First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework

TL;DR

This paper presents a new formalism to calculate the Dzyaloshinskii-Moriya interaction in non-collinear magnetic systems, demonstrating its significance even without spin-orbit coupling through first-principles methods.

Contribution

It introduces a general expression for DM interaction components in non-collinear configurations and implements it within a real space LMTO-ASA framework.

Findings

DM interaction varies significantly between collinear and non-collinear states

DM interaction can be substantial without spin-orbit coupling due to non-collinear magnetism

The formalism is validated on triangular trimers on metallic surfaces

Abstract

We have derived an expression of the Dzyaloshinskii-Moriya (DM) interaction, where all the three components of the DM vector can be calculated independently, for a general, non-collinear magnetic configuration. The formalism is implemented in a real space - linear muffin-tin orbital - atomic sphere approximation (RS-LMTO-ASA) method. We have chosen the Cr triangular trimer on Au(111) and Mn triangular trimers on Ag(111) and Au(111) surfaces as numerical examples. The results show that the DM interaction (module and direction) is drastically different for collinear and non-collinear states. Based on the relation between the spin and charge currents flowing in the system and their coupling to the non-collinear magnetic configuration of the triangular trimer, we demonstrate that the DM interaction can be significant, even in the absence of spin-orbit coupling. This is shown to emanate from the non-collinear magnetic structure, that can induce significant spin and charge currents even with spin-orbit coupling is ignored.