ATOMS uses several tools for description and depiction of magnetic structures, loosely gathered in the "Shubnikov" tab.
These tools include 1) constant vector orientation for all atoms in a site; 2) full Shubnikov symmetry in that the vectors themselves obey the full specified symmetry; 3) Shubnikov symmetry with vector orientations remaining constant except for inversion; and 3) lattice inversion or magnetic supercells independent of Shubnikov symmetry.
Magnetic or other Shubnikov symmetry may involve entries in three different places: 1) The Space Group from Table symmetry option, including the Shubnikov Tab (this dialog); 2) The Atomic Vectors dialog (Input1 menu), to set the display parameters of the vectors; and 3) the Revise Atom dialog, Vector Tab for individual input atoms, to set the orientation of the vectors on the atoms.
In the upper part of this dialog, the methods of Display and Application of the Shubnikov symmetry are selected.
Display:
1) Labels +/-. In this mode, only the two "colors", signified by the +/- symbols, are shown. Select the size and other properties of the symbols with the dialog called up by the Labels button. Caution : this option may not be suitable for showing Shubnikov magnetic symmetry. Whether or not an atomic vector is reversed or inverted by the combination of ordinary and Shubnikov symmetry depends on the orientation of that vector with respect to the symmetry operator. Most published diagrams of magnetic structure using black and white or + and - atoms are not actually showing the Shubnikov inversions, they are showing symbolically the reversals of spin vectors which are typically in special orientations. If you want to show arbitrary black/white inversion which does not conform to Shubnikov symmetry, you can simple draw up a normal structure, convert Generated to Input (Transform menu) and recolor individual atoms as desired.
2) Vectors - reversal only. In this mode, each input atom has a vector, but the orientation is constant except that the direction may be reversed by the Shubnikov operators. This is not what most workers seem to understand by Shubnikov symmetry applied to atomic spin vectors, but it can be useful in illustrating many magnetic structures or in non-magnetic applications. Especially, it can be used to align all atoms in a particular site in the same direction, regardless of space-group symmetry. To do this, you should also uncheck the Shubnikov box in the Space-Group Symmetry: Basic Tab. Virtually any commensurate magnetic structure can then be illustrated by converting Generated to Input (Transform menu) and reversing or otherwise reorienting the vectors manually. When in the Input=generated mode, clicking on a magnetic atom brings up a dialog which has a button for vector reversal or inversion.
3) Vectors - full symmetry. In this mode, the orientation of the vector on each generated atom is subject to all symmetry operations, both standard and Shubnikov reversal.
Application :
1) Magnetic. Shubnikov inversion is considered to apply to the spin or electric current loop of a magnetic atom, rather than directly to the vector which shows the magnetic direction. This means that improper operations, including a center of inversion, planes of symmetry and improper (bar) axes, result in inversion or reversal of the magnetic spin vector when the operation is not primed or Shubnikov, and no inversion when the operation is primed or Shubnikov. Of course, the resulting spin-vector orientation depends also on the orientation of the spin with respect to the symmetry operator - when the vector is parallel to an axis or plane the result is completely different from when it is perpendicular.
2) Dipole or Black/White. In this case the inversions are applied directly to the vectors, not to the spin or electric current loops. Thus improper operations result in no inversion or reversal of the vector when the operation is not primed, and inversion when the operation is primed. This type of symmetry could be applied to atomic dipoles, or to displacements, for example.
See the table below for the various combinations of Display and Application.
Set the overall properties of atomic vectors with the Vectors dialog called up by the Vectors button; set the orientation of the vector for each input atom in the Revise Atom: Vector Tab. Whether each input atom has a Shubnikov reversal at all is also set in the Revise Atom: Basic Tab. In general, not every input atom is Shubnikov or even can be Shubnikov in display modes 1) and 3). The orientation of vectors in special positions may be restricted. Black-white reversal itself may be forbidden in some special positions. Such positions should be identified during the calculation and marked as non-Shubnikov.
Shubnikov Operators. This section of the dialog summarizes the information obtained from the Shubnikov symbol in the Basic Tab. The possibilities for the Shubnikov lattice type or Lattice centering are lower-case a, b, or c, indicating translation reversal in the respective axis direction, or S, indicating reversal on all three directions; or upper-case A, B, or C indicating a Shubnikov centering of the respective faces, or I, indicating Shubnikov body centering.
For non-translational Shubnikov symmetry, the possibilities are Inversion, and either Rotation parallel to, or Reflection perpendicular to any of the three axis directions. If present, rotation and reflection are indicated by capital letters A, B and/or C. The face diagonal [110] direction, indicated by AB, is also possible in high-symmetry crystals. The body diagonal [111] direction is not a possible Shubnikov operator orientation as it can only have a three-fold axis.
Note that there is little checking for self-consistency of Shubnikov operators. The user is responsible for entering a valid Shubnikov space group.
Table showing possibilities for Display and Application of Shubnikov symmetry
+/-
Reversal Only
Full Symmetry
Magnetic
bc
bc
abc
Dipole
bd
bd
abd
a) Operate on vector with ordinary space-group symmetry
b) Proper operators (lattice and non-bar axes) - reverse if primed, do not reverse if unprimed
c) Improper operators (inversion, reflection, bar axes) - reverse if unprimed, do not reverse if primed
d) Improper operators (inversion, reflection, bar axes) - do not reverse if unprimed, reverse if primed
Reverse means to change vector direction by 180 degrees, or to change + to - or vice-versa. The ordinary space-group symmetry operations are always applied to the positions of the atoms.
Lattice Inversions or Magnetic Supercell. This option is not actually part of Shubnikov symmetry, but it offers a simple means of describing many magnetic structures, either by itself or in combination with Shubnikov operators, often without changing the unit cell and overall symmetry from what describes the non-magnetic structure.
Checking one of the boxes causes all magnetic vectors to reverse with each translation on that axis. This normally results in a doubled magnetic axis or cell edge in that direction. When more than one lattice inversion is selected, the operations are applied successively. For example if there is inversion on a and b axes, the 100 and 010 unit cells have inversion, but the 110 unit cell does not.
If the unit cell is non-primitive you can use inversion on either the Bravais axes or the primitive axes, but not both.
Note that the Default Unit Cell boundary option uses the non-magnetic Bravais axes, not the doubled magnetic axes. To show the reversals adequately it may be necessary to select the -1 to 1 inclusive option in the Default Unit Cell boundary option, or to use the Translation Limits boundary option.
This option is definitely not the same as using non-primitive Shubnikov lattices, and is apparently equivalent to specifying a magnetic "wave vector". Compare the samples FCCMAG, FCCMAGR, and FCCFULL_II for different ways of showing Type II FCC (MnO) magnetic structure - the most concise is FCCFULL_II which uses inversions on all three primitive (face-centering) lattice translations, with the full Fm3m X-ray symmetry of MnO.
See also the CRCL2MAGD sample, which uses magnetic lattice inversions on two axes in combination with a Shubnikov space group Pnnm' which is simply related to the non-magnetic group Pnnm.
Irreducible Representations. ATOMS could in principle be programmed to use the method of description of magnetic structures by means of the irreducible representations of space groups, as pioneered by Bertaut and others and described in the book by Izyumov, Naish and Ozerov (Neutron Diffraction of Magnetic Materials). This has obvious theoretical advantages over the ad hoc methods now used in ATOMS, but there are practical difficulties in that the representations are numbered in an arbitrary way and and must refer to an essentially arbitrary order of symmetry operators. A description of this type can be concise but it may convey little without reference to a standard compilation such as that of Kovalev.
If there is sufficient interest, using irreducible representations might be attempted in ATOMS.