1 The Early History of Spin .................................... 1
1.1 Spin .................................................... 1
1.2 The Bohr planetary model and space quantization ......... 3
1.3 The birth of "spin" ..................................... 4
1.4 The Stern-Gerlach experiment ............................ 5
1.5 The advent of Spintronics ............................... 8
1.6 Problems ............................................... 10
1.7 References ............................................. 13
2 The Quantum Mechanics of Spin ............................... 17
2.1 Pauli spin matrices .................................... 19
2.2 The Pauli Equation and spinors ......................... 23
2.3 More on the Pauli Equation ............................. 25
2.4 Extending the Pauli Equation - the Dirac Equation ...... 26
2.5 The time independent Dirac Equation .................... 30
2.6 Problems ............................................... 33
2.7 Appendix ............................................... 36
2.8 References ............................................. 43
3 The Bloch Sphere ............................................ 45
3.1 The spinor and the "qubit" ............................. 45
3.2 The Bloch sphere concept ............................... 47
3.3 Problems ............................................... 58
3.4 References ............................................. 63
4 Evolution of a Spinor on the Bloch Sphere ................... 65
4.1 Spin-1/2 particle in a constant magnetic field:
Larmor precession ...................................... 65
4.2 Preparing to derive the Rabi formula ................... 69
4.3 The Rabi formula ....................................... 74
4.4 Problems ............................................... 87
4.5 References ............................................. 89
5 The Density Matrix ......................................... 91
5.1 The density matrix concept: case of a pure state ....... 91
5.2 Properties of the density matrix ....................... 92
5.3 Pure versus mixed state ................................ 96
5.4 Concept of the Bloch ball .............................. 99
5.5 Time evolution of the density matrix: case of mixed
state ................................................. 101
5.6 The relaxation times T1 and T2 and the Bloch
equations ............................................. 105
5.7 Problems .............................................. 118
5.8 References ............................................ 130
6 Spin Orbit Interaction ..................................... 131
6.1 Spin orbit interaction in a solid ..................... 134
6.2 Problems .............................................. 137
6.3 References ............................................ 139
7 Magneto-Electric Subbands in Quantum Confined Structures
in the Presence of Spin-Orbit Interaction .................. 141
7.1 Dispersion relations of spin resolved magneto-
electric subbands and eigenspinors in
a two-dimensional electron gas in the presence of
spin-orbit interaction ................................ 141
7.2 Dispersion relations of spin resolved
magnetoelectric subbands and eigenspinors in a
one-dimensional electron gas in the presence of
spin-orbit interaction ................................ 153
7.3 Magnetic field perpendicular to wire axis and the
electric field causing Rashba effect (i.e., along
the z-axis) ........................................... 168
7.4 Eigenenergies of spin resolved subbands and
eigenspinors in a quantum dot in the presence of
spin-orbit interaction ................................ 171
7.5 Why are the dispersion relations important? ........... 176
7.6 The three types of Hall Effect ........................ 177
7.7 Problems .............................................. 191
7.8 References ............................................ 195
8 Spin Relaxation ............................................ 199
8.1 The spin-independent spin-orbit magnetic field ........ 201
8.2 Spin relaxation mechanisms ............................ 204
8.3 Spin relaxation in a quantum dot ...................... 216
8.4 The Spin Galvanic Effect .............................. 223
8.5 Another example of current flow without a battery ..... 224
8.6 Problems .............................................. 228
8.7 References ............................................ 238
9 Exchange Interaction ....................................... 243
9.1 Identical particles and the Pauli Exclusion
Principle ............................................. 243
9.2 Hartree and Hartree-Fock approximations ............... 256
9.3 The role of exchange in ferromagnetism ................ 258
9.4 The Heisenberg Hamiltonian ............................ 260
9.5 Problems .............................................. 261
9.6 References ............................................ 265
10 Spin Transport in Solids ................................... 267
10.1 The drift-diffusion model ............................ 267
10.2 The semiclassical model .............................. 274
10.3 Concluding remarks ................................... 283
10.4 Problems ............................................. 285
10.5 References ........................................... 285
11 Passive Spintronic Devices and Related Concepts ............ 287
11.1 Spin valve ........................................... 287
11.2 Spin injection efficiency ............................ 289
11.3 Hysteresis in spin valve magnetoresistance ........... 320
11.4 Giant magnetoresistance .............................. 323
11.5 Spin accumulation .................................... 331
11.6 Spin injection across a ferromagnet/metal
interface ............................................ 336
11.7 Spin injection in a spin valve ....................... 341
11.8 Spin extraction at the interface between
a ferromagnet and a semiconductor .................... 347
11.9 Problems ............................................. 353
11.10 References ........................................... 356
12 Hybrid Spintronics: Active Devices Based on Spin and
Charge ..................................................... 361
12.1 Spin-based transistors ............................... 361
12.2 Spin field effect transistors (SPINFET) .............. 363
12.3 Device performance of SPINFETs ....................... 382
12.4 Power dissipation estimates .......................... 387
12.5 Other types of SPINFETs .............................. 387
12.6 The importance of the spin injection efficiency ...... 392
12.7 Transconductance, gain, bandwidth and isolation ...... 396
12.8 Spin Bipolar Junction Transistors (SBJT) ............. 398
12.9 GMR-based transistors ................................ 400
12.10 Concluding remarks ................................... 406
12.11 Problems ............................................. 407
12.12 References ........................................... 409
13 Monolithic Spintronics: All-Spin Logic Processors .......... 413
13.1 Monolithic spintronics ............................... 413
13.2 Reading and writing single spin ...................... 415
13.3 Single Spin Logic .................................... 416
13.4 Energy dissipation issues ............................ 432
13.5 Comparison between hybrid and monolithic
spintronics .......................................... 436
13.6 Concluding remarks ................................... 437
13.7 Problems ............................................. 437
13.8 References ........................................... 439
14 Quantum Computing with Spins ............................... 443
14.1 The quantum inverter ................................. 443
14.2 Can the NAND gate be switched without dissipating
energy? .............................................. 448
14.3 Universal reversible gate: the Toffoli-Fredkin
gate ................................................. 453
14.4 A-matrix ............................................. 456
14.5 Quantum gates ........................................ 456
14.6 Qubits ............................................... 458
14.7 Superposition states ................................. 460
14.8 Quantum parallelism .................................. 461
14.9 Universal quantum gates .............................. 463
14.10 A 2-qubit "spintronic" universal quantum gate ........ 464
14.11 Conclusion ........................................... 468
14.12 Problems ............................................. 469
14.13 References ........................................... 470
15 A Quantum Mechanics Primer ................................. 475
15.1 Blackbody radiation and quantization of
electromagnetic energy ............................... 475
15.2 The concept of the photon ............................ 476
15.3 Wave-particle duality and the De Broglie wavelength .. 479
15.4 Postulates of quantum mechanics ...................... 482
15.5 Some elements of semiconductor physics: particular
applications in nanostructures ....................... 493
15.6 The Rayleigh-Ritz variational procedure .............. 507
15.7 The transfer matrix formalism ........................ 512
15.8 Problems ............................................. 520
15.9 References ........................................... 521
Index ......................................................... 523
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