Preface |
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xv | |
Acknowledgments |
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xxi | |
1 Early History of Spin |
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1 | (16) |
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1 | (2) |
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1.2 Bohr planetary model and space quantization |
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3 | (1) |
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4 | (2) |
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1.4 The Stern-Gerlach experiment |
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6 | (3) |
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1.5 Advent of spintronics |
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9 | (1) |
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10 | (4) |
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14 | (3) |
2 Quantum Mechanics of Spin |
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17 | (28) |
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19 | (4) |
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2.1.1 Eigenvectors of the Pauli matrices: Spinors |
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22 | (1) |
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2.2 The Pauli equation and spinors |
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23 | (2) |
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2.3 More on the Pauli equation |
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25 | (1) |
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2.4 Extending the Pauli equation - the Dirac equation |
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26 | (4) |
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2.4.1 Connection to Einstein's relativistic equation |
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30 | (1) |
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2.5 Time-independent Dirac equation |
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30 | (4) |
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2.5.1 Non-relativistic approximation to the Dirac equation |
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31 | (1) |
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2.5.2 Relationship between the non-relativistic approximation to the Dirac equation and the Pauli equation |
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32 | (2) |
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34 | (3) |
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37 | (7) |
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2.7.1 Working with spin operators |
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37 | (1) |
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2.7.2 Two useful theorems |
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38 | (2) |
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2.7.3 Applications of the Postulates of Quantum Mechanics to a few spin problems |
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40 | (3) |
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2.7.4 The Heisenberg principle for spin components |
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43 | (1) |
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44 | (1) |
3 Bloch Sphere |
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45 | (20) |
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45 | (2) |
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47 | (11) |
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47 | (3) |
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3.2.2 Connection between the Bloch sphere concept and the classical interpretation of the spin of an electron |
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50 | (1) |
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3.2.3 Relationship with qubit |
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51 | (2) |
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53 | (1) |
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54 | (1) |
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3.2.6 Excursions on the Bloch sphere: Pauli matrices revisited |
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54 | (4) |
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58 | (5) |
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63 | (2) |
4 Evolution of a Spinor on the Bloch Sphere |
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65 | (26) |
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4.1 Spin-1/2 particle in a constant magnetic field: Larmor precession |
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65 | (4) |
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4.1.1 Rotation on the Bloch sphere |
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67 | (2) |
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4.2 Preparing to derive the Rabi formula |
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69 | (5) |
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74 | (13) |
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77 | (10) |
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87 | (2) |
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89 | (2) |
5 The Density Matrix |
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91 | (40) |
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5.1 Density matrix concept: Case of a pure state |
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91 | (1) |
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5.2 Properties of the density matrix |
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92 | (4) |
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5.3 Pure versus mixed state |
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96 | (3) |
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5.4 Concept of the Bloch ball |
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99 | (2) |
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5.5 Time evolution of the density matrix: Case of mixed state |
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101 | (4) |
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5.6 Relaxation times T1 and T2 and the Bloch equations |
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105 | (13) |
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118 | (11) |
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129 | (2) |
6 Spin-Orbit Interaction |
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131 | (16) |
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6.1 Microscopic or intrinsic spin-orbit interaction in an atom |
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132 | (3) |
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6.2 Macroscopic or extrinsic spin-orbit interaction |
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135 | (6) |
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136 | (3) |
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6.2.2 Dresselhaus interaction |
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139 | (2) |
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141 | (3) |
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144 | (3) |
7 Magneto-Electric Subbands in Quantum Confined Structures in the Presence of Spin-Orbit Interaction |
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147 | (48) |
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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 |
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147 | (15) |
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7.1.1 Magnetic field in the plane of the 2-DEG |
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151 | (10) |
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7.1.2 Magnetic field perpendicular to the plane of the 2-DEG |
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161 | (1) |
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7.2 Dispersion relations of spin resolved magneto-electric subbands and eigenspinors in a one-dimensional electron gas in the presence of spin-orbit interaction |
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162 | (15) |
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7.2.1 Magnetic field directed along the wire axis (x-axis) |
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162 | (3) |
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165 | (5) |
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7.2.3 Magnetic field perpendicular to wire axis and along the electric field causing Rashba effect (i.e., along y-axis) |
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170 | (5) |
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175 | (2) |
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7.3 Magnetic field perpendicular to the wire axis and the electric field causing the Rashba effect (i.e., along the z-axis) |
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177 | (3) |
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179 | (1) |
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179 | (1) |
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7.4 Eigenenergies of spin resolved subbands and eigenspinors in a quantum dot in the presence of spin-orbit interaction |
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180 | (5) |
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7.5 Why are the dispersion relations important? |
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185 | (1) |
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186 | (6) |
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192 | (3) |
8 Spin Relaxation |
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195 | (40) |
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8.1 Spin-independent spin-orbit magnetic field |
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197 | (3) |
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8.2 Spin relaxation mechanisms |
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200 | (12) |
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8.2.1 Elliott-Yafet mechanism |
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200 | (3) |
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8.2.2 D'yakonov Perel' mechanism |
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203 | (8) |
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8.2.3 Bir-Aronov-Pikus mechanism |
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211 | (1) |
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8.2.4 Hyperfine interactions with nuclear spins |
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212 | (1) |
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8.3 Spin relaxation in a quantum dot |
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212 | (8) |
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8.3.1 Longitudinal and transverse spin relaxation times in a quantum dot |
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215 | (5) |
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220 | (10) |
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230 | (5) |
9 Some Spin Phenomena |
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235 | (42) |
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235 | (18) |
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9.1.1 The intrinsic Spin Hall effect |
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241 | (12) |
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9.2 The Spin Galvanic effect |
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253 | (4) |
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257 | (5) |
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9.4 The Spin Transfer Torque |
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262 | (2) |
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9.5 The Spin Hanle effect |
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264 | (2) |
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9.6 The Spin Seebeck effect |
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266 | (2) |
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9.7 The Spin Peltier effect |
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268 | (1) |
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268 | (3) |
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271 | (6) |
10 Exchange Interaction |
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277 | (24) |
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10.1 Identical particles and the Pauli exclusion principle |
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277 | (13) |
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278 | (9) |
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10.1.2 The Heitler-London model of the hydrogen molecule |
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287 | (3) |
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10.2 Hartree and Hartree-Fock approximations |
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290 | (2) |
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10.3 The role of exchange in ferromagnetism |
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292 | (2) |
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10.3.1 The Bloch model of ferromagnetism |
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292 | (1) |
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10.3.2 The Heisenberg model of ferromagnetism |
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293 | (1) |
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10.4 The Heisenberg Hamiltonian |
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294 | (1) |
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295 | (4) |
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299 | (2) |
11 Spin Transport in Solids |
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301 | (20) |
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11.1 The drift-diffusion model |
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301 | (8) |
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11.1.1 Derivation of the simplified steady-state spin driftdiffusion equation |
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305 | (4) |
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11.2 The semiclassical model |
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309 | (8) |
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11.2.1 Spin transport in a quantum wire: Monte Carlo simulation |
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310 | (1) |
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11.2.2 Monte Carlo simulation |
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311 | (1) |
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11.2.3 Specific examples: Temporal decay of spin polarization |
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312 | (1) |
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11.2.4 Specific examples: Spatial decay of spin polarization |
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313 | (1) |
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11.2.5 Upstream transport |
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313 | (4) |
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317 | (2) |
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319 | (1) |
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319 | (2) |
12 Passive Spintronic Devices and Related Concepts |
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321 | (74) |
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321 | (2) |
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12.2 Spin injection efficiency |
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323 | (31) |
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12.2.1 Stoner-Wohlfarth model of a ferromagnet |
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324 | (4) |
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12.2.2 A simple two-resistor model to understand the spin valve |
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328 | (3) |
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12.2.3 More advanced treatment of the spin valve |
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331 | (7) |
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12.2.4 A transfer matrix model |
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338 | (15) |
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12.2.5 Application of the Jullike formula to extract the spin diffusion length in a paramagnet from spin valve experiments |
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353 | (1) |
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12.2.6 Spin valve experiments |
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354 | (1) |
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12.3 Hysteresis in spin valve magnetoresistance |
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354 | (6) |
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12.4 Giant magnetoresistance |
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360 | (6) |
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12.4.1 Applications of the spin valve and GMR effects |
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361 | (5) |
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366 | (5) |
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12.6 Spin injection across a ferromagnet/metal interface |
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371 | (5) |
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12.7 Spin injection in a spin valve |
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376 | (6) |
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12.8 Spin extraction at the interface between a ferromagnet and a semiconductor |
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382 | (4) |
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386 | (5) |
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391 | (4) |
13 Active Devices Based on Spin and Charge |
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395 | (58) |
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13.1 Spin-based transistors |
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395 | (1) |
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13.2 Spin field effect transistors (SPINFET) |
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396 | (15) |
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13.2.1 Particle viewpoint |
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398 | (2) |
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400 | (2) |
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13.2.3 Effect of scattering on the Datta-Das SPINFET |
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402 | (1) |
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13.2.4 Transfer characteristic of the Datta-Das transistor |
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403 | (2) |
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13.2.5 Sub-threshold slope |
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405 | (2) |
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13.2.6 Effect of non-idealities |
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407 | (3) |
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13.2.7 The quantum well SPINFET |
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410 | (1) |
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13.3 Analysis of the two-dimensional SPINFET |
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411 | (8) |
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13.3.1 SPINFET based on the Dresselhaus spin-orbit interaction |
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417 | (2) |
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13.4 Device performance of SPINFETs |
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419 | (6) |
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13.4.1 Comparison between MISFET and SPINFET |
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422 | (1) |
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13.4.2 Comparison between HEMT and SPINFET |
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423 | (2) |
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13.5 Power dissipation estimates |
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425 | (1) |
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13.6 Other types of SPINFETs |
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426 | (6) |
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13.6.1 Non-ballistic SPINFET |
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426 | (3) |
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13.6.2 Spin relaxation transistor |
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429 | (3) |
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13.7 Importance of spin injection efficiency |
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432 | (3) |
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13.8 Transconductance, gain, bandwidth, and isolation |
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435 | (3) |
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437 | (1) |
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13.9 Spin Bipolar Junction Transistors (SBJT) |
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438 | (1) |
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13.10 GMR-based transistors |
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439 | (7) |
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13.10.1 All-metal spin transistor |
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440 | (1) |
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13.10.2 Spin valve transistor |
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440 | (6) |
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446 | (1) |
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447 | (2) |
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449 | (4) |
14 All-Electric spintronics with Quantum Point Contacts |
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453 | (32) |
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14.1 Quantum point contacts |
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453 | (3) |
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14.2 Recent experimental results with QPCs and QDs |
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456 | (3) |
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459 | (1) |
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14.4 Rashba spin-orbit coupling (RSOC) |
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460 | (2) |
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14.5 Lateral spin-orbit coupling (LSOC) |
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462 | (3) |
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14.6 Stern-Gerlach type spatial spin separation in a QPC structure |
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465 | (1) |
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14.7 Detection of spin polarization |
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466 | (2) |
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14.8 Observation of a 0.5 Go conductance plateau in asymmetrically biased QPCs with in-plane side gates |
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468 | (4) |
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14.9 Prospect for generation of spin-polarized current at higher temperatures |
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472 | (1) |
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14.10 Prospect for an all-electric SpinFET |
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473 | (2) |
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475 | (1) |
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475 | (5) |
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480 | (5) |
15 Single Spin Processors |
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485 | (32) |
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485 | (2) |
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15.1.1 Bit stability and fidelity |
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486 | (1) |
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15.2 Reading and writing single spin |
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487 | (1) |
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488 | (17) |
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488 | (1) |
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15.3.2 Input-dependent ground states of the NAND gate |
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489 | (9) |
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15.3.3 Ground state computing with spins |
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498 | (7) |
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15.4 Energy dissipation issues |
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505 | (4) |
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15.4.1 Energy dissipated in the gate during switching |
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505 | (4) |
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15.4.2 Energy dissipated in the clocking circuit |
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509 | (1) |
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15.5 Comparison between spin transistors and single-spin-processors |
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509 | (1) |
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510 | (1) |
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511 | (2) |
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513 | (4) |
16 Quantum Computing with Spins |
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517 | (32) |
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517 | (5) |
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16.2 Can the NAND gate be switched without dissipating energy? |
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522 | (5) |
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16.3 Universal reversible gate: Toffoli-Fredkin gate |
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527 | (2) |
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16.3.1 Dynamics of the T-F gate |
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529 | (1) |
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529 | (1) |
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530 | (2) |
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16.5.1 The strange nature of true quantum gates: The "square root of NOT" gate |
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530 | (2) |
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532 | (2) |
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16.7 Superposition states |
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534 | (2) |
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536 | (1) |
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16.9 Universal quantum gates |
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537 | (1) |
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16.9.1 Two-qubit universal quantum gates |
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538 | (1) |
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16.10 A 2-qubit "spintronic" universal quantum gate |
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538 | (4) |
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16.10.1 Silicon quantum computer based on nuclear spins |
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539 | (1) |
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16.10.2 Quantum dot-based spintronic model of universal quantum gate |
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540 | (2) |
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542 | (1) |
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543 | (2) |
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545 | (4) |
17 Nanomagnetic Logic: Computing with Giant Classical Spins |
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549 | (28) |
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17.1 Nanomagnetic logic and Bennett clocking |
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553 | (8) |
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561 | (8) |
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562 | (4) |
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17.2.2 Magneto-elastic magneto-tunneling junction logic |
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566 | (3) |
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569 | (3) |
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572 | (5) |
18 A Brief Quantum Mechanics Primer |
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577 | (50) |
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18.1 Blackbody radiation and quantization of electromagnetic energy |
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577 | (1) |
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18.1.1 Blackbody radiation |
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577 | (1) |
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18.2 Concept of the photon |
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578 | (3) |
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18.3 Wave-particle duality and the De Broglie wavelength |
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581 | (3) |
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18.4 Postulates of quantum mechanics |
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584 | (11) |
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18.4.1 Interpretation of the Heisenberg Uncertainty Principle |
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590 | (3) |
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18.4.2 Time evolution of expectation values: Ehrenfest theorem |
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593 | (2) |
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18.5 Some elements of semiconductor physics: Particular applications in nanostructures |
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595 | (14) |
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18.5.1 Density of states: Bulk (3-D) to quantum dot (0-D) |
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595 | (14) |
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18.6 Rayleigh-Ritz variational procedure |
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609 | (5) |
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18.7 The transfer matrix formalism |
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614 | (8) |
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18.7.1 Linearly independent solutions of the Schrodinger equa- tion |
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615 | (1) |
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18.7.2 Concept of Wronskian |
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616 | (1) |
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18.7.3 Concept of transfer matrix |
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617 | (1) |
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18.7.4 Cascading rule for transfer matrices |
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617 | (5) |
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18.8 Peierls' transformation |
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622 | (2) |
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624 | (1) |
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625 | (2) |
Index |
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627 | |