EFFECT OF IMPERFECTIONS ON SPIN WAVES IN FERROMAGNETS

A general theoretical approach is developed to treat the effect of point imperfections on the spin waves in a ferromagnetic crystal. Special attention is paid to the formation of localized modes. As an example, the calculations have been carried out for a one-dimensional linear lattice. The main results obtained indicate the following features. A substitutional magnetic impurity atom may introduce more than one localized mode of spin waves. The conditions for the localized modes to appear and the positions of their energy levels are given in terms of J′S′/JS and J′/J. Here S′ and S are respectively the spin quantum number of the impurity and that of the normal atoms. J′ and J are respectively the exchange integral between an impurity and its neighbors and that between the normal neighboring atoms. Highly concentrated strains and interstitial atoms which cause the exchange interaction between the atoms in their neighborhood to increase lead also to the formation of localized modes. Furthermore, the dipole-dipole interaction has been taken into consideration with the conclusion reached that it should not destroy the existence of these localized modes. Discussions have been given to the discrete energy levels which appear below the continuous spectrum in case of J′<0. It is pointed out that the Holstein-Primakoff approximation adopted in the present work is not quite legitimate for certain cases in which on one or more atoms the spin deviation becomes not very much smaller than 2S or 2S′.