The Physical Principles of Magnetism

An IEEE Press Classic Reissue

THE PHYSICAL PRINCIPLES OF MAGNETISM

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An IEEE Press Classic Reissue

THE PHYSICAL PRINCIPLES OF MAGNETISM

Allan H. Morrish DepartmentofPhysicsandAstronomy University ofManitoba, Canada

IEEE Magnetics Society, Sponsor

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IEEE PRESS

The Institute of Electrical and Electronics Engineers, NewYork

This book and other books may be purchasedat a discount from the publisher when ordered in bulk quantities. Contact: IEEE Press Marketing Attn: Special Sales 445 Hoes Lane, ~O. Box 1331 Piscataway, NJ 08855-1331 Fax: + 1 732 981 9334 For more informationabout IEEE Press products, visit the IEEE Online Catalog & Store: http://www.ieee.org/store. Original edition in 1965,published by John Wiley & Sons, Inc. Reprinted in 1980byRobertE. KriegerPublishingCompany, Inc. © 2001 by The Instituteof Electrical and ElectronicsEngineers, Inc.

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ISBN O·7803·6029·X IEEE Order No. PCS877 Library of Congress Cataloglng-m-Publication Data

Morrish,Allan H. The physical principlesof magnetism I Allan H. Morrish. p.cm. Originally published: NewYork: Wiley, 1965,in series: Wiley series on the science and technology of materials. "An IEEE Press classic reissue." "IEEE order no. PC5877"--T.p. verso. Includes bibliographical referencesand indexes. ISBN 0-7803-6029-X 1. Magnetism. I. Title. QC753.2 .M67 2001 538--dc21

00-053912

To My Parents

Foreword to the Classic Reissue

The IEEEMagneticsSocietyhas embarkedon a programof reissues of classic works in magnetism. These bookshaveservedas an invaluable resource for understanding magneticphenomena. The Physical Principles ofMagnetism by Allan Henry Monish is such a classic-a comprehensive introduction to all aspects of magnetism. Since its publication in 1965,it has been used by many scientiststo learn the basicsof magnetismin considerabledepth. The corrected reissue is a welcomeaddition to this much-needed archivalseries. Dr. Morrishpresentsan excellentintroduction to the physics and mathematics of magnetismwithoutoversimplification. Althoughgreatprogress has been made in technology in the 35 years since it first appeared in print, the basic principles of magnetism are unchanged. This respected and timeless classic book clearly elucidatesthese principles. Dr. Morrish is a distinguished professor of physics at the University of Manitoba. He is a fellowof The RoyalSociety of Canada and The Institute of Physics (U.K.), as well as a former fellow of The American Physical Society. Also, he was president of The Canadian Association of Physicists and was awardedtheir goldmedalfor achievements in physics.A prolificresearcher,Dr. Morrish has written over 250 papers and served on many national and international committees. It is with great pleasure that we welcomethis book back in print. Edward Della Torre The George Washington University President ofthe IEEEMagnetics Society

Preface

Whatever else may be said concerning. the two decades following World War II, they have been wonderful years for science. All of the scientific countries of the world have contributed to the great increase in knowledge. Although advances have been made in almost all areas, some have been favored over others. One of the subjects that has received the greatest attention is that of magnetism. Although the appearance of a vast amount of literature is in itself laudable, it has created educational problems. The scientist or engineer who desires or requires an integrated knowledge of magnetism has found it increasingly difficult to satisfy this need. This book was written with such readers primarily in mind. The material between these covers has formed the basis for several solid state courses offered at the University of Minnesota since 1958. Some of the more elementary parts have been employed for the third quarter of a first course in solid state physics. However, the major use of this text has been as a three-quarter graduate cours.e in magnetism. The students attending the lectures have come from chemistry, physics, electrical engineering, physical metallurgy, and geophysics departments. Since the backgrounds of the audience varied so much, the course was developed by starting as far as possible from first principles. However, it was necessary to begin somewhere, and consequently first courses in solid state physics and quantum mechanics were usually assumed as prerequisites. Magnetic phenomena are discussed both from an experimental and theoretical point of view. The plan has been first to present the underlying physical principles and then to follow up with appropriate macroscopic or microscopic theories. Although quantum mechanical theories are given, a phenomenological approach is emphasized. More than half the 'ii

viii

PREFACE

book is devoted to a discussion of strongly coupled dipole systems, and in this area the molecular field theory is stressed. The principles and theories have been illustrated by selections from the experimental data, and various tables have been included in an attempt to give some idea of the scope of the literature. Very few references to 1964 papers are included because of publication deadlines. The utter impossibility of completely surveying all aspects of the subject may be illustrated by considering the 1964 Magnetic Materials Digest." This publication, which attempts to summarize the 1963 literature pertaining to fundamental studies of ordered magnetic materials, contains more than 1700 references! The particular topics chosen to be discussed at greatest length in this book were determined, as it is usually put, by my own interests. This, of course, really means my own knowledge, experience, talents, and limitations as shaped by contact with colleagues, teaching assignments, and availability of research and travel grants. The coverage of some topics, for example alloys and superconductivity, inadequately reflects the number and extent of current investigations. Other topics, for example, magnetohydrodynamics, group theoretical analysis, and the magnetoelectric effect, have been completely omitted. Nevertheless, the book is rather long and indeed contains more material than can normally be covered in a one-year course. The question of notation has been a vexing problem. In a book as comprehensive as this one, there are simply not enough symbols to go around. A partial solution has been sought in the use of different kinds of type for the same letter. For example, ~ and p, represent the dipole magnetic moment and the permeability, Hand Je represent the magnetic field and Hamiltonian, and D, ~, and 1) represent the demagnetizing factor, the crystal field spin parameter, and the Dzialoshinski vector, respectively. Even so, it was found necessary sometimes to employ the same symbol for more than one quantity; it is only hoped that the context will reduce, if not entirely remove, the danger of ambiguity. Although in general I have tried to adhere to the symbols commonly found in the literature, some deliberate departures have been made. In publications on nuclear magnetic resonance, and to some degree in electron paramagnetic resonance, T with some subscript denotes relaxation time. However, I prefer to reserve T for either temperature or period of time and have therefore taken the liberty of representing relaxation times by T plus a subscript; this usage at least has the merit of being consistent with that in all other branches of science and engineering. Other, though less important examples, include the use of M H for the magnetization 1 A. H. Morrish, R. J. Prosen, and S. M. Rubens, editors, 1964 Magnetic Materials Digest, M. W. Lads Publishing Co., Philadelphia, Pa. (1964).

PREFACE

ix

along the direction of an applied field, HI for the amplitude of an alternating magnetic field, H, for the effective magnetic field, H", for the molecular field, J, for an exchange interaction constant, TFN for the Neel temperature of a ferrimagnet, and N with some subscript for the Weiss molecular field constants. For the Bohr magneton a choice between ~B and fJ was possible; I have selected ILB mainly because fJ also represents an angle or the relativistic quantity ole. I have substituted the term "uncompensated poles" for "free poles," since the latter may be taken to imply the existence of monopoles, and they have never been observed in nature. The phrase "intensity of magnetization," common in the British literature, has been eliminated on the grounds that it is both inappropriate and inept. The symbol e for the elementary electric charge represents either type; that is, a negative number is to be substituted for an electron and a positive number for a proton or positron. Except as otherwise noted, the gaussian cgs system of units is employed. There remains the pleasant task of thanking those who have played some role in the production of this book. I am very grateful to Professor A. J. Dekker, now at Groningen, The Netherlands, who first interested me in doing research in solid state physics and who encouraged me to write this book. I have been fortunate in having Professor W. F. Brown, Jr., as a colleague during part of my tenure at the University of Minnesota. The discussions we have had have left their imprint on a number of these pages. In addition, a critical reading of the first chapter by Dr. Brown has led to its improvement. The response and comments of my graduate students have greatly aided me in the removal of errors, inconsistencies, and obscurities. They have also demonstrated that almost all the problems are soluble. I am indebted to the many publishers and individuals who have given me permission to reproduce figures and tables; these sources are acknowledged at the pertinent places in the text. Finally, I wish to thank my wife for her help with the arduous tasks of proofreading and index preparation.

University of Manitoba Winnipeg, Canada April 1965

ALLAN

H. MORRISH

Contents

1. The Magnetic Field

1

1. Historical The Magnetic field Vector H The Magnetization Vector M Magnetic Induction, the Vector B The Demagnetization Factor 0 6. Energy of Interaction 7. Magnetic Effects ofCurrents. The Magnetic Shell. Faraday's Law 8. Maxwell's and Lorentz's Equations 9. The Magnetic Circuit 10. Dipole in a Uniform Field

2. 3. 4. 5.

2. Diamagnetic and Paramagnetic Susceptibilities 1. Introduction 2. Review of Quantum Mechanical and Other Results

1

1 3 6 8 11 15 22 25 27

31 31 32

38

Diamagnetism 3. The Langevin Formula for Diamagnetic Susceptibility 4. Susceptibility of Atoms and Ions 5. Susceptibility of Molecules

38 39 42

Paramagnetism

46

6. 7. 8. 9. 10.

46 47 51 54 57

Curie's Law Theoretical Derivations of Curie's Law Quantum Mechanical Treatment Susceptibility of Quasi-free Ions: the Rare Earths The Effect of the Crystalline Field xi

CONTENTS

xii

11. The Iron Group Salts Covalent Binding and the 3d, 4d, Sd. and Sf-6d Transition Groups 13. Saturation in Paramagnetic Substances 14. Paramagnetic Molecules 15. Paramagnetic Susceptibility of the Nucleus

63

12.

68 70 73 7S

3. Thermal, Relaxation, and Resonance Phenomena in Paramagnetic Materials 1.

Introduction

Dermal Phenomena 2. Summary of Thermodynamic Relationships 3. The Magnetocaloric Effect: The Production and Measurement of Low Temperatures

Paramagnetic Relaxation

4. The Susceptibility in an Alternating Magnetic Field S. Spin-Lattice Relaxation

78 78

79 79 83

87 87

6. Spin-spin Relaxation

90 101

Paramagnetic Resonaaee

106

7. Conditions for Paramagnetic Resonance 8. Line Widths: the Effect of Damping 9. Fine and Hyperfine Structure: the Spin-Hamiltonian 10. The Spectra of the Transition Group Ions The 3d group ions Covalent binding and the 3d, 4d, Sd, and Sf-6d groups 4f rare earth ions in salts Transition ions in various host lattices 11. The Spectra of Paramagnetic Molecules and Other Systems Paramagnetic gases Free radicals Donors and acceptors in semiconductors Traps, F-centers, etc. Defects from radiation damage 12. The Three-Level Maser and Laser

4. Nuclear Magnetic Resonance 1. Introduction Line Shapes and Widths 3. Resonance in Nonmetallic Solids 4. The Influence of Nuclear Motion on Line Widths and Relaxations The Chemical Shift: Fine Structure 6. Transient Effects: the Spin-Echo Method 2.

s.

106

111

119 127 128

130 130 132

133

133

134 138 140 141 142

149 149 158

161 164 170

171

CONTENTS

7. Negative Temperatures 8. Quadrupole Effects and Resonance 9. Nuclear Orientation

10. Double Resonance 11. Beam Methods

5. The Magnetic Properties of an Electron Gas

xiii

177 181 183

18S

186

194

1. Statistical and Thermodynamic Functions for an Electron Gas

2. The Spin Paramagnetism of the Electron Gas 3. The Diamagnetism of the Electron Gas 4.

Comparison of Susceptibility Theory with Experiment

S. The De Haas-Van Alphen Effect

6. Galvanomagnetic, Thermomagnetic, and Magnetoacoustic 7. 8. 9. 10.

Effects Electron Spin Resonance in Metals Cyclotron Resonance Nuclear Magnetic Resonance in Metals Some Magnetic Properties of Superconductors

194 204 211 220 224 228 231 232 238 240

6. Ferromagnetism

259

1. Introduction

259

2. The Classical Molecular Field Theory and Comparison with

3.

4.

s,

6.

7. 8. 9. 10.

Experiment The spontaneous magnetization region The paramagnetic region Thermal effects The Exchange Interaction The Series Expansion Method The Bethe..Peierls-Weiss Method Spin Waves Band Model Theories of Ferromagnetism Ferromagnetic Metals and Alloys Crystalline Anisotropy Magnetoelastic Effects

7. The Magnetization of Ferromagnetic Materials 1. Introduction 2. Single-Domain Particles Critical size Hysteresis loops Incoherent rotations Some experimental results Other effects

261 262 268 270 275 284 287 292 300

307 310 321

332 332 340 340 344

3S4

356 359

xiv

CONTENTS

3. Superparamagnetic Particles

360

4. Permanent Magnet Materials 5. Domain Walls

363

6. Domain Structure 7. The Analysis of the Magnetization Curves of Bulk Material Domain wall movements Coercive force Initial permeability Picture frame specimens The approach to saturation Remanence Nucleation of domains: whiskers Barkhausen effect Preisach-type models External stresses Minor hysteresis loops 8. Thermal Effects Associated with the Hysteresis Loop 9. Soft Magnetic Materials 10. Time Effects 11. Thin Films

8. Antiferromagnetism 1. Introduction 2. Neutron Diffraction Studies 3. Molecular Field Theory of Antiferromagnetism Behavior above the Neel temperature The Neel temperature Susceptibility below the Nee} temperature Sublattice arrangements The paramagnetic-antiferromagnetic transition in the presence of an applied magnetic field Thermal effects 4. Some Experimental Results for Antiferromagnetic Compounds 5. The Indirect Exchange Interaction 6. More Advanced Theories of Antiferromagnetism The series expansion method The Bethe-Peierls-Weiss method Spin waves 7. Crystalline Anisotropy: Spin Flopping 8. Metals and Alloys 9. Canted Spin Arrangements 10. Domains in Antiferromagnetic Materials 11. Interfacial Exchange Anisotropy

367 374 382 383 385 392 393 394 395 396

398 399 400

403 404 407 411 416

432 432 433 447 448 449

450 454

457 458 459

464 467 467 468 469 470 476 479 481 483

CONTENTS

9. Ferrimagnetism 1. Introduction 2. The Molecular Field Theory of Ferrimagnetisrn Paramagnetic region The ferrimagnetic Neel temperature Spontaneous magnetization Extension to include additional molecular fields Triangular and other spin arrangements Three sublattice systems Ferromagnetic interaction between sublattices 3. Spinels 4. Garnets 5. Other Ferrimagnetic Materials 6. Some Quantum Mechanical Results 7. Soft Ferrimagnetic Materials 8. Some Topics in Geophysics

10. Resonance iii Strongly Coupled Dipole Systems I. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11.

12. 13.

14. 15.

16.

Introduction Magnetomechanical Effects Ferromagnetic Resonance Energy Formulation of the Equations of Motion Resonance in Ferromagnetic Metals and Alloys Ferromagnetic Resonance of Poor Conductors Magnetostatic Modes Relaxation Processes Relaxation via spin waves in insulators Relaxation via spin waves in conductors Fast relaxation via paramagnetic ions Slow relaxation via electron redistribution Nonlinear Effects Spin-Wave Spectra of Thin Films Electromagnetic Wave Propagation in Gyromagnetic Media Resonance in Unsaturated Samples Ferrimagnetic Resonance Antiferromagnetic Resonance Nuclear Magnetic Resonance in Ordered Magnetic Materials The Mossbauer Effect

xv

486 486 490 491 494 494 498 499 500 501 503 511

521 526 529 532

539 539

5"39 S42 551

556 559 563

568 569 574 574 577 578

588 593 599 607 616 624 629

Appendix I. Systems of Units

641

Appendix II. Demagnetization Factors for Ellipsoids of Revolution Appendix III. Periodic Table of the Elements

645 646

Appendix IV. Numerical Values for Some Important Physical Constants Author Index Subject Index

649 651 671