Threshold Current Density for Perpendicular Magnetization Switching Through Spin-Orbit Torque

We theoretically investigate the threshold current density for spin-orbit-torque- (SOT) induced perpendicular magnetization switching. According to the relative sign of fieldlike torque (FLT) and dampinglike torque (DLT), we derive the corresponding analytical formulas of the threshold current density J(th) required to switch magnetization from equilibrium states to nearly in-plane states. These formulas, which agree well with numerical results among a wide range of material parameters, indicate that SOT current density can be significantly reduced in the presence of a large FLT. The conditions are then explored to achieve complete magnetization reversal after removing the SOT currents. When the ratio of FLT to DLT eta is negative in our sign convention, we find that SOT pulses with long enough fall time, for example, 0.2 ns in our simulations, can guarantee stable switching. In contrast, a small in-plane magnetic field or a large damping is necessary when eta > 0. Based on the conditions, the measured threshold current densities in several reported experiments, which deviate from previous models, can be well reproduced by our derived J(th). We further study the possible incubation delay induced by SOT, clarifying the recent contradiction on incubation time during SOT switching. Our work sheds insights on the SOT material optimization and the comprehension of magnetization switching dynamics induced by SOT.