r 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 ... /' / LlRC r \\MCAS."'T __ -a ______________________________________________
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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
References Further reading Exercises
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
References Further reading Exercises
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
References Further reading Exercises
5 Magnetic properties 5.1 Hysteresis and related properties 5.2 The Barkhausen effect and related phenomena 5.3 Magnetostriction 5.4 Magnetoresistance
References Further reading Exercises
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
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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References Further reading Exercises
9 Magnetic order and critical phenomena 9.1 Theories of paramagnetism and diamagnetism 9.2 Theories of ordered magnetism 9.3 Magnetic structure
References Further reading Exercises
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
References Further reading Exercises
11 Quantum theory of magnetism 11.1 Electron-electron interactions 11.2 The localized electron theory 11.3 The itinerant electron theory
References Further reading Exercises
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,
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
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
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
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
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
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
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
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