Rotation-reversal symmetries in crystals and handed structures

Venkatraman Gopalan, Daniel B. Litvin

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


Symmetry is a powerful framework to perceive and predict the physical world. The structure of materials is 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-Â or left-handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new roto-trade; symmetries predict new forms for rotog-trade; properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They enable a 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 materials and structures with static rotations.

Original languageEnglish (US)
Pages (from-to)376-381
Number of pages6
JournalNature Materials
Issue number5
StatePublished - May 2011

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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