title: Stability of Polar Vortex Lattice in Ferroelectric Superlattices.
abstract: 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.
authors.affiliation: Department of Materials Science and Engineering, The Pennsylvania State University , University Park, Pennsylvania 16802, United States.
authors.forename: Zijian
authors.identifier: 0000-0002-3491-0884
authors.initials: Z
authors.lastname: Hong
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.
authors.forename: Anoop R
authors.initials: AR
authors.lastname: Damodaran
authors.affiliation: Department of Materials Science and Engineering, The Pennsylvania State University , University Park, Pennsylvania 16802, United States.
authors.forename: Fei
authors.initials: F
authors.lastname: Xue
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.|Materials Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.|Department of Physics, University of California , Berkeley, California 94720, United States.
authors.forename: Shang-Lin
authors.initials: SL
authors.lastname: Hsu
authors.affiliation: Department of Materials Science and Engineering, The Pennsylvania State University , University Park, Pennsylvania 16802, United States.
authors.forename: Jason
authors.initials: J
authors.lastname: Britson
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.|Materials Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.
authors.forename: Ajay K
authors.identifier: 0000-0001-5088-6506
authors.initials: AK
authors.lastname: Yadav
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.|Materials Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.
authors.forename: Christopher T
authors.initials: CT
authors.lastname: Nelson
authors.affiliation: Department of Materials Science and Engineering, The Pennsylvania State University , University Park, Pennsylvania 16802, United States.
authors.forename: Jian-Jun
authors.initials: JJ
authors.lastname: Wang
authors.affiliation: Schools of Chemistry and Physics, University of St Andrews , St Andrews KY16 9ST, U.K.
authors.forename: James F
authors.initials: JF
authors.lastname: Scott
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.|Materials Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.
authors.forename: Lane W
authors.initials: LW
authors.lastname: Martin
authors.affiliation: Department of Materials Science and Engineering, University of California , Berkeley, California 94720, United States.|Materials Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.|Department of Physics, University of California , Berkeley, California 94720, United States.
authors.forename: Ramamoorthy
authors.initials: R
authors.lastname: Ramesh
authors.affiliation: Department of Materials Science and Engineering, The Pennsylvania State University , University Park, Pennsylvania 16802, United States.
authors.forename: Long-Qing
authors.initials: LQ
authors.lastname: Chen
keywords: Ferroelectric superlattices; geometric length scale; phase-field simulations; topological structures by design; ultrafine polar vortex