title: Observation of polar vortices in oxide superlattices.
abstract: The complex interplay of spin, charge, orbital and lattice degrees of freedom provides a plethora of exotic phases and physical phenomena. In recent years, complex spin topologies have emerged as a consequence of the electronic band structure and the interplay between spin and spin-orbit coupling in materials. Here we produce complex topologies of electrical polarization--namely, nanometre-scale vortex-antivortex (that is, clockwise-anticlockwise) arrays that are reminiscent of rotational spin topologies--by making use of the competition between charge, orbital and lattice degrees of freedom in superlattices of alternating lead titanate and strontium titanate layers. Atomic-scale mapping of the polar atomic displacements by scanning transmission electron microscopy reveals the presence of long-range ordered vortex-antivortex arrays that exhibit nearly continuous polarization rotation. Phase-field modelling confirms that the vortex array is the low-energy state for a range of superlattice periods. Within this range, the large gradient energy from the vortex structure is counterbalanced by the corresponding large reduction in overall electrostatic energy (which would otherwise arise from polar discontinuities at the lead titanate/strontium titanate interfaces) and the elastic energy associated with epitaxial constraints and domain formation. These observations have implications for the creation of new states of matter (such as dipolar skyrmions, hedgehog states) and associated phenomena in ferroic materials, such as electrically controllable chirality.
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: A K
authors.initials: AK
authors.lastname: Yadav
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.|National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: C T
authors.initials: CT
authors.lastname: Nelson
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.|National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: S L
authors.initials: SL
authors.lastname: Hsu
authors.affiliation: Department of Materials Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16802, USA.
authors.forename: Z
authors.initials: Z
authors.lastname: Hong
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: J D
authors.initials: JD
authors.lastname: Clarkson
authors.affiliation: Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA.
authors.forename: C M
authors.initials: CM
authors.lastname: Schlepütz
authors.affiliation: Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA.
authors.forename: C M
authors.initials: CM
authors.lastname: Schlepüetz
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.
authors.forename: A R
authors.initials: AR
authors.lastname: Damodaran
authors.affiliation: Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: P
authors.initials: P
authors.lastname: Shafer
authors.affiliation: Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: E
authors.initials: E
authors.lastname: Arenholz
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.
authors.forename: L R
authors.initials: LR
authors.lastname: Dedon
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: D
authors.initials: D
authors.lastname: Chen
authors.affiliation: Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: A
authors.initials: A
authors.lastname: Vishwanath
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.|National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: A M
authors.initials: AM
authors.lastname: Minor
authors.affiliation: Department of Materials Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16802, USA.
authors.forename: L Q
authors.initials: LQ
authors.lastname: Chen
authors.affiliation: Schools of Chemistry and Physics, University of St Andrews, St Andrews KY16 9ST, UK.
authors.forename: J F
authors.initials: JF
authors.lastname: Scott
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: L W
authors.initials: LW
authors.lastname: Martin
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.|Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: R
authors.initials: R
authors.lastname: Ramesh