Dispersion relations and low relaxation of spin waves in thin magnetic films

Abstract

We study spin excitations in thin magnetic films in the Heisenberg model with magnetic dipole and exchange interactions by the spin operator diagram technique and make comparison of their parameters with characteristics of spin waves in thick films. Dispersion relations of spin waves in thin magnetic films (in two-dimensional magnetic monolayer and bilayer lattices) and the spin-wave resonance spectrum in $N$-layer structures are found. For thick magnetic films, spin excitations are determined by simultaneous solution of the generalized Landau-Lifshitz equations and the equation for the magnetostatic potential. Generalized Landau-Lifshitz equations are derived from first principles and have the integral (pseudodifferential) form. It is found that dispersion relations of spin waves in monolayers and in bilayers differ from dispersion relations of spin waves in continuous thick magnetic films. For normal magnetized ferromagnetic films, the spin-wave damping is calculated in the one-loop approximation for a diagram expansion of the Green functions at low temperature. In thick magnetic films, the magnetic dipole interaction makes a major contribution to the relaxation of long-wavelength spin waves. Thin films have a region of the low relaxation of long-wavelength spin waves. In thin magnetic films, four-spin-wave processes take place and the exchange interaction makes a major contribution to the damping. It is found that the damping of spin waves propagating in a magnetic monolayer is proportional to the quadratic dependence on the temperature and is very low for spin waves with small wave vectors.