When nanometric, noncoplanar spin textures with scalar spin chirality (SSC) are coupled to itinerant electrons, they endow the quasiparticle wave functions with a gauge field, termed Berry curvature, in a way that bears analogy to relativistic spin-orbit coupling (SOC). The resulting deflection of moving charge carriers is termed the geometrical (or topological) Hall effect. Previous experimental studies modeled this signal as a real-space motion of wave packets under the influence of a quantum-mechanical phase. In contrast, we here compare the modification of Bloch waves themselves and of their energy dispersion due to SOC and SSC. Using the canted pyrochlore ferromagnet ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ as a model compound, our transport experiments and first-principles calculations show that SOC impartially mixes electronic bands with equal or opposite spin, while SSC is much more effective for opposite-spin band pairs.

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• Electronic structure
• Magnetic texture
• Spin-orbit coupling
• Topological materials