Thermal stability in spin-torque-driven magnetization dynamics

In this article, thermal fluctuations in spin-torque-driven magnetization dynamics are described phenomenologically by introducing a Gaussian white noise term in the Landau-Lifshitz-Slonczewski equation. The ensuing stochastic magnetization dynamics is studied by considering the Fokker-Planck equation for the probability distribution of magnetization. The corresponding Fokker-Planck for the energy probability distribution is then derived in the limit of small fluctuations by averaging with respect to fast-time-scale precessional dynamics. By using this equation the stationary probability distribution of energy is analytically determined. This distribution has peaks around stable stationary states as well as around self-oscillatory regimes. On this basis, we define an effective potential barrier controlling switching between stable equilibrium states and self-oscillatory regimes.