Figure 6: Extraction of the SOF coefficient from longitudinal MOKE.

(a) Experimental setup for using longitudinal MOKE to detect the SOF. The setup is identical with the polar MOKE shown in Fig. 1a, except that the laser is obliquely incident on the sample in the xy plane. The incident angle is set to be about 20°. (b) Measured voltage from the lock-in amplifier when passing an ac current 100 mA through the sample (500 μm in width) is shown in the top curve. The curve is asymmetric owing to the out-of-plane magnetization reorientation because of the SOT. The calibration is performed by applying an ac current through a metallic wire behind the sample, which generates an Oersted field (216±8 A m⁻¹) that drives the in-plane magnetization reorientation. As shown in the lower graph, the curve is symmetric since the calibration field has no torque-like term. (c) The magnetization reorientation because of the SOF (top curve) and SOT (bottom curve) can be separated by their different symmetries. (d) The magnitude of the SOF is extracted using a linear regression algorithm by comparing the top curve in Fig. 2c and the calibration curve in Fig. 2b. Only data between 50 and 300 Gauss are used in the fitting, where the magnetization is well saturated. In this example fitting, the ratio between the current-induced effective field and the calibration field is 0.74±0.03, which gives rise to a current-induced field of 160±16 A m⁻¹. After removing the 104 A m⁻¹ Oersted field generated by the current, we obtain a h_SOF=56±16 A m⁻¹. (e) The extracted SOF is linearly proportional to the bias current, suggesting that the measurement is still in the linear regime.