Introduction to the Physics of Diluted Magnetic Semiconductors (eBook)

Jacek Kossut and Jan Gaj belong to the group of researchers whose early work has put diluted magnetic semiconductors on the map. All contributing authors are prominent scientists who gave continue to give extensive input to each subfield they deal with.

Introduction to the Physics of Diluted Magnetic Semiconductors 3
Preface 5
Contents 11
Contributors 19
Chapter 1 Basic Consequences of sp-d and d-d Interactions in DMS 21
1.1 Introduction 21
1.2 Giant Faraday and Zeeman Effects 22
1.2.1 Giant Faraday Effect and its Origin 22
1.2.1.1 Experimental Faraday Rotation Measurements 22
1.2.1.2 Empirical Description of the Faraday Effect 23
1.2.1.3 Sources of the Faraday Rotation 24
1.2.1.4 Dispersion Relations 25
1.2.1.5 Three Types of the Faraday Rotation 27
1.2.1.6 Description of Examples of Experimental FaradayRotation Spectra 28
1.2.1.7 Model Description of Faraday Rotation in (Cd,Mn)Te 29
1.2.2 Excitonic Zeeman Effect in (Cd,Mn)Te 31
1.2.2.1 Zeeman Effect Measurements 31
1.2.2.2 Energy Band Splitting Pattern 31
1.2.2.3 Magnetization Measurements 34
1.2.2.4 Zeeman Splittings vs. Magnetization 35
1.2.3 Mean Field Approximation, Ion-carrier (sp-d) Exchange Integrals in (Cd,Mn)Te 36
1.2.4 Giant Zeeman Effect in Narrow Gap Materials 38
1.3 Values of sp-d Exchange Integrals 43
1.3.1 Experimental Determination 43
1.3.1.1 Photoluminescence in Magnetic Field 43
1.3.1.2 Spin Flip Raman Scattering 44
1.3.1.3 Knight Shift 44
1.3.1.4 Peculiarities of Large Gap Materials 46
1.3.2 Numerical Values of sp-d Exchange Integrals, Chemical Trends 47
1.3.3 Zeeman Effect for Excitons Above the Fundamental Energy Gap 48
1.4 Beyond the Mean Field Approximation 50
1.5 Ion–ion (d-d) Exchange Interaction 51
References 54
Chapter 2 Optical Spectroscopy of Wide-Gap Diluted MagneticSemiconductors 57
2.1 Introduction 57
2.1.1 Specific Properties of Wide Gap Diluted Magnetic Semiconductors 57
2.1.2 Quest for Room Temperature Ferromagnetism 58
2.2 Magnetooptical Spectroscopy of Excitonsin Wide Gap DMS 59
2.2.1 Reflectivity 59
2.2.2 Absorption 65
2.2.3 Magnetic Circular Dichroism 66
2.2.4 Photoluminescence 68
2.2.5 Effective Exchange Integrals 68
2.3 Description of the Giant Zeeman Effect in Wurtzite DMS with Large Energy Gap 70
2.3.1 Giant Zeeman Splitting of Bands 72
2.3.2 Giant Zeeman Splitting of Excitons 73
2.3.2.1 Selection Rules in the Magnetic Field 73
2.3.2.2 Electron–Hole Exchange 74
2.3.2.3 Direct Influence of the Magnetic Field on Excitons 75
2.3.2.4 Excitonic Hamiltonian 75
2.3.2.5 Giant Zeeman Effect in the Faraday Configuration, B B B Bck 76
2.3.2.6 Other Configurations of the Magnetic Field, Crystal c-axis, and Propagation Vector 78
2.4 Magnetic Anisotropy 78
2.5 Conclusions 80
References 81
Chapter 3 Exchange Interaction Between Carriers and Magnetic Ions in Quantum Size Heterostructures 84
3.1 Introduction 84
3.2 Energy Band Structure and Wave Functions of the Electrons and Holes 85
3.2.1 Electrons and Holes in 3D GaAs-like Crystals 85
3.2.2 Electrons in a Symmetrical 2D Quantum Well 88
3.2.3 Holes in a Symmetrical 2D Quantum Well 89
3.2.4 Holes in a Spherical Quantum Dot 90
3.3 Anisotropic Exchange Interaction Between Carriers and Magnetic ions 92
3.3.1 Carriers and Magnetic Ions Exchange Interaction in 3D Crystals 92
3.3.2 The General form of the Exchange Hamiltonian in 2D Heterostructures 93
3.3.3 Exchange Hamiltonian for Heavy and Light Holes at the Bottom of 2D Subband 95
3.3.4 Exchange Hamiltonian for Heavy and Light Holes near the Bottom of 2D Subband 96
3.3.5 Exchange Hamiltonian for the Hole Scattering 98
3.3.6 Exchange Hamiltonian for Holesin a Spherical Quantum Dot 98
3.4 Exchange Interaction Between Electrons and Magnetic Ions in Narrow and Deep Quantum-confined Structures 101
3.4.1 Renormalization of the Exchange Interaction for 3D Electrons with High Kinetic Energy 101
3.4.2 The Exchange Interaction for 2D Electrons in a Narrow Quantum Well 105
3.5 Comparison with Experiment 109
3.5.1 Anisotropy of the Giant Spitting of the Exciton States in Quantum Wells 109
3.5.2 Spin Dynamics for Carriers with Anisotropic g-factor 111
3.5.3 Renormalization of the Exchange Interaction Between Magnetic Ions and Electrons Confined in Narrow Quantum Well 114
3.6 Conclusions 114
References 119
Chapter 4 Band-Offset Engineering in Magnetic/Non-Magnetic Semiconductor Quantum Structures 121
4.1 Introduction 121
4.2 Single Quantum Well 122
4.2.1 Determination of Band Offset Using DMS Properties in Rectangular QWs 122
4.2.2 Graded Potential Quantum Wells 125
4.3 The Double Quantum Well 130
4.3.1 Control of Coupling Between Wells 130
4.3.2 Intra-Well and Inter-Well Excitons 135
4.4 Multiple Quantum Wells 138
4.4.1 Wave Function Mapping 138
4.4.2 Wave Function Transfer in QWs at Off-Resonance Conditions 143
4.5 Superlattices 147
4.5.1 Spin Superlattice 147
4.5.2 Magnetic-Field-Induced Type-I to Type-II Transition 149
4.6 Above-Barrier States 150
4.6.1 Single Barrier 150
4.6.2 Above-Barrier States in Type-I Superlattice 152
4.6.3 Above-Barrier States in Type-II Superlattices 154
4.7 DMS-Based Quantum Dots: Inter-dot Spin–spin Interactions 156
4.7.1 Inter-dot Interactions in DMS/Non-DMS Double Layer QD Systems 157
4.7.2 Interaction Between Non-DMS Quantum Dots and a DMS Quantum Well 160
4.7.3 General Comments on Spin–Spin Interaction in Multiple Quantum Dot Systems 161
4.8 Spin Tracing 163
4.8.1 Spin Profiles Formed During Growth 164
4.8.2 Inter-diffusion at Interfaces Mapped by the Spin Tracing Approach 168
4.8.3 General Remarks on Spin Tracing 168
4.9 Spin-polarized Devices Based on Band-offset Tuning 169
4.9.1 Spin-Polarized Light-Emitting Diodes 169
4.9.2 DMS-based Resonant Tunneling Diodes 172
References 174
Chapter 5 Diluted Magnetic Quantum Dots 179
5.1 Introduction 179
5.2 Epitaxial Growth of II–VI Quantum Dot Structures 180
5.3 Exchange Interactions Under Three-Dimensional Carrier Confinement 183
5.4 Dynamic Processes 190
5.4.1 Interplay Between QD and Internal Mn States 190
5.4.2 Magneto-Polaron Formation 192
5.4.3 Spin Temperature Dynamics 194
5.5 Single-Dot Spectroscopy: From Magnetic Fluctuations to Single Magnetic Moments 199
5.6 Outlook: Novel Interactions and Configurations 205
References 206
Chapter 6 Magnetic Ion–Carrier Interactions in Quantum Dots 209
6.1 Introduction 209
6.2 One Electron States in a Quantum Dot 210
6.2.1 Conduction Band Electron States 210
6.2.2 Valence Band Hole States 211
6.2.3 Tight-Binding Models 214
6.3 Total Spin of Many-Electron Quantum Dots 216
6.4 Energy Spectrum of Magnetic Ions in Semiconductors 216
6.5 Mn–Mn Interaction 217
6.6 Magnetic Ion–Electron Exchange Interaction 218
6.7 Hybrid System of Magnetic Ions and Carriers 218
6.8 Magnetic Ion–Many Electron Interaction 219
6.8.1 Engineering Mn–Carrier Exchange Interaction Matrix Elements 220
6.8.2 Mn–Carrier Spin Interaction 221
6.8.3 Addition Spectrum of N-Electron Quantum Dot with a Mn Ion 223
6.8.4 Electron Spectral Function of a N-Electron Quantum Dot with a Mn Ion 225
6.8.5 Magnetic Ion in III–V Self-Assembled Quantum Dots 225
6.9 Mn–Mn Interactions Mediated by Interacting Electrons 226
6.9.1 RKKY Mn–Mn Interactions for Closed Shells 227
6.9.2 Magneto-Polarons in Partially Filled Shells 230
6.10 Control of Ferromagnetism in Quantum Dots 232
6.11 Summary and Outlook 235
References 235
Chapter 7 Magnetic Polarons 238
7.1 Introduction 238
7.2 Theoretical Aspects 241
7.2.1 Stability of Magnetic Polarons in Systems of Different Dimensionality 243
7.2.2 Dynamics of Magnetic Polaron Formation 246
7.2.3 Parameters of Exciton Magnetic Polaron 249
7.3 Optical Study of Exciton Magnetic Polarons by the Method of Selective Excitation 251
7.4 Exciton Magnetic Polarons in 3D Systems 255
7.4.1 Magnetic Polarons in (Cd,Mn)Te 255
7.4.2 Role of Nonmagnetic Localization 257
7.4.3 Magnetic Polaron Effect on Exciton Mobility 259
7.4.4 Modification of Magnetic Susceptibility: Suppression of Spin Glass Phase 261
7.5 Exciton Magnetic Polarons in Low-Dimensional Systems 262
7.5.1 Reduction of Dimensionality from 3D to 2D 262
7.5.2 Magnetic Polaron in Spin Superlattice 264
7.5.3 Anisotropic Spin Structure of 2D Magnetic Polaron 265
7.6 Spin Dynamics of Exciton Magnetic Polaron Formation 268
7.6.1 Magnetic Polaron Formation in 3D and 2D Systems 268
7.6.2 Optical Orientation of Magnetic Polarons 270
7.6.3 Hierarchy of Spin Dynamics Contributing to Magnetic Polaron Formation 275
7.7 Conclusions 275
References 276
Chapter 8 Spin and Energy Transfer Between Carriers, Magnetic Ions, and Lattice 280
8.1 Introduction 280
8.2 Systems Responsible for Spin Dynamics in DMS 282
8.3 Theoretical View on Coupled Transfer of Spin and Energy 283
8.4 Experimental Technique 289
8.4.1 Optical Detection of Mn-Spin Temperature 290
8.4.1.1 Optical Spectra and Giant Zeeman Splitting of Excitons in (Zn,Mn)Se QWs 291
8.4.1.2 Suppression of Giant Zeeman Splitting Under Continuous-Wave Excitation 292
8.4.1.3 Time-Resolved Measurements of Spin Dynamics 293
8.4.2 Tools to Address the Mn-Spin System 295
8.4.2.1 Microwave Heating 295
8.4.2.2 Heat Pulse of Nonequilibrium Phonons 296
8.4.2.3 Electric Field Heating via Free Carriers 297
8.5 Spin-Lattice Relaxation of Mn System 298
8.5.1 Concentration Dependence of SLR Dynamics 299
8.5.2 Mn Profile Engineering 300
8.5.2.1 Digital Alloys 300
8.5.2.2 Heteromagnetic Structures 302
8.5.3 Acceleration by Free Carriers 304
8.5.4 Regime of Degenerate 2DEG 305
8.6 Spin and Energy Transfer from Carriers to Mn System 308
8.6.1 Direct Spin and Energy Transfer 309
8.6.2 Multiple Transfer of Angular Momentum Quanta from Holes 310
8.6.3 Double Impact of Laser Pulses for Mn Heating 312
8.6.4 Competition of Direct and Indirect Transfer 314
8.7 Conclusions 317
References 317
Chapter 9 Coherent Spin Dynamics of Carriers and Magnetic Ions in Diluted Magnetic Semiconductors 321
9.1 Introduction 321
9.2 Origins of the Magneto-Optical Faraday Effect in Diluted Magnetic Semiconductors 322
9.3 Time-Resolved Faraday Rotation 326
9.4 Spin Relaxation in Zero Magnetic Field 328
9.5 Spin Dynamics in Longitudinal Magnetic Fields 330
9.6 Electron and Hole Dynamics and Spin Coherence in Transverse Magnetic Fields 331
9.6.1 Terahertz Electron Spin Precession 333
9.6.2 Tuning Electron Spin Precessionvia Wavefunction Control 334
9.6.3 Separating Electron and Hole Spin Dynamics 336
9.6.4 Electron and Hole Spin Relaxationand Dephasing in DMS 338
9.6.5 Spin Precession Overtones and Electron Entanglement 339
9.7 Coherent Spin Precession of the Embedded Mn Ions 340
9.7.1 Long-Lived Oscillations from Mn Spin Precession 341
9.7.2 A Model for Coherent ``Tipping'' of the Mn Ensemble 342
9.7.3 Amplitude and Phase of the Mn Free-Induction Decay 344
9.7.4 Exchange Fields, Tipping Angles, and Mn-Spin Manipulation 345
9.7.5 All-Optical Time-Domain Paramagnetic Resonance of Submonolayer Magnetic Planes 346
9.8 Conclusions 348
References 348
Chapter 10 Spectroscopy of Spin-Polarized 2D Carrier Gas, Spin-Resolved Interactions 351
10.1 Introduction 351
10.2 Preliminaries 352
10.2.1 Typical Samples with Spin-Polarized Carriers 352
10.2.2 Modeling of Spin Polarized 2D Carrier Gas in II1-xMnxVI Quantum Wells 354
10.2.2.1 Two Coupled Spin SubSystems 354
10.2.2.2 Spin-Polarized 2DEG in a Paramagnetic Phase 356
10.3 Properties of Quantum Well with Spin-Polarized Carrier Gas: Interband Spectroscopy 358
10.3.1 Low Carrier Density: Charged Excitons 359
10.3.1.1 Intensity of Neutral and Charged Absorption Lines 362
10.3.2 Photoluminescence 368
10.3.3 Spectroscopy of Spin-Polarized Carrier Gas with High Densities of Carriers 369
10.4 Intraband Excitations: Raman Scattering 376
10.4.1 Probing Spin-Flip Excitations 377
10.4.1.1 Larmor Theorem in (Cd,Mn)Te Quantum Wells 380
10.4.2 Dispersion of Spin-Flip Excitations of the Spin-Polarized Two-Dimensional Electron Gas 382
10.4.2.1 Spin-Flip Single Particle Excitations 384
10.4.2.2 Spin-Flip Waves 386
10.4.2.3 Interplay Between Individual and Collective Excitations 387
10.4.2.4 Dispersion of Spin-Flip Excitations 388
10.4.2.5 Damping of the Spin-Flip Waves 389
10.4.3 Beyond the Decoupled Model 391
10.5 Conclusions and Outlook 393
References 394
Chapter 11 Quantum Transport in Diluted Magnetic Semiconductors 398
11.1 Magnetically Doped Low-Dimensional SemiconductorStructures 398
11.2 Quantum Phenomena in Diffusive Transport Regime 400
11.3 Magnetoresistance 402
11.3.1 Paramagnetic Phase 402
11.3.2 Magnetic Polarons or Nanoclustering 404
11.3.3 Metal-Insulator Transition in Magnetic 2D Systems 405
11.3.4 Magnetoresistance in Ferromagnetic Semiconductors 406
11.4 Universal Conductance Fluctuations in Diluted Magnetic Semiconductors 408
11.4.1 Spin-Splitting Driven Conductance Fluctuations 408
11.4.2 Conductance Fluctuations in Modulation Doped Wires 409
11.4.3 Magnetization Steps Observed by Means of Conductance Fluctuations 410
11.4.4 Time-Dependent Conductance Fluctuations in the Spin Glass Phase 410
11.4.5 Mesoscopic Transport in III-Mn-V Semiconductors 412
11.5 Anomalous Hall Effect 413
11.6 Quantum Hall Effect in Diluted Magnetic Semiconductors 416
11.6.1 Introduction to the Integer Quantum Hall Effect 416
11.6.2 Dramatic Modification of Energy Diagram by a Giant s-d Exchange 417
11.6.3 Early Observations of Landau Quantization in Diluted Magnetic Semiconductors 418
11.6.4 Quantum Hall Effect Scaling 419
11.6.5 Temperature Scaling 420
11.6.6 QHE Scaling in Small Samples: Dimensional Effects 420
11.6.7 Quantum Hall-Insulator Transition 420
11.6.8 Dramatic Modification of Shubnikov–deHaas Oscillations 422
11.6.9 Quantum Hall Ferromagnetism in Diluted Magnetic Semiconductors 425
11.7 Summary and Perspectives 429
References 430
Chapter 12 Neutron Scattering Studies of Interlayer Magnetic Coupling 434
12.1 Introduction 434
12.2 Neutron Scattering Tools 437
12.2.1 Neutron Diffractometry 437
12.2.2 Neutron Reflectometry 444
12.3 Studies of Ferromagnetic Semiconductor Superlattices (Primarily, by Neutron Reflectometry) 447
12.3.1 EuS-Based Multilayers 447
12.3.2 Neutron Reflectometry Studies of Ga1-xMnxAs/GaAs Superlattices 456
12.4 Neutron Diffraction Studies of Antiferromagnetic Multilayered Systems 464
12.4.1 EuTe/PbTe Superlattices 464
12.4.2 II–VI-Based Systems 472
12.5 Closing Remarks 475
References 477
Index 479