Geometrical Hall effect and momentum-space Berry curvature from spin-reversed band pairs

When nanometric, noncoplanar spin textures with scalar spin chirality (SSC) are coupled to itinerant electrons, they endow the quasiparticle wavefunctions 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 geometrical (or topological) Hall effect. Previous experimental studies modeled this signal as a real-space motion of wavepackets 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 Nd$_2$Mo$_2$O$_7$ as a model compound, our transport experiments and first-principle calculations show that SOC impartially mixes electronic bands with equal or opposite spin, while SSC is much more effective for opposite spin band pairs.