Rotating-frame nuclear spin-lattice relaxation due to the motion-induced time variation of quadrupolar and dipolar interactions in crystals

Abstract

Starting from Hebel and Slichter's single-spin-temperature theory, the comprehensive perturbation formalism developed recently for the calculation of $T_{1\rho }$ due to the motion-induced time dependence of nuclear dipole interactions in both high and low rotating fields is extended to include quadrupolar effects in crystals. The total relaxation rate $T_{1\rho }^{-1\mathrm{}}$ is written in terms of dipolar and quadrupolar "lattice correlation functions" associated with the internal motions, and "spin correlation functions" governed by processes of internal equilibration of the Zeeman, dipolar, and quadrupolar Hamiltonians of the spin system. While the lattice correlation functions are found to determine the high-field $T_{1\rho }$ minima in the motionally-narrowed regions, low field $T_{1\rho }$ minima occurring at temperatures between the weak- and strong-collision regions are found to be strongly influenced by the processes accounted for by the spin correlation functions. In the limiting case of strong collisions (so-called Slichter-Ailion region) the results of Rowland and Fradin are confirmed. The applicability of the present method to interpret rotating-frame relaxation studies of defect migration in cubic crystals such as, e.g., self- or impurity diffusion via randomly migrating point defects, or dislocation dynamics during plastic deformation, is discussed.