On the spin-phonon interaction in anharmonic crystals

Abstract

In this paper, a theory is developed for examining the influence of the spin-phonon interaction on the phonon dynamics in anharmonic crystals. In contrast to a harmonic approximation such an approach allows for comparing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities. Explicit expressions are derived for the phonon self-energy using successively higher approximations obtained from a cumulant expansion of the density of interparticle distances. It is shown that even in the harmonic approximation the two-spin correlation function and the four-spin correlation function enter into the expression of the generalized dynamical matrix in deviation from previous results. The modification of this harmonic dynamical matrix due to the renormalization of the harmonic phonons and due to phonon-phonon scattering processes is given employing a “weak coupling” approximation between the localized spins and the interparticle-distance density of the crystal. The resemblance of the present approach to an earlier microscopic treatment of electronic contributions to phonon dynamics in anharmonic crystals is pointed out.