Self-Energy and Damping of Long-Wavelength Magnons in Amorphous Ferromagnets

Abstract

The influence of extended stochastic structure fluctuations on the self-energy and damping of long-wavelength magnons in amorphous ferromagnets is investigated within the Heisenberg model. By improving the Matsubara-Kaneyoshi formalism (MKF) the magnon energy in “improved quasi-crystalline” approximation is derived as a start approximation in the equation of motion for the Green's function, thus containing already important structural information. The typical static structure factor in the small-angle region is approximated by convenient analytical model functions. We derive the renormalization R(q) of the stiffness constant D and the magnon damping Γ(q), where the latter shows a characteristic q5-behaviour in the small-q range that can be explained by “magnetic Rayleigh-scattering” due to the magnetic inhomogeneities acting as “point defects” for long-wavelength magnons. In the larger-q range the magnon damping, in agreement with other authors, is found to obey a q3-law. The general behaviour of the renormalization R(q) for long-wavelength magnons is found to be similar for all model functions used for the static structure factor. Linear extrapolation of Dq2R(q) from the larger-q region supplies an apparent gap energy due to the amorphous structure (independent from the magnetic dipole–dipole interaction, which is neglected in this paper). The explanation of this apparent gap energy is given by “compensational magnons” that accompany the magnon, compensating the inhomogeneities, thus forming a “magnon-dressed” magnon.