Lifetime of Coupled Spin-Phonon Excitations

In this paper we examine the lifetime of the normal modes of a system of noninteracting paramagnetic spins coupled to phonons. It is found that scattering from spatial fluctuations in the $z$ component of the spin density is the most effective means of attenuating the excitations. If the spin-phonon coupling constant is sufficiently large, scattering from the spatial fluctuations in $S_z$ may dominate absorption by the direct process. A simple argument suggests that the ${\mathrm{Cr}}^{4+}$ ion may couple to the lattice strongly enough for this to occur.