Effects of long-wave inhomogeneities of the exchange and elastic force constants in the framework of the coherent potential approximation

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Abstract
The formalism of averaged Green’s functions in the continuum is developed for spin waves in ferromagnets with inhomogeneities of the exchange constant and elastic waves in media with inhomogeneities of the force constant. The integral self-consisted equation in the coherent potential approximation is developed for taking into account effects of inhomogeneities of these nonlocal characteristics of the material on the wave spectrum in it. The obtained general results are applied to the study of effects of one-dimensional inhomogeneities of the exchange constant on the wave spectrum in a ferromagnet.