Thickness and temperature dependent nonlinear Hall effect in untwinned Weyl metal SrRuO₃ thin films

The nonlinear Hall effect (NLHE) refers to a higher harmonic transverse response driven by a longitudinal current bias. It serves as a tool for probing quantum geometric effects in solids, as well as for identifying novel phases of matter with broken symmetries. Recent advancements in SrRuO₃ (SRO) thin film growth using adsorption-controlled techniques have resulted in low defect levels, facilitating the recent discovery of unusually large NLHE in SRO thin films at low temperatures [1].

A key approach to elucidating the mechanism responsible for the observed NLHE is to determine the exponent n in the relation of σ_yxx^2ω ∝ τ_dⁿ, where σ_yxx^2ω and τ_dⁿ represent the nonlinear Hall conductivity and the bulk Drude lifetime, respectively. NLHE resulting from quantum metric dipole and Berry curvature dipole gives n = 0 and 1, respectively, while NLHE due to the Drude term and the skew scattering results in n = 2 and 3.

In this study, we report rigorous T-dependent NLHE measurements in untwinned thin films of the Weyl metal SRO (t) / SrTiO₃(001) thin films with t = 8 and 13.7 nm. By plotting σ_yxx^2ω / σ_xx² versus σ_xx², the rapid rise of σ_yxx^2ω / σ_xx² below 10 K does not conform to previously established exponents (n = 0, 1, 2, and 3) in σ_yxx^2ω ∝ τ_dⁿ. This suggests the behavior is more likely associated with a crossover from bulk-dominated to surface-dominated charge transport. Additionally, we note that the magnitude of the σ_yxx^2ω / σ_xx² appears to increase with t from 8 to 13.7 nm. The robustness of the observed NLHE signal in SRO is supported by consistent behaviors observed across samples with different ts, including another t = 13.7 nm sample with a 10 nm SrTiO₃ capping layer. Our results highlight nonreciprocal and nonlinear charge transport measurements as an effective probe for revealing topological surface states in a topological system.