Preface ...................................................... vii
List of Contributors ......................................... xvii
1 Basics of Semiconductor and Spin Physics ..................... 1
M.I. Dyakonov ................................................ 1
1.1 Historical Background ................................... 1
1.2 Spin Interactions ....................................... 2
1.2.1 The Pauli Principle .............................. 2
1.2.2 Exchange Interaction ............................. 3
1.2.3 Spin-Orbit Interaction ........................... 3
1.2.4 Hyperfine Interaction with Nuclear Spins ......... 4
1.2.5 Magnetic Interaction ............................. 5
1.3 Basics of Semiconductor Physics ......................... 5
1.3.1 Electron Energy Spectrum in a Crystal ............ 5
1.3.2 Effective Masses of Electrons and Holes .......... 5
1.3.3 The Effective Mass Approximation ................. 6
1.3.4 Role of Impurities ............................... 7
1.3.5 Excitons ......................................... 8
1.3.6 The Structure of the Valence Band. Light and
Heavy Holes ...................................... 8
1.3.7 Band Structure of GaAs .......................... 11
1.3.8 Photo-generation of Carriers and Luminescence ... 11
1.3.9 Angular Momentum Conservation in Optical
Transitions ..................................... 12
1.3.10 Low Dimensional Semiconductor Structures ........ 13
1.4 Overview of Spin Physics in Semiconductors ............. 15
1.4.1 Optical Spin Orientation and Detection .......... 15
1.4.2 Spin Relaxation ................................. 16
1.4.3 Hanle Effect .................................... 21
1.4.4 Mutual Transformations of Spin and Charge
Currents ........................................ 22
1.4.5 Interaction between the Electron and Nuclear
Spin Systems .................................... 23
1.5 Overview of the Book Content ........................... 25
References .................................................. 26
2 Spin Dynamics of Free Carriers in Quantum Wells ............. 29
R.T. Harley ................................................. 29
2.1 Introduction ........................................... 29
2.2 Optical Measurements of Spin Dynamics .................. 29
2.3 Mechanisms of Spin Relaxation of Free Electrons ........ 32
2.4 Electron Spin Relaxation in Bulk Semiconductors ........ 35
2.5 Electron Spin Relaxation in [001]-Oriented Quantum
Wells .................................................. 37
2.5.1 Symmetrical [001]-Oriented Quantum Wells ........ 37
2.5.2 Structural Inversion Asymmetry in [001]-
Oriented Quantum Wells .......................... 40
2.5.3 Natural Interface Asymmetry in Quantum Wells .... 42
2.5.4 Oscillatory Spin-Dynamics in Two-dimensional
Electron Gases .................................. 45
2.6 Spin Dynamics of Free Holes in Bulk Material and
Quantum Wells .......................................... 47
2.7 Engineering and Controlling the Spin Dynamics in
Quantum Wells .......................................... 49
2.8 Conclusions ............................................ 51
References .................................................. 52
3 Exciton Spin Dynamics in Semiconductor Quantum Wells ........ 55
T. Amand and X. Marie ....................................... 55
3.1 Two-dimensional Exciton Fine Structure ................. 55
3.1.1 Short-Range Electron-Hole Exchange .............. 56
3.1.2 Long-Range Electron-Hole Exchange ............... 57
3.2 Optical Orientation of Exciton Spin in Quantum Wells ... 58
3.3 Exciton Spin Dynamics in Quantum Wells ................. 60
3.3.1 Exciton Formation in Quantum Wells .............. 60
3.3.2 Spin Relaxation of Exciton-Bound Hole ........... 62
3.3.3 Spin Relaxation of Exciton-Bound Electron ....... 65
3.3.4 Exciton Spin Relaxation Mechanism ............... 66
3.4 Exciton Exchange Energy and g-Factor in Quantum
Wells .................................................. 72
3.4.1 Exchange Interaction of Excitons and g-Factor
Measured with cw Magneto-Photoluminescence
Spectroscopy .................................... 73
3.4.2 Exciton Spin Quantum Beats Spectroscopy ......... 76
3.5 Exciton Spin Dynamics in Type II Quantum Wells ......... 81
3.6 Spin Dynamics in Dense Excitonic Systems ............... 83
References .................................................. 86
4 Exciton Spin Dynamics in Semiconductor Quantum Dots ......... 91
X. Marie, B. Urbaszek, O. Krebs and T. Amand ................ 91
4.1 Introduction ........................................... 91
4.2 Electron-Hole Complexes in Quantum Dots ................ 92
4.2.1 Coulomb Corrections to the Single Particle
Picture ......................................... 93
4.2.2 Fine Structure of Neutral Excitons .............. 93
4.3 Exciton Spin Dynamics in Neutral Quantum Dots without
Applied Magnetic Fields ................................ 95
4.3.1 Exciton Spin Dynamics under Resonant
Excitation ...................................... 95
4.3.2 Exciton Spin Quantum Beats: The Role of
Anisotropic Exchange ............................ 97
4.4 Exciton Spin Dynamics in Neutral Quantum Dots in
External Magnetic Fields ............................... 98
4.4.1 Zeeman Effect Versus Anisotropic Exchange
Splittings in Single Dot Spectroscopy ........... 98
4.4.2 Exciton Spin Quantum Beats in Applied
Magnetic Fields ................................ 100
4.5 Charged Exciton Complexes: Spin Dynamics without
Applied Magnetic Fields ............................... 101
4.5.1 Formation of Trions: Doped and Charge
Tuneable Structures ............................ 102
4.5.2 Fine Structure and Polarization of X+ and X-
Excitons ....................................... 103
4.5.3 Spin Dynamics in Negatively Charged Exciton
Complexes Xn- .................................. 104
4.5.4 Spin Memory of Trapped Electrons ............... 106
4.6 Charged Exciton Complexes: Spin Dynamics in Applied
Magnetic Fields ....................................... 106
4.6.1 Electron Spin Polarization in Positively
Charged Excitons in Longitudinal Magnetic
Fields ......................................... 107
4.6.2 Electron Spin Coherence in Positively Charged
Excitons in Transverse Magnetic Fields ......... 109
4.7 Conclusions ........................................... 110
References ................................................. 110
5 Time-Resolved Spin Dynamics and Spin Noise
Spectroscopy ............................................... 115
J. Hübner and M. Oestreich ................................. 115
5.1 Introduction .......................................... 115
5.2 Time- and Polarization-Resolved Photoluminescence ..... 116
5.2.1 Experimental Technique ......................... 117
5.2.2 Experimental Example I: Spin Relaxation in
(110) Oriented Quantum Wells ................... 119
5.2.3 Experimental Example II: Coherent Dynamics
of Coupled Electron and Hole Spins in
Semiconductors ................................. 122
5.2.4 Photoluminescence and Spin-Optoelectronic
Devices ........................................ 123
5.3 Time-Resolved Faraday/Kerr Rotation ................... 123
5.3.1 Experimental Set-Up ............................ 125
5.3.2 Experimental Example: Spin Amplification ....... 127
5.4 Spin Noise Spectroscopy ............................... 129
5.4.1 Experimental Realization ....................... 129
5.5 Spin Noise Measurements in n-GaAs ..................... 131
5.6 Conclusions ........................................... 132
References ................................................. 133
6 Coherent Spin Dynamics of Carriers ......................... 135
D.R. Yakovlev and M. Bayer ................................. 135
6.1 Introduction .......................................... 135
6.1.1 Spin Coherence and Spin Dephasing Times ........ 136
6.1.2 Optical Generation of Spin Coherent Carriers ... 137
6.1.3 Experimental Technique ......................... 138
6.2 Spin Coherence in Quantum Wells ....................... 140
6.2.1 Electron Spin Coherence ........................ 141
6.2.2 Hole Spin Coherence ............................ 151
6.3 Spin Coherence in Singly Charged Quantum Dots ......... 153
6.3.1 Exciton and Electron Spin Beats Probed by
Faraday Rotation ............................... 155
6.3.2 Generation of Electron Spin Coherence .......... 157
6.3.3 Mode Locking of Spin Coherence in an Ensemble
of Quantum Dots ................................ 160
6.3.4 Nuclei Induced Frequency Focusing of Spin
Coherence ...................................... 169
6.4 Conclusions ........................................... 174
References ................................................. 175
7 Spin Properties of Confined Electrons in Si ................ 179
W. Jantsch and Z. Wilamowski ............................... 179
7.1 Introduction .......................................... 179
7.2 Spin-Orbit Effects in Si Quantum Wells ................ 182
7.2.1 The Bychkov-Rashba Field ....................... 182
7.3 Spin Relaxation of Conduction Electrons in Si/SiGe
Quantum Wells ......................................... 186
7.3.1 Mechanisms of Spin Relaxation of Conduction
Electrons ...................................... 186
7.3.2 Linewidth and the Longitudinal Relaxation
Time of the Two-dimensional Electron Gas in
Si/SiGe ........................................ 187
7.3.3 Dephasing and Longitudinal Spin Relaxation ..... 191
7.3.4 Comparison with Experiment ..................... 194
7.4 Current Induced Spin-Orbit Field ...................... 195
7.5 ESR Excited by an ac Current .......................... 197
7.5.1 Electric Dipole vs. Magnetic Dipole Spin
Excitation ..................................... 197
7.5.2 The ESR Signal Strength in Two-dimensional
Si/SiGe Structures—Experimental Results ........ 198
7.5.3 Modeling the Current Induced Excitation and
Detection of ESR ............................... 199
7.5.4 Power Absorption, Line Shape ................... 201
7.6 Spin Relaxation under Lateral Confinement ............. 201
7.6.1 Shallow Donors ................................. 202
7.6.2 From the Two-dimensional Electron Gas to
Quantum Dots ................................... 204
7.6.3 Spin Relaxation and Dephasing in Si Quantum
Dots ........................................... 205
7.7 Conclusions ........................................... 206
References ................................................. 207
8 Spin Hall Effect ........................................... 211
M.I. Dyakonov and A.V. Khaetskii ........................... 211
8.1 Background: Magnetotransport in Molecular Gases ....... 211
8.2 Phenomenology (with Inversion Symmetry) ............... 213
8.2.1 Preliminaries .................................. 213
8.2.2 Spin and Charge Current Coupling ............... 213
8.2.3 Phenomenological Equations ..................... 214
8.2.4 Physical Consequences of Spin-Charge
Coupling ....................................... 215
8.2.5 Related Problems ............................... 218
8.2.6 Electrical Effects of Second Order in Spin-
Orbit Interaction .............................. 219
8.3 Phenomenology (without Inversion Symmetry) ............ 222
8.4 Microscopic Mechanisms ................................ 223
8.4.1 Spin Asymmetry in Electron Scattering .......... 223
8.4.2 The Side Jump Mechanism ........................ 226
8.4.3 Intrinsic Mechanism ............................ 231
8.5 Experiments ........................................... 235
8.6 Conclusion ............................................ 239
Appendix A: The Generalized Kinetic Equation .......... 239
References ............................................ 241
9 Spin-Photogalvanics ........................................ 245
E.L. Ivchenko and S. Ganichev .............................. 245
9.1 Introduction. Phenomenological Description ............ 245
9.2 Circular Photogalvanic Effect ......................... 247
9.2.1 Historical Background .......................... 247
9.2.2 Basic Experiments .............................. 248
9.2.3 Microscopic Model for Inter-Sub-Band
Transitions .................................... 251
9.2.4 Relation to A:-Linear Terms .................... 251
9.2.5 Circular PGE Due to Inter-Sub-Band
Transitions .................................... 251
9.2.6 Interband Optical Transitions .................. 253
9.2.7 Spin-Sensitive Bleaching ....................... 254
9.3 Spin-Galvanic Effect .................................. 256
9.3.1 Microscopic Mechanisms ......................... 257
9.3.2 Spin-Galvanic Photocurrent Induced by the
Hanle Effect ................................... 259
9.3.3 Spin-Galvanic Effect at Zero Magnetic Field .... 261
9.3.4 Determination of the Rashba/Dresselhaus Spin
Splitting Ratio ................................ 262
9.4 Inverse Spin-Galvanic Effect .......................... 263
9.4.1 Spin-Flip Mediated Current-Induced
Polarization ................................... 264
9.4.2 Precessional Mechanism ......................... 265
9.4.3 Current Induced Spin Faraday Rotation .......... 266
9.4.4 Current Induced Polarization of
Photoluminescence .............................. 267
9.5 Pure Spin Currents .................................... 268
9.5.1 Pure Spin Current Injected by a Linearly
Polarized Beam ................................. 269
9.5.2 Pure Spin Currents Due to Spin-Dependent
Scattering ..................................... 271
9.6 Concluding Remarks ................................... 274
References ................................................. 274
10 Spin Injection ............................................. 279
M. Johnson ................................................. 279
10.1 Introduction .......................................... 279
10.1.1 History ........................................ 279
10.2 Theoretical Models of Spin Injection and Spin
Accumulation .......................................... 281
10.2.1 Heuristic Introduction ......................... 281
10.2.2 Microscopic Transport Model .................... 285
10.2.3 Thermodynamic Theory of Spin Transport ......... 286
10.2.4 Hanle Effect ................................... 292
10.3 Spin Injection Experiments in Metals .................. 292
10.4 Spin Injection in Semiconductors ...................... 295
10.4.1 Optical Experiments ............................ 297
10.4.2 Transport Experiments .......................... 301
10.5 Related Topics ........................................ 305
References ................................................. 306
11 Dynamic Nuclear Polarization and Nuclear Fields ............ 309
V.K. Kalevich, K.V. Kavokin and L.A. Merkulov .............. 309
11.1 Electron-Nuclear Spin System of the Semiconductor:
Characteristic Values of Effective Fields and Spin
Precession Frequencies ................................ 310
11.1.1 Zeeman Splitting of Spin Levels ................ 310
11.1.2 Quadrupole Interaction ......................... 311
11.1.3 Hyperfine Interaction .......................... 311
11.1.4 Nuclear Dipole-Dipole Interaction .............. 313
11.2 Electron Spin Relaxation by Nuclei: from Short to
Long Correlation Time ................................. 314
11.3 Dynamic Polarization of Nuclear Spins ................. 316
11.3.1 Electron Spin Splitting in the Overhauser
Field .......................................... 317
11.3.2 Stationary States of the Electron-Nuclear
Spin System in Faraday Geometry ................ 319
11.3.3 Dynamic Polarization by Localized Electrons .... 320
11.3.4 Cooling of the Nuclear Spin System ............. 322
11.3.5 Polarization of Nuclei by Excitons in Neutral
Quantum Dots ................................... 324
11.3.6 Current-Induced Dynamic Polarization in
Tunnel-Coupled Quantum Dots .................... 325
11.3.7 Self-Polarization of Nuclear Spins ............. 325
11.4 Dynamic Nuclear Polarization in Oblique Magnetic
Field ................................................. 326
11.4.1 Larmor Electron Spin Precession ................ 327
11.4.2 Polarization of Electron-Nuclear Spin-System
in an Oblique Magnetic Field ................... 329
11.4.3 Bistability of the Electron-Nuclear Spin
System in Structures with Anisotropic
Electron g-Factor and Spin Relaxation Time ..... 331
11.5 Optically Detected and Optically Induced Nuclear
Magnetic Resonances ................................... 333
11.5.1 Optically Detected Nuclear Magnetic
Resonance ...................................... 333
11.5.2 Multispin and Multiquantum NMR ................. 333
11.5.3 Optically Induced NMR .......................... 335
11.6 Spin Conservation in the Electron-Nuclear Spin
System of a Quantum Dot ............................... 337
11.6.1 Time Scales for Preservation of Spin
Direction and Spin Temperature ................. 337
11.6.2 A Guide to Interpretation of Experiments on
"Spin Memory" .................................. 338
11.7 Conclusions ........................................... 342
References ................................................. 343
12 Nuclear-Electron Spin Interactions in the Quantum Hall
Regime ..................................................... 347
Y.Q. Li and J.H. Smet ...................................... 347
12.1 Introduction .......................................... 348
12.1.1 The Quantum Hall Effects in a Nutshell ......... 348
12.1.2 Electron Spin Phenomena in the Quantum Hall
Effects ........................................ 353
12.1.3 Nuclear Spins in GaAs-Based 2D Electron
Systems ........................................ 356
12.2 Experimental Techniques ............................... 360
12.3 Nuclear Spin Phenomena in the Quantum Hall Regime ..... 362
12.3.1 The Role of Disorder ........................... 362
12.3.2 Edge Channel Scattering ........................ 364
12.3.3 Skyrmions ...................................... 367
12.3.4 Nuclear-Electron Spin Interactions at
v = 2/3 ........................................ 369
12.3.5 Resistively Detected NMR at v = 2/3 ............ 371
12.3.6 Composite Fermion Fermi Sea at v = 1/2 ......... 379
12.3.7 Other Cases .................................... 382
12.4 Summary and Outlook ................................... 384
References ................................................. 384
13 Diluted Magnetic Semiconductors: Basic Physics and
Optical Properties ......................................... 389
J. Cibert and D. Scalbert .................................. 389
13.1 Introduction .......................................... 389
13.2 Band Structure of II-VI and III-V DMS ................. 390
13.3 Exchange Interactions in DMS .......................... 392
13.3.1 s, p-d Exchange Interaction .................... 392
13.3.2 d-d Exchange Interactions ...................... 394
13.4 Magnetic Properties ................................... 396
13.4.1 UndopedDMS ..................................... 396
13.4.2 Carrier-Induced Ferromagnetism ................. 399
13.5 Basic Optical Properties .............................. 402
13.5.1 Giant Zeeman Effect ............................ 402
13.5.2 Optically Detected Ferromagnetism in II-VI
DMS ............................................ 408
13.5.3 Quantum Dots ................................... 410
13.5.4 Spin-Light Emitting Diodes ..................... 412
13.5.5 III-V Diluted Magnetic Semiconductors .......... 412
13.6 Spin Dynamics ......................................... 414
13.6.1 Electron Spin Relaxation Induced by s-d
Exchange ....................................... 415
13.6.2 Mn Spin Relaxation ............................. 415
13.6.3 Collective Spin Excitations in CdMnTe
Quantum Wells .................................. 419
13.7 Advanced Time-Resolved Optical Experiments ............ 422
13.7.1 Carrier Spin Dynamics .......................... 423
13.7.2 Magnetization Dynamics ......................... 424
References ............................................ 427
Index ......................................................... 433
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