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Keywords:

  • spin groups;
  • quasi-one-dimensional magnets;
  • line groups

Spin line groups describe the symmetries of spin arrangements in quasi-one-dimensional systems. These groups are derived for the first family of line groups. Among them, magnetic groups are singled out as a special case. Spin arrangements generated by the derived groups are first discussed for single-orbit systems and then the conclusions are extended to multi-orbit cases. The results are illustrated by the examples of a CuO2 zigzag chain, a 13C nanotube and the hexaferrite Ba2Mg2Fe12O22. Applications to neutron diffraction and classical ground-state determination are indicated.