High-throughput study of the anomalous Hall effect

TL;DR

This study employs high-throughput calculations to systematically analyze the intrinsic anomalous Hall effect across nearly 2900 ferromagnetic materials, revealing its dependence on symmetry, spin-orbit coupling, and magnetization orientation.

Contribution

It introduces a large-scale computational approach to investigate the origins and properties of the anomalous Hall effect in diverse materials.

Findings

Large anomalous Hall effects are linked to symmetry-protected band degeneracies.

The effect varies significantly with magnetization direction in many materials.

Dependence on spin-orbit coupling influences the magnitude of the anomalous Hall effect.

Abstract

Despite being known for a long time the anomalous Hall effect still attracts attention because of its complex origins, its connection to topology and because it serves as a useful probe of the magnetic order. Here we study the anomalous Hall effect using automatic high-throughput calculation scheme. We calculate the intrinsic anomalous Hall effect in 2871 ferromagnetic materials. We use these results to study general properties of the anomalous Hall effect such as its dependence on the strength of the spin-orbit coupling or magnetization. We also examine the origin of the anomalous Hall effect in the materials with the largest effect and show that the origin of the large anomalous Hall effect is usually associated with symmetry protected band degeneracies in the non-relativistic electronic structure, typically mirror symmetry protected nodal lines. Additionally, we study the dependence of the anomalous Hall effect on the magnetization direction, showing that in many materials it differs significantly from the commonly assumed expression $\mathbf{j}^\text{AHE} \sim \mathbf{M} \times \mathbf{E}$.