Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques

TL;DR

This paper develops a Berry phase theory linking Dzyaloshinskii-Moriya interaction and spin-orbit torques, introducing new concepts like twist torque moment and spiralization, and applies it to compute DMI in various magnetic trilayers.

Contribution

It introduces a Berry phase framework for DMI and SOTs, establishing their relation and proposing new concepts like twist torque moment and spiralization.

Findings

DMI and SOTs are related via Berry phase in chiral magnets.

The formalism efficiently computes DMI using electronic structure.

DMI is highly anisotropic in studied magnetic trilayers.

Abstract

Recent experiments on current-induced domain wall motion in chiral magnets suggest important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the \textit{twist torque moment}, which probes the internal twist of wave packets in chiral magnets in a similar way like the orbital moment probes the wave packet's internal self rotation. We propose to interpret the Berry phase theory of DMI as a theory of \textit{spiralization} in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Pt/Co, Pt/Co/O and Pt/Co/Al magnetic trilayers and show that the DMI is highly anisotropic in these systems.