Doppler shift picture of the Dzyaloshinskii--Moriya interaction

TL;DR

This paper introduces a Doppler shift-based physical picture for the Dzyaloshinskii--Moriya interaction, linking it to intrinsic spin currents caused by spin--orbit coupling in non-centrosymmetric materials, supported by theoretical and experimental validation.

Contribution

It provides a new Doppler shift-based conceptual framework for understanding the DM interaction, supported by a rigorous effective Hamiltonian and first-principles calculations.

Findings

The DM coefficient equals the magnitude of the intrinsic spin current.

The theory aligns quantitatively with experimental data.

Clarifies the relation between electronic band structure and DM interaction.

Abstract

We present a physical picture for the emergence of the Dzyaloshinskii--Moriya (DM) interaction based on the idea of the Doppler shift by an intrinsic spin current induced by spin--orbit interaction under broken inversion symmetry. The picture is confirmed by a rigorous effective Hamiltonian theory, which reveals that the DM coefficient is given by the magnitude of the intrinsic spin current. The expression is directly applicable to first principles calculations and clarifies the relation between the interaction and the electronic band structures. Quantitative agreement with experimental results is obtained for the skyrmion compounds Mn$_{1-x}$Fe$_x$Ge and Fe$_{1-x}$Co$_x$Ge.