Molecular Nanomagnets

, by Gatteschi, Dante; Sessoli, Roberta; Villain, Jacques

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ISBN: 9780199602261 | 0199602263
Cover: Paperback
Copyright: 6/4/2011

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This book is the first attempt to cover in detail the new area of molecular nanomagnetism, for which no other book is available. In fact research and review articles, and book chapters are the only tools available for newcomers and the experts in the field. It is written by the chemists originators and by a theorist who has been one of the protagonists of the development of the field, and is explicitly addressed to an audience of chemists and physicists, aiming touse a language suitable for the two communities.

The spin Hamiltonian approach	p. 15
Introduction	p. 1
Magnetic interactions in molecular systems	p. 14
The spin Hamiltonian approach	p. 15
Zeeman and crystal field terms for isolated ions	p. 15
Electron nucleus (hyperfine) interaction terms	p. 20
Spin Hamiltonian for pairs	p. 21
Single ion levels	p. 23
Exchange interaction	p. 30
Delocalization effects	p. 30
Spin polarization effects	p. 32
Some examples	p. 34
Double exchange	p. 35
Towards quantitative calculations of exchange interactions	p. 36
Through-space and other interactions	p. 37
From pairs to clusters and beyond	p. 39
Isotropic coupling	p. 39
Magnetic anisotropy in clusters	p. 44
Observation of microscopic magnetism	p. 49
Magnetic techniques	p. 49
Standard magnetometry	p. 49
Time-dependent measurements	p. 58
Micro-SQUID and micro-Hall probe techniques	p. 61
Torque magnetometry	p. 64
AC susceptometry	p. 69
Specific heat measurements	p. 75
The specific heat and its magnetic part	p. 75
Magnetic specific heat at equilibrium	p. 76
Measurement of the magnetic specific heat: the relaxation method	p. 78
Magnetic specific heat in an alternating current	p. 80
Magnetic resonances	p. 81
Electron paramagnetic resonance	p. 81
Nuclear magnetic resonance	p. 89
Muon spin resonance (¿SR)	p. 95
Neutron techniques	p. 99
Polarized neutron diffraction	p. 99
Inelastic neutron scattering	p. 104
Single-molecule magnets	p. 108
Serendipity versus rational design of SMMs	p. 108
Synthetic strategies to SMMs	p. 109
The use of preformed building blocks	p. 118
Cyanide-based clusters	p. 118
the disruption of oxocentred carboxylate triangles	p. 123
Polyoxometalates	p. 126
The role of pentagons	p. 127
The templating effect	p. 129
Solvothermal synthesis	p. 132
A survey of the most investigated SMMs	p. 134
The archetypal Mn₁₂ acetate cluster	p. 135
The Mn₁₂ family	p. 146
The reduced species of Mn₁₂ clusters	p. 149
Fe₈ clusters	p. 151
Mn₄ clusters	p. 156
Thermally activated magnetic relaxation	p. 160
Relaxation and relaxation time	p. 160
Potential barrier	p. 161
Transition probabilities and the master equation	p. 163
Solution of the master equation	p. 165
Spin-phonon interaction	p. 167
Basic features	p. 167
Local rotation	p. 168
Local strain	p. 168
Terms linear in the spin operators	p. 169
Transition probabilities and the golden rule	p. 171
Qualitative formulae	p. 173
Multiphonon processes	p. 175
Spin-phonon interactions resulting from exchange	p. 176
Effect of photons	p. 177
Phonons and photons	p. 177
Photons at thermal equilibrium	p. 177
The beauty of light	p. 178
Classical electromagnetism and quantum electrodynamics	p. 180
Coherence and superradiance	p. 180
Limitations of the model	p. 180
Magnetic tunnelling of an isolated spin	p. 182
Spin tunnelling	p. 182
Particle tunnelling: a reminder	p. 182
An example	p. 183
The case s = 1/2	p. 184
Case of an arbitrary spin	p. 184
Delocalization	p. 185
Large spin = classical spin?	p. 187
Approximate localized eigenstates	p. 188
Symmetry and selection rules for tunnelling	p. 191
Tunnelling width for an isolated spin	p. 192
Tunnel splitting according to perturbation theory	p. 194
Time-dependent wavefunction: magnetic tunnelling	p. 197
Effect of a field along the hard axis	p. 199
Evaluation of the tunnel splitting for large spins	p. 199
General methods	p. 199
Example: the Hamiltonian (2.5)	p. 201
Diabolic points	p. 203
Degeneracy with an without symmetry	p. 203
The von Neumann-Wigner theorem	p. 204
The quest of the Devil	p. 205
Introduction to path integrals	p. 209
General ideas	p. 209
The anharmonic oscillator	p. 209
Tunnel effect and instantons	p. 210
The path integral method applied to spins	p. 213
Tunnelling in a time-dependent magnetic field at low temperature	p. 216
Advantages of a time-dependent magnetic field	p. 216
Fast sweeping and adiabatic limit	p. 218
Calculation of the reversal probability	p. 219
Equations of motion	p. 219
The solution of Landau, Zener, and Stückelberg	p. 221
Fast sweeping	p. 222
Sweeping back and forth through the resonances	p. 223
Interaction of a spin with the external world at low temperature	p. 225
Coherence, incoherence, and relaxation	p. 225
Low temperatures	p. 225
The window mechanism	p. 226
Hyperfine interactions	p. 227
The hyperfine field and its order of magnitude	p. 227
Experimental evidence of hyperfine interactions	p. 229
Linewidth of hyperfine origin	p. 234
Relaxation of hyperfine origin	p. 236
Effect of hyperfine interactions in the case of time-dependent fields	p. 237
How do nuclear spins relax?	p. 238
Relaxation by dipole interactions between molecular spins	p. 240
Other theoretical approaches	p. 244
The theory of Caldeira and Leggett	p. 244
Hyperfine interactions according to Prokofev and Stamp	p. 244
Hyperfine interactions as a random walk	p. 245
Tunnelling as an effect of hyperfine interactions	p. 247
Tunnelling between excited states	p. 248
The three relaxation regimes	p. 248
Tunnelling at resonance	p. 248
Tunnel probability into an excited state	p. 250
A remark about the dynamic susceptibility	p. 253
Two different types of relaxation	p. 253
Effect of a time-dependent field at T ≠ 0	p. 254
Role of excited spin states	p. 254
Magnetic specific heat in the presence of spin tunnelling	p. 255
Tunnelling out of resonance	p. 257
Coherence and decoherence	p. 258
The mystery of Schrödinger's cat	p. 258
The density matrix	p. 258
Master equation for the density matrix	p. 260
Properties of the master matrix ¿	p. 261
Coherence and muon spectroscopty	p. 262
Case of spin tunnelling	p. 263
Spin tunnelling between localized states	p. 264
Decoherence by nuclear spins in zero field	p. 265
Potential applications of quantum coherence: quantum computing	p. 267
Disorder and magnetic tunnelling	p. 269
Experimental evidence of disorder	p. 269
Landau-Zener-Stückelberg experiment with a distribution of tunnel frequencies	p. 269
The scaling law of Chudnovsky and Garanin	p. 271
Other distortion isomers in Mn₁₂ac	p. 274
Spin glass phases?	p. 274
Conclusion	p. 275
More experiments on single-molecule magnets	p. 276
The advantage of complexity	p. 276
Intercluster interactions in Mn₄ clusters	p. 278
the effects of intercluster interactions on magnetic tunnelling	p. 278
The effects of magnetic tunnelling on long-range magnetic order	p. 281
Tunnelling and electromagnetic radiation	p. 284
Other Magnetic Molecules	p. 287
Magnetic wheels	p. 289
Iron rings	p. 291
Grids	p. 297
three-dimensional clusters	p. 299
Spherical antiferromagnets	p. 299
Vanadium cluster	p. 301
Mixed-valence systems	p. 303
Emerging trends in molecular nanomagnetism	p. 306
SMMs based on a single metal ion	p. 308
Single chain magnets	p. 311
Systems of units, physical constants and basic mathematical tools	p. 319
International system of units, electromagnetic, CGS and electrostatic CGS systems	p. 319
Gauss' system of units	p. 320
Other common units	p. 320
Physical constants	p. 320
Stevens operators	p. 321
3j- and 6j-symbols	p. 321
Different notation	p. 322
The magnetic field	p. 324
A complication vocabulary	p. 324
Demagnetizing field and local field	p. 324
Free energy	p. 325
How irreversibility comes in	p. 327
Basic properties of the master equation	p. 329
Derivation of the Arrhenius law	p. 331
Phonons and how to use them	p. 333
Memento of the basic formulae	p. 333
Numerical calculation of the relaxation rate	p. 336
High-order perturbation theory	p. 340
Proof of the Landau-Zener-Stückelberg formula	p. 343
Tunnelling between hyperfine states	p. 346
Specific heat	p. 349
Specific heat at equilibrium and at high frequency	p. 349
Frequency-dependent specific heat	p. 350
Master equation for the density matrix	p. 352
Basic hypotheses	p. 352
An expression of the density matrix of a spin system	p. 353
Perturbation theory	p. 354
Diagrammatic expansion	p. 354
First an second diagrams	p. 355
Third to sixth diagrams	p. 358
Summary of this section	p. 360
Tunnelling	p. 361
References	p. 363
Index	p. 389
Table of Contents provided by Ingram. All Rights Reserved.

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Molecular Nanomagnets

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