Symmetr: a Python package for determining symmetry properties of crystals

TL;DR

Symmetr is a Python package that determines symmetry properties of crystals, especially magnetic materials, aiding in understanding their physical response tensors and other properties based on symmetry constraints.

Contribution

It introduces a comprehensive Python tool for analyzing symmetry-restricted forms of physical property tensors in crystals, including magnetic and non-relativistic cases.

Findings

Supports symmetry analysis using magnetic space groups and spin groups.

Handles site-specific quantities and magnetic order parameter expansions.

Operable via command line and Python API.

Abstract

Condensed matter compounds typically form crystals, which break the rotational and translational invariance of space but remain invariant under a discrete set of symmetry operations. Understanding the effects allowed by this symmetry breaking, as well as the constraints imposed by the crystal structure, is a crucial problem in condensed matter physics. Here, we present a Python package for determining the symmetry-restricted forms of tensors describing physical properties of crystals, focusing particularly on magnetic materials. The primary focus is on response tensors; however, the program can also describe equilibrium properties and other physical properties, such as magnetic interactions. The program can describe the symmetry using the conventional magnetic space groups, as well as using the spin groups that describe the non-relativistic limit. Additional functionality includes the treatment of quantities projected onto a particular site and expansions in the magnetic order parameter. The code can be used either from the command line or via a Python API.