Spin-Transfer Torque Magnetization Reversal in Uniaxial Nanomagnets with   Thermal Noise
  We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory underlying the magnetization switching rates of a thin film uniaxial magnet subject to spin-torque effects and thermal fluctuations (thermal noise). After discussing the various dynamical regimes governing the switching phenomena, we present analytical results for the mean switching time behavior. Our approach, based on explicitly solving the first passage time problem, allows for a straightforward analysis of the thermally assisted, low spin-torque, switching asymptotics of thin film magnets. To verify our theory, we have developed an efficient GPU-based micromagnetic code to simulate the stochastic LLG dynamics out to millisecond timescales. We explore the effects of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted dynamics. We find that even in the absence of axial symmetry, the switching times can be functionally described in a form virtually identical to the collinear case. We further verify that asymptotic behavior is reached fairly slowly, thus quantifying the role of thermal noise in the crossover regime linking deterministic to thermally assisted magnetization reversal. 
D. Pinna, A. D. Kent, D. L. Stein
cond-mat.mes-hall cond-mat.mtrl-sci