Calculation of distribution function of one-magnon excitations in a ferromagnet

A method is proposed for constructing in general form an analytic approximation to the energy distribution function g(ϵ) of spin waves in an ideal Heisenberg ferromagnet. The method is based on the construction of subspaces which are invariant under the Heisenberg operator, which enables one to express the function g(ϵ) as the arithmetic mean of the spectral densities of some Jacobi matrices. The method is illustrated by the construction of the distribution function g(ϵ) for the three simplest ferromagnetic lattices: simple cubic, bcc and fcc. An analtyic approximation of the magnon distribution function is presented for a complex ferromagnetic lattice of the NaCl type, which has two bands in the energy spectrum.

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