Relaxation and nonradiative decay in disordered systems. III. Statistical character of Raman (two-quanta) spin-lattice relaxation

Vibrational-mode localization leads to a statistical distribution scrP(W) for the (two-quanta) Raman spin-lattice relaxation rate, W≡1/$T_1$. The characteristic function of the distribution and the cumulant moments are calculated. The time dependence of the recovery of the magnetization after saturation is obtained. It is shown that the observed Raman spin-lattice relaxation rate should exhibit a ‘‘staircaselike’’ structure. The length of the ‘‘steps’’ is random and their slope is proportional to the square of the temperature $T^2$. The steps are centered about the average value of W. A procedure is suggested for analyzing experimental data in a manner which will exhibit these features, if present. Observation of these predictions will serve as proof that localized vibrations contribute to the spin-lattice relaxation process.