Green's Function Theory of Parametric Amplification in a Magnetic System

Abstract

In an ordered magnetic system the imaginary part of the susceptibility declines at a much lower signal level than is predicted by the usual linear theory of magnetic resonance. This phenomenon is called premature saturation and is due to the parametric amplification of nonuniform spin-wave modes which are degenerate with the uniform mode. In order to explain this phenomenon a model is proposed in which two spin-wave modes are coupled via one- and two-magnon processes. This system is treated by the method of time dependent Green's functions. Even in the lowest-order approximation several types of two-, three-, and four-time Green's functions must be calculated. Relations between these Green's functions are investigated, and then the amplitude of the nonuniform spin-wave mode is calculated through the third order in the amplitude of the applied field. A criterion for the onset of parametric amplification is found and comparison is made with previous semiclassical treatments.