New Symmetries in Crystals and Handed Structures

TL;DR

This paper introduces new symmetry operations in crystal and structural analysis by recognizing rotation reversal as a distinct symmetry, revealing more complex symmetries in helices, spirals, and antidistorted structures, and predicting novel properties and phenomena.

Contribution

It identifies additional symmetry operations involving rotation reversal, expanding the understanding of structural symmetries in materials with static rotations.

Findings

Many helices and spirals possess combined symmetries with rotation reversal.

Antidistorted perovskites have twice the symmetry elements traditionally recognized.

New roto properties and phenomena, such as multiferroicity, are predicted based on these symmetries.

Abstract

For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and counterclockwise directions as a distinct symmetry operation, here we show that there are many more structural symmetries than are currently recognized in right- or left-handed handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, though a helix or spiral cannot possess conventional mirror or inversion symmetries, they can possess them in combination with the rotation reversal symmetry. Similarly, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new symmetries predict new forms for "roto" properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They also enable symmetry-based search for new phenomena, such as multiferroicity involving a coupling of spins, electric polarization and static rotations. This work is relevant to structure-property relationships in all material structures with static rotations such as minerals, polymers, proteins, and engineered structures.