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The amorphous iron-germanium system ($a$-Fe$_x$Ge$_{1-x}$) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of aFeGe 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 $mathbf{k}$ being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity $rho_{xy}^{mathrm{AH}}$ relative to crystalline FeGe; this $rho_{xy}^{mathrm{AH}}$ 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 $mathbf{k}$-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 $a$-Fe$_x$Ge$_{1-x}$ ($0.38 leq x leq 0.61$). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to $mathbf{k}$-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.
Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalou
A detailed study of the magnetic and transport properties of Si1-xMnx (X = 0.35) films is presented. We observe the anomalous Hall effect (AHE) in these films up to room temperature. The results of the magnetic measurements and the AHE data are consi
We predict an anomalous thermal Hall effect (ATHE) mediated by photons in networks of Weyl semi-metals. Contrary to the photon thermal Hall effect in magneto-optical systems which requires the application of an external magnetic field the ATHE in a W
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phon
The nonlinear Hall effect is mostly studied as a Berry curvature dipole effect in nonmagnetic materials, which depends linearly on the relaxation time. On the other hand, in magnetic materials, an intrinsic nonlinear Hall effect can exist, which does