Zijian Hong, Hanyu Liu, Pablo García-Fernández, H. Zhou, James D. Clarkson, Anoop R. Damodaran, Andreas Scholl, Ramamoorthy Ramesh, Javier Junquera, Z. Cai, Jorge Íñiguez, Ajay K. Yadav, Lane W. Martin, Long Qing Chen, Christopher T. Nelson, Shang-Li Hsu, Kyoung-Duck Park, Yongqi Dong, Margaret McCarter, Vasily Kravtsov, Markus B. Raschke, Alan Farhan, Pablo Aguado-Puente, Dillon D. Fong, Fonds National de la Recherche Luxembourg, Ministerio de Economía y Competitividad (España), Swiss National Science Foundation, National Science Foundation (US), Department of the Army (US), Department of Energy (US), and Gordon and Betty Moore Foundation
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 PbTiO>3/SrTiO>3 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., 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.I. 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-C02-05CH11231. 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).