Hidden Antipolar Order Parameter and Entangled Néel-Type Charged Domain Walls in Hybrid Improper Ferroelectrics

Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF ${(\mathrm{Ca},\mathrm{Sr})}_{3}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of N\'eel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width N\'eel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.