Noncollinear antiferroelectricity with C3 polarization rotation: Ferroic domain configurations

The macroscopic Landau's theory implies the analogy between traditional (anti)ferroelectricity and (anti)ferromagnetism, and mainly considers spatial collinear configurations of ferroic orders. Expanding the rationale, noncollinear ferromagnetism also has an electric counterpart, termed as noncollinear ferroelectricity. However, for a long time, noncollinear antiferromagnetism loses its corresponding counterpart, i.e., noncollinear antiferroelectricity. Herein, we designed an intrinsic noncollinear antiferroelectricity as well as its dual noncollinear ferroelectricity in two-dimensional ${\mathrm{SiS}}_{2}$, induced by a mirror symmetry operation of tetrahedral antipolar tilting through its rotation. We found an additional coupling factor $\ensuremath{\varphi}$, pertaining to the antipolar displacement mode, which induces the ``super-hybrid improper'' (anti)ferroelectricity with sixfold-degenerated variants and endows the in-plane polarization with a new ${C}_{3}$ rotational behavior. This indicates an intrinsic ${Z}_{3}$ vortice in the ${Z}_{6}\ifmmode\times\else\texttimes\fi{}{Z}_{1}$ domains. Our results complete the Landau's one-to-one correspondence scenario, broaden the horizon of ferroic orders for noncollinearity, and give an in-depth insight into the hybrid coupling mechanism.