Localized Magnons in a Heisenberg Ferromagnet with an Anisotropic Impurity Spin

Abstract

Localized magnons around an impurity spin in a linear Heisenberg ferromagnet are investigated up to three-magnon states. The easy axis of the host spins is assumed to be in the z direction, while that of the impurity spin is in the x y plane. Two- and three-magnon localized states are obtained by the method similar to that of the one-magnon problem. It can be applicable over the whole intensity region of the single-ion anisotropy constant D ' of the impurity spin. In case of large D ', the ground state is a one-magnon localized state when the magnitude S ' of the impurity spin is 1; while, for S '=3/2, the ground state may be a one- or more-than-one-magnon localized state depending on relative magnitudes of the single-ion anisotropy of the host spins, host-host exchange interactions, and impurity-host exchange interactions.