Fig. 2: Angular evolution of octupole-driven and chirality-driven Hall responses.

Transverse Hall resistance measured as a function of magnetic field applied (a) out of the kagome plane and (b, c) within the plane at two representative in-plane field angles. Black symbols show experimental data; green curves are fits to the combined model in Eq. (2), consisting of an octupole-driven term (red curves) and a scalar-chirality-driven term (blue curves). Small arrows indicate the direction of hysteresis loop shift. d–f Schematics of the magnetic-field directions corresponding to the measurements in (a–c). g Device geometry used for magnetotransport measurements, indicating crystallographic axes and the orientation of current and voltage lines. h Extracted amplitudes of the octupole-driven contribution \({R}_{xy}^{Oct}\) (red) and the scalar-chirality contribution \({R}_{xy}^{SSC}\) (black) as functions of in-plane angle. Both show an approximate 120^∘ periodicity. Error bars represent the standard deviation of five repeated measurements. i Symmetry-based theoretical calculation of scalar spin chirality, displaying the same 120^∘ periodicity but with an opposite sign compared to the octupole contribution.