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1 Introduction 1

1.1 Magnetism:Magical yet Practical 1

1.2 History of Magnetism 3

1.3 Magnetism,Neutrons,Polarized Electrons,and X-rays 12

1.3.1 Spin Polarized Electrons and Magnetism 15

1.3.2 Polarized X-rays and Magnetism 22

1.4 Developments in the Second Half of the 20th Century 25

1.5 Some Thoughts about the Future 30

1.6 About the Present Book 32

Part Ⅰ Fields and Moments 39

2 Electric Fields,Currents,and Magnetic Fields 39

2.1 Signs and Units in Magnetism 39

2.2 The Electric Field 39

2.3 The Electric Current and its Magnetic Field 40

2.4 High Current Densities 45

2.5 Magnetic and Electric Fields inside Materials 47

2.6 The Relation of the Three Magnetic Vectors in Magnetic Materials 49

2.6.1 Stray and Demagnetizing Fields of Thin Films 52

2.6.2 Applications of Stray and Demagnetizing Fields 54

2.7 Symmetry Properties of Electric and Magnetic Fields 57

2.7.1 Parity 57

2.7.2 Time Reversal 59

3 Magnetic Moments and their Interactions with Magnetic Fields 61

3.1 The Classical Definition of the Magnetic Moment 61

3.2 From Classical to Quantum Mechanical Magnetic Moments 64

3.2.1 The Bohr Magneton 65

3.2.2 Spin and Orbital Magnetic Moments 66

3.3 Magnetic Dipole Moments in an External Magnetic Field 68

3.4 The Energy of a Magnetic Dipole in a Magnetic Field 69

3.5 The Force on a Magnetic Dipole in an Inhomogeneous Field 72

3.5.1 The Stern-Gerlach Experiment 74

3.5.2 The Mott Detector 79

3.5.3 Magnetic Force Microscopy 83

3.6 The Torque on a Magnetic Moment in a Magnetic Field 84

3.6.1 Precession of Moments 85

3.6.2 Damping of the Precession 87

3.6.3 Magnetic Resonance 91

3.7 Time-Energy Correlation 97

3.7.1 The Heisenberg Uncertainty Principle 97

3.7.2 Classieal Spin Precession 98

3.7.3 Quantum Mechanical Spin Precession 99

4 Time Dependent Fields 105

4.1 Overview 105

4.2 Basic Concepts of Relativistic Motion 106

4.2.1 Length and Time Transformations Between Inertial Systems 106

4.2.2 Electric and Magnetic Field Transformations between Inertial Systems 107

4.3 Fields of a Charge in Uniform Motion:Velocity Fields 109

4.3.1 Characteristics of Velocity Fields 109

4.3.2 Creation of Large Currents and Magnetic Fields 112

4.3.3 Creation of Ultrashort Electron Pulses and Fields 115

4.3.4 The Temporal Nature of Velocity Fields 118

4.4 Acceleration Fields:Creation of EM Radiation 121

4.4.1 Polarized X-rays:Synchrotron Radiation 125

4.4.2 Brighter and Shorter X-ray Pulses:From Undulators to Free Electron Lasers 133

5 Polarized Electromagnetic Waves 141

5.1 Maxwell's Equations and their Symmetries 142

5.2 The Electromagnetic Wave Equation 143

5.3 Intensity,Flux,Energy,and Momentum of EM Waves 145

5.4 The Basis States of Polarized EM Waves 147

5.4.1 Photon Angular Momentum 147

5.4.2 Linearly Polarized Basis States 148

5.4.3 Circularly Polarized Basis States 149

5.4.4 Chirality and Angular Momentum of Circular EM Waves 153

5.4.5 Summary of Unit Polarization Vectors 154

5.5 Natural and Elliptical Polarization 155

5.5.1 Natural Polarization 155

5.5.2 Elliptical Polarization 156

5.5.3 The Degree of Photon Polarization 157

5.6 Transmission of EM Waves through Chiral and Magnetic Media 159

Part Ⅱ History and Concepts of Magnetic Interactions 167

6 Exchange,Spin-Orbit,and Zeeman Interactions 167

6.1 Overview 167

6.2 The Spin Dependent Atomic Hamiltonian or Pauli Equation 169

6.2.1 Independent Electrons in a Central Field 170

6.2.2 Interactions between two Particles-Symmetrization Postulate and Exclusion Principle 172

6.3 The Exchange Interaction 175

6.3.1 Electron Exchange in Atoms 175

6.3.2 Electron Exchange in Molecules 180

6.3.3 Magnetism and the Chemical Bond 186

6.3.4 From Molecules to Solids 188

6.3.5 The Heisenberg Hamiltonian 190

6.3.6 The Hubbard Hamiltonian 193

6.3.7 Heisenberg and Hubbard Models for H2 195

6.3.8 Summary and Some General Rules for Electron Exchange 202

6.4 The Spin-Orbit Interaction 203

6.4.1 Fine Structure in Atomic Spectra 203

6.4.2 Semiclassical Model for the Spin-Orbit Interaction 204

6.4.3 The Spin-Orbit Hamiltonian 206

6.4.4 Importance of the Spin-Orbit Interaction 209

6.5 Hund's Rules 209

6.6 The Zeeman Interaction 212

6.6.1 History and Theory of the Zeeman Effect 212

6.6.2 Zeeman Versus Exchange Splitting of Electronic States 218

6.6.3 Importance of the Zeeman Interaction 220

7 Electronic and Magnetic Interactions in Solids 221

7.1 Chapter Overview 221

7.2 Localized versus Itinerant Magnetism:The Role of the Centrifugal Potential 223

7.3 The Relative Size of Interactions in Solids 230

7.4 The Band Model of Ferromagnetism 234

7.4.1 The Puzzle of the Broken Bohr Magneton Numbers 234

7.4.2 The Stoner Model 235

7.4.3 Origin of Band Structure 240

7.4.4 Density Functional Theory 243

7.5 Ligand Field Theory 245

7.5.1 Independent-Electron Ligand Field Theory 247

7.5.2 Multiplet Ligand Field Theory 256

7.6 The Importance of Electron Correlation and Excited States 261

7.6.1 Why are Oxides often Insulators? 262

7.6.2 Correlation Effects in Rare Earths and Transition Metal Oxides 264

7.6.3 From Delocalized to Localized Behavior:Hubbard and LDA+U Models 271

7.7 Magnetism in Transition Metal Oxides 274

7.7.1 Superexchange 274

7.7.2 Double Exchange 279

7.7.3 Colossal Magnetoresistance 282

7.7.4 Magnetism of Magnetite 283

7.8 RKKY Exchange 290

7.8.1 Point-like Spins in a Conduction Electron Sea 291

7.8.2 Metallic Multilayers 292

7.9 Spin-Orbit Interaction:Origin of the Magnetocrystalline Anisotropy 294

7.9.1 The Bruno Model 295

7.9.2 Description of Anisotropic Bonding 297

7.9.3 Bonding,Orbital Moment,and Magnetocrystalline Anisotropy 299

Part Ⅲ Polarized Electron and X-Ray Techniques 313

8 Polarized Electrons and Magnetism 313

8.1 Introduction 313

8.2 Generation of Spin-Polarized Electron Beams 314

8.2.1 Separation of the Two Spin States 314

8.2.2 The GaAs Spin-Polarized Electron Source 315

8.3 Spin-Polarized Electrons and Magnetic Materials:Overview of Experiments 318

8.4 Formal Description of Spin-Polarized Electrons 319

8.4.1 Quantum Behavior of the Spin 319

8.4.2 Single Electron Polarization in the Pauli Spinor Formalism 320

8.4.3 Description of a Spin-Polarized Electron Beam 324

8.5 Description of Spin Analyzers and Filters 327

8.5.1 Incident Beam Polarization:Spin Analyzer 327

8.5.2 Transmitted Beam Polarization:Spin Filter 328

8.5.3 Determination of Analyzer Parameters 329

8.6 Interactions of Polarized Electrons with Materials 329

8.6.1 Bearm Transmission through a Spin Filter 329

8.6.2 The Fundamental Interactions of a Spin-Polarized Beam with Matter 331

8.6.3 Interaction of Polarized Electrons with Magnetic Materials:Poincaré's Sphere 337

8.7 Link Between Electron Polarization and Photon Polarization 342

8.7.1 Photon Polarization in the Vector Field Representation 343

8.7.2 Photon Polarization in the Spinor Representation 344

8.7.3 Transmission of Polarized Photons through Magnetic Materials:Poincaré Formalism 345

8.7.4 X-ray Faraday Effect and Poincaré Formalism 348

8.7.5 Poincaré and Stokes Formalism 350

9 Interactions of Polarized Photons with Matter 351

9.1 Overview 351

9.2 Terminology of Polarization Dependent Effects 352

9.3 SemiClassical Treatment of X-ray Scattering by Charges and Spins 355

9.3.1 Scattering by a Single Electron 355

9.3.2 Scattering by an Atom 360

9.4 SemiClassical Treatment of Resonant Interactions 361

9.4.1 X-ray Absorption 361

9.4.2 Resonant Scattering 364

9.4.3 Correspondence between Resonant Scattering and Absorption 368

9.4.4 The Kramers-Kronig Relations 368

9.5 Quantum-Theoretical Concepts 370

9.5.1 One-Electron and Configuration Pictures of X-ray Absorption 370

9.5.2 Fermi's Golden Rule and Kramers-Heisenberg Relation 372

9.5.3 Resonant Processes in the Electric Dipole Approximation 374

9.5.4 The Polarization Dependent Dipole Operator 376

9.5.5 The Atomic Transition Matrix Element 378

9.5.6 Transition Matrix Element for Atoms in Solids 381

9.6 The Orientation-Averaged Intensity:Charge and Magnetic Moment Sum Rules 385

9.6.1 The Orientation-Averaged Resonance Intensity 385

9.6.2 Derivation of the Intensity Sum Rule for the Charge 386

9.6.3 Origin of the XMCD Effect 389

9.6.4 Two-Step Model for the XMCD Intensity 393

9.6.5 The Orientation Averaged Sum Rules 397

9.7 The Orientation-Dependent Intensity:Charge and Magnetic Moment Anisotropies 401

9.7.1 Concepts of Linear Dichroism 401

9.7.2 X-ray Natural Linear Dichroism 401

9.7.3 Theory of X-ray Natural Linear Dichroism 403

9.7.4 XNLD and Quadrupole Moment of the Charge 406

9.7.5 X-ray Magnetic Linear Dichroism 407

9.7.6 Simple Theory of X-ray Magnetic Linear Dichroism 408

9.7.7 XMLD of the First and Second Kind 411

9.7.8 Enhanced XMLD through Multiplet Effects 415

9.7.9 The Orientation-Dependent Sum Rules 421

9.8 Magnetic Dichroism in X-ray Absorption and Scattering 424

9.8.1 The Resonant Magnetic Scattering Intensity 425

9.8.2 Link of Magnetic Resonant Scattering and Absorption 427

10 X-rays and Magnetism:Spectroscopy and Microscopy 431

10.1 Introduction 431

10.2 Overview of Different Types of X-ray Dichroism 432

10.3 Experimental Concepts of X-ray Absorption Spectroscopy 437

10.3.1 General Concepts 437

10.3.2 Experimental Arrangements 441

10.3.3 Quantitative Analysis of Experimental Absorption Spectra 445

10.3.4 Some Important Experimental Absorption Spectra 449

10.3.5 XMCD Spectra of Magnetic Atoms:From Thin Films to Isolated Atoms 451

10.3.6 Sum Rule Analysis of XMCD Spectra:Enhanced Orbital Moments in Small Clusters 454

10.3.7 Measurement of Small Spin and Orbital Moments:Pauli Paramagnetism 457

10.4 Magnetic Imaging with X-rays 458

10.4.1 X-ray Microscopy Methods 459

10.4.2 Lensless Imaging by Coherent Scattering 463

10.4.3 Overview of Magnetic Imaging Results 468

Part Ⅳ Properties of and Phenomena in the Ferromagnetic Metals 468

11 The Spontaneous Magnetization,Anisotropy,Domains 479

11.1 The Spontaneous Magnetization 480

11.1.1 Temperature Dependence of the Magnetization in the Molecular Field Approximation 481

11.1.2 Curie Temperature in the Weiss-Heisenberg Model 484

11.1.3 Curie Temperature in the Stoner Model 488

11.1.4 The Meaning of"Exchange"in the Weiss-Heisenberg and Stoner Models 491

11.1.5 Thermal Excitations:Spin Waves 494

11.1.6 Critical Fluctuations 499

11.2 The Magnetic Anisotropy 504

11.2.1 The Shape Anisotropy 507

11.2.2 The Magneto-Crystalline Anisotropy 508

11.2.3 The Discovery of the Surface Induced Magnetic Anisotropy 510

11.3 The Magnetic Microstructure:Magnetic Domains and Domain Walls 511

11.3.1 Ferromagnetic Domains 511

11.3.2 Antiferromagnetic Domains 515

11.4 Magnetization Curves and Hysteresis Loops 515

11.5 Magnetism in Small Particles 517

11.5.1 Néel and Stoner-Wohlfarth Models 517

11.5.2 Thermal Stability 520

12 Magnetism of Metals 521

12.1 Overview 521

12.2 Band Theoretical Results for the Transition Metals 523

12.2.1 Basic Results for the Density of States 523

12.2.2 Prediction of Magnetic Properties 525

12.3 The Rare Earth Metals:Band Theory versus Atomic Behavior 530

12.4 Spectroscopic Tests of the Band Model of Ferromagnetism 534

12.4.1 Spin Resolved Inverse Photoemission 535

12.4.2 Spin Resolved Photoemission 539

12.5 Resistivity of Transition Metals 548

12.5.1 Conduction in Nonmagnetic Metals 548

12.5.2 The Two Current Model 553

12.5.3 Anisotropic Magnetoresistance of Metals 556

12.6 Spin Conserving Electron Transitions in Metals 558

12.6.1 Spin Conserving Transitions and the Photoemission Mean Free Path 558

12.6.2 Determination of the Spin-Dependent Mean Free Path using the Magnetic Tunnel Transistor 562

12.6.3 Probability of Spin-Conserving relative to Spin-Non-Conserving Transitions 565

12.6.4 The Complete Spin-Polarized Transmission Experiment 569

12.7 Transitions Between Opposite Spin States in Metals 573

12.7.1 Classification of Transitions Between Opposite Spin States 573

12.7.2 The Detection of Transitions between Opposite Spin States 575

12.8 Remaining Challenges 582

Part Ⅴ Topics in Contemporary Magnetism 587

13 Surfaces and Interfaces of Ferromagnetic Metals 587

13.1 Overview 587

13.2 Spin-Polarized Electron Emission from Ferromagnetic Metals 588

13.2.1 Electron Emission into Vacuum 588

13.2.2 Spin-Polarized Electron Tunneling between Solids 593

13.2.3 Spin-Polarized Electron Tunneling Microscopy 598

13.3 Reflection of Electrons from a Ferromagnetic Surface 601

13.3.1 Simple Reflection Experiments 603

13.3.2 The Complete Reflection Experiment 608

13.4 Static Magnetic Coupling at Interfaces 613

13.4.1 Magnetostatic Coupling 614

13.4.2 Direct Coupling between Magnetic Layers 615

13.4.3 Exchange Bias 617

13.4.4 Induced Magnetism in Paramagnets and Diamagnets 629

13.4.5 Coupling of Two Ferromagnets across a Nonmagnetic Spacer Layer 632

14 Electron and Spin Transport 637

14.1 Currents Across Interfaces Between a Ferromagnet and a Nonmagnet 637

14.1.1 The Spin Accumulation Voltage in a Transparent Metallic Contact 638

14.1.2 The Diffusion Equation for the Spins 642

14.1.3 Spin Equilibration Processes,Distances and Times 644

14.1.4 Giant Magneto-Resistance(GMR) 647

14.1.5 Measurement of Spin Diffusion Lengths in Nonmagnets 651

14.1.6 Typical Values for the Spin Accumulation Voltage,Boundary Resistance and GMR Effect 654

14.1.7 The Important Role of Interfaces in GMR 655

14.2 Spin-Injection into a Ferromagnet 656

14.2.1 Origin and Properties of Spin Injection Torques 657

14.2.2 Switching of the Magnetization with Spin Currents:Concepts 665

14.2.3 Excitation and Switching of the Magnetization with Spin Currents:Experiments 667

14.3 Spin Currents in Metals and Semiconductors 672

14.4 Spin-Based Transistors and Amplifiers 675

15 Ultrafast Magnetization Dynamics 679

15.1 Introduction 679

15.2 Energy and Angular Momentum Exchange between Physical Reservoirs 682

15.2.1 Thermodynamic Considerations 682

15.2.2 Quantum Mechanical Considerations:The Importance of Orbital Angular Momentum 684

15.3 Spin Relaxation and the Pauli Susceptibility 687

15.4 Probing the Magnetization after Laser Excitation 690

15.4.1 Probing with Spin-Polarized Photoelectron Yield 691

15.4.2 Probing with Energy Resolved Photoelectrons With or Without Spin Analysis 696

15.4.3 Probing with the Magneto-Optic Kerr Effect 702

15.5 Dynamics Following Excitation with Magnetic Field Pulses 705

15.5.1 Excitation with Weak Magnetic Field Pulses 712

15.5.2 Excitation of a Magnetic Vortex 715

15.6 Switching of the Magnetization 723

15.6.1 Precessional Switching of the In-Plane Magnetization 725

15.6.2 Precessional Switching of the Magnetization for Perpendicular Recording Media 733

15.6.3 Switching by Spin Injection and its Dynamics 744

15.6.4 On the Possibility of All-Optical Switching 751

15.6.5 The Hübner Model of All-Optical Switching 753

15.6.6 All-Optical Manipulation of the Magnetization 757

15.7 Dynamics of Antiferromagnetic Spins 759

Part Ⅵ Appendices 763

Appendices 763

A.1 The International System of Units(SI) 763

A.2 The Cross Product 765

A.3 s,P,and d Orbitals 766

A.4 Spherical Tensors 767

A.5 Sum Rules for Spherical Tensor Matrix Elements 768

A.6 Polarization Dependent Dipole Operators 769

A.7 Spin-Orbit Basis Functions for p and d Orbitals 770

A.8 Quadrupole Moment and the X-ray Absorption Intensity 771

A.9 Lorentzian Line Shape and Integral 774

A.10 Gaussian Line Shape and Its Fourier Transform 774

A.11 Gaussian Pulses,Half-Cycle Pulses and Transforms 775

References 777

Index 805

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