MSGCorep

A mathematica package for irreducible corepresentations (coreps) of all the 1651 magnetic space group in three-dimensional space, using the BC convention. Here, "BC convention" means the convention used in the the famous book “The mathematical theory of symmetry in solids” by C. J. Bradley & A. P. Cracknell. This package is based on our previous package SpaceGroupIrep.

Communications

• Users can join WeChat group for communications: the QR code. If you cannot join the WeChat group, please contact me through gbliu(AT)bit(dot)edu(dot)cn.
• 点击上面链接加入 SpaceGroupIrep/MSGCorep 使用交流微信群，如无法加入可邮件联系。

Please refer to the following papers for details of the code:

• Comput. Phys. Commun. 288 , 108722 (2023) (arXiv:2211.10740)
• Comput. Phys. Commun. 265 , 107993 (2021) (arXiv:2012.08871)

If you use this package in your research, please cite the above papers.

Functionalities of MSGCorep

• Elements of any magnetic space group (MSG), magnetic little group (MLG), magnetic point group (MPG), and their double groups can be easily obtained.
• Obtain and show the small coreps (MLG coreps) at any k-point for any MSG.
• Obtain and show the full coreps (MSG coreps) of any magnetic k-star for any MSG.
• Both single-valued and double-valued coreps are supported.
• Calculate the decomposition of the direct product of full coreps for any two magnetic k-stars.
• Determine the small coreps of Bloch states in energy bands.
• Support all the 122 MPGs, including their coreps and direct product of coreps.

In a word, the package MSGCorep is an offline database and tool set for easy access to complete corep data of all 1651 MSGs and 122 MPGs, and it is very useful for both study and research.

Files

• MSGCorep.wl The main file.
• MSGData.wl Contains the MSG data used by MSGCorep.wl.
• Usage.wl The usages for the functions in MSGCorep.
• libMLGCorep.mx This file contains the small corep data used by the getBandCorep function.
• libMLGCorep.mx_RaspberryPi On raspberry pi, use this file and rename it to libMLGCorep.mx. Note that mathematica can be used free of charge on raspberry pi for non-commercial use, see this page.
• examples/examples-in-the-paper.nb A simple demo file for the examples in the paper.
• BC_MSG_elements/*.txt Use one of the files in this directory and rename it to msg.txt when using MagVasp2trace.

Dependence

SpaceGroupIrep (https://github.com/goodluck1982/SpaceGroupIrep)

Installation

Please install SpaceGroupIrep package first. Then place the directory MSGCorep containing at least the four files, i.e. MSGCorep.wl, MSGData.wl, Usage.wl, and libMLGCorep.mx, under any of the following paths:

• $InstallationDirectory/AddOns/Packages/
• $InstallationDirectory/AddOns/Applications/
• $BaseDirectory/Applications/
• $UserBaseDirectory/Applications/

where $InstallationDirectory is the installation directory of Mathematica (version ≥ 11.2), and $BaseDirectory and $UserBaseDirectory are the directories containing respectively systemwide and user-specific files loaded by Mathematica. The concrete values of $InstallationDirectory, $BaseDirectory, and $UserBaseDirectory can be obtained by running them in Mathematica because they are all built-in symbols.

Then one can use the package after running <<MSGCorep` or <<"MSGCorep`".

Tips: Use ?MSGCorep`* to obtain a list of all public functions and vairables in the package. And similarly, you can also use ?MSGCorep`*MLG* to obtain a list of all public functions and variables whose names contain "MLG".

Exhibition

1. Show the list of MSGs specified by their family numbers

2. The small coreps of the P point of MSG 97.155

3. The full coreps of the magnetic star ^*X of MSG 79.27

4. The direct product of full coreps between magnetic stars ^*X and ^*R for MSG 75.4

5. Determined small coreps for energy bands

6. MPG support