Table of constants (see inside front cover)
Preface ...................................................... xvii
1 Introduction to Magnetism and Magnetic Materials ............ 1
1.1 Basic Electromagnetism ..................................... 2
1.1.1 Magnetic Field: Biot-Savart and Ampere Laws ......... 2
1.1.2 Magneticlnduction or Flux Density ................... 4
1.1.3 The Magnetic Flux ................................... 6
1.2 Elementary Magnetostatics .................................. 7
1.2.1 Magnetic Charges: "Monopoles" and Dipoles ........... 7
1.2.2 Magnetic Dipole Moment .............................. 8
1.2.3 Field Due to a Magnetic Dipole ...................... 9
1.3 The Magnetic Moment: Equivalence of Dipoles and Current
Loops ..................................................... 11
1.4 Sources of Magnetic Fields ................................ 12
1.4.1 Field Generated by a Circular Current Loop ......... 12
1.4.2 Field Generated by a Solenoid ...................... 14
1.4.3 Helmholtz Coils .................................... 15
1.4.4 A Planar Coil: Archimedean Spiral .................. 16
1.5 Intensity of Magnetization ................................ 17
1.6 Relationship between Magnetization, Field, and Induction .. 18
1.7 Susceptibility and Permeability ........................... 20
1.8 An Overview of the Types of Magnetic Behavior in
Materials ................................................. 22
1.8.1 Diamagnetism ....................................... 22
1.8.2 Paramagnetism ...................................... 23
1.8.3 Ferromagnetism ..................................... 23
1.8.4 Antiferromagnetism ................................. 25
1.8.5 Ferrimagnetism ..................................... 25
1.9 Hysteresis ................................................ 26
1.10 Work Done by the External Field in Hysteresis ............. 28
1.11 Demagnetization ........................................... 29
1.11.1 Calculation of Demagnetizing Factors ............... 31
1.11.2 Gauss Law .......................................... 34
1.11.3 Demagnetization Energy ............................. 36
1.11.4 Practical Consequences of the Demagnetization
Field .............................................. 37
1.12 Maxwell Equations ......................................... 38
Summary ................................................... 39
Further Reading ........................................... 40
References ................................................ 41
Exercises ................................................. 41
2 Atomic Origins of Magnetism ............................... 47
2.1 Quantization of Energy .................................... 48
2.2 Quantization of Angular Momentum .......................... 50
2.3 Spatial Quantization of the Angular Momentum .............. 50
2.4 One-Electron Wave Functions Subject to a Central Force .... 52
2.5 Relationship Between the Orbital Angular Momentum and
the Magnetic Moment of an Electron ........................ 55
2.5.1 The Zeeman Effect: Evidence for Spatial
Quantization ....................................... 56
2.6 Electron Spin ............................................. 57
2.7 The Stern-Gerlach Experiment .............................. 58
2.7.1 Nuclear Spin ........................................ 60
2.8 The Spin-Orbit Interaction ................................ 61
2.9 The Electronic Strucnire of the Atom ...................... 63
2.10 Total Angular Momentum and the Magnetic Moment of the
Atom ...................................................... 66
2.11 Quenching of Orbital Angular Momentum ..................... 71
2.12 Electron Paramagnetic Resonance (EPR) and Determination
of the Landé g-Factor ..................................... 73
Summary ................................................... 75
Further Reading ........................................... 75
Reference ................................................. 75
Exercises .................................................
3 Magnetic Materials: From Isolated Moments to Ordered
Arrangements .............................................. 79
3.1 Langevin Theory of Diamagnetism ........................... 80
3.2 Introduction to Superconductors ........................... 82
3.3 Langevin Theory of Paramagnetism .......................... 84
3.4 Quantum Theory of Paramagnetism ........................... 87
3.5 Weiss Theory of Ferromagnetism ............................ 90
3.6 Law of Corresponding States ............................... 95
3.7 Mean-Field Approximation, Critical Phenomena, and
Exponents ................................................. 98
3.8 Exchange Interactions .................................... 102
3.9 Nature of the Exchange Integral and the Bethe-Slater
Curve .................................................... 105
3.10 Helical Structures ....................................... 107
3.11 The Physical Meaning of Long-Range and Short-Range
Forces ................................................... 108
Summary .................................................. 109
Further Reading .......................................... 110
References ............................................... 110
Exercises ................................................ 110
4 Other Ordered Magnetic Materials: Antiferromagnetism
and Ferrimagnetism ....................................... 115
4.1 Introduction to Antiferromagnetism ....................... 115
4.2 Molecular Field Theory of Antiferromagnetism ............. 117
4.2.1 Temperature T > TN ................................ 117
4.2.2 Temperature T < TN ................................ 118
4.2.3 Field Applied Perpendicular to the Spin Lattice
Direction ......................................... 120
4.2.4 Field Applied Parallel to the Spin Direction
(T < TN) .......................................... 120
4.2.5 Powder or Polycrystalline Samples ................. 122
4.3 Spin-Flopping and Metamagnetism .......................... 123
4.4 Introduction to Ferrimagnetic Materials .................. 124
4.5 Molecular Field Theory of Ferrimagnetism ................. 125
4.5.1 At High Temperatures, T > TC ...................... 126
4.5.2 For Low Temperature, T > TC ....................... 127
4.6 Indirect Exchange Interactions ........................... 129
4.6.1 Super-Exchange Interactions ....................... 130
4.6.2 Double-Exchange Interaction ....................... 132
4.7 Role of Local Symmetry and the Environment ............... 133
4.8 Determination of Magnetic Order: Neutron Scattering ...... 136
4.9 Examples of Antiferromagnetic and Ferrimagnetic
Materials ................................................ 140
4.9.1 Rock-Salt Structures .............................. 140
4.9.2 Spinel Structure Compounds (Ferrites) ............. 141
4.9.3 The Garnet Structure .............................. 145
4.9.4 Perovskites ....................................... 147
4.9.5 Hexagonal Iron Oxide Structures ................... 149
Summary .................................................. 151
Further Reading .......................................... 152
References ............................................... 153
Exercises ................................................ 153
5 Magnetism in Metals and Alloys ........................... 157
5.1 Introduction to the Electronic Structure of Metals ....... 158
5.2 Free Electron Theory of Metals ........................... 159
5.3 Pauli Paramagnetism ...................................... 163
5.4 Stoner Model of Ferromagnetism ........................... 165
5.5 Ferromagnetism of 3d Transition Metals and Alloys ........ 168
5.6 The Slater-Pauling Curve ................................. 174
5.7 Spin Density Waves ....................................... 176
5.8 The Indirect RKKY Interaction ............................ 178
5.8.1 Spin Glass and Frustration ........................ 180
5.8.2 The Kondo Effect .................................. 181
5.9 Amorphous Ferromagnetic Metals and Alloys ................ 182
5.10 Examples of Magnetic Alloys .............................. 185
Summary .................................................. 187
Further Reading .......................................... 188
References ............................................... 189
Exercises ................................................ 190
6 Magnetic Anisotropy ...................................... 193
6.1 Magnetocrystalline Anisotropy ............................ 193
6.1.1 Cubic Crystals .................................... 195
6.1.2 Uniaxial (Hexagonal) Crystals ..................... 197
6.1.3 General Crystal Structures ........................ 200
6.2 Anisotropy Measurements .................................. 200
6.2.1 Torque Magnetometry ................................ 201
6.3 Determination of Anisotropy Constants from
Magnetization ............................................ 207
6.3.1 Fitting Magnetization Curves ...................... 208
6.3.2 Areas of Magnetization Curves ..................... 212
6.4 Anisotropy Field ......................................... 213
6.5 Magnetic Resonance ....................................... 213
6.6 Nature of Magnetocrystalline Anisotropy .................. 214
6.7 Shape or Magnetostatic Anisotropy (Revisited) ............ 217
6.8 Magnetostriction or Magnetoelastic Anisotropy ............ 217
6.8.1 Phenomenological Theory of Magnetostriction
(Magnetoelastic Energy) ........................... 221
6.8.2 Magnetostriction and the Effect of Stress ......... 225
6.9 Mixed Anisotropics ....................................... 226
6.9.1 An Example ........................................ 226
6.9.2 A Graphical Solution .............................. 226
6.10 Anisotropy in Amorphous Magnets .......................... 227
6.11 Induced Anisotropy ....................................... 228
Summary .................................................. 229
Further Reading .......................................... 229
References ............................................... 230
Exercises ................................................ 230
7 Magnetic Domains and the Process of Magnetization ........ 234
7.1 The Domain Postulate ..................................... 234
7.2 Contributions to the Domain Energy ....................... 238
7.2.1 Continuum Approximation of the Exchange Energy .... 239
7.2.2 Magnetostatic or Demagnetizing Energy (Shape
Anisotropy) ....................................... 241
7.2.3 Magnetocrystalline and Magnetoelastic Energy ...... 244
7.3 The Bloch Wall ........................................... 245
7.3.1 Wall Energy and its Optimal Thickness ............. 246
7.3.2 Detailed Derivation of the Structure of a 180°
Wall .............................................. 248
7.3.3 90° Domain Walls .................................. 254
7.4 Bloch, Neel, and Cross-Tie Walls ......................... 257
7.5 Domain Structures in Particular Configurations ........... 260
7.5.1 Thin Films ........................................ 261
7.5.2 Fine Particles .................................... 266
7.6 Coherent Rotation: the Stoner-Wohlfarth Model ............ 271
7.7 Domain Wall Processes .................................... 280
7.7.1 Forces on a Domain Wall and the Potential
Approximation ..................................... 281
7.7.2 The Picture Frame Experiment ...................... 285
7.7.3 Interaction of Walls with Inclusions .............. 287
7.7.4 Inclusions and Voids .............................. 289
7.7.5 Low Energy Domain Walls: the Wall-Bowing
Approximation ..................................... 290
7.7.6 Stress as a Hindrance to Wall Motion .............. 292
7.8 The Magnetization Process ................................ 295
7.8.1 Magnetization in High Fields: Approach to
Saturation ........................................ 296
7.8.2 Magnetization in Low Fields: the Rayleigh Regime .. 297
7.8.3 Domains and the Magnetization Process ............. 298
Summary .................................................. 300
Further Reading .......................................... 301
References ............................................... 301
Exercises ................................................ 303
8 Micromagnetic Imaging and Modeling ....................... 307
8.1 Introduction ............................................. 308
8.2 Imaging Stray Magnetic Fields ............................ 310
8.2.1 Bitter Pattern Methods ............................ 310
8.2.2 Magnetic Force Microscopy ......................... 312
8.3 Imaging the Sample Induction Distribution ................ 315
8.3.1 Interactions of Electrons with Magnetic Samples ... 315
8.3.2 Electron-Specimen Interactions in a ТЕМ ........... 317
8.3.3 Lorentz Microscopy: Fresnel and Foucault Imaging .. 319
8.3.4 Lorentz Microscopy: Differential Phase Contrast
(DPC) Imaging ..................................... 320
8.3.5 Electron Holography ............................... 322
8.3.6 Off-Axis Electron Holography ...................... 323
8.3.7 Coherent Foucault Imaging ......................... 325
8.3.8 Scanning Electron Microscopy - Types I and II
Contrast .......................................... 326
8.4 Imaging the Magnetization Distribution with
Polarization Analysis .................................... 328
8.4.1 Secondary Electron Microscopy with Polarization
Analysis (SEMPA) .................................. 328
8.4.2 Spin-Polarized Low Energy Electron Microscopy
(SPLEEM) .......................................... 331
8.5 Imaging using Sample-Photon Interactions: the Magneto-
Optical Effect ........................................... 333
8.6 Magnetic Imaging with Element Specificity ................ 337
8.6.1 Principles of X-Ray Magnetic Circular Dichroism
(XMCD) ............................................ 338
8.6.2 Transmission X-Ray Microscopy (TXM) ............... 341
8.6.3 X-Ray Photoemission Electron Microscopy (X-PEEM) .. 342
8.7 Basics of Micromagnetic Modeling ......................... 345
8.7.1 Energy Terms ...................................... 346
8.7.2 Brown's Static Equations .......................... 350
8.7.3 Numerical Micromagnetics: the Dynamical
Equations ......................................... 351
Summary .................................................. 352
Further Reading .......................................... 353
References ............................................... 353
9 Fine Particles and Nanostructured Materials .............. 358
9.1 Introduction ............................................. 358
9.2 Classification of Fine Particles and Nanostructured
Materials ................................................ 360
9.3 Incoherent Magnetization Reversal: the Curling Mode ...... 362
9.4 Superparamagnetism and the Blocking Temperature .......... 364
9.4.1 Determining Size Distribution of
Superparamagnetic Particles ....................... 370
9.4.2 The Blocking Temperature: Zero-Field-Cooled
(ZFC) and Field-Cooled (FC) Measurements .......... 373
9.5 Coercivity of Fine Particles as a Function of Size ....... 375
9.6 Magnetization Dynamics ................................... 377
9.7 Finite Size and Surface Effects .......................... 382
9.8 Inter-Particle Interactions .............................. 388
9.8.1 Magnetic Order Arising from Dipolar Interactions .. 390
9.8.2 Remanence Measurements and Interaction Effects .... 392
9.9 Ferrofluids .............................................. 394
9.10 Response of Fine Particles to Alternating Fields ......... 398
9.11 Mössbauer Spectroscopy ................................... 402
Summary .................................................. 404
Further Reading .......................................... 404
References ............................................... 405
10 Magnetic Surfaces, Interfaces, and Thin Films ............ 409
10.1 Introduction ............................................. 409
10.2 Growth Methods and Modes ................................. 410
10.3 Electronic Structure and Magnetism ....................... 415
10.3.1 Energy Bands ...................................... 415
10.3.2 Magnetic Exchange Splitting, δEex, Excitations,
and Transitions ................................... 417
10.3.3 Magnetization, Curie Temperature, and Critical
Behavior in Low Dimensions ........................ 421
10.3.4 Interactions and Coupling ......................... 424
10.3.5 Anisotropy and Magnetostriction ................... 426
10.4 Thin Films ............................................... 428
10.4.1 Metastable Phases ................................. 428
10.4.2 Critical Phenomena and Transitions from 3D to
2D Behavior ....................................... 431
10.5 Magnetism in Two Dimensions: Monolayers, Ultrathin
Films, and Interfaces .................................... 433
10.5.1 Monolayer Magnetic Moments ........................ 433
10.5.2 Surface/Interface Anisotropy and Perpendicular
Magnetization ..................................... 437
10.5.3 Domains and Two-Dimensional Magnetic Phase
Transitions ....................................... 441
10.6 Oscillatory Exchange Coupling ............................ 446
10.6.1 Experimental Observations ......................... 446
10.6.2 RKKY Description .................................. 448
10.6.3 Spin Polarized Quantum Well Description ........... 453
10.7 Exchange Anisotropy/Bias ................................. 454
10.8 Exchange Spring .......................................... 466
Summary .................................................. 468
Further Reading .......................................... 469
References ............................................... 470
11 Hard and Soft Magnets .................................... 476
11.1 Introduction ............................................. 476
11.2 Hysteresis and Operating Criteria for Hard Magnets ....... 480
11.2.1 Demagnetizing Field and the Open Magnetic
Circuit ........................................... 480
11.2.2 Energy Density Product, ВЯ ........................ 482
11.3 Magnetic Anisotropy and Mechanisms of Coercivity ......... 484
11.3.1 Phenomenological Discussion ....................... 484
11.3.2 Atomic Description ................................ 487
11.4 Microstructure and Hard Magnetic Behavior ................ 490
11.4.1 Brown's Paradox ................................... 490
11.4.2 Exchange-Spring Magnets and Remanence
Enhancement ....................................... 492
11.5 Soft Magnets ............................................. 494
11.5.1 Alternating Field Response and Eddy Current
Losses ............................................ 495
11.5.2 Random Anisotropy ................................. 497
11.5.3 Nanostructured Materials as a Route to Achieving
Soft Magnetic Properties .......................... 498
11.6 Survey of Soft and Hard Magnetic Materials ............... 500
11.6.1 Crystalline Soft Magnets .......................... 500
11.6.2 Amorphous and Nanocrystalline Soft Magnets ........ 503
11.6.3 AlNiCo Permanent Magnet ........................... 505
11.6.4 FeCrCo Magnets .................................... 506
11.6.5 Pt-Co and Fe-Pt Alloys ............................ 506
11.6.6 Hard Ferrites (Hexaferrites) ...................... 508
11.6.7 RE-TM Permanent Magnets: Sm-Co and Fe-Nd-B
Alloys ............................................ 509
Summary .................................................. 514
Further Reading .......................................... 516
References ............................................... 516
12 Magnetic Materials in Medicine and Biology ............... 519
12.1 Introduction ............................................. 519
12.2 Magnetic Carriers for Biomedical Applications ............ 526
12.2.1 Synthesis of Magnetic Nanoparticles ............... 527
12.2.2 Core-Shell Structures ............................. 537
12.2.3 Biogenic and Biomimetic Synthesis ................. 542
12.2.4 Design and Functionalization of Nanoparticles
for in vivo Applications .......................... 545
12.2.5 Biocompatibility, Cytotoxicity, Biodistribution,
and Circulation ................................... 550
12.3 Imaging .................................................. 557
12.3.1 Magnetic Resonance Imaging ........................ 557
12.3.2 Contrast Agents in Magnetic Resonance Imaging ..... 566
12.3.3 Magnetic Particle Imaging (MPI) ................... 573
12.3.4 Optimizing Magnetic Nanoparticle Tracers for MPI .. 583
12.4 Separation and Diagnostics ............................... 590
12.4.1 Magnetic Separation ............................... 590
12.4.2 Forces on Magnetic Particles ...................... 591
12.4.3 Design of Magnetic Separators ..................... 593
12.4.4 Magnetophoretic Microsystems ...................... 596
12.4.5 Applications of Magnetic Separation ............... 598
12.4.6 On-Chip Magnetic Biosensors ....................... 599
12.4.7 Magnetorelaxometry: Binding Specific Detection
Methods ........................................... 603
12.5 Therapy .................................................. 606
12.5.1 Hyperthermia Treatment of Cancer: Biological
Factors ........................................... 606
12.5.2 Physics of Heating Ferrofluids with Alternating
Magnetic Fields ................................... 610
12.5.3 Magnetic Fluid Hyperthermia (MFH) in Practice ..... 620
12.5.4 Drug and Gene Delivery ............................ 626
12.6 Magnetoreception in Animals .............................. 630
12.6.1 The Earth's Geomagnetic Field ..................... 631
12.6.2 Possible Mechanisms of Magnetoreception ........... 632
Summary .................................................. 639
Further Reading .......................................... 641
References ............................................... 642
13 Spin Electronics ......................................... 655
13.1 Introduction ............................................. 655
13.2 Fundamentals of Spin Transport ........................... 657
13.2.1 The Two-Spin-Channel Model of Conduction .......... 658
13.2.2 Spin Asymmetry .................................... 660
13.2.3 Spin Polarization and Half-Metallic Ferromagnets .. 661
13.2.4 Spin Injection and Spin Accumulation .............. 664
13.2.5 Spin Transport in Diffusive Systems: the
"Standard" Model .................................. 667
13.2.6 Spin Injection and Spin Diffusion Length in
Semiconductors .................................... 671
13.2.7 Spin-Dependent Tunneling .......................... 675
13.2.8 Spin Transfer Torque: Current-Induced
Magnetization Reversal and Domain Wall Motion ..... 679
13.2.9 Hall Effect, Anomalous Hall Effect, and Spin
Hall Effect ....................................... 685
13.2.10 Spin Caloritronics ............................... 688
13.2.11 Quantum Hall Effect and Topological Insulators ... 690
13.3 Two-Terminal Devices ..................................... 692
13.3.1 Giant Magnetoresistance in CIP and CPP
Geometries ........................................ 692
13.3.2 Magnetic Tunnel Junctions (MTJ) and Magnetic
Random Access Memories (MRAM) ..................... 698
13.3.3 Spin-Polarized Light Emitting Diodes .............. 701
13.4 Three-Terminal Devices ................................... 702
13.4.1 The Johnson All-Metal Transistor .................. 703
13.4.2 The Monsma Spin-Valve Transistor .................. 704
13.4.3 The Magnetic Tunneling Transistor ................. 706
13.4.4 The Datta-Das Spin-Field-Effect Transistor
(SFET) ............................................ 707
13.4.5 Spin-Polarized Injection Current Emitter (SPICE)
Transistor ........................................ 708
Summary .................................................. 708
Further Reading .......................................... 710
References ............................................... 711
14 Magnetic Information Storage ............................. 716
14.1 Introduction ............................................. 716
14.2 The Basic Principles of Magnetic Recording ............... 717
14.3 Physics of Magnetic Recording ............................ 720
14.3.1 Field Efficiency of an Inductive Head ............. 720
14.3.2 Karlquist Approximation of the Field of a Ring
Head .............................................. 721
14.3.3 The Write Process: Widtii of a Recorded
Transition ........................................ 723
14.3.4 The Readback Process Using an Inductive Head ...... 726
14.3.5 The Readback Process Using a Magnetoresistive
Head .............................................. 729
14.3.6 Noise Sources ..................................... 735
14.3.7 Thermally Activated Magnetization Reversal ........ 738
14.3.8 The "Trilemma" in Hard Disk Magnetic Recording .... 741
14.4 Perpendicular Magnetic Recording ......................... 743
14.5 Materials and Structures: Recording Media ................ 746
14.6 Approaches to Increasing Areal Densities in Magnetic
Recording ................................................ 749
14.6.1 Antiferromagnetically Coupled (AFC) Media ......... 749
14.6.2 Composite Exchange-Spring Media ................... 750
14.6.3 Heat-Assisted Magnetic Recording (HAMR) ........... 753
14.6.4 Bit-Patterned Media (BPM) ......................... 755
14.7 Magneto-Optic Recording .................................. 758
14.8 Solid-State Non-Volatile Magnetic Memory ................. 760
14.8.1 Magnetic Random Access Memory (MRAM) .............. 761
14.8.2 Toggle MRAM Device ................................ 762
14.8.1 Spin Transfer Torque Magnetic Random Access
Memory (STT-MRAM) ................................. 764
14.8.4 Current-Driven Domain Wall Motion and Related
Devices ........................................... 766
Summary .................................................. 769
Further Reading .......................................... 770
References ............................................... 771
Afterword ..................................................... 775
Index ......................................................... 777
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