The program k-SUBGROUPSMAG
Given a space group of a paramagnetic phase (gray group) and a magnetic propagation wave-vector, this program calculates all the posible magnetic space subgroups compatible with the propagation vector.
The output of the program can be chosen to be the list of subgroups or a graph showing the subgroup-tree. In both cases the groups are grouped into conjugacy-classes. More information about the conjugacy-classes and the subgroups can be obtained: members of the conjugacy classes, transformation matrix to a standard or reference (default) setting of every group, lists of general positions, etc... All the groups are given in the BNS setting.
Alternative input data and optional filters for the output.
The program allows different input data sets and different conditions to be fulfilled by the subgroups given in the output. These are the alternative input/output conditions (ordered as in the main page of the program):
- Instead of the space group of the paramagnetic phase (i.e. instead of a gray group), an alternative non-gray group in its standard setting can be chosen.
- The magnetic group (gray or non-gray group) can be given in a non standard BNS setting, introducing a set of generators of the group.
- Possible limitations of the subgroup list. By default, the program calculates all the subgroups compatible with the input data, being the last subgroup (the subgroup with the lowest symmetry) P1( #1.1) or P_{S}1 (#1.3). It is also possible to limit the bottom of the subgroup-tree (or the list of subgroups) giving one of these options:
- Lowest magnetic group to be considered. The number of the group at the bottom of the list/graph should be given. The output (as a list or as a graph) shows all the subgroups of the given group which are also supergroups of the chosen "lowest magnetic group".
- Lowest point group to be considered. The number of the point group at the bottom of the list/graph should be given. The output (as a list or as a graph) shows all the subgroups of the given group which have as point group the given "lowest point group" or a supergroup of this lowest point group.
- Only subgroups of a given crystal system. The output (as a list or as a graph) shows all the subgroups of the given group which belong to the chosen crystal system or which are supergroups of a group of the chosen crystal system.
- Only maximal subgroups. It gives only the maximal subgroups of the given groups which fulfill all the conditions of the input.
- Further limitations considering physical properties of the point groups. The list/graph of the output can be restricted to those magnetic groups whose point group is:
- Centrosymmetric or non-centrosymmetric.
- Polar or non-polar.
- Propagation wave-vector or wave-vectors. By default, the user must introduce a commensurate propagation wave-vector. The options offered by the program are:
- Show the independent vectors of the star. Clicking on this sentence the program will show all the independent wave-vectors of the star of the previously introduced propagation wave-vector (in those stars where -k belongs to the star it is not shown.) One the complete list is shown, the user can choose some vectors of the star or the whole star, as propagation wave-vectors.
- The option More wave-vectors needed allows to introduce as propagation wave-vectors vectors which belong to different stars. This option can be combined with the previous one.
- Checking the box Choose the whole star of the propagation vector(s) the whole set of vectors of the star(s) of the given wave-vectors (with respect to the point group of the given magnetic group) are considered as propagation wave-vectors.
- Instead of a set of propagation wave-vector, a set of basis vectors of the supercell can be given, clicking on Alternatively give the basis vectors of the supercell. Once this option has been chosen, the user must introduce the components of the unit cell vectors of the supercell (in the basis of the setting chosen for the given group at the beginning) and specify whether the supercell is centered or not.
- Optional: non-magnetic modulation wave-vector. In some cases, the magnetic order is accompanied by a non-magnetic distortion defined by a modulation wave-vector or a set of modulation wave-vectors. One can introduce this vector clicking on Optionally give also non-magnetic modulation wave-vectors. The same options as for the (magnetic) propagation wave-vectors will be available.
- Selecting the box Include the subgroups compatible with intermediate cells. the output shows all the subgroups compatible with intermediate unit cells (all intermediate unit cells between the unit cell of the given group and the supercell or the supercell determined by the introduced modulation wave-vectors.)
- Wyckoff positions of the magnetic atoms. The list or graph of subgroups can be further refined when the magnetic atoms occupy special positions in the unit cell. Some, in general, compatible subgroups can be incompatible provided that all magnetic atoms should have a non-zero magnetic moment. Clicking on Wyckoff, the wyckoff positions of the magnetic atoms (and the positions of the non-magnetic atoms if a non-magnetic modulation vector has also been introduced) can be given. In this case, the program shows only the subgroups compatible with a non-zero magnetic moment for all the magnetic atoms.
- Active irreducible representations (irreps). Clicking on Representations, the program shows the list or magnetic irreps corresponding to the given propagation wave-vectors (and the non-magnetic irreps if a non-magnetic modulation vector has also been introduced). The user can check some of those irreps. The program will show only those subgroups that come from magnetic orderings
which correspond to these magnetic irreps. If non-magnetic modulation wave-vectors have also been introduced an a set of non-magnetic irreps chosen, the output will include groups which correspond to distortions coming from these irreps. When the option Wyckoff positions of the magnetic atoms has been previously used, the clickable irreps are only those compatible with the given wyckoff positions.
Alternative output.
By default, the program gives the list or graph of all the subgroups compatible with the given conditions. But, when the option Wyckoff positions of the magnetic atoms has been chosen, after the first (default) output, these two outputs can also been obtained:
- Subgroups compatible with, at least, one magnetic atom with a non-cero magnetic moment. This option is less restrictive than the default option.
- Subgroups compatible with sets of co-linear magnetic moments for all the magnetic atoms. This option is more restrictive than the default option.
If thew option Representations has been chosen, the default output gives the subgroups compatible with all the chosen representations. Once this first output is shown, it is possible to get the subgroups compatible with at least one chosen irrep.