Title: Magneto-optical detection of spin-orbit torque vector with first-order Kerr effects

Abstract: We have developed a novel, compact and cost-effective magneto-optical method for quantifying the spin-orbit torque (SOT) effective field vector (hSO) in magnetic thin films subjected to spin current injection. The damping-like (hSODL) component of the vector is obtained by the polar Kerr response arising from the out-of-plane magnetization tilting, whereas the field-like component (hSODL) is obtained by current-induced hysteresis-loop shifting study, using conventional longitudinal Kerr magnetometry.
We tested our method in FM/NM bilayers comprising NiFe, CoFeB (ferromagnetic layers) and Pt, Pd, Ta (non-magnetic layers). Our findings revealed a damping-like SOT efficiency xiDL of 0.089 pm 0.006,0.019 pm 0.002, and -0.132 pm 0.009 for Pt, Pd, and Ta, respectively. The hSOFL/hSODL ratio was 0.35 pm 0.02 for NiFe/Pt and 0.14 pm 0.002 for Ta/CoFeB bilayers when the ferromagnetic layer thickness is 4nm.
A key advancement over the state-of-art magneto-optical methods is the use of an oblique light incidence angle, which allows switching between measuring modes for hSODL and hSOFL, without altering the experimental setup. Moreover, our approach relies exclusively on first-order Kerr effects, thereby ensuring its broad applicability to any type of ferromagnetic material.