01943nas a2200337 4500008004100000022001400041245006900055210006900124260001200193300001400205490000700219520090800226653003201134653002701166653002801193653003701221653002701258100001701285700002501302700001301327700001901340700001901359700002001378700002801398700001901426700002101445700002101466700002401487700002001511856007401531 2017 eng d a1530-698400aStability of Polar Vortex Lattice in Ferroelectric Superlattices0 aStability of Polar Vortex Lattice in Ferroelectric Superlattices c04/2017 a2246-22520 v173 aA novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO_{3}/SrTiO_{3}. 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.

10aFerroelectric superlattices10ageometric length scale10aphase-field simulations10atopological structures by design10aultrafine polar vortex1 aHong, Zijian1 aDamodaran, Anoop, R.1 aXue, Fei1 aHsu, Shang-Lin1 aBritson, Jason1 aYadav, Ajay, K.1 aNelson, Christopher, T.1 aWang, Jian-Jun1 aScott, James, F.1 aMartin, Lane, W.1 aRamesh, Ramamoorthy1 aChen, Long-Qing uhttps://rameshlab.lbl.gov/publications/stability-polar-vortex-lattice