MSGCorep: A package for corepresentations of magnetic space groups

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 (type-I, -III, and -IV MSGs) and nonmagnetic (type-II MSGs) materials. Program summary: Program title: MSGCorep CPC Library link to program files: https://doi.org/10.17632/zt9r8pp8kr.1 Developer's repository link: https://github.com/goodluck1982/MSGCorep Licensing provisions: GNU General Public Licence 3.0 Programming language: Wolfram External routines/libraries used: SpaceGroupIrep (https://github.com/goodluck1982/SpaceGroupIrep) Nature of problem: The package MSGCorep provides offline database and tools for easy access to 1651 magnetic space groups, 122 magnetic point groups, and their corepresentations (coreps). MSGCorep is the first package that is able to calculate the direct product of full coreps for any magnetic space group and able to determine small coreps of energy bands for general purpose. Solution method: Coreps of a magnetic group are constructed from the representations of the maximal unitary subgroup of the magnetic group. Based on the complete representation data of 230 space groups provided by SpaceGroupIrep package, complete corep data of 1651 magnetic space groups are derived in MSGCorep package. A more convenient equation of induced corep, i.e. Eq. (2), is introduced to calculate the full coreps of all MSGs.