Magnetoelastic interaction in rare earth systems

A theory of rotationally invariant spin-lattice interactions in rare earth systems is presented. It is shown that rotational invariance to leading order is ensured only if rotational interactions of first and second order in the displacements are included simultaneously in the spin-lattice Hamiltonian. The rotational second-order interactions yield effects which are as large as those of the linear rotational interaction. It is pointed out that a corresponding statement should hold also for pure strain interactions.The phonon Green's function is calculated for the paramagnetic phase of rare earth systems. It is found that in an applied magnetic field the rotational interactions cause measureable changes of the phonon dispersion and the sound velocity even for cubic symmetry. These effects turn out to be of the same order of magnitude as the conventional field-dependent strain effects and are qualitatively different from the latter. The results of our theory are illustrated by the example of SmSb, and quantitative predictions for the transverse sound velocities are given.