Molecular nanomagnets

0198567537......Page 1
Contents......Page 8
1 Introduction......Page 14
2 Magnetic interactions in molecular systems......Page 27
2.1.1 Zeeman and crystal field terms for isolated ions......Page 28
2.1.2 Electron nucleus (hyperfine) interaction terms......Page 33
2.1.3 Spin Hamiltonian for pairs......Page 34
2.2 Single ion levels......Page 36
2.3.1 Delocalization effects......Page 43
2.3.2 Spin polarization effects......Page 45
2.3.3 Some examples......Page 47
2.3.4 Double exchange......Page 48
2.3.5 Towards quantitative calculations of exchange interactions......Page 49
2.4 Through-space and other interactions......Page 50
2.5.1 Isotropic coupling......Page 52
2.5.2 Magnetic anisotropy in clusters......Page 57
3.1.1 Standard magnetometry......Page 62
3.1.2 Time-dependent measurements......Page 71
3.1.3 Micro-SQUID and micro-Hall probe techniques......Page 74
3.1.4 Torque magnetometry......Page 77
3.1.5 AC susceptometry......Page 82
3.2.1 The specific heat and its magnetic part......Page 88
3.2.2 Magnetic specific heat at equilibrium......Page 89
3.2.3 Measurement of the magnetic specific heat: the relaxation method......Page 91
3.2.4 Magnetic specific heat in an alternating current......Page 93
3.3.1 Electron paramagnetic resonance......Page 94
3.3.2 Nuclear magnetic resonance......Page 102
3.3.3 Muon spin resonance (μSR)......Page 108
3.4.1 Polarized neutron diffraction......Page 112
3.4.2 Inelastic neutron scattering......Page 117
4.1 Serendipity versus rational design of SMMs......Page 121
4.2 Synthetic strategies to SMMs......Page 122
4.3.1 Cyanide-based clusters......Page 131
4.3.2 The disruption of oxocentred carboxylate triangles......Page 136
4.4 Polyoxometalates......Page 139
4.4.1 The role of pentagons......Page 140
4.5 The templating effect......Page 142
4.6 Solvothermal synthesis......Page 145
4.7 A survey of the most investigated SMMs......Page 147
4.7.1 The archetypal Mn[sub(12)] acetate cluster......Page 148
4.7.2 The Mn[sub(12)] family......Page 159
4.7.3 The reduced species of Mn[sub(12)] clusters......Page 162
4.7.4 Fe[sub(8)] clusters......Page 164
4.7.5 Mn[sub(4)] clusters......Page 169
5.1 Relaxation and relaxation time......Page 173
5.2 Potential barrier......Page 174
5.3 Transition probabilities and the master equation......Page 176
5.4 Solution of the master equation......Page 178
5.5.1 Basic features......Page 180
5.5.3 Local strain......Page 181
5.5.4 Terms linear in the spin operators......Page 182
5.6 Transition probabilities and the golden rule......Page 184
5.7 Qualitative formulae......Page 186
5.8 Multiphonon processes......Page 188
5.9 Spin–phonon interactions resulting from exchange......Page 189
5.10.2 Photons at thermal equilibrium......Page 190
5.10.3 The beauty of light......Page 191
5.11 Limitations of the model......Page 193
6.1.1 Particle tunnelling: a reminder......Page 195
6.1.2 An example......Page 196
6.1.4 Case of an arbitrary spin......Page 197
6.1.5 Delocalization......Page 198
6.1.6 Large spin = classical spin?......Page 200
6.1.7 Approximate localized eigenstates......Page 201
6.2 Symmetry and selection rules for tunnelling......Page 204
6.3 Tunnelling width for an isolated spin......Page 205
6.4 Tunnel splitting according to perturbation theory......Page 207
6.5 Time-dependent wavefunction: magnetic tunnelling......Page 210
6.7.1 General methods......Page 212
6.7.2 Example: the Hamiltonian (2.5)......Page 214
6.8.1 Degeneracy with and without symmetry......Page 216
6.8.2 The von Neumann–Wigner theorem......Page 217
6.8.3 The quest of the Devil......Page 218
7.2 The anharmonic oscillator......Page 222
7.3 Tunnel effect and instantons......Page 223
7.4 The path integral method applied to spins......Page 226
8.1 Advantages of a time-dependent magnetic field......Page 229
8.2 Fast sweeping and adiabatic limit......Page 231
8.3.1 Equations of motion......Page 232
8.3.2 The solution of Landau, Zener, and Stückelberg......Page 234
8.3.3 Fast sweeping......Page 235
8.3.4 Sweeping back and forth through the resonances......Page 236
9.1.1 Low temperatures......Page 238
9.1.2 The window mechanism......Page 239
9.2.1 The hyperfine field and its order of magnitude......Page 240
9.2.2 Experimental evidence of hyperfine interactions......Page 242
9.2.3 Linewidth of hyperfine origin......Page 247
9.2.4 Relaxation of hyperfine origin......Page 249
9.2.5 Effect of hyperfine interactions in the case of time-dependent fields......Page 250
9.2.6 How do nuclear spins relax?......Page 251
9.3 Relaxation by dipole interactions between molecular spins......Page 253
9.4.2 Hyperfine interactions according to Prokofev and Stamp......Page 257
9.4.3 Hyperfine interactions as a random walk......Page 258
9.4.4 Tunnelling as an effect of hyperfine interactions......Page 260
10.2 Tunnelling at resonance......Page 261
10.3 Tunnel probability into an excited state......Page 263
10.5 Two different types of relaxation......Page 266
10.7 Role of excited spin states......Page 267
10.8 Magnetic specific heat in the presence of spin tunnelling......Page 268
10.9 Tunnelling out of resonance......Page 270
11.2 The density matrix......Page 271
11.3 Master equation for the density matrix......Page 273
11.4 Properties of the master matrix Λ......Page 274
11.5 Coherence and muon spectroscopy......Page 275
11.6 Case of spin tunnelling......Page 276
11.7 Spin tunnelling between localized states......Page 277
11.7.1 Decoherence by nuclear spins in zero field......Page 278
11.8 Potential applications of quantum coherence: quantum computing......Page 280
12.2 Landau–Zener–Stückelberg experiment with a distribution of tunnel frequencies......Page 282
12.3 The scaling law of Chudnovsky and Garanin......Page 284
12.5 Spin glass phases?......Page 287
12.6 Conclusion......Page 288
13.1 The advantages of complexity......Page 289
13.2.1 The effects of intercluster interactions on magnetic tunnelling......Page 291
13.2.2 The effects of magnetic tunnelling on long-range magnetic order......Page 294
13.3 Tunnelling and electromagnetic radiation......Page 297
14 Other Magnetic Molecules......Page 300
14.1 Magnetic wheels......Page 302
14.1.1 Iron rings......Page 304
14.2 Grids......Page 310
14.3.1 Spherical antiferromagnets......Page 312
14.3.2 Vanadium cluster......Page 314
14.3.3 Mixed-valence systems......Page 316
15 Emerging trends in molecular nanomagnetism......Page 319
15.1 SMMs based on a single metal ion......Page 321
15.2 Single chain magnets......Page 324
A.1 International system of units, electromagnetic CGS and electrostatic CGS systems......Page 332
A.4 Physical constants......Page 333
A.6 3j- and 6j-symbols......Page 334
A.7 Different notation......Page 335
B.2 Demagnetizing field and local field......Page 337
B.3 Free energy......Page 338
C How irreversibility comes in......Page 340
D Basic properties of the master equation......Page 342
E Derivation of the Arrhenius law......Page 344
F.1 Memento of the basic formulae......Page 346
F.2 Numerical calculation of the relaxation rate......Page 349
G High-order perturbation theory......Page 353
H Proof of the Landau–Zener–Stückelberg formula......Page 356
I Tunnelling between hyperfine states......Page 359
J.1 Specific heat at equilibrium and at high frequency......Page 362
J.2 Frequency-dependent specific heat......Page 363
K.1 Basic hypotheses......Page 365
K.2 An expression for the density matrix of a spin system......Page 366
K.3.1 Diagrammatic expansion......Page 367
K.3.2 First and second diagrams......Page 368
K.3.3 Third to sixth diagrams......Page 371
K.3.4 Summary of this section......Page 373
K.4 Tunnelling......Page 374
References......Page 376
C......Page 402
F......Page 403
L......Page 404
M......Page 405
R......Page 406
T......Page 407
Z......Page 408