Application of Hubbard operators in the theory of magnetoelastic waves

A scheme of microscopic description of magnetoelastic wavjes in the Heisenberg ferromagnets with the one-ion anisotropy of the easy plane and easy axis type is constructed. The scheme is based on the representation of spin operators in terms of the Hubbard operators. This makes it possible to take exactly into account the effects of the one-ion anisotropy and magnetoelastic interaction. For the both classes of magnets considered the dispersion equation for the magnetoelastic waves is obtained in the whole range of temperatures. It is shown that the softening of the phonon mode near the reorientation phase transition takes place at arbitrary temperatures up to the Curie point.