Fig. 6: SOT switching of canted GdCo moments with magnetic canting angle of 56 degrees (sample-56).

a Thin film magnetometry (Magnetization - applied magnetic field) of sample-56 via vibrating sample magnetometer measured in both in-plane and out-of-plane direction. b Angle-dependent anomalous Hall effect measurement and the linear fit to data above the coercive field region for obtaining the slope. c Slope in the field region above the coercive field as a function of field angle. The minimum slope resides at 56.25^∘ from the \(\hat{z}\)-axis. d, e Spin-orbit torque switching curve with starting current value of  − 27 mA. The four different switching curves are obtained with four different combinations of initialization field (± 100 mT) and symmetry breaking field (± 2.5 mT). f Spin-orbit torque switching curve with a starting current value of  − 27 mA without a symmetry-breaking field. The two curves show the dependence of the initialization direction. g SOT switching curves with varying external symmetry breaking field (B_x) and initialization with B_set,z of 100 mT. The current pulse sequence starts from a small positive current (1 mA), then traverses in the positive direction to the positive critical switching current and back to the negative critical current density, then stops at the positive critical current. The Ratchet effect is visible with the effect amplified at zero symmetry breaking field. The symmetry-breaking field-dependent SOT switching curve and ratchet effect of the other combinations [I_start = ± 1 mA, B_set,z = ± 100 mT] are shown in Fig S5. h Extracted information of each switching curve as a function of symmetry breaking field for the case of B_set,z = 100 mT. We extracted the ΔR_AHE of maximum and minimum R_AHE throughout the entire switching curve, the ΔR_AHE of R_AHE at the zero current crossing, the minimum R_AHE, and the maximum R_AHE.