Introduction to Magnetism and Magnetic Materials

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Introduction to Magnetism and Magnetic Materials

Second edition

David Jiles Ames Laboratory, US Department of Energy

Department of Materials Science and Engineering and Department of Electrical and Computer Engineering, Iowa State University, Ames, Iowa, USA

CHAPMAN & HALL London· Weinheim . New York· Tokyo· Melbourne· Madras

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Contents

Preface to the first edition Preface to the second edition Foreword Acknowledgements Glossary of symbols SI units, symbols and dimensions Values of selected physical constants

vu ix xi

xvii xxiii xxix xxxi

Part 1 Electromagnetism - magnetic phenomena on the macroscopic scale 1

1 Magnetic fields 1.1 The magnetic field 1.2 Magnetic induction 1.3 Magnetic field calculations

References Further reading Exercises

2 Magnetization and magnetic moment 2.1 Magnetic moment 2.2 Magnetic poles and Amperian bound currents 2.3 Magnetization . 2.4 Magnetic circuits and demagnetizing field 2.5 Penetration of alternating magnetic fields into materials


3 Magnetic measurements 3.1 Induction methods 3.2 Force methods 3.3 Methods depending on changes in material properties 3.4 SQUIDS

3 3 9

18 32 33 33

35 35 40 44 48 57 61 61 61

65 65 71 76 83

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XIV Contents


4 Magnetic materials 4.1 Classification of magnetic materials 4.2 Magnetic properties of ferromagnets 4.3 Different types of ferromagnetic materials for applications 4.4 Paramagnetism and diamagnetism


5 Magnetic properties 5.1 Hysteresis and related properties 5.2 The Barkhausen effect and related phenomena 5.3 Magnetostriction 5.4 Magnetoresistance


Part 2 Magnetism in materials - magnetic phenomena on the microscopic scale

6 Magnetic domains 6.1 Development of domain theory 6.2 Energy considerations and domain patterns


86 86 86

89 89 91 96

103 108 109 109

111 111 119 121

128 129 l30 130

133

135 l35 146 153 154 154

7 Domain walls 157 7.1 Properties of domain boundaries 157 7.2 Domain-wall motion 168

References 175 Further reading 176 Exercises 176

8 Domain processes 179 8.1 Reversible and irreversible domain processes 179 8.2 Determination of magnetization curves from pinning models 189 8.3 Theory of ferromagnetic hysteresis· 198 8.4 Dynamics of domain magnetization processes 205

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9 Magnetic order and critical phenomena 9.1 Theories of paramagnetism and diamagnetism 9.2 Theories of ordered magnetism 9.3 Magnetic structure


10 Electronic magnetic moments 10.1 Classical model of magnetic moments of electrons 10.2 Quantum mechanical model of magnetic moments

of electrons 10.3 Magnetic properties of free atoms


11 Quantum theory of magnetism 11.1 Electron-electron interactions 11.2 The localized electron theory 11.3 The itinerant electron theory


Part 3 Magnetics - technological applications

12 Soft magnetic materials 12.1 Properties and applications 12.2 Materials for a.c. applications 12.3 Materials for d.c. applications 12.4 Materials for magnetic shielding

References Further reading

13 Hard magnetic materials 13.1 Properties and applications 13.2 Permanent magnet materials

References Further reading

Contents xv

212 214 215

217 217 228 239 258 260 260

263 263

266 280 288 289 289

291 291 301 309 319 320 320

323

325 325 329 350 356 359 360

363 363 376 391 393

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XVI Contents

14 Magnetic recording 395

~ 14.1 Magnetic recording media 395 14.2 Recording heads and the recording process 409 14.3 Modeling the magnetic recording process 419 , ~;

References 420 "I{ Further reading 421 I~ 1\ "- 15 Magnetic evaluation of materials 423 f 15.1 Methods for evaluation of intrinsic properties 423

~ 15.2 Methods for detection of flaws and other inhomogeneities 433 .~ 15.3 Magnetic imaging methods 447 I 15.4 Conclusions 453 ~ References 455

I Further reading 457

Solutions 459

I Appendix 1: The magnetic field as a relativistic correction to the electric field 511

m Appendix 2: Derivation of Maxwell's equation from the relativistic Lorentz

transformation 515

Author index 521

Subject index 529

Subject Index

a.c. applications, materials for, 329 a.c. bias recording, 418 a.c. losses in transformers, 326 adiabatic demagnetization of

paramagnets, 107 alignment of magnetic moments, 140 alnico,377 alternating fields, penetration into

materials, 57 alternating gradient force magnetometer,

74 aluminum-iron alloys, 335 amorphous magnetic fibers, 346 amorphous metals, 98, 339 Ampere's circuital law, 7 Ampere's hypothesis, 136 Amperian current model, 40 Amperian currents and poles, 40 analytical balance, 72 angular momentum of electrons, 265, 267,

268,269 wave mechanical corrections to, 271

anhysteretic magnetization, 115 measurement of, 116

anisotropic materials, 125 anisotropy, 114, 150

constants, 152 cubic, 152 and domain rotation, 150, 370 energy of domain wall, 158 hexagonal, 151

antiferromagnetism, 168, 234 antiparallel spin alignment, 234 artificially structured materials, 348 atomic force microscopy, 145 atomic magnetic moment, 90, 135,281

atomic orbital angular momentum, 282 atomic spin angular momentum, 283 atomic total angular momentum, 284

band theory of ferromagnetism, 311 band theory of magnetism, 309 band theory of paramagnetism, 310 Barkhausen effect, 119, 141, 197, 424

for detection of stress, 424 for evaluation of microstructure, 425 theory, 120, 197

bending of domain walls, 173 Bethe-Slater curve, 299 Biot-Savart law, 4 Bitter patterns, 142 Bloch walls, 157 bound currents and poles, 40 boundary element technique, 29 Brillouin function, 303

ceramic magnets, 103 chromium dioxjde, 404

tapes, 100 circuits, 368 classical eddy current power dissipation,

60, 327 classical theory of diamagnetism, 218 classical theory of ferromagnetism, 228 classical theory of paramagnetism, 223 closure domains, 166 . cobalt-chromium recording media, 400 cobalt-chromium recording tapes, 404 cobalt-iron alloys, 354 cobalt-platinum, 382 cobalt-samarium, 384

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530 Subject Index

cobalt surface-modified gamma iron oxide, 403

coercimeter, 428, 431 coercivity 95, 113, 325, 365 colossal magnetoresistance, 413 composite magnetic materials, 348 computational magnetics, 31 core losses, 98 correlation effects among electron spins,

316 Cotton-Mouton effect, 80 critical behaviour at the ordering

temperature, 252 critical magnetic field

under strong pinning, 187 under weak pinning, 188

cubic anisotropy, 152 Curie temperature, 95

and the mean field interaction, 233 and thermal energy, 159

Curie-Weiss law, 224, 259, 306 Curie's law, 105, 222, 304 Current loop dipole, 15

d.c. applications of soft magnetic materials, 350

data storage densities, 395 predicted, 398

definition of ampere per meter, 5 demagnetization curve, of permanent

magnet, 368 demagnetizing factors, 50 demagnetizing field, effect on

measurements, 51 demagnetizing fields, 48, 50 density of magnetic recording, 417 diamagnetism, theory of, 217 diamagnets, 89, 103, 107

susceptibility of, 89 dipole, as a current loop, 15 dipole, model for leakage field calculation,

441 dipole moment, 38 discontinuous magnetization, 119, 197 disks, magnetic recording, 395 dissipation, anomalous or excess, 328 dissipation, classical eddy current, 327

domain patterns and energy minimization, 146 processes, reversible and irreversible

179 ' rotation, 149, 152, 179

and anisotropy, 150 wall motion, 149, 168,424

domain dynamics, damping, 211 dOl1!ain dynamics, relaxation effects, 211 domain magnetization, 152 domain magnetization dynamics, 205 domain walls

anisotropy and exchange energies, 163 Bloch walls, 157 bowing, 173 defect interactions, 191 effects of stress on, 166 effects of weak fields on, 169 energy, 158 energy balance in, 169 forces on, 169 motion, 207

and the Barkhausen effect, 197, 424 and magneto acoustic emission, 426 and magnetostriction, 198

Neel walls, 167 non-180°, 166 180°, 166 pinning

by inclusions, 184 by strains, 181 strong pinning, 187 weak pinning, 188

planar displacement of walls, 170 surface energy, 161, 169 thickness, 1"57, 162

domains, 135 and the magnetizing process, 148 nucleation, 148 observation of, 141, 143 single, 146 Weiss domain theory, 137

eddy current dissipation, 327 eddy current inspection methods

applications of, 446 for magnetic materials, 445

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eddy currents, 59 effect of demagnetizing field, 51 elastic constant anomalies at critical

temperatures, 254 electric motors, 329 electrical losses, 98

in transformers, 326 electromagnetic field equations, 16 electromagnetic induction, 13 electromagnetic relays, 99 electromagnets, 97, 327 electron band theory of magnetism, 309 electron-electron interactions, 291 electron microscopy

SEM,145 TEM,144

electron spin, 270 and exchange energy, 295 resonance, 101

electron states, occupancy according to Hund's rules, 284

electronic energy levels, splitting by magnetic field, 277

electronic magnetic moment, quantum theory of, 266

electronic magnetic moments, 263 electronic orbital magnetic moment, 263 electronic spin magnetic moment, 264 electronic total magnetic moment, 265 energy loss through wall pinning, 198 energy minimization and domain

structure, 146 energy product, 139, 366

typical values for permanent magnets, 101

energy states of magnetic moment configurations, 140

equivalent current model, 15 exchange coupling in insulators, 308 exchange, direct, 297 exchange energy, 158

dependence on interatomic spacing, 299 and electron spin, 295 between electrons in filled shells, 299 values for various solids, 298

exchange, indirect, 317 exchange integral, 293

Subject Index 531

exchange interaction, 294, 295 hydrogen molecule model, 293 oxygen molecule model, 296 sinusoidal, 239

exchange, RKKY type, 318 exchange spring magnets, 387 exchange stiffness, 160 exchange, superexchange, 308 excited states and spin waves, 251

Faraday effect, 80, 143 Faraday's law of induction, 13, 65 fatigue, effects of, on magnetic properties,

425 ferrimagnetism, 236 ferrites, 102, 103, 349, 381

hard, 103, 381 soft, 102, 349

ferrofluids, 142 ferromagnetic resonance, 208 ferromagnetism, 228 ferromagnets, 89,91, 136

applications of, 96 ferroprobes (fluxgates), 429 fibers, magnetic, 346 field due to Amperian currents, 42, 43 field due to poles, 41, 42, 43 field lines, 50 finite element methods, 31 finite element techniques, 29 flaw detection using magnetic methods, 434 flux

coil moving, 66 stationary, ~6

leakage, 435 application of flux leakage method to

NDE,435 lines, 49 quantization, 83 rate of change of, 65

fluxgate magnetometer, 70 fluxgates (ferroprobes), 429 fluxmeter, 66 flying height for recording heads, 401 force between moving charges, 4 force on a current loop, 39

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force on a dipole, 39 force on current-carrying conductor in a

field H, 12 free atoms, 280 Frohlich-Kennelly equation, 115

gamma iron oxide, 100, 399,403 generators, 329 giant magnetoresistance, 318 Globus---Guyot model, 196

Hall coefficient, 78 Hall effect, 76

magnetometers, 76 hard disks, structure, 401 hard magnetic materials, 96, 363 Heisenberg model of ferromagnetism, 297 Heitler-London approximation, 293 Heitler-London model, 293 he1imagnetism, 238 Helmholz coils, 22 Heusler alloys, 300 hexagonal anisotropy, 151 hexagonal ferrites, 405 high-frequency applications, 349 Hubbard model, 316 Hund's rules, 284 hysteresis, 93, 111

coefficients and magnetic properties, 201

effects of microstructure and deformation on, 204

loss, 113 macroscopic mean field theory of, 198 parameters, 112 stress dependence of, 428

hysteresis graphs, 66

inclusion theory of domain-wall pinning, 184

inductance cores, 102 induction coil methods, 65 initial permeability, 113 initial susceptibility

in the planar wall approximation, 173 in the wall bending approximation, 174

intensity of magnetization, 44

interatomic spacing, effect on exchange energy, 299

iron and low-carbon steels, 350 iron oxide, 403 iron-aluminum alloys, 335 iron--cobalt alloys, 354 iron-neodymium-boron, 384 iron-nickel alloys, 337, 352 iron-silicon alloys, 330 irreversible magnetization changes, 199 Ising model, 192, 255 isolated single domains, 152 itinerant and local moment models, 316 itinerant electron model, 309

criticism of, 315 itinerant electron theory, 309 itinerant exchange, 311

J-J coupling, 286

Kerr effect, 80, 143 Kundt's constant, 80

Landau-Lifschitz-Gilbert model, 206 Langevin function, 107 Langevin theory

of diamagnetism, 218 of paramagnetism, 223

Langevin-Weiss theory, critique of, 227 laser magneto-optic microscope, 144 law of approach to saturation, 118 leakage fields, 434

calculation and modelling of, 441 finite element calculation of, 443

Lenz's law of induction, 13 local pinning fields, 207 localized atomic moments, 301 localized electron model, criticism of, 308 localized electron theory, 301 localized theory of electronic magnetic

moments, 301 Lorentz microscopy, 144

magnet assemblies, 370 magnetic circuits, 48, 54, 368 magnetic dipole, 14 magnetic fibers, 346

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magnetic field of circular coil, 20 definition, 3, 5 generation, 3 due to long conductor, 5 of long thin solenoid, 18 in magnetic materials, 57 numerical methods for calculation of,

29 patterns around conductor, 4 of a short thick solenoid, 25 of short thin solenoid, 24 of two coaxial coils, 22

magnetic field computation, 31 magnetic field, definition of unit, 5 magnetic field as a relativistic effect, 4 magnetic fields, sizes in various situations,

10 magnetic flux, energy associated with, 10 magnetic flux leakage, 439

applications of, 441 instruments for automation of, 442 models for, 441

magnetic force microscopy, 74, 145,448 tip/specimen interactions, 450

magnetic hysteresis, 428 applications in NDE, 429

magnetic imaging, 447 magnetic induction, 9

definition of tesla, 11 lines of, 12

magnetic moment, 35, 135, 263 of closed shell of electrons, 280 of electron, 263

due to orbital angular momentum, 263

due to spin angular momentum, 264 total, 265

magnetic order, 136,247 magnetic particle inspection, 434

applications of, 435 'dry' method, 435 fluorescent particles, 435 optimum conditions for, 437 'wet' method, 435

magnetic pole model, 14 magnetic properties

Subject Index 533

of free atoms, 280 microscopic, typical values of, 165

magnetic quantum numbers, 268 magnetic recording

history, 396 materials, 99 media, 395

materials for, 403 tapes, 397

magnetic resonance, 208 magnetic shielding, 356 magnetic storage densities, 395 magnetic structure, 239, 247 magnetic tapes, 397 magnetic units, 15 magnetite (lodestone), 376 magnetization, 44

in materials with few defects, 195 microstructural effects, 189 relation to Band H, 45 relation to magnetic moment, 15 saturation, 46, 93 strain effects, 189 technical saturation, 124, 148

magneto-acoustic emission, 121, 426 stress dependence of, 427

magnetographic method of leakage flux detection, 434

magnetomechanical effect, 428 ,magnetometers, 65 magnetomotive force, 79 magneto-optic disk drives, 407 magneto-optic recording devices, 406 magnetoresistance, 128

colossal, 413 giant, 318

magnetoresistive multilayers,413 magnetoresistors, 79 magnetostatic energy, 146 magneto stricti on, 121

at an angle () to the magnetic field, 124 field induced, 126 forced, 124 polycrystalline, 126 saturation, 123 single-crystal magnetostriction

constant, cubic, 125

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534 Subject Index

spontaneous, 122 numerical methods for calculation of in terms of single crystal magnetic fields, 29

magnetostriction constants, 125 transverse, 127 orbital magnetic moment

~. magnetostrictive devices, 79 of atom, 281 magnetostrictive materials, 128 of electron, 263

~ market for hard disk drives, 397 orbital momentum quantum number, 267 market for permanent magnets, 364 orbital wave functions, two electron

~ maximum energy product, 101 system, Heitler-London model, " Maxwell's equations, 16 293 v:

~ mean field, 137, 230 order in rare earth solids, 247

I metallic glasses, 339 ordered magnetism, theories of, 228 metglas, 340 ordering temperature, 95, 252 micromagnetic modeling, 211 oxygen molecule model for exchange, 296 modelling of magnetization curves based

on pinning, 189 paramagnetism, 221 molecular field, 137 classical (Langevin) theory, 223 moment of inertia, 264 classical (W eiss) theory, 225

I motors, 329 of 'free' electrons, Pauli theory, 310 moving coil, 66 theory of, 217, 223, 225

galvanometer, 67 paramagnets, 89, 104 multilayers, 128, 318 applications of, 106 mumetal, 337 field dependence of susceptibility, 105

properties of, 104 nanocomposite permanent magnets, 387 susceptibility of, 89 nanocrystalline materials, 347 temperature dependence of nanostructured permanent magnets, 386, susceptibility, 105

387 Paschen-Back effect, 288 NDE, magnetic methods for, 423 Pauli paramagnetism, 310 nearest neighbour interactions, 232 penetration depth, 58

~ Neel temperature, 235, 236 permalloy, 337, 352 Neel walls, 167 permanent magnet steels, 376 neodymium-iron-boron, 100, 384, 391 permanent magnets, 100

f~gv1 . neutron diffraction, 240 applications, 375 antiferromagnetic scattering, 244 materials, 376

I Bragg diffraction peaks, 241 properties, 363 elastic scattering, 241 comparison, 390

." ferromagnetic scattering, 243 stability, 376 inelastic scattering, 245 permeability, 11,46,92, 136

I1I magnetic diffraction peaks, 242 demagnetizing corrections, 53

~\ paramagnetic scattering, 242 differential, 46, 95

- topography, 143 initial, 113 > nickel-iron alloys, 337, 352 relative, 47 / ninety degree (90°) domain-wall motion, permeance coefficient, 369

427 permendur, 354 nitrogenation of permanent magnets, 389 perpendicular recording media, 100,406 non-integral atomic magnetic moments, pinning of domain walls

312 critical field, 187, 188

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d by inclusions, 184 by strains, 181

pinning models, 189 platinum--cobalt, 382 pole model, 14,40 pole strength, 14, 37 poles and Amperian currents, 40 poles and bound currents, 40 potential approximation for domain-wall

motion, 170 power dissipation due to classical eddy

currents, 60 Preisach model, 419

use in magnetic recording industry, 420 principal quantum number, 267 proton precession magnetometers, 72

quantization of angular momentum, 269 of electron spin, 276

quantum mechanical exchange interaction, 294

quantum number 1,267 m], 268 ms, 268 n,267 s,267

quantum theory of electron-electron interactions, 291 electronic magnetic moments, 266 ferromagnetism, 306 paramagnetism, 302

quenching of orbital angular momentum, 286

Rayleigh's law, 117 recording density, 417 recording devices, 395 recording heads, 409

flying height, 401 inductive, 410, 411 magnetoresistive, 410, 413

recording materials, 99 recording media, 99

magnetic properties comparison, 403 recording process, 409

Subject Index 535

reading, 418 writing, 413, 415

recording track density, 402 relative permeability, 47 relays, 99, 328 reluctance, 54 remanence, 94, 113, 365, 432 remanence enhanced magnets, 387 residual field, 432 resistance magnetometers, 79 resonance, magnetic, 208 resonance magnetometers, 81 retentivity, 92 reversible magnetization changes, 200 rigid band model of ferromagnetism

(Slater-Pauling), 314 rigid domain-wall motion, 170

initial susceptibility of, 172 RKKY exchange coupling, 318 rotating coil, 67 Russell-Saunders coupling, 285

samarium--cobalt, 100, 382 samarium-iron-nitride, 383, 389 saturable coil magnetometers, 70 saturation, law of approach to, 117 saturation magnetization, 46, 93, 365

technical, 124, 148 scanning SQUID microscopy, 452 search coil, 66 shielding, magnetic, 356 shielding, multiple, 358 shielding factor, 358 silicon-iron alloys, 330 skin depth, 58 Slater-Pau1ing curve, 314 soft ferrites, 349 soft iron, 350 soft magnetic materials, 96, 325

a.c. losses, 326 coercivity, 325 hysteresis loss, 326 permeability, 325 saturation magnetization, 326

solenoid general formula for field of, 27 magnetic field

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of a long thin, 18 thin-film magnetometers, 80 of a short thick, 25 thin film recording tapes, 404

1'-of a short thin, 24 three-d (3d) band electrons, magnetic

optimization of geometry, 26 properties, 313 ! i power considerations, 26 time dependent magnetic fields, 17

~ specific heat anomalies at critical torque, 14

I, temperatures, 254 magnetometer, 72

spin magnetic moment, 264 torsion balance, 72 ~ of atom, 283 total atomic orbital angular momentum,

~ spin quantum number, 267 284 I' spin waves, 251 track density, 402 I

~ spontaneous magnetization, 307 transformers, 98, 329 .~

temperature dependence of, 307 transverse magnetostriction, 127 I stability of permanent magnets, 376 steel, production, 423 ultrasonic velocity, field dependence in Stern-Gerlach experiment, 278 steels, 433 Stoner-Slater (electron band) theory of units in magnetism, 15

ferromagnetism, 311 Stoner-Wohlfarth model, 370, 420 vector model of the atom, 281 stored energy density, 366 Verdet's constant, 80 strain theory of domain-wall pinning, 181 vibrating coil, 68 Street and Woolley model, 211 magnetometer,68 stress, effects of, on bulk magnetization, vibrating-sample magnetometer, 68

204 stress dependent magnetization, 428 wall bowing approximation, 173 strong magnetic fields, effect on electron wave equation for electromagnetic fields,

coupling, 288 18 supermalloy, 337 wave function of two-electron system, 291 susceptibility, 46, 136 including spin, 294

anomalies at critical temperatures, 254 wave mechanical corrections to angular balance, 72 momentum of electrons, 271 demagnetizing corrections, 53 Weiss domain theory, 137 differential, 46 Weiss mean field theory, 137

consequences of, 227 tapes, magnetic recording, 397 critique of, 227 technical saturation magnetization, 46, of ferromagnetism, 228

148 of paramagnetism, 225 temperature dependent paramagnetic wires, magnetic, 346

susceptibility (Curie), 105, 304 temperature independent paramagnetic X-ray topography, 145

susceptibility (Pauli), 310 theories of magnetic ordering, 228 Zeeman effect thermal expansion anomalies at critical anomalous, 277 / temperature, 254 normal,273

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Introduction to Magnetism and Magnetic Materials