Rotation-reversal symmetries in crystals and handed structures

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

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
Volume10
Issue number5
DOIs
StatePublished - Jan 1 2011

Fingerprint

Crystal symmetry
Crystals
symmetry
crystals
handedness
perovskites
helices
Polarization
inversions
polarization

All Science Journal Classification (ASJC) codes

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

Cite this

@article{567b31f5a1cf4b7ea48891b42511ed8b,
title = "Rotation-reversal symmetries in crystals and handed structures",
abstract = "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-{\^A} 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.",
author = "Venkatraman Gopalan and Litvin, {Daniel Bernard}",
year = "2011",
month = "1",
day = "1",
doi = "10.1038/nmat2987",
language = "English (US)",
volume = "10",
pages = "376--381",
journal = "Nature Materials",
issn = "1476-1122",
publisher = "Nature Publishing Group",
number = "5",

}

Rotation-reversal symmetries in crystals and handed structures. / Gopalan, Venkatraman; Litvin, Daniel Bernard.

In: Nature Materials, Vol. 10, No. 5, 01.01.2011, p. 376-381.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Rotation-reversal symmetries in crystals and handed structures

AU - Gopalan, Venkatraman

AU - Litvin, Daniel Bernard

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79954992070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954992070&partnerID=8YFLogxK

U2 - 10.1038/nmat2987

DO - 10.1038/nmat2987

M3 - Article

VL - 10

SP - 376

EP - 381

JO - Nature Materials

JF - Nature Materials

SN - 1476-1122

IS - 5

ER -