02196nas a2200457 4500008004100000022001300041245006900054210006900123260003000192300001400222490000700236520091400243653001201157653001601169653002101185653003101206653002101237653002101258653002401279653002701303653001701330653001701347653001501364653003001379653002601409653001301435653001601448100001301464700002001477700001201497700001501509700001601524700001601540700001701556700001601573700001601589700001701605700002401622700001601646856007601662 2017 eng d a1530698400aStability of Polar Vortex Lattice in Ferroelectric Superlattices0 aStability of Polar Vortex Lattice in Ferroelectric Superlattices bAmerican Chemical Society a2246-22520 v173 aA 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.10aArticle10acompetition10aCrystal lattices10aFerroelectric superlattice10aferroelectricity10aGeometric length10aNeodymium compounds10aPhase-field simulation10aPolar vortex10aPolarization10asimulation10aSuperconducting materials10aTopological structure10aTopology10aVortex flow1 aHong, Z.1 aDamodaran, A.R.1 aXue, F.1 aHsu, S.-L.1 aBritson, J.1 aYadav, A.K.1 aNelson, C.T.1 aWang, J.-J.1 aScott, J.F.1 aMartin, L.W.1 aRamesh, Ramamoorthy1 aChen, L.-Q. uhttps://rameshlab.lbl.gov/publications/stability-polar-vortex-lattice-0