Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structure

TL;DR

This paper introduces algorithms for identifying magnetic symmetry operations and magnetic space groups in magnetic crystal structures, extending existing crystal symmetry search methods to magnetic materials with stable and efficient procedures.

Contribution

It presents new algorithms for magnetic symmetry analysis, including determination, classification, and symmetrization of magnetic space groups, integrated into the spglib software.

Findings

Algorithms are numerically stable and minimally modify existing methods.

Magnetic space-group types and transformations are identified via a two-step approach.

The implementation is available as open-source in spglib v2.0.2.

Abstract

A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs) remains limited. In this paper, algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types of given MSGs, searching for transformations to a BNS setting, and symmetrizing the magnetic crystal structures using the MSGs are presented. The determination of magnetic symmetry operations is numerically stable and is implemented with minimal modifications from the existing crystal symmetry search. Magnetic space-group types and transformations to the BNS setting are identified by a two-step approach combining space-group type identification and the use of affine normalizers. Point coordinates and magnetic moments of the magnetic crystal structures are symmetrized by projection operators for the MSGs. An implementation is distributed with a permissive free software license in spglib v2.0.2: https://github.com/spglib/spglib.