Phonons in a ferromagnetic crystal

A general method is proposed for determining the frequency and damping of the lattice vibrations ofananharmonic ferromagnetic crystal. An exact equation is derived for the irreducible Green's functions; it describes the propagation of self-consistent phonons and the inelastic processes of scattering of these phonons due to the effective phonon-phonon and spin-phonon interactions, The self-energy operator is calculated with allowance for the three-phonon scattoting processes.