Symmetry of antiferroelectric crystals crystallized in polar point groups

Symmetry is an essential concept in physics, chemistry and materials science. Comprehensive, authoritative and accessible symmetry theory can provide a strong impetus for the development of related materials science. Through the sustained efforts of physicists and crystallographers, researchers have mastered the relationship between structural symmetry and ferroelectricity, which demands crystallization in the 10 polar point groups. However, the symmetry requirement for antiferroelectricity is still ambiguous, and polar crystals possessing antiferroelectricity seem contradictory. This work systematically and comprehensively studies the transformation of dipole moments under symmetry operations, using accessible geometric methods and group theory. The results indicate crystals that crystallize in polar point groups 2 (C (2)), m (C (1h)), mm2 (C (2v)), 4 (C (4)), 4mm (C (4v)), 3m (C (3v)), 6 (C (6)) and 6mm (C (6v)) also possess anti-polar structure and are capable of Kittel-type antiferroelectricity. The anti-polar direction of each point group is also highlighted, which could provide a straightforward guide for antiferroelectric property measurement. Like ferroelectric crystals, antiferroelectric crystals belonging to polar point groups have great potential to become a family of important multifunctional electroactive and optical materials. This contribution refines antiferroelectric theory, will help facilitate and stimulate the discovery and rational design of novel antiferroelectric crystals, and enrich the potential functional applications of antiferroelectric materials.