Bertotti G. — Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers :: Электронная библиотека попечительского совета мехмата МГУ

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Bertotti G. — Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers

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Название: Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers

Автор: Bertotti G.

Аннотация:

The book provides a comprehensive treatment of the physics of hysteresis in magnetish, and of the mathematical tools used to describe it. The relations of hysteresis to Maxwell's equations, equilibrium and non equilibrium thermodynamics, non-linear system dynamics, micromagnetics and domain theory are discussed from a unified viewpoint. These aspects are then applied to the interpretation of magnetization reversal mechanisms: coherent rotation and switching in magnetic particles, stochastic domain wall motion and the Barkhausen effect, coercivity mechanisms and magnetic viscosity, rate-dependent hysteresis and eddy-current losses. Emphasis is given to the connection between basic physical ideas and phenomenological models of interest to applications, and, in particular, to the conceptual path going from Maxwell's equations abnd thermodynamics to micro-magnetics and to Preisach hysteresis modeling.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1998

Количество страниц: 558

Добавлена в каталог: 12.04.2010

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Предметный указатель

Domain theory, qualitative description      190
Domain wall      220(b)
Domain wall and domain theory      190
Domain wall as singularity in Van den Berg construction      208—209
Domain wall dynamics      294(b)
Domain wall dynamics and Barkhausen effect      257 280
Domain wall dynamics and eddy-current damping      258—262
Domain wall dynamics and loss separation      262 281
Domain wall dynamics and structural disorder      266 287—288
Domain wall dynamics in picture-frame single crystal      257 261 262(f)
Domain wall dynamics under Wiener-like pinning field      270—272
Domain wall dynamics, correlation properties      280—281
Domain wall dynamics, equivalence to Preisach system      471
Domain wall dynamics, field-velocity relation      260 261 262(f)
Domain wall dynamics, fundamental equation      266—267 468
Domain wall dynamics, intermittent versus continuous motion      272 277 288 272(f) 277(f)
Domain wall dynamics, rate-independent trajectory      469 473 470(f) 474(f)
Domain wall dynamics, return-point memory and congruency      465—466
Domain wall dynamics, self-similar properties      278—280 279(f)
Domain wall dynamics, stochastic nature      273
Domain wall, concept of single wall      255—256
Domain wall, free energy      198 266 268 359
Domain wall, free energy, dimensionless form      361—362
Domain wall, internal structure      197—204 197(f) 220(b)
Domain wall, internal structure and film thickness      202—204 203(f)
Domain wall, internal structure and magnetostatic energy      202
Domain wall, internal structure, competition of exchange and anisotropy      198 199
Domain wall, internal structure, cubic anisotropy      201
Domain wall, internal structure, energy density      199 200(f)
Domain wall, internal structure, magnetization orientation      199 200(f)
Domain wall, internal structure, uniaxial anisotropy      200
Domain wall, multiplication process      420
Domain wall, orientation $180^{\circ}$ versus $90^{\circ}$       197
Domain wall, surface tension      201
Domain wall, surface tension and coercivity      380 381
Domain wall, surface tension and mean-field effect      451—452
Domain wall, surface tension and wall bowing      419
Domain wall, surface tension and wall pinning      357 359—360 366
Domain wall, surface tension, typical values      517(t)
Domain wall, thickness      200—201
Domain wall, thickness parameter, $\lambda_{W}$       171 380
Domain wall, thickness parameter, $\lambda_{W}$ , typical values      517(t)
Domain wall, thickness, order-of-magnitude estimate      174—175 197—198
Doob’s theorem      525—526
Dynamic loss, statistical interpretation      397—399
Dynamical system      55—60 70(b)
Dynamical system and domain wall motion      267 272 468—469
Dynamical system and nonequilibrium thermodynamics      55
Dynamical system, nonlinearity      57—60
Dynamical system, order-preserving evolution      462
Dynamical system, partial ordering      462
Dynamical system, rate-independent evolution      462
Easy axis      146 149 150
Easy cone      153
Easy plane      149
Eddy currents      100 101
Eddy currents and rate-independent hysteresis      100—101 109
Eddy currents as dissipation mechanism      25 99—102 258 262—263 392
Eddy currents, complexity of space-time behavior      393
Eddy-current density around Barkhausen jump      264 265 395
Eddy-current density around domain wall      258—259 260(f)
Eddy-current density for Barkhausen jump sequence      264 396
Eddy-current density for homogeneous system      400 410
Eddy-current density for periodic domain structure      414
Eddy-current density for random domain structure      417
Eddy-current field      101 400
Eddy-current field, pressure on domain wall      261 419—420
Eddy-current loss and Maxwell’s equations      100
Eddy-current loss as statistical average      391
Eddy-current loss, dependence on magnetization frequency      399
Eddy-current loss, dependence on peak magnetization      399
Eddy-current loss, fundamental equation      392
Eddy-current loss, fundamental equation for slab geometry      395
Effective field and return-point memory      467
Effective field in magnetic viscosity      341—342
Effective field in micromagnetics      179 300—301
Effective field in Preisach system      450—451
Elementary volume in Maxwell’s equations      73—74 100 105 102(b)
Elementary volume in micromagnetics      15 130 165
Energy barrier in coherent rotation      233 340 377
Energy barrier in magnetic viscosity      333 336—337
Energy barrier in thermal relaxation      68 376
Energy loss due to eddy currents      see “Eddy-current loss”
Energy loss in bistable system      46—48 60
Energy loss in coherent rotation      242—245 243(f)
Energy loss in domain wall, annihilation      322
Energy loss in domain wall, motion      259—260
Energy loss in hysteresis loop      24—25 36
Energy loss in linear system      36 56
Energy loss, along open curve      60 61
Energy product      10—11 325—326 12(f) 344(b)
Enthalpy      117
entropy      116
Entropy in nonequilibrium thermodynamics      120—122
Entropy production      120—124 453
Entropy production in cyclic or open transformation      123—124
Entropy production in Preisach system      453—454
Equilibrium point in catastrophe theory      49
Excess field      422 424 427 423(f)
Excess field as pressure on correlation region      424—425
Excess field, analytical expression      425
Excess field, upper limit      423
Excess loss      429—430(b)
Excess loss, $n(H_{exc})$ representation      426—427 428(f)
Excess loss, dependence on magnetization frequency      398 427
Excess loss, dependence on microstructure      425—426
Excess loss, dependence on peak magnetization      398 427
Excess loss, periodic domain structure      412—415
Excess loss, periodic domain structure, boundary conditions      413
Excess loss, periodic domain structure, dependence on domain size      415
Excess loss, periodic domain structure, eddy-current density      414
Excess loss, periodic domain structure, instantaneous loss      414—415
Excess loss, qualitative description      27 392 411—412
Excess loss, random domain structure      416—418
Excess loss, random domain structure, eddy-current density      417
Excess loss, random domain structure, instantaneous loss      418 422
Excess loss, statistical interpretation      398
Exchange constant, A      167
Exchange constant, A, typical values      517(t)
Exchange energy      7
Exchange energy in micromagnetics      166—167 172
Exchange energy in molecular field approximation      106 141 165
exchange interaction      129 162(b)
Exchange interaction and effective anisotropy      384—386
Exchange interaction, anisotropic correction      157
Exchange interaction, isotropic nature      142—143 142(f)
Exchange interaction, quantum origin      137—138
Exchange length, $\lambda_{EX}$       171 350
Exchange length, $\lambda_{EX}$ , typical values      517(t)
Exit problem      see “First-passage time”
External field      see “Applied field”
External field as input variable in hysteresis      31
Faraday effect      191 217(f)
Faraday’s law      75
Feedback in hysteresis loop measurement      321
Feedback in system response      31—32
Ferrimagnetism      113 138
Ferrite      10 517(t) 253(f)
ferromagnetism      6 112—113 138
Fine particle      see “Magnetic particle”
First-order magnetization process      245—247 246(f) 254(b)
First-passage time      529—533
First-passage time and domain wall dynamics      469 473
Fluctuation field and coercive field      382
Fluctuation field in magnetic viscosity      341 343 344(b)
Fluctuation field in Preisach system      494
Fluctuation-dissipation theorem      70(b)
Fokker — Planck equation      523
Fokker — Planck equation for domain wall motion      274—275
Fokker — Planck equation for thermal relaxation      66

Fokker — Planck equation, backward equation      524
Fokker — Planck equation, diffusion term      523
Fokker — Planck equation, drift term      523
Fokker — Planck equation, forward equation      523—524
Fold catastrophe      50—51 50(f)
Fourier’s law      122
Fractal geometry      294(b)
Free charges      see “Magnetic charges”
Free energy as thermodynamic potential      117—118 453
Free energy of bistable system      44 45(f)
Free energy of bistable system under varying field      45 45(f)
Free energy of domain wall      198 266 268 359—361
Free energy of magnetic material      19 194
Free energy of magnetic medium      119—120
Free energy of magnetic particle      226—227 235
Free energy of paramagnetic system      132 133
Free energy of phase mixture      54
Free energy of picture-frame single crystal      321—322 452 323(f)
Free energy of Preisach system      450—451 453—455
Free energy of Preisach unit      436—437 436(f)
Free energy, density, space-dependent      164—168 187(b)
Free energy, density, space-dependent and return-point memory      466—468
Free energy, Gibbs versus Helmholtz energy      119
Free energy, Gibbs versus Landau energy      40—41
Free poles      see “Magnetic charges”
Garnet crystal      217(f)
Generalized susceptibility in linear system      35 56
Gibbs free energy      40 117—118
Gibbs free energy of magnetic medium      119
Gibbs free energy of magnetic medium, estimated from magnetization curve      120 120(f)
Gibbs function      see “Gibbs free energy”
Gilbert’s equation      184 187(b)
Gilbert’s equation, equivalence with Landau — Lifshitz equation      185
Gilbert’s equation, extension to eddy currents      186
Gilbert’s equation, geometrical representation      184 184(f)
Gilbert’s equation, Lagrangian interpretation      187(b)
Gilbert’s equation, limit of infinite damping      184 329
Hard magnetic material      347 375 29(b) 344(b)
Hard magnetic material in micromagnetics      171 176—177
Hard magnetic material in micromagnetics, definition      171
Hard magnetic material, nucleation-type versus pinning-type      318 318(f)
Hard magnetic material, overview      10—11
Hardness parameter, K      171 308 350 361
Hardness parameter, K, typical values      517(t)
Heisenberg Hamiltonian      138 142 166
Helmholtz free energy      117
Helmholtz free energy of magnetic medium      119
Helmholtz free energy of magnetic medium, estimated from magnetization curve      120 120(f)
Helmholtz function      see “Helmholtz free energy”
Henkel plot      250—251 492(f) 254(b)
Henkel plot in Preisach system      490—493 490(f)
Henkel plot in Preisach system and mean-field effect      492 493
Henkel plot in Preisach system, analytic law      490 491
Hermite polynomial      276 525
Hessian matrix in catastrophe theory      49
Hysteresis and branching      38 38(f)
Hysteresis and dissipation      36—37
Hysteresis and lag      33—35 34(f)
Hysteresis and memory      37—39
Hysteresis and metastability      40—44 466
Hysteresis and nonequilibrium thermodynamics      31 123 466
Hysteresis field      324—325 347 397 424
Hysteresis field and excess loss      425
Hysteresis in magnetic material      3 16—19
Hysteresis loop      4—16
Hysteresis loop and anisotropy, in soft material      319—320 320(f)
Hysteresis loop and magnetic domains      7—9 15—16 9(f)
Hysteresis loop and magnetization process      317 319
Hysteresis loop and specimen geometry      13 13(f) 14(f)
Hysteresis loop in bistable system      46 59 47(f) 59(f)
Hysteresis loop in coherent rotation      241—242 240(f) 241(f)
Hysteresis loop in domain wall dynamics      469—470 470(f) 474(f)
Hysteresis loop in particle assembly      248 248(f)
Hysteresis loop in particle assembly, singularity      251—253
Hysteresis loop in Preisach system      481—482 449(f) 482(f) 483(f)
Hysteresis loop in Preisach system, elementary      438—439 438(f)
Hysteresis loop of particular type, minor      19 20(f)
Hysteresis loop of particular type, reentrant      318—319 321—323 322(f)
Hysteresis loop of particular type, saturation      17
Hysteresis loop, area as energy loss      24—25 36 60 324—325 394
Hysteresis loop, B(H) versus M(H)      11 12(f)
Hysteresis loop, difficulty of interpretation      11—16
Hysteresis loop, example      5(f) 14(f) 20(f) 322(f)
Hysteresis loop, measurement method      13(f)
Hysteresis loop, rate-dependence      59—60
Hysteresis loop, rate-dependence due to eddy currents      24—25 392 401—402 405 410 402(f) 423(f)
Hysteresis loop, rate-dependence due to thermal relaxation      29 331 494 503—504
Hysteresis loop, rate-dependence, loop shape      24(f) 59(f) 406(f) 410(f)
Hysteresis loss      324—325
Hysteresis loss and Maxwell’s equations      100
Hysteresis loss, dependence on eddy-current shielding      403
Hysteresis loss, dependence on magnetization frequency      397
Hysteresis loss, qualitative description      26 392
Hysteresis loss, statistical interpretation      396—397
Hysteresis, consistency rules for      466
Hysteresis, mathematical description      33 69(b) 476(b)
Hysteresis, rate-independence versus rate-dependence      23—24 33
Hysteresis, scalar versus vector approach      32
Identification problem for Preisach system      480—481
Impulse response in linear system      34
Inclusion as pinning source      374
Initial susceptibility      19 307
Initial susceptibility and pinning field      308—309
Initial susceptibility in coherent rotation      307—308
Initial susceptibility in domain wall bowing      309—310 309(f)
Initial susceptibility in particle assembly      248—249 307—308
Input variable in hysteresis      see “Control parameter”
Internal energy in thermodynamics      116 117
Iron      517(t)
Irreversible transformation in thermodynamics      120 123 449
Ito equation      see “Stochastic differential equation”
Ito versus Stratonovitch calculus      528
Joule dissipation      99 (see also “Eddy currents”)
Kerr effect      191 8(f) 209(f)
Kramers equation      343(b)
Kramers equation and pinning field      315
Laguerre polynomial      275 276 280
Landau free energy      41—42 70(b)
Landau free energy and nonlocal memory      43
Landau free energy and partition function      41
Landau free energy in ferromagnet around Curie point      139 140(f)
Landau free energy in micromagnetics      164 168—169 455
Landau free energy in Preisach system      454—455
Landau — Lifshitz equation      185 187(b)
Landau — Lifshitz equation, equivalence with Gilbert’s equation      185
Langevin equation      526—527
Langevin equation for domain wall motion      273—274
Langevin equation for domain wall motion and Brownian motion      273 276
Langevin equation for domain wall motion, mathematical structure      274
Langevin equation for domain wall motion, physical interpretation      273
Langevin equation for pinning field      268—269
Langevin equation for thermal relaxation      65—66
Langevin function in paramagnetism      132 133(f)
Level-crossing problem      see “First-passage time”
Linear system, energy loss      36
Linear system, input-output relationship      34
Linear system, instantaneous versus delayed response      34
Linear system, memory      37
Linear-response theory      70(b)
Local memory      39
Lorentz force      76 96
Lorentz microscopy      192
Loss angle in linear system      35
Loss angle in power loss measurement      37
Loss per cycle in magnetic material      25 36
Loss per cycle in magnetic material, frequency dependence      25—26 26(f) 428(f)
Loss separation      429—430(b)
Loss separation and domain wall motion      262 281
Loss separation and internal degrees of freedom      262 263—265
Loss separation and Maxwell’s equations      100

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