Thermal fluctuation effects on spin torque induced switching: Mean and variations

Abstract

Thermal fluctuation effects on mean and variation of spin torque induced magnetic element switching are analyzed. Asymptotic forms of the switching time distribution from the stochastic Landau–Lifshitz–Gilbert equation, and numerical solutions of the first and second moments of switching time from the corresponding Fokker–Planck equation, are used to characterize switching time and switching current density for the whole time range, from the second thermal reversal region to the nanosecond dynamic reversal region. It is shown that as time scales become shorter, switching time distributions become narrower, whereas switching current distributions may become broader. This paper provides a physical understanding of these different scaling behaviors.