Fig. 2: Temperature dependence of linear and non-linear responses in ML-WTe₂/Cr₂Ge₂Te₆ heterostructure.

a Schematic illustration of measurement geometry. An AC current of 3 \(\mu A\) flows in the ML-WTe₂ flake through channel 3–8 (x-direction), and the 1\(f\) and 2\(f\) voltage responses are measured from channel 4-7 in sweeping H_z with f = 13 Hz here. The thick arrows with color gradient across the device boundary indicate the direction of heat dissipation, i.e., \(-\nabla {T}_{{ip}}\), where \(\nabla {T}_{{ip}}\) is the in-plane component of the temperature gradient. b Magnetic field dependence of the raw 1\(f\), \({V}_{4-7}^{1f}\) (top), 1f H_z-symmetric, \({V}_{4-7}^{1f-S}\) and H_z-antisymmetric, \({V}_{4-7}^{1f-{AS}}\) (middle), and 2 f \({V}_{4-7}^{2f}\)voltage (bottom) at 4 K. c Temperature dependence of the magnetoresistance (MR) ratio (top), AHE voltage (middle) and 2\(f\) voltage (bottom) taken from the data in d–f below. MR ratio magnitude is defined as [\({V}_{4-7}^{1f}\)(5 kOe)- \({V}_{4-7}^{1f}\)(0 Oe)]/\({V}_{4-7}^{1f}\)(0 Oe), and \(\triangle {V}_{4-7}^{2f}={V}_{4-7}^{2f}\left({H}_{s}\right)-{V}_{4-7}^{2f}\left(0\right)\). \({H}_{s}\) is the saturation magnetic field of \({V}_{4-7}^{2f}\). d–f Magnetic field dependence of MR ratio (d), \({V}_{4-7}^{1f-{AS}}\) (e) and \({V}_{4-7}^{2f}\) (f) voltage at various temperatures. The temperatures denoted here are read from the thermometer of the measurement system and the actual sample temperature should be higher due to local heating.