Nuclear quadrupolar spin-lattice relaxation in zinc-blende lattices by acoustic phonons

Abstract

The nuclear quadrupolar spin-lattice relaxation by acoustic phonons in zinc-blende-type crystals is calculated for a general Raman process, in which pairs of phonons couple to the nucleus by an arbitrary type of mechanism. Over the temperature range of experimental interest ($T>4.2$ K) it is shown that (i) regardless of the phonon-spin coupling mechanism, the quadrupolar relaxation rate has the form ${W}_{Q}=A{T}^{2}{E}_{A}(\frac{kT}{\ensuremath{\eta}\ensuremath{\hbar}{\ensuremath{\omega}}_{\mathrm{TA}}})$, where ${E}_{A}$ is a known function, and $A$ and $\ensuremath{\eta}$ are parameters which in principle can be calculated from a model for the interaction, but in practice are fitted to the data; (ii) the LA phonons contribute relatively little to the total relaxation, an amount which can vary by less than 3% of the total relaxation over the entire temperature range; (iii) relaxation is due predominately to phonons near the Brillouin-zone boundary; and (iv) phonons associated with various symmetry points on the Brillouin-zone boundary couple differently to the group-III than to the group-V nuclear sites.