The program BNS2OG
Given a set of generators of a magnetic space group in an arbitrary basis in the BNS or OG setting, this program:
Identifies the group and gives the transformation matrices to the standard or reference (default) BNS and OG settings.
Gives the set of symmetry operations in a "reasonable" basis for the description of the magnetic group in the other setting (OG when the set operations are given in the BNS setting and viceversa). It tries to keep the description in the second setting as close as possible to the one given in the first setting, i.e., it tries to keep the a, b and c basis vectors parallel to the original ones, or it tries to keep a relation between both basis similar to the relation between the two basis of the standard BNS and OG settings.
It gives an alternative second description in the OG using:
- The rotational operations (one symmetry operation for each rotational element) of the space group defined by the atomic positions with -1 or +1 added, when time reversal is included or not, respectively, in the symmetry operation.
- The set of centering operations of the space group of the atomic positions (mod 1).
- A propagation wave-vector k which satisfies 2k=K, where K belongs to the reciprocal lattice to the lattice of translations of the atomic positions.
In this alternative description, the sets of translations and antitranslations of the magnetic moments are determined if we take into account that a translation t of the lattice of translations of the atomic positions is kept as a translation of the magnetic moments when the following relation is fulfilled:
and it remains as an antitranslation when