Y. P. Kalmykov, W. T. Coffey, S. V. Titov, J. E. Wegrowe, D. Byrne
Thermal fluctuations of nanomagnets driven by spin-polarized currents are treated via the Landau-Lifshitz-Gilbert equation generalized to include both the random thermal noise field torques and the Slonczewski spin-torque term. By averaging this stochastic (Langevin) equation over its realizations, the explicit infinite hierarchy of differential-recurrence relations for statistical moments (averaged spherical harmonics) is derived for arbitrary demagnetizing factors and magnetocrystalline anisotropy for the generic model of a nanopillar with two magnetic strata constituting the free and fixed layers and a non-magnetic conducting spacer all sandwiched between two ohmic contacts. The effects of thermal fluctuations and spin-transfer-torques on relevant switching characteristics, such as the stationary magnetization, the magnetization reversal time, etc., are then treated by solving the hierarchy for wide ranges of temperature, damping, external magnetic field, and spin-polarized current. The approach developed allows us to predict new spin-torque effects in the thermally assisted magnetization reversal which may comprise several orders of magnitude. In particular, a strong dependence of the switching characteristics on the directions of the external magnetic field and the spin polarization exists.
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http://arxiv.org/abs/1303.3476
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