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

TL;DR

This paper investigates how spin textures and spin-orbit coupling influence electronic band structures and Berry curvature, revealing that scalar spin chirality significantly affects opposite spin band pairs, leading to a geometrical Hall effect.

Contribution

It provides a comparative analysis of SOC and SSC effects on Bloch waves and energy dispersion in a pyrochlore ferromagnet, highlighting SSC's stronger impact on opposite spin bands.

Findings

SOC mixes bands with equal or opposite spins

SSC predominantly affects opposite spin band pairs

Transport experiments confirm theoretical predictions

Abstract

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.