Nuclear quadrupole spin-lattice relaxation in anharmonic molecular crystals

Abstract

An approach for nuclear quadrupole spin relaxation by anharmonic lattice vibrations of quadrupole nuclei situated at molecular or ion groups is presented. The temperature dependence at constant crystalline configuration is analyzed. This approach takes advantage of the existence of tightly bound molecules or molecular groups. Fluctuations causing relaxation are considered as collective vibrations of the whole lattice. Anharmonicity is explicitly included by involving cubic and quartic terms of the lattice vibrations Hamiltonian. The spectral densities of the spin-lattice Hamiltonian are expressed in terms of the phonon spectral densities and the temperature Green-function perturbation formalism is used for calculating the lower-order contributions. Three kinds of processes are found to contribute mainly to the spin-lattice relaxation time (${\mathit{T}}_{1}$), namely, anharmonic Raman (AR), first-order Raman (1R), and a third mechanism originated in the self-energy effects on the two-particle spectral density. The AR and 1R processes yield a quadratic temperature dependence of ${\mathit{T}}_{1}$ while the third mechanism gives a cubic temperature dependence. This last term, being characteristic of molecular crystals, represents a sort of mixing of the AR and 1R mechanisms, and its influence strongly depends on the crystal symmetry.