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.
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