Anomalous Hall effect due to noncollinearity in pyrochlore compounds: Role of orbital Aharonov-Bohm effect

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 wave function in the presence of spin-orbit interaction. This orbital Aharonov-Bohm (AB) effect produces the AHC that is drastically changed in the presence of noncollinear spin structure. In both ferromagnetic compound Nd2Mo2O7 and paramagnetic compound Pr2Ir2O7, 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. Especially, finite AHC in the absence of magnetization observed in Pr2Ir2O7 can be explained in terms of the orbital mechanism by assuming small magnetic order of Ir 5d electrons.