Coexistence of polar and antipolar phases in ferroelectric halide perovskite CsGeBr${}_3$

Recently ferroelectricity has been demonstrated in the family of halide perovskites: CsGeX${}_3$ (X=Cl, Br, I). We develop a first-principles-based computational approach to probe finite-temperature properties of \cgb. Our computations reveal the existence of a dynamic antipolar phase above the Curie temperature. The phase can be stabilized below the Curie temperature through quenching. Furthermore, competition between the polar and antipolar phases results in the formation of rare polar-antipolar domains. We demonstrate that such polar-antipolar domains can result in the formation of unusual polarization fields with head-to-head and tail-to-tail dipole arrangements, which not only offers an explanation for the recent experimental findings but could also lead to the discovery of novel topological polar structures.