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 model reproduces the Gilbert-Brown form of the equation in the classical limit. The magnetic moment is linearly coupled to a reservoir of bosonic degrees of freedom. 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 stochastic description of the thermal field follows from our result. As an example, we go beyond the linear-response method and show how the thermal fluctuations become anisotropy-dependent even in the uniaxial case.