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IRSSG: An Open-Source Software Package for Spin Space Groups

Sheng Zhang, Ziyin Song, Zhong Fang, Hongming Weng, Zhijun Wang

TL;DR

IRSSG presents an open-source framework to determine irreducible corepresentations of magnetic states in spin space groups, bridging DFT wavefunctions with SSG symmetry analysis. It identifies SSG operations, assigns an international symbol, constructs $k$-point little groups, and computes traces of matrix representations to label magnetic energy bands with coirreps, integrating plane-wave and Wannier-based approaches. The tool is compatible with common DFT codes via Wannier90 interfaces and can handle all crystallographic symmetry settings (CSGs and MSGs) given an appropriate $ssg.data$. Demonstrated on systems like NpBi and Eu$_3$PbO, IRSSG reveals symmetry-protected band features such as fourfold nodal lines and EF-enforced degeneracies, enabling targeted $k\cdot p$ modeling and magnetic topology exploration. The method advances the study of magnons, altermagnetism, and high-degeneracy excitations by providing direct symmetry labels for magnetic energy bands from first-principles calculations.

Abstract

We present an open-source software package IRSSG for investigating magnetic systems with spin space groups (SSGs). The package works within the density functional theory (DFT) framework and requires wavefunctions from DFT codes, such as VASP, Quantum ESPRESSO, as well as any other code that has an interface to Wannier90. We introduce a set of compact SSG international symbols by combining non-crystallographic point groups with the 230 crystallographic space groups. The program first identifies all SSG operations and determines the SSG international symbol for a given magnetic system. It then generates the SSG character tables of little groups at any $k$ point. Finally, it computes the traces of matrix presentations of SSG operations and assigns irreducible corepresentation labels to magnetic energy bands. The program is not only timely but also essential for advancing research on the study of magnons, altermagnetism, magnetic topology, and novel high-degeneracy excitations in SSG systems.

IRSSG: An Open-Source Software Package for Spin Space Groups

TL;DR

IRSSG presents an open-source framework to determine irreducible corepresentations of magnetic states in spin space groups, bridging DFT wavefunctions with SSG symmetry analysis. It identifies SSG operations, assigns an international symbol, constructs -point little groups, and computes traces of matrix representations to label magnetic energy bands with coirreps, integrating plane-wave and Wannier-based approaches. The tool is compatible with common DFT codes via Wannier90 interfaces and can handle all crystallographic symmetry settings (CSGs and MSGs) given an appropriate . Demonstrated on systems like NpBi and EuPbO, IRSSG reveals symmetry-protected band features such as fourfold nodal lines and EF-enforced degeneracies, enabling targeted modeling and magnetic topology exploration. The method advances the study of magnons, altermagnetism, and high-degeneracy excitations by providing direct symmetry labels for magnetic energy bands from first-principles calculations.

Abstract

We present an open-source software package IRSSG for investigating magnetic systems with spin space groups (SSGs). The package works within the density functional theory (DFT) framework and requires wavefunctions from DFT codes, such as VASP, Quantum ESPRESSO, as well as any other code that has an interface to Wannier90. We introduce a set of compact SSG international symbols by combining non-crystallographic point groups with the 230 crystallographic space groups. The program first identifies all SSG operations and determines the SSG international symbol for a given magnetic system. It then generates the SSG character tables of little groups at any point. Finally, it computes the traces of matrix presentations of SSG operations and assigns irreducible corepresentation labels to magnetic energy bands. The program is not only timely but also essential for advancing research on the study of magnons, altermagnetism, magnetic topology, and novel high-degeneracy excitations in SSG systems.

Paper Structure

This paper contains 26 sections, 26 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Basic concepts of spin space groups and coirreps
  3. Spin space groups and international symbols
  4. Coirreps of spin space groups
  5. Traces of matrix presentations of SSG operations
  6. Plane-wave basis
  7. Localized Wannier basis
  8. Implementations and Features
  9. Reading the structure and magnetic moments
  10. Finding SSG operations and international symbol
  11. Character tables at high-symmetry k points
  12. Obtaining the SSG k-little group
  13. Generating the character table of the k-little group
  14. Obtaining compatibility relations
  15. Computing the coirreps of magnetic energy bands
  16. ...and 11 more sections

Figures (7)

  • Figure 1: Workflow of IRSSG for spin space groups.
  • Figure 2: (a) Magnetic crystal structure of Mn$_3$Sn with coplanar configuration. (b) The modified POSCAR.
  • Figure 3: Screenshot of 'ssg.out'.
  • Figure 4: (a) Magnetic energy bands of Mn$_3$Sn with a type-II configuration. (b) Screenshot of 'chart.dat'.
  • Figure 5: The band coirreps determined by IRSSG, which are output in 'irssg.out'. The first three columns give band indices, degeneracies, and energies (without subtracting the Fermi level $E_F$), respectively. Then the band characters of each unitary operation and the band coirreps are given in the following lines. Panels (a)–(c) correspond to the two DT points (two dash-dotted lines in Fig. \ref{['Mn3Snbands']}(a)) and the K point.
  • ...and 2 more figures