IRSSG

An Open-Source Software Package for Spin Space Sroups

Ref: Zhang, Sheng et al, arXiv:2511.21921 (2025). https://arxiv.org/abs/2511.21821

We develop the package IRSSG to obtain the irreducible (co)representations of spin space groups (SSGs) for magnetic materials in the absence of spin–orbit coupling (SOC), and to analyze the band topology and symmetry of energy bands.

IRSSG

• finds all SSG operators and the SSG international notation for any given magnetic crystal structure,
• generates the character tables of SSG little groups for high-symmetry k-points,
• computes the traces of matrix representations of SSG operators and assigns the corresponding (co-)irrep labels to magnetic energy bands.

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1. SSG detection from POSCAR

By providing a modified POSCAR, where magnetic moments follow the internal atomic positions, IRSSG returns:

• the SSG type,
• the spin-only group (S_0),
• the subgroup (G_0),
• and the SSG international notation,

by executing:

irssg -ssg [-c filename] [--tolerance dl] [--magtolerance dm] > ssg.out

where:

• filename is the name of the POSCAR file,
• dl is the real-space symmetry tolerance (in units of length),
• dm is the magnetic-moment matching tolerance used in the magnetic symmetry search (in units of μB).

At the same time, a file ssg.data is written, which is later used to compute band characters and (co)irreps under plane-wave or Wannier bases.

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2. Plane-wave (VASP) interface

To obtain the band characters and (co)irreps for bands generated by VASP, the user should provide three input files before running IRSSG:

• OUTCAR
• WAVECAR
• ssg.data

The former two are generated by VASP; ssg.data comes from the previous -ssg step.

With ssg.data prepared and a finished VASP calculation (producing WAVECAR and OUTCAR), IRSSG returns:

• the character tables of the SSG coirreps on the k-point interval ([a, b]),
• together with the band characters and (co)irreps for the band index range ([m, n]),

by executing:

irssg -pw [-nk a b] [-nb m n] [-tolE dE] > irssg.out

where:

• dE is the upper bound on the energy difference of the bands associated with a given irreducible representation.

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3. Wannier (tight-binding) interface

To obtain band characters and (co)irreps under a Wannier basis, the user should provide three input files:

• wannier90_hr.dat
• tbbox.in
• ssg.data

IRSSG then returns the character tables of the SSG coirreps, together with the band characters and (co)irreps, by executing:

irssg -wann [-nk a b] [-nb m n] [-tolE dE] > irssg.out

The meanings of a, b, m, n, and dE are the same as in the -pw mode.

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POS2SSG

Similar to POS2MSG, which automatically generates all possible magnetic space groups (MSGs) with the highest symmetry, a minor tool POS2SSG is developed to generate all highest-symmetry magnetic configurations by assigning magnetic moments to all magnetic atoms, each configuration corresponding to a specific SSG number.