Antisymmetry: Fundamentals and Applications

Abstract

Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review covers the fundamental concepts of antisymmetry, and focuses on four antisymmetries, namely spatial inversion in point groups, time reversal, distortion reversal and wedge reversion. The distinction between classical and quantum mechanical descriptions of time reversal is presented. Applications of these antisymmetries in crystallography, diffraction, determining the form of property tensors, classifying distortion pathways in transition state theory, finding minimum energy pathways, diffusion, magnetic structures and properties, ferroelectric and multiferroic switching, classifying physical properties in arbitrary dimensions, and antisymmetry-protected topological phenomena are presented.

When citing this paper, please use the following: Padmanabhan H, Munro JM, Dabo I, Gopalan V. 2020. Antisymmetry: Fundamentals and Applications. Annu. Rev. Mat. Res.: Submitted. DOI: 10.1146/annurev-matsci-100219-101404

References in corpus (4)

• Topological Insulators with Inversion Symmetry
• First principles study of the multiferroics BiFeO${}_3$, Bi${}_2$FeCrO${}_6$, and BiCrO${}_3$: Structure, polarization, and magnetic ordering temperature
• Electric-field switchable magnetization via the Dzyaloshinskii-Moriya interaction: FeTiO_3 versus BiFeO_3
• A historical introduction to the symmetries of magnetic structures: Part 1. Early quantum theory, neutron powder diffraction and the colored space groups

Cited by in corpus (1)

• Relativistic spacetime crystals