  Anisotropic single-molecule magnets may be thought of as molecular switches,
with possible applications to molecular spintronics. In this paper, we consider
current-induced switching in single-molecule junctions containing an
anisotropic magnetic molecule. We assume that the carriers interact with the
magnetic molecule through the exchange interaction and focus on the regime of
high currents in which the molecular spin dynamics is slow compared to the time
which the electrons spend on the molecule. In this limit, the molecular spin
obeys a non-equilibrium Langevin equation which takes the form of a generalized
Landau-Lifshitz-Gilbert equation and which we derive microscopically by means
of a non-equilibrium Born-Oppenheimer approximation. We exploit this Langevin
equation to identify the relevant switching mechanisms and to derive the
current-induced switching rates. As a byproduct, we also derive S-matrix
expressions for the various torques entering into the Landau-Lifshitz-Gilbert
equation which generalize previous expressions in the literature to
non-equilibrium situations.
