Spin-phonon coupling

The scaling parameter cOq in (9.8a) determines the strength of spin-phonon coupling. 

The temperature dependence of the MRD profile for the protein-water systems where the protein is magnetically a solid, is remarkably weak. The relaxation rate is proportional to IjT, which is consistent with Eq. (4) that was derived on the assumption that the relaxation process is a direct spin-phonon coupling rather than an indirect or Raman process. If it were a Raman process, there would be no magnetic field dependence of the relaxation rate therefore, the temperature dependence provides good evidence in support of the theoretical foundations of Eq. (6). 

Molecules with small spin have also been discussed. For example, time-resolved magnetization measurements were performed on a spin 1/2 molecular complex, so-called V15 [81]. Despite the absence of a barrier, magnetic hysteresis is observed over a time scale of several seconds. A detailed analysis in terms of a dissipative two-level model has been given, in which fluctuations and splittings are of the same energy. Spin-phonon coupling leads to long relaxation times and to a particular butterfly hysteresis loop [58, 82],... 

Phase transitions. Low-dimensional conductors undergo several types of specific structural phase transitions, such as the Peierls distortion (electron-phonon coupling), the spin-Peierls distortion (spin-phonon coupling), anion-ordering transitions, and so on. These first have to be detected and then measured and understood. However, the foregoing distortions may be very small and difficult to observe, and up to now, only a few lattice distortions have been fully measured and described. 

In ideally one-dimensional systems, only intrachain electron-phonon and spin-phonon couplings are, within mean-field approximation, at the origin of electronic-Peierls and/or spin-Peierls transitions, respectively. In real systems, such as the TCNQ salts under concern here, it is clear, however, that one should take properly into account the coupling of the electrons to external potentials also and, in the first case, to the periodic electrostatic cation potential. 

Here p is the density of phonons, n(co) is the Planck number corresponding to the thermal distribution of phonon excitations and k(co) is the spin-phonon coupling constant written as a function of frequency (instead of the wave-vector star k and the phonon branch index, as previously). Only those phonons with energy equal to the Zeeman energy h coa are of interest in a direct relaxation process. This energy is characteristically 0.1 cm-1 and the relevant phonons are of the long-wave acoustic type. Their role is to modulate the crystal field interacting with the electron. 

AcAc, acetylacetonate EPR, electron paramagnetic resonance DPM, dipivaloylmethane Tc, Correlation time for molecular tumbling A/x, concentration of spins X (per unit volume) D, mutual translational self-diffusion coefficient of the molecules containing A and X a, distance of closest approach of A and X ye, magnetogyric ratio for the electron C, spin-rotation interaction constant (assumed to be isotropic) Ashielding anisotropy <7 <7j ) coo, Debye frequency 0d, the corresponding Debye temperature Fa, spin-phonon coupling constant. 

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