Spin Physics in Semiconductors (eBook)

From 1962 to 1998 M. I. Dyakonov was a researcher at the Ioffe Institute in St. Petersburg. In 1998 he became professor at Université Montpellier II, France. His name is accociated with the Dyakonov-Perel mechanism of spin relaxation in semiconductors, the Dyakonov-Shur plasma instability in two-dimensional electron fluid, and the Dyakonov waves at interfaces of transparent anisotropic materials. In 1971, together with V.I. Perel he has predicted new spin-related transport phenomena, one of which, now called the Spin Hall Effect, has become a subject of extensive experimental and theoretical studies. He was awarded the State Prize of USSR in 1973 and the Ioffe prize of the Russian Academy of Sciences in 1993.

Preface 7
Contents 8
List of Contributors 16
Basics of Semiconductor and Spin Physics 18
Historical Background 18
Spin Interactions 19
The Pauli Principle 19
Exchange Interaction 20
Spin-Orbit Interaction 20
Hyperfine Interaction with Nuclear Spins 21
Magnetic Interaction 22
Basics of Semiconductor Physics 22
Electron Energy Spectrum in a Crystal 22
Effective Masses of Electrons and Holes 22
The Effective Mass Approximation 23
Role of Impurities 24
Excitons 25
The Structure of the Valence Band. Light and Heavy Holes 25
Neglecting Spin-Orbit Interaction 25
Effects of Spin-Orbit Interaction 26
Gapless Semiconductors 27
Warping of the Iso-energetic Surfaces 27
Oddities in the Behavior of Light and Heavy Holes 27
Band Structure of GaAs 28
Photo-generation of Carriers and Luminescence 28
Angular Momentum Conservation in Optical Transitions 29
Low Dimensional Semiconductor Structures 30
Energy Spectrum of Electrons and Holes in a Quantum Well 30
Quantum Dots 32
Overview of Spin Physics in Semiconductors 32
Optical Spin Orientation and Detection 32
Spin Relaxation 33
Generalities 33
omegatauc«1 (Most Frequent Case) 34
omegatauc»1 34
Spin Relaxation Mechanisms 34
Elliott-Yafet Mechanism [15, 16] 34
Dyakonov-Perel Mechanism [9, 17] 35
Bir-Aronov-Pikus Mechanism [19] 35
Relaxation via Hyperfine Interaction with Nuclear Spins 36
Spin Relaxation of Holes in the Valence Band 36
Influence of Magnetic Field on Spin Relaxation 36
Spin Relaxation of Two-dimensional Electrons and Holes 37
Hanle Effect 38
Mutual Transformations of Spin and Charge Currents 39
Interaction between the Electron and Nuclear Spin Systems 40
Hyperfine Interaction between Electron and Nuclear Spins 40
Dipole-Dipole Interaction between Nuclear Spins 41
Zeeman Interaction of Electron and Nuclear Spins 41
Overview of the Book Content 42
Time-Resolved Optical Techniques. 42
Spin Dynamics in Quantum Wells and Quantum Dots. 42
Spin Noise Spectroscopy. 42
Coherent Spin Dynamics in Quantum Dots. 42
Spin Properties of Confined Electrons in Silicon. 43
Coupling of Spin and Charge Currents. 43
Spin Injection. 43
Nuclear Spin Effects in Optics and Electron Transport. 43
Spin Dynamics in Diluted Magnetic Semiconductors. 43
References 43
Spin Dynamics of Free Carriers in Quantum Wells 46
Introduction 46
Optical Measurements of Spin Dynamics 46
Mechanisms of Spin Relaxation of Free Electrons 49
Electron Spin Relaxation in Bulk Semiconductors 52
Electron Spin Relaxation in [001]-Oriented Quantum Wells 54
Symmetrical [001]-Oriented Quantum Wells 54
Structural Inversion Asymmetry in [001]-Oriented Quantum Wells 57
Natural Interface Asymmetry in Quantum Wells 59
Oscillatory Spin-Dynamics in Two-dimensional Electron Gases 62
Spin Dynamics of Free Holes in Bulk Material and Quantum Wells 64
Engineering and Controlling the Spin Dynamics in Quantum Wells 66
Conclusions 68
References 69
Exciton Spin Dynamics in Semiconductor Quantum Wells 72
Two-dimensional Exciton Fine Structure 72
Short-Range Electron-Hole Exchange 73
Long-Range Electron-Hole Exchange 74
Optical Orientation of Exciton Spin in Quantum Wells 75
Exciton Spin Dynamics in Quantum Wells 77
Exciton Formation in Quantum Wells 77
Spin Relaxation of Exciton-Bound Hole 79
Measurement of the Hole Spin Relaxation Time by Monitoring the Total Luminescence Intensity Dynamics 80
Measurement of the Hole Spin Relaxation with a Two-photon Excitation Process 81
Spin Relaxation of Exciton-Bound Electron 82
Exciton Spin Relaxation Mechanism 83
Exciton Spin Relaxation Due to Electron-Hole Exchange: The Maille, Andrada e Silva, and Sham Mechanism 83
Measurement of the Maille, Andrada e Silva, and Sham Spin Relaxation Time 85
Electric Field Dependence of the Exciton Spin Relaxation Time 89
Exciton Exchange Energy and g-Factor in Quantum Wells 89
Exchange Interaction of Excitons and g-Factor Measured with cw Magneto-Photoluminescence Spectroscopy 90
Exciton Exchange Energy 90
Exciton g-Factor 93
Exciton Spin Quantum Beats Spectroscopy 93
Exciton Spin Quantum Beats in Longitudinal Magnetic Fields 94
Exciton Spin Quantum Beats in Transverse Magnetic Fields 95
Exciton Spin Dynamics in Type II Quantum Wells 98
Spin Dynamics in Dense Excitonic Systems 100
References 103
Exciton Spin Dynamics in Semiconductor Quantum Dots 107
Introduction 107
Electron-Hole Complexes in Quantum Dots 108
Coulomb Corrections to the Single Particle Picture 109
Fine Structure of Neutral Excitons 109
Exciton Spin Dynamics in Neutral Quantum Dots without Applied Magnetic Fields 111
Exciton Spin Dynamics under Resonant Excitation 111
Exciton Spin Quantum Beats: The Role of Anisotropic Exchange 113
Exciton Spin Dynamics in Neutral Quantum Dots in External Magnetic Fields 114
Zeeman Effect Versus Anisotropic Exchange Splittings in Single Dot Spectroscopy 114
Faraday Configuration 114
Voigt Configuration 116
Exciton Spin Quantum Beats in Applied Magnetic Fields 116
Faraday Configuration 116
Voigt Configuration 117
Charged Exciton Complexes: Spin Dynamics without Applied Magnetic Fields 117
Formation of Trions: Doped and Charge Tuneable Structures 118
Fine Structure and Polarization of X+ and X- Excitons 119
Spin Dynamics in Negatively Charged Exciton Complexes Xn- 120
Spin Memory of Trapped Electrons 122
Charged Exciton Complexes: Spin Dynamics in Applied Magnetic Fields 122
Electron Spin Polarization in Positively Charged Excitons in Longitudinal Magnetic Fields 123
Electron Spin Coherence in Positively Charged Excitons in Transverse Magnetic Fields 125
Conclusions 126
References 126
Time-Resolved Spin Dynamics and Spin Noise Spectroscopy 130
Introduction 130
Time- and Polarization-Resolved Photoluminescence 131
Experimental Technique 132
Experimental Example I: Spin Relaxation in (110) Oriented Quantum Wells 134
Experimental Example II: Coherent Dynamics of Coupled Electron and Hole Spins in Semiconductors 137
Photoluminescence and Spin-Optoelectronic Devices 138
Time-Resolved Faraday/Kerr Rotation 138
Experimental Set-Up 140
Experimental Example: Spin Amplification 142
Spin Noise Spectroscopy 144
Experimental Realization 144
Spin Noise Measurements in n-GaAs 146
Conclusions 147
References 148
Coherent Spin Dynamics of Carriers 150
Introduction 150
Spin Coherence and Spin Dephasing Times 151
Optical Generation of Spin Coherent Carriers 152
Experimental Technique 153
Spin Coherence in Quantum Wells 155
Samples. 155
Electron Spin Coherence 156
Optical Spectra of the CdTe/CdMgTe Quantum Well 156
Long-Lived Electron Spin Coherence 157
Generation Mechanism: Model Considerations 159
Resonant Excitation of Trions 160
Resonant Excitation of Excitons in a Diluted 2DEG 162
Detection Aspects 162
Two-Color Pump-Probe Experiments 163
Pump Power Dependence of the Kerr Rotation Amplitude 165
Hole Spin Coherence 166
Spin Coherence in Singly Charged Quantum Dots 168
Samples. 169
Exciton and Electron Spin Beats Probed by Faraday Rotation 170
Experiment. 170
Spectral Dependence of the Electron g-Factor 172
Anisotropy of Electron g-Factor in Quantum Dot Plane 172
Generation of Electron Spin Coherence 172
Mode Locking of Spin Coherence in an Ensemble of Quantum Dots 175
Spin Coherence Time of an Individual Electron 175
Mechanism of Spin Synchronization 176
Control of Ensemble Spin Precession 179
Two Pump Pulse Excitation Protocol 179
Signal Shaping by Changing Delay between Pump Pulses 181
Polarization Control of Signal Phase 182
Stability Against Temperature Increase and Magnetic Field Variation 183
Requirements for Quantum Dot Ensemble 183
Nuclei Induced Frequency Focusing of Spin Coherence 184
Conclusions 189
References 190
Spin Properties of Confined Electrons in Si 193
Introduction 193
Spin-Orbit Effects in Si Quantum Wells 196
The Bychkov-Rashba Field 196
Thermal Distribution of the Bychkov-Rashba Field 197
g-Factor Anisotropy-Bychkov-Rashba Field in Si/SiGe Structures 198
Spin Relaxation of Conduction Electrons in Si/SiGe Quantum Wells 200
Mechanisms of Spin Relaxation of Conduction Electrons 200
Linewidth and the Longitudinal Relaxation Time of the Two-dimensional Electron Gas in Si/SiGe 201
Dephasing and Longitudinal Spin Relaxation 205
Transverse and Longitudinal Relaxation Originating from the Classical Dyakonov-Perel Relaxation 205
Angular Dependence of the Dyakonov-Perel Spin Relaxation 207
Comparison with Experiment 208
Current Induced Spin-Orbit Field 209
ESR Excited by an ac Current 211
Electric Dipole vs. Magnetic Dipole Spin Excitation 211
The ESR Signal Strength in Two-dimensional Si/SiGe Structures-Experimental Results 212
Sensitivity of ESR in Two-dimensional Si/SiGe 212
Temperature Dependence 212
Power Dependence of the Line Shape and Amplitude 213
Angular Dependence of the Amplitudes of ESR Signals 213
Modeling the Current Induced Excitation and Detection of ESR 213
Power Absorption, Line Shape 215
Spin Relaxation under Lateral Confinement 215
Shallow Donors 216
Hyperfine Interaction in Shallow Donors 216
Longitudinal Spin Relaxation in Donors 218
From the Two-dimensional Electron Gas to Quantum Dots 218
Spin Relaxation and Dephasing in Si Quantum Dots 219
Conclusions 220
References 221
Spin Hall Effect 224
Background: Magnetotransport in Molecular Gases 224
Phenomenology (with Inversion Symmetry) 226
Preliminaries 226
Spin and Charge Current Coupling 226
Phenomenological Equations 227
Physical Consequences of Spin-Charge Coupling 228
Anomalous Hall Effect 228
Electric Current Induced by curlP 228
Current-Induced Spin Accumulation, or Spin Hall Effect 229
The Degree of Polarization in the Spin Layer 230
Related Problems 231
The Validity of the Approach Based on the Diffusion Equation 231
How the Spin Current Should Be Defined 231
Additional Terms in (8.6) 232
Electrical Effects of Second Order in Spin-Orbit Interaction 232
Bulk Effects 233
Surface Effects 234
Phenomenology (without Inversion Symmetry) 235
Microscopic Mechanisms 236
Spin Asymmetry in Electron Scattering 236
Electron Spin Rotates 237
The Scattering Angle Depends on Spin 237
Spin Rotation is Correlated with Scattering 238
The Value of gamma for Skew Scattering 238
The Side Jump Mechanism 239
Classical Mechanics of a Spinning Particle 240
Reflection from a Flat Wall 241
Scattering by a Hard Sphere 242
Side Jump versus Skew Scattering 243
Intrinsic Mechanism 244
Spin Current of Bulk J=3/2 Holes 244
Intrinsic Mechanism for 2D Electrons and Holes 246
Spin Accumulation in the Ballistic Regime 246
Experiments 248
First Observation of the Spin Hall Effect 248
Spin Hall Effect for 2D Holes 249
Spin Hall Effect for 2D Electrons 250
Observation of the Inverse Spin Hall Effect in Metals 250
Room Temperature Spin Hall Effect in Semiconductors 251
Conclusion 252
The Generalized Kinetic Equation 252
References 254
Spin-Photogalvanics 257
Introduction. Phenomenological Description 257
Circular Photogalvanic Effect 257
Spin-Galvanic and Inverse Spin-Galvanic Effects 258
Pure Spin Photocurrents 259
Magneto-Photogalvanic Effects 259
Circular Photogalvanic Effect 259
Historical Background 259
Basic Experiments 260
Microscopic Model for Inter-Sub-Band Transitions 263
Relation to k-Linear Terms 263
Circular PGE Due to Inter-Sub-Band Transitions 263
Interband Optical Transitions 265
Spin-Sensitive Bleaching 266
Spin-Galvanic Effect 268
Microscopic Mechanisms 269
Spin-Galvanic Photocurrent Induced by the Hanle Effect 271
Spin-Galvanic Effect at Zero Magnetic Field 273
Determination of the Rashba/Dresselhaus Spin Splitting Ratio 274
Inverse Spin-Galvanic Effect 275
Spin-Flip Mediated Current-Induced Polarization 276
Precessional Mechanism 277
Current Induced Spin Faraday Rotation 278
Current Induced Polarization of Photoluminescence 279
Pure Spin Currents 280
Pure Spin Current Injected by a Linearly Polarized Beam 281
Pure Spin Currents Due to Spin-Dependent Scattering 283
Magneto-Gyrotropic Effects 285
Concluding Remarks 286
References 286
Spin Injection 290
Introduction 290
History 290
Theoretical Models of Spin Injection and Spin Accumulation 292
Heuristic Introduction 292
Microscopic Transport Model 296
Thermodynamic Theory of Spin Transport 297
Thermodynamic Equations of Motion 297
Boundary Conditions for Charge and Spin Diffusion 299
Detailed Model of an F / N Interface 299
Resistance Mismatch at an F / N Interface 302
Hanle Effect 303
Spin Injection Experiments in Metals 303
Spin Injection in Semiconductors 306
Optical Experiments 308
Spin Injection 308
Spin Dynamics and Lifetimes 311
Transport Experiments 312
Large Spin-Orbit Effects 312
Experimental Progress 313
Related Topics 316
References 317
Dynamic Nuclear Polarization and Nuclear Fields 319
Electron-Nuclear Spin System of the Semiconductor: Characteristic Values of Effective Fields and Spin Precession Frequencies 320
Zeeman Splitting of Spin Levels 320
Quadrupole Interaction 321
Hyperfine Interaction 321
Overhauser Field 322
The Field of Nuclear Spin Fluctuation 322
Knight Field 322
Nuclear Dipole-Dipole Interaction 323
Electron Spin Relaxation by Nuclei: from Short to Long Correlation Time 324
Dynamic Polarization of Nuclear Spins 326
Electron Spin Splitting in the Overhauser Field 327
Stationary States of the Electron-Nuclear Spin System in Faraday Geometry 329
Dynamic Polarization by Localized Electrons 330
Cooling of the Nuclear Spin System 332
Polarization of Nuclei by Excitons in Neutral Quantum Dots 334
Current-Induced Dynamic Polarization in Tunnel-Coupled Quantum Dots 335
Self-Polarization of Nuclear Spins 335
Dynamic Nuclear Polarization in Oblique Magnetic Field 336
Larmor Electron Spin Precession 337
Polarization of Electron-Nuclear Spin-System in an Oblique Magnetic Field 339
Bistability of the Electron-Nuclear Spin System in Structures with Anisotropic Electron g-Factor and Spin Relaxation Time 341
Bistability of Electron-Nuclear Spin System Induced by Anisotropy of Electron g-Factor 342
Bistability of the Electron-Nuclear Spin System, Induced by Anisotropy of Electron Spin Relaxation 342
Optically Detected and Optically Induced Nuclear Magnetic Resonances 343
Optically Detected Nuclear Magnetic Resonance 343
Multispin and Multiquantum NMR 343
Multispin resonances 343
Optically Induced NMR 345
Spin Conservation in the Electron-Nuclear Spin System of a Quantum Dot 347
Time Scales for Preservation of Spin Direction and Spin Temperature 347
A Guide to Interpretation of Experiments on ``Spin Memory'' 348
Conclusions 352
References 353
Nuclear-Electron Spin Interactions in the Quantum Hall Regime 357
Introduction 358
The Quantum Hall Effects in a Nutshell 358
Electron Spin Phenomena in the Quantum Hall Effects 363
Nuclear Spins in GaAs-Based 2D Electron Systems 366
Hyperfine Coupling 367
Nuclear Spin Relaxation in High Magnetic Fields 369
Nuclear Spin Diffusion 370
Experimental Techniques 370
Nuclear Spin Phenomena in the Quantum Hall Regime 372
The Role of Disorder 372
Edge Channel Scattering 374
Skyrmions 377
Nuclear-Electron Spin Interactions at nu=2/3 379
Ising Ferromagnetism and Domains 379
Resistively Detected NMR at nu= 2/3 382
Current Induced Nuclear Spin Polarization 382
Storage Capability of Nuclear Spins 383
Nuclear Magnetometry Based on the nu2/3 Spin Transition 384
Example 1: Filling Factor Dependence of the Nuclear Spin Relaxation Rate 384
Example 2: Suppression of Skyrmion Enhanced Nuclear Spin Relaxation 385
Example 3: The Filling Factor Dependence of the Nuclear Spin Polarization 387
Other Examples 388
Composite Fermion Fermi Sea at nu=1/2 389
Spin Polarization of the Composite Fermion Fermi Sea 389
Nuclear Spin Relaxation at nu=1/2 391
Other Cases 392
The Breakdown Regime of the Quantum Hall Effect 392
The Wigner Crystal Phase of the 2D Electron System 392
Two Sub-Band Systems 393
Bilayer Systems 393
Summary and Outlook 394
References 394
Diluted Magnetic Semiconductors: Basic Physics and Optical Properties 399
Introduction 399
Band Structure of II-VI and III-V DMS 400
Exchange Interactions in DMS 402
s,p-d Exchange Interaction 402
s-d Exchange Interaction 402
p-d Exchange Interaction 403
Deviations from Local Exchange 403
d-d Exchange Interactions 404
Superexchange 404
Double Exchange 405
RKKY 405
Magnetic Properties 406
Undoped DMS 406
Paramagnetism and the Brillouin Function 406
Antiferromagnetism and the Modified Brillouin Function 407
Carrier-Induced Ferromagnetism 409
Zener Model 409
Role of the Valence Band 411
Disorder 411
Basic Optical Properties 412
Giant Zeeman Effect 412
Linear Approximation for the Spin-Carrier Interaction 412
Determination of Exchange Integrals 414
Deviations from the Simple Model 414
Other Magneto-Optical Spectroscopic Techniques 417
Optically Detected Ferromagnetism in II-VI DMS 418
Quantum Dots 420
Spin-Light Emitting Diodes 422
III-V Diluted Magnetic Semiconductors 422
Spin Dynamics 424
Electron Spin Relaxation Induced by s-d Exchange 425
Mn Spin Relaxation 425
Spin-Lattice Relaxation of Isolated Mn Spins 426
Spin-Lattice Relaxation via Mn Spin Clusters 426
Spin-Spin Relaxation 427
Spin Relaxation Assisted by Carriers 428
Collective Spin Excitations in CdMnTe Quantum Wells 429
Soft Precession Mode in p-Doped Quantum Wells 430
Mixed Modes in n-Doped Quantum Wells 431
Advanced Time-Resolved Optical Experiments 432
Carrier Spin Dynamics 433
Magnetization Dynamics 434
Magnetization Precession Induced by an Exchange Field 434
Demagnetization by Hot Carriers 435
References 437
Index 442