Longitudinal spin relaxation in simple stochastic models for disordered systems

The relaxation of single probe spins was investigated for simple models of systems with quenched disorder. The spin relaxation was calculated for a two-site model with arbitrarily oriented magnetic fields and the result was averaged over various distributions of the fields, and of the hopping rates of the spin. On an intermediate time scale, a modified Kubo-Toyabe behavior is obtained for large hopping rates, in agreement with recent SR experiments. A stretched-exponential decay of the spin polarization is obtained at longer times. The Kohlrausch exponent is found to be field and hopping-rate dependent, in qualitative agreement with recent NMR and -NMR experiments. The resulting longitudinal relaxation rate still does not show the significant deviations from the Bloembergen-Purcell-Pound (BPP) behavior that are typical for glassy systems. Therefore, the random two-frequency model was extended to include time-dependent renewals of the environment. This modification may yield asymmetric peaks for the longitudinal relaxation rate in the BPP plot for very large renewal rates. © 1995 The American Physical Society