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

TL;DR

This paper proposes an orbital Aharonov-Bohm effect mechanism in pyrochlore compounds that explains the anomalous Hall effect driven by non-collinear spin structures, emphasizing the role of orbital wavefunctions and spin-orbit interaction.

Contribution

It introduces the orbital Aharonov-Bohm effect as a dominant mechanism for the anomalous Hall effect in pyrochlore compounds, surpassing spin chirality explanations.

Findings

Orbital AB effect explains AHE in Nd2Mo2O7 and Pr2Ir2O7.

Finite AHC in Pr2Ir2O7 occurs without net magnetization.

The model aligns with experimental observations of spin structure and AHC.

Abstract

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. Especially, ``finite AHC in the absence of magnetization'' observed in Pr$_2$Ir$_2$O$_7$ can be explained in terms of the orbital mechanism by assuming small magnetic order of Ir 5d-electrons.