## Research Papers in Physics and Astronomy

#### Date of this Version

1-2-2020

#### Document Type

Article

#### Citation

PHYSICAL REVIEW B 101, 014402 (2020)

DOI: 10.1103/PhysRevB.101.014402

#### Abstract

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 a-Fe_{x}Ge_{1-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_{xy}^{AH }relative to crystalline FeGe; this ρ_{xy}^{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** 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≤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.

#### Included in

Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics Commons, Other Physics Commons

## Comments

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