Table Of ContentAmorphous
Magnetism
Takahito Kaneyoshi, D.Sc.
Department of Physics
Nagoya University
Nagoya, Japan
Boca Raton London New York
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Kaneyoshi, Takahito, 1940-
Amorphous magnetism
Bibliography: p.
Includes index.
1. Amorphous substances—Magnetic properties.
I. Title.
QC766.A4K36 1984 538 83-3740
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PREFACE
I first started to think about topologically disordered magnetic materials (or amorphous
magnets) in 1969, when I read two pioneer papers written by A. I. GubanovandR. Hasegawa.
At the time our understanding of the properties of amorphous magnets was distinctly limited.
In fact, it was in 1967 that a topologically disordered ferromagnetic alloy was first made
by Duwez and Lin directly from a liquid state by means of a rapid-quenched technique. As
early as 1960 Gubanov had first developed a theory to treat the question of whether or not
ferromagnetism exists in amorphous solids.
In recent years there have been many important advances in the understanding of amor-
phous magnets. Magnetically ordered solids exhibit a wide range of interesting new phe-
nomena involving the nature of magnetic ordering and the dynamical interaction between
elementary excitations of the system, in contrast with those of crystalline magnetic systems.
The present monograph is addressed to a microscopic treatment of these new phenomena
in amorphous magnets with emphasis on the underlying interaction mechanisms and various
magnetic effects associated with topologically disordered structure. From this point of view
it differs distinctly from the existing texts. This new field is extremely rich in possibilities,
both for theorists and experimentalists, and the rapid expansion still continues.
In this book, I attempt to present some of the methods used in the theory of amorphous
magnetism, from a single standpoint that amorphous magnets have a topologically disordered
structure of the type given by the dense random packing of hard spheres. The primary aim
is to show systematically the present theoretical apparatus in a form which would allow the
reader to use it in investigations of still unsolved problems. Even within these limits, the
theory of amorphous magnetism is now a very large subject. It is not designed to review
all of the recent developments in this rapidly developing area. This monograph is, however,
primarily intended for the novice in this new field, rather than the specialist. I have spe-
cifically tried to keep in mind the needs of the graduate student and of the experienced
physicist and metallurgist who are looking into the field of amorphous magnetism for the
first time. I have tried to keep the discussions at such a level that they are at least familiar
with elementary quantum theory of magnetism. For the general reader who wants no more
than a quick bird's-eye view of this subject, suggested reading is Chapter 2 which I con-
tributed to Glassy Metals: Magnetic, Chemical, and Structural Properties (CRC Press, 1983).
The first part of Amorphous Magnetism begins with a brief introduction in which the basic
topics and definitions of the physics of amorphous magnetism are presented. In Chapter 2
the atomic structure of amorphous magnets is described. This is useful in understanding the
magnetic properties in amorphous magnets, which is the main theme of this book. In Chapters
2 to 5 the emphasis is on the magnetic properties of amorphous transition metal-metalloid
alloys, and Chapter 6 is concerned with those of amorphous rare earth alloys. However,
each of the six chapters is written as a more or less continuous narrative.
This book is an outcome of two lectures given at Bussei Wakate Summer School in 1977
and at Universidade Federal de Pernambuco in 1979. I am very grateful to Professor I. P.
Fittipaldi and his colleagues in Departamento de Fisica of Universidade Federal de Pernam-
buco for their contributions in making my visits beneficial and pleasurable. I owe a deep
debt of gratitude to Professor T. Matsubara, who first directed my attention to disordered
systems. I am indebted to Mr. B. J. Starkoff, President of CRC Press, for his interest in
the present book and also to the staff for their assistance in so many ways.
T. Kaneyoshi
THE AUTHOR
Takahito Kaneyoshi, M.Sc., D.Sc. has been Research Associate in Department of Phys-
ics, Nagoya University since 1968.
He received his B.S. degree from Waseda University in 1963, his M.Sc. in 1965 and his
D. Sc. in 1969 from Kyoto University. He was also twice a visiting professor at Universidade
Federal de Pernambuco, and a guest scientist at Universitat Duisburg Gesamthochschule.
He is author of over 60 papers and has contributed a chapter to the book, Glassy Metals:
Magnetic, Chemical, and Structural Properties. His areas of research interest include physics
of disordered condensed matters, especially for amorphous magnetism, amorphous semi-
conductors, and liquid metals, and statistical mechanics.
Dr. Kaneyoshi is a member of Physical Society of Japan, and of Applied Magnetic Society
of Japan.
To my parents,
Chukichi and Ine
TABLE OF CONTENTS
Chapter 1
Introduction
1.1 General Information and Definitions 1
Ferromagnets 1
Ferrimagnets 3
Canted (Noncollinear Ferrimagnets) 4
1.2 Spin Hamiltonians and Exchange Interactions 5
Exchange Interactions 6
Chapter 2
The Structure
2.1 Statistical Description of the Structure 11
Mixtures 18
2.2 The Structure of Amorphous Magnets 19
2.3 Structural Model 22
Chapter 3
Effective Field Theories
3.1 The Weiss Molecular Field 27
Random Configuration Average 29
3.2 Effective Field Theories of Amorphous Magnets 30
Amorphous Ferromagnets 30
A Unified Effective Field Theory 35
Handrich-Kaneyoshi Approximation 36
Gauss Approximation 36
3.3 Quasiclassical Method and Critical Concentration 38
Critical Concentration 43
3.4 Spin-Glass Phase 44
Replica Method 46
3.5 Effective Field Theory of Amorphous Antiferromagnets 50
3.6 Inelastic Scattering of Neutrons in the Spin-Glass Phase 54
3.7 Analyses of Experimental Results 59
Saturation Magnetization 59
Curie Temperature 61
Mixtures 62
Reduced Magnetization Curves 68
Critical Concentration 69
Spin-Glass Phase 71
Paramagnetic Curie Temperature 73
Amorphous Ferrimagnets 74
Chapter 4
Elementary Excitations
4.1 Green Function Method 79
4.2 Spin Waves at Low Temperatures 83
Diluted Ferromagnets 91
4.3 Spin Waves at Finite Temperatures 95
4.4 Computer Experiments 100
Krey's Method 100
Alben's Method 103
4.5 Inelastic Scattering of Neutrons 105
Chapter 5
Nonuniform Distribution of Local Fields
5.1 Mbssbauer Experiments Ill
5.2 Theoretical Attempts 120
5.3 Discussion on the Existence of Amorphous Antiferromagnets 126
5.4 Critical Phenomena 131
Landau Theory 133
Analyses of Critical Exponents 136
Inverse Paramagnetic Susceptibility and Arrott Plots 138
5.5 Ferromagnetism and Resistivity Minimum 146
Kondo-Type Effect 147
Structural Effect 148
Chapter 6
Random Magnetic Anisotropy
6.1 Origin of Random Magnetic Anisotropy 153
Crystal Field in the R.C.P. of Atomic Spheres 155
6.2 Coercivity and the Ground State 157
6.3 Molecular Field Theories 159
The Classical Calculation 160
Coercivity 162
Quantum Mechanical Calculations 164
Analysis of a Sperimagnet 167
6.4 Spin Waves 164
References 175
Index 183
1
Chapter 1
INTRODUCTION
There is now a rich variety of amorphous magnetic materials that exhibit spontaneous
long-range ordering of localized magnetic moments below a critical temperature which is
characteristic for each substance. Although crystalline magnetic systems are in general
classified in four categories according to the nature of its long-range order (or ferromagnetic,
antiferromagnetic, ferrimagnetic, and helimagnetic systems), a number of amorphous mag-
nets with new-type spin ordering not classified by those of crystalline systems have been
found, because of its topologically disordered nature. The topological disorder is at the heart
of the special aspects of amorphous magnets. The key to the difference between crystalline
and noncrystalline solids is that no two atomic sites are equivalent in amorphous substances,
whereas all macroscopic directions may be equivalent in the bulk. In this monograph, the
theoretical aspects of amorphous magnetism are discussed from a view point that amorphous
magnets have a topologically disordered structure of the type given by the dense random
packing of hard spheres (D.R.P.H.S.) The D.R.P.H.S. state can be studied on the mac-
roscopic scale; namely by pouring a lot of rigid ball bearings into a container and shaking
them together until they can not be compressed further. The structural aspects will be
discussed in next chapter.
At first we should note that*'amorphous" and "disordered" do not mean the same thing.
"Amorphous" refers to the lack of a crystalline lattice, which implies that amorphous
magnets are disordered. But not all disordered magnets are amorphous. There are also
disordered crystalline alloys. For example, in a random solid solution of magnetic elements,
the atomic positions are fixed by the crystal structure but the magnitude of the localized
magnetic moment varies in an aperiodic random fashion. A spin glass is a dilute solution
of a magnetic element in a nonmagnetic host crystal, in which the atomic positions are fixed
but the spin distribution is random. The spin system of solid solution compounds is periodic
in magnitude and spacing, but may be aperiodic in the strength of the exchange interaction.
For comparison, a classification of disorder in magnetic systems is shown in Table 1.1.
Thus, amorphous magnets constitute a class of systems with the highest level of disorder.
The main concern of this monograph is to clarify the physical properties of this most
disordered case.
In amorphous magnetic materials, although the long-range order for the distribution of
magnetic atoms does not exist, a magnetic long-range order is possible, since its magnetism
is determined by exchange interactions between neighboring atoms and also randomly dis-
tributed local magnetic anisotropies. Accordingly, these magnetic systems have been mainly
classified into three categories according to the nature of long-range order.1 In this chapter,
we present general information and definitions about the natures of these three categories.
1.1 GENERAL INFORMATION AND DEFINITIONS
In this section, we shall adumbrate some important physical properties of the three cat-
egories given by Figure 1.1.
Ferromagnets
In an amorphous ferromagnet the spins are all oriented in the same direction but the
topological arrangement of spins is not regular. Some typical examples of amorphous fer-
romagnetic materials are transition metal-metalloid alloys, Fe _ B _, (Fe^i^JgoB^P^,
80 x 20 x
etc. Below the critical (Curie) temperature Tc, all the spins are, on the average, oriented
parallel to one another, giving rise t€> a large spontaneous magnetization of the sample in
