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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, or chemical species. 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 described. 

Ferroelectric materials such as barium titanate (BaTiO3) have a wide range of applications in nano scale electronic devices due to their outstanding properties. In this study, we developed an easily extendable atomistic ReaxFF reactive force field for BaTiO3 that can capture both its field- as well as temperature-induced ferroelectric hysteresis and corresponding changes due to surface chemistry and bulk defects. Using our force field, we were able to reproduce and explain a number of experimental observations: (1) existence of a critical thickness of 4.8 nm below which ferroelectricity vanishes in BaTiO3; (2) migration and clustering of oxygen vacancies (OVs) in BaTiO3 and reduction in the polarization and the curie temperature due to the OVs; (3) domain wall interaction with surface chemistry to influence ferroelectric switching and polarization magnitude. This new computational tool opens up a wide range of possibilities for making predictions for realistic ferroelectric interfaces in energy-conversion, electronic and neuromorphic systems.