Thermally-Assisted Spin-Transfer Torque Magnetization Reversal of Uniaxial Nanomagnets in Energy Space

We propose a new analytical method for studying the asymptotic behavior of switching time as a function of current in macrospins under the effects of both spin-torque and thermal noise by focusing on their diffusive energy space dynamics. We test our method on the well understood uniaxial macrospin model and confirm the switching scaling dependence (I -> 0, <tau > alpha exp(-xi(1 - I)(2)). The analysis also shows that when there is an angle between spin current and magnet's uniaxial axes the mean switching time in the low current limit depends on the spin-current projection on the easy axis, but otherwise has the same functional form as that in the collinear case. These results have implications for modeling the energetics of thermally assisted magnetization reversal of spin transfer magnetic random access memory bit cells.