Fluctuations and dissipation of coherent magnetization

A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The magnetic moment is linearly coupled to a reservoir of bosonic degrees of freedom. The model reproduces the Gilbert-Brown form of the equation in the classical limit for a particular choice of the bath parameters. Use of generalized coherent states makes the semiclassical limit more transparent within a path-integral formulation. A general fluctuation-dissipation theorem is derived. The magnitude of the magnetic moment also fluctuates beyond the Gaussian approximation. We discuss how the approximate classical stochastic description of the thermal field follows from our result. We apply these results to the calculation of the correlation functions of the magnetization in a thin film with an easy axis and a hard axis within a linear-response approximation.