Fig. 4: Nonvolatile electric-field control of the spin–orbit torques.

a Gate electric-field dependence of the spin–orbit torques anti-damping-like effective field µ₀H_AD. The points A–D are examined in (c). b Measured portion p of the current injected in the 2DEG as a function of the gate-electric-field E_g. c Normalized second-harmonic Hall resistance at shifted electrical remanence E_g,r after successive application of negative (blue) or positive (red) gate-electric-field pulses of ±2.6 kV cm⁻¹. Dashed and dotted lines are linear fits, yielding SOT effective fields µ₀H_AD/j = +0.29, −0.20, +0.32, and −0.18 mT/(A cm⁻¹), respectively. All data have been measured at 10 K with a linear AC current density of j = 4 A cm⁻¹ (I₀ = 40 µA) and a nearly in-plane magnetic field (θ_H = 85°, φ_H = 45°).