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

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, Ic and Ic*. At Ic, the initial state parallel to the easy axis becomes unstable while at Ic*(1.27Ic) the switching occurs without the thermal fluctuation. The current dependence of the exponent of the switching rate is well described by (1-I/Ic*)ᵇ, where the value of the exponent b is approximately unity for I≤Ic while b rapidly increases up to ~2.2 with increasing current for Ic≤I≤Ic*. The linear dependence for I≤Ic agrees with the other works, while the nonlinear dependence for Ic≤I≤Ic* 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 Ic≤I≤Ic*.