Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium*

The amorphous iron-germanium system (a-Fe_xGe_1-x) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of a-Fe_xGe_1-x is well explained by the Stoner model for x ≥ 0.4, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-3d states sufficiently to polarize the electronic structure despite k being a bad quantum number. Measurements show an enhanced anomalous Hall resistivity relative to crystalline FeGe; comparison to density functional theory calculations of the anomalous Hall conductivity (AHC) resolves its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied k-states but equivalent to the density of curvature (DOC) integrated over occupied energies, dominates the AHC of a-Fe_xGe_1-x (0.38 ≤ x ≤ 0.61). The DOC is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to k. This result and the accompanying Stoner-like model for the intrinsic AHC establish a unified understanding of the physics of the anomalous Hall effect in both crystalline and disordered systems.
D. S. Bouma et al., arXiv:1908.06055, 2019