Influence of non-uniform magnetization perturbation on spin-orbit torque measurements

Measurements of spin–orbit torques in a ferromagnetic/nonmagnetic multilayer are typically based on an assumption that the entire ferromagnetic layer uniformly responds to the spin–orbit torque. This assumption breaks down when the thickness of the ferromagnetic layer is comparable to the dynamic exchange coupling length, which can be as short as a few nanometers in certain measurement geometries. The nonuniform magnetization perturbation coupled with nonuniform contribution of each magnetic sublayer to the magnetoresistance or the Kerr effect may impact the accuracy in the extrapolation of spin–orbit torque, particularly if a thick ferromagnetic layer is used. In this paper, we use numerical models to investigate such an impact in three different techniques: the magneto-optic-Kerr-effect method, the second-harmonic method and the spin torque ferromagnetic resonance method. We show that the second-harmonic and magneto-optic-Kerr-effect methods are prone to be influenced by the nonuniform magnetization reorientation, while the spin torque ferromagnetic resonance method is much less impacted.