Anomalous Hall Effect due to Non-collinearily in Pyrochlore Compounds: Role of Orbital Aharonov-Bohm Effect

Understand

To elucidate the origin of spin structure-driven anomalous Hall effect (AHE) in pyrochlore compounds, we construct the $t_{2g}$-orbital kagome lattice model and analyze the anomalous Hall conductivity (AHC).

• We reveal that a conduction electron acquires a Berry phase due to the complex d-orbital wavefunction in the presence of spin-orbit interaction.
• This ``orbital Aharonov-Bohm (AB) effect'' produces the AHC that is drastically changed in the presence of non-collinear spin structure.
• In both ferromagnetic compound Nd$_2$Mo$_2$O$_7$ and paramagnetic compound Pr$_2$Ir$_2$O$_7$, the AHC given by the orbital AB effect totally dominates the spin chirality mechanism, and succeeds in explaining the experimental relation between the spin structure and the AHC.