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`INTRODUCTION TO
`MAGNETIC MATERIALS
`
`Second Edition
`
`B. D. CULLITY
`University of Notre Dame
`
`C. D. GRAHAM
`University of Pennsylvania
`
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`INTRODUCTION TO
`MAGNETIC MATERIALS
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`IEEE Press
`445 Hoes Lane
`Piscataway, NJ 08854
`
`IEEE Press Editorial Board
`Lajos Hanzo, Editor in Chief
`
`R. Abari
`J. Anderson
`S. Basu
`A. Chatterjee
`
`T. Chen
`T. G. Croda
`S. Farshchi
`B. M. Hammerli
`
`O. Malik
`S. Nahavandi
`M. S. Newman
`W. Reeve
`
`Kenneth Moore, Director of IEEE Book and Information Services (BIS)
`Steve Welch, Acquisitions Editor
`Jeanne Audino, Project Editor
`
`IEEE Magnetics Society, Sponsor
`IEEE Magnetics Society Liaisons to IEEE Press, Liesl Folks and John T. Scott
`
`Technical Reviewers
`Stanley H. Charap, Emeritus Professor, Carnegie Mellon University
`John T. Scott, American Institute of Physics, Retired
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`INTRODUCTION TO
`MAGNETIC MATERIALS
`
`Second Edition
`
`B. D. CULLITY
`University of Notre Dame
`
`C. D. GRAHAM
`University of Pennsylvania
`
`Ex.1019 / IPR2022-00117 / Page 6 of 565
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`Copyright # 2009 by the Institute of Electrical and Electronics Engineers, Inc.
`
`Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.
`Published simultaneously in Canada
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`No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any
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`Library of Congress Cataloging-in-Publication Data is available:
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`ISBN 978-0-471-47741-9
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`Printed in the United States of America
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`CONTENTS
`
`PREFACE TO THE FIRST EDITION
`
`PREFACE TO THE SECOND EDITION
`
`1 DEFINITIONS AND UNITS
`Introduction / 1
`1.1
`1.2 The cgs–emu System of Units / 2
`1.2.1 Magnetic Poles / 2
`1.3 Magnetic Moment / 5
`Intensity of Magnetization / 6
`1.4
`1.5 Magnetic Dipoles / 7
`1.6 Magnetic Effects of Currents / 8
`1.7 Magnetic Materials / 10
`1.8 SI Units / 16
`1.9 Magnetization Curves and Hysteresis Loops / 18
`
`2 EXPERIMENTAL METHODS
`Introduction / 23
`2.1
`2.2 Field Production By Solenoids / 24
`2.2.1 Normal Solenoids / 24
`2.2.2 High Field Solenoids / 28
`2.2.3 Superconducting Solenoids / 31
`2.3 Field Production by Electromagnets / 33
`2.4 Field Production by Permanent Magnets / 36
`
`xiii
`
`xvi
`
`1
`
`23
`
`v
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`CONTENTS
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`2.5 Measurement of Field Strength / 38
`2.5.1 Hall Effect / 38
`2.5.2 Electronic Integrator or Fluxmeter / 39
`2.5.3 Other Methods / 41
`2.6 Magnetic Measurements in Closed Circuits / 44
`2.7 Demagnetizing Fields / 48
`2.8 Magnetic Shielding / 51
`2.9 Demagnetizing Factors / 52
`2.10 Magnetic Measurements in Open Circuits / 62
`Instruments for Measuring Magnetization / 66
`2.11
`2.11.1 Extraction Method / 66
`2.11.2 Vibrating-Sample Magnetometer / 67
`2.11.3 Alternating (Field) Gradient Magnetometer—AFGM or AGM
`(also called Vibrating Reed Magnetometer) / 70
`Image Effect / 70
`2.11.4
`2.11.5 SQUID Magnetometer / 73
`2.11.6 Standard Samples / 73
`2.11.7 Background Fields / 73
`2.12 Magnetic Circuits and Permeameters / 73
`2.12.1 Permeameter / 77
`2.12.2 Permanent Magnet Materials / 79
`2.13 Susceptibility Measurements / 80
`Problems / 85
`
`3 DIAMAGNETISM AND PARAMAGNETISM
`Introduction / 87
`3.1
`3.2 Magnetic Moments of Electrons / 87
`3.3 Magnetic Moments of Atoms / 89
`3.4 Theory of Diamagnetism / 90
`3.5 Diamagnetic Substances / 90
`3.6 Classical Theory of Paramagnetism / 91
`3.7 Quantum Theory of Paramagnetism / 99
`3.7.1 Gyromagnetic Effect / 102
`3.7.2 Magnetic Resonance / 103
`3.8 Paramagnetic Substances / 110
`3.8.1 Salts of the Transition Elements / 110
`3.8.2 Salts and Oxides of the Rare Earths / 110
`3.8.3 Rare-Earth Elements / 110
`3.8.4 Metals / 111
`3.8.5 General / 111
`Problems / 113
`
`87
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`CONTENTS
`
`vii
`
`115
`
`151
`
`175
`
`4 FERROMAGNETISM
`Introduction / 115
`4.1
`4.2 Molecular Field Theory / 117
`4.3 Exchange Forces / 129
`4.4 Band Theory / 133
`4.5 Ferromagnetic Alloys / 141
`4.6 Thermal Effects / 145
`4.7 Theories of Ferromagnetism / 146
`4.8 Magnetic Analysis / 147
`Problems / 149
`
`5 ANTIFERROMAGNETISM
`Introduction / 151
`5.1
`5.2 Molecular Field Theory / 154
`5.2.1 Above TN / 154
`5.2.2 Below TN / 156
`5.2.3 Comparison with Experiment / 161
`5.3 Neutron Diffraction / 163
`5.3.1 Antiferromagnetic / 171
`5.3.2 Ferromagnetic / 171
`5.4 Rare Earths / 171
`5.5 Antiferromagnetic Alloys / 172
`Problems / 173
`
`6 FERRIMAGNETISM
`Introduction / 175
`6.1
`6.2 Structure of Cubic Ferrites / 178
`6.3 Saturation Magnetization / 180
`6.4 Molecular Field Theory / 183
`6.4.1 Above Tc / 184
`6.4.2 Below Tc / 186
`6.4.3 General Conclusions / 189
`6.5 Hexagonal Ferrites / 190
`6.6 Other Ferrimagnetic Substances / 192
`6.6.1 g-Fe2O3 / 192
`6.6.2 Garnets / 193
`6.6.3 Alloys / 193
`6.7 Summary: Kinds of Magnetism / 194
`Problems / 195
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`CONTENTS
`
`7 MAGNETIC ANISOTROPY
`Introduction / 197
`7.1
`7.2 Anisotropy in Cubic Crystals / 198
`7.3 Anisotropy in Hexagonal Crystals / 202
`7.4 Physical Origin of Crystal Anisotropy / 204
`7.5 Anisotropy Measurement / 205
`7.5.1 Torque Curves / 206
`7.5.2 Torque Magnetometers / 212
`7.5.3 Calibration / 215
`7.5.4 Torsion-Pendulum Method / 217
`7.6 Anisotropy Measurement (from Magnetization Curves) / 218
`7.6.1 Fitted Magnetization Curve / 218
`7.6.2 Area Method / 222
`7.6.3 Anisotropy Field / 226
`7.7 Anisotropy Constants / 227
`7.8 Polycrystalline Materials / 229
`7.9 Anisotropy in Antiferromagnetics / 232
`7.10 Shape Anisotropy / 234
`7.11 Mixed Anisotropies / 237
`Problems / 238
`
`8 MAGNETOSTRICTION AND THE EFFECTS OF STRESS
`Introduction / 241
`8.1
`8.2 Magnetostriction of Single Crystals / 243
`8.2.1 Cubic Crystals / 245
`8.2.2 Hexagonal Crystals / 251
`8.3 Magnetostriction of Polycrystals / 254
`8.4 Physical Origin of Magnetostriction / 257
`8.4.1 Form Effect / 258
`8.5 Effect of Stress on Magnetic Properties / 258
`8.6 Effect of Stress on Magnetostriction / 266
`8.7 Applications of Magnetostriction / 268
`8.8 DE Effect / 270
`8.9 Magnetoresistance / 271
`Problems / 272
`
`9 DOMAINS AND THE MAGNETIZATION PROCESS
`Introduction / 275
`9.1
`9.2 Domain Wall Structure / 276
`9.2.1 Ne´el Walls / 283
`
`197
`
`241
`
`275
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`335
`
`9.3 Domain Wall Observation / 284
`9.3.1 Bitter Method / 284
`9.3.2 Transmission Electron Microscopy / 287
`9.3.3 Optical Effects / 288
`9.3.4 Scanning Probe; Magnetic Force
`Microscope / 290
`9.3.5 Scanning Electron Microscopy with
`Polarization Analysis / 292
`9.4 Magnetostatic Energy and Domain Structure / 292
`9.4.1 Uniaxial Crystals / 292
`9.4.2 Cubic Crystals / 295
`9.5 Single-Domain Particles / 300
`9.6 Micromagnetics / 301
`9.7 Domain Wall Motion / 302
`9.8 Hindrances to Wall Motion (Inclusions) / 305
`9.8.1 Surface Roughness / 308
`9.9 Residual Stress / 308
`9.10 Hindrances to Wall Motion (Microstress) / 312
`9.11 Hindrances to Wall Motion (General) / 312
`9.12 Magnetization by Rotation / 314
`9.12.1 Prolate Spheroid (Cigar) / 314
`9.12.2 Planetary (Oblate) Spheroid / 320
`9.12.3 Remarks / 321
`9.13 Magnetization in Low Fields / 321
`9.14 Magnetization in High Fields / 325
`9.15 Shapes of Hysteresis Loops / 326
`9.16 Effect of Plastic Deformation (Cold Work) / 329
`Problems / 332
`
`10 INDUCED MAGNETIC ANISOTROPY
`Introduction / 335
`10.1
`10.2 Magnetic Annealing (Substitutional
`Solid Solutions) / 336
`10.3 Magnetic Annealing (Interstitial
`Solid Solutions) / 345
`10.4 Stress Annealing / 348
`10.5 Plastic Deformation (Alloys) / 349
`10.6 Plastic Deformation (Pure Metals) / 352
`10.7 Magnetic Irradiation / 354
`10.8 Summary of Anisotropies / 357
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`CONTENTS
`
`11 FINE PARTICLES AND THIN FILMS
`11.1 Introduction / 359
`11.2 Single-Domain vs Multi-Domain Behavior / 360
`11.3 Coercivity of Fine Particles / 360
`11.4 Magnetization Reversal by Spin Rotation / 364
`11.4.1 Fanning / 364
`11.4.2 Curling / 368
`11.5 Magnetization Reversal by Wall Motion / 373
`11.6 Superparamagnetism in Fine Particles / 383
`11.7 Superparamagnetism in Alloys / 390
`11.8 Exchange Anisotropy / 394
`11.9 Preparation and Structure of Thin Films / 397
`Induced Anisotropy in Films / 399
`11.10
`11.11 Domain Walls in Films / 400
`11.12 Domains in Films / 405
`Problems / 408
`
`12 MAGNETIZATION DYNAMICS
`Introduction / 409
`12.1
`12.2 Eddy Currents / 409
`12.3 Domain Wall Velocity / 412
`12.3.1 Eddy-Current Damping / 415
`12.4 Switching in Thin Films / 418
`12.5 Time Effects / 421
`12.5.1 Time Decrease of Permeability / 422
`12.5.2 Magnetic After-Effect / 424
`12.5.3 Thermal Fluctuation After-Effect / 426
`12.6 Magnetic Damping / 428
`12.6.1 General / 433
`12.7 Magnetic Resonance / 433
`12.7.1 Electron Paramagnetic Resonance / 433
`12.7.2 Ferromagnetic Resonance / 435
`12.7.3 Nuclear Magnetic Resonance / 436
`Problems / 438
`
`13 Soft Magnetic Materials
`Introduction / 439
`13.1
`13.2 Eddy Currents / 440
`13.3 Losses in Electrical Machines / 445
`13.3.1 Transformers / 445
`13.3.2 Motors and Generators / 450
`
`359
`
`409
`
`439
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`477
`
`13.4 Electrical Steel / 452
`13.4.1 Low-Carbon Steel / 453
`13.4.2 Nonoriented Silicon Steel / 454
`13.4.3 Grain-Oriented Silicon Steel / 456
`13.4.4 Six Percent Silicon Steel / 460
`13.4.5 General / 461
`13.5 Special Alloys / 463
`13.5.1 Iron–Cobalt Alloys / 466
`13.5.2 Amorphous and Nanocrystalline
`Alloys / 466
`13.5.3 Temperature Compensation Alloys / 467
`13.5.4 Uses of Soft Magnetic Materials / 467
`13.6 Soft Ferrites / 471
`Problems / 476
`
`14 HARD MAGNETIC MATERIALS
`14.1 Introduction / 477
`14.2 Operation of Permanent Magnets / 478
`14.3 Magnet Steels / 484
`14.4 Alnico / 485
`14.5 Barium and Strontium Ferrite / 487
`14.6 Rare Earth Magnets / 489
`14.6.1 SmCo5 / 489
`14.6.2 Sm2Co17 / 490
`14.6.3 FeNdB / 491
`14.7 Exchange-Spring Magnets / 492
`14.8 Nitride Magnets / 492
`14.9 Ductile Permanent Magnets / 492
`14.9.1 Cobalt Platinum / 493
`14.10 Artificial Single Domain Particle
`Magnets (Lodex) / 493
`14.11 Bonded Magnets / 494
`14.12 Magnet Stability / 495
`14.12.1 External Fields / 495
`14.12.2 Temperature Changes / 496
`14.13 Summary of Magnetically Hard Materials / 497
`14.14 Applications / 498
`14.14.1 Electrical-to-Mechanical / 498
`14.14.2 Mechanical-to-Electrical / 501
`14.14.3 Microwave Equipment / 501
`14.14.4 Wigglers and Undulators / 501
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`CONTENTS
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`14.14.5 Force Applications / 501
`14.14.6 Magnetic Levitation / 503
`Problems / 504
`
`15 MAGNETIC MATERIALS FOR RECORDING
`AND COMPUTERS
`Introduction / 505
`15.1
`15.2 Magnetic Recording / 505
`15.2.1 Analog Audio and Video Recording / 505
`15.3 Principles of Magnetic Recording / 506
`15.3.1 Materials Considerations / 507
`15.3.2 AC Bias / 507
`15.3.3 Video Recording / 508
`15.4 Magnetic Digital Recording / 509
`15.4.1 Magnetoresistive Read Heads / 509
`15.4.2 Colossal Magnetoresistance / 511
`15.4.3 Digital Recording Media / 511
`15.5 Perpendicular Recording / 512
`15.6 Possible Future Developments / 513
`15.7 Magneto-Optic Recording / 513
`15.8 Magnetic Memory / 514
`15.8.1 Brief History / 514
`15.8.2 Magnetic Random Access Memory / 515
`15.8.3 Future Possibilities / 515
`
`16 MAGNETIC PROPERTIES OF SUPERCONDUCTORS
`Introduction / 517
`16.1
`16.2 Type I Superconductors / 519
`16.3 Type II Superconductors / 520
`16.4 Susceptibility Measurements / 523
`16.5 Demagnetizing Effects / 525
`
`APPENDIX 1: DIPOLE FIELDS AND ENERGIES
`
`APPENDIX 2: DATA ON FERROMAGNETIC ELEMENTS
`
`APPENDIX 3: CONVERSION OF UNITS
`
`APPENDIX 4: PHYSICAL CONSTANTS
`
`INDEX
`
`505
`
`517
`
`527
`
`531
`
`533
`
`535
`
`537
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`PREFACE TO THE FIRST EDITION
`
`Take a pocket compass, place it on a table, and watch the needle. It will jiggle around,
`oscillate, and finally come to rest, pointing more or less north. Therein lie two mysteries.
`The first is the origin of the earth’s magnetic field, which directs the needle. The second
`is the origin of the magnetism of the needle, which allows it to be directed. This book
`is about the second mystery, and a mystery indeed it is, for although a great deal is
`known about magnetism in general, and about the magnetism of iron in particular, it
`is still impossible to predict from first principles that iron is strongly magnetic.
`This book is for the beginner. By that I mean a senior or first-year graduate student in
`engineering, who has had only the usual undergraduate courses in physics and materials
`science taken by all engineers, or anyone else with a similar background. No knowledge
`of magnetism itself is assumed.
`People who become interested in magnetism usually bring quite different backgrounds to
`their study of the subject. They are metallurgists and physicists, electrical engineers and
`chemists, geologists and ceramists. Each one has a different amount of knowledge of
`such fundamentals as atomic theory, crystallography, electric circuits, and crystal chemistry.
`I have tried to write understandably for all groups. Thus some portions of the book will be
`extremely elementary for most readers, but not the same portions for all readers.
`Despite the popularity of the mks system of units in electricity, the overwhelming
`majority of magneticians still speak the language of the cgs system, both in the laboratory
`and in the plant. The student must learn that language sooner or later. This book is therefore
`written in the cgs system.
`The beginner in magnetism is bewildered by a host of strange units and even stranger
`measurements. The subject is often presented on too theoretical a level, with the result
`that the student has no real physical understanding of the various quantities involved,
`simply because he has no clear idea of how these quantities are measured. For this
`reason methods of measurement are stressed throughout the book. All of the second
`chapter is devoted to the most common methods, while more specialized techniques are
`described in appropriate later chapters.
`
`xiii
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`xiv
`
`PREFACE TO THE FIRST EDITION
`
`The book is divided into four parts:
`
`1. Units and measurements.
`2. Kinds of magnetism, or the difference, for example, between a ferromagnetic and a
`paramagnetic.
`3. Phenomena in strongly magnetic substances, such as anisotropy and magnetostriction.
`4. Commercial magnetic materials and their applications.
`
`The references, selected from the enormous literature of magnetism, are mainly of two
`kinds, review papers and classic papers, together with other references required to buttress
`particular statements in the text. In addition, a list of books is given, together with brief indi-
`cations of the kind of material that each contains.
`Magnetism has its roots in antiquity. No one knows when the first lodestone, a natural
`oxide of iron magnetized by a bolt of lightning, was picked up and found to attract bits of
`other lodestones or pieces of iron. It was a subject bound to attract the superstitious, and it
`did. In the sixteenth century Gilbert began to formulate some clear principles.
`In the late nineteenth and early twentieth centuries came the really great contributions of
`Curie, Langevin, and Weiss, made over a span of scarcely more than ten years. For the next
`forty years the study of magnetism can be said to have languished, except for the work of a
`few devotees who found in the subject that fascinations so eloquently described by the late
`Professor E. C. Stoner:
`
`The rich diversity of ferromagnetic phenomena, the perennial
`challenge to skill in experiment and to physical insight in
`coordinating the results, the vast range of actual and
`possible applications of ferromagnetic materials, and the
`fundamental character of the essential theoretical problems
`raised have all combined to give ferromagnetism a width of
`interest which contrasts strongly with the apparent narrowness
`of its subject matter, namely, certain particular properties
`of a very limited number of substances.
`
`Then, with the end of World War II, came a great revival of interest, and the study of
`magnetism has never been livelier than it is today. This renewed interest came mainly
`from three developments:
`
`1. A new material. An entirely new class of magnetic materials, the ferrites, was devel-
`oped, explained, and put to use.
`2. A new tool. Neutron diffraction, which enables us to “see” the magnetic moments of
`individual atoms, has given new depth to the field of magnetochemistry.
`3. A new application. The rise of computers, in which magnetic devices play an essen-
`tial role, has spurred research on both old and new magnetic materials.
`
`And all this was aided by a better understanding, gained about the same time, of magnetic
`domains and how they behave.
`In writing this book, two thoughts have occurred to me again and again. The first is that
`magnetism is peculiarly a hidden subject, in the sense that it is all around us, part of our
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`PREFACE TO THE FIRST EDITION
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`xv
`
`daily lives, and yet most people, including engineers, are unaware or have forgotten that
`their lives would be utterly different without magnetism. There would be no electric
`power as we know it, no electric motors, no radio, no TV. If electricity and magnetism
`are sister sciences, then magnetism is surely the poor relation. The second point concerns
`the curious reversal, in the United States, of the usual roles of university and industrial lab-
`oratories in the area of magnetic research. While Americans have made sizable contri-
`butions to the international pool of knowledge of magnetic materials, virtually all of
`these contributions have come from industry. This is not true of other countries or other
`subjects. I do not pretend to know the reason for this imbalance, but it would certainly
`seem to be time for the universities to do their share.
`Most technical books, unless written by an authority in the field, are the result of a
`collaborative effort, and I have had many collaborators. Many people in industry have
`given freely from their fund of special knowledge and experiences. Many others have
`kindly given me original photographs. The following have critically read portions of the
`book or have otherwise helped me with difficult points: Charles W. Allen, Joseph J.
`Becker, Ami E. Berkowitz, David Cohen, N. F. Fiore, C. D. Graham, Jr., Robert G.
`Hayes, Eugene W. Henry, Conyers Herring, Gerald L. Jones, Fred E. Luborsky, Walter
`C. Miller, R. Pauthenet, and E. P. Wohlfarth. To these and all others who have aided in
`my magnetic education, my best thanks.
`
`B. D. C.
`
`Notre Dame, Indiana
`February 1972
`
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`PREFACE TO THE SECOND EDITION
`
`B. D. (Barney) Cullity (1917–1978) was a gifted writer on technical topics. He could
`present complicated subjects in a clear, coherent, concise way that made his books
`popular with students and teachers alike. His first book, on X-ray diffraction, taught the
`elements of crystallography and structure and X-rays to generations of metallurgists. It
`was first published in 1967, with a second edition in 1978 and a third updated version in
`2001, by Stuart R. Stock. His book on magnetic materials appeared in 1972 and was simi-
`larly successful; it remained in print for many years and was widely used as an introduction
`to the subjects of magnetism, magnetic measurements, and magnetic materials.
`The Magnetics Society of the Institute of Electrical and Electronic Engineers (IEEE) has
`for a number of years sponsored the reprinting of classic books and papers in the field of
`magnetism, including perhaps most notably the reprinting in 1993 of R. M. Bozorth’s
`monumental book Ferromagnetism, first published in 1952. Cullity’s Introduction to
`Magnetic Materials was another candidate for reprinting, but after some debate it was
`decided to encourage the production of a revised and updated edition instead. I had for
`many years entertained the notion of making such a revision, and volunteered for the
`job. It has taken considerably longer than I anticipated, and I have in the end made
`fewer changes than might have been expected.
`Cullity wrote explicitly for the beginner in magnetism, for an undergraduate student
`or beginning graduate student with no prior exposure to the subject and with only a
`general undergraduate knowledge of chemistry, physics, and mathematics. He emphasized
`measurements and materials, especially materials of engineering importance. His treatment
`of quantum phenomena is elementary. I have followed the original text quite closely in
`organization and approach, and have left substantial portions largely unchanged. The
`major changes include the following:
`
`1. I have used both cgs and SI units throughout, where Cullity chose cgs only. Using
`both undoubtedly makes for a certain clumsiness and repetition, but if (as I hope)
`
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`PREFACE TO THE SECOND EDITION
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`xvii
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`the book remains useful for as many years as the original, SI units will be increasingly
`important.
`2. The treatment of measurements has been considerably revised. The ballistic galvano-
`meter and the moving-coil fluxmeter have been compressed into a single sentence.
`The electronic integrator appears, along with the alternating-gradient magnetometer,
`the SQUID, and the use of computers for data collection. No big surprises here.
`3. There is a new chapter on magnetic materials for use in computers, and a brief chapter
`on the magnetic behavior of superconductors.
`4. Amorphous magnetic alloys and rare-earth permanent magnets appear, the treatment
`of domain-wall structure and energy is expanded, and some work on the effect of
`mechanical stresses on domain wall motion (a topic of special interest to Cullity)
`has been dropped.
`
`I considered various ways to deal with quantum mechanics. As noted above, Cullity’s treat-
`ment is sketchy, and little use is made of quantum phenomena in most of the book. One
`possibility was simply to drop the subject entirely, and stick to classical physics. The
`idea of expanding the treatment was quickly dropped. Apart from my personal limitations,
`I do not believe it is possible to embed a useful textbook on quantum mechanics as a chapter
`or two in a book that deals mainly with other subjects. In the end, I pretty much stuck with
`Cullity’s original. It gives some feeling for the subject, without pretending to be rigorous or
`detailed.
`
`References
`
`All technical book authors, including Cullity in 1972, bemoan the vastness of the technical
`literature and the impossibility of keeping up with even a fraction of it. In working closely
`with the book over several years, I became conscious of the fact that it has remained useful
`even as its many references became obsolete. I also convinced myself that readers of the
`revised edition will fall mainly into two categories: beginners, who will not need or
`desire to go beyond what appears in the text; and more advanced students and research
`workers, who will have easy access to computerized literature searches that will give
`them up-to-date information on topics of interest rather than the aging references in an
`aging text. So most of the references have been dropped. Those that remain appear
`embedded in the text, and are to old original work, or to special sources of information
`on specific topics, or to recent (in 2007) textbooks. No doubt this decision will disappoint
`some readers, and perhaps it is simply a manifestation of authorial cowardice, but I felt it
`was the only practical way to proceed.
`I would like to express my thanks to Ron Goldfarb and his colleagues at the National
`Institute of Science and Technology in Boulder, Colorado, for reading and criticizing the
`individual chapters. I have adopted most of their suggestions.
`
`C. D. GRAHAM
`
`Philadelphia, Pennsylvania
`May 2008
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`CHAPTER 1
`
`DEFINITIONS AND UNITS
`
`1.1 INTRODUCTION
`
`The story of magnetism begins with a mineral called magnetite (Fe3O4), the first magnetic
`material known to man. Its early history is obscure, but its power of attracting iron was cer-
`tainly known 2500 years ago. Magnetite is widely distributed. In the ancient world the most
`plentiful deposits occurred in the district of Magnesia, in what is now modern Turkey, and
`our word magnet is derived from a similar Greek word, said to come from the name of this
`district. It was also known to the Greeks that a piece of iron would itself become magnetic if
`it were touched, or, better, rubbed with magnetite.
`Later on, but at an unknown date, it was found that a properly shaped piece of magnetite,
`if supported so as to float on water, would turn until it pointed approximately north and
`south. So would a pivoted iron needle, if previously rubbed with magnetite. Thus was
`the mariner’s compass born. This north-pointing property of magnetite accounts for the
`old English word lodestone for this substance; it means “waystone,” because it points
`the way.
`The first truly scientific study of magnetism was made by the Englishman William
`Gilbert (1540–1603), who published his classic book On the Magnet in 1600. He experi-
`mented with lodestones and iron magnets, formed a clear picture of the Earth’s magnetic
`field, and cleared away many superstitions that had clouded the subject. For more than a
`century and a half after Gilbert, no discoveries of any fundamental importance were
`made, although there were many practical improvements in the manufacture of magnets.
`Thus, in the eighteenth century, compound steel magnets were made, composed of many
`magnetized steel strips fastened together, which could lift 28 times their own weight of
`iron. This is all the more remarkable when we realize that there was only one way of
`making magnets at that time: the iron or steel had to be rubbed with a lodestone, or with
`
`Introduction to Magnetic Materials, Second Edition. By B. D. Cullity and C. D. Graham
`Copyright # 2009 the Institute of Electrical and Electronics Engineers, Inc.
`
`1
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`2
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`DEFINITIONS AND UNITS
`
`another magnet which in turn had been rubbed with a lodestone. There was no other way
`until the first electromagnet was made in 1825, following the great discovery made in 1820
`by Hans Christian Oersted (1775–1851) that an electric current produces a magnetic field.
`Research on magnetic materials can be said to date from the invention of the electromagnet,
`which made available much more powerful fields than those produced by lodestones, or
`magnets made from them.
`In this book we shall consider basic magnetic quantities and the units in which they are
`expressed, ways of making magnetic measurements, theories of magnetism, magnetic beha-
`vior of materials, and, finally, the properties of commercially important magnetic materials.
`The study of this subject is complicated by the existence of two different systems of units:
`the SI (International System) or mks, and the cgs (electromagnetic or emu) systems. The SI
`system, currently taught in all physics courses, is standard for scientific work throughout the
`world. It has not, however, been enthusiastically accepted by workers in magnetism.
`Although both systems describe the same physical reality, they start from somewhat differ-
`ent ways of visualizing that reality. As a consequence, converting from one system to the
`other sometimes involves more than multiplication by a simple numerical factor. In
`addition, the designers of the SI system left open the possibility of expressing some mag-
`netic quantities in more than one way, which has not helped in speeding its adoption.
`The SI system has a clear advantage when electrical and magnetic behavior must be con-
`sidered together, as when dealing with electric currents generated inside a material by mag-
`netic effects (eddy currents). Combining electromagnetic and electrostatic cgs units gets
`very messy, whereas using SI it is straightforward.
`At present (early twenty-first century), the SI system is widely used in Europe, especially
`for soft magnetic materials (i.e., materials other than permanent magnets). In the USA and
`Japan, the cgs–emu system is still used by the majority of research workers, although the
`use of SI is slowly increasing. Both systems are found in reference works, research papers,
`materials and instrument specifications, so this book will use both sets of units. In Chapter
`1, the basic equations of each system will be developed sequentially; in subsequent chapters
`the two systems will be used in parallel. However, not every equation or numerical value
`will be duplicated; the aim is to provide conversions in cases where they are not obvious
`or where they are needed for clarity.
`Many of the equations in this introductory chapter and the next are stated without proof
`because their derivations can be found in most physics textbooks.
`
`1.2 THE cgs–emu SYSTEM OF UNITS
`
`1.2.1 Magnetic Poles
`
`Almost everyone as a child has played with magnets and felt the mysterious forces of
`attraction and repulsion between them. These forces appear to originate in regions called
`poles, located near the ends of the magnet. The end of a pivoted bar magnet which
`points approximately toward the north geographic pole of the Earth is called the north-
`seeking pole, or, more briefly, the north pole. Since unlike poles attract, and like poles
`repel, this convention means that there is a region of south polarity near the north geo-
`graphic pole. The law governing the forces between poles was discovered independently
`in England in 1750 by John Michell (1724–1793) and in France in 1785 by Charles
`Coulomb (1736–1806). This law states that the force F between two poles is proportional
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`1.2 THE cgs–emu SYSTEM OF UNITS
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`3
`
`Fig. 1.1 Torsion balance for measuring the forces between poles.
`
`to the product of their pole strengths p1 and p2 and inversely proportional to the squar