New Symmetries in Crystals and Handed Structures

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.

15 Pages, 4 figures, 3 Tables; Fig. 2b has errors

References in corpus (3)

• Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite
• Coexistence of Weak Ferromagnetism and Ferroelectricity in the High Pressure LiNbO3-type Phase of FeTiO3
• Hybrid Improper Ferroelectricity: A Mechanism for Controllable Magnetization-Polarization Coupling

Cited by in corpus (37)

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• Direct measurement of broken time-reversal symmetry in centrosymmetric and non-centrosymmetric atomically thin crystals with nonlinear Kerr rotation
• Intrinsic structural instabilities of domain walls driven by gradient couplings: meandering anferrodistortive-ferroelectric domain walls in BiFeO3