
Phase coexistence and electric-field control of toroidal order in oxide superlattices
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ABSTRACT Systems that exhibit phase competition, order parameter coexistence, and emergent order parameter topologies constitute a major part of modern condensed-matter physics. Here, by
applying a range of characterization techniques, and simulations, we observe that in PbTiO3/SrTiO3 superlattices all of these effects can be found. By exploring superlattice period-,
temperature- and field-dependent evolution of these structures, we observe several new features. First, it is possible to engineer phase coexistence mediated by a first-order phase
transition between an emergent, low-temperature vortex phase with electric toroidal order and a high-temperature ferroelectric _a_1/_a_2 phase. At room temperature, the coexisting vortex and
ferroelectric phases form a mesoscale, fibre-textured hierarchical superstructure. The vortex phase possesses an axial polarization, set by the net polarization of the surrounding
ferroelectric domains, such that it possesses a multi-order-parameter state and belongs to a class of gyrotropic electrotoroidal compounds. Finally, application of electric fields to this
mixed-phase system permits interconversion between the vortex and the ferroelectric phases concomitant with order-of-magnitude changes in piezoelectric and nonlinear optical responses. Our
findings suggest new cross-coupled functionalities. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS
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ACKNOWLEDGEMENTS A.R.D. acknowledges support from the Army Research Office under grant W911NF-14-1-0104 and the Department of Energy, Office of Science, Office of Basic Energy Sciences under
grant no. DE-SC0012375 for synthesis and structural study of the materials. Z.H. acknowledges support from NSF-MRSEC grant number DMR-1420620 and NSF-MWN grant number DMR-1210588. A.K.Y.
acknowledges support from the Office of Basic Energy Sciences, US Department of Energy DE-AC02-05CH11231. C.T.N. acknowledge support from the Office of Basic Energy Sciences, US Department
of Energy DE-AC02-05CH11231. S.L.H. acknowledges support from the National Science Foundation under the MRSEC programme (DMR-1420620). M.R.M. acknowledges support from the National Science
Foundation Graduate Research Fellowship under grant number DGE-1106400. K.-D.P., V.K. and M.B.R. acknowledge support from the US Department of Energy, Office of Basic Sciences, Division of
Material Sciences and Engineering, under Award No. DE-SC0008807. A.F. acknowledges support from the Swiss National Science Foundation. P.G.-F. and J.J. acknowledge financial support from the
Spanish Ministry of Economy and Competitiveness through grant number FIS2015-64886-C5-2-P.J.Í. is supported by the Luxembourg National Research Fund (Grant FNR/C15/MS/10458889 NEWALLS).
L.-Q.C. is supported by the US Department of Energy, Office of Basic Energy Sciences under Award FG02-07ER46417. R.R. and L.W.M. acknowledge support from the Gordon and Betty Moore
Foundation’s EPiQS Initiative, under grant GBMF5307. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of
Energy under Contract No. DE-AC02-05CH11231. Nanodiffraction measurements were supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials
Sciences and Engineering Division. This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of
Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Electron microscopy of superlattice structures was performed at the Molecular Foundry at Lawrence Berkeley
National Laboratory, supported by the Office of Science, Office of Basic Energy Sciences, US Department of Energy (DE-AC02-05CH11231). AUTHOR INFORMATION Author notes * A. R. Damodaran and
J. D. Clarkson: These authors contributed equally to this work. AUTHORS AND AFFILIATIONS * Department of Materials Science and Engineering, University of California, Berkeley, California,
94720, USA A. R. Damodaran, J. D. Clarkson, A. K. Yadav, C. T. Nelson, S.-L. Hsu, R. Ramesh & L. W. Martin * Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,
California, 94720, USA A. R. Damodaran, J. D. Clarkson, A. K. Yadav, R. Ramesh & L. W. Martin * Department of Materials Science and Engineering, Pennsylvania State University, State
College, Pennsylvania, 16802, USA Z. Hong & L.-Q. Chen * Materials Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, USA H. Liu, Y. Dong & D. D. Fong * School
of Electrical Engineering and Computer Science, UC Berkeley, Berkeley, California, 94720, USA A. K. Yadav * National Center for Electron Microscopy, Lawrence Berkeley National Laboratory,
Berkeley, California, 94720, USA C. T. Nelson & S.-L. Hsu * Department of Physics, University of California, Berkeley, Berkeley, California, 94720, USA M. R. McCarter & R. Ramesh *
Department of Physics, Department of Chemistry, and JILA, University of Colorado, Boulder, Boulder, Colorado, 80309, USA K.-D. Park, V. Kravtsov & M. B. Raschke * Advanced Light Source,
Lawrence Berkeley National Laboratory, Berkeley, California, 94720, USA A. Farhan & A. Scholl * X-ray Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, USA Z. Cai
& H. Zhou * Centro de Física de Materiales, Universidad del País Vasco, 20018 San Sebastián, Spain P. Aguado-Puente * Donostia International Physics Center, 20018 San Sebastián, Spain P.
Aguado-Puente * Departmento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, Cantabria Campus Internacional, avenida de los Castros s/n, 39005
Santander, Spain P. García-Fernández & J. Junquera * Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), 5 avenue des Hauts-Fourneaux,
L-4362 Esch/Alzette, Luxembourg J. Íñiguez Authors * A. R. Damodaran View author publications You can also search for this author inPubMed Google Scholar * J. D. Clarkson View author
publications You can also search for this author inPubMed Google Scholar * Z. Hong View author publications You can also search for this author inPubMed Google Scholar * H. Liu View author
publications You can also search for this author inPubMed Google Scholar * A. K. Yadav View author publications You can also search for this author inPubMed Google Scholar * C. T. Nelson
View author publications You can also search for this author inPubMed Google Scholar * S.-L. Hsu View author publications You can also search for this author inPubMed Google Scholar * M. R.
McCarter View author publications You can also search for this author inPubMed Google Scholar * K.-D. Park View author publications You can also search for this author inPubMed Google
Scholar * V. Kravtsov View author publications You can also search for this author inPubMed Google Scholar * A. Farhan View author publications You can also search for this author inPubMed
Google Scholar * Y. Dong View author publications You can also search for this author inPubMed Google Scholar * Z. Cai View author publications You can also search for this author inPubMed
Google Scholar * H. Zhou View author publications You can also search for this author inPubMed Google Scholar * P. Aguado-Puente View author publications You can also search for this author
inPubMed Google Scholar * P. García-Fernández View author publications You can also search for this author inPubMed Google Scholar * J. Íñiguez View author publications You can also search
for this author inPubMed Google Scholar * J. Junquera View author publications You can also search for this author inPubMed Google Scholar * A. Scholl View author publications You can also
search for this author inPubMed Google Scholar * M. B. Raschke View author publications You can also search for this author inPubMed Google Scholar * L.-Q. Chen View author publications You
can also search for this author inPubMed Google Scholar * D. D. Fong View author publications You can also search for this author inPubMed Google Scholar * R. Ramesh View author publications
You can also search for this author inPubMed Google Scholar * L. W. Martin View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS A.R.D., J.D.C.,
R.R. and L.W.M. conceived of the central concepts and designed the experiments. A.R.D., H.L. and M.R.M. conducted the synchrotron and laboratory X-ray diffraction studies. J.D.C. and A.R.D.
conducted the scanning probe-based PFM measurements. Z.H. performed and analysed the phase-field simulations. A.K.Y. and M.R.M. synthesized the materials. C.T.N. and S.L.H. performed the
TEM-based characterization of the superlattice samples, along with the detailed polarization vector analysis. K.-D.P. and V.K. performed the near- and far-field SHG measurements. A.F.
conducted the PEEM measurements. Y.D., Z.C., H.Z. and H.L. conducted the synchrotron nanodiffraction studies. P.A.-P. and J.J. completed the second-principles simulations that were analysed
by P.A.-P., P.G.-F., J.Í. and J.J. A.S., M.B.R., L.-Q.C. and D.D.F. contributed to analysis, discussions, and understanding of the data and the development of the manuscript. A.R.D., R.R.
and L.W.M. wrote the manuscript. All authors discussed the results and implications of the work and read, edited and commented on the manuscript at all stages. CORRESPONDING AUTHOR
Correspondence to L. W. Martin. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION
Supplementary Information (PDF 1647 kb) RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Damodaran, A., Clarkson, J., Hong, Z. _et al._ Phase coexistence
and electric-field control of toroidal order in oxide superlattices. _Nature Mater_ 16, 1003–1009 (2017). https://doi.org/10.1038/nmat4951 Download citation * Received: 17 December 2016 *
Accepted: 28 June 2017 * Published: 07 August 2017 * Issue Date: 01 October 2017 * DOI: https://doi.org/10.1038/nmat4951 SHARE THIS ARTICLE Anyone you share the following link with will be
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