This directory or folder contains several files illustrating the capabilities of ATOMS for displaying atomic vectors.

MAGNETIC STRUCTURES

Note that for magnetic structures you probably need to enter information in three separate dialogs, all in the Input1 menu.  For more details, see the on-screen Help for each dialog  (Help button or F1 key in Windows).

1) Symmetry - Space Group.  If you are using Shubnikov symmetry, in the Basic Tab, enter either the Hermann-Maughin (H-M) or Hall symbol with magnetic extensions, and check the Shubnikov box.  In the Shubnikov tab, select the vector Display and Application modes (illustrations of these below).

2) Atomic Vectors.  This sets the display properties of the vectors themselves.

3) Atoms/Revise Atom.  In the Vector tab, set the orientation using crystal-system vector indices and the length, which can be absolute since there is a scale factor in the Atomic Vectors dialog.  If there is no vector tab, go back to step 2 to allocate memory for vectors.

ATOMS  is capable of  illustrating any commensurate magnetic structure, i.e. one in which there is a definite magnetic unit cell, whether or not that cell is the same as the X-ray unit cell.  It is not restricted to structures with Shubnikov symmetry, nor is it even restricted to using Shubnikov symmetry as it is commonly understood.  Consider the following examples.

A)  Full Vector Shubnikov symmetry -  GARMAG.STR
This is an observed ferrimagnetic structure of a chromium garnet, in which the 16(a) site contains magnetic chromium atoms with magnetic vectors either [001] or [00-1].  The magnetic unit cell is the same as the X-ray cell, and the Shubnikov space group, I41'/ac'd, keeps the same multiplicity for the Cr atoms as the X-ray space group, Ia3d.  In the Magnetic Tab of the Space-Group symmetry dialog in ATOM, under Display mode we must select  Vectors - full symmetry, and under Application select Magnetic.

The various permutations of the file P2_M.STR demonstrate all the Shubnikov black-and-white space groups derived from the standard space group P2/m.  These use an atom in a general position and a [001] magnetic vector.

B)  Reversal Shubnikov symmetry only - FCCMAG.STR
MnO and several other ferrimagnets have the NaCl structure in space group Fm3m.  The magnetic Mn atom is at 0,0,0.  The magnetic unit cell is double the x-ray cell.  We can use Shubnikov group Fsm3m, and we need to add another Mn atom, at 0, 1/4, 1/4 (there are also two oxygen atoms, not shown).  The key step in this structure is in the Shubnikov Tab of the Space-Group symmetry dialog in ATOMS - under Display mode we must select  Vectors - reversal only.  This means that the ordinary space-group rotational matrices are not applied to the orientation of the spin vector - the orientation of the vectors for atoms in a given site remain constant, EXCEPT for 180 degree reversal or inversion according to Shubnikov black/white symmetry.  The only black/white operation in this case is lattice translation.  If we give both Mn atoms the same spin vector orientation, the result is layers on (111) with spins in opposite directions.  The spin vector orientation in this case is [011] so that the vectors lie in the (111) planes, but as far as the symmetry is concerned there is no restriction on orientation.  This is a perfectly valid application of Shubnikov symmetry, provided we restrict it only to the spin reversals and not the orientations.  This description preserves the true magnetic Bravais unit cell

C)  Lattice inversion only - FCCMAGR.STR, FCCFULL_I, FCCFULL_II
Using the lattice inversion flags in the Shubnikov Tab of the Space-Group symmetry dialog allows preservation of the true crystallographic unit cell in many cases.  
FCCMAGR - true magnetic Shubnikov cell. In MnO (same magnetic structure as B) the true cell is the primitive rhombohedral cell with vectors (1/2,1/2,0), (1/2,0,1/2), (0,1/2,1/2), among other possibilities, in the Bravais cubic cell.  The original cubic MnO structure can be converted from cubic face-centered to rhombohedral with the utility program Cryscon (www.shapesoftware.com)
FCCFULL_I and FCCFULL_II - Full X-ray symmetry with inversion on primitive (non-Bravais.  These two examples use the full X-ray symmetry of the MnO structure, but have lattice inversions on two primitive axes in FCCFULL_I (type I magnetic structure) resulting in tetragonal symmetry, and on three axes in FCCFULL_II (type II, same as MnO above), resulting in trigonal symmetry.  This symmetry refers to the +/- or reversal state of the magnetic atoms only - full magnetic symmetry including vectors depends on their orientation and may be lower.  The option "Reversal only" (or +-) in the Shubnikov tab of the Space Group symmetry option in ATOMS must be selected if full X-ray symmetry is used.   

D) Reversal Shubnikov symmetry only - CRCL2MAG.str
CrCl2 has the rutile structure, with symmetry reduced from P42/mnm to Pnnm.  In the magnetic structure, both b and c are magnetic inversion directions, which gives a Shubnikov lattice which can be described either as Ab or Ac.  The resulting Shubnikov group is Ab 1 1 2/m (CRCL2MAG) or Ac 1 1 2/m (CRCL2MAGB), again ignoring tranformation of the vector direction by the ordinary space-group rotations, but including the Shubnikov inversions.   An additional pair of Cr and Cl atoms is required, with spin of the Cr opposite the original one.  For special vector orientations other symmetry may be possible, but this description is independent of orientation.  We can also use Pc 21/b 1 1 (CRCL2MAGC) which has a smaller cell volume. In this cell the spin layers are parallel to a unit-cell face - they are parallel to (011) in the original cell.

E) Reversal Shubnikov symmetry plus lattice inversion - CRCL2MAGD.STR
In this case we preserve the original number of atoms, the crystallographic unit cell and conventional space group, but use Shubnikov group Pnnm' (spin reversal only) to give a spin reversal to the central Cr atom, and spin lattice inversions on b and c to give the magnetic unit cell.  This is actually about as concise a description as possible for this structure.

F) Ordinary Space Group symmetry plus constant vectors - SPINMAG.STR
In magnetite and several other magnetic spinels (space group Fd3m), the spins of the atoms in 8(b) are all parallel, and opposite to those of the atoms in 16(c).  In this case we do not need to use any Shubnikov symmetry at all, just assign opposite vectors to the two atoms in the conventional space group, and select "Vectors - reversal only" in the Shubnikov Tab of the Space-Group symmetry dialog.  It is interesting that the antiparallelism of the two sites (b) and (c) is an intrinsic part of this magnetic structure, but  apparently can not be described by symmetry.  This description of the magnetic structure thus appears to be as complete as it is possible to be.

G) Quasi-arbitrary vector directions.  It may be that neither full-vector Shubnikov symmetry nor inversion only is sufficient to describe a structure.  In this case, it is easy to use one or the other of these approaches to provide a starting point, and then to invert or otherwise reorient individual vectors by hand.  To do this, after generating the starting structure with vectors on all magnetic atoms as closely oriented as possible, choose the Generated to Input conversion in the Transform menu.  After this conversion, when you click on an atom with the mouse the resulting dialog has a button for 180 degree reversal or inversion of the vector.  There is also a button which calls up the Revise Atom dialog in case it is necessary to change the vector orientation.

The subfolder FCCMagnetic in the folder Vector reproduces six different types of ordering the in the cubic FCC MnO structure, as shown by Izyumov et al. p. 274.  Starting from a a base cell with no symmetry and 4 magnetic atoms, the different variations were obtained by 1) inverting the spins by clicking atoms on screen; and 1) setting the lattice inversions in the Shubnikov tab (Space-Group Symmetry).

NON-MAGNETIC SHUBNIKOV SYMMETRY

Shubnikov black/white reversal is considered to apply to the spin or electric current loop of an atom rather than the vector which represents the axis of spin.  This means that improper symmetry operations, including centers of inversion, mirror plane and bar axes, reverse the magnetic vector if they are primed or Shubnikov and do not reverse it if they are non-primed.  If the reversal is considered to apply to simple vector properties such as electric dipole of an atom, displacements etc. this behavior is reversed.  Proper rotation axes and lattice translations always reverse the vector direction if they are primed, although a 2-fold rotation axis may itself reverse the direction if the vector is perpendicular to the axis, giving no net change.  These two types of behavior of the improper operators may be selected in ATOMS with the Application group in the Shubnikov Tab of the Space-Group symmetry dialog.

IRREDUCIBLE REPRESENTATIONS AND MAGNETIC STRUCTURES

Irreducible representations of the space groups provide a complete and rigorous method of describing the symmetry of magnetic structures (Izyumov, Naish and Ozerov, Neutron Diffraction of Magnetic Materials, published in English by Plenum, 1991).  This method may be implemented in ATOMS in the future, depending on interest.  However, such descriptions are often not as readily understandable as more ad hoc descriptions such as those above because the representations are assigned arbitrary numbers, and the coefficients of the representations must refer to a particular order of the symmetry matrices

USING BLACK AND WHITE OR + AND - TO REPRESENT MAGNETIC STRUCTURE.

ATOMS has an option to display Shubnikov symmetry using + and - symbols on the atoms which is equivalent to using two colors.  However, using these symbols to try to describe magnetic symmetry can be very misleading and/or frustrating.  There are many illustrations of magnetic structure in the literature which use black and white atoms, but even when the structure conforms to a Shubnikov space group these two colors often do NOT represent Shubnikov inversion, rather special vector orientations which are the result of a combination of conventional and Shubnikov symmetry operations.  A magnetic vector may be completely inverted or not changed in direction at all by proper symmetry operators (non-bar axes) or improper operators (mirror planes and bar axes), whether the operator in question is primed (Shubnikov) or not.  This depends on the orientation of the vector with respect to the symmetry operator  (the behavior of lattice translations and inversion centers is constant). 

Although the +/- symbols are thus not recommended for general illustration of  Shubnikov  magnetic symmetry they can be used in special cases and for other types of Shubnikov structures.   ATOMS does not have an option for arbitrary reversal of the +/- symbols, but if necessary you can use actual color.   After carrying out the Generated to Input conversion in the Transform menu, you can change the color of individual atoms.

.MOT file from the VIBRATZ (or VIBRAT) program - DIOP.MOT

The VIBRATZ program (www.shapesoftware.com) will calculate all the optical vibrational frequencies and atomic displacements therein for any molecular or crystal structure.   It writes special .MOT files giving atomic displacements; these files were originally used in some simple DOS programs for plotting the structures and displacements.  

Whenever you read in a .MOT file, using the Import Files option in the File menu, ATOMS will write a special .MDS file with information on each vibrational mode.  You can select the different modes with the Vibrational Modes option in the Input1 menu.  You must then save the .STR file as usual.  When you re-read the .STR file, only the vibrational mode which was selected when the .STR file was saved will be shown.  To select other modes, you use the Vibrational Modes option (Input1 menu).

The properties of the vectors representing the atomic displacements are set in the Atomic Vectors dialog in the Input1 menu.  The symmetry of the drawings made from the .MOT files is always "No symmetry" and there is no need to modify it.  The components of the vectors on each atom can be seen in the Vector Tab of the Revise Atom dialog, but there should be no reason to change these - adjust the overall scaling (length) of the vectors with the Atomic vectors dialog.

