Domain switching dynamics in topological antiferroelectric vortex domains

Hexagonal manganites can exhibit intriguing ferroelectric (FE) and partially undistorted antiferroelectric (PUA) ${Z}_{6}$-vortex domain patterns, which are dual to each other. Due to the same origin, it can be expected that the two real-space topological structures will behave the same way in terms of nonelectric properties such as domain topology and scaling of vortex density. However, their electric properties would be very different from each other, while these differences are rarely understood due to the absence of investigation on PUA ${Z}_{6}$-vortex domain patterns. In this work, we study the response of the PUA $P\text{\ensuremath{-}}3c1$ structure to external electric fields and the switching dynamics of PUA ${Z}_{6}$-vortex domain patterns by combining Landau theory and phase-field simulations. We find that an electric field along the $c$ axis can tune the trimerizing tilting angle of the ${\mathrm{MnO}}_{5}$ trigonal bipyramids in PUA $P\text{\ensuremath{-}}3c1$ structure while no such effect is present in the FE $P{6}_{3}cm$ structure. As a result, a continuous phase transition sequence $P\text{\ensuremath{-}}3c1\ensuremath{\rightarrow}P3c1\ensuremath{\rightarrow}P{6}_{3}cm$ can be induced. For both the PUA ${Z}_{6}$-vortex domain pattern and the single PUA domain, the variation of the total polarization with a sinusoidal electric field manifests as a double-hysteresis loop. We find out that this is because the transition from $P{6}_{3}cm$ back to $P3c1$ is a first-order transition. The switching dynamics of PUA ${Z}_{6}$-vortex domain patterns is found to be very different from that observed on FE ${Z}_{6}$-vortex domain patterns. Our results advance the understanding of real-space topological structures and suggest that the PUA $P\text{\ensuremath{-}}3c1$ structure may exhibit excellent performance in dielectric energy storage.