The scaling of the anomalous Hall effect (AHE) was investigated using amorphous and epitaxial FexSi1-x (0.43 < x < 0.71) magnetic thin films by varying the longitudinal conductivity using two different approaches: modifying the carrier mean free path with chemical or structural disorder while holding the carrier concentration constant or varying n h and keeping l constant. The anomalous Hall conductivity , when suitably normalized by magnetization and n h, is shown to be independent of for all samples. This observation suggests a primary dependence on an intrinsic mechanism, unsurprising for the epitaxial high conductivity films where the Berry phase curvature mechanism is expected, but remarkable for the amorphous samples. That the amorphous samples show this scaling indicates a local atomic level description of a Berry phase, resulting in an intrinsic AHE in a system that lacks lattice periodicity.

The anomalous Hall effect (AHE), and magnetic and electronic transport properties were investigated in a series of amorphous transition metal thin films - FexSi1-x, FexGe1-x, CoxGe1-x, CoxSi1-x, and Fe1-yCoySi. The experimental results are compared with density functional theory calculations of the density of Berry curvature and intrinsic anomalous Hall conductivity. In all samples, the longitudinal conductivity (σxx), magnetization (M), and Hall resistivity (ρxy) increase with increasing transition metal concentration; due to the structural disorder σxx is lower in all samples than a typical crystalline metal. In the systems with Fe as the transition metal (including Fe1-yCoySi), the magnetization and AHE are large and in some cases greater than the crystalline analog. In all samples, the AHE is dominated by the intrinsic mechanism, arising from a nonzero, locally derived Berry curvature. The anomalous Hall angle (AHA) (=σxy/σxx) is as large as 5% at low temperature. These results are compared with the AHAs reported in a broad range of crystalline and amorphous materials. Previous work has shown that in a typical crystalline ferromagnet the Hall conductivity (σxy) and σxx are correlated and are usually either both large or both small, resulting in an AHA that decreases with increasing σxy. By contrast, the AHA increases linearly with increasing σxy in the amorphous systems. This trend is attributed to a generally low σxx, while σxy varies and can be large. In the amorphous systems, σxx and σxy are not coupled, and there may thus exist the potential to further increase the AHA by increasing σxy.

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 ρxyAH relative to crystalline FeGe; this ρxyAH 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.

Point contact Andreev reflection spectroscopy has been utilized to determine the spin polarization of both amorphous and crystalline FexSi1-x (0.58