Anomalous Hall effect in antiferromagnetic perovskites

TL;DR

This paper theoretically investigates the anomalous Hall effect in antiferromagnetic perovskites, revealing how specific AFM spin structures and orbital interactions induce AHE in these materials.

Contribution

It demonstrates that collinear AFM states in perovskites can produce AHE due to Berry phase effects, expanding understanding of AHE beyond ferromagnetic systems.

Findings

AFM states can exhibit AHE in perovskites.

Orbital mixing and lattice distortion activate Berry curvature.

Collinear AFM components, not ferromagnetic ones, cause AHE.

Abstract

We theoretically study the anomalous Hall effect (AHE) in perovskites with antiferromagnetic (AFM) orderings. By studying the multiorbital Hubbard model for $d$ electrons in perovskite transition metal oxides under the GdFeO$_3$-type distortion within the Hartree-Fock approximation, we investigate the behavior of intrinsic AHE owing to the atomic spin-orbit coupling via the linear response theory. We consider the cases where there exist two ($d^2$) and three ($d^3$) electrons in the $t_{2g}$ orbitals, and show that AFM ordered states can exhibit AHE. In the $d^2$ case, $C$-type AFM states give rise to dc AHE in metals and optical (finite-$\omega$) AHE in insulators accompanying orbital ordering, while in the $d^3$ case, a $G$-type AFM insulating state supports the optical AHE. By resolving the components in the spin patterns compatible with the space group symmetry, we specify the collinear AFM component to be responsible for the AHE, rather than the small ferromagnetic component. We discuss the microscopic origin of the AHE: the collinear AFM spin structure produces a nonzero Berry phase from the triangular units of the lattice, activated by the complex orbital mixing terms owing to the GdFeO$_3$-type distortion, and results in the microscopic Lorentz force.