introduction to magnetism and magnetic...
TRANSCRIPT
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 ______________________________________________ ~~~~~.. T~
--
-,
r "
l
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
,
I 1
:1
I
I I
L ~--
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
References Further reading Exercises
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
5
,
I
I:
I _I --_I
I I I
I
I I
i i
... -.rIII:.- \
' .. I
l
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
, I 11
05
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
III
~i i
I ,p
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
1 1
_______________________________ ~~.iTTTTtT I nT1T!TITITrTIT:-TnTTrrrfl I
,: ,
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
·1
I I i I
I j
I 11
11
!I :1
\11 !j 11
! i
I ,I
_~~ I
532 Subject Index
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
, ,
m
m:
ml m: ml
i j
m! m
m\
rnl m.l
i m.1
m:
i
I m:1 m:1
1 \': m:
______________________________ ~~.tTTTTT1TJI-l-rrrrITITrrTn-'--~r
I' i
IfllIiMf&; ... _.,...i
I, :c; , i' ij-:o'
• '<;\*1, :\g~t:
- ~ I . -, I:
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
~ Q, I[ , I I
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
----___ ~~.·TTTTlll nTn-r-ITITrT "TI-I- -nT
1---1
1
! , ...• 1 , , !
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
I
I I I I ! I
I j
I I
I I 1
,) , 1
~I /!1 I
III I!
1I !I 'I
11 11 11
u , 536 Subject Index
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
• _____________________________________ TTT .-.~t-,-,_,-,-n-n-,-rrrrTlTrlh._.