Unified first-order Green's-function theory of anisotropic Heisenberg ferromagnets forS=12

Abstract

A unified first-order Green's-function theory of anisotropic Heisenberg ferromagnets with $S=\frac{1}{2}$ is designed to decouple the higher-order Green's functions obtained in writing down the equations of motion of the first-order Green's functions. By defining the commutator and the anticommutator brackets, the equations of motion of the two kinds of Green's functions ${G}^{\ensuremath{-}}$ and ${G}^{+}$ are written down. With the use of suitable decoupling parameters, a generalized decoupling scheme is suggested. In order to determine the relation between these decoupling parameters we define two conditions: (1) self-consistency and (2) vanishing of the equal-time correlation functions. Using this decoupling scheme, we calculate the thermodynamic properties of the anisotropic Heisenberg ferromagnets with $S=\frac{1}{2}$ at low temperatures. Finally, we also calculate the effect of the decoupling scheme on the magnon conductivity at low temperatures. We clearly find that the magnon conductivity is modified appreciably by the different decoupling parameters and by the anisotropy of the system.