Fig. 2: Second harmonic voltage measurements and spin-orbit torque (SOT) efficiency analysis.
a Schematic diagram of spin torques (τDL and τFL) in the second harmonic voltage measurement. b First-order harmonic resistance \({R}_{{xy}}^{1\omega }\) of SIO/NiO (2)/LSMO as a function of magnetic field angle φ (the angle between Hext and Iac). c Second-order resistance \({R}_{{xy}}^{2\omega }\) of SIO/NiO (2)/LSMO as a function of φ. The red and purple fitting line is the damping-like term (\({R}_{{DL}+\nabla T}\cos \varphi\)) and the field-like term (\({R}_{{FL}+{Oe}}(2{\cos }^{3}\varphi -\cos \varphi )\)), respectively. d The linear dependence of \({R}_{{DL}+\nabla T}/{R}_{{AHE}}\) versus \(1/{H}_{K}+{H}_{{ext}}\) for heterostructures with different tNiO. e The linear dependence of \({R}_{{FL}+{Oe}}/{R}_{{PHE}}\) versus \(1/{H}_{{ext}}\). f Damping-like SOT efficiencies (ξDL) as a function of tNiO for SIO/NiO (t)/LSMO, Pt/NiO (t)/LSMO, and NiO (t)/LSMO heterostructures. The dashed blue line is just guide to the eyes. Error bars represent standard deviation.
