Theory of two magnon dissipation in disordered ferromagnets II. Energy spectra and relaxation frequencies of magnons

The lattice of two kinds of interacting harmonic oscillators is considered as an idealized model of mixed system. Energies of modes with well defined wave vectork are calculated on the basis of the statistical concept developed in the previous part of the paper. The results are applied to the investigation of mixed ferromagnet by using the Kranendonk and Van Vleck interpretation. The method of calculation of relaxation frequencies (or lifetimes) of magnons on the basis of independent cluster model is given. This is further used for the estimation of resonance linewidth in the case of completely disordered state, which is compared with the linewidth in the case of appreciable clustering. It is shown that the linewidth H measured in usual ferromagnetic resonance experiments rapidly increases with the clustering of identical ions. This fact is accepted for explaining the controversy of Callen's theory with the experiment. Finally, the statistical concept used throughout the paper is justified proving that relaxation frequencies are good variables in the sense defined in the preceding part of the paper.The author feels obliged to express his sincere thanks to Dr. S. Krupicka for encouraging him during this work and for many valuable discussions of the problems connected with it.