Double Antisymmetry and the Rotation-Reversal Space Groups

TL;DR

This paper introduces double antisymmetry space groups incorporating rotation-reversal symmetry, expanding crystallographic symmetry classification and aiding understanding of crystal rotations and magnetic structures.

Contribution

It presents the concept of double antisymmetry space groups, including a comprehensive list, to enhance crystallographic symmetry analysis involving rotation-reversal and time-reversal symmetries.

Findings

Identifies 17,803 double antisymmetry space groups.

Provides a complete listing of these groups in supplemental materials.

Highlights implications for crystal polyhedral rotations and magnetic structures.

Abstract

Rotation-reversal symmetry was recently introduced to generalize the symmetry classification of rigid static rotations in crystals such as tilted octahedra in perovskite structures and tilted tetrahedral in silica structures. This operation has important implications for crystallographic group theory, namely that new symmetry groups are necessary to properly describe observations of rotation-reversal symmetry in crystals. When both rotation-reversal symmetry and time-reversal symmetry are considered in conjunction with space group symmetry, it is found that there are 17,803 types of symmetry, called double antisymmetry, which a crystal structure can exhibit. These symmetry groups have the potential to advance understanding of polyhedral rotations in crystals, the magnetic structure of crystals, and the coupling thereof. The full listing of the double antisymmetry space groups can be found in the supplemental materials of the present work and online at our website: http://sites.psu.edu/gopalan/research/symmetry/