Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium

D. S. Bouma, Z. Chen, B. Zhang, F. Bruni, M. E. Flatté, R. Streubel, L. -W. Wang, R. Q. Wu, F. Hellman

Published 2019-08-16Version 1

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 $\mathbf{k}$ 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 equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of $a$-Fe$_x$Ge$_{1-x}$ ($0.38 \leq x \leq 0.61$).