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Hidden Roto Symmetries in Nature Discovered

MRSEC researchers have discovered a missing spatial operation in nature called rotation-reversal symmetry that reverses the sense of all static rotations in a crystal.  Certain minerals, organic crystals or metamaterials are composed of subunits that can exist in two states: clockwise or counter-clockwise rotated.  The symmetry of a crystal lattice helps determine the material’s properties, and certain properties can only exist in lattices with special symmetries.  In perovskite complex oxides, for example,  oxygen cages counter-rotate (see image); these crystals have twice as many new “roto” symmetries as previously recognized  These new symmetries imply new materials properties: lattice rotation coupled to magnetism,  ferroelectricity, multiferroicity, charge ordering, elasticity, and optical.  These properties could be useful in electrical control of magnetism, high-speed transistors based on correlated phenomena and high-temperature actuators.