Anisotropic nuclear spin relaxation in single-crystal xenon

Abstract

We extend the theory of longitudinal spin relaxation of ${}^{129}\mathrm{Xe}$ nuclei in frozen xenon to the case of single-crystal samples, where the relaxation rate depends on the direction of the applied magnetic field with respect to the crystalline axes. For sufficiently large magnetic fields, the relaxation is dominated by spin-flip Raman scattering of lattice phonons. Two closely related interactions couple the lattice phonons to the spins of ${}^{129}\mathrm{Xe}$ nuclei: the nuclear spin-rotation interaction between nearest-neighbor atoms, which leads to an isotropic, field-independent relaxation rate, and the paramagnetic antishielding of the externally applied field at the site of ${}^{129}\mathrm{Xe}$ nuclei by the electrons of neighboring Xe atoms. The latter interaction, also known as the chemical shift anisotropy (CSA) interaction, leads to an anisotropic relaxation rate proportional to the square of the applied field. This mechanism dominates spin relaxation at fields of the order of the Debye field ${B}_{D}{=k}_{B}{T}_{D}/{\ensuremath{\mu}}_{B}=82 \mathrm{T}.$