Slonczewski spin-torque as negative damping: Fokker-Planck computation of energy distribution

In this paper we study the application of the Fokker-Planck (FP) equation to the dynamics of a thin-film element subject to a current-induced spin torque. We use a recently derived FP equation for the energy distribution to find an exact non-equilibrium steady state of the spin-torque system. In the present paper we verify this distribution by Landau-Lifshitz simulation including the Slonczewski form of the spin torque. We find that the exact distribution can be expressed in terms of an energy-dependent effective temperature Teff(E), which turns out to be roughly constant, thus providing a precise foundation for heuristic “effective spin temperature” viewpoints.