Polar and quadratic magneto-optical Kerr effects in nonmagnetic/ferromagnet bilayers for spin-orbit torque measurements

Recent studies have revealed that spin Hall magnetoresistance (SMR) contributes to both the anomalous and planar Hall resistances in nonmagnetic metal (NM)/ferromagnetic metal (FM) bilayers. This effect becomes pronounced when the NM layer exhibits a large spin Hall angle, as in W/CoFeB bilayers. In such systems, the ratio of planar to anomalous Hall resistances, normally small in single CoFeB layers, can approach unity. This unusually large ratio complicates the determination of spin-torque efficiency using harmonic Hall voltage measurements. To overcome this limitation, magneto-optical Kerr effect (MOKE) measurements have been proposed as an alternative approach. Here, we investigate the polar and quadratic MOKE components, which correspond to, respectively, the anomalous and planar Hall resistances in the low-frequency limit to clarify whether the MOKE measurements are suitable for characterizing the spin-torque efficiency. We find that the ratio of quadratic to polar MOKE signals in NM/FM bilayers is significantly smaller than the corresponding Hall resistance ratio, indicating that SMR contributes negligibly to the MOKE response in the visible range. Consequently, the spin-torque efficiency extracted from MOKE measurements agree well with those expected from the spin Hall angle of the NM layer. These results clarify the reason why MOKE measurements provide reliable determination of the spin-torque efficiency.