Raman relaxation processes of electron spin-lattice relaxation and Debye temperature of crystals

Electron spin-lattice relaxation data were collected for various single crystals with small concentration of paramagnetic centers. The temperature dependence of the relaxation rate 1/T-1 was analyzed in terms of the direct and Raman relaxation processes giving Debye temperature Theta(D) of the crystals. The experimental dependencies were also described, in intermediate temperature range, by power law 1/T-1 proportional to T-alpha with noninteger alpha = 5-9. We have tried to find an interrelation between Theta(D) and alpha-coefficient. An analysis of the theoretical predictions shown that the power law can not arise from Raman processes alone. When linear temperature dependence is considered at low temperatures the power law approximation can be used, in temperature range 10-20 K only, where contributions from the direct and Raman processes are comparable. However such power law behaviour does not describe at all the experimental data, i.e. does not exist a correlation between Theta(D) and alpha-coefficient. Possible explanations are suggested.