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HELP of SpGENPOS: General Positions of the Spin Point Groups

  • SPGENPOS provides the list of symmetry operations {U‖R} of a chosen spin point group (SpPG). First, the user must select a parent point group (point group of the R operations in the orbital space) and the type of point group: collinear, coplanar, non-coplanar or a SpPG that results as the direct product of one of the previous groups with a group that contains the identity and the time-reversal (TR) symmetry.

  • Non-coplanar groups. The output gives a single list that includes all the operations.

  • Coplanar groups. The setting is chosen so that the mirror plane of the trivial group is perpendicular to w (the third basis vector in the spin space).
    The output gives a single list that includes all the operations.

  • Collinear groups. The setting of the collinear groups is chosen so that the rotation axis of the trivial group is parallel to w (the third basis vector in the spin space)
    The output contains two lists: the first one shows the operations of the non-trivial SpPG and the second one the operations of the spin-only group. If TR has not been added, it consists of two symmetry operations: a rotation of angle φ around the w axis and a mirror plane that contains the w axis and forms and angle φ with the u direction. If TR has been added, the output includes also the two previous operations multiplied with TR.
  • In all the cases, the operations are given using three formats: (1) the x,y,z,u,v,w form, (2) the U and R matrices in the spin and orbital space, respectively, and (3) the generalized Seitz notation.

k-Subgroupsmag
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