Fig. 3: Second harmonic Hall measurements to obtain h_L and h_T.

a Measurement schematic to obtain the SOT effective fields. The magnitude of the external magnetic field (B_ext) is swept while its direction is fixed in the X–Y plane of the film stack, either parallel (ϕ_B = 90°) or perpendicular (ϕ_B = 0°) to the current direction. R_2ω is obtained by dividing the second harmonic quadrature component of the anomalous Hall voltage by the R.M.S of the AC current excitation. Obtained second harmonic response of the devices made from b stack A, c stack B, and d stack C. The top panel shows measurement results for the ϕ_B = 90° configuration and the bottom panel shows that for the ϕ_B = 0° configuration. The longitudinal (h_L) and transverse (h_T) effective fields are obtained by fitting the high field regions (highlighted in yellow) of the measured curve (black symbols) with the expression given in Eq. 1 (plotted in red line). The required values of R_A and H_K are obtained previously as shown in Fig. 2. Note here that for the longitudinal configuration, the R_2ω curve is anti-symmetric while for the transverse configuration it is symmetric, as expected from the sign change of SOT effective fields with the change in magnetization direction. All extracted parameters are listed in the table shown in e.