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1 Introduction1

1.1 Magnetism:Magical yet Practical1

1.2 History of Magnetism3

1.3 Magnetism,Neutrons,Polarized Electrons,and X-rays12

1.3.1 Spin Polarized Electrons and Magnetism15

1.3.2 Polarized X-rays and Magnetism22

1.4 Developments in the Second Half of the 20th Century25

1.5 Some Thoughts about the Future30

1.6 About the Present Book32

Part Ⅰ Fields and Moments39

2 Electric Fields,Currents,and Magnetic Fields39

2.1 Signs and Units in Magnetism39

2.2 The Electric Field39

2.3 The Electric Current and its Magnetic Field40

2.4 High Current Densities45

2.5 Magnetic and Electric Fields inside Materials47

2.6 The Relation of the Three Magnetic Vectors in Magnetic Materials49

2.6.1 Stray and Demagnetizing Fields of Thin Films52

2.6.2 Applications of Stray and Demagnetizing Fields54

2.7 Symmetry Properties of Electric and Magnetic Fields57

2.7.1 Parity57

2.7.2 Time Reversal59

3 Magnetic Moments and their Interactions with Magnetic Fields61

3.1 The Classical Definition of the Magnetic Moment61

3.2 From Classical to Quantum Mechanical Magnetic Moments64

3.2.1 The Bohr Magneton65

3.2.2 Spin and Orbital Magnetic Moments66

3.3 Magnetic Dipole Moments in an External Magnetic Field68

3.4 The Energy of a Magnetic Dipole in a Magnetic Field69

3.5 The Force on a Magnetic Dipole in an Inhomogeneous Field72

3.5.1 The Stern-Gerlach Experiment74

3.5.2 The Mott Detector79

3.5.3 Magnetic Force Microscopy83

3.6 The Torque on a Magnetic Moment in a Magnetic Field84

3.6.1 Precession of Moments85

3.6.2 Damping of the Precession87

3.6.3 Magnetic Resonance91

3.7 Time-Energy Correlation97

3.7.1 The Heisenberg Uncertainty Principle97

3.7.2 Classieal Spin Precession98

3.7.3 Quantum Mechanical Spin Precession99

4 Time Dependent Fields105

4.1 Overview105

4.2 Basic Concepts of Relativistic Motion106

4.2.1 Length and Time Transformations Between Inertial Systems106

4.2.2 Electric and Magnetic Field Transformations between Inertial Systems107

4.3 Fields of a Charge in Uniform Motion:Velocity Fields109

4.3.1 Characteristics of Velocity Fields109

4.3.2 Creation of Large Currents and Magnetic Fields112

4.3.3 Creation of Ultrashort Electron Pulses and Fields115

4.3.4 The Temporal Nature of Velocity Fields118

4.4 Acceleration Fields:Creation of EM Radiation121

4.4.1 Polarized X-rays:Synchrotron Radiation125

4.4.2 Brighter and Shorter X-ray Pulses:From Undulators to Free Electron Lasers133

5 Polarized Electromagnetic Waves141

5.1 Maxwell's Equations and their Symmetries142

5.2 The Electromagnetic Wave Equation143

5.3 Intensity,Flux,Energy,and Momentum of EM Waves145

5.4 The Basis States of Polarized EM Waves147

5.4.1 Photon Angular Momentum147

5.4.2 Linearly Polarized Basis States148

5.4.3 Circularly Polarized Basis States149

5.4.4 Chirality and Angular Momentum of Circular EM Waves153

5.4.5 Summary of Unit Polarization Vectors154

5.5 Natural and Elliptical Polarization155

5.5.1 Natural Polarization155

5.5.2 Elliptical Polarization156

5.5.3 The Degree of Photon Polarization157

5.6 Transmission of EM Waves through Chiral and Magnetic Media159

Part Ⅱ History and Concepts of Magnetic Interactions167

6 Exchange,Spin-Orbit,and Zeeman Interactions167

6.1 Overview167

6.2 The Spin Dependent Atomic Hamiltonian or Pauli Equation169

6.2.1 Independent Electrons in a Central Field170

6.2.2 Interactions between two Particles-Symmetrization Postulate and Exclusion Principle172

6.3 The Exchange Interaction175

6.3.1 Electron Exchange in Atoms175

6.3.2 Electron Exchange in Molecules180

6.3.3 Magnetism and the Chemical Bond186

6.3.4 From Molecules to Solids188

6.3.5 The Heisenberg Hamiltonian190

6.3.6 The Hubbard Hamiltonian193

6.3.7 Heisenberg and Hubbard Models for H2195

6.3.8 Summary and Some General Rules for Electron Exchange202

6.4 The Spin-Orbit Interaction203

6.4.1 Fine Structure in Atomic Spectra203

6.4.2 Semiclassical Model for the Spin-Orbit Interaction204

6.4.3 The Spin-Orbit Hamiltonian206

6.4.4 Importance of the Spin-Orbit Interaction209

6.5 Hund's Rules209

6.6 The Zeeman Interaction212

6.6.1 History and Theory of the Zeeman Effect212

6.6.2 Zeeman Versus Exchange Splitting of Electronic States218

6.6.3 Importance of the Zeeman Interaction220

7 Electronic and Magnetic Interactions in Solids221

7.1 Chapter Overview221

7.2 Localized versus Itinerant Magnetism:The Role of the Centrifugal Potential223

7.3 The Relative Size of Interactions in Solids230

7.4 The Band Model of Ferromagnetism234

7.4.1 The Puzzle of the Broken Bohr Magneton Numbers234

7.4.2 The Stoner Model235

7.4.3 Origin of Band Structure240

7.4.4 Density Functional Theory243

7.5 Ligand Field Theory245

7.5.1 Independent-Electron Ligand Field Theory247

7.5.2 Multiplet Ligand Field Theory256

7.6 The Importance of Electron Correlation and Excited States261

7.6.1 Why are Oxides often Insulators?262

7.6.2 Correlation Effects in Rare Earths and Transition Metal Oxides264

7.6.3 From Delocalized to Localized Behavior:Hubbard and LDA+U Models271

7.7 Magnetism in Transition Metal Oxides274

7.7.1 Superexchange274

7.7.2 Double Exchange279

7.7.3 Colossal Magnetoresistance282

7.7.4 Magnetism of Magnetite283

7.8 RKKY Exchange290

7.8.1 Point-like Spins in a Conduction Electron Sea291

7.8.2 Metallic Multilayers292

7.9 Spin-Orbit Interaction:Origin of the Magnetocrystalline Anisotropy294

7.9.1 The Bruno Model295

7.9.2 Description of Anisotropic Bonding297

7.9.3 Bonding,Orbital Moment,and Magnetocrystalline Anisotropy299

Part Ⅲ Polarized Electron and X-Ray Techniques313

8 Polarized Electrons and Magnetism313

8.1 Introduction313

8.2 Generation of Spin-Polarized Electron Beams314

8.2.1 Separation of the Two Spin States314

8.2.2 The GaAs Spin-Polarized Electron Source315

8.3 Spin-Polarized Electrons and Magnetic Materials:Overview of Experiments318

8.4 Formal Description of Spin-Polarized Electrons319

8.4.1 Quantum Behavior of the Spin319

8.4.2 Single Electron Polarization in the Pauli Spinor Formalism320

8.4.3 Description of a Spin-Polarized Electron Beam324

8.5 Description of Spin Analyzers and Filters327

8.5.1 Incident Beam Polarization:Spin Analyzer327

8.5.2 Transmitted Beam Polarization:Spin Filter328

8.5.3 Determination of Analyzer Parameters329

8.6 Interactions of Polarized Electrons with Materials329

8.6.1 Bearm Transmission through a Spin Filter329

8.6.2 The Fundamental Interactions of a Spin-Polarized Beam with Matter331

8.6.3 Interaction of Polarized Electrons with Magnetic Materials:Poincaré's Sphere337

8.7 Link Between Electron Polarization and Photon Polarization342

8.7.1 Photon Polarization in the Vector Field Representation343

8.7.2 Photon Polarization in the Spinor Representation344

8.7.3 Transmission of Polarized Photons through Magnetic Materials:Poincaré Formalism345

8.7.4 X-ray Faraday Effect and Poincaré Formalism348

8.7.5 Poincaré and Stokes Formalism350

9 Interactions of Polarized Photons with Matter351

9.1 Overview351

9.2 Terminology of Polarization Dependent Effects352

9.3 SemiClassical Treatment of X-ray Scattering by Charges and Spins355

9.3.1 Scattering by a Single Electron355

9.3.2 Scattering by an Atom360

9.4 SemiClassical Treatment of Resonant Interactions361

9.4.1 X-ray Absorption361

9.4.2 Resonant Scattering364

9.4.3 Correspondence between Resonant Scattering and Absorption368

9.4.4 The Kramers-Kronig Relations368

9.5 Quantum-Theoretical Concepts370

9.5.1 One-Electron and Configuration Pictures of X-ray Absorption370

9.5.2 Fermi's Golden Rule and Kramers-Heisenberg Relation372

9.5.3 Resonant Processes in the Electric Dipole Approximation374

9.5.4 The Polarization Dependent Dipole Operator376

9.5.5 The Atomic Transition Matrix Element378

9.5.6 Transition Matrix Element for Atoms in Solids381

9.6 The Orientation-Averaged Intensity:Charge and Magnetic Moment Sum Rules385

9.6.1 The Orientation-Averaged Resonance Intensity385

9.6.2 Derivation of the Intensity Sum Rule for the Charge386

9.6.3 Origin of the XMCD Effect389

9.6.4 Two-Step Model for the XMCD Intensity393

9.6.5 The Orientation Averaged Sum Rules397

9.7 The Orientation-Dependent Intensity:Charge and Magnetic Moment Anisotropies401

9.7.1 Concepts of Linear Dichroism401

9.7.2 X-ray Natural Linear Dichroism401

9.7.3 Theory of X-ray Natural Linear Dichroism403

9.7.4 XNLD and Quadrupole Moment of the Charge406

9.7.5 X-ray Magnetic Linear Dichroism407

9.7.6 Simple Theory of X-ray Magnetic Linear Dichroism408

9.7.7 XMLD of the First and Second Kind411

9.7.8 Enhanced XMLD through Multiplet Effects415

9.7.9 The Orientation-Dependent Sum Rules421

9.8 Magnetic Dichroism in X-ray Absorption and Scattering424

9.8.1 The Resonant Magnetic Scattering Intensity425

9.8.2 Link of Magnetic Resonant Scattering and Absorption427

10 X-rays and Magnetism:Spectroscopy and Microscopy431

10.1 Introduction431

10.2 Overview of Different Types of X-ray Dichroism432

10.3 Experimental Concepts of X-ray Absorption Spectroscopy437

10.3.1 General Concepts437

10.3.2 Experimental Arrangements441

10.3.3 Quantitative Analysis of Experimental Absorption Spectra445

10.3.4 Some Important Experimental Absorption Spectra449

10.3.5 XMCD Spectra of Magnetic Atoms:From Thin Films to Isolated Atoms451

10.3.6 Sum Rule Analysis of XMCD Spectra:Enhanced Orbital Moments in Small Clusters454

10.3.7 Measurement of Small Spin and Orbital Moments:Pauli Paramagnetism457

10.4 Magnetic Imaging with X-rays458

10.4.1 X-ray Microscopy Methods459

10.4.2 Lensless Imaging by Coherent Scattering463

10.4.3 Overview of Magnetic Imaging Results468

Part Ⅳ Properties of and Phenomena in the Ferromagnetic Metals468

11 The Spontaneous Magnetization,Anisotropy,Domains479

11.1 The Spontaneous Magnetization480

11.1.1 Temperature Dependence of the Magnetization in the Molecular Field Approximation481

11.1.2 Curie Temperature in the Weiss-Heisenberg Model484

11.1.3 Curie Temperature in the Stoner Model488

11.1.4 The Meaning of"Exchange"in the Weiss-Heisenberg and Stoner Models491

11.1.5 Thermal Excitations:Spin Waves494

11.1.6 Critical Fluctuations499

11.2 The Magnetic Anisotropy504

11.2.1 The Shape Anisotropy507

11.2.2 The Magneto-Crystalline Anisotropy508

11.2.3 The Discovery of the Surface Induced Magnetic Anisotropy510

11.3 The Magnetic Microstructure:Magnetic Domains and Domain Walls511

11.3.1 Ferromagnetic Domains511

11.3.2 Antiferromagnetic Domains515

11.4 Magnetization Curves and Hysteresis Loops515

11.5 Magnetism in Small Particles517

11.5.1 Néel and Stoner-Wohlfarth Models517

11.5.2 Thermal Stability520

12 Magnetism of Metals521

12.1 Overview521

12.2 Band Theoretical Results for the Transition Metals523

12.2.1 Basic Results for the Density of States523

12.2.2 Prediction of Magnetic Properties525

12.3 The Rare Earth Metals:Band Theory versus Atomic Behavior530

12.4 Spectroscopic Tests of the Band Model of Ferromagnetism534

12.4.1 Spin Resolved Inverse Photoemission535

12.4.2 Spin Resolved Photoemission539

12.5 Resistivity of Transition Metals548

12.5.1 Conduction in Nonmagnetic Metals548

12.5.2 The Two Current Model553

12.5.3 Anisotropic Magnetoresistance of Metals556

12.6 Spin Conserving Electron Transitions in Metals558

12.6.1 Spin Conserving Transitions and the Photoemission Mean Free Path558

12.6.2 Determination of the Spin-Dependent Mean Free Path using the Magnetic Tunnel Transistor562

12.6.3 Probability of Spin-Conserving relative to Spin-Non-Conserving Transitions565

12.6.4 The Complete Spin-Polarized Transmission Experiment569

12.7 Transitions Between Opposite Spin States in Metals573

12.7.1 Classification of Transitions Between Opposite Spin States573

12.7.2 The Detection of Transitions between Opposite Spin States575

12.8 Remaining Challenges582

Part Ⅴ Topics in Contemporary Magnetism587

13 Surfaces and Interfaces of Ferromagnetic Metals587

13.1 Overview587

13.2 Spin-Polarized Electron Emission from Ferromagnetic Metals588

13.2.1 Electron Emission into Vacuum588

13.2.2 Spin-Polarized Electron Tunneling between Solids593

13.2.3 Spin-Polarized Electron Tunneling Microscopy598

13.3 Reflection of Electrons from a Ferromagnetic Surface601

13.3.1 Simple Reflection Experiments603

13.3.2 The Complete Reflection Experiment608

13.4 Static Magnetic Coupling at Interfaces613

13.4.1 Magnetostatic Coupling614

13.4.2 Direct Coupling between Magnetic Layers615

13.4.3 Exchange Bias617

13.4.4 Induced Magnetism in Paramagnets and Diamagnets629

13.4.5 Coupling of Two Ferromagnets across a Nonmagnetic Spacer Layer632

14 Electron and Spin Transport637

14.1 Currents Across Interfaces Between a Ferromagnet and a Nonmagnet637

14.1.1 The Spin Accumulation Voltage in a Transparent Metallic Contact638

14.1.2 The Diffusion Equation for the Spins642

14.1.3 Spin Equilibration Processes,Distances and Times644

14.1.4 Giant Magneto-Resistance(GMR)647

14.1.5 Measurement of Spin Diffusion Lengths in Nonmagnets651

14.1.6 Typical Values for the Spin Accumulation Voltage,Boundary Resistance and GMR Effect654

14.1.7 The Important Role of Interfaces in GMR655

14.2 Spin-Injection into a Ferromagnet656

14.2.1 Origin and Properties of Spin Injection Torques657

14.2.2 Switching of the Magnetization with Spin Currents:Concepts665

14.2.3 Excitation and Switching of the Magnetization with Spin Currents:Experiments667

14.3 Spin Currents in Metals and Semiconductors672

14.4 Spin-Based Transistors and Amplifiers675

15 Ultrafast Magnetization Dynamics679

15.1 Introduction679

15.2 Energy and Angular Momentum Exchange between Physical Reservoirs682

15.2.1 Thermodynamic Considerations682

15.2.2 Quantum Mechanical Considerations:The Importance of Orbital Angular Momentum684

15.3 Spin Relaxation and the Pauli Susceptibility687

15.4 Probing the Magnetization after Laser Excitation690

15.4.1 Probing with Spin-Polarized Photoelectron Yield691

15.4.2 Probing with Energy Resolved Photoelectrons With or Without Spin Analysis696

15.4.3 Probing with the Magneto-Optic Kerr Effect702

15.5 Dynamics Following Excitation with Magnetic Field Pulses705

15.5.1 Excitation with Weak Magnetic Field Pulses712

15.5.2 Excitation of a Magnetic Vortex715

15.6 Switching of the Magnetization723

15.6.1 Precessional Switching of the In-Plane Magnetization725

15.6.2 Precessional Switching of the Magnetization for Perpendicular Recording Media733

15.6.3 Switching by Spin Injection and its Dynamics744

15.6.4 On the Possibility of All-Optical Switching751

15.6.5 The Hübner Model of All-Optical Switching753

15.6.6 All-Optical Manipulation of the Magnetization757

15.7 Dynamics of Antiferromagnetic Spins759

Part Ⅵ Appendices763

Appendices763

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

A.2 The Cross Product765

A.3 s,P,and d Orbitals766

A.4 Spherical Tensors767

A.5 Sum Rules for Spherical Tensor Matrix Elements768

A.6 Polarization Dependent Dipole Operators769

A.7 Spin-Orbit Basis Functions for p and d Orbitals770

A.8 Quadrupole Moment and the X-ray Absorption Intensity771

A.9 Lorentzian Line Shape and Integral774

A.10 Gaussian Line Shape and Its Fourier Transform774

A.11 Gaussian Pulses,Half-Cycle Pulses and Transforms775

References777

Index805