IRSSG

An open-source software package for spin space groups

We develop package IRSSG to obtain the irreps of spin space groups (SSG) for magnetic materials in the absence of SOC, to analyze the band topology and symmetry of energy bands. It first finds all SSG operators and the SSG international notations for any given magnetic crystal strucute. Next, it generates the character tables of SSG little groups for high-symmetry k points. Finally, it computes the traces of matrix presentations of SSG operators and assigns the corresponding coirrep labels for magnetic energy bands.

By providing modified POSCAR, where magnetic moments follow the inner atomic positions, IRSSG will return SSG type, spin only group S0, subgroup G0, and the international notation, by excuting the following command $ irssg -ssg [ -c $filename ] [ --tolerance $dl ] [ --magtolerance $dm ] > ssg.out

where filename is the name of POSCAR file, dl is the real-space symmetry tolerance (in units of length), and dm is the magnetic moment matching tolerance used in the magnetic symmetry search (in the unit of μB). Meanwhile, a file ssg.data will be output, which is used to compute the band characters and coreps under plane-wave basis or Wannier basis. To obtain the band characters and coreps of bands generated by VASP, the user should provide three input files before running IRSSG: OUTCAR, WAVECAR and ssg.data. The former two input files are generated by VASP. After executing IRSSG with ssg.data output and running VASP with WAVECAR and OUTCAR output, IRSSG returns the character table of the SSG’s coirreps on the k-point interval [a, b], together with the band characters and coreps for the band range [m, n], by executing the following command $ 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 corep. In addition, to obtain the band characters and coreps of bands under Wannier basis, the user should provide three input files before running IRSSG: wannier90 hr.dat, tbbox.in and ssg.data. tbbox.in supports an optional soc = T/F flag (default false) to indicate SOC. IRSSG returns the character table of the SSG’s coirreps, together with the band characters and coreps, by executing the following command $ irssg -wann [ -nk $a $b ] [ -nb $m $n ] [ -tolE $dE ] > irssg.out

API

• load_ssg_list() — load the bundled SSG dataset list
• identify_SG_lattice(gid) — returns (lattice_symbol, prim_vec), use prim_vec as primitive basis (columns)
• findAllOp(cell_new, tol=..., tolm=1e-4) — compute symmetry operations; returns ops_dic
• load_one_ssg(ssgnum_in) — load a single SSG entry; returns ssgdic
• pos2abr(cell_prim) — convert to A/B/R centered setting; returns (cell_pos2abr, shift)
• generate_irssg_in(...) — generate IRSSG input files from a cell/arguments
• get_SSG_label(ssgnum, ssg_list) — get formatted SSG label for display