Orbach mechanism

In real systems, a distribution in the characteristic time may lead to a stretched exponential decay. In the thermally activated regime where the relaxation of the magnetization is due to the Orbach mechanism, the temperature dependence of the relaxation time may be described by an Arrhenius law of the form ... 

The same approach has been developed for systems in solutions (15,16), and was found relevant in some cases. The electron relaxation time is described in the cases of Orbach-type mechanism by the equation (17)... 

The Orbach-type process as well as the collisional process (inducing either ZFS, g anisotropy or hyperfine coupling modulation) are mechanisms that can provide electron relaxation independently on reorientation. Electron relaxation is certainly not modulated by reorientational motions... 

The Cua site, common in biology (inset in Fig. 5.42), is dinuclear with two copper atoms bridged by the thiolate sulfurs of two cysteine ligands. One unpaired electron is delocalized over two metals, which are thus Cul 5+. The NMR spectra show narrow lines from the copper ligands (Fig. 5.42) [120,121], corresponding to an electron relaxation time of 10 11 s, as in Cu2+-Cu2+ dimers (see Section 6.3.2). However, in Cua there is no magnetic coupling between the two centers, as they contain only one unpaired electron just as an isolated Cu2+ ion. Electron relaxation of Cua may be fast because the orbital overlap between the two copper centers provides new relaxation mechanisms not available to a monomer (as Orbach or Raman relaxation). 

Av is the frequency difference between two anisotropic ESR resonance lines, the resulting spectrum is the superposition of the individual configurations. On the contrary, if r < (2 JtAv), we have an isotropic spectrum the resonance frequency is the average of the anisotropic components of the individual configurations As discussed in detail by Ham , motional narrowing can be produced by three relaxation mechanisms, which are characterized by a different temperature dependence an Arrhenius-type dependence (r" = Voe ) for an Orbach process, and a linear dependence or proportional to T for direct and Raman processes, respectively. Therefore, the temperature dependence of the isotropic spectrum gives information about the relaxation mechanism and consequently on the vibronic level scheme. 

Finally, it should be noted that the phonon part in eq. (14) also leads to an effective quadrupolar interaction between 4f ions if the phonon coordinates are eliminated in second-order perturbation theory. This virtual phonon exchange mechanism is important in insulators, see Orbach and Tachiki (1967). In R intermetallics such as TmZn and TmCd, however, the electronic origin of effective interactions is now established, Levy et al. (1979). 

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