Simplified Fokker-Plank Equation Treatment of Finite-temperature Spin-torque Problems

摘要

A Legendre function expansion method is proposed to solve the simplified Fokker-Plank equation to study the dynamics of a macrospin under spin-torque-driven magnetic reversal at finite temperature. The first and second eigenvalues (λτ_0)_1 and (λτ_0)_2 as functions of I/Ic and H_k are obtained, in agreement with the previous results using the Taylor series expansion method. The Legendre function expansion method compared with the Taylor series expansion method has faster convergence properties and clear physical means. Besides, it is found that in some case, especially the second eigenvalue (λτ_0)_2 can become complex, that means that the probability density P not only decays with time, but also oscillates with time.