Microscopic theory of spin-wave interactions and relaxation in ferromagnetic films (abstract)

Abstract

A diagrammatic perturbation method is employed to study the nonlinear dynamics of spin waves in thin ferromagnetic films, including the effects of the short-range exchange coupling and the longer-range magnetic dipole-dipole coupling between the spins. It is well known1 that, in the linear approximation, the spin-wave spectrum of a finite-thickness film may consist of several discrete branches describing the localized surface modes and the quantized (or standing) bulk modes. When higher-order effects are taken into account, we obtain a description of interactions between these modes where the dominant relaxation terms are due to three- and four-magnon scattering processes, by analogy with infinite ferromagnets.2 However, in the film geometry, the interaction terms may involve spin waves from either the same or different discrete branches, and so the temperature and wave-vector dependence of the spin wave energy shift and damping are modified. Our results represent a generalization of previous calculations for semi-infinite Heisenberg ferromagnets3 to include the dipole-dipole terms and finite film thickness. We employ a microscopic approach with a Hamiltonian, by contrast with previous theories for dipole-exchange spin-wave interactions, which have generally employed a macroscopic (or continuous-medium) approach using Maxwell’s equations. This enables us to obtain results applicable for ultrathin films and/or for all wave vectors.