High-throughput study of the anomalous Hall effect

Despite its long history, the anomalous Hall continues to attract attention due to its complex origins, its connection to topology, and its use as a probe of magnetic order. In this work we investigate the anomalous Hall effect in 2871 ferromagnetic materials using an automatic high-throughput calculation scheme. We analyze general properties of the effect, such as its reliance on spin-orbit coupling strength and magnetization. In materials with the largest anomalous Hall effect, we find that symmetry-protected band degeneracies in the non-relativistic electronic structure, such as mirror symmetry-protected nodal lines, are typically responsible for the large effect. Furthermore, we examine the dependence of the anomalous Hall effect on magnetization direction and demonstrate deviations from the commonly assumed expression jAHE ~ M × E.