Fig. 3. Harmonic measurements under different temperatures in Bi₂Te₃(8)/Fe₃GeTe₂(3) heterostructure.

a Second-harmonic Hall resistance ($R_{xy}^{2\mathrm{\omega }}$) under different J_a.c. at 200 K. The inset displays the oscillation of the magnetic moment at the equilibrium position in harmonic measurement. b Second-harmonic Hall resistance ($R_{xy}^{2\mathrm{\omega }}$) as a function of in-plane magnetic field (H_x) at different temperatures under a constant write current density. The inset schematically displays the field dependencies of anomalous Nernst resistance. c Damping-like effective field (H_DL) as a function of the current density extracted by fitting the second harmonic Hall signal. The inset shows a typical $R_{xy}^{2\mathrm{\omega }}$–H_x curve under the large magnetic field range for fitting out the H_DL. The error bars denote the standard deviation of multiple measurements.