The amorphous iron-germanium system (a-FexGe1−x) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of a-FexGe1−x is well explained by the Stoner model for Fe concentrations x above the onset of magnetic order around 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 reveal an enhanced anomalous Hall resistivity ρ AH xy relative to crystalline FeGe; this ρ AH xy is compared to density functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied k-states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of a-FexGe1−x (0.38 ≤ x ≤ 0.61). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to k-space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.

PACS 73.50.-h-Electronic transport phenomena in thin films PACS 73.61.Jc-Amorphous semiconductors; glasses PACS 73.50.Jt-Galvanomagnetic and other magnetotransport effects (including thermomagnetic effects) Abstract-The scaling of the anomalous Hall effect (AHE) was investigated using amorphous and epitaxial FexSi1−x (0.43

Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii-Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe-Ge thick films. These results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. Disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strain manipulation. The discovery of unprecedented physical properties and application potential of topologically protected non-collinear states in condensed matter has greatly influenced the direction of