Dzyaloshinskii-Moriya interaction and Hall effects in the skyrmion phase of MnFeGe alloys

TL;DR

This study uses density functional theory to analyze Berry phase effects in the skyrmion phase of MnFeGe alloys, revealing how Dzyaloshinskii-Moriya interactions and Hall effects vary with composition and are explained by a tight-binding model.

Contribution

It demonstrates the correlation between Dzyaloshinskii-Moriya interaction, Berry phases, and Hall effects in MnFeGe alloys, and introduces a simple model to explain these phenomena.

Findings

Dzyaloshinskii-Moriya interaction changes sign with alloy composition.

Computed Hall effects agree with experimental data.

Adiabatic Berry phase picture breaks down in Mn-rich alloys.

Abstract

We carry out density functional theory calculations which demonstrate that the electron dynamics in the skyrmion phase of Fe-rich Mn$_{1-x}$Fe$_x$Ge alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya interaction, directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration $x$ in direct correlation with the data of Shibata {\it et al.}, Nature Nanotech. {\bf 8}, 723 (2013). The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.