Influence of nonuniform magnetization reorientation on spin-orbit torque measurements

Measurement of spin-orbit torque in a ferromagnetic/nonmagnetic multilayer is typically based on the 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 exchange length, which is only a few nanometers for typical 3d transition ferromagnets. The nonuniform magnetization reorientation coupled with a nonuniform contribution of each magnetic sublayer to the magnetoresistance or the Kerr effect may impact the accuracy in the extrapolation of spin-orbit torque. In this presentation, we use a numerical model to investigate the impact nonuniform magnetization tilting has on spin-orbit torque measurements using three different experimental techniques: the second-harmonic method, the spin torque ferromagnetic resonance method, and the magneto-optic-Kerr-effect method.