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 |  موضوع: كتاب Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes - Second Edition الجمعة 29 مارس 2024, 1:12 am | |
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Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes - Second Edition
Carmine Vittoria
و المحتوى كما يلي :
Contents
Preface xii
Preface to the Second Edition xv
Acknowledgments .xvi
Author xvii
Chapter 1 Review of Maxwell Equations and Units .1
Maxwell Equations in MKS System of Units 1
Major and Minor Magnetic Hysteresis Loops 2
Tensor and Dyadic Quantities 6
Maxwell Equations in Gaussian System of Units 10
External, Surface, and Internal Electromagnetic Fields . 11
Problems . 14
Appendix 1.A: Conversion of Units . 15
References 18
Solutions . 18
Chapter 2 Classical Principles of Magnetism .27
Historical Background 27
First Observation of Magnetic Resonance .27
Definition of Magnetic Dipole Moment .28
Magnetostatics of Magnetized Bodies . 33
Electrostatics of Electric Dipole Moment 39
Relationship between B and H Fields . 41
General Definition of Magnetic Moment .44
Classical Motion of the Magnetic Moment 46
Problems .49
Appendix 2.A .50
Bibliography . 51
Solutions . 51
Chapter 3 Introduction to Magnetism .59
Energy Levels and Wave Functions of Atoms 61
Spin Motion 64
Intra-Exchange Interactions . 67
Heisenberg Representation of Exchange Coupling 72
Multiplet States 72
Hund Rules . 75
Spin–Orbit Interaction 77
Lande gJ-Factor 78
Effects of Magnetic Field on a Free Atom .80viii Contents
Crystal-Field Effects on Magnetic Ions 85
Superexchange Coupling between Magnetic Ions .89
Double Superexchange Coupling .99
Ferromagnetism in Magnetic Metals 101
Problems . 106
Appendix 3.A: Matrix Representation of Quantum Mechanics . 108
Bibliography 110
Solutions . 111
Chapter 4 Deposition of Ferrite Films at the Atomic Scale by the
ATLAD Technique . 119
Historical Background to the Development of the ATLAD
Technique . 119
Deposition of Ferrite Films by the Laser Ablation Technique .120
Deposition of Spinel Ferrite Films at the Atomic Scale—
ATLAD Technique 121
Deposition of Hexaferrite Films at the Atomic Scale—
ATLAD Technique 126
Concluding Remarks 134
Problems . 135
References 135
ATLAD References 135
Supplemental References 136
Solutions . 136
Chapter 5 Free Magnetic Energy 137
Thermodynamics of Noninteracting Spins: Paramagnets 137
Ferromagnetic Interaction in Solids . 139
Ferrimagnetic Ordering 144
Spin Wave Energy 147
Effects of Thermal Spin Wave Excitations . 151
Free Magnetic Energy 152
Single Ion Model for Magnetic Anisotropy . 153
Pair Model 155
Demagnetizing Field Contribution to Free Energy 156
Numerical Examples 160
Cubic Magnetic Anisotropy Energy . 164
Uniaxial Magnetic Anisotropy Energy . 165
Problems . 167
Bibliography 167
Solutions . 168
Chapter 6 Phenomenological Theory 182
Smit and Beljers Formulation . 182
Examples of Ferromagnetic Resonance . 184Contents ix
Simple Model for Hysteresis 196
General Formulation . 201
Connection between Free Energy and Internal Fields 203
Static Field Equations .204
Dynamic Equations of Motion .205
Microwave Permeability . 211
Normal Modes 214
Magnetic Relaxation . 218
Free Energy of Multi-Domains 223
Problems .227
Appendix 6.A: Magnetic Damping Parameter Calculated
from First Principles .227
Bibliography .229
Solutions .229
Chapter 7 Electrical Properties of Magneto-Dielectric Films 244
Basic Difference between Electric and Magnetic Dipole Moments .244
Electric Dipole Orientation in a Field 244
Equation of Motion of Electrical Dipole Moment in a Solid .246
Free Energy of Electrical Materials 247
Magneto-Elastic Coupling 249
Microwave Properties of Perfect Conductors . 252
Principles of Superconductivity: Type I . 253
Magnetic Susceptibility of Superconductors: Type I .259
London’s Penetration Depth .259
Type II Superconductors 261
Microwave Surface Impedance 264
Conduction through a Non-Superconducting Constriction 265
Isotopic Spin Representation of Feynman Equations .268
Problems . 272
Bibliography 274
Solutions . 275
Chapter 8 Kramers–Kronig Equations .282
Problems .287
Bibliography 288
Solutions .288
Chapter 9 Electromagnetic Wave Propagation in Anisotropic
Magneto-Dielectric Media .292
Spin Wave Dispersions for Semi-Infinite Medium .296
Spin Wave Dispersion at High k-Values .297
The k = 0 Spin Wave Limit .298
Sphere .298
Thin Films 300x Contents
Parallel FMR Configuration .300
Needle . 301
Surface or Localized Spin Wave Excitations 302
Pure Electromagnetic Modes of Propagation:
Semi-Infinite Medium 305
Coupling of the Equation of Motion and Maxwell’s Equations .306
Metals . 314
Dielectrics . 315
Solution for k2 . 315
Normal Modes of Spin Wave Excitations 318
Magnetostatic Wave Excitations . 323
M
Perpendicular to Film Plane 323
a. θ
k = 0: . 323
b. θ
k = π/2: 326
H
in the Film Plane 330
a. θ
k = 0: . 330
b. θ
k = π/2: 331
Case 1 . 331
Case 2 . 332
Ferrite Bounded by Parallel Plates . 333
Problems . 336
Appendix 9.A . 337
Empty Microwave cavity 337
At Resonance 337
Perpendicular Case .340
In-Plane Case 341
Bibliography 342
Solutions .342
Chapter 10 ATLAD Deposition of Magnetoelectric Hexaferrite Films and
Their Properties 346
Basic Definitions of Ordered Ferroic Materials .346
Parity and Time Reversal Symmetry in Ferroics 347
Tensor Properties of the Magnetoelectric Coupling in Hexaferrites .347
Deposition of Single-Crystal ME Hexaferrite Films of the
M-Type by the ATLAD 351
Magnetometry and Magnetoelectric Measurements 354
Free Magnetic Energy Representation of the Spin
Spiral Configuration . 359
Free Energy of ME Hexaferrite 360
Electromagnetic Wave Dispersion of Magnetoelectric Hexaferrite .362
Analog to a Semiconductor Transistor Three-Terminal Network 363
Problem 365
Solution 366
Bibliography .366Contents xi
Chapter 11 Spin Surface Boundary Conditions .367
A Quantitative Estimate of Magnetic Surface Energy . 369
Another Source of Surface Magnetic Energy . 370
Static Field Boundary Conditions 372
Dynamic Field Boundary Conditions . 373
Applications of Boundary Conditions 375
H ⊥
to the Film Plane 375
H
// to the Film Plane 380
Electromagnetic Spin Boundary Conditions 380
Problems . 384
Appendix 11.A . 385
Perpendicular Case . 385
In-Plane Case 394
Bibliography . 405
Solutions . 405
Chapter 12 Matrix Representation of Wave Propagation . 414
Matrix Representation of Wave Propagation in Single Layers 414
(//) Case 414
(⊥) Case 419
The Incident Field 420
Ferromagnetic Resonance in Composite Structures:
No Exchange Coupling 423
Ferromagnetic Resonance in Composite Structures:
Exchange Coupling 428
(⊥) Case 428
Boundary Conditions . 431
Procedure for Solution . 433
(//) Case 436
Boundary Conditions (// FMR) . 436
Problems . 439
Appendix 12.A .440
Calculation of Transmission Line Parameters from [A] Matrix .440
Microwave Response to Microwave Cavity Loaded with
Magnetic Thin Film 453
References 458
Solutions . 458
Index 467
Index
Note: Bold page numbers refer to tables and italic page numbers refer to figures.
alternate target laser ablation deposition
(ATLAD) technique 119–135,
346–366
deposition of ME hexaferrite films 346–366
development of 119–120
hexaferrite films deposition at atomic scale
126–134
spinel ferrite films deposition at atomic scale
121–126
A matrix 417, 420, 425, 426, 429, 431, 434,
440–453
angular momentum 44–46, 61, 77, 82, 83, 85,
253, 355
angular momentum quantum number 63–65,
75, 137
angular velocity 48, 58
antiferroelectrics 346
antiferromagnetic ordering 173
antiferromagnetic state 71, 72, 91, 97, 98, 102,
103, 346
anti-resonance FMR (AFMR) frequency 213
atomic number 61, 77, 114
atoms 61–64, 85, 246, 369
band gap energy 255
bandwidth 222
barium hexaferrite (BaFe12O19) 351
magnetoplumbite hexagonal structure 162
single crystal film deposition 127–131
Bernoulli’s equation 137
B-field 7, 14, 31, 41–44
Bloch–Bloembergen model 221
body center cubic (BCC) 137, 140, 171, 171, 370
Bohr magneton 32, 46, 58, 64, 137
Bohr’s radius 32, 62
Boltzmann statistics 137
Boltzman’s constant 245
boson operators 268
boundary condition 13, 14, 212, 367–404, 414,
419, 422, 424, 430, 431–433, 436,
445, 462
applications 375–380
dynamic field 373, 373–375
electromagnetic spin 380–384
spin-pinning 424
spin surface 367–384
static field 372–373
wave propagation in single layers 414
Brillouin function 138, 151, 172
Brillouin zone 297–298
bubble domains 223, 224, 225
Cauchy probability function 197, 198, 200
characteristic impedance 11, 264, 417, 419, 432,
440, 443, 454, 464
charge density 50, 258
circular coil 33, 33
circular polarization 2, 5, 376, 420
coaxial line 420
cobalt ions 352, 358
coercive field 199, 201, 365
collinear magnetic sublattice 144, 144
commutation relations 268, 270
composite structures, FMR in 423–438
conduction 43, 254, 259, 265–268, 270
current 43
through non-superconducting constriction
265, 265–267
conductivity 2, 101, 252, 253, 379, 380, 424
conductors 252–253
constitutive relations 1, 9, 10
constriction 266, 268
contour integral 291
converse ME effect 348
conversion of units 15, 16, 17
Cooper pair 253, 254, 257, 258
Coulomb force 62
Coulomb interaction 67
Coulomb repulsion energy 118
coupling constant 266
critical magnetic fields 261
crystal-field effects, on magnetic ions 85–89
electrostatic interaction 86
multiplet splittings 88, 88–89
3d electronic configuration 89, 89
3d wave functions 88
wave functions 86–88, 90
cubic magnetic anisotropy energy 164–165, 166
CuFe2O4, single crystal film deposition of
124–126
Curie’s law 139
Curie temperature 142
current density 1, 2, 31, 42, 43, 267
db 8, 328, 329
DC permeability 193
DC susceptibility 190, 193
De Broglie’s equation 59468 Index
degeneracy 65, 68, 70, 75, 85, 87, 99–101
degrees of freedom 64, 65
delay time 328
delta splitting 89
demagnetizing energy 39, 186, 225, 226,
325–327, 331, 332, 360
demagnetizing factors 157, 158, 186, 212, 225
demagnetizing field 156–160, 159, 187, 187,
292–294
density 129
diamagnetic energy 84
diamagnetism 169, 258
dielectric constant 2, 12, 335, 355
dielectrics 315
dielectric tensor 273, 278
dipole–dipole interaction 39, 157, 174, 369,
409–412
Dirac’s equation 64
direct ME effect 348
discrete 59, 61, 227, 327, 329
dispersion 132, 207, 292, 296–302, 305, 306, 308,
310, 311, 313–333, 340, 345, 362–363,
423, 428, 461
dielectrics 315
magnetic metals 314–315
relation 318, 320
resonant spin wave mode 318
displacement current 43
dissipation loss 4
domain wall 225
double exchange 99, 101
double superexchange coupling 99–101
dyadic operator 309
dyadic permeability 43
dyadic quantities 6–10
dyadic susceptibility 44
dyadic vector 9
dynamic equations of motion 205–211
dynamic field boundary condition 373, 373–375
dynamic magnetic field 130, 203
dynamic motion 147
Dzyaloshinskii–Morya interaction 347, 359
Earth’s field 56
effective conductivity 441, 444
effective permeability 288, 444
effective propagation constant 419, 443
E-field 272, 275, 344, 355, 463
eigen energies 96
eigen function 69, 70
elastic constants 247
electrical bridge technique 28
electric dipole moment 39–41, 40, 347
definition 244
electric displacement 247
in field 244–246
lattice motion 246, 246
in solid 246–247
electric displacement 247
electric field 17, 21, 23, 40, 40, 41, 81, 244, 252,
347, 348, 362, 380
electric susceptibility 2, 247
electromagnetic energy 14
electromagnetic fields 48
external 11–14, 12
internal 11–14, 12
surface 11–14, 12
electromagnetic spin boundary condition
380–384
electromagnetic wave propagation 292–336
dielectrics 315
equation of motion and Maxwell’s equations
306–314
ferrite bounded by parallel plates
333–336, 334
high k-values, spin wave dispersion at
297–298, 298
in insulator 305, 305
magnetic metals, dispersion for 314–315
magnetoelectric hexaferrite 362–363
magnetostatic wave excitations 323–333
for metal 305, 306
semi-infinite medium 305–306
solution for k 2 315–317
sphere 298–299
spin wave dispersions for semi-infinite
medium 296, 297
spin wave excitations, normal modes of
318–323
spin wave limit 298
surface spin wave excitations 302–305
electron 32, 56, 59
electron beam deposition 119
electronic configuration 75, 91, 100, 160
electrostatic interaction 28, 85, 86
electrostatic repulsion energy 68, 71
electrostatics, of electric dipole moment
39–41, 40
electrostriction 346
energy dispersive X-ray spectroscopy
(EDS) 352
energy levels 61–64, 71, 88, 89, 153
EPR equipment 340
equation of motion 47, 82, 183, 306–314
equilibrium condition 184, 185, 188, 191,
193–195, 204, 373
equivalent circuit 14, 14, 337, 453, 459
exchange coupling, Heisenberg representation
of 72
exchange energy 103, 140, 152
exchange field 141, 293
exchange integral 93, 140
exchange interaction 28, 75, 80, 139, 140, 147,
346, 369Index 469
exchange stiffness constant 150, 228, 307, 361,
363, 424
excitation matrix 434
extended X-ray absorption fine structure
(EXAFS) technique 125, 132, 133
face center cubic (FCC) 137, 384, 411
Faraday’s law 256, 308
Fermi energy 103, 254, 256
Fermi’s correlation probability function 72
Fermi’s radius 103
Fermi velocity 255
ferrimagnetic ordering 144–147, 172
ferrimagnetics 346
ferrite films deposition, by ATLAD technique
119–135
hexaferrite films 126–134
spinel ferrite films 121–126
ferrites 27, 86, 119–122, 127, 131, 227
ferroelectrics 346
ferroics, parity and time reversal symmetry
in 347
ferromagnetic interaction, in solids 139–144
Curie temperature 142
exchange field 141
magnetic potential energy 140
magnetization vs. temperature 142
normalized magnetization 143, 143
susceptibility ratio 142
thermal magnetization 141
ferromagnetic resonance (FMR) 119, 184–196,
329, 355, 423–439
in composite structures 423–438
exchange coupling 428–438, 435
magnetostatic wave excitation 323, 324, 326,
329–330
needle-shaped magnetic sample 187, 187–188
no exchange coupling 423–428
semi-infinite magnetic medium 184–186, 185
spherical magnetic sample 186–187
thin-film magnetic sample 188–192, 189
uniaxial magnetic anisotropy energy 192,
192–196, 194–196
ferromagnetic state 71, 91, 97, 100–103, 146, 346
ferromagnetism, in magnetic metals 101–106
Feynman equations, isotopic spin representation
of 268–272
Fourier transform 282
free atom 80, 85
free electron gas 103
free energy 182, 184, 202
of electrical materials 247–249
and internal fields connection 203–204
Maxwell’s equations 307
of ME hexaferrite 360–362
of multi-domains 223–226
spin spiral configuration 359–360, 360
surface anisotropy energy density 374
free magnetic energy 137–181
cubic magnetic anisotropy energy
164–165, 166
demagnetizing field 156–160, 159
ferrimagnetic ordering 144–147
ferromagnetic interaction in solids 139–144
Gibbs free energy 152
Helmholtz free energy 152
noninteracting spins, thermodynamics of
137–139
pair model 155–156
single ion model for magnetic anisotropy
153–155
spin wave energy 147–150
thermal spin wave excitations 151, 151–152
uniaxial magnetic anisotropy energy 165–166
Gaussian system of units 10–11
Gauss law 294
general formulation 201–203
g-factor 136, 372
giant magnetoresistance (GMR) 364, 364
Gibbs free energy 152
Gilbert damping parameter 218, 220, 222, 228,
228, 308, 377, 378
Gilbert relaxation model 308
Green’s theorem 368
ground state energy 63, 91, 102, 255, 257
ground-state multiplet
for rare earth ions 76
for transition metal ions 76
gyromagnetic ratio 45
Hamiltonian 61, 78, 80, 81, 90, 102, 203, 255,
256, 268
Hamilton–Jacobi equation 246, 252
Heisenberg Exchange model 72, 103
Helmholtz free energy 152
hexaferrite films deposition, by ATLAD
technique 126–134
BaFe12–xMnxO19 131–134
barium hexaferrite (BaFe12O19) 127–131, 130
hexaferrites 120, 122, 126–134, 166, 208–211,
346–366
crystal structure 162, 163
magnetoelectric coupling in 347–351
M-type 351–353
single-crystal ME films 351–353
hexagonal symmetry 160, 412, 413
H-field 41–44
Hund’s rule 75–76, 160
hysteresis model 196–200
Cauchy probability function 197, 198, 200
ferromagnetic resonance 199, 201
loop 197, 200
saturation field effects 196, 197470 Index
incident electric field 420
incident electromagnetic field 420–423
incident voltage 420, 454
induced current 281
induced magnetization 258, 356
interfacial region 304
internal energy 152
internal magnetic field 203, 307, 380
internal supercurrents 259
intra-exchange interactions 67–72
Coulomb interaction 67
eigen functions 69, 70
electrostatic repulsion energy 68, 71
energy levels 71, 71
Fermi’s correlation probability
function 72
Pauli’s exclusion principle 71
Schrodinger equation 68
spin angular momentum 70
ionic bonding 154
iris cavity hole 337, 418
iron 140–142, 146, 150, 370
isotopic spin 268–272
Josephson equation 267, 268, 271, 272
kinetic energy 81–83, 102
Kramers–Kronig equations 282–288
contour of integration 284, 284
Fourier transform 282
magnetic flux density 283
magnetic system 282
mathematical poles 284, 284
Kramer’s rule 417
Lame constants 252
Landau–Lifshitz damping parameter 218–221,
308, 359, 360
Lande gJ-factor 78–80
Langevin function 245
Larmor frequency 48, 270, 271
lattice displacement 248
lattice motion 246, 254, 357
Laurent series 275
Legendre polynomial expansion 155
Lenz law 84
linear momentum 59
linear polarization 5, 419
linewidth 27, 119, 133, 222, 227, 328
liquid phase epitaxy (LPE) 119
lithium ferrite (Li0.5Fe2.5O4) doped with Al2O3
121–122
London’s penetration depth 259–261
loop rotation 30
Lorentz’s law 28, 81, 252
lowering operator 268
magnetic anisotropy energy 153, 160, 164–165,
166, 192–196, 223, 225, 226, 296, 360,
369, 423, 430
cubic symmetry 164–165, 166
uniaxial symmetry 165–166
magnetic current 42, 43
magnetic damping 227–228
magnetic dipole moment 15, 244, 369
angular momentum 44–46
Bohr magneton 32, 46
classical motion 46–49
current-carrying wire loop 28, 29
current density 31, 42
definition 28–32, 44–46
graphic representation 45
loop rotation 30
potential energy 30, 31
torque 29, 30, 46
Zeeman magnetizing energy 31
magnetic domain 187, 224, 355
magnetic field effects, on free atom 80–85
equation of motion 82
Hamiltonian 80, 81
kinetic energy 81–83
Lenz law 84
Lorentz’s law 81
magnetic moment 83–85, 84
magnetic field excitation 208–211
magnetic fluctuation 152
magnetic flux density 2, 6, 15, 283
magnetic hysteresis loops 2–6
magnetic ions 85–99, 121, 122, 124, 126, 131,
136, 150, 153, 154, 348, 352, 353,
358, 369
crystal-field effects on 85–89
superexchange coupling between 89–99
magnetic metals 86, 101–105, 312, 314, 364, 426,
435, 441
dispersion of 314–315
ferromagnetism in 101–106
magnetic moment 8, 15, 30, 32, 36
classical motion 46–49
general definition 28–32, 44–46
magnetic order 354
magnetic polarization 250, 250
magnetic potential energy 31, 38, 77, 80, 81, 83,
140, 150, 152, 262, 263
magnetic relaxation 218–223, 227, 357
Gilbert damping 218, 220, 222
Landau–Lifshitz damping 218–221
permeability tensor element 222, 223
relaxation mechanism 221, 222
magnetic resonance 27–28, 28, 49
magnetic sublattice 85, 86, 121, 126, 160, 161, 292
magnetic surface energy 369–370
magnetic susceptibility 2, 3, 9, 259, 260Index 471
magnetic tunnel junction (MTJ) 364, 364
magnetism 27–49, 59–110, 126, 127, 131, 133,
139, 152, 162, 348, 369, 438
B and H fields 41–44
crystal-field effects 85–89
double superexchange coupling 99–101
electric dipole moment 39–41, 40
energy levels and wave functions of atoms
61–64
ferromagnetism 101–105
Heisenberg representation 72
Hund rules 75–76
intra-exchange interactions 67–72
Lande gJ-factor 78–80
magnetic dipole moment 28–32
magnetic field effects on free atom 80–85
magnetic moment 44–49
magnetic resonance 27–28, 28
magnetostatics 33–39
multiplet states 72–75
spin motion 64–67
spin–orbit interaction 77–78
superexchange coupling 89–99
magnetization 3, 41
magnetization vector 41, 157, 292, 359
magnetized bodies, magnetostatics of 3–39
magneto-dielectric films 244–272
electric dipole moment 244–247
Feynman equations, isotopic spin
representation of 268–272
free energy of electrical materials 247–249
London’s penetration depth 259–261
magnetic dipole moment 244
magneto-elastic coupling 249–252
microwave properties of perfect conductors
252–253
microwave surface impedance 264–265
non-superconducting constriction 265,
265–267
type I superconductivity principles 253–258
type I superconductors 259, 260
type II superconductors 261–263, 262
magneto-elastic coupling 249–252
elastic equations of motion 252
strain 249–251, 250
magnetoelectric hexaferrite 346–365
electromagnetic wave dispersion 362–363
free energy 360–362
single-crystal films 351–353
magnetoelectric measurements 354–359, 355
magneto-impedance 383
magnetometry 354–359
magnetostatic backward volume wave
(MSBW) 331
magnetostatics 33–39, 40, 323, 324, 325, 329,
330, 331, 423
circular coil 33, 33
earth’s magnetic field generation model 37, 38
Lorentz condition 34
of magnetized bodies 3–39
Zeeman interaction energy 38
magnetostatic surface wave (MSSW) 333
magnetostatic wave excitation 323–333
approximate spin wave dispersion 326,
327, 331
delay line device 324
ferromagnetic resonance 323, 324, 326,
329–330
higher mode excitations 329
magnetostatic surface wave 333
magnetostatic waves 323, 327
microwave signal propagation 325
pure spin wave 323–325, 324, 332
slope 327
spin wave resonance 325
standing spin wave mode 325
static magnetization 323–325, 324, 330, 331
surface demagnetizing field 324–327,
330–333
YIG propagation loss 328
magnetostatic waves (MSW) 323, 327, 327,
328, 332
magnetostriction 346
major magnetic hysteresis loop 2–6, 3
manganese ferrite (MnFe2O4) 122, 123, 124, 125
ATLAD film deposition 122–124
magnetic inversion factor 124
single crystal film deposition of 122–124
mathematical poles 284, 284
mathematical singularity 194, 195
MATLAB program 286, 288, 323, 340, 379,
383, 442
matrix elements 10, 11, 92, 94, 102, 103, 109, 350,
358, 416, 422
matrix representation of wave propagation
FMR in composite structures 423–438
MATLAB program 438, 442–453
microwave response to microwave cavity
453–458
reflection and transmission coefficient
416, 453
transmission line parameters 440–453
wave propagation in single layers 414–423
Maxwell boundary condition 212
Maxwell’s equation 33, 43, 156, 260
equation of motion and 306–314
in Gaussian system of units 10–11
in MKS system of units 1–2
Meissner effect 259, 261
microwave cavity 337, 340, 453–458
microwave permeability 202, 211–214
microwave surface impedance 264–265
microwave susceptibility 235, 237, 240, 242, 243
minor magnetic hysteresis loop 2–6, 3472 Index
MKS system of units 1–2
molecular field 103, 105, 140, 144, 145, 292, 293
molecular polarizability 23
monolithic microwave integrated circuit
(MMIC) 119
multi-domains, free energy of 223–226
magnetic bubble domains configuration
223–225, 224
magnetic domain configuration 223, 224
magnetic stripe domains 223–225, 225
multiferroics 346
multiplet energy splittings 74, 74
multiplet splittings 88, 88–89
nearest neighbor 89, 103, 140, 149, 155, 369, 370,
410, 411
Neel temperature 124, 145, 358
Newton’s second law 58
nickel 146
noninteracting spins, thermodynamics of 137–139
Brillouin function 138
Curie’s law 139
magnetization 139, 139
total magnetic moment 137
nonlinear analysis 206
non-resonant mode 216, 314, 316
non-superconducting constriction 265, 265–267
nuclear magnetic resonance 27, 28
octahedral 86, 86–89, 121
off resonance 337, 464
Ohm’s law 19, 24, 253, 383
orbital 64, 68
orbital angular momentum 75, 77, 82, 83
orbital quantum number 64
orbital wave function 68
ordered ferroic materials 346
pair model 155–156
parallel FMR 300–302
parallelism 204
parallel plates, ferrite bounded by 333–336, 334
paramagnetics 141, 142, 221
partition function 170
Pauli’s exclusion principle 66, 71–73, 101
permalloy 143, 222, 323, 364
permeability 1
permeability tensor 7–9, 14, 222, 223, 306–308
permittivity 1
permittivity tensor 15, 307
perpendicular FMR 192, 300, 304
perturbation method 322
phenomenological theory 182–227
dynamic equations of motion 205–211
ferromagnetic resonance 184–196
free energy and internal fields connection
203–204
free energy of multi-domains 223–226
general formulation 201–203
hysteresis model 196–201
magnetic damping parameter 227–228, 228
magnetic relaxation 218–223
microwave permeability 211–214
normal modes 214–217
Smit and Beljers formulation 182–184
static field equations 204–205
physical constants 17
piezoelectric coupling energy 361
piezoelectricity 346
piezomagnetics 346
piezomagnetic tensor 349
Planck’s constant 59
polarization fields 11
polarization vector 23
polyvinyl alcohol (PVA) 352
potential energy 30, 31, 51, 52
potential magnetic energy 80
power loss 4, 6
Poynting integral 11, 14, 379
probability function 71, 72, 109
propagation constant 228, 265, 295, 316, 329, 367,
419, 421, 432, 463
proton 46
pulse laser deposition (PLD) 123
quantum fluxoid 257
quantum mechanics 32, 59, 77, 108–110, 148,
256, 268
matrix representation 108–110
Racah parameters 73, 74
radial wave function 74
reflection coefficient 339, 340, 453, 454
repulsive electrostatic energy 88
resonance condition 187, 188, 214, 300
ring resonator 59
saturating fields 191
scalar permeability 6
scalar potential 157, 233, 234
scattering S parameters 414, 416
Schrodinger’s equation 60–62, 68, 114, 170, 303
semiconductors 363–365
semi-infinite medium 7, 184–187, 220, 296–299,
305–306, 323
pure electromagnetic modes of propagation
305–306
spin wave dispersion for 296, 297
simple cubic (SC) symmetry 137
single ion model, for magnetic anisotropy
153–155
single-loop Cooper carrier 257
skin depth 14, 20, 25
Slater determinant 73, 101Index 473
Slater function 63
Smit and Beljers formulation 182–184, 202, 207
spherical magnetic sample 186–187
spin angular momentum 70, 77, 83
spinel ferrite films deposition, by ATLAD
technique 121–126
CuFe2O4, single crystal film of 124–126
lithium ferrite (Li0.5Fe2.5O4) doped with Al2O3
121–122
MnFe
2O4, single crystal film of 122–124
spin matrix 269
spin motion 32, 47, 64–67
degeneracy 65
degrees of freedom 64, 65
magnetic moment 64
Pauli exclusion principle 66
wave function 65, 66, 67
spin–orbit interaction 77–78
spin–phonon interactions 227
spin-pinning boundary condition 424
spin spiral configuration 359–360, 360
spin surface boundary conditions 367–405
applications 367, 375–380
dynamic field 373, 373–375
magnetic surface energy 369–370
static field 372–373
surface magnetic energy 370–372, 371
spin wave dispersion 292
at high k-values 297–298, 298
for semi-infinite medium 296, 297
spin wave energy 147–150
spin wave excitation 292
FMR condition 295
isotropic case 319
in magnetic cylinders 301, 302
normal modes 318–323
resonant spin wave mode 318
surface or localized 302–305
spin wave limit k = 0 298
needle 301–302, 302
parallel FMR configuration 300–301, 301
sphere 298–299, 299
thin films 300, 300
spin wave motion 147, 148
spin wave resonance (SWR) 325
SrCo2Ti2Fe8O19 353, 356, 357
magnetoelectricity in 351–352
site occupancy of transition metal cations in
357, 357
static field boundary condition 372–373
static field equations 204–205
static magnetic field 8, 270, 281, 295, 325, 372,
423, 428
Stokes theorem 31
stripe domains 225, 225
strontium hexaferrite 127
superconductivity 253–259
superconductors 253–256, 258, 259–263, 265,
273, 279, 280, 463
type I 259, 260
type II 261–263, 262
supercurrent 252, 257, 259, 261
superexchange coupling, magnetic ions 89–99
surface boundary condition 372, 407, 431
surface demagnetizing field 330–333
surface energy 332, 369–370, 409
surface impedance 264–265, 378, 379, 385,
426–428, 434, 435, 441
surface magnetic energy 370–372, 371
surface magnetism 369
surface spin wave excitation 302–305
surface torque 369
susceptibility tensor 213
Taylor series expansion 42, 148, 183
tensor quantities 6–10
tetrahedral symmetry 86, 88, 89, 121, 124,
126, 146
thermal magnetization 141
thermal spin wave excitations 151, 151–152
thermodynamics 137–139
3d electron 72, 89
three-terminal network 363–365
time dependence 7, 8, 108, 109, 183, 282, 318, 328
time response 2, 3
titanium 100
torque 29, 30, 46, 51, 52
transfer function matrix 418, 434, 459, 459, 461,
463, 464
transition temperature 179, 256
transverse electromagnetic (TEM) wave of
propagation 306
tunnel magnetoresistance ratio (TMR) 365
type I superconductivity principles 253–259
Fermi energy 254, 256
hypothetical motion of Cooper pair 253, 257
internal supercurrents 259
magnetization vs. external field 258, 258
single-loop Cooper carrier 257
superconducting carriers motion 254, 254
type I superconductors, magnetic susceptibility
of 259, 260
type II superconductors 261–263, 262
uniaxial symmetry 156, 160, 192, 193
uniaxial magnetic anisotropy energy 165–166,
192, 192–196, 194–196, 223
units 1–26
conversion of 15, 16, 17
Gaussian system 10–11
MKS system 1–2
vector electric potential 39
vector magnetic potential 31474 Index
vibrating sample magnetometer (VSM) 7,
354, 355
volume demagnetizing field 292, 294, 298, 312,
319, 326, 330–333
wave function 60, 61, 63, 65, 70, 71, 73, 74,
86–88, 90–92, 99, 101, 102, 107–109,
115–118, 255, 257, 265, 266, 268
orbital 68
radial 74
spin motion 65, 66, 67
3d electron 88, 99
waveguide 418–420, 454, 464
wavelength 59, 129, 131, 292, 296, 297, 326,
332, 333
wave propagation, in single layers 414–423
boundary condition equations 414
field excitations 414, 419
FMR in composite structures 423–438
incident electric field 420
incident field 420–423
incident voltage 420, 454
Kramer’s rule 417
mathematical procedure 416
2×2 matrices 415, 418, 434
matrix element calculation 422
reflected signal 421
transmission scattering S-parameters 416
transmitted signal 421
X-ray absorption spectroscopy (XAS) 355–356
X-ray magnetic dichroism 356
yttrium iron garnet (YIG) 146
deposition by laser ablation 119–120
dispersions 316, 317, 323
magnetization 146
MSSW velocity 333
Zeeman energy 140, 153, 186, 224
Zeeman interaction energy 38
Zeeman magnetizing energy 31
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