Dynamical Spin Correlations in Many-Spin Systems

Abstract

Time-dependent correlations in many spin systems with anisotropic Heisenberg exchange interactions of arbitrary range are analyzed, using quantum-statistical Green's functions. The discussion is restricted to the ferromagnetic case and to two sublattice antiferromagnetic and ferrimagnetic orderings. A scheme of higher-order random phase approximations, i.e., RPA II and modified RPA, is developed, thus extending the usual treatments involving the unembellished RPA. The RPA II leads to a set of coupled nonlinear integral equations which cannot be solved at general temperatures. However, due to the simplicity of the ferromagnetic ground state, at low temperatures a rapidly convergent iterative procedure leads to a satisfactory solution which reproduces the spin-wave results. The intra- and inter-sublattice longitudinal correlation functions are calculated in the modified RPA scheme, which consists in approximating the RPA II by the substitution of the usual RPA solutions for the transverse Green's functions, and the results are found to be satisfactory over the entire range of temperatures.