Critical switching current of a perpendicular magnetic tunnel junction owing to the interplay of spin-transfer torque and spin-orbit torque

Using the linearized Landau-Lifshitz-Gilbert (LLG) equation in the rotation coordinate, we calculate the critical switching current density of a perpendicular magnetic tunnel junction (MTJ), where magnetization switching is achieved by the interplay of spin-transfer and spin-orbit torques. In terms of the critical current density, we find that as the current density inducing the spin-orbit torque (j(SOT)) increases, the current density inducing the spin-transfer torque (j(STT)) decreases nonlinearly. In the presence of the spin-orbit field-like torque (beta), the critical switching current density by the spin-transfer torque is proportional to the damping constant (alpha) as the conventional spin-transfer torque switching, while the critical switching current density by the spin-orbit torque increases with root alpha when H-eff >> H-SOT. We also investigated the beta dependence of the critical switching current density. For a given j(SOT), the critical switching current density for the spin-transfer torque, j(STT,c) decreases linearly with increasing beta and nonlinearly decreases with increasing j(SOT) for a given beta. Further, we discuss the beta dependence of the critical switching current density on energy.