Spin torque switching of an in-plane magnetized system in a thermally activated region

TL;DR

This paper analytically investigates the current dependence of spin torque switching rates in in-plane magnetized systems, revealing a nonlinear behavior in a key current region, which is crucial for interpreting experimental results.

Contribution

It derives analytical expressions for critical currents and uncovers a nonlinear current dependence of the switching rate exponent in the thermally activated region.

Findings

The exponent b is approximately 1 for I < I_c.

b increases rapidly up to 2.2 for I_c < I < I_c^*.

Nonlinear dependence of switching rate exponent was newly identified.

Abstract

The current dependence of the exponent of the spin torque switching rate of an in-plane magnetized system was investigated by solving the Fokker-Planck equation with low temperature and small damping and current approximations. We derived the analytical expressions of the critical currents, I_{c} and I_{c}^{*}. At I_{c}, the initial state parallel to the easy axis becomes unstable, while at I_{c}^{*} (\simeq 1.27 I_{c}) the switching occurs without the thermal fluctuation. The current dependence of the exponent of the switching rate is well described by (1-I/I_{c}^{*})^{b}, where the value of the exponent b is approximately unity for I < I_{c}, while b rapidly increases up to 2.2 with increasing current for I_{c} < I < I_{c}^{*}. The linear dependence for I < I_{c} agrees with the other works, while the nonlinear dependence for I_{c} < I < I_{c}^{*} was newly found by the present work. The nonlinear dependence is important for analysis of the experimental results, because most experiments are performed in the current region of I_{c} < I < I_{c}^{*}.