Theory of two-magnon dissipation in disordered ferromagnets I. Relation to sample statistics

The theory of two-magnon dissipation in disordered ferromagnetic materials is developed. Fluctuations of one-ion anisotropy energy due to the disorder are assumed to be the source of the linewidth broadening (relaxation of magnons by two-magnon scattering). Ordinary two-magnon theory is reconsidered on the basis of the sample statistics. The main idea of it is to describe the macroscopic properties of materials by means of quantities, whose relative fluctuations over the ensemble of configurations are negligibly small for sufficiently large sample. The energies of magnons — modes with well defined wave vectork — and their lifetimes are shown to be such variables. Further, possible models for a two-component ferromagnet are considered in the approximation of high external field. The energies of magnons in mixed crystal are obtained as linear combinations of those in parent crystals. Finally, the dependence of magnon lifetimes on the ordering is separated from the dependence on the magnitude of anisotropy variations.