Application of the recursion method to spin-wave analysis of ferromagnetic resonance in defected ferromagnets

Abstract

A general theory of ferromagnetic resonance (FMR) is developed from the assumptions of inhomogeneous local crystalline anisotropy and static magnetic field. The Hamiltonian is given in the harmonic approximation. The high-frequency magnetisation is calculated from the very general thermodynamic formula m+or-=Tr( rho M+or-), with density matrix rho in the Kubo approximation. The Green function is expressed by a continued fraction, with coefficients given by the moments of the spectral density of magnons. The theory is applied to ferromagnetic metals with dislocations. FMR gives information on the spectrum of spin waves localised at dislocation lines. Numerical calculations are given for the spectral density width of magnon excitations. The paper contains novel general considerations on the application of the recursion method to the description of the resonance line in defected ferromagnets. In the literature, the higher moments are generally too great and bear no information about magnon excitations in FMR. The author removes this difficulty by limiting the calculations of the moments to a region of the magnon band that is quasi-degenerate with the signal frequency for different static fields in the FMR experiment. The latter is realised by cut-off wavevectors. The moments are calculated from the spectral density for the low-frequency region of the magnon band. Effects of elliptical terms due to defects as well as high-lying excitations are included in the second-order perturbation theory. The paper is aimed at calculating the shape of the resonance line in ferromagnets with dislocations.