A DMI guide to magnets micro-world

TL;DR

This paper reviews methods for calculating Dzyaloshinskii-Moriya interaction (DMI) from first principles, highlighting their importance in understanding complex magnetic structures like skyrmions and spin spirals.

Contribution

The paper introduces and discusses several methods developed by the authors for first-principles calculation of DMI in magnetic materials.

Findings

Methods enable accurate DMI calculations from electronic structure data

Application to real materials reveals insights into magnetic phenomena

Facilitates design of materials with specific magnetic properties

Abstract

Dzyaloshinskii-Moriya interaction, DMI in short, represents an antisymmetric type of magnetic interactions that favour orthogonal orientation of spins and competes with Heisenberg exchange. Being introduced to explain weak ferromagnetism in antiferromagnets without an inversion center between magnetic atoms such an anisotropic interaction can be used to analyze other non-trivial magnetic structures of technological importance including spin spirals and skyrmions. Despite the fact that the corresponding DMI contribution to the magnetic energy of the system has a very compact form of the vector product of spins, the determination of DMI from first-principles electronic structure is a very challenging methodological and technical problem whose solution opens a door into the fascinating microscopic world of complex magnetic materials. In this paper we review a few such methods developed by us for calculating DMI and their applications to study the properties of real materials.