MSGCorep: A package for corepresentations of magnetic space groups

TL;DR

MSGCorep is a comprehensive Mathematica package providing offline access to corepresentations of all magnetic space groups and point groups, facilitating symmetry analysis in magnetic and nonmagnetic materials.

Contribution

It is the first package capable of calculating direct products of full coreps for any magnetic space group and determining small coreps of energy bands.

Findings

Supports both single-valued and double-valued coreps

Calculates and visualizes coreps and their decompositions

Provides tools for symmetry analysis in magnetic materials

Abstract

Motivated by easy access to complete corepresentation (corep) data of all the 1651 magnetic space groups (MSGs) in three-dimensional space, we have developed a Mathematica package MSGCorep to provide an offline database of coreps and various functions to manipulate them, based on our previous package SpaceGroupIrep. One can use the package MSGCorep to obtain the elements of any MSG and magnetic little group, to calculate the multiplication of group elements, to obtain the small coreps at any k-point and full coreps of any magnetic k-star for any MSG and show them in a user-friendly table form, to calculate and show the decomposition of direct products of full coreps between any two specified magnetic k-stars, and to determine the small coreps of energy bands. Both single-valued and double-valued coreps are supported. In addition, the 122 magnetic point groups (MPGs) and their coreps are also supported by this package. To the best of our knowledge, MSGCorep is the first package that is able to calculate the direct product of full coreps for any MSG and able to determine small coreps of energy bands for general purpose. In a word, the MSGCorep package is an offline database and tool set for MSGs, MPGs, and their coreps, and it is very useful to study the symmetries in magnetic and nonmagnetic materials.