Double antisymmetry in magnetic structures

This work follows from the recent introduction of the rotation-reversal operation intended to be analogous to the time-reversal operation used to describe the symmetry of magnetic structures. As a second independent antisymmetry operation, this operation "doubles" the antisymmetry of the magnetic space groups, hence the term double antisymmetry. Supposing the consideration of both rotation-reversal and time-reversal symmetry, it was found that there are 17,803 types of symmetry that a crystal could exhibit; the 1,651 magnetic space group types being a subset of these, just as the 230 crystallographic space group types are a subset of the magnetic space group types. In addition to discussing the methods applied to determine these types, describing their properties, and listing their symmetry diagrams (available online), the implications for symmetry constraints in magnetic structure determination will be explored.

The 17,803 types of double antisymmetry space groups

"Double antisymmetry, as a type of color symmetry, refers to the consideration of two independent color-reversing operations. We found that there are 17,803 types of double antisymmetry space groups. The ""types"" of double antisymmetry space groups being the proper affine equivalence classes thereof, i.e. if two groups differ only by changes in origin, lattice constants, and angles then they are considered the same type of group, just as with the 230 types of crystallographic space groups. The significance of listing the types of double antisymmetry space groups is that it gives all possible symmetries of a crystal when two independent antisymmetries are considered in conjunction with the conventional 3D Euclidean space symmetry. Examples from our listing of their properties and symmetry diagrams (available online) will be given."