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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/
Tables of crystallographic properties of double antisymmetry space groups, including symmetry element diagrams, general position diagrams, and positions, with multiplicities, site symmetries, coordinates, spin and roto vectors are presented.
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review covers th
Distortions are ubiquitous in nature. Under perturbations such as stresses, fields, or other changes, a physical system reconfigures by following a path from one state to another; this path, often a collection of atomic trajectories, describes a dist
In chiral magnetic materials, numerous intriguing phenomena such as built in chiral magnetic domain walls (DWs) and skyrmions are generated by the Dzyaloshinskii Moriya interaction (DMI). The DMI also results in asymmetric DW speed under in plane mag
Symmetry principles play a critical role in formulating the fundamental laws of nature, with a large number of symmetry-protected topological states identified in recent studies of quantum materials. As compelling examples, massless Dirac fermions ar