Spin dynamics in solid dilute paramagnets

Abstract

The free-induction decay signals for the two-spin clusters, the “matrix,” and the entire spin system as a whole are calculated for a real dipole-dipole interaction on the basis of a method for the cluster expansion of correlation functions previously developed by the authors. The intracluster interactions, which generate a discrete spectrum, are taken into account exactly, and the interactions outside the clusters are taken into account on the basis of the Anderson-Weiss-Kubo (AWK) theory of phase relaxation. The corresponding shape functions of the resonance line are calculated. Before the clusters are separated, an AWK analysis in the limit of slow fluctuations of the local fields is in satisfactory agreement with the exact results obtained in the Anderson model of dipolar interactions, but a similar analysis for realistic fluctuation rates and Dt?1 leads to a significant qualitative difference: exp(−Dt) transforms into $\exp ( - \sqrt {D_1 t} )$. After the clusters are separated, this difference is obliterated. The free-induction decay is almost exponential up to Dt∼10, and nonexponential behavior of the long-time asymptote appears sooner. This finding is not altered significantly when the analysis is complicated by raising the maximum rank of the clusters to 3 or more.