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

Abstract

Abstract We present a magneto-optical method for quantifying both components of the spin-orbit torque (SOT) effective field vector h_SO in magnetic thin films that, unlike previous complete-vector magneto-optical schemes relying on quadratic Kerr effects for at least one component, relies exclusively on first-order Kerr effects. The damping-like (h_SO^DL) component is obtained through the polar Kerr response arising from out-of-plane magnetization tilting, while the field-like (h_SO^FL) component is obtained from current-induced hysteresis-loop shifts detected with conventional longitudinal Kerr magnetometry. Because both signals derive from first-order Kerr coefficients, which scale directly with the saturation magnetization of the ferromagnetic layer and are not constrained by the crystallographic-symmetry dependence inherent to quadratic (second-order) Kerr effects, the technique is applicable to a broad range of ferromagnetic materials, subject to the magneto-optical signal-to-noise ratio attainable in each case. The use of an oblique light incidence angle is a further advantage over state-of-the-art magneto-optical schemes, as it enables switching between the measurement modes for h_SO^DL and h_SO^FL without modifying the optical setup. We tested our method in bilayers comprising NiFe and CoFeB ferromagnetic layers with Pt and Ta non-magnetic layers. As the primary comparison criterion with previous literature, we use the field-like to damping-like effective-field ratio h_SO^FL/h_SO^DL, obtaining 0.34 ± 0.02 for NiFe/Pt and 0.14 ± 0.04 for Ta/CoFeB in bilayers with a 4 nm ferromagnetic layer. These ratios are consistent with published ST-FMR results on comparable bilayers. Because that comparison is made on nominally similar rather than on the same samples, we regard it as indicative rather than conclusive; taken with our own measurements at t_FM = 8 nm, it suggests a convergence of magneto-optical and ST-FMR determinations of SOTs in the ultrathin-ferromagnet regime — precisely where standard ST-FMR analysis is most reliable — while the present method remains applicable in regimes where electrical detection is hindered.