Revisiting the Analytical Solution of Spin-Orbit Torque Switched Nanoscale Perpendicular Ferromagnet

The scaling of magnetic memory into nanometer size calls for a theoretical model to accurately predict the switching current. Previous models show large discrepancy with experiments in studying the spin-orbit torque switching of perpendicular magnet. In this work, we find that the trajectory of magnetization shows a smooth transition during the switching. This contradicts the key assumption in previous models that magnetization needs to align to the spin polarization (\sigma) before the switching occurs. We demonstrate that aligning magnetization to \sigma requires a very large current, resulting in the unsatisfactory fitting between the previous models and experiments. In contrast, the smooth transition permits a lower switching current that is comparable to experiments. Guided by this refined physical picture, we pinpoint the reversal of precession chirality as a pivotal factor for achieving deterministic switching. This insight leads to the formulation of a new analytical model that demonstrates remarkable agreement with experimental data. Our work resolves an important issue confronting the experiment and theory. We provide a clear physical picture of the current-induced magnetization switching, which is invaluable in the development of spin-orbit torque magnetic random-access memory.