting in the light of the fact that the FK phase is constructed of precisely the same icosahedral units which are thought to exist in the I phase. Bruhwiler et al. (1988) have performed careful studies of the electronic structure of both the QC and FK phases of A1-Cu-Li and A1-Cu-Mg alloys. Alloys of composition A156CuloLi34 and A152.4Culz.6Mg3s were examined. Electronic structure parameters were determined from a combination of transport, heat capacity and soft X-ray measurements. Both from transport and X-ray spectroscopy, it was determined that the A1-Cu-Li density of states D(EF) was a factor of three less than that in A1-Cu-Mg alloys in either the I or the FK phase. The A1-Cu-Mg values are close to the free-electron value (see table 2). It was shown that, for both alloys, the calculated electronic properties were essentially similar between the I and FK phases. The authors point out that the properties of the I and FK phases remain alike because of essentially similar structure factors based on local icosahedral units. This is consistent with the notion that the local structure determines much of the detail in the electronic structure. Graebner and Chen (1987) have measured the specific heat for the cubic FrankKasper, icosahedral and amorphous phases of composition A12Mg3 Zn3. All three phases were reported to be superconducting with an T¢ of 0.32, 0.41 and 0.75K, respectively. It was concluded that the icosahedral phase resembled the FrankKasper phase in most respects and that its electronic density of states was very close to that predicted by a free-electron model (as determined from the linear specific heat term). Lattice softening was strong in the amorphous phase and weaker but

474

R.C. O'HANDLEY ET AL.

i ~

oo

r

~

~

I

~

I

0

+l+l+l+l

.u.l

I

I

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V

I .,i~~

,-1 I

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.2 ~o

¢}

.=

ta

o

.

6

~

.

MAGNETISM AND QUASICRYSTALS

475

significant in the I-phase. Thus, the renormalized electron-phonon coupling term 2 was observed to decrease with increasing order. Wagner et al. (1989) have studied the electronic properties of icosahedral alloys, Ga-Mg-Zn, A1-Cu-Fe and AI-Cu-V. The stable I phases of G a - M g - Z n and AICu-Fe show significantly lower values of D(EF) than expected from free-electron theory and smaller than observed in their metastable I phases. These factors are interpreted to suggest a type of Hume-Rothery stabilization due to reduction in D(EF) by a coincident peak in the QC structure factor. Icosahedral AI-Cu-V shows a D(EF) close to its free-electron value. The magnetic susceptibility of i-Al-Cu-Fe shows a strong departure from Curie behavior at low temperatures and a spin-glasslike peak near 1.6 K. General consensus now exists that decreased resistivities in the A1-Li-Cu and Mg[A1, Zr] class of quasicrystals, relative to the A1-Mn-Si class of materials, result mainly from the absence of s-d scattering. The electronic properties of these icosahedral systems are closely related to those of Frank-Kasper phases of similar composition. An appealing explanation for this similarity lies in the similar local packing units, and, therefore, structure factors, in these materials. Several of these alloys exhibit electronic state densities which do not differ appreciably from those predicted by free-electron theory. However, strong compositional variation in the density of states is not easily explained by a free-electron picture. Spectroscopic measurements to resolutions of ,-~0.6 eV have ruled out van Hove singularities.

3.2. Structure of Al-transition-metal quasicrystals The first discovered and most abundant class of quasiperiodic structures remains the A1-T-M icosahedral alloys IT--transition metal at 10-22at.%, M = metalloid Si or Ge at 0-8at.%]. Once it was established that AI-Mn and AI-Mn-Si were quasiperiodic with diffraction patterns indicating icosahedral symmetry (Shechtman et al. 1984, Bancel et al. 1985), it became a matter of much speculation and controversy as to exactly how to model the structure and how to decorate the quasilattice with the various atoms. Models considered included the three-dimensional Penrose tiling (3-D PT) (Elser 1985, Elser and Henley 1985, Levine and Steinhardt 1986, Henley 1986b), the modified ~-AI-Mn-Si structure (Guyot and Audier 1985, Audier and Guyot 1986), and the icosahedral glass (Shechtman and Blech 1985, Stephens and Goldman 1986). When modeled as a 3-D PT, the AI-Mn-Si QC alloys have a quasilattice constant (edge of either of the rhombohedra that make up the structure) of 4.6A. Their QC structure is more disordered than is that of i - P d - U - S i , Si additions reduce the disorder as judged by narrower diffraction peaks (Kofalt et al. 1986), and the AI-Mn pair correlations are much stronger than those of AI-A1 (Nanao et al. 1987, 1988). The competition between these three structural models can be followed in papers by Henley (1986a), Egami and Pooh (1988) and Janot and Dubois (1988a,b). For the A I - T - M (T -- Mn or Cr) family of QCs at least, the question of structure is no longer a matter of speculation. A series of neutron-diffraction experiments, making use of contrast variation due to the opposite scattering lengths of Mn and Cr (Dubois et al. 1986) has allowed the structure of A174Mn21Si6 to be deduced

476

R.C. O'HANDLEY ET AL.

(o)

(b)

Fig. 11. Decoration of Penrose bricks deduced by Janot and Dubois (1988a) from extensive scattering data on A1-Mn(Cr)-Si quasicrystals. Location of the atomic sites in (a) the prolate and (b) the oblate rhombohedra: [O, O] vertex sites occupiedmainly by Mn atoms; (D, II) A1 sites on faces;(~?) A1 sites on the triad axis of the prolate rhombohedra (from Janot et al. 1989a). without assumptions (de Boissieu et al. 1988, Janot et al. 1989a, Janot and Dubois 1988a,b). Partial pair correlation functions indicate that Mn atoms approach each other no closer than 4.5 A, while the A1-A1 pair correlations are similar to those of ~-A1MnSi. In six dimensions, the structure has a primitive CsCl-like space group symmetry which allows determination of the atomic density in three dimensions. The three-dimensional decoration of the 4.6A prolate and oblate Penrose icosahedra deduced from the neutron data (Janot et al. 1989a) are illustrated in fig. 11. Mn atoms occupy the vertices of the prolate rhombus with an average occupancy of 87%; one of these Mn sites has nearly spherical local environment symmetry (de Boissieu et al. 1988). On the oblate rhombus, Mn atoms rarely occupy adjacent vertices at the ends of the short body diagonals. A1 has three sites in the prolate rhombus: type I a 10% occupation of the vertices especially those at the ends of the short body diagonals; type II a 25% average occupation at distances of 2.57 or 6.78A along the triad axis; and type III an 81% occupation at 2.98 or 4.83A along the long face diagonals. No edge sites are occupied. Fragments of icosahedra of different sizes are found in the QC structure and some of them are occupied by either A1 or Mn atoms of different sizes (de Boissieu et al. 1988). This clearly rules out ~A1 M n - S i (where icosahedral sites are vacant) as a structural model for i-A1-MnSi QCs. With this decoration in mind, it can be shown that the Mn at the acute vertex has a reasonable probability of having nearly icosahedral symmetry. However, Mn clearly has at least one other environment (the obtuse vertex sites) which may create a different environment for magnetism. This multiplicity of Mn sites has ubiquitous effects on magnetic properties. Our understanding of the magnetism of QCs depends not only upon extending this sort of firmly established picture of atomic environments to other classes of QCs, but also on gaining an insight into the nature and extent of the defects in these materials.

3.3. Paramagnetic quasicrystals 3.3.1. AI- T Al-based QCs without a metalloid have narrow formation ranges. For T = Mn, the stoichiometric QC composition has 21.6 at.% Mn. Less Mn results in an appreciable

MAGNETISM AND QUASICRYSTALS

477

amount offcc A1 in the alloy (Dunlap and Dini 1985) and more Mn gives a decagonal phase (Machado et al. 1987b). The interpretation of magnetic behavior in A1-T QCs is invariably complicated by the presence of a second phase. Inoue et al. (1987) have reported a rapid increase in resistivity in A1-Mn and A1-Cr QC alloys with increasing T content. This has been explained by the disappearance of the fcc A1 phase with increasing T content. Pavuna et al. (1986) have reported an increasing resistivity upon increasing Mn content in A1-Mn alloys. Certain of the A1-T alloys, A1-Mn (Inoue et al. 1987) and A1-Co (Dunlap et al. 1986), exhibit Kondo-like resistance minima as a function of temperature. Cyrot and Cyrot-Lackmann (1986) have attributed large low temperature resistivities, comparable to those of metallic glasses, to magnetic scattering from virtual bound states in Mn or U containing QCs. A1-T QCs are all paramagnets and some show spin-glass freezing at low temperatures (Hauser et al. 1986). Further work on the icosahedral A18oMn2o phase and the decagonal (T-phase) A178Mn22 material (Machado et al. 1988) showed values of the transverse magnetic resistance to be comparable to those of other spin-glass systems. The longitudinal magnetoresistance was positive for the I phase and negative for the T phase. The electrical and magnetic properties of AI-T QCs are reviewed by Fukamichi and Goto (1989). The effective paramagnetic moments are derived by fitting the paramagnetic susceptibility to the form

Z = Zo + C / ( T - 0), C-

Npe2f

(4)

3kB '

where N is the concentration of the magnetic species, Peffis the effective paramagnetic moment in Bohr magnetons (#B) and kB is Boltzmann's constant. The effective paramagnetic moments determined from this equation and a linear fit to the susceptibility require an assumption about N, the concentration of the species responsible for the moment. If N is assumed to be the chemical concentration of a transition-metal (T) species, Peff will be in error if not all of the T atoms contribute equally to the moment. Fitting the field and temperature dependence of magnetization beyond the range linear in H/T with a Brillouin function allows independent determination of N and Perf"This approach has been taken by Machado et al. (1987a) on A18oMn2o QCs. They found that a moment of ll#B should be associated with a cluster of approximately 100 Mn atoms. Without this high-field data, their Curie constant is the same as that measured in this system by most other groups and, therefore, would give the same value, Peff"~ 1.2#B/Mn, as generally reported. Despite the additional parameter determined by including high-field data, this method cannot specify how the moment is distributed among the 100 atoms. These authors (Machado et al. 1987a) also measured the specific heat of this alloy (fig. 12) and found that only the full Brillouin-function-determined moment and concentration (11#B per 100 Mn atoms), and not Peff 1.2#B/Mn, gives a magnetic entropy ASm = NkBn(2S + 1) consistent with their specific heat data. Other specific =

478

R.C. O'HANDLEY ET AL. 1000 500 200

i

i

i iiii

I

L-AIsoMn2o

1oc 50

0.2

i

171111

j'

,~A T3

20 O lc 2

i

•~ e " Z

,,C// 0.5

1 2 Temperature (K)

5

10

Fig. 12. Heat capacity, Cp, in gJK -1 versus absolute temperature, T (in K) for a 35mg sample of icosahedral Also Mn2o with zero magnetic field: solid circles. The T 3 and T solid lines indicate the phonon and (upper limit) electronic contribution, respectively, while the broken line indicates their sum (Machado et al. 1987a).

heat and AC susceptibility data (Lasjaunias et al. 1987) support the model that most Mn atoms are not magnetic. The difficulty of interpreting data in this low-temperature regime near the onset of spin-glass behavior (bump just below 1 K, fig. 12) has been pointed out (Eibschutz et al. 1987). Berger and Prejean (1990) have completed a thorough study of the spin-glass behavior of i-A173Mn21Si6. They also find only a small fraction (~ 1%) of the Mn atoms present bear moments, and clusters of these atoms exhibit moments in excess of 7#B (see section 3.3.2.1). In light of these findings, we must regard with caution all values of Peefdetermined only by linear fits. This includes all values (other than the 11/~Bper 100 Mn and the 7.5#B mentioned above) reviewed in this chapter. The effective moment (linear fits) of All -xMnx QCs reported for x = 0.2 vary from 1.0#B to 1.3#~ per Mn and increase with increasing Mn content (Younquist et al. 1986, Goto et al. 1988). Hauser et al. (1986) have observed a nearly quadratic dependence of Poef on the Mn content in A1-Mn and A1-Mn-Si QCs. This is taken to suggest that Mn moment formation is due to M n - M n pair interactions. A problem with interpreting the variations in Mn moment with x is that as x varies, the composition of the QC phase does not change significantly from its strict stoiehiometric ratio A178.gMnzl.6 and second phases of varying composition occur that obscure any true trends. When data for amorphous and crystalline alloys are compared, the moments of the icosahedral phases are higher than those of the crystalline phases which also increase with increasing x. However, the M6ssbauer spectra of both crystalline and icosahedral A1Mn(Fe) alloys suggest equally low symmetry for the Fe sites (Swartzendruber et al. 1985). The stronger moment formation in i-A1Mn QCs is reflected in the strength of the magnetic interactions involved in the spinglass behavior. Berger et al. (1988a) find the spin-glass contribution to the specific heat at 1 to 2 K in i-Als6Mn14 and near 0.2K in amorphous A18sMn~s. The consistently negative values of 0 determined for A1-Mn QCs also suggest antiferromagnetic M n - M n interactions. These antiferromagnetic interactions, in combination with the disorder common to QCs, may be responsible for the spin-

M A G N E T I S M AND QUASICRYSTALS

479

glass behavior. The spin-glass freezing temperature Tg increases from 1 to 9 K as the Mn concentration increases from 14 to 22 at.% (Fukamichi et al. 1987). In A1-Fe, icosahedral QCs plus fcc A1 are found at x = 14at.% Fe (Dunlap et al. 1988a). Others report a decagonal phase at this composition (Zou et al. 1987). The only moment present in these A1-Fe QCs appears to be due to ~-Fe precipitates. Specific heat measurements on icosahedral A18oMn2o were compared with those for a crystalline hexagonal A14Mn phase, a hexagonal A17~Fe19Silo phase and a cubic A15oM12Si 7 phase by Maurer et al. (1987). They concluded that the DOS at Ev was a factor of three larger for the icosahedral phase and the hexagonal A14Mn phase as compared with the other crystalline phases and that of fcc aluminium. From this, they concluded similar local structures in the In and A14Mn phase were responsible for the enhanced DOS. This local structure was significantly different from that of fcc A1. It was further observed that increasingly Mn content in the In phase notably contributed to the specific heat. In this way, the Mn behaves like an impurity. It was further suggested that Mn was twelve-fold coordinated without Mn nearest neighbors. 3.3.2. A I - T - S i 3.3.2.1. AI-Mn-Si.

Si is found to broaden the range over which A1-T-based QCs can be formed (Chen and Chen 1986). Typical compositions have a Si content of 6% and Mn contents from 16 to 22%. While the structure of these materials has often been modeled as a distorted a-A1-Mn-Si phase (Guyot and Audier 1985, Audier and Guyot 1986), it is now clear that this model is not accurate. The structure and rhombohedral decoration deduced from careful neutron-diffraction studies without assumptions has been described above (section 3.2). Effective paramagnetic moments per Mn atom for these QCs are shown in fig. 13. Crystalline alloys of the same compositions show consistently lower effective moments (McHenry et al. 1988b). This difference has been attributed to several effects. (1) M n - M n neighbors do not exist in the crystalline phase. Disorder in the QCs would allow increased M n - M n pair formation with increasing Mn concentration (Hauser et al. 1986). 1.8 1.6

+

"~m 1# al

1.2 1.0

0.81

16

I

I

I

18 2~0 x (at% l'ln)

I

212

Fig. 13. Effective paramagnetic moment per Mn atom for icosahedral A1-Mn-Si. Data are from (+) Hauser et al. (1986), (©) McHenry et al. (1988a), (O)Eibschutz et al. (1988), (A) Bellisent et al. (1987) and (A) Edagawa et al. (1987).

480

R.C. O'HANDLEYET AL.

(2) Icosahedral sites are not occupied in cz-A1-Mn-Si. Increased occupation by Mn of high-symmetry, nearly icosahedral sites in the QCs could lead to enhanced moments on Mn atoms at those sites (McHenry et al. 1986a) (section 2.1.3). Recent analysis of neutron scattering data from A1-Mn-Si QCs suggests that about 20% of Mn atoms occupy such sites (Nanao 1987). (3) The existence of two classes of Mn sites has been postulated in QCs (Eibschutz et al. 1987). These were originally suggested to be at the periphery of a Mackay icosahedroia: the nonmagnetic sites are involved in bonding between adjacent icosahedra and the magnetic ones are not (Eibschutz et al. 1987). The definitive structural results described above (section 3.2) preclude M n - M n nearest-neighbor pairs (hypothesis 1 above) in QCs at least up to 21 at.% Mn. The neutron scattering data (Janot et al. 1989a) also show that the modified Mackay icosahedron model (on which hypothesis 3 above was based) cannot be valid. It appears, then, that hypothesis 2 is presently a leading candidate to explain the larger paramagnetic Mn moments in the QC phases relative to the crystalline phase. Some specific heat measurements support this view, indicating higher values of D(EF) in QC phases (Maurer et al. 1987, Berger et al. 1988a), others do not (Machado et al. 1987a). It is likely that a distribution of sites is available to Mn; those with higher symmetry may be magnetic. This is not incompatible with hypothesis 3 if the connection with the Mackay structure is omitted. The two classes of Mn sites could be (a) nonmagnetic, bonding, low-symmetry sites and (b) magnetic, nonbonding, high-symmetry sites. Berger and Prejean (1990) analyzed their detailed linear and nonlinear susceptibility data for i-A173Mn21Si 6 and determined that only 1.3% of the Mn atoms nominally present bear moments. The moment-bearing Mn atoms are clustered in groups with average cluster moment of 7.5#B. This conclusion bears out a similar result found by Machado et al. (1987a) for A1-Mn QCs (section 3.3.1). The electric field gradient distributions have been carefully analyzed in several 57Fe-doped icosahedral and decagonal A1-Mn-Si QCs and compared with results for various related crystalline phases (Le Caer et al. 1987, Brand et al. 1990). A strong similarity in local order is indicated for the icosahedral phase and for the hexagonal f3-A1-Mn-Si phase. [When A1-Mn-Si alloys are rapidly solidified by gas atomization, the/3 phase appears in larger particles and the icosahedral phase in smaller particles (McHenry et al. 1988a). This suggests that there is a structural kinship between these two phases because the/3 phase nucleates and grows from the icosahedral phase when the quench rate is slower.] Le Caer et al. (1987) and Brand et al. (1988) also find no evidence for a two-site model in QCs at the level of Fe concentration they studied (Mn14Fe6). We will review below (section 3.3.2.2 to 3.3.2.4) abundant evidence for the distribution of Mn sites at higher levels of substitution of Cr, V or Fe for Mn. Again, for the A1-Mn-Si alloys, strong arguments for Mn virtual bound states have been made through consideration of transport and other measurements. Berger et al. (1988c) showed that the large electrical resistivities in A1-Mn-Si alloys were well accounted for within an extended Friedel-Anderson s-d model. A large excess specific heat term was shown to scale with Mn concentration and was taken to imply the existence of narrow-band resonant Mn states near EF. In complementary work,

MAGNETISM AND QUASICRYSTALS

481

Berger et al. (1988b) have explored canonical spin-glass behavior in A1-Mn-Si quasicrystals, demonstrating the existence of a cusp in the AC susceptibility with a frequency dependence similar to that of (Ag)Mn or (Cu)Mn. A1-Mn-Si QCs with 20 at.% Mn show spin-glass behavior at low temperatures (McHenry et al. 1988a), similar to that observed in A1-Mn QCs. Below the spinglass freezing temperature, the susceptibility is hysteretic, taking on different values for field-cooled and zero-field-cooled conditions (see fig. 14). Tg increases with Mn content as illustrated in fig. 15. Berger and Prejean (1990) established that the spinglass behavior in i-Alv3Mn2~Si6 is three dimensional and results from an almost equal fraction of ferromagnetic and antiferromagnetic interactions. We now consider the magnetic effects of V, Cr and Fe substitutions for Mn in A174Mn2o Si6 QCs.

3.3.2.2. Al-(Mn, V)-Si.

Eibschutz et al. (1988) showed that V may be substituted for Mn in i-A174Mnzo_xVxSi 6 up to 12at.%. The QC diffraction patterns are not significantly altered by these substitutions and very little residual fcc A1 second phase is present. The motivation for this study apparently was to test the hypothesis that two classes of Mn sites exist, a larger, magnetic site and a smaller, nonmagnetic site. Vanadium, being larger than Mn, is assumed to substitute preferentially in the larger Mn sites. The quasilattice constant, aR, was observed to increase from 4.595 to 4.660A as the amount of V increased from 0 to 12at.%. On the other hand, replacement of Mn by Fe (section 3.3.2.4) decreases ak. The susceptibilities of AI-(Mn,V)-Si QCs are described by eq. (4) quite well, giving ~'~

120

,o-'140[ "...fc

I

I

/". ~ 80

~I 0 0 ~ . 0

°

o 40

5

T (K)

10

o

i

°°°*

00

~

°

,,

o Q

50 100 150 200 250 T (K)

Fig. 14. Susceptibility for A|-Mn-Si showing evidence of spin-glass behavior (McHenry eta]. 1988b).

4-

2

16

'

18

'

20

'

22

x (of %Mn) Fig.15. Spin-glass freezing temperature T~ for icosahedra] A194_,MnxSi6. Data are from (+) Hauser eta]. (1986), (©) McHenry et a]. (1988b), and (Q) Bel]isent et al. (1987).

482

R.C. O ' H A N D L E Y ET AL.

0 values ranging from - 9 to - 3 K as the V content decreases from 0 to 12 at.% (Eibschutz et al. 1988). Using a clever, but simple and plausible method of analysis, Eibschutz et al. (1988) derived the x dependence of the effective paramagnetic moment per Mn p(x)= (-dpZef/dx) 1/z. p(x) decreases with decreasing x, vanishing near x = 12 at.%. The implication is that the Mn moments replaced by V are large initially, p(0) = 2.2#B/Mn, and decrease to p(12) = 0. The distribution of moment magnitudes P(p) was then obtained from

p=

;o

p'P(p') dp,

(5)

with p = 1.1#B averaged over all magnetic sites and 40% of the sites having p = 0. Figure 16 shows the average moment per Mn atom obtained in this way (Eibschutz et al. 1988). The kink marks the point at which, for increasing V content, two thirds of the moment-bearing Mn sites are occupied by nonmagnetic V atoms. Beyond that concentration, V apparently occupies the smaller, nonmagnetic sites and the alloy retains an effective moment due to the magnetic Mn atoms that were not replaced. These results provided the first experimental evidence that the distribution of Mn sites available in the (disordered) QC state is responsible for a distribution of effective Mn moments.

3.3.2.3. Al-(Mn, Cr)-Si.

Additional information concerning the distribution of magnetic sites in Al-based QCs has been provided by an investigation of the A 1 7 4 M n 2 o _ x C r x S i 6 series (McHenry et al. 1989a). This series is similar to the A1(Mn, V)-Si series discussed above since Mn is replaced by a larger transition metal. AI-(Mn, Cr)-Si alloys form single-phase, icosahedral QCs over the range of 0 ~<x ~<20 and on the basis of the sharpness of the X-ray diffraction peaks, they were judged to be well ordered and relatively free from strains. The magnetic susceptibilities obtained from SQUID magnetization measurements are illustrated as a function of temperature in fig. 17. The alloy with x = 20 shows no Curie-like behavior at low temperatures, indicating the lack of a local moment on Cr in these alloys. Alloys with x ~< 17 show Curie-like behavior at low temperatures and this has been evaluated on the basis of eq. (4) to obtain the effective paramagnetic moment, poff. (These results are shown in fig. 18.) The x = 20 alloy shows a gradual increase

1.5 ~. 1.0 " ~ 0.5 ~ I

5

[

I

10 15 x (al% V)

20

Fig. 16. Effective moment per Mn atom for A174Mn2o_xVxSi 6 quasicrystals. Data are from Eibschutz et al. (1988).

MAGNETISM AND QUASICRYSTALS

483

B0 "3E

~t,o

o

-0

o

100 200 T (K)

300

Fig. 17. Magnetic susceptibility for icosahedral A174Mn20_xCr=Si 6 alloy measured in an applied field of 10kOe. [[2] x = 0 , [,$] 5, [11] 10, [ © ] 14, [ 0 ] 17, and [ O ] 20. Data are from McHenry et al. (1989a).

in susceptibility with increasing temperature. This same behavior is seen to a lesser extent superimposed on the Curie behavior of the x = 17 and x = 14 samples. While no definite explanation for this non-Curie-like susceptibility can be given at this time, it is suggestive of Pauli paramagnetism (White 1970). It is interesting that Srinivas et al. (1989) have reported Pauli paramagnetism in quasicrystalline A 1 - M o - F e and A1-Ta-Fe (sections 3.3.4.2 and 3.3.4.3). The presence of a Pauli-like susceptibility suggests a high density of free-electron states at the Fermi level and may be characteristic of those QCs which contain elements with a low d-electron concentration and hence a more delocalized d band. The compositional variation of the moment per Mn atom seen in the present series follows the same general trend as has been seen in the AI-(Mn, V)-Si alloys discussed above (section 3.3.2.2). McHenry et al. (1989a) have analyzed the magnetic moment data for the AI-(Mn, Cr)-Si series on the basis of two distinct classes of transitionmetal sites. Mn atoms in the less magnetic sites are assumed to carry a localized moment of Pl, while those on the more magnetic sites are assumed to carry a localized moment of P2. It is assumed on the basis of studies on other similar series as well as on the data shown in fig. 18, that Cr (larger than Mn) substitutes into the larger, more magnetic class of Mn sites. It is, therefore, possible to express the average 1.5-2 1.0"~

o.s~

-

0

~850

~oo I

7so

is x (of°/oCr)

20

Fig. 18. Effective paramagnetic moment per Mn atom in the A174Mn2o_xCrxSi 6 quasicrystals as a function of x and crystallization temperatures established on the basis of the onset, the exothermic differential thermal analysis peak measured with a heating rate of 20 K min-1. The solid line for the susceptibility data shows a least square fit to eq. (6). Data are from McHenry et al. (1989a).

484

R.C. O'HANDLEY ET AL.

effective Mn moment as p(x) = [-(xc- x)pz + (20 - xo)pl]/(20 - x), Pl,

x < x~.

(6)

X > Xc,

where xc is the concentration of the less magnetic sites. This model gives Pl = 0.43#B and P2 = 1.76#B with a value of x~ of 11.3 at.% or 57% of the transition-metal sites. Again, as in the case of the AI-(Mn, V)-Si alloys, the compositional dependence of the average effective Mn moment cannot be described by a quadratic dependence on Mn content ( 2 0 - x) which, because Pcr= 0, is constrained to pass through the origin (at x = 20). It is reasonable to suggest that crystallization temperatures, T~, are related to the bond stability and hence to the d-band structure of these alloys (Dunlap and Dini 1986, Walker 1981). The thermal stability of AI-(Mn, Cr)-Si QCs has been reported by McHenry et al. (1989a). Results of this investigation are shown in fig. 18. The correlation between T~ and Pe~ in Alv4Mn2o-~CrxSi6 QCs for x > 0 suggests that moment formation may have a stabilizing influence of the electronic and atomic structure. The series Alv4Mn2o_xFe~Si 6 was reported by Eibschutz et al. (1987) to be quasicrystalline up to 7.5 at.% Fe. Up to that point, the average moment per Mn, as shown in fig. 19, does not change significantly with Fe substitution, indicating that Fe has the same moment as the Mn atoms it replaces. M6ssbauer measurements at 4.2 K (fig. 20) show no hyperfine splitting at the Fe sites, and exhibit the same quadrupole splitting in H = 80 kOe as for H = 0, indicating the iron moment is zero. Thus, it is concluded that Fe is substituting for the nonmagnetic Mn, i.e., those in the smaller Mn sites. This result is consistent with those obtained for V and Cr substitutions in A1-Mn-Si: T species larger than Mn (e.g., V, Cr) substitute in the larger, magnetic Mn sites which comprise approximately 60% of the total transition-metal sites and T species smaller than Mn (e.g., Fe) substitute in the smaller, nonmagnetic sites (Edagawa et al. 1987, O'Handley et al. 1990). De Boissieu et al. (1988) found that many Mn atoms in icosahedral AI-(Mn, Fe)-Si reside at sites of icosahedral symmetry. If Fe were substituted for those icosahedral Mn atoms, we would expect to see an appreciable component in the M6ssbauer spectrum having zero quadrupole splitting. The fact that this was not observed by Eibschutz et al. 3.3.2.4. A l - ( M n , F e ) - S i .

2"01o , ....

x { a t % Fe)

Fig. 19. Average moment per Mn atom in quasicrystalline A174Mn2o_=Fe~Si6 alloys. Data are from Eibschutz et al. (1987).

MAGNETISM AND QUASICRYSTALS "1.5 -1.0 -0.5

0

0.5

1.0

485

1.5

./H=O \\~,/

(a)

• ~-i " H=8OkOe (b) ? I

I

I

I

I

I

I

-8 -6 -4 -2 0 2 4 Velocity (mm/s)

~

I

6

8

Fig. 20. M 6 s s b a u e r spectra of A17~Mn15 Fe 5 Si 6 at 4.2 K, (a) without an external magnetic field and (b) in an external field of 8 T. D a t a are from Eibschutz et al. (1987).

(1987) in i-Al-(Mn, Fe)-Si is further evidence that the Fe atoms occupy the nonmagnetic (lower symmetry) Mn sites. The structural instability of the icosahedral phase beyond 7.5 at.% Fe may be associated with the filling of the larger nonmagnetic sites.

3.3.3. Al-(Mn, Cr)-Ge A1-Mn-Ge and A1-Cr-Ge systems have recently been shown to exhibit a QC phase (Inoue et al. 1987). Of interest is both the ferromagnetic behavior observed in A152.5Mn2s Gez2.5 and the related phase A14oMnz5 Culo Ge25 (Tsai et al. 1988), which will be discussed in a later section (section3.4.2), and the precursor to this strong magnetism seen in the local moment behavior observed for A16sMn2o-xCrxGe15 alloys. Seemingly, these phases involve the simple isoelectronic substitution of Ge for Si in well-known A1-Mn-Si QCs. However, this substitution, presumably due to size effects, changes both the structural stability (specifically its composition dependence) and the magnetic properties of the Ge containing alloys. In the series A165Mn2o_xCr~Ge15, an increasing lattice constant, aR, has been observed with increasing x (McHenry et al. 1989b). Further, a decreasing line width Aq of the X-ray peaks is observed on increasing x. Since the X-ray diffraction line widths are a manifestation of atomic disorder or strains (phason or phonon), these results indicate decreasing order with increasing Mn content. Prior work by Srinivas et al. (1990) in the series A165Fe2o_xCr~Ge15 also indicated an increasing Aq with increasing x. These results point to the conclusion that, in the A165T2oGe~5 alloys, Cr is the best single transition metal for promoting QC order. This behavior is to be contrasted with that seen for A174T2oSi6 alloys in which Mn is the best single transition metal for accommodation in the QC. However, in A174T2oSi6 an even more ordered alloy can be obtained with a combination of larger (Cr) and smaller (Fe) atoms. The shift to larger T species in A16sMn2o_~Cr~Ge~5 reflects both the

486

R.C. O'HANDLEY ET AL.

larger metalloid size as well as the increased metalloid concentration. Further studies are required comparing A1-T-Si and A1-T-Ge QCs to elucidate the details of this behavior. The differences in the A1-T-Ge and A1-T-Si quasicrystals are further manifested in their magnetic properties. Whereas the largest moment observed to date in A1-T and A1-T-Si QCs has been the ~l.3/~B moment observed for T = Mn, the alloy A165MnzoGe15 has been shown to exhibit a moment of 2.1#B per Mn. Further, Cr, which has no moment in A1-T or A1-T-Si QCs, exhibits a sizeable local moment of 0.45#B in A165Mn2o Gel5 (McHenry et al. 1989b). Table 3 summarizes the results of Curie law fits to magnetic susceptibility data for the series A165Mn2o-xCrxGets as reported by McHenry et al. (1989b). Striking in this data is the size of the moment in A165Mn2oGe15, the existence on a Cr moment in A165Mnzo_xCr~Ge~s, and the magnitude of the paramagnetic Curie temperature 0, which ranged from - 9 to - 2 8 K in contrast to the - 2 to - 1 0 K observed in A174T2oSi6 QCs. Of further interest in the magnetic properties of the A1-T-Ge QCs is the existence of a spin-glass transition and magnetic relaxation at low temperatures. In a field of 1 T, a spin-glass transition of 8K is reported for the alloy of composition A16sMn2oGe~5. Magnetic relaxation measurements (M versus t) have been made in a field of 1 T from the zero-field cooled state revealing a logarithmic time dependence of the magnetization as shown in fig. 21. A simple kinetic analysis, using a first-order TABLE 3 Results of Curie law fits to magnetic susceptibility data for the alloys A165Crzo-xMnxGe15 (x = 0, 5, 10, 15, 20). Data from McHenry et al. (1990). x (at.%)

Z~ (106)

C (emu/g Oe)

0 (K)

poff (/~B)

0 5 I0 15 20

1.67 2.09 1.90 1.90 1.28

1.31 5.71 6.50 8.91 28.0

10.9 14.4 9.9 9.2 28.1

0.45 0.94 1.01 1.18 2.10

1.012

2Y/

~ 1.00~ ii

~ 1.004 1.000

1.7KK e I

102

[

I

~ lllll

103 t (sec)

i

I

~ i ill

104

Fig. 21. Time dependence of the magnetic susceptibility in a field of 1 T for A165Mn2oGels. Measurements were made at [A] 1.7K, [ A ] 2.0K, [@] 2.5K and [ O ] 3.0K. Data are from McHenry et al. (1989b).

MAGNETISM AND QUASICRYSTALS

487

rate equation and a distribution of energy barriers, reveals an average energy barrier of 6.8 meV, which can be associated with a mean exchange fluctuation energy in the spin glass. 3.3.4. A 1 - T 1 - T 2

Bancel and Heiney (1986) extended the early A1-T QCs to include two dissimilar transition metals in the same alloy, e.g., A179CrlTRU4 or A179MnlTRU 4. These materials fall into the same structural class as A1-Mn-Si QCs (Henley 1986a). More recently QCs have been fabricated based on A1, Cu and a third transition metal, e.g., Fe. These differ structurally from the A1-Mn-Si QCs. One of these, A165Cu2oFe~5 (section 3.3.4.1) has been found to be stable against crystallization (Tsai et al. 1987). At the same time, we review magnetic and M6ssbauer effect measurements on A1M o - F e (section 3.3.4.2) and A1-Ta-Fe (section 3.3.4.3) QCs. A1-Cu-Fe QCs (Tsai et al. 1987) are particularly interesting because they can be produced in the icosahedral phase either by rapid solidification or by slow cooling, and, as a result, this QC phase has been found to be thermodynamically stable. Thermal analysis measurements (Tsai et al. 1987) have shown no crystallization exotherms prior to the melting endotherm. The structure of the stable icosahedral phase of A165Cu2o Fe15 has been determined by Ebalard and Spaepen (1989). Its reciprocal lattice is found to be a projection in three dimensions of the six-dimensional body-centered cubic lattice. Thus, its real space six-dimensional quasi-periodic lattice is face-centered (F-type), unlike the primitive (P-type) six-dimensional cubic cell found by Janot et al. (1989a,b) (section 3.2) for A1-Mn-Si QCs. Those authors (Ebalard and Spaepen 1990) have now confirmed that the metastable A1-Cu-Mn and A1-Cu-Cr QCs (He et al. 1988) also show F-type ordering upon annealing. Fukamichi et al. (1988a) have shown that A1-Cu-Fe which has been prepared by rapid solidification exhibits weak Curie-like paramagnetism superimposed on a temperature independent susceptibility. Replacement of Fe by Cr weakens the Curie component while replacement by Mn strengthens it. The magnetic susceptibility of A1-Cu-Fe has also been measured between 1.5 and 77K (Stadnik et al. 1989). A temperature independent diamagnetic behavior is reported for this alloy with -)~[T] < 2.5 x 10-Semu/gOe. M6ssbauer spectroscopy results (Kataoka et al. 1988, Stadnik and Stroink 1988) suggest that the Fe environment of icosahedral A1-Cu-Fe QCs made by liquid quenching (ICL) differs from those made by devitrification (ICA) (fig. 22) and that these differ from the Fe environment in the tetragonal crystalline (TC) phase A17CuzFel. The quadrupole splitting increases markedly from TC to ICL to ICA. These Fe environment differences exist between ICL and ICA despite the fact that the X-ray diffraction patterns of the two alloYs are essentially the same. Quasiperiodic crystals have also been fabricated in the A165Cuz0Mn15 and A165Cu2oCo15 systems and are found to be two-dimensional decagonal phases (He et al. 1988). 3.3.4.1. Al-Cu-Fe.

488

R . C . O ' H A N D L E Y ET AL.

D~c~0=~o q ~

ICL

.t

==

.

, .

•~

*

, •

I

%****~,

** .

o

-1.0

ooq,oOOco

I

J

0

+1.0

(mm/s)

v

Fig. 22. R o o m temperature 57 Fe M6ssbauer effect spectrum of icosahedral A165Fels Cu2o. ICL and ICA stand for icosahedral phases obtained from liquid quenching and from annealing, respectively. Data are from K a t a o k a et al. (1988).

3.3.4.2. Al-Mo-Fe. Pseudobinary Al-transition-metal alloys (T1-T2) have been found to form particularly well-ordered icosahedral QCs when the relative sizes and stoichiometries of the two transition metals are well adapted to fill the size distribution of transition-metal sites assumed to be available in the icosahedral network (Lawther et al. 1989). A18oMo9Fell is an alloy which falls into this category and the presence of Fe as an intrinsic component allows for the use of M6ssbauer spectroscopy for a better characterization of its physical properties. Hui and Chen (1988) have recently reported the formation of a single-phase icosahedral structure in this material and Srinivas et al. (1989) have subsequently reported X-ray diffraction, magnetic susceptibility and M6ssbauer effect studies of this alloy. Figure 23 shows the results of magnetic susceptibility measurements of icosahedral A18oMo9Felt (Srinivas et al. 1989). These results indicate the presence of a Curielike behavior at low temperatures but a linearly decreasing component that is most evident above about 50 K. This suggests a combination of Curie-behavior and Pauli 1.2 'o x

1.1

~1.0

*%%**•******oo **°ooo. °

I

I

r

100 T

I

I

200 (K)

Fig. 23. Magnetic susceptibility of icosahedral A18oMo9Fell obtained from S Q U I D magnetization measurements in an applied field of I0 kOe plotted as a function of temperature. Data are from Srinivas et al. (1989).

M A G N E T I S M AND QUASICRYSTALS

489

paramagnetism (White 1970). These data, therefore, have been fitted to the expression (7)

z(T) = a + b T + C / ( T - 0),

C is defined in eq. (4). Parameters from this equation are given in table 4. In the above, a and b are arbitrary constants related to Pauli paramagnetic behavior. The data show that there is a small localized magnetic moment formed on the Fe atoms. The negative coefficient b implies that the susceptibility is near a maximum for that T concentration and this may imply that D(E) exhibits a maximum at Ev (White 1970). Additional information concerning the relationship of magnetic and structural properties of this alloy can be obtained on the basis of M6ssbauer spectroscopy. A room temperature 57Fe M6ssbauer spectrum of AlsoMo9Felt from Srinivas et al. (1989) is illustrated in fig. 24. The details of an appropriate fitting procedure for paramagnetic icosahedral alloys is not universally agreed upon. The validity of a particular fitting method is difficult to establish. However, any method which provides a reasonable quality-of-fit is useful in determining average values of the M6ssbauer parameters, such as isomer shift and quadrupole splitting, as well as yielding parameters which are useful in establishing systematics in the context of M6ssbauer measurements of related alloys. A fit to an asymmetric Lorentzian doublet yields anomalous line widths (,-~0.4mm/s FWHM). Dunlap et al. (1991) have accounted for this broadening using several models for the quadrupole splitting distribution in this alloy. In table 5, we show the results from Dunlap et al. (1989a) for a fit to the A1-MoTABLE 4 Parameters from a least squares fit to eq. (7) for icosahedral A 1 - M o - F e and A1-Ta-Fe. Data are from Srinivas et al. (1989). Alloy

a (emu/g Oe)

b (emu/g Oe K)

Peff (/~B)

0 (K)

AlsoMo9Feax m17oTa10Fe20

1.02 x 10 -5 9.28 × 10 -5

--5 x 10 -9 - 4 . 3 2 × 10 - s

0.19 0.48

3.9 2.6

! ~ tJ

,, ",

.: /

(a) "

"~ ": =r- - / " ", \ / ~ i ;

o

(b)

E

I

I

-1.0

I

0 v

*1.0 (ram/s)

Fig. 24. Room temperature 57Fe M6ssbauer effect spectra of icosahedral (a) A180Mo9Feu, and (b) A17oTaloFe2o. Data are from Srinivas et al. (1989).

490

R.C. O'HANDLEY ET AL.

TABLE 5 Results of the shell model fit to room temperature SVFe M6ssbauer spectra of icosahedral A1-Mo-Fe and A1-Ta-Fe. ~o is the isomer shift relative to ~-Fe from eq. (9). A is the mean quadrupole splitting and (A) is the width (FHWM) of the quadrupole splitting distribution. Data for A1-Mo-Fe and A1-Ta-Fe are from Srinivas et al. (1989). Alloy

6 (mm/s)

n

a (ram/s)

a

A (mm/s)

(A> (mm/s)

AlsoMogFela

+0.274 +0.237

1.48 1.14

0.351 0.363

+0.005 -0.103

0.444 0.410

0.579 0.585

A17oTaxoFezo

Fe and A 1 - T a - F e spectra using the shell model (Czjzek 1982, Eibschutz et al. 1986, Stadnik and Stroink 1988). This model expands the quadrupole splitting, A, distribution as

P(A)(A/a)" e x p [ - A 2/(2o.2)],

(8)

where n and o- are fitting parameters. In order to account for the expected symmetry, the isomer shift, 5, and quadrupole splitting are correlated as 5(A) oc go + ~A,

(9)

where 50 and ~ also are obtained from the fits. These results will be considered below in the context of measurements on icosahedral A 1 - T a - F e . F o r the m o m e n t , it is interesting to note that the large value of n is suggestive of a structure with little disorder (Dunlap et al. 1989a). This is consistent, as well, with diffraction studies of this alloy (Hiraga et al. 1988, Ishimasa et al. 1985).

3.3.4.3. Al-Ta-Fe.

The existence of a single-phase icosahedral alloy with a c o m p o sition A17oTatoFe2o has been recently reported (Tsai et al. 1989). The temperature dependence of the magnetic susceptibility as reported by Srinivas et al. (1989) is illustrated in fig. 25. This shows behavior which is quantitatively the same as that for AlsoMo 9 F e l t . Parameters obtained from a fit to eq. (7) are given in table 4. These 12 ~_. 11 x

.~10 -~.

\

°°°*°'=oo.Q,~,

X B

'

'1 o' T

(K)

'3 o

Fig. 25. Magnetic susceptibility of icosahedral AlvoTatoFe2o obtained from SQUID magnetization measurements in an applied field of 10 kOe plotted as a function of temperature. Data are from Srinivas et al. (1989).

M A G N E T I S M A N D QUASICRYSTALS

491

results are similar to those in AI-Mo-Fe except that values of a, b and the Fe moment are significantly larger for the A1-Ta-Fe alloy. This may reflect the higher Fe content of the Ta-containing alloy. A room temperature 57Fe MSssbauer effect spectrum of icosahedral A1-Ta-Fe is illustrated in fig. 24. Parameters from a fit to the shell model [eqs. (8) and (9)] for this spectrum are given in table 5. The obvious difference between the A I - M o - F e and A1-Ta-Fe spectra lies in the asymmetry parameter e in the table. It is interesting to note that, in the case of A1-Ta-Fe, e is large and negative, meaning that the more positive velocity line is more intense. What is perhaps more significant are the values of n and tr given for A1-Mo-Fe and A1-Ta-Fe. For amorphous materials, n is assumed to be unity (Czjzek 1982). In well-ordered QCs, n has been found to be around 2. In a systematic investigation of the effects of disorder on the parameters n and a in single-phase icosahedral AI-(Cr, Fe)-Ge alloys, Srinivas et al. (1990) have suggested for quasicrystals that n approaching unity (from above) and a increasing indicate increasing atomic disorder. In the case of A1-Mo-Fe and A1-Ta-Fe, it is not possible to separate the effects of composition and order on the magnetic properties. However, an increase in the magnitude of the magnetic properties (Port, table 4) in the alloy which shows greater microscopic disorder (n, table 5) is certainly not inconsistent with the situation in crystalline and icosahedral A1-Mn-Si alloys (section 3.3.2). The data of tables 4 and 5 and the above comments suggest a correlation between the magnitude of the magnetic moment and the degree of disorder present in the alloy. Stadnik et al. (1989) have concluded that the degree of disorder is the only relevant parameter for magnetic moment formation in these alloys. This conclusion is consistent with the investigation of rapidly quenched and annealed A1-Cu-Fe quasicrystals presented by Fukamichi et al. (1988a). While the data presented here, as shown in fig. 26, certainly show a correlation between disorder and magnetic moment formation, there is also a clear correlation between the magnitude of the localized Fe moment and the amount of Fe in the alloys. Further systematic studies

0.2/*

I

,

o- (mm/s) 0.30 0.36 ,

,

,

,

0.6

0.4 "G u..

•~

3.2

0.6

:::k 0.4 0.2 0

I

I

10

15 x

I

20

(ai%Fe]

Fig. 26. Correlation between the parameter ~r from the shell model fit to 57Fe MSssbauer spectra and the localized Fe moment. Data are from Dunlap et al. (1991) and references therein.

492

R.C. O'HANDLEY ET AL.

are necessary to determine the relative importance of order, structure and composition on the resulting magnetic properties.

3.4. Ferromagnetic quasicrystals 3.4.1. Al-Mn-Si alloys Ferromagnetic and spin-glass behavior has been reported in amorphous A1-Mn-Si alloys (20at.% < Si < 30at.%) by Hauser et al. (1986) and Fukamichi et al. (1988b). These alloys contain a much larger percentage of Si than the paramagnetic QC A1Mn-Si alloys reviewed in section 3.3.2. Inoue et al. (1988) have shown that some of these melt-spun amorphous alloys could be annealed to form an icosahedral phase (see fig. 27). Dunlap et al. (1989b) have subsequently shown that these single phase ieosahedral A1-Mn-Si alloys exhibit ferromagnetism as well. A more thorough investigation of the A1-Mn-Si phase diagram by Srinivas and Dunlap (1989) has shown that ferromagnetic A1-Mn-Si quasicrystals can be prepared directly by melt spinning over a wide range of compositions (fig. 28). Magnetic measurements on two ferromagnetic A1-Mn-Si quasicrystals, Also Mn2o Siso and A15sMn2oSi25, have been reported by Dunlap et al. (1989b). Both

5

2O

I

I

/~0

I

I

6O 2 O (degrees)

I

80

Fig. 27. Cu Kc~ X-ray diffraction patterns of AlsoMn2oSiso, (a) as cast (amorphous), and (b) annealed at 648 K for 90 min (icosahedral). Data are from Dunlap et al. (1989a). Icosahedral indices are given according to the scheme given by Bancel et al. (1985).

At ~

Mn

'4

',0 si

Fig. 28. Phase diagram of the A1-Mn-Si system for greater than 20 at.% Si content. (Q) ferromagnetic quasicrystal as-quenched, (~) ferromagnetic quasicrystal prepared by annealing amorphous precursor, (O) amorphous, (A) mixed phase. All alloys were quenched onto a single Cu roller with a surface velocity of 60m s-1. Data are from Srinivas and Dunlap (1989).

MAGNETISM AND QUASICRYSTALS

493

of these alloys show essentially the same magnetic behavior. Figure 29 shows a typical low-field hysteresis loop for one of these alloys in the ferromagnetic regime. The coercivity is about 20 Oe, showing that these materials are not particularly hard magnets, but neither are they as soft as might be expected on the basis of theoretical predictions (section 2.5). Figure 30 shows the low-field magnetization curve (100 Oe) for A15oMn2o Si3o; for comparison, the figure also shows the 100 Oe magnetization curve of amorphous A15sMn2oSi2s. Table 6 compares the magnetic properties of icosahedral and amorphous A1-Mn-Si ferromagnets. Both alloys show similar Curie temperatures but have two important differences:

°11// flV

I

L

-0

i

I

600 H

i

1200 (Oe)

Fig. 29. Low-field hysteresis loop for icosahedral AlsoMn2oSiso at 10K. Data are from Dunlap et al. (1989a). 02 o°.

o

..~ =

"(a)

0.1

Z

•••e •o

tm io

o;

lOO 1so T(K)

Fig. 30. Magnetization curves measured in a field of 100Oe for (i) icosahedral A15oMn2oSiao and (a) amorphous A155Mn2oSi25 (Dunlap et al. 1989a). TABLE 6 Magnetic properties of icosahedral and amorphous A150Mn2o Si3o and A155Mn2o Si25 alloys; I = icosahedral, A = amorphous. Data are from Dunlap et al. (1989b). Alloy

Phase

A15oMn2oSiao

I A I A

AlssMn2oSi2s

Ms ( 100 Oe) (emu/g)

Tc (K)

Peff ( #B)

0.12 0.21 0.07 0.16

112 110 115 107

0.24 0.032 -

494

R.C. O'HANDLEY ET AL.

(1) the magnetization at 100 Oe for the amorphous alloy is somewhat greater than that for the icosahedral one; and (2) the icosahedral alloy shows a magnetization which has a slight upturn below about 15 K. This upturn is more apparent in larger applied fields, as illustrated in fig. 31 for i-AlavMn3oSi33 (Chatterjee et al. 1990). At the highest applied fields (H ~>5 kOe) the M - T behavior is almost Curie-like. At intermediate fields (100kOe ~
t

I

~

3 "~

0.4

I

~H=I5kOe

~2

I

:~ O.lk__~ O[rT .... 0 40 80

0

120

T(K)

\ , 5kOe \ / 2 kOe

100

200

300

I

l -I

,t

400

500

Temperature ( K )

Fig. 31. Temperature dependence of magnetization of icosahedral AlaTMn3oSi33 measured in various applied fields (Chatterjee et al. 1990). 5

i-N3-rMn3oSi33

4

M2

5 2 1 0

80 [

120

150

,')2.2 5 4 lO-4H/M

5

6

Fig. 32. Arrott plot of field- and temperature-dependent magnetization for A137Mn3o Si33 QCs (Chatterjee et al. 1990).

MAGNETISM AND QUASICRYSTALS

495

One further piece of evidence of concentrated spin-glass behavior in these systems is the strong time dependence in the magnetization in an applied field after zerofield cooling (Chatterjee et al. 1990). While further studies are under way, it is clear at this point that the time dependence is not generally logarithmic in time. This mixed magnetic behavior, combining spin-glass and ferromagnetic features, will be compared in section 5 with the dilute spin-glass behavior exhibited by QCs containing less Mn. A ferromagnetic resonance (FMR) study of icosahedral A155Mn2oSiz5 has been reported by Misra et al. (1989). A typical FMR signal below the Curie temperature (i.e., at liquid-nitrogen temperature) is illustrated in fig. 33. The strong peak at about 1400 Oe is observed only below Tc = 120 K. Its position and strength are sensitive functions of temperature. The weak response at 2900 Oe was found to be relatively insensitive to temperature even above Tc. Misra et al. suggested that the strong signal was associated with ferromagnetically ordered Mn while the weak FMR response (actually an electronic paramagnetic resonance) was to be associated with paramagnetic Mn. Since FMR data were reported only for in-plane applied field H, it was not possible to determine both the g factor and the magnetization independently from a single FMR measurement. The g factor, assumed to be temperature independent, was inferred from the extrapolation of the position of the FMR peak as it vanished at T = To. The resulting g factor is 2.3. The temperature dependence of the position (and area) of the main FMR line can then be analyzed to give 4~Ms(0) = 6.35 kG with Ms(T) as shown in fig. 34. These F M R data provide convincing evidence that the unusual magnetic properties of ferromagnetic A1-Mn-Si QCs are an intrinsic property of the QC phase and are not due to a precipitate or impurity phase. The upturn in M(T) at low temperature (fig. 34) is consistent with that observed in SQUID measurements. Also, if the two resonance signals were assumed to arise from two different phases in the QC, then the paramagnetic phase should see an effective field made up of the vector sum of the applied field plus a temperature dependent contribution from adjacent ferromagnetic regions. Since the paramagnetic resonance is essentially temperature independent, this is not the case. However, a basic difficulty becomes evident if the magnetization inferred from the FMR data (6.35 kOe) is compared with that obtained from magnetometer measure-

g, u._ 0

100

200 300 H(mT}

~-00

500

Fig. 33. Ferromagnetic resonance signal observed at 79.5 K for icosahedral A155Mn20 Si25. This result was obtained using a conventional X-band (9.5 GHz) ESR spectrometer. The line corresponding to the D P P H marker is indicated. Data are from Misra et al. (1989).

496

R.C. O'HANDLEY ET AL.

i•

-~300 c

.o o

200

•l o °oo

o

a

• o

~Z

• o

i=n

"4

100

;2-

o; 2;

o

T

s; 8'o 1;o

14o

(K)

Fig. 34. Amplitude of the principal FMR peak in icosahedral A155Mn2oSi25 measured at 9.5 GHz. The effective g factor for the principal FMR peak in icosahedral A155Mn2o Si25 is measured at 9.5 GHz. Data are from Misra et al. (1989).

ments, invariably a few emu/g or less, which corresponds to 4nMs at least two orders of magnitude smaller than the FMR value. Also, Artman (1990) points out inconsistencies in the shape (the observed F M R peak is a mixture of a Lorentzian and its derivative) and area (the QC and amorphous phases show FMR peaks that differ by a factor of 5 or 6 in intensity) of the resonance curves that suggest that these FMR data are not yet properly understood. The small magnetization, in conjunction with the moderately high Curie temperature, is a typical feature of ferromagnetism in icosahedral Al-based materials discovered so far. This will be seen for the other Al-based ferromagnets discussed below. The total of the evidence accumulated thus far for icosahedral ferromagnets points to the fact that the ferromagnetism is an intrinsic property of the material. No evidence of an additional phase has been seen in X-ray diffraction patterns of either amorphous or icosahedral phases of the present alloys. Finally, scanning electron microscopy studies (Fukamichi et al. 1988b, Foldeaki and Dunlap 1989) have revealed no compositional inhomogeneties at grain boundaries. Further high-resolution microscopy is needed. 3.4.2. A1-Mn-Ge and related alloys Ferromagnetic order was first reported in icosahedral A1-Mn-Ge and related alloys by Tsai et al. (1988). As in the case of i-A1-Mn-Si, Ge-based alloys with relatively small metalloid content are paramagnetic, while alloys with higher metalloid content are ferromagnetic. Although the alloys reported by Tsai et al. (1988) as ferromagnetic all contain 22.5 to 25 at.% Ge, a systematic study of magnetism in lower Ge-content alloys has not been reported. It is clear, however, that A165MnzoGels, as reported by McHenry et al. (1989b) and described in section 3.3.3, does not order ferromagnetically. Figure 35 shows magnetization results for A14oMnzsCuloGe25 and A152.sMnzsGe22.5 (Tsai et al. 1988). Although the measurements shown here have

MAGNETISM AND QUASICRYSTALS

497

2.0

$1.o z '

(b)

100

300 500 T(K) Fig. 35. Temperature dependence of the magnetization of icosahedral (a) A14oMn25CuloOe25, and (b) A152.5Mn25Ge22.5,measured in an applied field of 4kOe. Data are from Tsai et al. (1988). only been reported for T > 100K, the following interesting features are apparent from the figure: (1) Both alloys show approximately the same Tc despite differences in composition and sizeable differences in the magnetization at low temperatures. This phenomenon has also been seen in ferromagnetic A1 M n - S i quasicrystals (McHenry et al. 1990). (2) The magnetization at low temperature is larger than that observed in icosahedral A1-Mn-Si ferromagnets, but Ms/Tc is comparable in magnitude in the two systems. (3) Both Ge based i-alloys show a concave upward behavior below about 200 K which is reminiscent of the upturn in the magnetization seen at low temperatures in i-A1-Mn-Si ferromagnets. McHenry et al. (1990) have measured the magnetization of the related quasicrystals A14oMn2s Fe3 CuT Ge25 and A14oMn25 Fe6 Cu4Ge25 down to ~ 5 K. Results for the latter alloy are shown in fig. 36; the former behaves the same, qualitatively. While the shape of the 100-400K portion of this curve is consistent with the data from A140Mn2sCuloGe25, the data below 100 K and the strong field dependence clearly 20

I

I

I

--

I

I

I

i

=

5

H--0.01T I

I

100

t

I

200

,

:500

400

Temperoture( K) Fig. 36. Temperature dependence of the magnetization in different applied fields for icosahedral AlaoMn25Fe6Cu4Ge25. Data are from McHenry et al. (1988b).

498

R.C. O'HANDLEY ET AL.

illustrate the complex behavior of this system. The addition of Fe has dramatically increased the magnetization relative to that of the alloys in fig. 35. The magnetization of 19emu/g corrresponds to a ferromagnetic moment per transition-metal atom of about 0.6#B. The addition of iron has also decreased Tc to about 400K. A very strong field dependence is observed in the magnetization over the entire temperature range and an anomalous low-temperature component to the magnetization appears below 100K in higher applied fields. Thus, this QC appears to have appreciable second phase with a magnetization that is more field dependent than the matrix. A departure of the zero-field-cooled magnetization from Curie-like behavior observed at low temperatures is associated with spin-glass ordering below about 15 K. The hysteretic behavior of the A1-Mn-Ge and A1-Mn-Cu-Ge alloys reported by Tsai eta L (1988) is illustrated in fig. 37. This figure reveals the difficulty in saturating these alloys, especially the A1-Mn-Ge, even in large applied fields, and shows their sizable coercive force. This latter characteristic is clearly at odds with the prediction of magnetic softness in magnetic QCs (McHenry et al. 1987, McHenry and O'Handley 1987) (section 2.5). Similarly, McHenry et al. (1990) have observed a coercive force of about 1.8 kOe at 4.2 K in A14oMn25Fe3CuTCu3Ge25. From the extrapolated saturation value of the magnetization (i.e., about 4 emu/g), the average ferromagnetic moment per Mn is determined to be ~0.12#B. Dunlap and Srinivas (1989) have recently reported 57Fe M6ssbauer effect studies of the ferromagnetic quasicrystal A14oMn2sFeaCuTGe25. Typical spectra obtained in this study are shown in fig. 38. Dunlap and Srinivas have shown that these spectra indicate an internal Fe hyperfine field of + 17 kOe. The hyperfine field distributions obtained from these spectra, using the fitting method of LeCaer and Dubois (1979), are shown in fig. 39. This figure shows a clear shift of the peak in P(H) towards higher field when an external field is applied and indicates the positive sign of the internal Fe field. Dunlap and Srinivas (1989) have shown, as well, that the temperature

(a)

0.2

i

(12

H

(k0e}

Fig. 37. Room temperature hysteresis for icosahedral (a) A152.sMn25 G%2.5, and (b) A14oMn25Cu~oGe25. Data are from Tsai et al. (1988).

MAGNETISM AND QUASICRYSTALS

2_ .-'~.,~ .~:,,..~.

.= -

.,.,.v.~. ~z

"""~'V.;:

.,"'~" " :" Ca)

~ ".'.. -

?

..

.~

;. g "~f"~" ,~.,~>.z.:. •, f Cb) \ -

E

i

"~"..'.,r,,'~.,

499

I

-1.0

(~

v

[minis)

+1.0

Fig. 38. Room temperature 57Fe M6ssbauer effect spectra of Al40 Mnz5 F% Cur Ge2s (a) without an external magnetic field, and (b) with an external magnetic field of 4.8 kOe. Data are from Dunlap and Srinivas (1989).

1 V

2_ 'E

J F-'--"

A

1]

(a)

I (b) t

I

0

[

i

10 H

(kOe)

2~0

~

30

Fig. 39. Room-temperature Fe hyperfine field distributions obtained from the M6ssbauer spectra of fig. 38, as described in the text. Data are from Dunlap and Srinivas (1989).

dependence of this hyperfine field is consistent with a value of Tc between 400 and 500 K. On the basis of the measured Fe hyperfine field, we estimate the average localized Fe magnetic moment to be 17 kOe/(150 kOe/#a) = 0.11#~. This value is similar to the value of the average Mn moment obtained in these materials on the basis of bulk magnetization studies. This is additional evidence that the weak ferromagnetic behavior, in conjuction with relatively high values of Tc, as seen in both the A1-Mn-Si and A1-Mn-Ge systems, is an intrinsic property of ferromagnetic A1-Mn-based quasicrystals. Comparisons have been made between icosahedral and amorphous phases of ferromagnetic A1-Mn-Si (section 3.4.1). No information concerning the magnetic properties of analogous crystalline alloys has been found in the literature. Some comparisons of the magnetic properties of the ferromagnetic A1-Mn-Si and A1-Mn-Ge quasicrystals with those of the crystalline equiatomic A1GeMn ( C u z S b structure) phases are noteworthy. Crystalline MnA1Ge shows a Tc of 484K, a ferromagnetic moment of 1.7#a/Mn and an effective moment from the paramagnetic susceptibility of 2.9#B/Mn (Shibata et al. 1972, Shinohara et al. 1981, Kamimura et

500

R.C. O'HANDLEYET AL.

al. 1985). Although these crystalline materials show Curie temperatures similar to those of the icosahedral alloys, they show significantly larger saturation magnetizations (55 emu/g), and larger average Mn moments than the QCs. The amount of this crystalline phase necessary as an impurity to account for the magnetic properties of icosahedral A1-Mn-(Cu)-Ge (1 or 2%) would certainly not be observed in X-ray diffraction measurements (McHenry et al. 1989b). However, the amount needed to account for the magnetic properties of A1-Mn-Fe-Cu-Ge QCs certainly could not be missed by diffraction experiments. Electron microscopy (Tsai et al. 1988) has so far shown no evidence of crystalline A1MnGe precipitates. It is interesting to note that Fe substituted into crystalline ferromagnetic A1MnGe can occupy either the A1 or Mn sites. At neither site does Fe bear a moment (Shinohara et al. 1981). Also, other Mn-containing Cu2 Sb structures are antiferromagnetic [e.g., Mn2Si (Wilkinson et al. 1957)]. This illustrates the sensitivity of the sign of the M n - M n magnetic coupling to changes in chemical composition or MnMn distance. More careful comparison of magnetism in icosahedral A1-Mn-based materials with that of analogous crystalline compounds may be insightful, although it is important to consider the fact that quasicrystalline materials are intrinsically disordered. 3.4.3. A I - F e - C e alloys

Ferromagnetism has been reported in the icosahedral and decagonal QC phases of A165.3Fe27.3CeT.4 obtained by annealing the amorphous phase (Zhao et al. 1988). The magnetization curves show a strong paramagnetic component (4.5 x 10-5 emu/ g Oe) at 1.5 K superimposed on the weak spontaneous magnetization. The effective paramagnetic moment is reported to be 3.9#a/Fe for the icosahedral phase. The magnetization of the decagonal phase in H = 3 kOe, namely 2 emu/g, corresponds to a net ferromagnetic moment of 0.054#a/Fe. The spontaneous magnetization vanishes at Tc = 340 K. The M - H and M - T curves for these phases are shown in figs. 40 and 41. The weak spontaneous magnetization of the icosahedral phase is masked in fig. 40 by the strong paramagnetism in both the M - H (fig. 40) and M - T (fig. 41)

6 •

E 4 OA

z

x o

°•

_.'j*

x o

I •

l

i?

10

i

i

40 H (kOe)

i

60

Fig. 40. Magnetization versus applied field curves for Al-Ce-Fe alloys in the ((3) icosahedral, (O) decagonaland (x) amorphousphases at 1.5K. Data are from Zhao et al. (1988).

MAGNETISM AND QUASICRYSTALS

--~

501

(ca)

£ li

[',.,~

0[

0

.......

(b) ,

"~"-T-

100

"=',-'~

°-B: ~

200

----._

'"~ I I

300

T (K)

Fig. 41. Temperature dependence of the magnetization of AI-Ce-Fe in the (a) decagonal, (b) icosahedral and (c) amorphous phases. Data are from Zhao et al. (1988).

curve. In both curves, the decagonal QC phase shows a behavior more typical of ferromagnetism. Zhao (1989) reports other nearly equiatomic A1-Fe R (R = rare earth) QCs which have saturation magnetizations from 40 to 50 emu/g. 4. Quasierystals not based on AI

4.1. Ti-Ni based quasicrystals Kuo and coworkers (Zhang et at. 1985, Zhang and Kuo 1986) first reported the presence of small grains of a decagonal quasicrystalline phase in Ti2_xVxNi alloys. Part of the interest in this system stems from two factors: first, that it is based entirely on transition metals, and second that the fcc structure of crystalline TizNi (Yurko et al. 1959) contains two interpenetrating icosahedra with central sites occupied by Ni atoms. Given the importance attached by theoretical considerations (sections 2.1.1 and 2.1.3) to transition metals in high-symmetry sites, the occupation of such sites in this crystalline phase and their nonoccupation in ~-A1-Mn-Si, the crystalline analog of A1 Mn-Si QCs was significant at the time ~-A1MnSi was a possible structural model for A1-Mn-Si QCs. It no longer is (de Boissieu et al. 1988). Chatterjee and O'Handley (1989) were able to fabricate single icosahedral phase QCs having large grains in the Tis6Ni28 Si16 system. Magnetic susceptibility shows Curie-like behavior at low temperature with an effective paramagnetic moment of only 0.05#B/Ni. The structure of this new class of QCs (Dunlap et al. 1988c, 1989b) appears to be quite different from that typical of other QCs (sections 3.2 and 3.3.4). In the TiNiSi QCs, the intensity of the [110000] peak is 4 to 5 times that of [100000]. In A1 M n Si, the [100000] peak is more intense than the [110000]. Structure factor calculations (Ishihara and Shingu 1986) for different decorations of the prolate and oblate rhombohedra of three-dimensional Penrose lattice show that the observed dominance of the [110000] reflection can only be accounted for in such a lattice by a decoration with atoms at both the vertices and edges of the rhombohedra (Dunlap et al. 1988c). This is in contrast to the three-dimensional real space structure determined for A1-MnSi (Janot et al. 1989a) which has vertex, face- and body-centered sites but no edge sites (fig. 11).

502

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Substitution of Fe for Ni in Ti56Ni28_xFexSiz6 QCs improved the ease of icosahedral phase formation. Magnetic measurements on these materials gave the following results. For the first time in a QC, Fe exhibited a local moment of order 0.2#B (X = 15) (Dunlap et al. 1988b). Magnetization measurements for alloys with x up to about 8 at.% Fe (Christie et al. 1990) reveal anomalous behavior of the susceptibility as shown in fig. 42. This figure indicates Curie-like behavior for x = 5 at low temperatures and an increasing, possibly Pauli paramagnetic behavior, at high temperatures. For higher Fe concentrations (x = 10), the Curie behavior dominates the temperature dependence of Z. There is, however, a large residual value of Zo. Since the temperature dependence of the Pauli contribution to the susceptibility is fairly sensitive to the density of states at the Fermi energy, it is not surprising that the substitution of one transition metal for another can, in cases where Pauli paramagnetism is observed, have substantial effects on the temperature dependence of Z (White 1970). M6ssbauer effect spectroscopy showed no detectable quadrupole splitting (0___0.05ram/s) at the Fe sites in Ti-(Ni, Fe)-Si QCs (Dunlap et al. 1989b). In contrast, A1-Mn-Si QCs show a mean quadrupole splitting of order 0.4mm/s. Clearly, the Fe sites in Ti-(Ni, Fe)-Si QCs see a crystalline electric field of considerably higher symmetry than the Fe sites in A1-Mn-Si QCs. Because there are no sites of cubic symmetry in a three-dimensional Penrose lattice, it appears likely that Fe occupies sites of nearly icosahedral symmetry in Ti-(Ni, Fe)-Si. Figure 43 compares the M6ssbauer spectra for several related Ti-(Ni, Fe)-Si phases. The M6ssbauer spectrum of Ti2Nio.85 Feo.15 (which has the fcc Ti2Ni structure) shows a nonzero electric quadrupole splitting as expected for this structure. The addition of Si stabilizes the bcc TiNi phase in Ti56Ni2s.sFe2.sSi16 and this crystalline phase shows no quadrupole splitting as would be expected for the nearly cubic environment of Fe in a bcc structure. Amorphous Ti-(Ni, Fe)-Si shows a quadrupole splitting comparable to that of fcc Ti(Ni, Fe). It is instructive to consider the magnetic results on i-Ti-(Ni, Fe)-Si in light of the structure of these materials, particularly the implication of vertex and edge site occupation on the acute Penrose bricks. The implication of the low quadrupole splitting is that Fe (and Ni) occupy the acute vertices of the prolate rhombohedron, one of which may be at an icosahedral site. In this respect, the structure of i-Ti-(Ni, Fe)-Si may resemble that determined by neutron scattering on i-A1-Mn-Si (Janot

3.6 x=5

2 3.2 *....

x=lO * * o

.

~ 213

T (K) Fig. 42. Magnetic susceptibility of Ti56Ni23 Fe 5 Si16 and Ti56NilsFeloSi 6 measured in an applied field of 1 T. Data are from Christie et al. (1990).

M A G N E T I S M AND QUASICRYSTALS

503

(') '\ , [ t'

t

8

L

I

I

-1.0

I

V

I

I

L

I

0 +1.0 {mm/s)

Fig. 43.57Fe M6ssbauer-effect spectra obtained at room temperature for (a) crystalline Ti2Nio.85Fe0.1s, (b) crystalline Tis6Nizs.s Fe2.5 Si16, (c) icosahedral Ti~6Ni25.sFe2. s Six6 , (d) icosahedral Tis6Ni23 Fe5 Si16, (e) icosahedral Ti56Ni2o.sFev.sSi16, and (f) amorphous Tis6Ni25.sFe2.sSi16. The full lines represent computer fits to two doublets for (a) and to one singlet for (b)-(e) and one doublet for (f). Data are from Dunlap et al. (1989b).

et al. 1989a), where a high probability of Mn at the apices of the acute rhombohedron is deduced for that structure. However, the prolate rhombohedron in A1-Mn-Si is face and body occupied, whereas for Ti-(Ni, Fe)-Si it appears to be edge occupied.

4.2. Other quasicrystals Quasicrystals have also been made in a variety of alloy classes not yet discussed here. These include Pd6oUzoSi (Poon et al. 1985), Ni-Zr (Jiang et al. 1985), TizFe (Dong et al. 1986), and GaMg2.1Zn3.8 (Ohashi and Spaepen 1987) which are icosahedral, (V or Cr)-Ni-Si (Wang et al. 1987) and Mn4Si (Cao et al. 1989) which are octagonal, and (TiV)2 Ni (Fung et al. 1986), Ni-Cr (lshimasa et al. 1985) and T - N i Si (T = V, Cr, or Mn) (Wang et al. 1987) which are decagonal. For most of these, no magnetic properties have been reported. The magnetic susceptibility of i-PdUSi is very well described by eq. (4) with Pelf = 2.3#B/U atom, 0 = - 1 0 K and Xo = 0.22 x 10-3 emu/mol. Consideration of the magnitude of the contributions to Xo suggests that the I phase has a lower density of states at EF than the amorphous or crystalline counterparts (Pooh et al. 1985, Bretcher 1987). The AC susceptibility shows a peak at 5.5 K which is not suppressed by a DC field (Wong and Poon 1986). It is suggested to be linked to the onset of an antiferromagnetic state. The low temperature specific heat shows a large electronic term, 7 = 165mJ/ mol U K 2, 37% greater than that of the amorphous phase (Wosnitza et al. 1988).

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R.C. O'HANDLEYET AL.

5. Conclusions and outlook

We have seen that Al-based quasicrystals show magnetic behavior that ranges from diamagnetic (A1-Cu-Fe) to ferromagnetic (A1-Ce-Fe, A1-Mn-Si, AI-Mn-Ge and related alloys). Paramagnetic and spin-glass behavior is observed in many Cu- Mnor Fe-containing alloys. The strength of the magnetic interactions is closely correlated to the degree of disorder in the alloy and appears to be governed by a distribution of transition-metal environments. The possible bimodality of this site distribution has been the subject of controversy and appears still to be an open question. The only nonlinear determinations of the effective paramagnetic moment concentration in QCs are based on a fit to the magnetization data beyond the regime linear in H/T (Machado et al. 1987a) or on detailed linear and nonlinear susceptibility measurements at low temperature (Berger and Prejean 1990). The former indicates a moment of 11#~ per cluster of 100 Mn atoms and the latter suggests only 1.3% of the Mn bear moments and they are grouped in clusters having a moment of 7.5#B. These results are clearly at odds with the results of linear fits (1.2#B/Mn in A1-MnSi QCs). Only the former results are compatible with specific heat measurements. Despite this glaring deficiency in the linear data, we have reviewed it in order to reveal trends in p~ff with composition and structure. Plausible fits to the Peel versus x data in Al-(Mnzo_xTx)-Si QCs strongly suggest a distribution, largely bimodal, of moments: larger (smaller) moments appear on Mn atoms in larger (smaller) sites. Thus, to speak of magnetic species concentration as equivalent to Mn concentration is probably wrong. The concentration of magnetic moments is much less than the Mn (or other moment-bearing T species) concentration. Weak ferromagnetism has been found in A1-Ce-Fe and high metalloid, high Mn content in A1-Mn-Si and A1 Mn-Ge quasicrystals. The substitution of Ge for Si in paramagnetic quasicrystals enhances the ability of Cr and Mn to form a localized moment. In the case of ferromagnetic quasicrystals, substitution of Ge for Si increases the Curie temperature and the saturation magnetization. With saturation magnetizations in some A 1 - M n - F e - C u - G e quasicrystals approaching 20 emu/g the possibility that their ferromagnetism is due to an undetected crystalline precipitate seems unlikely. These ferromagnetic QCs typically show paramagnetic or spin-glass behavior combined with the ferromagnetic ordering. This is manifested by anomalies in the low-temperature magnetization and differences between the field-cooled and zerofield-cooled behavior. It is possible that some of the behavior described as ferromagnetism in certain QCs (e.g., A155Mn2o Si25) is in fact concentrated spin-glass or mixed magnetic behavior with a time-dependent remanence that decays to zero only after long times for Tg < T < Tc, and in experimental times near Tg. That lower Mn content QCs (e.g., A174Mn20 Si6) exhibit dilute spin-glass behavior is well documented in the literature. The term dilute is not inappropriate because, as mentioned above, although the Mn concentration may be 20at.%, only a small fraction of these Mn atoms appear to bear moments. The compositional trend in measured Tgs (fig. 15) is consistent with compositional scaling theories

M A G N E T I S M A N D QUASICRYSTALS

505

for spin glasses (Sherrington and Kirkpatrick 1975). It may also be described by a more general formalism (Sellmyer and Naris 1985), if it is accepted that the mean exchange interaction Jo increases with increasing Mn content (fig. 44). Thus, the relative magnitude of the exchange fluctuations 6 AJ/J o decreases with increasing Mn content. Further, increases in Mn content and possible QC structural stabilization with increasing Si (Ge) content (e.g., A137Mn3oSi33) decreases 6 even more, moving the alloys into the mixed ferromagnetic spin-glass regime. This accounts for the timedependence, anomalous Arrott plots and large high-field susceptibility of some of the so-called ferromagnetic QCs (section 3.4.1). It is important to establish whether the fluctuations responsible for the spin-glass behavior are a necessary concomitant of perfect quasiperiodicity or whether they are associated with the disorder in all the QCs studied so far. To this end, it will be important to look for signs of spin-glass behavior in stable QCs such as A1-Cu-Fe (Burkof 1989). In this alloy, it is possible to anneal-out many of the defects without loss of the quasiperiodicity. It has been five years since quasicrystals were discovered. During that time, and since mid-1988 in particular, the diverse and unusual magnetic properties have become known from extensive experimental work. Also, a number of theoretical considerations of the effects of QC order on magnetism have appeared. Experimental and theoretical efforts in this area have, however, made separate progress without significant interaction. For example, a clear comparison of measured and predicted state densities has not been made and is certainly an area in which future work could be highly informative. There is a great opportunity to explore the phase diagrams and critical behavior of QCs exhibiting mixed magnetic and reentrant spin-glass behavior. The major question here is the origin of the random exchange interactions. Coercivities are another case in point. Predictions of magnetic softness have not been realized; ferromagnetic QCs are frequently very hard magnetically. Are the coercivities strongly time dependent? Measured Ms values of, at most, a few emu/g and mediocre coercivities, until recently, seemed to suggest little hope for commercial utilization of magnetic QCs. Now, QC alloys with Ms values approaching those of =

!

"~T.~ M I SG

i

S" Fig. 44. Sellmyer-Nafis phase diagram (Sellmyer and Naris 1985) for r a n d o m exchange systems, t = kB T/ Jo, ~ = A J / J o , F = ferromagnetic, P = paramagnetic, SG = spin-glass and M = mixed magnetic phase fields. Some of the QCs reviewed here are located on the 6 axis.

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ferrites, modestly high Tc values and coercivities approaching 2 kOe, certainly encourage further research in this area. Most recently, reports of Fe-rich QCs, Fe85Cu15 (Shang and Liu 1989), seem to offer hope for continued growth and interest in magnetic quasicrystals. Acknowledgements The authors gratefully acknowledge the hospitality of Los Alamos National Laboratory for a period in 1989 which this chapter was begun. The work at MIT was supported initially by a grant from the National Science Foundation (DMR 8318829) and is continued under U.S. Army Research Office contract DAAL-03-87-K-0099. Work at Dalhousie University was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada (operating grant OGP0005604) and a NSERC Cooperative Research and Development grant (CRD0039103) in conjunction with Alcan International Limited. The technical assistance of Robin Lippincott on the manuscript, the references and the figures, is deeply appreciated. References Aharony, A., and E. Pytte, 1980, Phys. Rev. Lett. 45, 1583. Alben, R.A., J.I. Budnick and G.S. Cargill III, 1978a, in: Metallic Glasses, eds J.J. Gilman and H.J. Leamy (ASM, Metals Park) p. 304. Alben, R.A., J.J. Becker and M.C. Chi, 1978b, J. Appl. Phys. 49, 1653. Artman, J.O., 1990, personal communication. Audier, M., and P. Guyot, 1986, Philos. Mag. B 53, L43. Bagayoko, D.N., N. Brener, D. Kanhere and J. Callaway, 1987, Phys. Rev. B 36, 9263. Ball, M., and D.J. Lloyd, 1985, Scr. Metall. 19, 1065. Bancel, P.A., and P.A. Heiney, 1986, Phys. Rev. 33, 7917. Bancel, P.A., P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, 1985, Phys. Rev. Lett. 54, 2422. Baxter, D.V., R. Richter and J.O. Str6m-Olsen, 1987, Phys. Rev. B 35, 4819. Bellisent, R., F. Hippert, P. Monod and F. Vigneron, 1987, Phys. Rev. B 36, 5540. Bendersky, L., 1985, Phys. Rev. Lett. 55, 1461. Berger, C., and J.J. Prejean, 1990, Phys. Rev. Lett. 64, 1769. Berger, C., K. Hasselbach, J.C. Lasjaunias, C. Panlsen and P. Germi, 1988a, J. Less-Common Metals 145, 565. Berger, C., J.C. Lasjaunias, J.L. Tholence, D.

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chapter 6 MAGNETISM OF HYDRIDES

G. WlESINGER and G. HILSCHER Institute for Experimental Physics, TU Vienna A-1040 Vienna, Austria

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991 511

CONTENTS 1.

Intr oduct:'on

2.

Formation

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E l e c t r o n i c !0rol:erties

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Basic aspecls of nnagnetism

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R e v i e w o f e ~ p e r i r r e n t a l a n d tl~eoretical r e s u l t s Binary rare-earth 1Ddr:des

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534

Binary actinide hydrides

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5.2.1.

ThHx

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535

5.2.2.

PaI-t~

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5.2.4.

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5.2.5.

PuHx

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5.3.

Binary transition-metal

54.

Ternary rare-earth-transition-melal 5.4.1.

5.4.2.

h3drides .

Hydrides of Mn compcunds 5.4.1.1.

General feattres

5.4.1.2.

R6 M n 2 3

5.4.1.3.

RMn 2 .

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536

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536 .

537

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537

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537

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540

Hydrides of Fe compounc's 5.4.2.1.

General feattres

5.4,2.2.

RFe12 .

5.4.2.3.

R2Fel7

5,4.2.4.

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. .

. . . . . . .

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541

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541

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541

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R2 F e 1 4 B .

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543

512

MAGNETISM 5.4.2.5.

RFe5

OF HYDRIDES

513

. . . . . . . . . . . . . . . . . . . . . . . .

544

5.4.2.6. R6 Ee23 . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.7. R F e 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.8. R F e 2 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.9. R F e . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.10. R 2 F e , R 3 F e . . . . . . . . . . . . . . . . . . . . . 5.4.2.11. R v F e 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3. H y d r i c ' e s of C o c o n : p o u n d s . . . . . . . . . . . . . . . . . . . 5.4.3.1. G e r e r a l f e a t u r e s . . . . . . . . . . . . . . . . . . . . 5.4.3.2. R / C o 1 4 B . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.3. g C o 5 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.4. R 2 C o v . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.5. R C o 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.6. R C o 2 , R T C o 3 . . . . . . . . . . . . . . . . . . . . . . 5.4.3.7. U C o , U 6 C o 5.44. Hydrides of Ni compcunds . . . . . . . . . . . . . . . . . . . 5.4.4.1. G e r e r a l f~atures . . . . . . . . . . . . . . . . . . . . 5.4.4.2. R N i 5 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4.3. R 2 N i 7, R N i 3 . . . . . . . . . . . . . . . . . . . . . 5.4.4.4. R a N i . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4.5. R T N i 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.5. H y d r i & s o f m i s c e l l a n e o u s c o m p e t n d s . . . . . . . . . . . . . . . 5.4.5.1. R a r e - e a r t h a n d ~ctinide c o m p o u n d s . . . . . . . . . . . . . 5.4.5.2. P u r e a n d o x y g e n - s t a b i l i z e d Ti a n d Z r c o m p o u n d s . . . . . . . . 5.5. H y d r i d e s c f a m o r p h o u s alloys . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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548 549 550 553 554 554 554 554 554 554 558 559 560 560 561 561 561 562 562 563 563 563 566 567 570

1. Introduction

Intermetallic compounds of 3d metals (particularly Mn, Fe, Co and Ni) with rareearth elements exhibit a large variety of interesting physical properties. The magnetic properties of these intermetallics [-for reviews see, e.g., Wallace (1973) Buschow (1977a, 1980a) and Kirchmayr and Poldy (1979)] are a matter of interest for two main reasons. Firstly, their study helps to elucidate some of the fundamental principles of magnetism (RKKY interaction, crystal-field effects, valence instabilities, magnetoelastic properties, coexistence of superconductivity and magnetic order). Secondly, they are of technical interest, because several compounds (RCos, R2Co17, NdzFelgB ) were found to be a suitable basis for high-performance permanent magnets. More recently, the unique soft-magnetic properties made amorphous metal-metalloid alloys to a further class of materials which are of considerable importance with regard to industrial application. Since the discovery of LaNi5 as a hydrogen storage material roughly two decades ago, a vast number of intermetallic compounds and alloys has been involved in studies of the hydrogen-induced changes of their physical properties. A large variety of techniques has been applied in order to elucidate the mechanism of hydrogen uptake which is particularly complex in intermetallic compounds. They can roughly be divided into surface-sensitive methods (photoemission and related spectroscopies, transmission electron microscopy, conversion electron M6ssbauer spectroscopy and to some extent susceptibility measurements, N M R and ESR) and surface-insensitive experiments, where only the bulk properties can be studied (magnetic measurements, neutron- and X-ray diffraction, X-ray absorption, transmission M6ssbauer spectroscopy). Despite the complex hydrogen-absorption mechanism, some general statements concerning the influence of hydrogen upon the physical properties can be made. Hydrogen uptake commonly leads to a considerable lattice expansion. Although the absorption of hydrogen can lead to a volume increase of up to 30%, the overall crystal structure frequently is retained. The hydrogen-induced rise in volume is to a large extent the essential reason for the altered magnetic properties in the hydrides. A larger volume implies narrower bands which, on the other hand, may reduce a hybridization having perhaps been present in the host compound. When a transition metal (TM) is alloyed to a rare earth or a related metal (R), the R-3d exchange interaction (3d-5d overlap) leads to a significant reduction of the TM moment. The strong hydrogen affinity of the R metals brings about a decrease of the 3d-5d overlap 514

MAGNETISM OF HYDRIDES

515

in the hydrides. Thus, the absorption of hydrogen commonly cancels this moment depression to a certain degree. This partial restoration of the 3d moment is interpreted as a hydrogen-induced screening effect. The predominant part of published results connected with magnetism considers binary R hydrides (R = rare-earth element) and hydrides of binary compounds of the general formula RyTMz, R being a rare-earth element, which may be replaced by elements such as Sc, Y, Zr, Ti; and TM standing for a transition metal. Particularly Mn, Fe, Co and Ni compounds have been examined with regard to hydrogenabsorption properties. Consequently, after some theoretical considerations, this chapter will deal with the experimental results regarding binary rare-earth hydrides, followed by a short treatment of transition-metal hydrides. The main part covers ternary hydrides along the element order mentioned above, the final part containing hydrides of less-common compounds and alloys (e.g., GdRh2, oxygen stabilized TiTM compounds, amorphous alloys). Experimental data are only to some extent mentioned in the text. They have been summarized in this chapter in several tables according to the transition element present in the compound. In order to limit the number of references to a reasonable number, attention is focused to the literature cited subsequently to 1980, except those papers which contain physical quantities given in the tables. For the remaining former literature, the reader is referred to the comprehensive review articles by Buschow et al. (1982a), Buschow (1984a) and Wiesinger and Hilscher (1988a).

2. Formation of stable hydrides In order to predict the formation of metal-hydrogen systems, the heat of formation has to be evaluated. Up to now, only a few first-principle calculations have been performed. However, empirical and semiempirical models have been proposed for the heat of formation and heat of solution of metal hydrides. For a recent review, we refer to chapter 6 of Hydrogen in Intermetallic Compounds I (Griessen and Riesterer 1988). The cellular model of Miedema et al. (1976) and, more recently, the band-structure model of Griessen and Driessen (Griessen and Driessen 1984a,b, Griessen et al. 1984) have successfully been applied in metal-hydride research. While the former model is already known fairly well and thus does not need to be introduced separately, the latter one shall be described briefly, particularly because the electronic band structure is involved and thus the connection with magnetism is obvious. Empirical linear relations are proposed between the standard heat of formation AH and characteristic band-structure energy parameters of the parent elements in order to predict AH of the ternary hydrides. In the case of binary metal hydrides, the standard heat of formation is correlated with the difference between the Fermi energy and the energy of the centre of the lowest s-like conduction band of the host metal. In the case of ternary metal hydrides, the energy difference for intermetallics of two d-band metals has been evaluated using the model of Cyrot and CyrotLackmann (1976). The exact density of states (DOS) of an alloy is approximated by a 'simple' DOS, where the individual contributions of the elements are acting in an additive way (coherent potential approximation). There are various steps involved

516

G. WIESINGER and G. HILSCHER

in the scaling of the DOS function of each metal. In the first step, the widths of the d bands of both metals are set equal to their weighted average and the (DOS) curves are brought to a common width. In the second step, the Fermi energies are equilibrated. The agreement of the calculated heat of formation values with the experiment was found to be remarkably good. In most of the cases, the band-structure model yields better results than the Miedema model, which furthermore has the disadvantage of involving more fit parameters.

3. Electronic properties The knowledge of the electronic properties (band structure, DOS) considerably helps in understanding the magnetic properties of a material. In the last few years, the number of papers dealing with band structure calculations has increased considerably (Gupta 1989). Moreover, the accuracy of the DOS and the Fermi-energy calculations has grown substantially. Decomposition of the DOS into site and angular momentum components are now available for many metal hydrides. Charge transfer calculations, however, are still at their beginning. The kind of the electronic charge transfer upon hydrogenation is an essential point for interpreting the hydrogen-induced change of the magnetic properties. In order to explain the magnetization data of rare-earth-transition-metal hydrides, a few earlier works favoured a hydrogen-transition-metal charge transfer in connection with the rigid-band model (see, e.g., Wallace 1978, 1982). A similar interpretation has been given more recently with regard to Mn, Fe and Ni hydrides (see, e.g., Antonov et al. 1989). However, theory [-energy band and DOS calculations, see, e.g., Vargas and Christensen (1987), Gupta (1982, 1987, 1989)] and experiment [M6ssbauer studies performed on R nuclei and X(U)PS investigations, see, e.g., Cohen et al. (1980), Schlapbach (1982), Schapbach et al. (1984), H6chst et al. (1985), Osterwalder et al. (1985)] proved the indefensibility of this position. Details will be found below in the common part of this chapter. There are a number of experimental methods in order to compare theory and experiment in the field of the electronic properties. The Pauli contribution of the magnetic susceptibility and the electronic specific heat coefficient ~ are proportional to N(EF). Resistivity measurements yield valuable results for binary hydrides (see section 5.1), for hydrides of intermetallic compounds this method is rarely applied because of experimental difficulties (contacting brittle samples or disintegration of the specimens into powder). Spectroscopic techniques such as electron and X-ray photoemission belong to the most powerful methods to study the electronic structure. A valence-band photoelectron spectrum resembles a one-electron DOS curve. Within some approximations, photoelectron spectra yield directly position and width of the occupied bands, charge transfer is indicated by XPS core level and M6ssbauer isomer shifts. In valence fluctuation systems, X-ray absorption experiments are particularly valuable. The X-ray absorption near-edge structure (XANES) contains information about the partial DOS and becomes an increasingly important technique. For the most recent comprehensive review covering experimental as well as theoretical work

MAGNETISM OF HYDRIDES

517

on hydrides, we refer to chapter 5 of Hydrogen in Intermetallic Compounds I (Gupta and Schlapbach 1988).

4. Basic aspects of magnetism Metallic magnetism covers a wide range of phenomena, which are intimately correlated with both the electronic structure and the metallurgy of a given metal or compound. Particularly the latter appears to be an important factor when considering the formation and properties of intermetallic compounds and binary (ternary) hydrides. Frequently, the studies of hydrides of intermetallic compounds have led to a deeper insight into the fundamental properties of the parent system. For quite a long time, 3d magnetism has been a controversial topic, where still some problems are not completely settled. The reason for this controversy is the absence of a general agreement upon the microscopic nature of the magnetic state above and below the Curie temperature. Two opposite standpoints have, so far, been used to explain the magnetic order as a function of temperature. In the Heisenberg model, magnetism is described in terms of localized moments and the magnetization vanishes at Tc because of disorder in the local moments due to thermal fluctuations. Nevertheless, their absolute value remains almost independent of temperature. In the Stoner-Wohlfarth itinerant-electron model, the magnetic moment is determined by the number of unpaired electrons in the exchange-split spin-up and spindown bands. Within this model, the thermal excitations of electron-hole pairs reduce the exchange splitting and thus favour the paramagnetic state. Consequently, the magnetization disappears only if the absolute value of the magnetic moment goes to zero, which only happens if the exchange splitting is zero too. This model sufficiently describes magnetism in metals at 0 K. Unfortunately, it predicts Curie temperatures which are 5-10 times larger than those observed experimentally. The controversy has been settled recently in favour of the itinerant-electron model. In an improved theory (spin-polarized band theory), a magnetic polarization exists, the direction of which may vary from one unit cell to the other. Thus, the global magnetization vanishes at Tc not because the magnetic moments are zero, but because they point in random directions (Gyorffy et al. 1985, Staunton et al. 1985). A great deal of progress was made in the theory of fluctuating moments in itinerant systems (Moriya 1987, Lonzarich 1987, Mohn and Wohlfarth 1987), which is a similar approach to solving the old problem of magnetism at elevated temperatures by taking account of the parallel and transversal components of the local fluctuating moments. Noting that the fluctuating moments must increase as the static magnetization decreases, it became clear that the Stoner model involving only single-particle excitations of itinerant electrons is insufficient for most systems and that collective excitations are also inevitably present to different degrees, depending on the temperature and the position in the co, q plane. At higher temperatures, Murata and Doniach (1972) made clear that spin fluctuations persist side by side with single-particle excitations, but it is difficult to describe these theoretically for realistic metals. A very much simpler and new approach to the problem has been developed recently by Wagner and Wohlfarth (1986) and Mohn and Wohlfarth (1987). This retains the

518

G. WIESINGER and G. HILSCHER

Stoner model in its equivalent expression as a Landau theory of phase transitions, but takes account of the influence of the parallel and transversal local fluctuating moments by appropriately renormalizing the Landau coefficients of the free-energy expansion. With this approach and the use of band-structure calculations, including correlation effects, rather good agreement is found with experimental Curie temperatures of Fe, Co, Ni and other intermetallic compounds. Furthermore, this formalism lead in a simple way to the pressure dependence of the Curie temperature and the magnetovolume effects as well as to a realistic description of the magnetic contribution to the heat capacity (Mohn et al. 1987, Mohn and Hilscher 1989). Contrary to the magnetism of the 3d-metals, the magnetic properties of the rareearth elements (R) are unambiguously described in terms of the RKKY theory; because of the localized nature of the 4f electrons no overlap exists between 4f wave functions on different lattice sites. Thus, the magnetic coupling can only proceed indirectly via the spatially nonuniform polarization of the conduction electrons. The pure 4f-4f interaction and its behaviour upon the absorption of hydrogen can be studied directly not only in binary rare-earth hydrides, but also in ternary hydrides with a zero transition-metal moment. As a first apgroximation, one would expect that hydrogen-induced changes in the magnetic properties of the latter can be explained in analogy with the binary hydrides, i.e., in terms of the anionic model. There, the conduction electron concentration is lowered after hydrogen uptake which in turn reduces the RKKY interaction. The rare earths form binary hydrides with the stoichiometries x = 2 and x = 3. In the case of x approaching 3, metallic conductivity disappears, which has been attributed by Switendick (1978) to the formation of a low-lying s-band with the capacity to hold six valence electrons. This in fact equals the number of electrons supplied to the conduction band by one R and three H atoms. Since this low-lying bonding band is completely filled up with electrons, in RH3 conduction electrons are no longer present, prohibiting the transmission of the RKKY interaction. This accounts for the suppression of the magnetic interactions, which indeed is generally observed experimentally. However, as will be seen later, details of the physical properties of the rare-earth hydrides in the a-phase and of the broad homogeneity range of the R-dihydrides are only partly solved and several exceptions from the simple approach can be found. In R-3d-intermetallics and their hydrides, where both R and the 3d element carry a magnetic moment, we can distinguish between three main types of magnetic interactions which are quite different in nature: that (i) between the localized 4f moments; (ii) between the more itinerant 3d moments; and (iii) between 3d and 4f moments. Generally, it is observed that these interactions decrease in the following sequence: 3d-3d > 4f-3d > 4f-4f. In contrast to the binary 4f hydrides, for ternary R-3d hydrides no similar straightforward arguments can be used about the hydrogen-induced change of the magnetic order. The only statement being generally valid is that upon hydrogen absorption the magnetic order of Co and Ni compounds is considerably weakened which is not observed in the case of Fe compounds. As will be described in detail below, hydrogen absorption usually weakens the

MAGNETISM OF HYDRIDES

519

magnetic coupling between the 4f and the 3d moments and can lead to substantial changes of the 3d transition-metal moment in either way. As mentioned earlier, hydrogen in the lattice reduces the 4f-3d exchange interaction. This is explained by a reduced overlap of the 3d-electron wave functions with the 5d-like ones due the narrower bands as a consequence of the hydrogen-induced increase in volume. Furthermore, concentration fluctuations of H atoms over a few atomic distances may frequently occur, leading to a difference in electron concentration between one site and another and, therefore, to a varying coupling strength. Additionally, a disturbance of the lattice periodicity takes place in the hydrides, reducing the mean free path of the conduction electrons (see section 5.1). This leads to a damping of the RKKY conduction electron polarization which in turn decreases the magnetic coupling strength. If the magnetic order in R-intermetallics is dominated by the 4f moments, the concept of an R - H charge transfer in analogy with the binary rare-earth hydrides has proved to be a reasonable explanation for the hydrogen-induced changes in magnetism (see the data containing an isomer shift obtained from Mrssbauer studies on rare-earth nuclei). In the case where 3d magnetism is dominant in the R-3d compounds, no general rule can be given. Commonly, hydrogen absorption leads to a loss in the 3d moment in Ni- and Co-based intermetallics, but to an enhancement of the Fe moment. For Mn-intermetallics, both changes from para- to ferromagnetism and vice versa are obtained. In Fe-containing intermetallic hydrides, the 3d states are localized to a greater extent compared to the parent compound. This leads to an enhancement of the molecular field which, on the other hand, is opposed by the influence of the grown Fe-Fe distance, tending to reduce it. As is observed experimentally, the former is apparently the dominating one, yielding an increased or at least an unchanged molecular field constant nRFe upon hydrogenation. When discussing the hydrogen-induced change of the magnetic properties, one is, among other things, faced with the problem of finding confidential moment data. Frequently, one has to rely on magnetization measurements, which may lead to wrong results in those cases where, from experimental reasons (lack of a high-field facility), only incomplete saturation has been achieved. As will be seen below, particularly in the case of ternary hydrides, magnetic saturation is difficult to obtain. An alternative way is offered by Mrssbauer measurements carried out in zero applied field. However, the problem of correlating the hyperfine field unambiguously with the magnetic moment (particularly in the case of the hydrides) still remains. Only in a few cases, one can refer to reliable data from neutron-diffraction experiments. For a detailed summary of the experimental data obtained up to now in the field, we refer to chapter 4 in Hydrogen in Intermetallic Compounds I (Yvon and Fischer 1988). 5. Review of experimental and theoretical results

5.1. Binary rare-earth hydrides 5.1.1. s-rare-earth hydrides Hydrogen is readily absorbed by the rare earth (R) and forms solid solutions (~phases) at high temperatures. The solubility limits at a certain temperature generally

520

G. WIESINGERand G. HILSCHER

increase with the atomic number. Vajda and Daou (1984) established that the heaviest trivalent lanthanides, Ho, Er, Tm and Lu, and the closely related elements Sc and Y (all of them have the hcp structure) retain hydrogen in solution down to 0 K without any evidence of an ~-13 phase transition but with a resistivity anomaly in the range between 150 and 180K. This anomaly was attributed to short-range ordering of the interstitial H atoms. In the case of c~-LuHx, it has been identified by neutron scattering as the creation of linear chains of H - H pairs on tetrahedral sites along the c axis surrounding a metal atom (Blaschko et al. 1985). Contrary to the heaviest rare earths, hydrogen in solution appears to be unstable in the lighter R elements at a certain temperature (decreasing from 700 to 400 K for La to Dy, respectively) and precipitates into the 13-phase (dihydride). ~-HoHx, cz-ErH~ and uTmH~ yield a hydrogen interstitial solubility limit of 3, 7 and 11 at.%, respectively (Daou and Vajda 1988), which was previously believed to be lower. Hydrogen in solution reduces the antiferromagnetic ordering temperature TN of Ho (133 K) at a rate of about 2 K/at.% H (D), which is in agreement with the results obtained for the two other magnetic R-hydrogen systems, ~-ErH~ and ~TmH~ (Daou et al. 1987). The effect of hydrogen absorption upon the magnetic properties in ~-ErHx has been studied by resistivity (Daou et al. 1980, Vajda et al. 1987b), magnetic (Vajda et al. 1983, Ito et al. 1984, Vajda and Daou 1984, Burger et al. 1986b, Burger 1987) and specific heat measurements (Schmitzer et al. 1987). Er is well known to exhibit three different magnetic structures: below the N6el temperature TN of 85 K there is a sinusoidally modulated magnetization along the c axis, while the basal-plane magnetization remains zero. The basal-plane component starts to order in a helicoidal structure at TH= 51 K and spiral (conical) ferromagnetism is stable below Tc = 19.5 K [for a review, see Coqblin (1977)]. The above-mentioned measurements show that TN and TH decrease, while Tc and Tcl (at which a transition to an incommensurate structure of 15 layers occurs) increase with H or D content (see fig. la,b). The rise of Tc is interpreted by Burger et al. (1986b, 1987) in terms of a hydrogen-induced dilation of the c axis as a consequence of the interplay between the uniaxial anisotropy and the magnetoelastic energy, and the coupling between the axial and basal-plane magnetization. The increase in the electronic specific heat with rising H content (up to 1.5 at.%), indicates a growing density of states at EF for Er in the cz-phase (at least at low concentrations), which leads to the suggestion that the decrease of TN, TIj and the spin disorder resistivity Pspd are due to a reduction in the exchange interaction, in agreement with magnetic measurements. The thermal variation of the resistivity and the specific heat in the ferromagnetic cone-structure regime (below Tc) gives evidence for the existence of a gap-like behaviour in the spin wave spectrum, which is reduced with the addition of hydrogen in solution. From this variation of the exchange-anisotropy gap and the nuclear specific heat, Schmitzer et al. (1987) and Vajda et al. (1987b) draw the same conclusion as above, namely that the exchange field is reduced with rising hydrogen content in u-ErHx. Contrary to ~-ErH~, for cz-TmH~ both TN (57.5 K) and the order-order transition at Tc (39.5 K) decrease with rising H content down to 45.5 and 29 K, respectively, for x = 0.1 (Vajda and Daou 1984). This different behaviour is suggested to arise

MAGNETISM OF HYDRIDES

521

Hydrogen in solid solution in erbium

25001(a)//o[l

I

1000 500 o

~ 2~

sb

r (K)

~..~'+"%,. L 7~

Fig. 1. (a) Variation of the magnetizationwith temperature for pure Er (x = 0) and ErH0.035. A field of H = 0.02T is applied parallel to the c axis [(O) x = 0, (+) x = 0.035] (Burger et al. 1986b). from the specific magnetic structures, which are, in the case of Tm, sinusoidally modulated antiferromagnetic below TN and gradually squares up to yield below Tc = 39 K an antiphase ferromagnet with three spins up and four spins down and has, therefore, no basal-plane component, in contrast to Er below Tc. The fall of TN and Tc in ~-TmHx is governed also by the reduction of the indirect exchange interaction. In Tm, there is no interaction present between the short-range ordered H - H pairs with the uniaxially aligned moments. On the other hand, in ~-ErHx a strong interaction between the H - H pairs and the conical structure appears to change the magnetoelastic energy, giving rise to a Tc enhancement in Er with H in solution. In fig. 2a,b, a global view of the temperature dependence of the electrical resistivity of an ~-TmH~ single crystal parallel to the b and c axis is presented, showing a significant different p(T) behaviour between the two crystal orientations with x. While the b-axis oriented crystal exhibits a nearly linear increase of the residual resistivity, p~, with x (fig. 2a), the apparent increase of p~ (p parallel to the c axis) is much larger and nonlinear. In fact, the resistivity decrease due to ferrimagnetic ordering is strongly suppressed by hydrogen in solution, disappearing completely for x > 0.05, which is attributed to the evolution of magnetic superzones, a phenomenon already observed to a smaller degree in single crystals of ~-ErH~ (Vajda et al. 1987b). The insert of fig. 2a shows a substantial rise of the magnetic contribution to the resistivity Pmag(r) with x. The analysis of these data in terms of a sum of a power function and an exponential expression for the anisotropy gap A, pbag(T ) = AT" + B T 2 e x p ( - A / k r ) ,

522

G. W I E S I N G E R and G. H I L S C H E R

(b)

o

(22,

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0.00

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20.00

i

30.00

i

i

40.00 Temp [K]

i

50,00

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Fig. 1. (b) Heat capacity of ~-ErHx with various hydrogen concentrations: (©) x = 0; ( ~ ) x = 0.01; ([~) x = 0.03 and (m) ErDo.o3 (Schmitzer et al. 1987).

shows that both n and A decrease with rising x. Specific heat measurements show a similar trend (Daou et al. 1988b), namely that an anisotropy gap occurs in the spin wave spectrum, and is reduced with growing amount of hydrogen and goes hand in hand with the development of a complex magnetic structure. Magnetization measurements of monocrystalline 0~-TmHxindicate that hydrogen gives rise to the following main effects: (i) a decrease of the antiferro- and ferrimagnetic (along the c axis) transition temperatures due to modifications of the electronic structure; (ii) a hardening of the ferrimagnetic M(H) relation along the c axis due to an increase in the coercivity or the pinning of the domain walls; (iii) a decrease of the anisotropy between the c axis and the basal-plane magnetization (Daou et al. 1981, 1990). Of the magnetically unordered elements, Sc, Y and Lu, the H system of the latter has been investigated thoroughly by specific heat and susceptibility measurements (Stierman and Gschneidner Jr 1984). These authors state that Lu is a spin fluctuation system, where the fluctuations are quickly degraded by impurities and by hydrogen in solid solution. Both the susceptibility Z and the electronic specific heat coefficient show a similar variation as a function of H-composition, yielding a peak at 3 and

MAGNETISM OF HYDRIDES

523

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150

200

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..

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~

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Fig. 2. (a) Temperature dependence of the resistivity parallel to the b axis for various ~-TmHx crystals with the x values labelled; the insert shows the magnified low-temperature region. The arrows indicate the high-temperature anomaly above 150 K as well as the variation of the N6el temperature TN. (b) The same as (a) for single crystals with an c axis orientation. Both figures after Daou et al. (1988b).

1.5 at.% H, respectively. This difference is attributed to hydrogen tunneling, giving rise to a linear contribution to the heat capacity. Correcting for this brings into good agreement the concentration dependence of both ~ and X with a peak at about 3 at.% H. In this context, it is worth to note that also in ~-ErH~ and presumably in ~-

524

G. WIESINGERand G. HILSCHER

TmHx an increase of the electronic specific heat with x is observed. However, in ~TmHx the increase of 7 with growing x is not established for x > 0.02, since in this regime the magnetic contribution to the heat capacity could not unambiguously be resolved, since a not yet determined magnetic structure occurs below 4 K (Daou et al. 1988b). Susceptibility measurements of ~-ScH~ by Volkenshtein et al. (1983) indicate that spin paramagnetism is reduced by a factor of two for x = 0.36. This can be associated (neglecting a possible change of the Stoner enhancement factor) with a decrease in the density of states at EF, whereby EF passes through a maximum of the N(E) curve down to lower energies. This trend of the m-phase is also observed in the dihydride. According to band-structure calculations, susceptibility measurements and the spinlattice relaxation time, the DOS at EF in comparison with that of parent Sc is reduced by a factor of 3.5, 3 and 4.5, respectively.

5.1.2. Rare-earth di- and trihydrides The rare earths commonly form dihydrides and trihydrides. The dihydrides exhibit a broad homogeneity range and crystallize, except for Eu and Yb, in the CaF/ structure. The CaF/ structure forms a fcc unit cell, where in the ideal case all tetrahedral (T) sites are occupied. On increasing the hydrogen content, the octahedral (O) sites become gradually filled up with hydrogen atoms to form the BiF3 structure. Dihydrides of Eu and Yb are of the orthorhombic (Pnma) structure. The trihydrides exhibit the hcp structure except for La and Ce where the cubic structure is sustained. While the trihydrides are ionic semiconductors, the dihydrides are metallic with low hydrogen content and semiconductors with high concentration of hydrogen (Libowitz 1972). In reality, the 'pure' dihydride is frequently substoichiometric. The occupation of the octahedral (O) sites already starts sometimes for x = 1.8, depending on the material purity; in particular the oxygen content is of importance, and also the sample shape (foils, powder, etc.) used for hydrogen loading. It seems that the larger the purity of the parent material, the closer is the approach to the ideal stoichiometry of the dihydride. In the case of a heavy rare earth with a purity of 99.9% and 99.99%, the stoichiometry of the dihydride is usually 1.90 < x < 1.95 and 1.96 < x < 1.98, respectively. The absorption of hydrogen affects the magnetic properties of the rare earths indirectly via a reduction of the number of conduction electrons and a volume expansion. Both effects lead to a drastic decrease of RKKY indirect exchange interaction between the localized 4f electrons mediated by the conduction electrons. Consequently, the magnetic ordering temperatures are much lower than in the parent metals (e.g., Tc= 291K for Gd, TN = 20K for GdH1.93 ). On raising the H content above the pure dihydride, it is obvious that a random and/or ordered occupation of the octahedral sites with H significantly influences the crystalline electric field (CEF). This plays an important role in the change of the magnetic properties of those compounds located in the intermediate range between the di- and trihydrides. The dihydride acts as a monovalent metal (one conduction electron per atom), the trihydride as an insulator or a semimetal. Whereas the electronic structure and the magnetic properties of stoichiometric dihydrides and trihydrides seem to be rather

MAGNETISM OF HYDRIDES

525

well understood, considerable confusion exists in the intermediate composition range (-0.15 to -0.05 < x < 1 of REH2+x). To elucidate the transition between these two extreme situations, this regime became, therefore, of growing interest during the last few years. Simplifying the matter, one may expect a continuous decrease of the conduction electron density with rising x, implying that each H atom depopulates the conduction band by one electron through the formation of a low-energy metalH band. However, this simple model is complicated by several structural transitions: attractive H - H interactions lead to a phase segregation with the formation of a dilute metallic phase (x = 0.1-0.2) and a concentrated nearly insulating phase or ? phase (x = 0.8-0.9). This seems to be the case in the heavy rare earths (R = Gd to Lu), where no homogeneous dihydride exists for x > 0.25. In the lightest rare earths (La, Ce and possibly Pr), such segregations are not observed and mainly orderdisorder transitions occur within the H-sublattice, presumably due to more repulsive H - H interactions (Burger et al. 1988). From electronic band-structure calculations, it is known that a charge transfer occurs from the metal atoms to the hydrogen atoms in the tetrahedral sites, whereas the hydrogen atoms at the octahedral sites can be considered as essentially neutral (Misemer and Harmon 1982, Fujimori et al. 1980). Although the theoretical values of the charges transferred are still a matter of debate, the occurrence of charge transfer is supported by experimental XPS data on the metal core-level shifts obtained on hydrogenation (Schlapbach 1982, Osterwalder 1985, Gupta and Schlapbach 1988). Negative charges at the tetrahedral sites yield crystal-field ground states that have been confirmed experimentally by neutron scattering, M6ssbauer spectroscopy, susceptibility and specific heat measurements. This favours the so-called anionic or hydridic model for the formation of binary rare-earh hydrides which, however, has to be regarded with some caution. The limits of this model have been assessed by Gupta and Burger (1980) by means of a site and angular momentum analysis of the DOS. These authors were able to show that there exists a considerable hybridization of the low-lying hydrogen-metal bands. For further discussions of band-structure calculations on RH2 and R H 3 we refer to Gupta and Schlapbach (1988). Their results support a metal to semiconductor transition, whereby the explanation concerning the origin and nature of the gap and its opening particularly in the intermediate concentration range is still not resolved. The rare-earth dihydrides order antiferromagnetically with ordering temperatures below 20 K, except for CeH2+x, NdHz +x and EuHz+x which exhibit ferromagnetic order. In view of their orthorhombic structure (Pnma), dihydrides of Eu and Yb are also an exception among their cubic neighbours. The magnetic structure of the RD1.95 for the light rare earth (R = Ce, Pr or Sin) and GdD1.95 has been resolved by neutron diffraction and appears to be rather similar: for Sm and Gd dideuterides ferromagnetic coupling occurs within the (111) plane, which couple antiferromagnetically with the adjacent sheets (MnO-type structure), while for Ce and Pr an additional modulation within the (111) plane is observed into the [1T0] and [112] direction, respectively (Arons and Schweizer 1982, Arons and Cable 1985). Thus, NdH1.95 is the only ferromagnet in the antiferromagnetic series of the R deuterides with the cubic C a F 2 or BiF3 structure and seems, therefore, to be an unresolved exception.

526

G. W I E S I N G E R and G. H I L S C H E R

The RDz compounds in which R is a heavy rare-earth element (R = Tb, Dy or Ho) exhibit modulated magnetic structures (see fig. 3) where the modulation period 4ao~/ll along [113] is commensurate with the crystallographic lattice (Shaked et al. 1984). This corresponds to a ferromagnetic coupling of the magnetic moments within the (113) planes and an antiferromagnetic alignment between those planes. The direction of the spin axis is [001] for Tb and Dy but [863] for HoDz. The magnetic structure of ErD2 contains both a commensurate component (belonging to the magnetic lattice, 4ao) and an additional incommensurate component which could not yet be resolved. The ordering temperatures and the magnetic structure of the single-phase dihydrides with the respective x values according to various authors are collected in table 1. The orthorhombic dihydrides of Eu and Yb are not included. From this table, it is obvious that those elements situated on the boundaries of the 4f series exhibit the more complicated antiferromagnetic structure, while Nd which is ferromagnetically ordered is rather exceptional in this type of compound. The transition temperatures reported for the pure dihydrides agree fairly well with each other, although the hydrogen content given for the pure dihydride varies significantly in particular cases. This indicates - as discussed above - that the purity of the starting material is of crucial importance since impurities presumably occupy the tetrahedral lattice sites which prevents the formation of the strictly stioehiometric dihydride RH2. This suggestion deduced from the comparison of the transition temperatures and magnetic phase diagrams (table 1, see also fig. 4) seems to be in contradiction with the statement of Arons et al. (1987c) that a stoichiometric dihydride with all tetrahedral sites occupied by H atoms does not exist, since the occupation of the octahedral sites starts already at RHt.g5 with 2.5% vacancies on the tetrahedral lattice sites. Already a slight increase of absorbed hydrogen leads to a loss of long-range magnetic order and shows sometimes spin-glass-like behaviour at low temperatures. In this context, it should be noted that the nature of the magnetic transition of hyperstoichiometric dihydrides at low temperatures depends sensitively on the cooling rate. From a resistivity anomaly at about 150 K, which is different for quenched and slowly cooled samples (103K/min and 0.3K/min), Vajda et al. (1985, 1989a) deduced that in the latter case short-range ordering occurs within the octahedral H

.[113]

(a)

/[113]

(b)

Fig. 3. Magnetic structure of T b D 2 and H o D 2 according to Shaked et al. (1984).

MAGNETISM OF HYDRIDES

527

TABLE 1 Magnetic properties of cubic single-phase dihydrides RH2 +x. R Ce Pr Nd Sm Gd Tb

Dy Ho Er

Transition temperature (K) 6.2 3.3 3.5 6.8 9.6

9.6 21 17.2 18.5 18.0 3.5 5.0 4.5 6.5 2.15 2.13

Type of magnetic order

AF AF AF F AF AF AF AF AF AF AF AF AF AF AF AF

MnO type modulated along the [110] axis MnO type modulated along the [112] axis

MnO type MnO type Commensurate modulated along [113], spin axis along [001] Commensurate modulated along r i l l ] , spin axis along [001] Commensurate modulated along [113], spin axis along [-863] Commensurate and incommensurate components no magnetic order down to 2 K

Tm

* References: [1] Arons et al. (1987c). [2] Arons et al. (1987a). [-3] Arons and Cable (1985). [-4] Vajda et al. (1989a). [5] Senoussi et al. (1987). [6] Arons and Schweizer (1982). [7] Vajda et al. (1989b).

[8] [9] [10] [11] [12] [13]

x

Ref.*

-0.05 -0.05 -O.03 0.0 -0.15 -0.12 -0.7 -~0.0 -0.5 -0.08 =0.0 -0.0 20.0 -~0.0 -~0.0 -0.1 -~0.0 0.0

[1] [-2, 3] [4] [5] [6] [7] [6] I-8] [9] [4] [8] [10] [8] [-10] [-8] [-11] [12] [13]

Shaked et al. (1984). Arons et al. (1982). Daou et al. (1988a). Oprychal and Bieganski (1976). Kubota and Wallace (1963b). Burger et al. (1986a).

Cell2÷ x ()O

o

Para 0

0

//

/

/

/ I

0.0

I

I

I

0.5

'II I

I

i'

AF I

I

1.0

X ~

Fig. 4. Magnetic phase diagram of Cell 2 +x determined by (©) susceptibility measurements (Arons et al. 1987a, Abeln 1987). Additional transitions are observed by (0) resistivity measurements (Vajda and Daou 1989, Vajda et al. 1990). The hydrogen stoichiometry of the latter data is shifted by x = -0.05 for comparison with the susceptibility data.

528

G. WIESINGERand G. HILSCHER

sublattice. This significantly affects the magnetic transition, presumably as a result of a modified crystal-field scheme due to local symmetry distortions. Valuable information about the behaviour of hydrogen in binary hydrides has first been obtained from the analysis of the susceptibility by Wallace and Mader (1968) and from the Schottky anomaly in the low-temperature specific heat (Bieganski 1972, Bieganski and Stalinski 1970, 1979). Further information is found in references given by Arons (1982). The energy level scheme which has been derived clearly favours the anionic model. Inelastic neutron scattering and M6ssbauer spectroscopy are further techniques which have been applied in order to determine the crystal-field level scheme in binary RHz hydrides (Knorr and Fender 1977, Knorr et al. 1978, Arons 1982, Arons et al. 1987b, Shenoy et al. 1976). From these results, the anionic state of the hydrogen ions has been corroborated also. In the heavy rare-earth dihydrides, the analysis of the paramagnetic spin-disorder resistivity in terms of crystalline-field effects gives furthermore reasonable agreement with the generally considered anionic H - model (Daou et al. 1988a). The rare-earth trihydrides (except for CeHz.75_3) do not show magnetic ordering down to liquid-helium temperature (Wallace 1978, Birrer et al. 1989). This is consistent with the assumption of anionic hydrogen has a completely depopulated conduction band, giving rise to the semiconducting or insulating behaviour of those hydrides. In the following, we present the main results since 1980, in particular concerning the intermediate range between the di- and trihydrides. For previous data of the magnetic properties of those hydrides we refer to the comprehensive compilation by Arons (1982) and the reviews by Libowitz and Maeland (1979) and Wallace (1978, 1979). Cerium and its compounds exhibit an exceptional behaviour in the series of the rare earth. The ambivalent character of the one 4f electron, behaving either atomic like as in 7-Ce or less-localized and stronger-hybridized as in ~-Ce, gives rise to fascinating magnetic and electronic properties as, e.g., mixed valency, Kondo and heavy fermion behaviour (Fisk et al. 1988). Figure 4 shows that the magnetic order changes from antiferromagnetism in the slightly hydrogen-deficient dihydride CED1.95 via no magnetic order at about x = 0.05 (for T > 1.3 K) to ferromagnetism for 0.1 < x < 0.75 and again to antiferromagnetism at x > 0.8 (Arons et al. 1987a). Additional magnetic transitions have been observed in CEH1.95 by heat capacity measurements (Abeln 1987) and by resistivity measurements at various x values, 0 < x < 0.4 (Vajda et al. 1990). These additional transitions, whose nature is not yet resolved, are also presented in the phase diagram proposed by Abeln (1987) and Arons et al. (1987a) (fig. 4). Good agreement between the two data sets of Abeln (1987), Vajda and Daou (1989) and Vajda et al. (1990) is obtained, if the hydrogen stoichiometry of the respective samples are shifted by 0.05at.% relative to each other. This means that the substoichiometric dihydride CEH1.95 of Abeln (1987) corresponds to CeH2.oo of Vajda and Daou (1989). The antiferromagnetic structure of CED1.95 and CeD2.91 is presented in fig. 5. The obvious difference between these magnetic structures is the additional antiferromagnetic modulation along the [110] direction with a period of 5ao for CED1.95. The magnetic 5.1.2.1. CeHe+ x.

MAGNETISM OF HYDRIDES

529

t

•

(a) ,

",,

I¢

'\

II"

oI--~ ",,, ~"--v

.1

"

(b)

j

(

--

7

aft --~

A --z ~

,-

f

Fig. 5. Magnetic structure of (a) CED1.95 and (b) CeDz.91 (after Abeln 1987). The antiferromagnetic coupling between (111) planes is additionally modulated along the [li0] direction for CeD1.9s.

moment determined by neutron diffraction (Schefer et al. 1984) in the ferromagnetic range (1.1#B at 1.3 K for x = 0.29) as well as in the antiferromagnetic CED2.96 (0.61#B at 1.3K) is by far smaller than that expected for a free Ce 3+ ion (2.14#B). These moments lie just between the calculated moments of 1.56#B and 0.71 #B corresponding to a/"8 and F? ground state, respectively. From high-field measurements, up to 30 T, on a single crystal also a rather low saturation moment of 0.9#B has been derived, which hardly changes with hydrogen content (Arons et al. 1984). Except for the ferromagnetic CeDz.46 compound, the moment attains 1.03#B. The reduced moment may be attributed to crystal-field effects since the overall crystal-field splitting was determined from susceptibility measurements by Osterwalder et al. (1983) to be 285 K (assuming the /"8 quartet to be the ground state). This finding is corroborated by inelastic neutron scattering and susceptibility measurements, according to which the F7 doublet is situated 20 meV above the Fs ground state (Abeln 1987). The four-fold degenerate/"8 ground state of CEH1.95 will be split into two doublets, separated by 12 K, as the hydrogen content is increased up to Cell2, but remains almost unchanged for higher hydrogen contents. Abeln (1987) deduced this from inelastic neutron scattering and from a pronounced Schottky anomaly occurring in the heat capacity of Cell 2 at about 5 K. Furthermore, no magnetic order could be detected in Cell2 down to below 1 K where the susceptibility becomes fiat. These findings, together with a rather high electronic heat capacity (Y = 179 mJ/molK z) strongly suggests that CeH2 is a Kondo system with a nonmagnetic ground state. Resistivity measurements (Vajda et al. 1990) confirm the above suggestion, since an incoherent and a coherent Kondo lattice behaviour has been observed above and below 20 K, respectively. The magnetic phase diagram in fig. 4 shows a narrow paramagnetic range separating the intermediate ferromagnetic- and the antiferromagnetic range for x > 0.8. In this context, it is worth noticing that Kaldis et al. (1987) reported on a miscibility gap for 0.56 < x < 0.64 between the tetragonally distorted and the cubic structure at room temperature. However, for Cell2.8, a two phase region (cubic and tetragonal) occurs below 238 K while above this temperature only the cubic phase appears to be stable. Schlapbach et al. (1986) excluded from photoemission experiments a metal

530

G. WIESINGER and G. HILSCHER

to semiconductor transition. They suggested a metal to semiconductor transition occurring at the surface, where upon cooling below 70 K hydrogen is removed from the more weakly bound octahedral-like surface hydrogen sites and is dissolved in the bulk. The electronic specific heat coefficient 7 of CEH2.65 is rather large (110 mJ/mol K z) and strongly enhanced (by a factor of 10) compared with the elemental 7-Ce, or the corresponding La compound with the similar electronic structure (LaH2.65~ < 0.04mJ/molK z) (Schlapbach et al. 1987). However, the absolute value of 7 is rather low in comparison with other Ce- and U-based heavy fermion compounds. Although the valency in Ce hydrides (3 +) is hardly changed (Gupta and Schlapbach 1988), the high 7 value of both compounds (Cell2 and the CEH2.65 ) indicates 4f hybridization with the conduction band. Thus, Ce hydrides have a tendency towards heavy fermion compounds.

5.1.2.2. PrHz+x. Below TN= 3.3K, PrD1.95 orders antiferromagnetically (MnO type, see above) with an ordered moment of 1.5#B/Pr atom (Arons et al. 1987c), while PrH2.25 is a weak Van Vleck paramagnet down to 2 K [Wallace and Mader (1968), and references given by Arons (1982)]. From the analysis of susceptibility measurements of PrH2 +x in terms of crystal-field effects, Wallace and Mader (1968) proposed the anionic model for hydrogen in these types of compounds which has later been supported by specific heat measurements (Bieganski 1973). Both experimental results are satisfactorily described by the F5 ground state caused by the crystal-field splitting of the degenerate 3H, ground state of Pr 3+ due to the surrounding of negatively charged hydrogen ions. This assumption is furthermore confirmed by inelastic and polarized neutron scattering (Knott and Fender 1977, Knorr et al. 1978, Arons et al. 1987a). The antiferromagnetic transition and the resistivity minimum at about 28 K was tentatively attributed by Vajda et al. (1989a) to Kondo scattering or to crystal-field effects if the first excited state F1 (nonmagnetic) is close to the ground state. Burger et al. (1990) explained the resistivity minimum in terms of spin-disorder resistivity taking the presence of crystal-field effects into account where the nonmagnetic first excited state (FI) is situated very close above the magnetic Fs ground state. For x > 0.0, the noncubic symmetry of the crystal field, induced by the supplementary H ions, may split the degenerate ground state Fs, causing suppression of both the magnetic order and the resistivity minimum. For samples with x > 0.2, neither susceptibility (Wallace and Mader 1968) nor resistivity measurements down to 1.5 K manifest magnetic order. According to the specific heat measurements (Drulis and Bieganski 1979), the ground state for PrH2.57 is a nonmagnetic singlet which appears to be in line with the nearly temperature independent Van Vleck susceptibility at low temperatures. The transition from antiferromagnetism to Van Vleck paramagnetism was explained by Arons et al. (1987b) in terms of a degeneracy of the magnetic F 5 and the singlet F1 states. However, this needs a change of the cubic crystal field parameter x [in the notation of Lea et al. (1962)] from x > 0.54 to x < 0.54 although the additional hydrogen atoms on octahedral sites should be considered as essentially

MAGNETISM OF HYDRIDES

531

neutral. In view of the significant resistance anomaly at 150 K, it seems likely that noncubic ordering of the octahedral hydrogens modifies the local symmetry of the crystal field. While for PrD 2 the crystal field experienced by the majority of Pr ions is cubic, Knorr et al. (1978) demonstrated by a careful analysis of their neutron data that in PrDz.5 the distribution of the octahedral hydrogen interstitials occurs not at random but rather in a mer-XA3 configuration leading to an orthorhombic crystal field at the Pr site. With this orthorhombic crystal-field symmetry, they could explain their neutron and susceptibility data of PrD2.5 satisfactorily. Furthermore, it is stated that Pr does not undergo a valence change from PrH2 to PrH2.5. Besides the pronounced resistivity anomaly at 150 K commonly found in these superstoichiometric samples, a further anomaly occurs in the hydrogen-richest compound x = 0.76 at about 220-250 K with indication for a first-order transition (similar to Ce and La) (Burger et al. 1988, Vajda et al. 1989a). The strongly x-dependent structural transformations affects the magnetic transitions at low temperatures via a modification of the local crystal-field symmetry. For high x-values, the analysis of the phonon and the residual resistivity by Burger et al. (1988) implies that the carrier density decreases strongly, and thus that the system approaches the metal-insulator transition. 5.1.2.3. NdHe+ ~. NdH 2 has been reported by Kubota and Wallace (1963a) to order ferromagnetically at 9.15 K with a moment of 1.36#a, while Carlin et al. (1982) found Tc = 5.6 K and a saturation moment of 1.9#B. The latter ordering temperature is in good agreement with specific heat measurements of Bieganski et al. (1975b) and N M R investigations (Kopp and Schreiber 1967). Both indicate magnetic ordering at 6.2K. Senoussi et al. (1987) performed systematic hysteresis measurements on NdH2 +x up to x = 0.7 which indicate, for x = 0, ferromagnetic behaviour below 6.8 K with a coercivity of 150 Oe and a spontaneous moment of 1.06/aB. For increasing H content, the spontaneous moment is drastically reduced. Moreover, thermomagnetic irreversibilities observed by zero-field-cooled (ZFC) and field-cooled (FC) M versus T measurements point to freezing effects and spin-glass behaviour. However, a clearcut spin-glass behaviour is rather unlikely for the stoichiometric dihydride since, in their specific heat measurements, Bieganski et al. (1975b) obtained a pronounced sharp peak at 6.2 K. Both the considerably reduced moment (relative to the free Nd 3 + value 3.37#B) and the freezing phenomena (growing with rising hydrogen content) may arise from a complex interplay between the RKKY interactions and the magnetic anisotropy. In particular the random uniaxial anisotropy, which could be induced by the crystal field and the local fluctuations of the hydrogen concentration on the octahedral interstitials, together with the reduced conduction-electron concentration are suggested to suppress long-range magnetic order for x > 0.

For the antiferromagnetic transitions in SmH2+x, good agreement is obtained from susceptibility and resistivity measurements (Arons and Schweizer 1982, Vajda et al. 1989a). However, the H stoichiometries of the corresponding samples differ significantly: the pure dihydride is referred to as SmH1.85

5.1.2.4. Smile+ x.

532

G. WIESINGER and G. HILSCHER

and as SmH1.98 by the above authors, respectively. With rising H content, TN is shifted from 9.6 K to lower temperatures [to 5.5 K for x = 0.08 (Arons 1982) and to 8 K for x = 0.16 (Vajda et al. 1989a)]. In the resistivity curve, the antiferromagnetic transition is observed as a sharp transition for x < 0.1 which becomes smoother at higher x values and disappears at x = 0.26. Furthermore, a resistivity minimum occurs just above TN, remaining observable up to x = 0.26. The p(T) minimum was tentatively attributed to incommensurate magnetic order or to corresponding critical fluctuations (Vajda et al. 1989b). The magnetic structure is of the M n O type and changes to an incommensurate structure, as found for GdH2 +x (Arons et al. 1987a). Vajda et al. (1989a) stated that not only the concentration of octahedral H atoms, but also their configuration is of importance for the shape of the transition. The reason for this is that quenching from room temperature introduces local disorder due to the presence of isolated H atoms on octahedral sites which can be recovered above about 150 K where a resistivity anomaly occurs.

5.1.2.5. EuH2+x. EuHz is a ferromagnetic semiconductor with Tc = 18.3K, 0 = 23.13K, Ms = 7.1/~B and peff= 7.94#B (Bischof et al. 1983). The semiconducting behaviour of the divalent dihydride is in accord with the anionic model.

5.1.2.6. GdH2+x. The antiferromagnetic MnO-type structure in GdD1.93 (with TN = 20K) changes into an incommensurate helical structure with the axis along [111] and TN = 15.5 K (Arons and Schweizer 1982, Arons 1982). The excess hydrogen (x) located on octahedral interstitials has a tendency to order below room temperature in short-range and long-range ordered structures which influences the type of magnetic order. Based on resistivity measurements, Vajda et al. (1990, 1991) proposed a structural and magnetic phase diagram for 0 ~<x ~<0.25 with MnO-type antiferromagnetic, helical and three incommensurate antiferromagnetic structures.

5.1.2.7. TbH2+x. In the dihydride TbH2+x, both the magnetic structure and the N6el temperature [TN = 18.5 K for x = -0.05; TN = 16.11 K for x = - 0 . 0 7 (M. Drulis et al. 1984, Bieganski et al. 1975a)] rises strongly with x up to TN = 4 0 K for x = 0.12 (Arons et al. 1982). For x = - 0 . 0 5 , a commensurate antiferromagnetic structure appears below 15.8 K. For larger hydrogen concentrations, different incommensurate structures with an axial sinusoidal modulation are observed which are stable from TN down to liquid-helium temperature. The transition from the former type of structure into the latter has been ascribed to the random occupation of some octahedral sites in the fcc Tb lattice. In TbH2 (TN = 17.2 K, x ~ 0.0), the saturation moment equals # = 7.2#B which is reduced by the crystal field as compared to the free-ion value of 9#B. Shaked et al. (1984) reported a modulation of the magnetic structure (period 4ao ~ i - , as mentioned above) that is commensurate with the crystal lattice. For higher x values, the magnetic contribution to the resistivity changes drastically (Vajda et al. 1987a): two peaks occur below 38 K for x = 0.16. Their height and absolute value depend furthermore upon the cooling rate. Vajda et al. (1989a) attributed this phenomenon to a symmetry change from cubic to axial due to an ordered H H pair structure which leads also to a local symmetry change of the

MAGNETISM OF HYDRIDES

533

crystal field. The importance of axial symmetry, but without taking an ordering process into account, was stressed by M. Drulis et al. (1984) to explain the specific heat data of TbH2.o6: hydrogen in the octahedral positions generate a crystal field with axial symmetry for 30% of the Tb 3 + ions with a doublet as the ground state, while the remaining 70% experience the cubic crystal-field potential with a singlet ground state. In this view, it seems rather plausible that the configuration of octahedral H interstitials determines the magnetic properties in the range 0 < x < 1, while a simple reduction of the conduction electrons with rising x would mainly lower the N6el temperature. The antiferromagnetic structure is modulated with a period of 4aox/i]- along [113] with an ordered moment of about 3#R--4/~B below TN= 3.5K (Shaked et al. 1984). From specific heat and M6ssbauer experiments [see references given by Arons (1982)], the ground state is determined to be the F7 doublet as expected for the anionic model. Furthermore, the large drop of the spin-disorder resistivity in the range from 140 K to TN is in good agreement with the crystal-field ground-state configuration (Daou et al. 1988a). 5.1.2.8. DyH2+~.

The magnetic structure is similar to those of the Tb and Dy dihydrides. However, the spin axis is along [863] with an ordered moment of 6.4 -T-0.4#a below TN= 4.5 K. The small moment, as compared to the free-ion moment, is due to moment reduction by the crystal field (Shaked et al. 1984).

5.1.2.9. HoHe+ ~.

The magnetic structure below TN= 2.15 K contains both a commensurate and an incommensurate component whereby the former belongs to a cubic magnetic lattice with a lattice parameter of 4ao (Shaked et al. 1984). References on M6ssbauer, susceptibility and specific heat measurement interpreted in terms of crystal-field effects (ground state F6) are given by Arons (1982). 5.1.2.10. ErHe+ ~.

No magnetic order was detected by susceptibility measurements (Kubota and Wallace 1963b, Bieganski and Stalinski 1973) and by resistivity measurements (Burger et al. 1986a) above 2 K. The spin-disorder resistivity is almost constant above 150 K and decreases rapidly at low temperatures with a tendency to vanish for T = 0 K. This result is interpreted by Burger et al. (1986a) on the basis of a nonmagnetic ground state separated from the first excited state by a gap of 150 K. 5.1.2.11. TmH2+~.

The orthorhombic dihydrides (YbH2+x, - 0 . 2 < x < 0 . 0 ) are semiconducting and divalent according to optical reemission measurements (Gupta and Schlapbach 1988, B/ichler et al. 1989). Semiconductivity of the dihydride appears to be the consequence of the divalency, as in EuH2. Substoichiometric trihydrides with x > 0.2 are metallic and are reported to be of the fcc structure (Drulis et al. 1988, Bfichler et al. 1989). Susceptibility measurements of YbHz.41, shown in fig. 6, indicate, together with specific heat measurements, the presence of a Kondo scattering mechanism and/or an intermediate valent behaviour: the effective moment of 3.82#B/ Yb is smaller than expected for a Yb 3+ ion (4.45#B), the susceptibility deviates from 5.1.2.12. YbH2+x.

534

G. WIESINGER and G. HILSCHER

48

I-t II

40 ~

oE F r

o

E

32

l× ;

F

|x,~' x

/ 0

%

o

#~

1

,

" .x,

/

," I

I 4

I

I 8

.,

4/ ~ . ~~

"',

424"

I

I T/ 12

T {,I

16 9 1 ~ _ . ~ ~

E

160 f ' " .~(X,'e'

:eft = 3"82

80

x x x x x xx x x Xxxxxxxxxx XxXXxxxxx'xXxxxx Xxxxxxxxxxxxxx>o,~xx~,~x ~,Xxxxxxxz'

/

0

24°T

i 0

I 80

i

I 160

i

I 240 T (K)

i

0 ~-

Fig. 6. Susceptibility of YbH2.41 as a function of temperature (Drulis et al. 1988).

the Curie-Weiss law and levels off below 4 K (fig. 6) and the heat capacity shows a pronounced upturn at low temperatures with a high C/T value of 589 mJ/mol K -z at 2.48 K (Drulis et al. 1988). Finally, the photoelectron spectra according to Biichler et al. (1989) clearly show a valence transition from the divalent YbHz with a 4 f 14 configuration to a mixed valent behaviour in YbH2.6 with a 4f13/4f 14 configuration.

5.2. Binary actinide hydrides The early actinide hydrides exhibit fascinating properties. In particular the structural properties may be classified as being unique in the periodic table. Complex phases form for the ThHx and UHx systems that are not observed for other metals. In the PaH~ system, simple bcc, cubic C15 Laves and A15 phases occur depending on temperature and composition. Rare-earth-like hydrides with the C a F 2 structure are found beyond uranium for the NpH~ and PuH~ systems with a trivalent metallic state. For a general review on the properties of actinide hydrogen systems, we refer to Ward (1985a). The magnetic and electronic properties of the actinides and their intermetallics are largely determined by the partly filled 5f shell [for details and references, we refer to the review by Sechovsk) and Havela (1988)]. Concerning the localization of the 5f electrons, the actinides may be placed between the d transition metals and the rareearth elements. The 5f electrons in the actinides are less localized than the 4f electrons in the corresponding rare-earth series, but the 5f-5f overlap decreases on going from the early to the late actinides. The fact that the degree of 5f localization is determined by the 5f-5f overlap is documented in the well-known Hill plot which correlates the simplest ground states (superconductivity, paramagnetism or magnetic order) with the actinide-actinide distances. Superconductivity occurs in the early actinides (Th,

MAGNETISM OF HYDRIDES

535

Pa and U) while spin-fluctuation effects are found in Np and Pu. For the transplutonium elements, the 5f electrons become more localized and thus, starting from Am, the series becomes rare-earth-like. As the hydrogen absorption generally expands the lattice and reduces the 5f-5f overlap, a more localized behaviour is expected and indeed observed in the hydrides than in the parent metals. Th4I-I~5 is a superconductor with a rather high transition temperature (8 K). Magnetism occurs in the U and Pa hydrides, but disappears in the NpHx system and reappears in the Pu hydrides. The 5f electrons finally become fully localized for the transplutonium elements and the heat of formation approaches that of typical rare-earths hydrides (Ward 1985a). The following actinide hydrogen systems are expected to exhibit properties similar to those of the rare earth. Unfortunately, very few experiments have been performed because of the intense radioactivity of the transplutonium elements.

5.2.1. ThHx ThH2 with the face-centred tetragonal structure is isostructural with the dihydrides of Ti, Zr and Hf, but exhibits an appreciably larger lattice constant. The higher hydride Th4H15 is superconducting below 8 K and crystallizes in a complex bcc structure containing 16 atoms per unit cell (Satterthwaite and Toepke 1970, Ward 1985a,b). No evidence for superconductivity could be found for ThH 2 down to 1 K, although the parent metal is superconducting below 1.37 K. The reappearance of superconductivity in Th4H15 initiated band-structure calculations, inelastic neutron scattering experiments and heat capacity measurements (Winter and Ries 1976, Dietrich et al. 1977, Miller et al. 1976). From specific heat measurements with and without external field Miller et al. (1976) concluded that Th4H15 is a bulk type-II superconductor whose properties are in fair agreement with the BCS theory. The electronic specific heat coefficient (7 = 8.07 mJ/mol K 2), the Debye temperature (0 = 211 K) and the electron-phonon enhancement factor (2 = 0.84) of Th4H15 is by 87%, 29.5% and 58% larger than in the parent metal. According to valence band spectra (Waever et al. 1977), the increase of the 7 value is not caused by an enhanced density of states at the Fermi energy. No significant increase of the phonon enhancement factor is derived from band-structure calculations by Winter and Ries (1976). According to their calculation, they predicted a Tc enhancement if Th is substituted by elements with a lower valency. This, however, is not in agreement with the experimental results which show a depression of Tc (Oesterreicher et al. 1977). 5.2.2. PaHx No magnetic order was detected by susceptibility measurements above 4 K in the C15 Laves phase and the A15 phase. The effective paramagnetic moment is 0.84#B and 0.98#B, respectively (Ward et al. 1984). 5.2.3. UHx Usually, the [~-UH3 phase occurs which crystallizes in the A15 structure, while the ~-UH3 phase is difficult to prepare and contains frequently a mixture of ~- and 13phases (Ward 1985b). Both crystal structures belong to the Pm3n group. There are many magnetic and N M R measurements of the [3-hydride and few of the m-hydride,

536

G. WIESINGERand G. HILSCHER

which are reviewed by Ward (1985a). Both order ferromagnetically. The paramagnetic Curie temperature of ~-UH3 is between 174 and 178 K. According to specific heat, neutron diffraction and magnetic measurements, Tc of [3-UHa is in the range between 170 and 181 K. Due to the lack of saturation, the data of the spontaneous moment exhibit a considerable scatter (0.87#B--l.18#B), while the neutron diffraction result of Shull and Wilkinson (1955) gives a moment of 1.39#B. This is obviously a consequence of a rather high magnetocrystalline anisotropy, which is also reflected in the heat capacity: Fernandes et al. (1985) analysed the specific heat data of Flotow and Osborne (1967) in terms of spin wave contributions and found good agreement with the experimental data if an energy gap of about 80 K is taken into account. The appearance of an energy gap in the ferromagnetic spin wave spectrum is a strong indication for a high magnetocrystalline anisotropy. The electronic specific heat coefficient of 13-UH3 (7 = 28.7 mJ/mol K 2) is nearly by a factor of three larger than that of U metal. By analogy with Ce hydrides, this 7 enhancement may presumably arise from a f-d correlation effect as in heavy fermion systems rather than from a simple increase of the density of states at the Fermi energy. 5.2.4. NpH~

Neptunium forms, analogous to the rare-earth hydrogen systems, a cubic dihydride (CaF2 structure) and a hexagonal trihydride. The susceptibility of NpHx (x = 2.04, 2.67, 3.0) exhibits only a weak temperature dependence which is nearly constant below 200 K (Aldred et al. 1979). A crystal-field calculation based on the Np a+ (5f 4) ground state yields good agreement with the experimental data. 5.2.5. P u l l x

Magnetic order occurs in the PuHx system for all x values (1.99 < x < 3.0) and changes from antiferromagnetic order in Pull1.99 (TN-- 30K) to ferromagnetism (Aldred et al. 1979, Ward 1985a). Instead of antiferromagnetism in the powdered dihydride, ferromagnetic order was reported for a bulk sample with x = 1.93 [Tc = 45 K; Willis et al. (1985)]. The Curie temperatures increase with the hydrogen content up to 101 K for the hexagonal trihydride, while the spontaneous moments decrease from 0.57#B for x = 1.93 to 0.353#B for x = 3.0. By analogy to the Np system, Aldred et al. (1979) suggested from susceptibility measurements a Pu 3+ (5f 5) ground state. With the same crystal-field parameters as for NpH2, the magnetic ground state consists mainly of the J = ~ manifold with 3 % admixture of J = 7. Thus, the expected ordered moment (1.0#B) is significantly higher than the experimental value (< 0.57#B). The ordered moment determined from neutron diffraction equals 0.8 T- 0.3#R for the three deuterium concentrations investigated (x = 2.25, 2.33 and 2.65) (Bartscher et al. 1985). The significant difference between the neutron and magnetization data of the magnetic moment is presumably due to a large magnetocrystalline anisotropy. 5.3. Binary transition-metal hydrides

The work on these systems until 1977 is covered by the review of Wallace (1978), where predominantly studies on the systems Ti-H and P d - H are treated. All d

MAGNETISM OF HYDRIDES

537

transition metals which were found to form stable hydrides are paramagnetic. In most of the cases, hydrogen uptake leads to a reduction of the susceptibility, which is attributed to a hydrogen-induced decline in the density of states. Limitations for the application of the rigid-band model in order to explain the susceptibility behaviour were found, which is due to the two-phase nature of the T M - H systems. Particularly for these systems, an appreciable number of theoretical studies on the electronic properties have been carried out, the early work of which having been reviewed by Switendick (1978). Aspects of both simple pictures, the proton model (electrons added at the Fermi level) and the anion model (low-lying states associated with electronic charge in the vicinity of the hydrogen) are found. Later on, the application of pressures in the GPa range lead to the preparation of further transition-metal hydrides [Cr-H (Ponyatovskii et al. 1982), M n - H (Antonov et al. 1980b, Fukai et al. 1989), F e - H (Antonov et al. 1981, 1989), Co-H, and N i - H (Antonov et al. 1980a, 1983, Hanson and Bauer 1988)]. Upon hydrogen uptake, the magnetic order is generally reduced. Antonov and co-workers interpreted their magnetization results within the framework of the rigid-band model, considering hydrogen as a donor of a fractional quantity of electrons to a common band. As, however, Vargas and Christensen (1987) and Vargas and Pisanty (1989) deduced from their linear muffin-tin orbital calculation for several transition-metal hydrides, the rigid-band approximation is not valid in the case of these transition-metal hydrides. The presence of hydrogen in the metal matrix strongly modifies the electronic structure, leading to new states far below the d band of the host and to an increase of the density of states at the Fermi level. Both facts have been verified experimentally by photoemission (see, e.g., Riesterer et al. 1985), soft X-ray emission (Fukai et al. 1976) and specific heat measurements, respectively (see, e.g., Wolf and Baranowski 1971). Valuable information in this respect may further be obtained from 1H-NMR Knight shift studies (Schmidt and Weiss 1989).

5.4. Ternary rare-earth-transmission-metal hydrides Different from section 5.1, here the symbol R means not only a rare-earth element but also elements such as Ti, Zr, Hf.

5.4.1. Hydrides of Mn compounds 5.4.1.1. Generalfeatures. Particular for Mn-containing ternary hydrides, no general prediction can be made of the changes in magnetic properties upon hydrogen uptake (table 2). Onset and complete loss of magnetic order after hydrogen absorption are found, as well as a substantial reduction of Tc and the magnetization. Moreover, spin-glass behaviour is frequently obtained for Mn-rich ternary hydrides which most probably has to be related to the presence of Mn segregations detected by means of XPS (Schlapbach 1982). The reason for these heterogeneous results lies in the specific sensitivity of the magnetic properties of Mn compounds upon interatomic distances. Particularly Buschow and Sherwood (1977) pointed to the importance of a critical M n - M n distance for the occurrence of magnetic order. However, in order to explain

538

G. WIESINGER and G. HILSCHER TABLE 2 Magnetic properties of R - M n compounds and their hydrides.

Compound

Structure

Space group

Tc (K)

#s (#B/f.u.)

#Mn (#B/Mn)

Y6Mn23

Yh 6 Mn23 Th 6 Mn23 Th6 Mn23 Th6 Mnz3

Fm3m Fm3m Fm3m Fm3m

486, 498 563 700 -

13.2, 13.8 -

0.4

Y6 Mn23 H9 Y6 Mn/3 H2o Y6 Mnz3 H2s Nd6 Mn23 Nd6 Mn23 Hx

Th6 Mn23 Th6 Mnz3

Fm3m Fm3m

438 220

4.8 20.8

[7] [7]

Sm6Mn23 Sm6 Mn23 Hx

Th6 Mn23 Th6 Mn23

Fm3m Fm3m

450 230

3.0 15.3

[7] [7]

Gd6 Mn23 Gd6 Mn23 H22

Th6 Mn23 Th6 Mn23

Fm3m Fm3m

461 140, 180

49 14.2

[2] [2, 8, 9]

Tb6Mn23 Tb6 Mn23 H/3

ThrMn23 Th6 Mn23

Fm3m Fm3m

455 220

49 17.2

[10] [ 10]

Dy6Mn23 Dy6Mn/3H23

ThrMn/3 Th6Mn23

Fm3m Fm3m

443,435 <4.2

49.6,40.5 -

Ho6 Mn23 Ho6 Mn23 H23

Th 6 Mn23 Th6 Mn23

Fm3m Fm3m

434 < 4.2

59.8 -

[8] [8]

Er6 Mn23 Er6 Mn23 H23

Th6 Mn23 Th6 Mn23

Fm3m Fm3m

415 < 4.2, 85

38 -

[8] [8, 13]

Tm6 Mn23 Tme Mn23 H~

Th6 Mn23 Th e Mnz3

Fm3m Fm3m

404 -

29.5 6.5

[11, 14] [11, 14]

Lu6 Mn23 Lu6 Mn23 Hx

Th6 Mn23 The Mn23

Fm3m Fm3m

378 266

8.9 3.4

[2] [2]

Th6 Mn23

Th6 Mnz3 Th6 Mn23 TheMn23

Fm3m Fm3m Fm3m

-

Th6 Mn23 Hzo Th6Mn23H3o

329

20 19.4

[15] [15] [16]

YMn 2 YMn/H3.4

MgCu 2 MgCu2

Fd3m Fd3m

100 284

2.7 0.52

GdMn 2 GdMn 2H~

MgCu 2 MgCu z

Fd3m Fd3m

10 260

4.8 3.2

[2] [2]

DyMn2 DyMn2H ~

MgCu 2 Fd3m No long-range order

41 <4.2

6.7 -

[12] [12]

ErMn 2 ErMnz H4

MgZn 2 MgZnz

ErMn2 H4.6

MgZnz

P63/mmc P63/mmc P63/mmc

25 > 4.2 < 1.5

-

[18] [18] [18]

LuMn 2 LuMn 2 H.

MgZn 2 MgZn 2

P63/mmc P63/mmc

201

ThMn 2 ThMn2 Hx

MgZn z MgZnz

P63/mmc P63/mmc

ScMn2 ScMn 2 H~

MgZn2 MgZn2

P63/mmc P63/mine

-

Ref.* [1-3] [4] [5] [1,4-6]

[10-12] [10]

0.25

[2, 17] [1,2]

0.16

[2] [2]

-

-

[2] [2]

210

-

[19] [ 19]

MAGNETISM OF HYDRIDES

539

TABLE 2 (continued) Compound

Structure

Space group

Tc (K)

TiMn 1.s TiMnl.sH0.97

MgZn2 MgZn2

P63/mmc P63/mmc

213

-

[20] [20]

ZrMnz ZrMn2 H3 ZrMn2H3.6 ZrMn2.sH3.6 ZrMn3.sH3.6

MgZn2 MgZn2 MgZn2 MgZn2 MgZn2

P63/mmc P63/mmc P63/mmc P63/mmc P63/mmc

175 148 139 133

0.04 0.04 0.12 0.18

[21] [21] [22] [22] [22]

* References: [1] Buschow (1977b). [2] Buschow and Sherwood (1977). [3] Delapalme et al. (1979). [4] Commandr6 et al. (1979). [5] Crowder and James (1983). [6] Stewart et al. (1981a). [7] Buschow (1981). [8] Pourarian et al. (1980a). [9] Wortmann and Zukrowski (1989). [10] Pourarian et al. (1980b). [11] Buschow et al. (1982b).

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

#s (/~B/f.u.)

#M~ (/~/Mn)

Ref.*

Gubbens et al. (1983a). Stewart et al. (1981b). Gubbens et al. (1983b). Boltich et al. (1982a,b). Malik et al. (1977). Nakamura (1983). Viccaro et al. (1980). Buschow (1982). Hempelmann et al. (1983). Didisheim and Fischer (1984). Fujii et al. (1982c).

the complex process of magnetic ordering present in these compounds, the density of states at the Fermi level, N(EF), has to be considered further.

5.4.1.2. R6Mn23. In the case of the R 6Mn23 (R = magnetic rare earth) compounds, hydrogen uptake commonly leads to a drastic reduction of both Curie temperature and magnetization (Buschow and Sherwood 1977, Buschow 1981, Buschow et al. 1982b, Pourarian et al. 1980a,b, Gubbens et al. 1983a). For R = Y, the absorption of hydrogen even leads to a complete loss of magnetic order down to 4 K (Buschow 1977b, Buschow and Sherwood 1977, Malik et al. 1977, Gubbens et al. 1983b). On the other hand, in the case of R = Th, the opposite behaviour is observed: the Pauli paramagnetic host material is converted into a magnetically ordered hydride (Buschow and Sherwood 1977, Malik et al. 1977, Boltich et al. 1982a,b). In order to elucidate the reason for this peculiar behaviour, the two latter compounds and their hydrides were subject to various neutron diffraction studies. F o r Y6MnzaD23, H a r d m a n - R h y n e et al. (1984a) observed a crystallographic phase transition (cubic-tetragonal) which is accompanied by the onset of a weakly antiferromagnetic ordering of some of the Mn moments. This interpretation is confirmed by a M6ssbauer study performed on 57Fe-doped sample (Stewart et al. 1981a). Th6Mnz3D16 suffers a low-temperature lattice distortion ( H a r d m a n et al. 1980); nothing of that kind had been observed for Th6Mn23D3o (Hardman-Rhyne et al. 1984b). Even at liquid-helium temperature, no long-range magnetic ordering is present in the former. The latter, however, exhibits almost ferromagnetic coupling (only 4 out of 92 Mn spins point into the opposite direction). The altered arrangement of the deuterium atoms, a deuterium-induced charge transfer and a change in the

540

G. WIESINGERand G. HILSCHER

band structure owing to the specific lattice expansion has been given as the main reasons for this behaviour. Dy and Tm M6ssbauer studies (Buschow et al. 1982b, Gubbens et al. 1983a,b) gave evidence that the small value of the hydride magnetization in Dy 6 Mn23- and Tm 6 Mn23-hydride had to be attributed to an antiferromagnetic arrangement of the R sublattice. 57Fe M6ssbauer spectra recorded on doped Er6Mn23 (Stewart et al. 1981b) revealed that the Mn atoms partly loose their moment after hydrogen absorption. While the magnetic order of the Mn sublattice is substantially reduced in the hydrides, the R moments have almost retained their host compound value. For 57Fe doped Gd 6 Mn23 H25, Wortmann and Zukrowski (1989) reported on a marked difference (170 K) between the ordering points of the magnetic sublattices. The low ordering temperature of the Gd sublattice compared to the case of R = Er (see above) is attributed to the lack of any crystal-field interaction in Gd.

5.4.1.3. RMne. As in the above case, a substantial hydrogen-induced reduction of magnetization and Curie temperature is obtained. In particular for GdMn2 hydrogen uptake was found to reduce the magnetization at low temperatures, whereas for temperatures above about 100 K an increase was observed (Buschow and Sherwood 1977). This was explained by the authors in terms of an alignment of the Gd moments, caused by the Mn moments, which are assumed to order close to the Curie temperature of YMn2 hydride (Tc = 284K). 161Dy and 166Er M6ssbauer studies have been reported for DyMn2Hx (Gubbens et al. 1983b) and ErMn2Hx (Viccaro et al. 1980), yielding a disappearance of the magnetic ordering after hydrogen absorption. The presence of a magnetic hyperfine field at 1.5K of about 500T in ErMn2H~. 6 was explained by intermediate relaxation rates. By a set of supplementary experiments, Nakamura (1983) could show that below TN = 100K YMn2 is an itinerant-electron antiferromagnet with a Mn moment of 2.7#~. At TN, the Mn moment collapses and, above TN, it again grows by thermal excitations of spin fluctuations (Shiga et al. 1983). Fujii et al. (1987) found that hydrogen absorption favours ferromagnetic ordering for moderate concentrations (/~' phase), whereas in the fully charged//phase antiferromagnetism or paramagnetism becomes stable (fig. 7a,b). In the case of the hydrides of the Pauli paramagnetic compounds ZrMnz, ScMn2 and LuMn2, spin-glass behaviour is found (van Essen and Buschow 1980b, Pourarian et al. 1981). Among these kind of compounds, ThMn2H~ is seen the only exception known so far, since it remains paramagnetic on hydriding (Buschow and Sherwood 1977). In the case of TiMn~, three paramagnetic phases have been found with Mn concentrations ranging from x = 1.08 to x = 2 (Hempelmann and Hilscher 1980). The corresponding hydrides order ferromagnetically which has been attributed to both the hydrogen-induced volume expansion and increase in N(Ev) (Hempelmann et al. 1983). By using the Rhodes-Wohlfarth plot, the Laves phase compound was classified as a localized moment system, the two other phases, however, as pure band ferromagnets. The hydrogen-induced onset of ferromagnetism in the Laves phase TiMnl.sH~ has been considered in view of the large increase of both the temperature-independent term of the paramagnetic susceptibility and the specific heat coefficient 7 upon

MAGNETISM OF HYDRIDES (a)

I

I

I

I

YMn2Hx

15

t~

I

x = 3.0

T=4.2K /

E

541

10

f

2.0

2.0

10 1.0 4.0

i.5~ 0

0

10

20

30

40

H (kOe)

50

60

I-.5

0

1 O0

200 T (K)

300

400 ~--

Fig. 7. (a) Magnetizationsat 4.2K as a functionof magneticfield for YMn2Hx and (b) magnetizations under 10kOe as a functionof temperature for YMn2Hx(Fujiiet al. 1987). hydrogen absorption. This has been correlated with a rise in the density of states at the Fermi level N(EF) which is supposed to grow continuously with the amount of hydrogen (Fruchart et al. 1984a).

5.4.2. Hydrides of Fe compounds 5.4.2.1. Generalfeatures. In this case, the hydrogen-induced influence on the magnetic properties is less pronounced than in Mn compounds. Various neutron diffraction experiments proved that there is an increase of the Fe sublattice moment after hydrogenation, whereas the rare-earth sublattice moment is generally reduced. The Curie temperature can show changes in either direction, the behaviour depending on the amount of Fe in the compound. Compensation points, whenever present in the parent material, are lowered upon the absorption of hydrogen, thus reflecting the reduced rare-earth sublattice contribution to the total magnetic order. When a hydrogen-induced rise in moment is observed, it only takes place up to a certain hydrogen concentration, from whereon a complete loss of any magnetic order is found, frequently accompanied by complete damage of the lattice periodicity.

5.4.2.2. RFe12. The search for novel permanent-magnet materials has led to the synthesis of ternary compounds of the type RFetoX 2 [X = Ti, V, Cr, etc., see, e.g., de Mooij and Buschow (1988)] with the tetragonal ThMnt2-type crystal structure. Hydriding studies performed thus far yielded a comparatively low rise in the Fe moment, with a larger hydrogen-induced increase found for Tc (Obbade et al. 1988). Although commonly the rare-earth contribution of the anisotropy is weakened upon hydrogen absorption, nothing of that kind could be found in the present case: the hysteresis loops of host compounds and hydrides showed no significant differences.

542

G. WlESINGER and G. HILSCHER

5.4.2.3. R eFe~ 7. Zukrowski et al. (1983) investigated some Fe-rich Dy2(Fe 1_yAlr)17

hydrides using both the 161Dy and the 57Fe M6ssbauer effect. For the host compounds only the hexagonal ThzNitT-type structure was obtained, which was found to be retained in the hydrides with the exception of the sample with y = 0.18, where hydrogen uptake converted the crystal structure to the rhombohedral Th2Znlv type. While upon hydrogenation the isomer shift and quadrupole splitting had increased in both cases, only the Fe hyperfine field showed a remarkable increase, the hyperfine field at the Dy nuclei remaining essentially unaffected. In a later publication, Rupp and Wiesinger (1988) where able to show that Nd2 Fe17 hydrides had preserved the rhombohedral crystal structure of the parent material. The magnetization was found to be almost unaffected upon hydrogen absorption, contrary to the Fe hyperfine field and Tc (fig. 8). While a maximum rise in the average Beff of 1.9 T (6%) was observed, the increase in Tc amounted to a remarkably high value of 320 K (95%). A preference of hydrogen for the h sites is reported, which is attributed to local atomic site influences (less Fe neighbours, more Nd neighbours). A similar situation is found in the case of the related system R2 Fe t4 BHx (see below). The data of Rupp and Wiesinger (1988) have been confirmed by Wang et al. (1988), who furthermore included Sm2 Felt Hx in their study. Hu and Coey (1988) compared the influence of hydrogen absorption upon Tc with that of substituting Fe by various elements (A1, Si, Co) in Nd2Fe~7. In both cases, an increase in Tc has been observed, which is claimed to be built up from distancedependent exchange interactions and band-structure effects.

30

I

I

I

I

I

I

~s

E

20

0.1

/

..-tO

10

E

-0.1 /

/

500 ~v

~

20

loo f,

4o0

80

~

~ 300 0

1

2

½

Z+

5

X in NdzFe17Hx

Fig. 8. Magnetization (T= 77 K), Curie temperature, average Fe hyperfine field and isomer shift (T= 295 K) of Nd2FelTH x (Rupp and Wiesinger 1988).

MAGNETISM OF HYDRIDES

543

5.4.2.4. ReFe14B. Compounds of this type have been synthesized while searching for an inexpensive (Co-free) permanent-magnet material. In a way, their crystal structure is related to the well-known CaCu5 type, the essential fact being the formation of several layers, which is the basis for a large anisotropy. Nd2Fe14B is a most valuable material with one exception; it suffers from a relatively low Curie temperature which makes technical operation of permanent magnets of this type above 100°C not feasible. Thus, the enhancement of Tc without reducing the other high quality properties was the main effort in the studies carried out up to now. The principle source of the unique hard-magnetic properties of NdFeB magnet materials is the intrinsic magnetocrystalline anisotropy of the tetragonal compound Nd2Fe14B which exhibits two Nd and six Fe sublattices (Herbst et al. 1984, Givord et al. 1984, Shoemaker et al. 1984). The metallurgical possibility for the formation of small crystallites of the Nd2 Fe14B phase gives rise to large values of the coercivity iHc. If another rare earth, with the exception of Eu and Yb, replaces Nd, the crystal structure remains unchanged. However, in the case of a heavy rare earth, the moments are aligned antiparallel to the Fe moments which prohibits the use of such a compound as a permanent magnet. Research performed on the parent material will not be covered in the present work. We just wish to mention that there is a similar situation as in the case of the R2 TM 17-type permanent magnets where multi-component systems have been developed, in order to overcome the anisotropy reduction caused by the substitution of elements which otherwise increase the Curie temperature. Since in Fe-containing compounds hydrogen uptake is known to frequently lead to an enhancement of the 3d moment and even of Tc, several groups began to study hydrides of Nd2Fe14B and isostructural systems with regard to their permanent magnetic properties. It turned out that, in fact, the Curie temperature rises upon hydrogen absorption (fig. 9, table 3). On the other hand, a dramatic loss in the anisotropy is observed simultaneously (Oesterreicher and Oesterreicher 1984, Wiesinger et al. 1987a,b, Pareti et al. 1988). Nevertheless, for technical application this material is still hydrided in order to gain a fine powder without the necessity of the milling procedure (Harris 1987, Harris et al. 1985, 1987). The latter powder then serves as the starting material for technical permanent magnets. Further studies were only devoted to basic research with the emphasis on the influence of hydrogen on the magnetic and the crystal-field interactions [for typical publications see, e.g., L'H6ritier et al. (1984), Dalmas de Reotier et al. (1985, 1987), Cadogan and Coey (1986), Sanchez et al. (1986), Coey et al. (1987), Fruchart et al. (1987b), Wiesinger et al. (1987a,b), Wiesinger and Hilscher (1988b), Zhang et al. (1988a), Fruchart et al. (1988)]. Besides the investigation of the bulk properties, great effort has been spent to study the hyperfine interactions in these systems. Ferreira et al. (1985) were the first to report on a systematic investigation of the sequence of hydrogen filling, which they deduced from the specific hydrogen-induced rise of both the various s7 Fe hyperfine fields and the corresponding isomer shifts. From neutrondiffraction experiments it was evidenced that the hydrogen atoms are located only in the vicinity of the R atoms. Apparently, hydrogen cannot be inserted in the double Fe slabs forming the sigma layers and in the tetrahedra consisting only of Fe and B

544

G. WIESINGER and G. HILSCHER I

I

I

I

I

~ --'~0~

~" 55O

650

I-

t-

Dy o," / o" / o/

!

/ /o / ~'---~.=Z.- .~%~.=wEr 500 I/Yz~J.~" ~

~ 0

600

Ce

/

/ 450

-/

/

550

/ I

I

I

I

I

1

2

3

4

5

x

Fig. 9. Curie temperature as a function of the amount of absorbed hydrogen of R2Fe14BHxfor R = Y, Ce, Dy or Er (Dalmas de Reotier et al. 1987).

atoms. The particular hydrogen-filling sequence also accounted for the significant hydrogen-induced depression of both the rare earth and the iron contributions to the magnetocrystaUine anisotropy which has been studied in detail for R = Y, Nd, Ho or Tm (Pareti et al. 1988). For all R2 Fel~ B compounds investigated, an increase of the magnetization as well as of the Curie temperature was found after hydrogen uptake. The Fe moments grow upon hydrogen absorption in a more or less uniform way. As far as it could be determined, the R moments are considered to be less sensitive to hydrogen loading (Friedt et al. 1986, Dalmas de Reotier et al. 1987). On the other hand, the effect of hydrogen on the spin reorientation temperature TSR was found to be distinctly element-specific (Dalmas de Reotier et al. 1987, Regnard et al. 1987). In certain cases, even the occurrence of a spin reorientation is induced by the absorption of hydrogen (see table 2). The shift of TsR has been explained by the hydrogen-induced increase of the fourth-order crystal-field parameter B ° which is in agreement with the rise of the anisotropy constant K 2 (being proportional to B °) determined by magnetization measurements (Fruchart et al. 1988).

5.4.2.5. RFes. For ThFes, Gubbens et al. (1984a) obtained only a slight hydrogeninduced increase of both the magnetization and the Curie temperature. As in the case of the parent compound, the hydride exhibited a sharp hyperfine pattern. However, the easy axis of magnetization was concluded to have turned from a direction between the c~ and the b axis to a direction along the a axis. The increase

MAGNETISM

OF HYDRIDES

545

TABLE 3 M a g n e t i c p r o p e r t i e s of R - F e c o m p o u n d s a n d their hydrides. Compound

Structure

Space group

Tc (K)

T~omp (K)

TsR (K)

/l~ (#B/f.u.)

#F~ (#B/Fe)

YFeloTi YFeloTiHo.55 Y F e 11 Ti YFeloV YFeloVH YFellV YFeVllH

ThMnl 2 ThMn12 ThMnl2 ThMnl2 ThMn12 ThMn12 ThMn12

I4/mmm I4/mmm I4/mmm I4/mmm I4/mmm I4/mmm I4/mmm

530 570 535 550 660 550 665

-

-

15.5 16.3 17.3 15.2 16.0 17.3 17.9

-

Nd2Fei7 Nd2FelTH3.2

Th2Znlv Th2 Z n l 7

R3m R~m

335 510

. .

. .

. .

. .

[2-4] [2-41

Sm2Fel7 Sm2FelvH2

Th2Zn17 Th2Zniv

R3m RJm

388 526

. .

. .

. .

. .

[3] [3]

Y2 F e 14 B Y2FeI4BH3.6

N d 2 Fe 14 B Nd2Fel4B

P42/mnm P42/mnm

558 615

-

-

30.7 32.5

2.2 2.3

Ref.*

[1] [11 [11 [11 [1] [1] [1]

[5] [6, 7]

La2Fe14B

Nd2Fei4B

P4z/mnm

530

-

-

30.6

2.2

[5]

Ce2Fe14B Ce2 Fel4BH3.7

NdzFel4B Nd2Fel4B

P42/mnm P42/mnm

425 560

-

-

30.2 30.5

2.1 -

[-5] [6]

Pr2Fel4B Pr2Fel4BHLo

Nd2Fel4B Nd2Fel4B

P42/mnm P42/mnm

565

-

32.3 36.6

-

[5] [9]

Nd2Fe14B Nd2Fea4B Nd2 Fe14BH4.92 Nd2 F e i 4 B

P4z/mnm P42/mnm

580 -

-

135 95

34.8 36.9

-

[5,8,9] [-8, 9]

Sm2Fe14B SmzFel4BH6

Nd2Fei4B NdzFei4B

P4z/mnm P42/mnm

616 -

-

-

34.8 32.7

-

[5] [9]

GdzFea4B Nd2Fel4B G d z Fel4BH4.4 N d z F e 1 4 B

P42/mnm P42/mnm

650 698

-

355

31.3 22.3

2.5

[5] [I0]

Tb2Fe14B Tbz Fel4BH4.4

Nd2Fel4B NdzFel4B

P42/mnm P42/mnm

620 657

-

-

12.9 13.6

2.2 2.3

[5, 10] [10]

Dy2Fel4B Dy2 Fel4BH4.6

Nd2Fel4B NdEFe14B

P42/mnm P42/mnm

585 638

-

45

11.0 13.7

2.2 2.4

[-5, 10] [-10,11]

Ho2Fel4B Nd2Fei4B Ho2Fe14BHs.4 Nd2Fe14B

P42/mnm P4z/mnm

565 615

-

65 -

10.9 14.1

2.2 2.3

[5, 10] [10]

Er2Fei4B Er2Fel~BHa.7

NdzFel4B Nd2Fe14B

P42/mnm P42/mnm

550 588

-

318 352

13.5 16.6

2.2 2.4

[-5, 10] [6, 10]

Tm2Fel4B Nd2Fe14B Tmz Fe 14 BH2.96 Nd2 Fe 14 B

P42/mnm P42/mnm

540

-

315 -

17.8 20

-

[5, 12] [-12]

LuzFel4B

Nd2Fel4B

P42/mnm

535

-

-

28.2

-

[-5]

ThFe5 ThFe5 Hx

CaCu~ CaCu5

P6/mmm P6/mmm

685 700

-

-

-

Y6 Fe23 Y6Fez3H

Th6 Mn23 Th6Mn2a

Fm3m Fm3m

485 743

-

-

-

H o 6 Fe23 HosFe23H16

Th6 Mn2a Th6Mn2a

Fm3m Fm3m

501 702

185 72

-

13.8 7.2

-

1.72 1.75

[13] [13]

1.65-1.9 [ 1 4 - 1 6 ] 1.96-2.59 [15, 16] -

[14, 171 [17, 18]

546

G. WlESINGER

and G. HILSCHER

TABLE Compound

Structure

Er6Fe23

Th6Mn23

Er6Fez3H14

Tetr.

T m 6 Fe23

Th6 Mn23

T m 6 Fe23 H 14

Tetr.

3

(continued)

Space

Tc

T~r~p

TSR

#s

#Fo

group

(K)

(K)

(K)

(#B/f.u.)

(#B/Fe)

Ref.*

Fm3m

493

95

-

8.2

-

[14, 17]

-

-

19.5

-

8.0

-

[17]

Fm3m

480

-

-

15.2

-

[14, 19]

-

550

-

-

23.6

-

[19]

L u 6 Fe23

Th 6 Mn23

Fm3m

.

.

.

.

1.54

[20]

L u 6 Fe23 H s

Th 6 Mn23

Fm3m

.

.

.

.

1.64

[20]

YFe3

PuNia

R3m

537

-

-

4.88

1.7

[15,21]

YFe3H 5

PuNi 3

R3m

545

-

-

5.7

1.9

[15]

GdFe 3

PuNi 3

R~m

728

600

-

1.62

-

[21]

GdFe3H3.1

PuNi 3

R3m

-

170

-

1.39

-

[22]

TbFe3

PuNi 3

R3m

648

610

-

3.19

-

[21]

TbFe 3H x

PuNi 3

R3m

300

205

-

2.9

-

[23]

DyFe3

PuNi3

R3m

602

523

-

4.29

-

[21]

DyFe3H 3

PuNi3

R~m

-

175

-

2.2

-

[22]

HoFe3

PuNi a

R3m

565

389

-

4.59

-

[21]

HoFeaH3. 6

PuNi a

R3m

-

112

-

2.53

-

[22]

ErFe3

PuNia

R~m

552

228

-

3.42

-

[21]

ErFeaHa.5

PuNia

R~m

-

81

-

2.05

-

[23]

TmFe a

PuNi a

R3m

542

112

-

1.47

-

[21]

TmFe3H a

PuNi 3

R3m

-

13

-

4.08

-

[23]

ThFe3

PuNi 3

R3m

425

-

250

-

1.36

[24]

-

386

-

250

-

1.46

[24]

ThFeaH

-

YFe 2

MgCu 2

Fd3m

545

-

-

2.9

1.45

[25, 2 6 ]

YFe2 H 4

MgCu 2

Fd3m

308

-

-

3.66

1.83

[25, 2 6 ]

YFe2H 4

MgCu 2

Fd3m

133

-

-

3.71

-

[27]

CeFe 2

MgCu 2

Fd3m

235

-

132

2.59

1.25

[24, 2 6 ]

CeFe 2

MgCu 2

Fd3m

-

-

-

2.66

1.08

[28]

CeFe2H~

n.l.o.

-

358

-

-

4.8

2.1

[25,26]

CeFe2H3. 7

n.l.o.

-

-

-

-

4.43

2.25

[28]

SmFe2

MgCu2

Fd3m

676

-

-

2.75

-

[26]

SmFe2H x

MgCu 2

Fd3m

333

-

-

3.2

-

[26]

GdFe 2

MgCu 2

Fd3m

785

-

-

2.80

-

[26, 2 7 ]

GdFezH x

MgCu 2

Fd3m

388

-

-

4.0

-

[26]

GdFe2H4.1

MgCu 2

Fd3m

338

180

-

5.39

-

[27]

TbFe2

MgCu2

Fd3m

711

-

-

4.72

-

[26, 2 9 ]

TbFe2H x

MgCu 2

Fd3m

303

-

-

4.6

-

[26]

TbFe2 H a

MgCu2

Fd3m

> 300

-

-

7.8

-

[29]

DyFe 2

MgCu 2

Fd3m

635

-

-

5.50

-

[26, 2 9 ]

DyFe2H x

MgCu 2

Fd3m

385

-

-

4.9

-

[26]

DyFe2 Ha. 5

MgCu2

Fd3m

> 300

-

-

7.6

HoFe2

MgCu2

Fd3m

612

-

-

5.50

1.7

[26,30]

HoFe2H~

MgCu 2

Fd3m

298

-

-

5.5

-

[26]

HoFe2Da. 5

MgCu 2

Fd3m

295

-

-

-

1.9

[30]

[29]

MAGNETISM OF HYDRIDES TABLE 3 Compound

Structure

Tc

547

(continued)

Space group

(K)

T~omp (K)

Tsa (K) -

#s (#B/f.u.)

Ref.*

1.6 1.5 1.6 2.1,2.7 -

[26, 27, 30] [27] [31] [27] [26] [27] [32] [30] [30] [33] [34] [27] [35]

ErFe2 ErFe2Ho.5 ErFe2HL6 ErFe2H 2 ErFe2 Hx ErFe2H3. 4 ErFeEH3.s ErFeEH3.5 ErFe2D3. 5 ErFe2H3.6 ErFezH3.7 ErFe2 H 4 ErFe2H4.1z

MgCu z MgCu2 MgCu 2 MgCu 2 MgCu2 MgCu 2 MgCu2 MgCu2 MgCu 2 Rhomb. Rhomb. MgCu2 Rhomb.

Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m -

590 265 265 450 440 300 <4 <4.2

500 395 266 251 152 70 80 . .

TmFe 2 TmFe2 Ha.5

MgCu2 MgCu2

Fd3m Fd3m

610 305

-

-

-

1.43 1.81

[30, 36] [30, 36]

LuFe2 LUFeEHa.z

MgCuz Rhomb.

Fd3m -

-

-

-

2.8 3.5

1.4 1.75

[36] [36]

ScFe z ScFe/H2 ScFeaH3.2

MgZnz MgZn2 MgZn2

P63/mmc P63/mmc P63/mmc

-

-

-

2.3-2.7 3.68-4.46 4.70

Hf2Fe Hf2FeH 3

Ti2Ni Ti2Ni

Fd3m Fd3m

. 73

.

Zr 3 Fe ZraFenL6

Fe 3 B -

Cmcm -

. 80

.

* References: [1] O b b a d e et al. (1988). [2] R u p p and Wiesinger (1988). [3] W a n g et al. (1988). [4] H u and Coey (1988). [5] Sinnema et al. (1984). [6] D a l m a s de Reotier et al. (1987). [7] Coey et al. (1986). [8] Wiesinger et al. (1987a). [9] P o u r a r i a n et al. (1986). [10] Z h a n g et al. (1988a). [11] Coey et al. (1987). [12] Pareti et al. (1988). [13] G u b b e n s et al. (1984a). [14] K i r c h m a y r and Poldy (1979). [15] Buschow (1976). [16] Pedziwiatr et al. (1983a). [17] Boltich et al. (1981). [18] Pedziwiatr et al. (1983b). [19] G u b b e n s et al. (1984b). [20] G u b b e n s et al. (1981). [21] Herbst and C r o a t (1982).

. .

. .

.

.

-

[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

.

.

1.15-1.35 [37-39] 1.84-2.23 [39] 2.35 [38]

.

.

.

4.80 5.2 5.2 . .

#re (#B/Fe)

0.9

. .

[42] [42]

.

Malik et al. (1976). Malik et al. (1983). van Diepen and Buschow Buschow and van Diepen Buschow (1977c). Oesterreicher and Bittner Deryagin et al. (1985). P o u r a r i a n et al. (1980c). Fish et al. (1979). de Saxc~ et al. (1985). P o u r a r i a n et al. (1982b). F r u c h a r t et al. (1987a). Deryagin et al. (1984a). D u n l a p et al. (1979). Deryagin et al. (1984b). Buschow et al. (1980). Niarchos et al. (1981). Smit et al. (1982). Buschow and van Diepen Vulliet et al. (1984). Aubertin et al. (1987).

[40] [40,41]

(1977). (1976). (1980).

(1979).

548

G. WIESINGER and G. HILSCHER

in isomer shift after charging has been explained by Gubbens et al. (1984a) on the basis of a modified Miedema-van der Woude model (Miedema and van der Woude 1980).

5.4.2.6. R6Fe23. The R moments are found to be less influenced by hydrogen absorption, compared to the Fe moment which frequently is raised substantially upon hydrogen uptake (Rhyne et al. 1983, Gubbens et al. 1984b, Pedziwiatr et al. 1985, Wallace et al. 1987). This leads to a rise in the 57Fe hyperfine field, whereas the compensation points, commonly observed for the parent intermetallics, are shifted towards lower temperatures when hydrogen (deuterium) is dissolved. In figs. 10 and 11, this is demonstrated for the case of Ho6Fez3 deuterides. Furthermore, a substantial rise in To, as well as a linear correlation between compensation temperature and absorbed hydrogen is obtained. A hydrogen-induced reduction and an increase in the magnetization can be observed below and above T~omp, respectively (Boltich et al. 1981, Pedziwiatr et al. 1983a, 1983b). In the case of R = Lu, a decrease of the individual Fe hyperfine field was reported by Gubbens et al. (1981) to have occurred after hydrogen uptake, which was unexpectedly accompanied by a rise in the magnetic moment. This peculiar behaviour has been interpreted by the authors to arise from a hydrogen-induced change in the conduction electron contribution to Boff. At this point, we wish to recall that in these ferrimagnetic compounds the R moment is predominant at low temperatures (T < T~omp),with the Fe moment dominating at higher temperatures. Thus, a reduced magnetization is not necessarily due to a diminished R moment. It can equally well be the result of an increase in the Fe moment. This has been ascertainedexperimentally by neutron-diffraction studies (Rhyne et al. 1983) as well as by molecular-field calculations, from which an enhancement of the Fe-Fe interaction and a pronounced 24

i

J

i

Ho6Fe23Disy "

Ho6Fe23DI2.~

16 H°6Fe23D8 2 Ho6Fe23 D1,5

=L 8

6Fe23

0

0

I

I

I

I00

200

300

T(K)

Fig. 10. Magnetization as a function of temperature for HosFeza and several of its deuterides (Wallace et al. 1987).

MAGNETISM OF HYDRIDES

i

g~

T:412K

96

i• :",/:i :;

,o nr

{::.

;.~i

i, -; ' .

: :~ . . . . 95 I00

549

i ' ~,' :.."

IT -6

:: ~: .:'"

I -3 Velocity

":

~:

I 0

J

i.

"~

: : : !t ~

Y 5

:

12. I

'.. ":t .,,

~1 6

,

(ram/s)

Fig. 11.27Fe M6ssbauerspectrafor I"Io 6 Fezaand for Ho6Fe23Dx. The fulllineis a least-squarescomputer fit, assuminga [111] easy axis direction(Wallaceet al. 1987). weakening of the R-Fe interaction upon hydrogen uptake have been derived (Gubbens et al. 1984b). Particular attention has been paid to the pseudobinaries Y6(Fe, Mn)23, where spectacular magnetic properties can be observed. Two critical concentrations for the onset of magnetic order have been obtained. While both end compounds exhibit Curie temperatures of about 500 K, there is no evidence for any long-range magnetic order in the concentration range 0.4 < x < 0.7. From an analysis of their highpressure magnetization data, Hilscher et al. (1977) suggested these compounds to form a spin-glass system, which was later confirmed by the neutron-scattering experiments of Lin et al. (1983). Antiferromagnetic short-range order of atomic moments has been claimed, with a correlation length of about 2.5 lattice constants. These results were ascertained by Hardman-Rhyne and Rhyne (1983), but almost simultaneously questioned by Crowder and James (1983). In agreement with the neutrondiffraction results, 5~M6ssbauer studies (Long et al. 1980) revealed the complete absence of magnetic moments on the Fe atoms for Mn concentrations exceeding x = 0.3. Oesterreicher and Bittner (1977) were the first to perform magnetization studies on various hydrides of this peculiar system. The general features of the host compounds remain almost unchanged, yet a shift of Tc and the magnetic moment to lower Mn concentrations is observed after hydrogen uptake. This has been interpreted as being due to the donation of electrons from hydrogen to the transition metals.

5.4.2.7. RFe3. Direct experimental evidence for the hydrogen-induced loss in the R moment compared to a rise in the Fe moment was obtained by Niarchos et al.

550

G. WIESINGERand G. HILSCHER

(1979, 1980) by using both the 57Fe and the 161Dy (26keV) M6ssbauer effect in DyFe3 and the 166Er (81 keV) M6ssbauer effect in ErFe3, respectively. While the Dy/Er hyperfine field is reduced with growing hydrogen concentration, the Fe hyperfine field increases as long as x < 2.5, but the changes are rather small. On the other hand, a substantial reduction in T~omphas been obtained which showed a linear dependence on the volume expansion, giving evidence for the dominating influence of the hydrogen-induced lattice expansion on the depression of the R-Fe exchange. Because of its complicated temperature dependence, the magnetic structure of ErFe3 is of particular interest. From M6ssbauer (van der Kraan et al. 1975, Bowden and Day 1977a, Wiesinger et al. 1981), powder neutron-diffraction experiments (Davis et al. 1977) and point-charge crystal-field calculations (Bowden and Day 1977b), it has been concluded that (1) ErFe3 magnetizes in or near the basal plane at ambient temperature; (2) a spin reorientation in the b-c plane occurs at about 130 K; and (3) a spin reorientation takes place at roughly 50 K, which leaves the magnetization directed along the c axis. The latter spin reorientation seems to proceed in a relatively large temperature range (20 K). The influence of hydrogen upon the spin reorientation process in ErFe3H~ has been examined by da Cunha and Vasquez (1981), da Cunha et al. (1982) and Malik et al. (1983). M6ssbauer spectroscopy and magnetization measurements proved the critical temperature TsR of 50 K to be drastically increased in the hydride up to about 210 K for x = 1.5, indicating a marked difference from the behaviour of the compensation points. Further hydrogen absorption did no longer significantly alter this value.

5.4.2.8. RFe2. A reduction of the overall Curie temperature on hydrogenation of as much as 50% of the host value can be observed. The question about the influence of hydrogen on the size of the magnetic moments can in some cases be readily answered, because decisive neutron-diffraction results are available (see, e.g., Fish et al. 1979, Rhyne et al. 1979). The magnitude of the Fe sublattice magnetization is found to remain almost constant or to increase slightly, as, e.g., in the case of HoFez H(D)x. The flat temperature dependence of the Fe sublattice magnetization remains in any case essentially unaffected by hydrogen absorption. A rise in the magnetic moment of Fe upon hydrogen uptake is only observed for moderate hydrogen concentrations Ix < 3.5 (Dunlap et al. 1979, Berthier et al. 1985)]. Larger amount of hydrogen lead to a complete breakdown of the 57Fe hyperfine field [Viccaro et al. (1979c), see also table 3]. The effect of the magnitude of the rare-earth moments is more pronounced. For hydrogen concentrations above x = 3.3, the rare-earth moment at 0 K in the hydride is remarkably reduced from its free-ion value in the parent compound. Moreover, the moment declines rapidly at elevated temperatures. This goes hand in hand with increasing difficulties to saturate the hydrides. These features convincingly demonstrate that hydrogen severely weakens the R-Fe as well as the R - R exchange interaction. The reduction of the R-Fe exchange is experimentally verified by the hydrogen-induced lowering of the compensation points (de Saxc6 et al. 1985, Shenoy

MAGNETISM OF HYDRIDES

551

et al. 1983), which has already been referred to in the case of R6Fe23 and RFe3, as well as by the rapid decline of the moment with increasing temperature (Viccaro et al. 1979a). The relative insensitivity of the Fe-Fe exchange upon hydrogen uptake has been explained by the nearest-neighbour direct-overlap exchange which should only be slightly influenced by the presence of hydrogen atoms. These suggestions, however, are inconsistent with several results from magnetic measurements, where the simple antiparallel arrangement of R and Fe spins is assumed to be retained in the hydrides, as was proposed prior to neutron-diffraction work (Buschow 1977e). More probably, a 'fanning' of the loosely coupled R moments takes place, arising from random local anisotropies. This, too, would explain the diffficulties experienced in saturating the RFe2 hydrides (even in fields as large as 16T, no evidence for saturation is visible) and the discrepancies in the magnitude of the Er moment as determined from neutron diffraction and from M6ssbauer spectroscopy (de Saxc6 et al. 1985). An alternative explanation has been offered by Deryagin et al. (1984b): a loss of collinearity of ferrimagnetic ordering due to the reduced R-Fe exhange interaction. For ErFe2Hx and HoFezHx, Deryagin et al. (1984a) furthermore obtained a significant rise in anisotropy after hydrogen uptake, which they attributed to the increased magnetoelastic interaction of domain walls with dislocations, their number being significantly larger in the hydrides than in the parent material. ScFe 2 is the only Fe bearing Laves phase which crystallizes in the hexagonal MgZnz-type structure (C14). Moreover, it shows a remarkable homogeneity range (Gr6ssinger et al. 1980). An unusual large hydrogen-induced increase of the magnetic moment as well as of the 57Fe hyperfine field has been observed (Smit and Buschow 1980, Smit et al. 1982, Niarchos et al. 1981). CeFe2 and related pseudobinaries have attracted considerable attention. They represent systems where a substantial 4f-3d hybridization is present. Thus, already slight changes in volume, which may arise from alloying as well as from hydrogenation, are supposed to end in significant changes of the magnetic properties. Moreover, Ce is known to be of an instable valence, which makes Ce containing compounds a worthwhile object for hydriding studies. In CeFe2, until recently, Ce was believed to act in a tetravalent state. Since, in this case, Ce carries no moment, normal ferromagnetic behaviour was quoted. X-ray absorption experiments, however, yielded a nominal Ce valence of 3.3 (Garcia et al. 1989, Wiesinger et al. 1989). Relativistic band-structure calculations also revealed a considerable magnetic moment on the Ce atoms coupled antiparallel to the Fe moment (Eriksson et al. 1988), which indeed could be verified by polarized neutrondiffraction experiments (Rainford and Hilscher 1989) and was also evidenced for Y and Fe in YFe2 (Ritter 1989). The strong d-f hybridization, present in this compound is supposed to prohibit the formation of a pure 4 + state. The magnetic order in CeFe2 and in related Fe-rich compounds appears to be most unstable. In pure CeFez, a spin reorientation at roughly 150 K is observed. If small amounts of Fe are replaced by elements like Co, A1, Si, a ferromagnetic to antiferromagnetic transition on lowering the temperature below about 100K is observed (Rastogi et al. 1988, Kennedy et al. 1989), which is also attributed to the strong 3d-4f hybridization mentioned above. If Ce compounds of that kind are

552

G. W I E S I N G E R and G. H I L S C H E R

exposed to hydrogenation, the rise in volume favours a higher degree of localization of the electronic states, leading to the formation of narrower bands than in the parent compounds. The resulting reduction of the hybridization gives rise to an exceptional increase in To the Fe moment and the hyperfine field (Wiesinger et al. 1989). Upon hydrogen uptake, the valency of Ce changes into 3 +. The spectacular features obtained for the parent compounds are no longer observed in the case of the hydrides; the CeFe/hydrides behave almost similar as the unloaded RFe2's, which is demonstrated in fig. 12a and b. In the case of pseudobinary Fe-rich Laves phases, the renowned arguments used on the occasion of hydrides of binary compounds again hold (Pourarian et al. 1982a,b). The verification of the postulate that the local moments residing at the Fe sites are retained in the Co-rich range could be verified in a high-field Mrssbauer experiment. By means of EPR studies, H. Drulis et al. (1984) showed that in hexagonal GdFeA1 the magnetic moment increases on hydrogen absorption up to the free-ion value of Gd 3 +. This was ascribed to a complete randomization of the Fe moments due to the weakened Gd-Fe exchange. Their assumption of an ordered Gd sublattice at low temperatures seems to be questionable. The breakdown of the Fe-Fe exchange interaction, however, is strongly supported by M6ssbauer studies on several RFeA1 hydrides (Wiesinger 1987) which, even at 4.2 K, yielded almost no magnetic hyperfine splitting. S9Co and 52 Mn NMR and 57Fe Mrssbauer spetroscopy have been applied by Fujii et al. (1983) and by Okamoto et al. (1982) to examine Y(Fe, Co)zHx and Y(Fe, Mn)zHx, respectively. In the former case, for a Co concentration ofx > 0.1, a common decrease of Fe and Co moment upon hydrogen absorption has been quoted. In the latter case, a hydrogen-induced enhancement of the Mn moment has been deduced from NMR frequency shifts. Competing coupling tendencies between the magnetic atoms were suggested as an explanation for the spin-glass-like magnetism in the Mnrich hydrides. In Zr(Fe, Mn)aHx, the magnetic order is enhanced upon hydrogenation in the whole composition range (Fujii et al. 1982a,c, 1987). This result, obtained from bulk

~(Am2/kg)

M(Am2/kg)

100

100

ooooooOOOOOOO ooooo°°°°

Ce{Fe%9Cooj)2 Hx 80

o o o

°°°oooooooo

80

°°°OOoooX=3, 2 °Oooo 6,0

40

°OOoo °

60

•

°e e

: (a) .....

• ?...." 50

oo

o o o

Ce(Fe0~gCo0A)2H × T=4,2 K

.o .......

~,,l~

40

x=O f ° ° ° ° e ° e

20

x= 3,2

o

x=O

••

20

", ,

,

100

150

(b)

" 200

T(K) 250

. • °

P°°°°°°I°°° 2

,"

,.,,e •

ooeOOlOOeoeoooo z,

•

~roH(T)

t

I

6

8

Fig. 12. (a) Magnetization as a function of temperature at #o H = 0.5 T, and (b) magnetization as a function of applied field at 4.2 K of Ce(Feo.gCoo.1)2Hx (Wiesinger et al. 1989).

MAGNETISM OF HYDRIDES

553

magnetic measurements, is confirmed by 57Fe M6ssbauer studies, where a substantial increase in Beffhas been observed (Wiesinger 1986). Similar results have been reported for Zr(Fe, Cr)2 by Jacob et al. (1980b) and by Hirosawa et al. (1984). In the case of Zr(Fe, V)2, hydrogen absorption leads to an enhancement of ferromagnetism in the Fe-rich region only, whereas a suppression of superconductivity was found in the V-rich range (Fujii et al. 1985). In Zr(Fe, A1)2, ferromagnetism is always strongly suppressed on hydrogenation (Fujii et al. 1982a,b, Rambabu et al. 1983). Frequently, spin-glass-like behaviour is observed, provided the hydrides just mentioned order magnetically. Only TiFe and Ti(Fe, Co) pseudobinaries have been studied with respect to hydrogen absorption. A more complete treatment can be found in a previous review (Wiesinger and Hilscher 1988a), where also the complete literature regarding the work on the host system is included. Here, we just wish to recall the most essential results. Because of its valuable hydrogen-storage properties, numerous studies have been carried out on TiFe hydrides (see, e.g., Hempelmann and Wicke 1977, Stucki et al. 1980, Schlapbach et al. 1981, Stucki 1982). The hydrogen-induced rise in the magnetization was found to be mainly due to surface effects. The formation of iron clusters could be detected by surface-sensitive methods [e.g., conversion electron M6ssbauer spectroscopy (B1/isius and Gonser 1980, Shenoy et al. 1980)]. The occurrence of local disorder in the CsCl-type matrix of the hydride has been proposed by Hempelmann and Wicke (1977) as an alternative interpretation for the enhanced susceptibility. A critical review about this particular topic has been given by Schlapbach and Riesterer (1983). The pseudobinaries Ti(Fe, Co) belong to those rare examples where the occurrence of misplaced atoms [i.e., atoms located on the wrong crystallographic sublattice and thus called antistructure (AS) atoms] has been predicted from the experimental as well as from the theoretical point of view and which later on has been confirmed experimentally (Hilscher et al. 1980, 1981). A further interesting fact is that the combination of two paramagnetic compounds (TiFe and TiCo) ends up in a ferromagnetic pseudobinary. High-pressure experiments point to the presence of localized moments in the Fe-rich regime, whereas for the Co-rich side itinerant ferromagnetism is indicated. The number of Fe-AS atoms carrying the local moments decreases, while N(EF) increases with the amount of Co. These two competing phenomena are supposed to lead to the occurrence of two critical concentrations for the onset of ferromagnetism. The hydrogen-induced change of Tc and of the magnetization is positive for high Fe and negative for high Co concentrations. This may be explained by the formation of further AS atoms by hydrogen uptake. Despite the surface segregations which have been observed experimentally by different methods, the dominant feature responsible for the complex magnetic behaviour of this system is attributed to the presence of local moments that trigger the long-range magnetic order. However, this solely concerns hydrogen-poor a-phase hydrides, whereas both the [3-phase (x ~ 1) 5.4.2.9. RFe.

554

G. WIESINGERand G. HILSCHER

and the ?-phase (x ,,~ 2) remain paramagnetic. This is explained by the reduced possibility for the formation of Fe-AS atoms in these noncubic compounds.

5.4.2.10. R2Fe, R3Fe. The absorption of hydrogen can convert Hf2Fe from a Pauli paramagnet into a ferromagnet (Buschow and van Diepen 1979, Tuscher 1979). The magnetic moment reaches its maximum value at a concentration of 3H atoms/f.u. The broadened M6ssbauer spectra were interpreted to reflect a disordered magnetic phase (Vulliet et al. 1984). Aubertin et al. (1989) separated the pure magnetic component from the complex hyperfine field distribution. A similar behaviour was found by Aubertin et al. (1987) for ZraFeH6.9, where at low temperatures a considerable hyperfine splitting has been obtained too. 5.4.2.11. R7Fe3. Th7Fe 3 was claimed to have turned to ferromagnetism after hydrogen uptake with a Curie temperature of about 350 K. However, a comprehensive investigation by Schlapbach et al. (1982) led to the result that ferromagnetism in these hydrides is obtained exclusively when Violent charging conditions are applied. This leads to a disproportionation into Th4H15 and a more Fe-rich compound which both exhibit Curie temperatures in the range cited earlier. After having been charged smoothly, the resulting hydride was found to remain paramagnetic at least down to 80 K. This confirms earlier M6ssbauer studies of Viccaro et al. (1979b) who reported an almost vanishing 57Fe hyperfine field. 5.4.3. Hydrides of Co compounds 5.4.3.1. General features. In any case, hydrogen uptake reduces the magnetic order. The values obtained for the Curie temperature and magnetic moment (R as well as Co moment) in the hydride are lower compared to that in their parent counterparts. The hydrides generally show a pronounced resistance against magnetic saturation. 5.4.3.2. R2Co14B. As in the case of their isostructural Fe-bearing counterparts, hydrogen makes the compounds magnetically softer, which is indicated by a significant reduction upon hydrogen uptake of both the anisotropy field and the spin reorientation temperature. For R = Nd, two types of spin reorientation are observed (table 4), both being reduced after hydrogenation [Zhang et al. (1988b), see also fig. 13]. At low temperatures (below TsR1),an easy cone magnetization has been presumed. Thus, hydrogen seems to favour uniaxial anisotropy at low temperatures, although it shrinks the region of axial anisotropy due to the depression of TSR2, above which the material exhibits a basal plane anisotropy. For the remaining cases, as in the Fe counterpart systems, the hydrides favour planar anisotropy. 5.4.3.3. RCo 5. Only compounds containing light rare earths have been examined so far. The reason lies in the outstanding permanent magnetic properties of these ferromagnetic materials which are lost in the case of the heavy rare earths, where ferrimagnetic coupling takes place between the R and the Co moments. Up to x = 4.5, the ferromagnetic behaviour of the light RCo5 compounds is preserved in the hydrides. Further hydrogen absorption leads to a complete loss of ferro-

MAGNETISM

OF HYDRIDES

555

TABLE 4 M a g n e t i c p r o p e r t i e s of C o c o m p o u n d s a n d their hydrides. Compound

Structure

Space group

Tc (K)

Teomp(TsR)

#s

(K)

(#B/f.u.)

#Co (/tB/Co)

Ref.*

Y2Col,B Y2Col,BH2.3

Nd2Fel,B Nd2Fel, B

P42/mnm P42/mnm

1016 -

-

20.0 19.6

1.43 1.40

[1] [1]

La2Cot4B LaECOl,BH3. 8

NdEFet4 B Nd2Fe14B

P42/mnm P42/mnm

957 -

-

20.5 19.8

1.46 1.41

[1] [1]

Pr2ColgB Pr2Cox4BH3. 5

NdzFex4B Nd2Fel~B

P4z/mnm P42/mnm

994 -

680(SR) 495(SR)

25.2 24.5

(1.45) 1.39

[1] [1]

Nd2Co14B

Nd2Fe14B

P42/mnm

1006

25.8

(1.45)

Nd2Co14BH3. 4

Nd2Fea~B

P42/mnm

-

550(SR1) 35(SR2) 385(SR1) <4.2(SR2)

25.5

1.42

[1] [1] [1] [1]

SmECO14B SmECO14BH3.6

NdEFetgB Nd2Fe14B

P42/mnm P42/mnm

1031 -

-

18.3 18.6

1.45 1.47

[1] [1]

Gd2Co14B GdzCo14BH3.1

Nd2Eea4B Nd2Fe14B

P42/mnm P42/mnm

1050 -

-

6.0 6.2

(1.45) 1.47

[1] [1]

TbzCol~B Tb2Co14BH2.1

NdzFe14B Nd2Fe14B

P42/mnm P42/mnm

1036 -

795(SR) 764(SR)

3.7 3.3

(1.45) 1.42

[1] [1]

YCos Y C % H0.4 YCo5 H2.s

CaCu5 CaCn5 CaCu5

P6/mmm P6/mmm P6/mmm

-

-

-

1.55 1.44 1.25

[2, 3] [2, 3] [2, 3]

LaCos LaCosHa.3s LaCosH4.3

CaCus Orthor. Orthor.

P6/mm -

CeCo 5 CeC%H2.s5

CaCu5 Orthor.

PrCos PrCosH2.8 PrCosH3. 6

840 >300 >300

-

7.3 5.6 1.64

1.5 1.14 0.33

[4] [5] [5]

P6/mmm -

737 -

-

6.5 4.4

0.98

[4] [5]

CaCu5 Orthor. Orthor.

P6/mmm -

912 >300

-

9.95 3.70

1.05 0.83

[4] [5] [5]

NdC% NdCo5 Ho.3 NdCosH2.s

CaCu5 CaCus Orthor.

P6/mmm P6/mmm -

910 > 300 >300

-

10.6 5.06

1.45 -

[4] [5] [5]

SmCo 5 SmCo5 H2.s

CaCus Orthor.

P6/mmm -

1020 > 300

-

7.3 -

0.2

[4] [5]

GdCo 5 GdCosH2. s

CaCu 5 -

P6/mmm -

953 480

-

1.70 0.44

1.74 1.49

[2] [2]

Y2Co7 Y2CoTH2 Y2CovH5 YzCovH6

Gd2Co 7 Gd2Co7 Gd2Co7 Gd2Cov

R3m R3m R3m R3m

639 540 470

-

La2Co7 LazCo-lHs

Gd2Co7 Gd2Co7

R3m R3m

490 >300

-

7 4.2

1 0.6

[8] [8]

Ce2Co7 Ce 2C o 7 H 7

Ce2Ni7 Ce 2Ni7

P63/mmc P63/mmc

50 233

-

0.9 3.8

-

[9] [9]

Nd2Co v Nd2CovH8. 5

Ce2Ni v Ce2Ni 7

P63/mmc P63/mmc

613 35

-

14.6 3.7

1.37 0.53

[10] [10]

Gd2Co 7 Gd2CovH7. 7

Gd2Co 7 Gd2Co 7

R3m R3m

775 420

-

4.2 7.7

1.4 0.9

[11] [11]

8.75-9.6 0.9 8.4 6.5

1.3-1.7 0.13 1.2 0.93

[4,6] [7] [7] [6]

556

G. WIESINGER

and G. HILSCHER

TABLE 4 Compound

Ho2Co 7

Structure

Space group

(continued) Tc (K)

Teomp(TSR)

#s (#B/f.u.)

#Co (#B/Co)

Ref.*

(K)

-

[12] [12]

no2Co7H2. 6

Gd2Co 7 Gd2Co 7

R3m R3m

670 200

230(C) -

6 1.7

YCo a Y C o 3H YCoa H 2 YC%Ha

PuNi a PuNi3 PuNi3 PuNi a

R3m R3m R3m R3m

-

-

2.4 0.9 1.95 0

CeCo a CeCoaH 4

PuNi a PuNi 3

R3m R3m

<10 80

-

GdCo a GdCo3H2. 2 GdCoaH4. 6

PuNi a PuNi a PuNi a

R3m R3m R3m

611 28

-

DyCo 3 DyCoaH4. a

PuNi 3 PuNi 3

R3m R3m

452 18

HoCo3 HoCo3H4.2

PuNi3 PuNi 3

R3m R3m

ErCo3 ErCoaH4. 2

PuNi3 PuNi 3

TmCo3 TmCo3H3.3

[7, 8] [8] [7] [8]

-

[9] [9]

2.29 3.37 3.92

1.2 1.03

[4] [13] [13]

-

4.4 3.82

-

[4] [13]

418 15

-

5.45 3.16

-

[4] [13]

R3m R3m

401 -

26(C) 170(C)

4.2 1.04

-

[14] [14]

PuNi3 PuNi3

R3m R3m

370 -

122(C) 164(C)

3.0 2.04

-

[14] [14]

PrCo2 PrCo2H4

MgCu2 n.l.o.

Fd3m -

40 -

-

GdCo 2 GdCo2H 4

MgCu 2 MgCu 2

Fd3m Fd3m

398 90

-

4.8 4.7

-

[16] [16]

TbCo 2 TbCozHa. 2

MgCu 2 MgCu 2

Fd3m Fd3m

230 50

-

6.65 4.15

-

[17] [17]

DyCo 2 DyCo2H3. a

MgCu 2 MgCu 2

Fd3m Fd3m

140 40

-

6.75 4.1

-

[17] [17]

HoCo 2 HoCo2Ha. 5

MgCu 2 MgCu 2

Fd3m Fd3m

76 40

-

7.4 4.7

-

[18] [18]

ErCo 2 ErCo2Ha. 5

MgCu 2 MgCu z

Fd3m Fd3m

35 25

-

7.0 4.35

-

[18] [18]

UCo

UCoH2. 7

Cubic

-

Param. 63

-

0.32

-

[19] [19]

U6Co U6CoHI8

[3-UH 3

-

Param. 185

-

1.2

-

[19] [19]

* References: [ 1 ] Z h a n g et al. (1988b). [ 2 ] Y a m a g u e h i et al. (1983). [ 3 ] Y a m a g u c h i et al. (1985b). [ 4 ] B u s c h o w (1977a). [ 5 ] K u i j p e r s (1973). [ 6 ] A n d r e e v et al. (1985a).

[7] [8] [9] [10] [11] [12] [13]

Y a m a g u c h i et al. (1985a). B u s c h o w a n d d e Ch~tel (1979). B u s c h o w (1980b). A n d r e e v et al. (1988). A n d r e e v et al. (1985). A p o s t o l o v et al. (1988). M a l i k et al. (1978).

<0.1 0.8

0.8 0.3 0.65 0

3.9 C o m p l e x (clusters)

[14] [t5] [16] [17] [18] [19]

[ 15] [15]

M a l i k et al. (1981). de J o n g h et al. (1981). B u s c h o w (1977d). P o u r a r i a n et al. (1982a). P o u r a r i a n et al. (1982b). A n d r e e v et al. (1986).

MAGNETISM OF HYDRIDES i

1

,

,

J

i"

557

I-

• II~ NdzCot4B o.LJ

m I11t Nd2Co,4BH~.4 120

300K

d" o 77K

t20 8O

4O

.... 0

4

;

-~'E'2"2~ 8

12

16

H (kOe)

Fig. 13. Field dependence of the magnetization for N d 2 Co 14B and for N d 2 Co 14BHa.¢ (top) at 300 K and (bottom) at 77 K (Zhang et al. 1988b).

magnetism. However, a weakening of the R-Co and the Co-Co exchange interaction is observed in any case (Kuijpers 1973, Yamaguchi et al. 1982a,b, 1983, Fujiwara et al. 1988). Since the magnetization is intimately correlated with the amount of hydrogen dissolved in the sample, H2 pressure-magnetization isotherms yield identical information about the presence of a certain phase and about phase transformations as conventional pressure-composition isotherms. The different phases are identified by the stepwise changes in magnetization observed in the magnetization-temperature isobars (Yamaguchi et al. 1982a,b, 1983, 1985b). 59Co NMR spin-echo measurements, carried out in the case of R = Y or Gd (Yamaguchi et al. 1980, Figiel 1982) show some discrepancies concerning the assignment of the various resonance lines to the two Co sites. Magnetic relaxation studies on hydrided (deuterated) RCos compounds of light rare-earth elements, performed by Herbst and Kronm/iller (1979) showed that the concentration of hydrogen (deuterium) in the planes containing R atoms, by far exceeds that in the Co-only planes. This result is in agreement with the higher hydrogen affinity of the rare earth compared to Co and refutes the analysis of Yamaguchi et al. (1980). Yamaguchi et al. (1987a), and later on Yamamoto et al. (1989), again picked up the idea of Kuijpers (1973) of studying the effect of magnetic fields on chemical reactions. Since the magnetic energy is small compared to the thermal energy, systems with a large moment and large applied magnetic fields are a prerequisite for obtaining reasonable effects. Hydrides of SmCo5 and LaCos have been investigated in static

558

G. WIESINGER and G. HILSCHER

fields up to 14T. The hydrogen pressure was found to considerably rise upon application of an external magnetic field. Hydrogen uptake furthermore increases the equilibrium constants substantially which can be explained by classical thermodynamics, taking into account the magnetic contribution of the material.

5.4.3.4. ReCo7. While in the case of

L a 2 C o 7 a usual behaviour for Co-containing compounds upon hydrogen uptake is observed (Buschow et al. 1980), an increase in magnetic moment and Curie temperature has been obtained after hydriding C e 2 C o 7 (Buschow 1980b). The latter result was explained in terms of a change in the Ce valency from 4 + to 3 +. The group of Andreev succeeded in preparing hydrides of single crystals (Andreev et al. 1985a,b). In Gd2Co 7, even 7.7 H atoms/f.u, could be dissolved (corresponding to a 15% increase in volume), without altering the symmetry of the single-crystal specimen. While the magnetocrystalline anisotropy was found to be substantially reduced upon hydrogen absorption, the coercive force had increased, which was attributed to hydrogen-induced processes preventing the growth of nuclei of reverse magnetization. At this point, we wish to note that in the Fe-containing Nd 2 Fe14Bbased magnets, hydrogen absorption leads to a considerable loss in coercivity. Obviously, in the latter case, the hydrogen induced reduction of the rare-earth sublattice anisotropy is too large to be overcome by defects favouring larger coercivity. At raising the temperature, a gradual transition from collinear ferrimagnetism to antiferromagnetism via a noncollinear intermediate structure was obtained in the hydrided Gdz C07 Hx sample. Single crystalline Y2 C07 H 6 was found to be antiferromagnetic with a metamagnetic transition to ferromagnetism occurring at fields above 2T, without the presence of an intermediate canted phase (fig. 14a). Instead, the application of a field in excess of the lower critical field gave rise to the formation of ferromagnetic domains, preferrentially near crystal defects. While the magnetic moment (induced by a field applied along the e axis) versus temperature decreases

A l

1

6

..... -12

T /

2

f

~4

o ,5 - -8

-4

I %

~8

/

-4 -2

i 1.6

32 H (MA/m)

(a) 0 4.8

0

I IO0

(b 300

200 T (K)

Fig. 14. (a) Field dependence of the magnetic moment (curve 1) and transverse magnetostriction (curve 2) at 4.2K along the c axis of a single crystal of Y2Co7H6.7 (Andreev et al. 1985a). (b) Temperature dependence of the field-induced magnetic moment (curve 1) along the c axis and of the basal plane magnetostriction (curve 2) of a single crystal of Yz Co7 H6. 7 during metamagnetic phase transition (Andreev et al. 1985a).

MAGNETISM OF HYDRIDES

559

monotonically, a pronounced upturn is obtained for the basal-plane magnetostriction 2perp. in the temperature range l l 0 K < T < 190K as can be seen from fig. 14b (Bartashevich et al. 1983, Bartashevich and Deryagin 1984, Andreev et al. 1985b). This rise in magnetostriction has been associated with an increase in the Co sublattice moment and with a diminuition of the elastic constants of the crystal due to atomic ordering effects of hydrogen atoms in the lattice• In situ magnetic measurements in static fields up to 14.5T and pulsed-field measurements up to 30 T have been used by Yamaguchi et al. (1985a, 1987a,b,c) in order to study the sensitivity of the magnetic moment to the amount of absorbed hydrogen in the [I-phase YzCo7 hydrides (1.7 < x < 2.8). A peculiar variation of the magnetic moments as a function of the hydrogen composition has been found (fig. 15a) which is completely different from that observed in YCo5 and will be discussed below together with results obtained YCo3 (fig. 15b).

5.4.3.5. RCo3. Similar to the R 2 T M 7 case, Pauli paramagnetic CeCo3 is converted to a ferromagnet after the absorption of hydrogen. This specific behaviour is also ascribed to a change in the valency of Ce from 4 + to 3 + (Buschow 1980b) which is confirmed by the large hydrogen-induced volume increase obtained by van Essen and Buschow (1980a). In the case of the heavy rare-earth compounds, ferrimagnetic order occurs, featuring compensation points. For GdCoa, Malik et al. (1978) obtained an increase in the magnetization upon charging which they attributed to a decrease in the Co moment. The strong hydrogen-induced reduction of Tc is a further consequence of the diminished Co moment, since Tc should be mainly determined by the Co-Co interaction. For R = Dy, Ho (Malik et al. 1978), Er or Tm (Malik et al. 1981), hydrogen absorption leads to a reduction of magnetization, Curie temperature and l

1.6 I

l

i

i

1.2 200

60

1.2 o

o 0.8 E E ._o

0.4

(a)

l

'~

-~ 0.8

m+

8

T

40 oE

E

tOO ~ 0.4

I

2

I

4

I

f

6

Hydrogen composition

0

8 x

w,.

0

f

1

I

I

I

2

3

4

Hydrogen composition

x

Fig. 15. (a) Dependence of the magnetic moment of YzCovHx (11, O, O) and critical fields (A, A) as a function of the hydrogen composition [ ( I ) 4.2K, 28T; (0) 4.2K, 1.45T; (O) 77K, 1.45T; (A) 4.2K in increasing field; (A) 4.2 K in decreasing field] (Yamaguchi et al. 1985a,b). (b) Dependence of the magnetic moment (II, O, O) and the critical field (&, A) of YCo 3H~ [(11) 4.2 K, 28 T; ( • ) 4.2 K, 1.45T; (O) 77 K, 1.45 T; (z~) 4.2 K in increasing field; (A) 4.2 K in decreasing field] (Yamaguchi et al. 1985a,b).

560

G. WlESINGERand G. HILSCHER

compensation point. A fanning out of the R moments as a function of temperature or applied field was given as an explanation for the observed resistance against saturation and the steep variation in the magnetization of the hydrides at low temperatures As already mentioned above, a striking hydrogen-induced variation of the Co moment is observed in the case of the 13phase in the systems Y2Co7Hx and YCoaH, (Yamaguchi et al. 1985a,b, 1987a). In fig. 15a,b the magnetic moment per Co atom is displayed as a function of the hydrogen composition x for Y2COTH ~ and YCo3H~, respectively. A pronounced minimum at x = 1.7 (1.0) (ill hydrides) followed by a maximum at x = 3.0(1.9) (fin hydrides) is obtained for Y2CoTHx (YCo3H,). This oscillatory manner of the Co moment is considered from the point of view of itinerant electron magnetism. In the flL hydrides, the exchange interaction [or equally well N(Er)] is supposed to be too weak to induce ferromagnetism. In the flH hydrides, the Stoner criterion is satisfied, which is correlated with the hydrogen-induced reduction of the exchange interaction. In order to study the relation of the magnetic moment with the density of states (DOS), hydrides of pseudobinary compounds have been included into this study recently (Yamaguchi et al. 1989). A considerable insensitivity of the DOS curve in the upper part of the 3d band upon hydrogen uptake has been the essential result.

5.4.3.6. RCoe, R7Co3. Besides the reduction of magnetic ordering after hydrogen absorption, the presence of clusters of free Co was proved by susceptibility measurements (de Jongh et al. 1981) and confirmed by a study of 57Fe-doped HoCo2H~ (Buschow and van der Kraan 1983). In the M6ssbauer spectra a hyperfine pattern could be detected which almost coincided with that of Fe impurities in Co metal. Hydrogen absorption leads to a rise in the susceptibility for Th 7Co 3 (Pauli paramagnetic and superconducting below about 2K). However, no evidence of magnetic order has been found in the hydride (Boltich et al. 1980, Malik et al. 1980b). 5.4.3.7. UCo, U6Co. Andreev et al. (1986) tested all U - C o compounds for hydrogen absorption up to 700 K and pressures up to 1.6 MPa. They found that only UCo and U6Co absorb hydrogen, whereas no evidence for hydrogen absorption was observed for the other intermetallics UCo2, UCo3, UCo4 and UCo5.3. UCoH2.7 exhibits a ferromagnetic transition at 63 K with a spontaneous magnetic moment of 0.32#B at 4.2 K. The occurrence of a coercive force of about 2.5 T at 4.2 K and freezing phenomena of the M(T) curves are indicative for magnetization processes of weakly interacting fine particles with high anisotropy. U6CoH18 crystallizes in the same cubic structure as [~-UH3. The Curie temperature (185 K) is slightly higher than that of ~-UH3 (174 K), but both compounds exhibit the same magnetic moment of about 1.2#B/f.u. As the parent compounds UCo and U6Co are superconducting (below 1.2 and 2.3 K, respectively), the transition to a magnetic ground state in the hydrides can be discussed in terms of a narrowing of the rather delocalized 5f states under hydrogen absorption.

MAGNETISM OF HYDRIDES

561

5.4.4. Hydrides of Ni compounds 5.4.4.1. General features. In all cases, a strong reduction of the magnetic order after hydrogen absorption is obtained (table 5), which frequently leads to a complete loss of long-range magnetic order. Particularly in Ni-containing hydrides of intermetallic compounds, the formation of Ni clusters can be observed. 5.4.4.2. RNi 5. The outstanding storage properties of LaNi 5 is the reason that materials based on this compound have attracted considerable attention. The results of the various magnetic measurements can be summarized as follows. When hydrogen is absorbed just once, the susceptibility of the Stoner-enhanced Pauli paramagnet LaNi5 is lowered by a factor of nearly four. This has been attributed by Schlapbach (1980) to a reduction of the enhancement factor. At this point, we wish to stress that just after one absorption process we are still dealing with a pure bulk phenomenon, since at this instance the specific surface area of the Ni segregations may be assumed as negligibly small. T h e 5 7 F e (E~ = 14.4keV) Mrssbauer effect results obtained on Fe-doped LaNi s (Campbell et al. 1983, Lamloumi et al. 1987) show some discrepancies in the interpretation of the room-temperature spectra, which points, we believe, to the influence of the metallurgy on the hyperfine parameters. In the case of the hydrides (Atzmony TABLE 5 Magnetic properties of Ni c o m p o u n d s and their hydrides. Compound

Structure

Space group

Magnetic properties

Ref.*

LaNi5 LaNisH6. 9

CaCu5 CaCu 5

P6/mmm P6/mmm

Zg = 5 x 10- 6 emu/g Xg = 1 x 1 0 . 6 e m u / g

[1,2] 1,1,2]

Y2Ni 7 Y2Ni7 H~

Gd2Co 7 Gd2Co7

R3m R3m

Tc = 57 K, Tc = 98K,

[3] [3]

La 2Ni 7 La2Ni7

Ce 2 Ni T -

P6 a / m m c P6a/mmc

Tc = 54 K Z~ = 1 x 1 0 - 6 e m u / g

1-4] I-4]

YNia YNi3 H4

PuNi3 PuNi3

R3m R3m

Tc = 35 K, )~g= 0.06/tB/Ni )fg = 7 x 10- 6 emu/g

[5] [5]

CeNi3 CeNiaHx

CeNia CeNia

-

)~g= 2 x 10- 6 emu/g 0 < 0, #elf = 2.5#B/Ce

1,6] [6]

GdNiz GdNi2H3. 5

MgCu2 Fd3m N o long-range order

Tc = 8 K, Tc = 8 K,

[7] 1-7]

Mg2Ni Mg2NiH3.8

-

-

X = 0.9 X 10 .6 emu/g )~= 0.8 X 10 -6 emu/g

I-2] I-2]

La7 Nia LaTNiaH19.3

Th7 Fe3 fcc

-

Z = 0.7 x 10- 6 emu/g )~= 0.8 X 1 0 . 6 e m u / g

[8] [8]

* References: 1,1] Palleau and Chouteau (1980). [2] Stucki and Schlapbach (1980). I-3] Buschow (1984b). 1,4] Buschow (1983).

[5] [6] 1,7] I-8]

#s = 0.08#B/Ni ps = 0.05/tB/Ni

/~s = 6.9#B #s = 4.2#B

Buschow and van Essen (1979). Buschow (1980b). Malik and Wallace (1977). Busch et al. (1978).

562

G. WIESINGERand G. HILSCHER

et al. 1981, Niarchos et al. 1981, Oliver et al. 1983), the data again suggest the presence of Ni clusters, whereas no evidence was found for the formation of Fe clusters. While for certain concentrations magnetic-ordering temperatures were substantially reduced after hydrogen uptake, the Fe hyperfine field at 4 K was proved to remain almost unchanged. The small change in the Fe-isomer shift upon hydrogenation points to the predominance of the L a - H interaction in this compound. The complete insensitivity to hydrogenation of the 119Sn (E~ = 23.8 keV) hyperfine parameters in Sn-doped LaNis, as reported by Oliver et al. (1985), once more confirms the dominance of the R - H charge transfer over the R - T M one. In heavily cycled LaNi5 hydride, a substantial increase of the susceptibility is observed which later on tends to become temperature and field dependent. As already mentioned, the bulk susceptibility of the pure ternary hydride is reduced compared to the host compound value. Schlapbach (1980) recognized the important influence of Ni clusters which increasingly form at the surface, when hydrogen is absorbed. The magnetization was treated in terms of two superimposed terms, a linear one due to the bulk, the other field-dependent term originating from the Ni precipitates at the surface. From a quantitative analysis of the M versus H curve, Schlapbach was able to estimate that the Ni clusters contain about 6000 atoms. The decomposition of the surface in LaNi5 hydride was confirmed by two other techniques, i.e., by ferromagnetic resonance (Shaltiel et al. 1981) and by 61Ni M6ssbauer spectroscopy (Rummel et al. 1982). In CeNisHx, Malik et al. (1980a) examined the substitution of A1 for Ni and obtained an increase in stability of the hydride which on the other hand was accompanied by a drastic decrease of the absorption capacity. The increase of the susceptibility upon hydrogenation has been attributed to the formation of Ni precipitations. The question about a change in valency of Ce from 4 + to 3 + upon hydrogenation remained unsolved. Pedziwiatr et al. (1984) reported gradual change of the Ce valency from 4+ to 3+ in Cu-substituted CeNis. Hydrogen uptake was found to further increase the Ce 3 + content in the sample.

5.4.4.3. ReNiz, RNi3. Both Y2Ni7 and YNi 3 order ferromagnetically. Surprisingly, in the former compound the Curie temperature rises upon hydriding [from pressure experiments in the parent compound, a drop in Tc has been predicted (Buschow 1984b)], whereas the latter becomes Pauli paramagnetic (Buschow and van Essen 1979). The magnetization of Y2Ni 7 hydride decreases to about one half of the value of its host compound (fig. 16). Unexpectedly, La2Ni7 is antiferromagnetic and becomes Pauli paramagnetic upon charging, which Buschow (1983) explained by a reduced 5d density of states at EF caused by the charge transfer between La and H. From X-ray diffraction experiments on Y2Ni 7Hx, a phase separation, giving rise to the enhanced value of Tc observed experimentally, could be ruled out. 5.4.4.4. R2Ni. Mg2Ni belongs to the group of suitable hydrogen storage materials. By applying surface-sensitive techniques, Stucki and Schlapbach (1980) and Shaltiel et al. (1981) demonstrated that, after continuous hydriding, a decomposition at the surface takes place, giving rise to the formation of superparamagnetic Ni clusters.

MAGNETISM OF HYDRIDES

T oJ E

563

5.0

~

4.0

<..% 13 3.0

i7

2.0

'%

Y2Ni7Hx

1.0 %

\': %

%

0

I 0

50

'%%~,~___

100

[

150

200

T(K)

Fig. 16. Magnetization as a function of temperature of Y2Ni 7 (full curve) and Y2NiTHx (broken curve) (Buschow 1984b).

The bulk susceptibility, however, decreases after hydrogen absorption. Recently, Aubertin et al. (1986) reported on M6ssbauer studies on isostructural Fe-doped ZrzNi hydrides. The unusual large hydrogen-induced rise in isomer shift (+ 0.58 mm/ s) has been attributed predominantly to charge transfer effects.

5.4.4.5. RTNi3. For LaTNi3 hydride, Busch et al. (1978) and Fischer et al. (1978) found that it was actually metastable, disintegrating into LaH3 and LaNis. Both the host compound and the hydride displayed Pauli paramagnetic behaviour. In Th7Ni 3, the susceptibility was reported to decrease upon hydrogen uptake (Malik et al. 1980b). 5.4.5. Hydrides of miscellaneous compounds 5.4.5.1. Rare-earth and actinide compounds. Gd compounds containing a nonmagnetic metal provide a possibility to directly study the influence of hydrogen on the R - R coupling. This has been done by using the 86 keV 155Gd M6ssbauer transition in GdCuzHx (de Graaf et al. 1982a) and in GdMzHx (M = Ru or Rh) (Jacob et al. 1980a). Upon hydrogenation, the Curie temperature behaves very differently in the two cases (table 6); a strong rise is observed in the former case compared to a decrease in the latter. This peculiarity has to be seen in the light of the influence of hydrogen on the oscillatory RKKY-type interaction present in these compounds. De Graaf et

G. W I E S I N G E R and G. H I L S C H E R

564

TABLE 6 Magnetic properties of miscellaneous R compounds. Compound

Structure

Tc, TN

0p

,Us

#eel

(K)

(K)

(/tB/R)

(#B/R)

EuMg 2 EuMg2H

MgZn 2 n.l.o.

TN = 32 4 < TN < 20

EuRh 2 EuRh2Hx

MgCu 2 MgCu2

Tc = 15.5

Gd3Pd 4 GdBPd4H x

PuBPd 4 -

TN = 18 Tc = 20

EuPd EuPdH

CrB CsC1

Tc = 48

GdCu GdeuH x

-

TN = 150 Tc = 30

-- 86 15

adRh GdRhHx

CsC1 CsC1

Tc = 29 (Tc = 20)

GdPd GdPdHx

CsC1 -

TN = 32 Tc = 40

GdAg GdAgH x

-

TN = 123 Tc = 25

GdAu GdAuHx

-

Tc = 35 Tc = 55

G d 7 Pd 3 Gd7 Pd3 Hx

Th 7 Fe a Th7 Fea

Gda Pd2 Gda Pdz Hx

Ref.* [i] [1]

5

7.85

[2] [2]

3.83

8.80 8.70

[3] [3]

1.5

8.2 7.5

[2] [-2]

3.62

8.45 8.40

1-4] 1-4]

28 (25)

6.6 1.9

7.7 8.08

[4] [4]

29 20

6.27 3.63

9.83 8.27

[3] [3]

- 57 50

4.38

8.80 7.80

1-4] 1-4]

25 32

2.85

8.52 8.16

[4] [4]

Tc = 311 -

276 - 15

7.03 -

8.22 8.11

[3] 1-3]

U3 Si2 U 3 Si 2

TN = 30 Tc = 30

-- 30 0

1.63

9.85 8.17

1-3] [3]

Euz IrH 5

fcc

Tc = 20

18

7.4

[5, 6]

GdCu2 GdCu2 Hx

CeCu2 MoSi2

TN = 37 Tc = 45

7 57

8.70 8.63

[7] [7]

GdRu 2 GdRu2 Ha

MgZn 2 -

Tc = 83 Tc = 65

GdRh 2 GdRh2 Ha

MgCu 2 Orthorh.

Tc = 73 Tc = 35

al. ( 1 9 8 2 a , b ) c o l l e c t e d n u m e r o u s substantial reduction

and

some

increase

-18 -10 5

* References: [1] Oliver et al. (1978). [-2] Buschow et al. (1977). [-3] Buschow and de Mooij (1984). [4] de Vries et al. (1985).

compounds

9

6.83 6.2 [5] [6] [7] [8]

isomer

of their hydrides.

in isomer

[8] 1-8] [8] [8]

Moyer Jr. and Lindsay (1980). Stadnik and Moyer Jr. (1984). de Graaf et al. (1982a). Jacob et al. (1980a).

shift and hyperfine Hydrogen

field data for binary

absorption

s h i f t (see, e.g., fig. 17) w h i c h

commonly is c o n s i s t e n t

Gd

yields a with

a

in s-electron density at the Gd nuclei. This indicates a charge transfer from

Gd to hydrogen,

a behaviour

w h i c h is g e n e r a l l y o b s e r v e d

when rare-earth

M6ssbauer

MAGNETISM OF HYDRIDES I

I

f

I

565 I

GdCu

=o 5

I

I

I

I

i

I

[

4--

GdCuH x 90

i

K

-2

0 ve[0city

I

2 frnm/s]

Fig. 17. MSssbauerspectrum of GdCu and GdCuHxat 4.2K (de Vrieset al. 1985).

data are considered. For several G d M 2 compounds and their hydrides, de Graaf et al. also claimed an almost linear correlation between the Gd isomer shift and the Gd hyperfine field. The positive conduction-electron contribution to the Gd hyperfine field is seen to be increasingly reduced with the (s-like) charge density at the nuclear site. This eventually leads to semimetallic G d H 2 , in which compound only the negative core contribution to Beefis left (Buschow 1984a). An analysis of the isomer shift in terms of the model of Miedema and van der Woude (1980) proved to yield reasonable results in the case of binary systems. For ternary systems, however, the application of this model appeared to be difficult (Buschow and de Mooij 1984, de Vries et al. 1985). GdTPd3 belong to those rare examples where Gd combined with a nonmagnetic element forms an intermetallic with a Curie temperature in excess of pure Gd metal. The magnetic ordering temperatures of the remaining compounds in the G d - P d system lie below 40K rBuschow and de Mooij (1984), see also fig. 18]. This figure furthermore demonstrates that the absorption of hydrogen leads to spectacular changes in the asymptotic Curie temperature 0p. It small absolute value obtained for the G d - P d hydrides arises from the hydrogen-induced reduction of the mean free path of the conduction electrons. As already mentioned in the introductory

566

G. WIESINGER and G. HILSCHER

300

g 20O

100

-100 I

I 0

I

t 0.2

I

I 0.4

i

I 0.6

i 0.8

Pd a t o m i c fraction

Fig. 18. Concentration dependence of the asymptotic Curie temperature 0p in the Gd-Pd compounds (full curve) and the corresponding hydride phases (broken curve) (Buschow and de Mooij 1984).

sections, this leads to a damping of the RKKY oscillations and, thus, implies an effective decrease of the range of the overall coupling strength. By proton NMR studies combined with susceptibility measurements, Zogal et al. (1984) studied Fe2P-type ThNiA1Hx and UNiA1Hx. The existence of two different antiferromagnetic phases, a hydride and a solid-solution phase, has been claimed for the latter. EuzIrHs has been claimed by Moyer Jr. and Lindsay (1980) to order ferromagnetically below 20 K, which has recently been corroborated by an tS~Eu M6ssbauer study of Stadnik and Moyer Jr. (1984). Remarkable similarities to binary EuH2 have been emphasized. 5.4.5.2. Pure and oxygen-stabilized 77 and Zr compounds. Huang et al. (1981) reported that the absorption of hydrogen had destroyed magnetic order in the weak itinerant ferromagnets Ti(Be, Cu)2 and ZrZnt.9, which has been explained by the influence of hydrogen on the peculiar band structure present in these materials. In contrast to Ti2Co and TizNi, pure Ti2Fe does not form (Tuscher 1980). Nevertheless, it can be stabilized by small amounts of oxygen (between 6 and 14%, depending on the exact Ti:Fe ratio) (Mintz et al. 1980, Stioui et al. 1981, Rupp 1984). The resulting ternary oxide (q-phase) is believed to play a significant role in the activation process of the storage compound TiFe (Schlapbach and Riesterer 1983, Venkert et al. 1984). Since for large-scale applications frequently instead of pure TiFe the technical alloy ferrotitanium is used, wherein substantial amounts of oxygen are dissolved, the knowledge about the absorption behaviour of the q-phase is of crucial importance.

MAGNETISM OF HYDRIDES

567

The oxygen-free compounds TizCo and Ti2Ni exhibit exchange-enhanced Pauli paramagnetism, displaying a complex temperature dependence (Tuscher 1980). After hydrogen uptake, a temperature-independent susceptibility was obtained. Isostructural TizFeOo.5 shows a Curie-Weiss-like behaviour. After hydrogenation, an increase in the susceptibility was detected, its magnitude depending on the hydrogen content in the sample. For a hydrogen content exceeding 2 H atoms/f.u., magnetic ordering at low temperatures was inferred from the substantial broadening of the NMR lines. Ternary oxides Tiz_yFe2Ox with varying Ti: Fe ratio and oxygen content were studied by Mintz et al. (1980) and, later on, were comprehensively reinvestigated by Rupp (1984), Rupp and Wiesinger (1984) and by Stioui et al. (1988). For a detailed reference list covering the field of hydrogen uptake by oxygen stabilized T i 2 Fe, we refer to the paper by Rupp. After hydrogenation, magnetic ordering has been observed at 4.2 K only in the case of Ti2 FeOo.2H2.6 . A quadrupole split spectrum and hence paramagnetism was observed for all the remaining hydrides. For [3-Ti (20 at.% Fe) as much as + 0.66 mm/s was found for the hydrogen-induced change in isomer shift, reflecting both a large increase in volume and a significant change of the electronic structure after charging. Additionally, Rupp and Wiesinger could demonstrate that segregations of magnetically ordered Fe in the parent alloys are a consequence of an activation heat treatment under rough vacuum conditions. The hyperfine pattern characteristic for ~-Fe which occurred in the transmission spectra indicated that those segregations had already achieved a volume large enough to be visible for 14.4 keV y-rays. In a further ternary oxide, the so called z-phase, only an insignificant rise in the susceptibility could by detected by Rupp and Tuscher (1984) after hydrogen uptake. When reinvestigating the Zr-Fe phase diagram, Aubertin et al. studied hydrides of Zr-rich alloys (Aubertin et al. 1984a) and of the rl-phase ZrzFeOo.3 (Aubertin et al. 1984b). Regarding the latter, the M6ssbauer spectrum differs from that of the Ti analogue presented by Rupp and Wiesinger (1984), which is most probably due to the different amount of hydrogen in the two samples (2.4 and 2.6% respectively).

5.5. Hydrides of amorphous alloys Hydriding studies have almost exclusively been performed on the systems Zr-Fe (Coey et al. 1982, Boliang et al. 1983, Wronski et al. 1984, Fries et al. 1984, 1985, Kuzman et al. 1987) and Y-Fe (Fujimori et al. 1982, Ryan et al. 1985). Zr-rich parent samples become superconducting at temperatures of the order of 3 K. At the Fe-rich side of the host system, a complex type of noncollinear magnetic ordering (asperomagnetism) can be observed. Details and a presentation of the complete phase diagram can be found in the articles of Coey et al. (1984) and Wiesinger and Hilscher (1988a). Hydrogen absorption studies have, so far, only been reported for Fe-rich samples, with the emphasis on M6ssbauer spectroscopy. The comparison of the room-temperature M6ssbauer spectra of the moderately hydrogenated samples with those obtained from the parent compound indicates a pronounced hydrogen-induced rise

568

G. WIESINGER and G. HILSCHER

of the Curie temperature (fig. 19). Larger hydrogen concentrations, however, lead to a reduction of Tc. Frequently, the formation of Fe precipitations are observed. The diverging results which can be found in the literature might be due to difficulties with the preparation of the samples and their homogeneity. In fact, direct evidence for inhomogeneities in the ribbon surface has been given by Fries et al. (1984) by comparing conversion electron M6ssbauer spectra with transition M6ssbauer spectra. The presence of m-iron segregations was confirmed on the shiny surface, whereas the dull surface, having been in contact with the wheel, and the bulk were found to be free of any m-iron impurities. General agreement, however, exists on the enhancement of Tc and the Fe moment upon hydrogen absorption (figs. 20 and 21), which was already known from crystalline Fe compounds. The transition to asperomagnetism on lowering the temperature which has frequently been reported is suppressed upon hydrogenation. The easy axis of magnetization that can be deduced from a given M6ssbauer spectrum was found in the charged sample (perpendicular to the ribbon plane) to differ from that in the host alloy (in the ribbon plane). This finding has to be attributed most probably to hydrogen-induced crystallization on the ribbon surface, tending to tilt the moments out of the ribbon plane. The magnetoelastic behaviour of ferromagnetic metal-metalloid alloys was studied by Berry and Pritchet (1981) with respect to the amount of hydrogen absorbed by the sample. A hydrogen-induced increase in the magnetic hardness accompanied by a decrease in the remanence has been observed. A pronounced Zr 4d charge transfer has been observed in several Zr-3d hydrides by means of XPS and M6ssbauer spectroscopy (Fries et al. 1985) and by soft X-ray emission spectroscopy (Tanaka et al. 1982), showing that the hydrogen atoms are mainly bonded to Zr in these hydrides. As in the case of the crystalline counterparts, the weakening of the R-Fe exchange upon hydrogen absorption is responsible for the substantial reduction of compensa-

(a)

"

:

(b)

E l--

-

.

I

I

I

-6

-4

-2

¢.

I

I

I

q

0

2

4

6

v (mms-D

~"

Fig. 19. Room-temperature M6ssbauer spectra of the ZraoFe90 amorphous alloy: (a) as quenched; (b) after charging at - 5 0 0 m V (Kuzmann et al. 1987).

MAGNETISM OF HYDRIDES

569

400 / /

300 -

200 -

100 I

I(")"

I

0

I

40

60

80

1 O0 X

Fig. 20. Phase diagram of amorphous Zrloo-~Fex and Zraoo_~Fe~H r alloy system. The transition temperatures Tc of the sputtered films and the melt-spun alloy are denoted as squares and triangles, respectively (Fries et al. 1987),

•

@

•

@

@

•

•

@

D-

S

• @

Fe89Zq 1H50

•

./

\ \ \ \

@

\ \

Fe89ZQ1

\

•

k \ I

0 0

200

I

I

4OO r (K)

Fig. 21. Magnetization of charged and uncharged amorphous Zr89Fell (Fries et al. 1984).

570

G. WIESINGER and G. HILSCHER

tion temperature and Curie point in the system Gd-FeHx (Forester et al. 1984). From anisotropy measurements carried out on hydrided (Fe, Ni)B-type metallic glasses, Berry and Prichet (1981) and Chambron et al. (1984) inferred a pronounced interaction of the hydrogen atoms with the Bloch walls. Rare-earth-rich metallic glasses frequently exhibit large coercive forces. Introducing hydrogen into these alloys greatly accellerated the trend away from ferromagnetism towards spin-glass order (Robbins et al. 1982, Sellmyer et al. 1984).

Acknowledgements We thank P. Vajda for many valuable comments. This work was partly supported by the "Fonds zur F6rderung wissenschaftlicher Forschung" under project 8276, and the "Jubil~iumsfonds der 6sterreichischen Nationalbank" under project 3492.

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SUBJECT INDEX

Abrikosov-Suhl resonance, 93 absorption, optical, 398, 400, 429 AC susceptibility, in quasicrystals, 481 activation energies - for crystallization, 307, 311,312, 314 for structural relaxation, 396 amorphous alloys - homogeneity, 297 - order, 322 - preparation conditions, 319 - resistance to corrosion, 424 - transport properties, 413 amorphous metallic alloys, 457 amorphous phase, 473, 499, 503 amorphous state, 457 amorphous structures, models for the description of, 303 anelastic deformation, 374 anisotropic magnetoresistance, 416 anisotropy, 95, 96, 139, 141,470 - stress-induced, 374, 378, 425 anisotropy constant, 139, 381 anisotropy energy, 143, 144, 471 anisotropy field, 41 annealing of amorphous alloys in a magnetic field, 395 annealing temperatures, 314 annealing time, 314, 315, 396 antibonding interactions, 465 antiferromagnetic coupling, 466 antiferromagnetic interactions, 478, 481 antiferromagnetic state, 503 antiferromagnetism, 315 antiferromagnets, 95-108, 111, 112, 115-117, 119, 121-127, 129, 132-134, 139-142, 144, 147, 148, 150, 151,153-156, 316

Arrott plots, 505 - anomalous, 494 asperomagnet, 316 asperomagnetic, 327, 339, 360 asperomagnetic order, 316, 336 atomic density, 476 atomic disorder, 485 atomic ordering, 303 atomic structure, 303

-

band gap, 469 band-gap model, 331 band-gap theory, 323 band structure calculations of hydrides, 516 band structure of ternary rare-earth compounds, 121, 148, 158 /3 phase in AI-Mn-Si alloys, 480 binding energies, 466 Bloch periodicity, 459 Bohr magnetons, 477 Boltzmann's constant, 477 bond model for amorphous alloys, 322 BPE approximation, 348 Brillouin function, 345,477 CaCu 5 structure, 7 carrier-to-noise ratio, 432, 433 CeCo4B structure, 50 charge transfer, 525, 562, 568 charge-transfer model, 322 chemical bonding, 460 close-packed structure, 303 cluster calculations, 460, 462 cluster moment, 466 - average, 480 cluster size effects, 465 635

636

SUBJECT INDEX

coercive energy, 389 coercive field, 319, 322, 385, 389, 391,395 coercive force, 498 coercivity, 31, 53, 63, 74, 385,389, 390, 392, 395, 426, 428, 429, 431,493 coherent potential approximation, 348, 352 coherent rotation, 387 collective magnetic order, 326 columnar structures, 301, 302 compensation composition, 363,407 compensation points, 548 Ho6Fe23Hx, 548 compensation temperature, 319, 360, 363,367, 368, 391,395, 407, 429, 430, 545-547, 555,556 Co compounds and their hydrides, 554, 556 Fe compounds and their hydrides, 545 complex refractive index, 398 composition resistivity, dependence of, 418 compositional compensation, 408 compositional dependence, 374-377, 384, 424 compositional variation of properties in amorphous alloys, 338, 340, 341,366, 367, 384, 392, 403, 404, 410, 2007 conduction, 472 conduction-electron density, 470 conductivity, 396, 397 conductivity tensor, 398 coordination bond model, 331 coordination numbers, 306, 308 corrosion, 395,425 corrosivity, 429 coupling strength, 468 critical composition, 338, 340 critical concentration, 326, 332, 334, 344, 349, 353, 357 critical exponents, 369, 371,372 critical magnetic fields, 559 - Y2Co7Hx, 559 crystal electric field, 94-97, 109, 112, 116, 143, 151, 158, 165, 170, 171 crystal field, 528 crystal-field effects, 461,466, 529, 531,533 crystal field for R ions in RT12_xMx, 23, 25 crystal field for R2FeI7C3_~, 46 crystal-field Hamiltonian, 23 crystal-field modeling for RT12-xMx, 27-30 crystal-field parameters, 25, 75 crystal-field symmetry, 461 crystal structure, 96, 99-102, 117, 118, 149, 152, 163, 538, 545-547, 555, 556, 3737 - Co compounds and their hydrides, 555,556 - Fe compounds and their hydrides, 545,546 Mn compounds and their hydrides, 538 -

-

-

-

crystal structure types AIB2, 97, 101, 102, 105, 106, 155, 162 BaNiSn3, 117, 118 - CaBe2Ge2, 109, 120, 151, 152, 154 - Cain2, 99, 102 CeAI2Si2, 154 - CeCu2, 97, 99, 103, 110 - CeNiC2, 113 CeNiSi2, 113 - Fe3C, 114, 117 - Fe2P, 97, 99-101, 104 LaIrSi, 97, 99 LaPtSi, 97, 99, 102, 108 - LuRuB2, 113 - MgAgAs, 97-100 - MgCu2, 97, 99, 100 MgZn2, 97, 99, 101, 104 NdNiGa2, 113 Ni2In, 97, 99, 101,105, 162 - PbFCI, 97, 99, 102, 108 - TbFeSi2, 113 - ThCr2Si2, 109, 117, 120, 133, 137, 149, 151,154 TiNiSi, 97, 99, 102, 103, 108, 109 - ZrNiAI, 100 - ZrOS, 97, 99, 100 crystalline anisotropy, 470 crystallization temperatures, 307, 309-311, 313, 314 CsCl-like space group, 476 cuboctahedral clusters, 465 Curie-behavior of icosahedral compounds, 488 Curie constant of quasicrystalline materials, 477 Curie law in quasicrystalline materials, 486 Curie-like paramagnetism, 487 Curie temperatures - amorphous alloys, 319-321,328, 339, 354-357, 359, 368-370, 414, 428 Co compounds and their hydrides, 555,556 compounds of transition elements with nonmetals, 162, 163 Fe compounds and their hydrides, 545-547 - FexZrloo_xHy, 569 - Gd-Pd compounds, 566 Mn compounds and their hydrides, 538 - Nd2Fe17Hx, 542 - quasicrystalline materials, 493, 495, 496, 498 - R2FelnBHx, 544 - R2Fel7C3_6, 44, 45 - ternary rare-earth compounds, 8, 22, 32, 33, 40, 44, 48, 51, 54, 56, 59, 61, 65, 67-70, 74, 100-104, 106, 108, 112, 113, 139, 146, 147, 151 Curie-Weiss law, 99, 100, 104-110, 114, 115, 117, 118, 121, 138, 149, 151-154, 157 -

-

-

-

-

-

-

-

-

-

-

-

-

-

SUBJECT INDEX d-band model for amorphous alloys, 347 d-band states in transition metal clusters, 467 d-electrons in quasicrystals, 472 d orbital degeneracy, 461 de Gennes factor (function), 95, 109, 111,159, 162, 163, 170, 365 decagonal phases, 479, 487, 503 decagonal quasicrystal, 500, 501 decagonal (T-phase), 477 degeneracy of d and f states, 461,462 demagnetizing energy, 430 demagnetizing field, 430 dense random-packing model, 305 dense random packing of hard spheres, 457 densities of amorphous alloys, 299 density of states (DOS), 121, 148, 149, 154, 157, 158, 461,468-470, 479 gaps in the DOS spectrum, 468 - local, 465 diamagnetic behavior, 114, 156, 487 dielectric tensor, 398 differential detection, 433 diffraction patterns, 475 diffraction peaks, 475 dipolar interactions, 374, 375 direct overwrite, 432, 433 disk velocity, 431 disorder in A1-Cu-Fe alloys, 491 domain nucleation, 429 domain wall, 430, 431,471 domain-wall energy, 394, 430 domain-wall motion, 387, 429 domain-wall pinning, 391 domain-wall thickness, 388 DOS, see density of states double group representation, 462

637

electronic states of aluminium, 465 electronic structure, 148, 461; 465, 469 ellipticity, 398, 399 environment model, 322, 331,340, 341 evaporation, 295,296, 299, 319, 375 exchange coefficient, 23 exchange constants, 360 exchange correlation, 467 exchange coupling, 317, 335,341,408 exchange coupling parameters, 361 exchange energy, 470 exchange fluctuation parameter, 346 exchange fluctuations, 346, 349, 371,485,504 exchange interactions, 94, 129, 159-161,326, 334, 336, 461,470 exchange splitting, 466 exchange stiffness constant, 388

-

effective medium technique, 470 effective paramagnetic moment, 482, 500 electric field component, 26 electric field gradient, 73, 480 electrical resistivities, 98, 104, 116, 117, 122, 133, 134, 136, 144, 146, 149, 480 electron localization in quasicrystals, 469 electron microscopy, 500 electron-electron interactions, 472 electron-phonon coupling, 475 electronic paramagnetic resonance, 495 electronic properties, 516 electronic specific heat, 486 electronic state densities, 475 electronic states, central peak in the distribution of, 468

f levels in cluster techniques, 461 F-type ordering of quasicrystals, 487 • Faraday effect, 398, 399 Faraday rotation, 398, 402, 408, 410, 412, 424 fcc clusters, 466 Fermi - energy, 121, 158, 463, 472 - level, 93, 148, 149, 154, 463, 465, 470, 472 - liquid, 92, 93, 153 - surface, 94, 157, 161 - vector, 161,163 ferrimagnetic materials, 104, 105, 107, 131,140, 142 ferrimagnetic order, 316, 340, 342 ferrimagnetism, 315, 339 - strong, 18 - weak, 15 ferromagnetic behavior, 485 - weak, 499 ferromagnetic interactions, 481 ferromagnetic materials, 316, 493,495,496 ferromagnetic moment, 498 ferromagnetic quasicrystals, 492, 497, 498, 504 ferromagnetic resonance, 495,561 ferromagnetism, 315, 467, 492 ferromagnets, 94, 95, 100-103, 108, 112, 115, 117, 118, 126-129, 134, 136, 137, 13%142, 147, 148, 150, 156 Fibonacci lattice, 467, 468 field dependence of magnetization in amorphous alloys, 337 figure of merit in magneto-optical recording, 429 first-order magnetization processes, 28 first-order rate equation, 486 five-fold symmetry, 468

638

SUBJECT INDEX

formation enthalphies of vacancies, 312, 314 formation of R2Fe 14C compounds, 58 Frank-Kasper disclination lines, 458 Frank-Kasper phase, 472, 473 free-electron behavior, 463 free-electron gas, 466 free-electron model, 473 free-electron theory, 475 free energy of alloys, 456 Friedel-Anderson s-d model, 480 g factor, 495 glassy alloys, 467 golden ratio, 468 gyromagneticfactor, 345 Hall coefficient, spontaneous, 420, 423, 424 Hall effect, spontaneous, 331,422, 423 Hall effect in R-3d alloys, 420 Hall resistivity of R-3d alloys, 414, 415,421 Hamiltonian techniques on quasilattices, 467 Hartree-Fock Hamiltonian, 466 hcp clusters, 466 heat capacity, 96, 134, 136, 152, 473 heavy fermions, 92, 93, 104, 108, 111,114, 121, 122 Heusler alloys, 114-116, 162, 171 highest occupied molecular orbital in metal clusters, 464 Hume-Rothery instability, 469 Hume-Rothery rules, 470 Hume-Rothery stabilization, 475 Hund's rule, 93 hydrides, 21 hyperfine field distribution in amorphous alloys, 328 hyperfine field in quasicrystals, 498, 499, 542 hysteresis loops, 40, 426 - low-field, 493 icosahedral alloys, 503 icosahedral cluster stability, 459 icosahedral clusters, 463,465-467 icosahedral coordination, 461,471 icosahedral crystal field, 461 icosahedral crystals, 471 icosahedral glass, 475 icosahedral group, 461 icosahedral network, 488 icosahedral phase stability, 470, 487 icosahedral phases, 478, 499 icosahedral point-group, 462 icosahedral quasicrystals, 455

icosahedral short-range order, 457, 467 icosahedral site symmetry, 462 icosahedral sites, 466, 468, 480, 502 - symmetry, 480 icosahedral symmetry, 456, 460, 462, 467, 470, 475,476, 502 - local, 459, 460 long-range, 471 icosahedral units, 456, 458, 467 - stability of, 467 I h group, 463 I h phase, 479 interband transitions, 399, 405,407, 408 interpenetrating icosahedra, 501 interstitial nitrides, 42, 45, 49, 74 intraband transitions, 399, 401,408 intrinsic quasicrystal resistivity, 472 iron magnetic moment, 8 iron sublattice anisotropy, 8 irreducible representations, 461,462 Ising model, 134, 468 isomer shift, 490, 542, 564 isotropic magnetoresistance, 416, 420 itinerant electron antiferromagnetism, 540 itinerant magnetism, 517, 553 -

J-mixing for Sm3+, 13 Kerr effect, 398, 427 Kerr rotation, 398.400, 402-405,407-409, 411, 429 - wavelength dependence, 407 Kondo - effect, 164, 165 - lattice, 122, 123 - system, 92, 116, 164 - temperature, 93, 122, 164 Kondo-like resistance minima, 477 lattice constant of A165Mn20_xCrxGe15, 485 Lennard-Jones potential, 458 local anisotropies, 317, 470 local band theories, 1825 local density functional, 469 local environment, 462 local icosahedral packing, 458 local random electrostatic field, 339 local strains, 379 localization of states, 465,469 localization theory, 473 localized Mn d states, 465 localized states, 468 long-range magnetic order, 468

SUBJECT INDEX Lorentz microscopy, 427, 428 Mackay icosahedron, 457, 467, 472, 480 magnetic anisotropy, 461 magnetic compensation, 357, 363 magnetic domains, 427, 428 magnetic entropy, 477 magnetic excitations, 392 magnetic force microscopy, 427, 428 magnetic instability, 465 magnetic interaction, 94, 96, 97, 133, 137, 139, 158-160, 164 magnetic measurements for DyMnGa, 98 magnetic Mn sites, 484 magnetic moment, 315,320, 323,339, 340, 467, 499, 538, 545-547, 555,556, 558, 559 - average in amorphous alloys, 339 - Co compounds and their hydrides, 555,556 Fe compounds and their hydrides, 545-547 localized, 489 Mn compounds and their hydrides, 538 - YzCo7Hx, 558, 559 magnetic phase diagram - CeHz+x, 527 - GdFe4+xA18_x, 34 RzFel4B, RzFe14C, 63 - RzFel4X, 64 magnetic phases for RFelITi, 13 magnetic properties, 527, 561,564 - concentration dependence in amorphous alloys, 327, 332, 354-356, 359 - Ni compounds and their hydrides, 561 - R compounds, 564 - RH2+x, 527 - RTla-xMx, 8 magnetic relaxation, 486 magnetic sites in quasicrystals, 484 magnetic structure (ordering), 100, 106-109, 112, 116, 117, 129, 133-139, 145, 146, 148, 151,161, 164, 315, 526, 529 - amorphous alloys, 316, 328 - antiferromagnetic, 104, 109-112, 114, 116, 120-122, 135, 13%140, 145, 146, 148, 149, 151, 153, 154 - antiphase, 136 - canted, 146 - CeD2+x, 529 - collinear, 109, 112, 133, 135, 137, 138, 145, 146, 154, 161 - commensurate, 106, 133, 151 - complex spiral, 111 - cycloidal, 106 - double flat spiral, 109 -

-

-

-

639

- ferrimagnetic, 145 - ferromagnetic, 104, 105, 108, 110, 112, 120, 138, 139, 146, 149 - HOD2, 526 - incommensurate, 106, 109, 121,122, 133, 135, 137, 153 - modulated, 98, 112, 133, 134, 136.138 - noncollinear, 97, 100, 109, 117, 137, 142 - oscillatory, 161 - sin modulated, 137, 138 - spiral, 95 - square modulated, 136-138 - TbD2, 526 - types, 100-102 magnetic susceptibility, 92, 96, 98, 100, 104-112, 114, 116-120, 122, 123, 130, 131,134, 135, 137, 138, 140, 146, 148, 149, 151,153, 154, 157, 160, 475,482, 487, 490, 501,503 logarithmic time dependence, 486 magnetic ternary compounds, 3 magnetic valence, 16, 73 magnetic valence model, 14 magnetism, basic aspects, 517 magnetization, 96, 104, 130-132, 136, 139, 140, 142-146, 157, 161, 171,327, 344, 354, 521,541, 542, 548, 552, 557, 563,569 - Ce(Fe0.9Co0.1)2Hx, 552 ErHx, 521 - Fe89ZrllHs0, 569 Ho6Fe23Dx, 548 - Nd2Col4BHx, 557 - spontaneous, 500 - YMn2Hx, 541 - Y2Ni7Hx, 563 magnetization curves, high field, 28 magneto-optic recorder, 432 magneto-optical disk, 432, 434 magneto-optical properties, 22, 398 magneto-optical recording, 425,433 magnetocrystalline anisotropy, 72 magnetoresistance, 413,416, 419, 477 magnetostriction, 62, 331,374, 379-381,383-387, 558 - Y2Co7Hx, 558 magnetovolume effects, 60 mean-field theory, 345,355,358, 359 mechanical alloying, 32 melt-spinning, 31,295 metallic glasses, 458, 477 micromagnetic exchange stiffness constant, 394, 395 microstructure, 299-301,319 Miedema parameter, 72 -

-

-

640

SUBJECT INDEX

mixed valence, 39, 91, 104, 112, 121-123, 151 Mn-Mn interactions, 478 molecular-dynamics simulations, 457 molecular field interaction, 23 molecular field model, 94, 95, 144 molecular orbital, 463 molecular-orbital calculations, 458 moment, 94, 357 - effective, 106, 108-110, 114, 149, 157, 158 - local, 461,466, 483, 485,486 - magnetic, 93, 96, 99, 104, 106, 108-112, 114, 116, 117, 120, 122, 133, 136-139, 146, 151,157, 158, 167, 171 - paramagnetic, 100-103, 123 saturation, 123, 142 moment formation, 466, 491 - local, 470 moment theory, local, 321 Monte Carlo simulations, 457 M6ssbauer effect - 57Fe, 65 - 57Fe M6ssbauer spectroscopy of amorphous alloys, 328, 329 - 57Fe M6ssbauer spectroscopy of hydrides, 540, 550, 561,562, 565,568 - 57Fe M6ssbauer spectroscopy of Nd2Fe14B-type compounds, 61 - 57Fe M6ssbauer spectroscopy of quasicrystalline alloys, 478, 484, 485,487, 488, 491,498, 502 - 57Fe M6ssbauer spectroscopy of ternary rare-earth intermetallics, 52, 66, 96, 100, 104, 108, 110, 112, 117, 120, 123, 149, 151,154 - 57Fe M6ssbauer spectroscopy of ThMn12-type ternary compounds, 20, 33, 40 - 155Gd, 53, 56 - 155Gd M6ssbauer spectroscopy of ternary Gd-based hydrides, 563 - J55Gd M6ssbauer spectroscopy of ternary Gd-based intermetallics, 73, 74 M6ssbauer spectroscopy J61Dy, 66 - 57Fe, 20, 28, 40, 42, 53 - 155Gd, 26, 66, 73, 74

negative exchange interactions, 338 neutron diffraction, 28, 33, 98, 104, 105, 109-112, 116, 117, 120, 133, 136-139, 146, 151,153,154, 161, 166, 475,479 neutron scattering, 480 - inelastic, 31 NMR, see nuclear magnetic resonance noncoltinear structure, 316, 317, 328, 383,393 nonlinear susceptibility, 480 nonmagnetic sites in quasicrystals, 484, 485 nuclear magnetic resonance (NMR), 104, 121, 151,534, 557 nucleation field for domains of reversed magnetization, 390

-

_

2N+2 rules, 458 Nd2Fel 7Hx - hyperfine field, 542 - isomer shift, 542 nearly free-electron model, 469 Ndel temperature, 98, 100-103, 106, 108, 111, 113, 116, 117, 122, 133-136, 138, 140, 147, 148, 151,159, 160, 162-165

oblate rhombus, 476 octagonal quasicrystals, 503 octahedral clusters, 463 one-subnetwork alloys, 320 oxidation of amorphous R-3d films, 396

p bonding orbitals, 464 p-d bonding, 331,466 p-d hybrid, 465 p-d hybridization, 323,333 packing fraction, 299, 300, 304 pair correlations, 475,476 pair ordering, 375 pair potential, 470 paramagnetic, 496 paramagnetic Curie temperature, 99-104, 106, 108, 109, 114, 129, 151, 157, 162, 163,486 paramagnetic moment, 477, 501 paramagnetic resonance, 495 paramagnetic susceptibility, 477 paramagnets, 99, 107, 108, 114, 132, 142, 147, 151,156 partial distribution functions, 305 Pauli paramagnet, 100-102, 106, 109, 111, 113-115, 117, 119-121,124-128, 150-157, 163 Pauti paramagnetic behavior, 489, 502 Pauli paramagnetism, 483,488, 502 Pauli susceptibility, 472 Penrose bricks, 502 Penrose !cosahedral lattice, 476 Penrose lattice, 468, 469 - three-dimensional, 501,502 Penrose tiling, 469 - three-dimensional, 475 permanent magnets, 63 phase diagram, 89, 112, 114, 121,131, 132, 142, 145-147

SUBJECT INDEX phase transition, 106, 114, 130, 131, 133, 136, 140, 146, 147, 156 photoemission, 463 photon energy, 409 polytope (3,3,5), 467 pressure effects, 140, 165 pressure-distance product, 300, 301 prolate rhombohedron, 502 prolate rhombus, 476 quadrupole splitting in M6ssbauer spectra of Fe-based quasicrystalline materials, 484, 487, 489, 490, 502 quantum structural diagrams, 470 - generalized coordinates, 470 quasicrystal formation, 470 quasicrystalline materials, 470 - 3d magnetic moments, 470 - superconducting properties, 473 superconducting transition temperature, 473 - susceptibility, 502, 503 quasicrystals, 469, 470 high-symmetry sites occupation, 501 six-dimensional description of, 476 solutions of the Schr6dinger equation, 642 - stable, 487 - ten-fold symmetry, 463 quasilattice, 475 quasilattice constant, 475,481 quasiperiodic superlattice, 468 quasiperiodicity, 468 -

-

-

-

-

R anisotropy for RT 12-xMx, 25 R-T exchange for RT12_xMx, 22 Racah operators, 30, 31 radial-distribution functions, 304, 306, 309, 315 random anisotropy, 338, 470, 494 random anisotropy model, 338 random axial anisotropy, 336 random local anisotropy, 318 random-packed hard-sphere, 303 random-packed structure, 298 rapid solidification, 455, 487 rapidly quenched, 491 rare-earth anisotropy, 53 rare-earth metal, icosahedral coordination, 461 relative magnetization, 337, 344 relative saturation magnetization, 351,352, 358 resistivity, 395,396, 413-416, 418, 419, 422, 425, 473, 477, 523,532 temperature dependence of, in amorphous alloys, 416 - TmHx, 523

641

resonant scattering, 469 RKKY interaction, 335,355,357, 518,563 RKKY theory (interaction), 94, 95, 104, 106, 154, 157, 159-162, 164, 165

s-d hybridization, 465 s-d overlap, 465 s-d scattering, 475 saturation magnetization, 338, 340, 341,345, 353, 359, 363, 364, 366, 414 scanning electron microscopy, 496 Schottky anomaly, 136 second-order crystal field coefficient, 8, 47, 53, 73 second-order crystal field parameter, systematic determination of, 75 second-order Stevens coefficient, 66 self-consistent field-scattered wave, 459 self-similarity of density of states in quasicrystals, 468 short-range atomic order, 305 short-range magnetic, 322 side jumb scattering, 420, 421 single crystals of hydrides, 558 single-ion anisotropy, 317, 328, 334 single-ion contribution, 376 single-ion model, 378, 379, 381 single-ion theory, 385 single-phase icosahedral AI-Mn-Si alloys, 492 single-phase icosahedral materials, 488, 490, 491 single-site anisotropy, 315 singular point detection, 28, 62 size effects, 485 skew scattering, 402, 420, 422 Slater-Pauling curve, 323,324 Slater-Pauling plots, 322, 325,326 soft-sphere model, 305 solid-state transformation, 63 sp-d hybridization, 323,465 specific heat, 92, 104, 108-110, 114, 116, 121,122, 133, 136, 137, 146, 149, 473, 477, 480, 503, 522 - ErHx, 522 specific magnetization, 320, 332, 344 sperimagnetic, 316, 317, 339, 357 sperimagnetic order, 316 speromagnetic, 316, 317, 330, 339, 352, 357 speromagnetic order, 316, 336 speromagnetic structures, 318 spin density, 148 spin density wave, 121 spin disorder resitivity, 533 spin fluctuations, 517, 535 spin-freezing temperature, 318, 327, 419

642

SUBJECT INDEX

spin-glass, 98, 100, 138, 139, 475,478, 481,495, 498, 504, 505 concentrated, 495 dilute, 495 spin-glass behavior, 318, 333,335,492 spin-glass freezing, 477, 481 spin-glass phase, 494 spin-glass transition, 486, 494 spin polarization, 401,402, 407, 408, 412 spin-polarized conduction electrons, 335 spin reorientation, 13, 20, 23, 26, 41,550, 554 - ErFe3Hx, 550 spin-reorientation temperature, 545-547 Fe compounds and their hydrides, 545-547 spin-wave stiffness constants, 349, 350, 392-394 spin-wave theory, 349, 355 spin waves, 136, 137, 392 spin-orbit coupling, 317, 328, 335, 373, 395,398, 401,461 spin-orbit interactions, 461,462 split bands, 330 sputtering, 32, 297, 299, 319, 321,322, 426 state density, 462, 463 static hypothesis, 369 Stevens coefficients, 25 Stevens operator, 25 Stoner condition, 148 Stoner criterion, 462, 467 structural and magnetic properties - for La(Tl_xSix)13 compounds (T= Fe, Co or -

-

-

of Faraday rotation in amorphous alloys, 412 of magnetization in amorphous alloys, 351-353, 358, 360, 362-364 - of magnetoresistance in amorphous alloys, 420 - of magnetostriction in amorphous alloys, 387 - of resistivity in amorphous alloys, 419 of spin wave stiffness in amorphous alloys, 393-395 of uniaxiale anisotropy in amorphous alloys, 380-382 temperature-independent susceptibility, 487 thermodynamical stability of A1-Cu-Fe quasicrystals, 487 ThMnl2 structure, 7, 24 Th2Ni17 structure, 7 3d anisotropy for RTlz_xMx, 18, 20, 21 3d magnetism for R2Fe~4C, 61 3d magnetism for RT4B, 53 3d moment for RT12 xMx, 13-17 3d-4f exchange, 22 tight-binding approach in quasicrystalline materials, 467, 468 tight-binding Hamiltonian, 468, 469 tight-binding model, 468 tiling, 468 two-dimensional, 469 time-dependence of magnetization in quasicrystals, 495 total energy of icosahedral arrangement, 456 tricritical points, 327, 333, 365 -

-

-

-

-

Ni), 5 RI+,T4B4, 65, 66 - R2Fel4C compounds, 60 - RzFeavC3_ 6 (T=Fe or Mn) compounds, 43, 47 R2Fel7Nx (R=Sm or Y) compounds, 48 - RT12B6, 57 RT4B, 49 - RT4B (T=Fe, Co or Ni) compounds, 50 - RzT12P7, 70 - RT4+xAla_x, 32-40 - RT12_xMx, 9-12 structural instability, 465 structural relaxation, 313,396 structure factors, 470, 473, 501 structures related to NaZn13, 4 sublattice magnetizations, 340, 342, 345,358, 360, 362, 394, 408, 422 superconductor, 99, 108, 111,112, 114, 116, 118, 120, 121, 153, 154 susceptibility, YbH2+x, 534 -

-

-

T-mixing, 29 temperature dependence of coercivity in amorphous alloys, 391

-

uniaxial anisotropy, 321,373-375, 377, 378, 380, 382, 389, 395,429 uniaxial anisotropy constant, 319, 373,376 uniaxial magnetic anisotropy, 373,428 valence bands, 330 valence change, 552, 558, 562 valence-electron concentration, 458 valence electrons, 472 valence transition, 534 valency fluctuation, 116, 121 van Hove singularity, 468 van Vleck behavior, 116, 148, 151,152 virtual bound states, 477 X-ray diffraction line width in quasicrystalline materials, 485,488 X-ray spectroscopy, 473 Xc~ local density function, 462 zero-field cooling, 486, 495 Ziman method, 469

MATERIALS INDEX

A165Cu2oMn 15,487 A165.3Fe27.3Ce7.4,500 A171Fe19Silo, 479 AI6Li3Cul, 472 AI5oMlzSi7, 479 AIzMg3Zn3, 473 All _xMnx, 478 AI4Mn, 479 AI78Mnz2, 477 Alvs.4Mn21 , 478 A18oMn2o, 477, 479 AI85Mn15, 478 AI86Mn14, 459 AI18Mn cluster, 466 A165Mnzo_xCrxGels, 485,486 A174Mn2o xCrxSi6, 482, 484 A14oMnzsCuloGe25, 485,496, 497 AI4oMnzsFe3Cu7Cu3 Ge25, 498 A14oMnzsFe3Cu7Ge25, 497, 498 A14oMn25Fe6Cu4Ge25, 497 Aly4Mnzo_xFexSi6, 484 AI52.sMnzsGez2.5, 483, 496 AI65Mn2oGe15 , 484, 496 AI79MnlvRU4, 487 AlsoMn2oSi3o, 492, 493 A155Mn2oSi25, 492, 493,495 Aly4Mn21Si6,475 AlsoMo9Fell, 488490 AI65T2oGe15, 485 A174T2oSi6, 485,486 A17oYaloFe2o, 490 c~-Al-Mn-Si, 457, 472, 475,476, 479, 480, 501 c~-Fe, 479 c~-rare-earth hydrides, 519 amorphous A1-Mn-Si, 492 anisotropy of RzFel4C , 62

(AI,Zn)49Mg32, 472 A1-Cr, 470, 477 Al-Cr-Ge, 485 A1-Cu-Cr, 487 A1-Cu-Fe, 475, 487 A1-Cu-Li, 472 AI-Cu-V, 475 A1-Fe, 479 A1-Fe-R, 501 A1-Li-Cu, 470 A1-Mg-Zn, 470, 472 A1-Mn, 470, 477, 478 AI-(Mn,Cr)-Si, 484 AI-(Mn,Fe)-Si, 484 AI-(Mn,V)-Si, 481,483, 484 AI-Mn-(Cu)-Ge, 498, 500 A1-Mn-Fe-Cu-Ge, 500 A1-Mn-Ge, 485,496, 498, 499 A1-Mn-Ge quasicrystals, 499 AI-Mn-Si, 478, 480, 481,484, 491,499, 502 AI-Mn-Si ferromagnets, 493 AI-Mo-Fe, 483,487, 491 AI-T, 470, 477, 479 AI-T-Ge, 486 AI-T-Si, 486 AI-Ta-Fe, 483,487, 491 AI-V, 470 A113 cluster, 462 A133 cluster, 462, 463 AI clusters, 463, 465 AlvgCr17Ru4, 487 A165Cu2oCols, 487 AlyCu2Fel, 487 A165Cu20Fe15, 487 AI56CuloLi34, 473 AI52.4Cu12.6Mg35, 471 643

644 anisotropy of RT4B, 54 Au, 466 AUl3 cluster, 465 B12 icosahedral, 458 BaCd11 structure compounds, 41 bcc Fe, 502 bcc TiNi phase, 502 fl-A1-Mn-Si phase, 480 binary actinide hydrides, 534

-

CaCu5 structure compounds, 50 Ce, 528 dihydride, 528 CeAgz_xCuxIn, 116 CeAgzln, 115, 116 CeAgzSi2, 127, 137, 165, 166 CeAlzGa2, 137, 149, 166 CeAlzSi2, 120 CeAuIn, 101, 104 CeAuzIn, 115, 116 CeAuzSi2, 127, 137, 165, 166 CeCozGe2, 128, 129 CeCoSi, 101 CeCoSi3, 118, 119 CeCozSi2, 124, 167 CeCuz_xCoxSi2, 122 CeCuzIn, 114-116 CeCuz_xNixSie, 122 CeCul.54S, 111, 113, 130 CeCuSi, 101,104, 171 CeCu2Si2, 92, 93, 121, 125, 166, 168 CeCuzl Si2, 121 CeCu2Si2_xGex, 122 CeCuSn, 102, 107 CeFe2, 551 CeFeSi2, 112 CeFe2Si2, 167 Ce 1+xInl_xPt4, 71 CelrGe, 102, 109 CeIrSi3, 119 CeIr2Si2, 154, 155, 169 Ce 1_xLaxMn2Si2, 146 CeLaRu2Si2, 122 CeMn2-2xCrzrSi2, 148 CeMn2_2~T2rSi2, 148 CeMn2Ge2, 141 CeMnSi2, 113 CeMn2Si2, 139, 141, 146, 167 CeMn2Si2_zrGe2x, 146, 147 Ce2Ni2All, 156 CeNi2As2, 152 CeNiC2, 113

MATERIALS INDEX CeNiGae, 113 CeNi2P2, 151,152 CeNiSi, 102 CeNiSi2, 110, 111, 113 CeNizSi2, 124, 167 CeNi2Sn2, 152 CeNi3 structure compounds, 55 CeOsSi2, 119 CeOszSi2, 122 CePdGa, 102, 109 CePdGe, 103, 110 CePdIn, 101, 104 CePdzSi, 117, 118 CePdzSi2, 126, 137, 165, 166, 168 CePdSn, 102, 109 CePtGa, 102, 109 CePtGe, 103, 110 CePtIn, 101, 104 CePtSi, 92, 102, 108 CePtzSi2, 153, 166 Ce 1_xRxRuzSi2, 122 CeRhz_z~Ru2xSi2, 137, 138 CeRhGe, 102, 109 CeRhzGe2, 129, 137 CeRhSi3, 119 CeRhzSi2, 126, 137, 165, 168 Ce2RhSi3, 156 CeRhl.8T0.2Si2, 137 CeRuzGe2, 128 CeRuSi, 92 CeRuzSi2, 92, 126, 168 CeTzGe2, 91, 92 CeTIn, 104 CeTPt4, 55 CeTSi3, 118 CeTzSi2, 91, 92, 121,122, 165 CeT2X2, 91, 164 Cel_xYxPdzSi2, 122 CeYRuzSi2, 122 CeZnSi, 101 (Co,Ni)zB, 216 CozAs, 238, 239, 241 CoAsxS2_x, 259 CoB, 187 Co2B, 187, 216 Co13 cluster, 467 Co clusters, 470 Co5 Ge3,275 CoNiAs, 238 CoNip, 227 (Co0.4Ni0.6)75P16B6A13, 494 CoNiSn, 220 CoP, 198, 202

MATERIALS INDEX

Co2P, 219, 224, 227 CoPxS2_x, 259 COS2, 258 CoSb, 211 CoSe2, 259 CoSexS2_x, 259 CoSi, 191 coercivityof RTIz_xMx, 31 (Cr,Co)2B, 216 (Cr,Fe)zB, 216 (Cr,Mn)Sb, 211 CrAs, 199, 203 CrzAs, 237, 238 CrAsl-xPx, 208 CrAsl-xSbx, 209 CrAsl xSex, 214 CrB2, 252, 253 Cr2B, 216 CrCoAs, 238 CrCoP, 227 Cq _tCrtSb, 212 CrFeAs, 224, 238 Cr~_tFetGe, 193 (Crl-tFet)2P, 232 CrFeP, 224, 227, 232 CrtFel _tSb2, 256 CrtFe2 tTe3,262 CrGe, 193 CrGel-xSix, 193 (Crl _tMnt)2As, 239 CrMnAs, 238, 240 Crl _tMntGe, 193 (Crl _tMnt)NiAs, 243 CrMnE 227 (Crl _tNit)2As, 242 (Crl tNit)As, 243 CrNiAs, 224, 238, 242 (Crl-tNit)2E 234 CrNiP, 224, 227 CrE 198, 202 Cr2E 227 (Cq tPdt)2As, 252 CrS, 212, 213 Cr2S3, 259, 260 Cr3S4, 260, 262 Cr5S6, 260, 263 Cr2S3_xTex, 262 CrSb, 210 CrSb2, 256 CrSe, 212, 213 Cr2Se3, 260 Cr3Se4, 260, 262 Cr2Se3_xTex, 262

Cr3Se4_xTex, 263 Cr(T I_tNit)As (T=Mn, Fe or Co), 243 Cq _tTe, 213 CrTe, 213 CrzTe3, 260 Cr3Te4, 260, 262 CrsTe6, 260, 264 CrTel-xSbx, 215 CrTel-xSex, 215 crystallineAIMnGe, 500 crystalline equiatomic AIGeMn (Cu2Sb structure), 499 Cu13 cluster, 467 CuCuzGe2, 122, 128, 137, 166 CuCuSiz, 111,113 Cu icosahedral clusters, 466 CuzSb, 500 DyAgGa, 103, 110 DyAgzIn, 115 DyAIGa, 102, 106, 107 DyAuGa, 102 DyAu2In, 115 DyAuzSi2, 127 DyCoA1, 101 DyCozB2, 150 DyCo2Ge2, 128 DyCoSiz, 111, 113 DyCoSi3, 119 DyCozSi2, 124, 166, 167 DyCoSn, 102 DyCrzGe2, 128 DyCrzSi2, 123 DyCuAI, 101 DyCuzGe2, 128 DyCuzIn, 115 DyCuSi, 105 DyCuzSi2, 125, 168 Dy dihydride, 533 DyFeAI, 101,104 DyFeSi3, 119 DyFezSi2, 123, 166, 167 DyIrSi3, 119 DyIr2Si2, 155, 169 DyMnGa, 98, 100 DyMnzGe2, 140-142, 144 DyMnSi, 102, 108 DyMnzSi2, 140, 141, 167 DyNiAI, 100 DyNiAI2, 113 DyzNi2Al, 156 DyNiC2, 113 DyNiGa2, 113

645

646 Dy2Ni2Ga, 156 DyNi2Ge2, 128 DyNi2P2, 142 DyNiSi, 102 DyNiSi2, 124, 168 DyNiSi3, 119 DyOszSi2, 127, 169, 170 DyPdzGe, 118 DyPdzSi, 118 DyPdzSi2, 127, 169 DyPd2Sn, 115-117 DyPtzSi2, 153 DyRhzGe2, 129 DyRhSi, 103 DyRhSi3, 119 DyRh2Si2, 126, 130, 166 DyzRhSi3, 156 DyRu2Ge2, 128 DyRuzSi2, 126, 131, 162, 168 dysprosium compounds, 156 ErAgGa, 103 ErAg2In, 115 ErAIGa, 102, 106 ErAuGa, 102 ErAuzIn, 115 ErAuzSi2, 127 ErCoAI, 101, 104 ErCozB2, 150 ErCozGe2, 128 ErCoSi2, 113 ErCozSi2, 124, 167 ErCoSn, 102 ErCr2Si2, 123 ErCuA1, 100 ErCu2Ge2, 128 ErCuzIn, 115 ErCuzSi2, 125, 168 Er dihydride, 533 ErFeAI, 101 ErFeSi3, 119 ErFezSi2, 123, 137, 167 ErIrzSi2, 155 ErMnAI, 98, 100 ErMnzGe2, 141, 144, 146 ErMnzSi2, 140, 141, 146, 167 ErMnzX2, 137 ErNiAI, 100 ErNiAI2, 113 ErzNizA1, 156 ErNiC2, 113 ErNiGa2, 113 ErNi2P2, 152

MATERIALS INDEX ErNiSi, 102 ErNiSi3, 119 ErNi2Si2, 124, 168 ErOs2Si2, 127, 169 ErPdzGe, 118 ErPdzSi, 118 ErPdzSi2, 127, 169 ErPdzSn, 115-117 ErPt2Si2, 153 ErRhSi, 103, 109 ErRhzSi2, 126, 130 ErzRhSi3, 156 ErRuzGe2, 129 ErRuzSi2, 126, 165, 166, 168 ErTzSi2, 160 erbium compounds, 156 EuAgSi, 101,107 EuAIzGe2, 154, 155 EuAI2Si2, 154, 155 EuAuzSi2, 127 EuCozGe2, 128 EuCo2P2, 151, 152 EuCuGa, 103, 110 EuCuzGe2, 128 EuCuzSi2, 125 Eu dihydride, 532 EuFe2P2, 151, 152 EuIrzSi2, 154 EuMnzGe2, 140, 141 EuNiAs2, 152 EuNi2Ge2, 128 EuNizP2, 152 EuPdzGe, 118 EuPdSi, 100 EuPtSi, 100 EuRhzGe2, 129 EuRhzSi2, 126 EuRuzGe2, 128 EuRu2Si2, 126 EuSxSel-x, 139 EuTGa, 110 EuTGe2, 160 EuTzX2, 91,122 europium compounds, 156 fcc A1, 463,481 fcc AI hosts, 465 fcc Ti(Ni,Fe), 502 (Fe,Co)2B, 216 (Fe,Cu)2,P, 231 (Fe,Ni)zB, 216 (Fe,T)sSn3 (T=Ni or Co), 276 FeAs, 199, 206

MATERIALS INDEX Fe2As, 224, 238, 239, 241 FeAsl _xPx, 209 FeB, 187, 217 FezB, 215-217 Fe clusters, 467 Fe13 clusters, 467 (Fe1_tCot)zAs, 241 FeCoAs, 238, 241 (Fel _tCot )2B, 217 FeCoGe, 223 (Fel-tCot)zP, 233 FeCoR 227 Fel_tCotSi, 191 FeCoSn, 220 FeGe, 188, 191,193 FeGe2, 254 Fe3Ge, 265,268 FesGe3, 271,274 (Fel _t Mnt)2B, 218 (FetMn 1--t)5 Ge3,274 (Fel _tNit)2,218 FeNiAs, 238 (Fel _tNit)3Ge, 269 FeNiGe, 220, 223 (Fel _,Nit)2P, 234 FeNiP, 227 (Feo.2Nio.8)75P16B6A13,494 FeNiSn, 220 FeP, 199, 202 Fe2_tP, 230, 231 Fe2P, 224, 225,227-231,272 Fe3P, 265, 269, 272 Fe2(RAs), 231 Fe2(P,B), 231 Fe2(RSi), 231, 243 Fe2PI _xAsx, 243, 245 FesPB2, 271,272 FeRhE 249, 250 FeRuP, 249, 250 FeSb, 210 Fel +tSb, 211 FeSi, 189, 192 Fe3Si, 265,267 FesSi3, 271, 275 FesSiB2, 271,272 FeSn, 194 FeSn2, 254 Fe3Sn, 265, 269 FesSn3, 271,276 (FetTl_t)sGe3 (T=Ni or Co), 275 Fe3 tTtSi, 268 Fe2Te3, 260, 262 (Fel_tVt)3Ge , 269

647

ferromagnetic AI-Mn-Ge, 500 ferromagnetic A1-Mn-Si, 499 ferromagnetic A1-Mn-Si quasicrystals, 492, 495 Ga-Mg-Zn, 475 GaMg2.1Zn3.8,503 gadolinium compounds, 91 GdAgGa, 103 GdAg2In, 115 GdAg2Si2, 127 GdAI2Si2, 154, 155 GdAuGa, 102, 109 GdAu2In, 115, 116 GdAu2Si2, 127 GdAuSn, 102, 108 GdCo2B2, 149, 150 GdCo2Ge2, 128 GdCoSi, 101,102, 108 GdCoSi2, 113 GdCo2Si2, 124, 167 GdCr2Si2, 123 GdCuAI, 100, 101,104 GdCuGe, 101, 104 GdCu2Ge2, 128 GdCuln2, 101 GdCu2In, 115 GdCuSi, 101, 162, 163 GdCu2Si2, 125, 168 GdCuSn, 102, 108 GdCUl_xZnxSi,106, 162, 163 Gd dihydride, 532 Gdl_yEUyS, 139 GdFeAI, 101 GdFel0A12, 12 GdFe2Ge2, 128 GdFeSi, 101 GdFeSi3, 119 GdFe2Si2, 123, 160, 162 GdlrSi3, 119 GdIr2Si2, 154, 155, 169 Gdl_xLaxCu2Si2, 157 GdMn2Ge2, 141-145 GdMnSi, 102, 108 GdMn2Si2, 140, 141,167 GdNC2, 113 GdNiA1, 100 GdNiAI2, 113 Gd2Ni2A1, 156 GdNiGa2, 113 Gd2Ni2Ga, 156 GdNi2Ge2, 128 GdNiIn, 101,104 GdNi2P2, 151, 152

648 GdNiSi, 102 GdNiSi3, 119 GdNi2Si2, 124, 167 GdOs2Si2, 127, 169 GdPdAI, 104 GdPd2Ge, 118 GdPdIn, 101, 104 GdPdzSi, 118 GdPd2Si2, 127, 169 GdPdSn, 102, 104, 109 GdPtzSi2, 153 GdPtSn, 99-101 GdRhzGe2, 129 GdRhSi, 103 GdRhSi3, 119 GdRh2Si2, 123, 126, 129, 130, 158, 168 Gd2RhSi3, 156 GdRuzGe2, 128 GdRu2Si2, 126, 131, 132, 168 GdTAI, 104 GdTzGe2, 160 GdT2Si2, 157, 158, 160-162 GdTSn, 104 GdTX, 104 Gd 1_xThxCuA1, 104 Gdl _xThxPdIn, 104 GdTiSi, 106 GdxYxSml_xMnzGe2, 140 GdZnSi, 101,162, 163 GeCoGe, 220 HoAgGa, 103 HoAg2In, 115 HoAuGa, 102 HoAu2In2, 115 HoAuzSi2, 127 HoCoAI, 101 HoCo1.96B2, 150 HoCo2Ge2, 128 HoCoSi2, 111, 113 HoCo2Si2, 124, 167 HoCoSn, 102 HoCr2Si2, 123 HoCuA1, 101 HoCu2Ge2, 128 HoCuSi, 101, 104 HoCu2Si2, 125, 168 Ho dihydride, 533 HoFeA1, t01 HoFeSi3, 119 HoFe2Si2, 123, 167 HoIr2Si2, 155, 169 HoMn2Ge2, 141, 142, 144

MATERIALS INDEX HoMnSi, 102, 108 HoMn2Si2, 141,167 HoNiA1, 100 HoNiAI2, 113 HozNizA1, 156 HoNiGa2, 113 Ho2NizGa, 156 HoNizGe2, 128, 137 HoNizP2, 152 HoNiSi, 102 HoNiSi3, 119 HoNizSi2, 124 HoOszSi2, 127, 162, 169 HoPdzGe, 118 HoPdzSi, 118 HoPdzSi2, 127, 169 HoPdSn, 115-117 HoPt2Si2, 153 . HoRh2Ge2, 129 HoRhSi, 103, 109 HoRh2Si2, I26, 130, 136, 166 HozRhSi3, 156 HoRu2Ge2, 129, 137 HoRu2Si2, 126, 131,162 HoZnSi, 101 holmium compounds, 140 hydrides of amorphous alloys,567 hydrides of Gd compounds, 563 hydrides of intermetallic rare-earth compounds, see ternary rare-earth transition metal hydrides hydrides of oxygen-stabilizedcompounds, 566 i-AI-Mn-Si, 472, 476, 496, 502 i-AIMn,478 i-A186Mn14,478 i-A137Mn30Si33,494 i-A173Mn21Si6,478, 480, 481 i-A174Mnz0_xVxSi6,481 i-Pd-U-Si, 475 i-Ti-(Ni,Fe)-Si, 502 lcosahedral AI-Ta-Fe, 490 LaCo2B2, 150 LaCo2Ge2, 128, 148 LaCo2P2, 151,152 LaCuzIn, 114, 115 LaCuSi, 105 LaCuzSi2, 114, 121, 124 LaCuzSn2, 154, 155 LaFezP2, 152 LaFeSi2, 112 LaFezSi2, 151

MATERIALS INDEX LaIrSi, 97, 99, 100 LaIrSi3, 118 LaIr2Si2, 154, 155 LaMn2Ge2, 139, 141,144, 148, 149 LaMnSi, 102, 108 LaMnSi2, 113 LaMnzSi2, 139, 141 La2NizAI, 162 LaNizAs2, 152 LaNiGa2, 113 LazNizGa, 156 LaNizP2, 151,152 LaNiSi, 102 LaNi2Sn2, 151,152 LaOszSi2, 127 LaPtzGe2, 153 LaPtSi, 97, 99 LaPt2Si2, 153 LaRhzGe2, 128 LaRhSi, 99 LaRhSi3, 118 LaRh2Si2, 126 LazRhSi3, 156 LaRu2Ge2, 128 LaRu2Si2, 126 Lal_xYxMn2Si2, 146 lanthanum compounds, 156 LuCo2Ge2, 128 LuCoSn, 102 LuCuA1, 101 LuCu2In, 114, 115 LuFeAI, 101 LuFeSi3, 119 LuMnzGe2, 141 LuMnzSi2, 141 LuNiA1, 100 LuNiAI2, 113 LuzNi2AI, 156 LuNiGa2, 113 Lu2NizGa, 156 LuNiSi, 102 LuNi2Sn, 115, 117 LuOsB2, 112 LuOszSi2, 127 LuRhzSi2, 126 LuRuB2, 112, 113 lutetium compounds, 156 metastable AI-Cu-Mn, 487 Mg32(All-xZnx)49,472 (Mn, Co)B, 188 (Mn, Fe)B, 188 (Mn,Co)zB, 216

(Mn,Fe)2B, 216 MnA112cluster, 462, 465 MnA132cluster, 462, 465 MnAs, 196, 203, 219 MnzAs, 224, 237, 238, 241 Mn(As,P), 219 MnAsl_xPx, 208 Mn2AsxSbl-x, 246 MnB, 187 MnB2, 253, 254 Mn2B, 216 MnBi, 211 Mn(Co,Ni)As, 241 (Mn1_t Cot)zAs, 241 MnCoAs, 238, 250 MnCoGe, 220, 223 Mn(COl_t Nit)Ge, 222 Mn(Col _tNil)Si, 221 (Mnl _t Cot)2P, 235 MnCoR 219, 227, 235,250 MnCo(Pl_xAsx), 245 Mnl _tCotSi, 192 MnCoSi, 219, 220 MnCo(Sil_xGe~), 222 MnCoSn, 220, 224 Mnl tCrtAs, 207 Mnl _tCrtAsl-xPx, 209 Mnl _tCrtP, 202 Mnl _tCrtSb, 212 Mnz_tCrtSb, 246 Mn(Fe,Co)As, 241 Mnl _~FetAs, 208 (Mnl _tFe~)2As, 240 MnFeAs, 238, 241 Mnl4Fe6 cluster, 480 MnFeGe, 220, 223 Mnl _tFetR 203 (Mnl_tFer)zP, 230, 232, 233 MnFeR 227, 233 MnFe(P1_xAsx), 243 Mn3Ge, 265,266 Mn5Ge3, 271,273 Mn5(Gel _xSix)3,273 MnNiAs, 238 MnNiGe, 220, 221,223 Mnl _tNitR 203 MnNiP, 227 MnNiSi, 220, 222 MnNi(SixGel-x), 223 MnE 196, 198, 199, 219 Mn2P, 224, 227, 233 Mn3E 265,269 Mn5PB2, 271,272

649

650 MnRhAs, 219, 249, 251 MnRhP, 249, 250 MnRhSi, 220, 223 MnRuAs, 249, 251 MnRuP, 249, 250 MnS, 213,214 MnS2, 257 MnSb, 210 MnzSb, 245 MnzSbj_xAsx, 248 MnSe, 213 MnSe2, 257 MnSi, 189 MnzSi, 500 Mn3Si, 264, 265 Mn4Si, 503 MnsSi3, 271,273 Mn5(Si,C)3,273 Mn5SiB2, 271,272 Mn5Si3Co.22,273 MnSn2, 255, 275 MnzSn, 275 Mn3Sn, 265 MnsSn3, 271,275 Mnl 1Sn3,275 Mnz_tTtSb (T=Ti, V, Fe, Co or Cu), 248 MnTe, 213,214 MnTe2, 257, 258 Mnl _tTitAs, 208 (Mnl_tTit)NiGe, 221 MnI_tTitSb, 212 NaZnl3 structure compounds, 4 NdAgGa, 103 NdAgzIn, 115, 116 NdAgSi, 101, 107 NdAIGa, 102, 106 NdAuzIn, 115 NdAuzSi2, 127 NdCozB2, 150 NdCozGe2, 128, 129, 131, 133, 134 NdCoSi2, 113 NdCozSi2, 124, 129, 133, 135 NdCo2Sn2, 155 NdCo2X2, 137 NdCuAI, 100 NdCuzIn, 115 NdCuSi, 101 NdCuzSi2, 125, 168 Nd dihydride, 531 NdFeGe, 107 NdFezGez, 128, 135, 166 NdFeSi2, 112, 113

MATERIALS INDEX NdFe2Si2, 123, 162, 167 Nd6Fe13Si, 67 Nd6Fej3Si compounds, 67 NdFellTiNx, 74 NdFe2X2, 137 NdIrSi, 100 NdMn2 2xCr2~Si2,148 NdMnGa, 100 NdMnzGe2, 141,166 NdMnSi2, 112, 113 NdMn2Si2, 139, 140, 167 NdNiAI, 100 NdzNizA1, 156 NdNi2As2, 152 NdNiC2, 113 NdNiGa2, 111, 113 NdNizGa, 156 NdNizGe2, 128 NdNizP2, 152 NdNiSi, 101, 102, 107 NdNizSi2, 124, 167 NdNizSn2, 152 NdNi2X2, 137 NdOszSi2, 127 NdPdzGe2, 118 NdPtSi, 102 NdPtzSi2, 153 NdRh2_exRu2~Si2, 138 NdRhzGe2, 129 NdRhzSi2, 126, 166, 168 NdzRhSi3, 156 NdRuzGe2, 128, 133, 134, 136, 162 NdRuzSi2, 126, 133, 134, 136, 168 NdRu2X2, 137 NdxSml_xMnzGe2, 140 NdZnSi, 101 neodymium compounds, 156 Ni-Cr, 503 Ni-Zr, 503 NiAs, 196 NizB, 216 Nii3 cluster, 467 Ni clusters, 466, 467 Ni5Ge3,275 NiP, 198 Ni2E 227 NiSz_xSex, 259 (Nil-tTt)zB, 218 Np hydride, 536 Pa hydride, 535 Pd60U20Si,503 PrAgGa, 140

MATERIALS INDEX PrAg2In, 115, 116 PrAu2In, 115 PrAu2Si2, 127 PrCo2B2, 150 PrCo2Ge2, 128, 131, 137 PrCo2Si2, 124, 129, 131,133, 137, 166 PrCuA1, 100 PrCu2Ge2, 128 PrCu2In, 115 PrCuSi, 101 PrCu2Si2, 168 PrCu2Sn2, 155 PrCu2X2, 137 Pr dihydride, 530 PrFe2Ge2, 128, 131-133, 137 PrFeSi2, 113 PrFe2Si2, 167 PrMn2Ge2, 139, 141,144 PrMnSi2, 112, 113 PrMn2Si2, 139, 140, 167 PrNiAI, 100 Pr2Ni2AI, 156 PrNi2As2, 152 PrNiGa2, 113 Pr2Ni2Ga, 156 PrNi2P2, 152 PrNiSi, 102 PrNi2Si2, 137, 166, 167 PrOs2Si2, 127 PrPt2Si2, 153 PrRh2Ge2, 129 PrRu2Ge2, 128 PrRu2Si2, 126 PrSn3, 91 praseodymium compounds, 140 Pu hydride, 536 RAgGa, 110 RAg2In, 114, 116, 162, 163 RAIGa, 106 RA12Ge2, 154 RA12Si2, 91,120, 154 RA12X2, 154, 155 RAuGa, 109 RAu2In, 114, 116, 154, 162 RAuNi4, 71 RCoAI, 105 RCo2B2, 148-150 RCo3B2, 54 RCo4B4, 67 RCo12B6, 56 R2Co7B3, 54 R3COllB4, 54

RCo3Ga2, 55 RCo8P5, 68, 69, 75 RCoSi2, 111 RCoSi3, 118 RCo2Si2, 130 RCoSn, 108 RCo2X2, 131,137, 162 RCuA1, 100 RCu2In, 114, 162, 163 RCuSi, 105 RCu2Si2, 157, 170 RCuSn, 107 RCu2Sn2, 154, 155 RCu2X2, 137 RCu0.6Zno.4Si, 163 RCul_xZnxSi, 106, 162 RFeAI, 104, 162, 163 t2Fe14B , 63 R3Fe62B14, 56 RsFe18B18, 66 R2Fel4C , 58, 64 R2Fe17C3_,5, 44, 45, 49 RFel0Cr2, 11 RFel0Mo2, 11 RFeSi2, 112 RFeSi3, 117 RFe2Si2, 137, 160 RFel0Si2, 10 RFe11Ti, 9 RFel 1TiNx, 9 RFel0V2, 10 RFel0.sW1.5, 12 RIrGe, 108 RIr2Si2, 153-155 R6Mn23 compounds, 539 RMnGa, 97 RMn2Ge2, 139, 141-145 RMnSi2, 112 RMn2Si2, 139, 141 RMn2X2, 139, 144, 146 RNiAI, 100 RNiA12, 111, 114 RNi2As2, 151 R3Ni7B2 compounds, 54, 55 RNiGa2, 111, 114 RNi2P2, 151 RNiSb, 99 RNiSi, 109 RNiSi2, 118 RNi2Si2, 137 RNi2Sn, 114 RNi2Sn2, 151 R2Ni2X, 157

651

652

MATERIALS INDEX

ROs2Si2, 130, 137 RPd2Ge , 117, 118 RPd2Si , 117, 118 RPd2Si2, 137 RPdzSn, 114, 116, 171 RPdzX, 117 RPtGe, 108 RPtSi, 108 RPt2Si2, 152, 153 RRh2As2, 151 RRh2Oe2, 135 RRh2P2, 151 RRhSi, 89, 109 RRhSi2, 89 RRh2Si2, 89, 129, 130, 135, 157, 158, 162 RRh3Si2, 89 R2RhSi3, 89, 155 RzRh3Si5, 89 R5Rh4Silo, 89 RRhzX2, 137 RRuB2, 111 RRuzSi2, 129, 131,157, 158 RSi2, 156 RTAI, 104 RTB2, 112 RT4B, 50 RT12B6, 56, 57 RI+eT4B4, 65 RzT23B3, 57 RTC2, 113 RzT14C , 58 R2T17C3_ & 43 R6T11Ga3, 67 RT2_xGex, 106 RT2Ge2, 91,128 RT2P2, 151 R2T12P7, 69 RTSi, 99 RTSi3, 118 RT2_xSix, 106 RT2Si2, 91, 114, 126, 167 RT9Si2, 41 RT10SiC0.5, 42 RT6Sn6, 64 RTX2, 110 RTX3, 117, 119 RT2X, 114, 115, 171 RT2X2, 7, 9, 34-37, 51, 64, 68, 75, 77, 78, 81, 82, 89, 105 RTX compounds, 97-100, 105, 108 rare-earth alloys, 333, 354 rare-earth compounds, I56 rare-earth dihydrides, 524 rare-earth trihydrides, 524

rare-earth-transition-metal alloys, 305, 310, 317, 339, 390, 405, 422 rare-earth-transition-metal (R-T) amorphous alloys, 310 samarium compounds, 89 ScB2, 253 Sc13 cluster, 459 Sm-Fe amorphous alloys, 320 SmAg2In, 115 SmAu2In, 121 SmAu2Si2, 127 SmCo2B2, 149, 150 SmCo2Ge2, 128 SmCoSi2, 113 SmCu2In, 115 SmCuSi, 105 SmCu2Si2, 125 SmCu2Sn2, 154, 155 Sm dihydride, 532 SmFeGe, 102 Sm2Fel7N3_6, 74 Sml_xGdxMn2Ge2, 142 SmGeSi, 101 SmMn2Ge2, 139-142 SmMn2Si2, 141 Sm2Ni2A1, 156 SmNi2As 2, 152 SmNiGa2, 113 SmNi2P2, 151,152 SmNiSi, 102 SmNiSi2, 113 SmNi2Sn2, 152 SmOs2Si2, 127 SmPtSi, 102 SmPt2Si2, 153 SmRh2Ge2, 129 SmRh2Si2, 126 SmRu2Ge2, 128 SmRu2Si2, 126 SmS, 91 sputtered amorphous thin films, 375 T-Ni-Si (T=V, Cr or Mn), 503 TbAgGa, 103 TbAg2In, 115 TbAIGa, 102, 106 TbAuGa, 102 TbAu2 In, 115 TbAu2Si2, 127 TbCoAI, 101 TbCol.8B2, 150 TbCol.92B2, 150 TbCo2Ge2, 128

MATERIALS INDEX TbCoSi2, 111-113 TbCoSi3, 119 TbCo2Si2, 124, 167 TbCoSn, 102 TbCrzSi2, 123 TbCuA1, 101 YbCu2Ge2, 128 TbCuzIn, 115 TbCuSi, 101, 105 TbCuzSi2, 125, 168 Tb dihydride, 532 TbFeAI, 101 TbFezGe2, 128 TbFeSi2, 110, 112, 113 TbFeSi3, 119 TbFe2Si2, 123, 167 TbIr2Si2, 137, 154, 155, 169 TbMn2, 98 TbMnA1, 98, 100 TbMn2Ge2, 141,142, 144, 146 TbMn2Si2, 141, 143, 144, 146, 167 TbMn2X2, 137 TbNiA1, 100 TbNiAI2, 113 Tb2NizAI, 156 TbNiGa, 103, 110 TbNiGa2, J:13 TbzNizGa, 156 TbNizGe2, 128 TbNizP2, 152 TbNiSi, 102 TbNiSi3, 119 TbNizSi2, 124, 134, 137, 167 TbOszSi2, 127, 162, 169 TbPdzGe, 118 TbPdzGe2, 129, 137 TbPd2Si, 117, 118 TbPd2Si2, 127, 169 TbPdzSn, 115 TbPtzSi2, 153 TbRhGe, 103, 109 TbRhzGe2, 129, 162 TbRhz_xIrxSi2, 138 TbRhRuSi2, 103 TbRh2_xRuxSi2, 138 TbRhSi, 103, 109 TbRhSi3, 119 TbRh2Si2, 123, 126, 129, 130, 138, 161,166, 168 Tb2RhSi3, 156 TbRhz_xTxSi2, 138 TbRuB2, 112, 113 TbRu2Ge2, 128, 137, 162 TbRuzSi2, 126, 131, 137, 162, 168 TbTzX2, 160

653

TbZnSi, 101 terbium compounds, 156 ternary actinide-transition metal hydrides - ThFes, 544 - U-Co compounds, 560 ternary rare-earth-transition metal hydrides, 537 - Co compounds, 554 Fe compounds, 541 - Mn compounds, 537 Ni compounds, 561 RCo 2 compounds, 560 - RCo3 compounds, 559 - RCo5 compounds, 554 - RzCo 7 compounds, 558, 560 R2Fel4B compounds, 542 RFe2 compounds, 550 RFe 3 compounds, 549 RFel2 compounds, 541 - R2Fe compounds, 553 RzFel7 compounds, 541 - R3Fe compounds, 553 R6Fe23 compounds, 548 - R7Fe 3 compounds, 554 RMn2 compounds, 540 RNi3 compounds, 562 RNi 5 compounds, 560 RzNi compounds, 562 RzNi 7 compounds, 562 RvNi3 compounds, 563 Th dihydride, 535 ThMn12 structure compounds, 6 Th2Nil7 structure compounds, 42 ThzZnl7 structure compounds, 42 thulium compounds, 156 (Ti,Cr)As, 206 (Ti,Fe)zB , 216 Ti-(Ni,Fe)-Si, 502, 503 TiB2, 253 TizFe , 503 Ti2Ni , 501 TizNi0.85Fe0.15,502 Ti56Ni25.5Fe2.5Sil6, 502 Ti56Niz8~FexSi16, 502 TiNiGe, 221 Ti56Ni28Si16, 501 TiE 198 (YiV)2,503 Ti2_xVxNi, 501 TmAgGa, 102 TmAg2In, 115 TmAuGa, 102 TmAuzIn, 115 TmCoSi2, 113 TmCo2Si2, 124, 167 -

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-

-

-

-

-

-

-

-

-

-

-

654

MATERIALS INDEX

TmCoSn, 102 TmCr2Si2, 123 TmCuA1, 101 TmCu2Ge2, 128 TmCuSi, 101,105 TmCuzSi2, 125, 137, 166, 168 Tm dihydride, 533 TmFeA1, 101 TmFeSi3, 119 TmFe2Si2, 166, 167 TmIrzSi2, 169 Tml-xLuxRuB2, 112, 114 TmMn2Ge2, 141 TmMn2Si2, 141, 166 TmNiA1, 100 TmNiA12, 113 Tm2Ni2A1, 156 TmNiC2, 113 TmNiGa2, 112 Tm2Ni2Ga, 156 TmNi2P2, 152 TmNiSi, 102 TmNiSi3, 119 TmNi2Si2, 124, 137, 168 TmOs2Si2, 127, 169 TmPd2Ge , 118 TmPd2Si2, 169 TmPd2Sn, 115 TmRh2Si2, 126, 168, 170 TmRuB2, 113 TmRu2Ge2, 128 TmRu2Si2, 126, 168 TmSe, 91 transition-metal alloys, 349 transition-metal-base alloys, 320 transition-metal clusters, 461,466 transition-metal glass, 467 transition-metal hydrides, 537 transition-metal-metalloid alloys, 305,307, 309, 315,322, 331,380, 386 U hydride, 536 (V,Co)2B, 216 (V,Cr)As, 206 (V,Fe)2B, 216 VB2,253 V l_tCrtB2, 254 VI tCrtSe, 214 VMnAs, 240 (V or Cr)-Ni-Si, 503 VP, 202 YAu2In, 115

YCo2B2, 150 YCozGe2, 128 YCo2Si2, 124 YCoSn, 109 YCuSi,.105 YFeAI, 101 Y2FelTCx, 44 YFeSi3, 119 YLaPtzSiz, 152 YMnzGe2, 139, 141,148, 149 YMnSi, 102 YMnzSi2, 139, 141 YMnzSiz_zrGe2x, 139 YNiAI2, 113 YzNizA1, 156 Y2NizGa, 156 YNiGe2, 113 YNiSi, 102 YNiSi3, 119 YOsB2, 112 YOs2Si2, 127 YPt2Si2, 153 YRh2Ge2, 128 YRh2Si2, 126 YRuB2, 112 YRu2Si2, 126 Y2RuSi3, 156 YZnSi, 106 YbAgGa, 110 YbAuGa, 110 YbCo2Ge2, 128 YbCuA1, 101 YbCuGa, 110 Yb dihydride, 533 YbMn2Ge2, 141 YbMn2Si2, 141,167 Yb2Ni2AI, 156 Yb2Ni2Ga, 156 YbNi2P2, 152 YbNiSi, 102 YbNi2Si2, 167 YbOs2Si2, 127 YbPdBi, 100 YbPd2Ge2, 127 YbPdSn, 100 YbPdX, 99 YbPt2Si2, 153 YbTGa, 110 YbT2X2, 91 ytterbium compounds, 156 yttrium compounds, 156