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High-throughput study of the anomalous Hall effect

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 $\mathbf{j}^\text{AHE} \sim \mathbf{M} \times \mathbf{E}$.