Extension of Hall-symbols of crystallographic space groups to magnetic space groups

TL;DR

This paper extends Hall-symbols to magnetic space groups, enabling unambiguous description of their generators, and introduces a computer program MHALL for parsing and analyzing these symbols.

Contribution

The work provides a systematic extension of Hall-symbols to magnetic space groups and develops MHALL for automated analysis and standardization.

Findings

Extended Hall-symbols to 1651 magnetic space groups

Developed MHALL software for parsing and transformation

Facilitated unambiguous symmetry description in magnetic crystallography

Abstract

The Hall-symbols for describing unambiguously the generators of space groups have been extended to describe whatever setting of the 1651 types of magnetic space groups (Shubnikov groups). A computer program called MHALL has been developed for parsing the Hall symbols, generate the full list of symmetry operators and identify the transformation to the standard setting.