  Starting from a model that consists of a semiclassical spin coupled to two
leads we present a microscopic derivation of the Langevin equation for the
direction of the spin. For slowly-changing direction it takes on the form of
the stochastic Landau-Lifschitz-Gilbert equation. We give expressions for the
Gilbert damping parameter and the strength of the fluctuations, including their
bias-voltage dependence. At nonzero bias-voltage the fluctuations and damping
are not related by the fluctuation-dissipation theorem. We find, however, that
in the low-frequency limit it is possible to introduce a voltage-dependent
effective temperature that characterizes the fluctuations in the direction of
the spin, and its transport-steady-state probability distribution function.
