Fig. 4: Anomalous Hall effect (AHE) and topological Hall effect (THE) obtained from terahertz and transport measurements.

a, b The decomposition of the experimental spectra into two resonances corresponding to the AHE (blue) and THE (red) at (a) 4.5 K and (b) 20 K. The experimental and theoretical spectra are shown by green and black curves, respectively. These spectra for 4.5 K are multiplied by a factor of two. c–f The magnetic-field dependence of the AHE (Re{σ_xy^α + σ_xy^const.}, filled circle) and THE (Re{σ_xy^β}, open circle) at ω = 0 obtained from the analysis for terahertz spectra; (c) 4.5 K, (d) 10 K, (e) 20 K, and (f) 30 K. The zero-frequency limit (ω = 0) of the AHE (σ_xy^α + σ_xy^const.) and THE (σ_xy^β) are displayed by filled and open circles also in a, respectively. The red and blue curves in c–f show the AH conductivity σ_xy^A and TH conductivity σ_xy^T deduced from the transport measurement, respectively. The total Hall conductivity is also shown by dotted curves. The decomposition of AHE and THE is possible in a relatively low field region (≤ 7 T) as exemplified in early works^21,33,36, whereas the steep increase of σ_xy at low temperatures and above 12 T in a field-aligned ferromagnetic region is supposed to stem from the spin-chirality skew scattering^38,39,40 (see also Supplementary Note 1).