Deterministic magnetization switching by spin–orbit torque in a ferromagnet with tilted magnetic anisotropy: A macrospin modeling

Abstract

Field-free magnetization switching by in-plane current injection via spin–orbit interactions in heavy-metal/ferromagnet bilayer systems is of great interest for applications of spin–orbit torque (SOT). Here, we demonstrate theoretically how to deterministically switch the magnetization of CoFeB with a tilted perpendicular magnetic anisotropy (PMA) by using the SOT effect from the viewpoint of energy landscape. It is found that magnetization switching is dependent both on the polar angle θ and the azimuthal angle φ of the tilted PMA. A tiny remnant magnetization component that deviates away from the film plane during the spin current pulse impulsion period is a key point for the subsequent switching. The underlying mechanism is attributed to the shift of PMA energy barrier with the magnetization angle, which dominates the state of the tiny magnetization component and thereafter the bipolar deterministic switching. Based on the simulation results, a phase diagram of deterministic switching regarding θ and φ is established. Moreover, the positive and negative critical switching current densities are demonstrated to exhibit an astroid-like characteristic as a function of θ. This study provides a fundamental insight into the nature of SOT-induced deterministic switching with the tilted PMA method.