  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.

Mesoscale and Nanoscale Physics;Materials Science