Fig. 5: Unconventional Hall effect in NdRuO₃ thin film.

Magnetic field dependence of ρ_AHE (a) and MRR (b) in the NRO film below 5 K at low-field region (B ≤ 4 T) with vertical offsets for clarity. The results of 0.5, 2, and 5 K are identical to the ones presented in Fig. 3e, f. For each curve in (a, b), its origin at B = 0 is indicated by a thick horizontal bar. Inset of (a) is a schematic of a non-coplanar spin texture that produces scalar spin chirality χ_S. The peak position of AHE and inflection point of MRR are indicated by square and triangle, respectively. c Magnetic field dependence of magnetic field derivatives of ρ_AHE (red curve, left axis) and MRR (blue curve, right axis) at 0.5 K. The square and triangle in (c) indicate the zero point in dρ_AHE/dB (i.e., peak in ρ_AHE) and the peak in dMRR/dB (i.e., an inflection point in MRR) around 1.3 T, respectively. The red-colored areas in (a–c) highlight the field region where the anomalies are observed at 0.5 K. d Schematic of a possible mechanism to generate the topological Hall effect. Itinerant electrons of Ru³⁺ interact with localized Nd³⁺ moments and acquire χ_S induced by non-coplanar spin texture of Nd³⁺. Note that Ru³⁺ locates at the body center of the deformed cube formed by Nd³⁺.