Chiral Structures and Phases of Polar Vortices Revealed Using a Polarization-Constrained Phase-Field Model

Chirality is a key feature of the polar vortex structures in ferroelectric superlattices and could potentially form the basis for next-generation functional devices. While conventional phase-field models have struggled to capture chiral features, here we demonstrate that applying a Lagrangian multiplier to fix the polarization magnitude enables the formation of Bloch-type chiral vortices. Simulations reveal nonzero axial components and helicity of the polarization vectors without requiring additional free energy terms. Two distinct chiral phases emerge depending on the polarization magnitude, which varies with temperature and layer thickness. The axial component and helicity distributions depend strongly on strain-polarization coupling. This minimal extension of the conventional model successfully reproduces key chiral features and provides a practical framework for studying the ferroelectric chirality. The approach opens new avenues for the design of chiral structure-based ferroelectric devices with enhanced functionality.