MAXMAGN - k-maximal magnetic space groups for a given propagation vector and the corresponding magnetic structures
Abbreviated tutorial: download
Extended tutorial: download
MAXMAGN is an interactive program whose main purpose is to provide the possible maximal magnetic symmetries that are compatible with a given parent space group Gp of a paramagnetic phase and a (single) commensurate propagation vector k (in conventional basis). This permits to know the possible maximal symmetries that a commensurate magnetic structure can have, starting from the knowledge of Gp and the k vector detected in the magnetic diffraction pattern. Only 1k magnetic orderings are considered. Optionally, the crystal structure of the paramagnetic phase can be introduced. If so, the magnetic orderings corresponding to each of the possible configurations of maximal magnetic symmetry can be obtained. These magnetic models are given in a cif-type form (mcif file), using Shubnikov magnetic space groups in BNS setting, with explicit indication of the symmetry constraints on the magnetic moments, and the parameters that can be refined in each case.
Most of the determined magnetic structures have a single primary propagation vector (1k structures) and display magnetic orderings that have a maximal symmetry compatible with its propagation vector k (i.e., no magnetic ordering can exist with this propagation vector and with a higher magnetic space group containing the one being observed). MAXMAGN therefore provides the set of magnetic orderings that are most probable for a given propagation vector. For simple vectors this set is very limited, not surpassing 10 in most cases, and being very often 4 or 6. In the exceptional case that these symmetries are too restrictive to explain the observations, MAXMAGN also allows a controlled descent to lower symmetries.
The permitted maximal magnetic symmetries are determined by the program as subgroups of the grey magnetic group Gp1', which represents the magnetic symmetry of the paramagnetic phase. Each of these subgroups should fulfill the condition that it is consistent with the propagation vector (k-vector) observed, and that there is no intermediate magnetic group between it and the paramagnetic space group Gp1' (i.e. supergroup of one and subgroup of the other), which is also consistent with the same k-vector. We shall call these subgroups "k-maximal" subgroups (not to be confused with klassengleiche subgroups), and they represent the set of possible maximal symmetries that a magnetic ordering with this k-vector can have.
MAXMAGN is very efficient for simple k-vectors that imply small multiplications of the magnetic primitive cell with respect to that of the paramagnetic structure. k-vectors with multiplication factors 0, 2, 3, 4 are the most frequent ones, and can be analyzed with this program using reasonable computing times. On the other hand, k-vectors implying large multiplication factors of the magnetic unit cell can be problematic, with the program exhausting the allowed computing time. In these cases, however, the use of a description in terms of Shubnikov magnetic space groups is normally not very useful, and a spin wave description using superspace magnetic groups, which is outside the scope of this program, is usually more appropriate. Thus, the highest multiplication factor accepted by MAXMAGN hash been set to 8, which is far enough for the purpose of the program.
LISTING OF k-MAXIMAL MAGNETIC SUBGROUPS
MAXMAGN first provides a table listing the k-maximal subgroups of Gp1'. The table gives for each subgroup the standard label in BNS setting corresponding to its magnetic space group type and a matrix and a vector, which describe the transformation from the setting of the parent space group Gp (parent setting) to the BNS standard setting of the subgroup. This information is sufficient to define the subset of operations of Gp1' that form the listed subgroup. An optional window (headed with the title general positions) can be clicked to have an explicit listing of the operations of the subgroup both in its standard setting, or in a setting similar to the parent setting, called parent-like setting. The subgroups belonging to the same conjugacy class under the parent group Gp1' represent the symmetries of physically equivalent magnetic domain-related configurations. The table therefore lists only one subgroup per conjugacy class, except if the class contains enantiomorphic pairs of subgroups with different magnetic structure types. In this latter case, one subgroup per each enantiomorphic group type is listed.
The table of subgroups also includes a link to the listing of the systematic absences of magnetic diffraction for each subgroup. This is obtained with MAGNEXT, so they are relevant for unpolarized neutron magnetic diffraction. Also, the button "alternatives (domain-related)" allows the user to choose and use an alternative subgroup belonging to the same conjugacy class (see below). This option permits to obtain all domain-related configurations of a magnetic ordering with one of these k-maximal magnetic symmetries. This option can also be used to choose an alternative standard setting for the subgroup.
Finally, if a particular crystal structure for the paramagnetic phase has been introduced, the alternative models of the magnetic structure complying with each of the listed k-maximal symmetries are available in the column "Magnetic Structure" of this first output page (see below).
Alternative matrices (domain-related)
The option "alternative matrices (domain-related)" for a chosen k-maximal subgroup in the first output table provides a list of all physically equivalent k-maximal subgroups that belong to the same conjugacy class, and have the same propagation vector. The user can then choose any of the listed subgroups as representative of the type of magnetic symmetry given by the listed class of subgroups, instead of the initially listed by the program.
The subgroups are defined by means of a matrix and a vector, which describe the transformation from the setting of the parent space group Gp (parent setting) to the BNS standard setting of the subgroup. This matrix is the one MAXMAGN uses, if the subgroup is chosen, for describing the magnetic structure and its symmetry in a standard setting. This setting transformation can be changed to another equally valid through the button "Alternatives". The listing of alternative transformations is not necessarily complete and the menu "Check your transformation" allows the introduction of a user-designed transformation, that can be used as an alternative. MAXMAGN checks if the introduced transformation is valid for defining one of the subgroups in the list. This option is only necessary, if the magnetic ordering is to be described in a specific standard setting.
Every possible choice of subgroup and corresponding transformation appearing in this option is shown with a "Choose" button. Clicking on this button, the program goes back to the listing of k-maximal subgroups, with the chosen alternative transformation replacing the initial one for defining the k-maximal subgroup. Thus,the same utilities available for the initial listed subgroup become available for the chosen alternative subgroup and/or alternative transformation to a standard setting. These changes are permanent and cumulative.
If initially the specific paramagnetic (parent) structure has been introduced, the Magnetic Structure button for a chosen k-maximal subgroup provides a table describing the resulting magnetic structure constrained under the magnetic symmetry defined by the chosen k-maximal subgroup. The structure is given in the so-called parent-like setting, i. e., a setting that keeps the origin used in the parent structure, and multiplies each of its unit cell parameters up to the period of the magnetic ordering along this direction. A set of symmetry-independent atoms is shown, listing their coordinates, their Wyckoff orbits of symmetry-related positions and moments (if existing), their multiplicity, and the symmetry-forced form of the magnetic moments (for magnetic atoms only). The explicit listing of the Wyckoff orbitspermits to see for each independent magnetic atom the spin correlations of the magnetic moments within its orbit of symmetry-related atoms. In principle, the assigned magnetic space group describes the symmetry constraints and symmetry relations not only of the atomic magnetic moments, but also of the atomic positions, allowing for lattice-spin coupling effects that may affect the positions of all atoms. The listed asymmetric unit can therefore be larger and contain more symmetry-independent atoms than the one of the paramagnetic structure, with some Wyckoff positions being split.
The description of the magnetic structure can be changed to a standard setting for its magnetic symmetry by clicking the appropriate button at the end of the output page. Alternatively, the user can introduce the description of a setting of its own choice (to be valid the chosen unit cell must be a supercell of the magnetic primitive cell).
Specific values (assumed to be given in Bohr magnetons) for the free parameters of the magnetic moments can be introduced in this page, and obtain with them a cif-like file of the resulting model for the magnetic structure to be downloaded. Clicking on the button "Export data to mcif file" a link to download the cif-like file is shown, as well as a non-editable textbox showing the content of the file. Also, for 3D visualization of magnetic structures with Jmol, a button to submit the cif-like file to MVISUALIZE is provided. This cif-like file (with extension .mcif ) follows the format created by the developers of ISOCIF and ISODISTORT and uses magnetic space group symmetry in a systematic and consistent form. These mcif files can be used for a refinement (as a starting model), for graphical purposes, for representation analysis, for generating a full listing of atomic positions and spins within a unit cell (to do ab-initio calculations, for instance), or for any other kind of study. The "mcif" format is supported at present by the programs JANA2006, ISODISTORT, ISOCIF, VESTA, MVISUALIZE and StrConvert. This latter is also a tool in the Bilbao Crystallographic Server, which allows to manipulate, edit and visualize this kind of files.
Finally, the option "Go to a subgroup" can be used to descend to lower subgroups (see below).
"Go to a subgroup" option
MAXMAGN lists k-maximal subgroups. In some cases (not often), magnetic orderings follow less-symmetrical arrangements. The symmetry of these magnetic structures is necessarily given by some subgroup of the k-maximal subgroups listed by MAXMAGN. Therefore, MAXMAGN includes the possibility of descending to subgroups of the listed subgroups by selecting, in the list of general positions, a set of generators of the chosen subgroup. The resulting non-maximal subgroup is then generated, its standard setting identified, and the corresponding systematic absences and magnetic structure are then available, with the possibility of creating a mcif file of the magnetic model, in a similar way as for the k-maximal symmetries.