A Study of Spin–Phonon Interactions in Ferromagnetic Insulators. I. The Spin Wave Spectrum

A field‐theoretical perturbation method is used to study the effects of Spin–phonon interactions in a Heisenberg ferromagnet. The calculations are carried out by employing an expansion in powers of the high‐density parameter 1/z, where z is the number of spins interacting with any given spin. In lowest order (1/z)0 this leads to molecular field theory, and the effects of spin fluctuations and Spin–phonon interactions are then introduced in higher orders of the perturbation expansion. The renormalised energy and damping of the spin wave excitations are evaluated to second order in the Spin–phonon coupling, and the dependence of these quantities on temperature, wave vector, and magnetic field is obtained. The calculations are valid over a wide range of temperature below Tc.