%0 Journal Article
%K competition
%K simulation
%K Polarization
%K ferroelectricity
%K Article
%K Vortex flow
%K Phase-field simulation
%K Ferroelectric superlattice
%K Superconducting materials
%K Topology
%K Neodymium compounds
%K Crystal lattices
%K Geometric length
%K Polar vortex
%K Topological structure
%A Z Hong
%A A.R Damodaran
%A F Xue
%A S.-L Hsu
%A J Britson
%A A.K Yadav
%A C.T Nelson
%A J.-J Wang
%A J.F Scott
%A L.W Martin
%A Ramamoorthy Ramesh
%A L.-Q Chen
%B Nano Letters
%D 2017
%G eng
%I American Chemical Society
%P 2246-2252
%R 10.1021/acs.nanolett.6b04875
%T Stability of Polar Vortex Lattice in Ferroelectric Superlattices
%V 17
%X A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems. © 2017 American Chemical Society.