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. 2017 Jul 5;7:4631. doi: 10.1038/s41598-017-04635-3

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© The Author(s) 2017

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Polar transitions of La-doped BaTiO₃films. (a) Temperature dependence of the c-axis lattice constant for non-doped BTO and La-BTO films grown on GSO (110) together with that of lattice constants for the cubic and tetragonal phases of BTO single crystal^{26, 27}. The dotted curve denotes the extrapolated lattice constant of BTO single crystals in the cubic phase. (b) Temperature dependence of the optical SHG intensity of the films. (c) La doping ([n]/Ti) dependence of in-plane strain ε. (d) Non-polar to polar transition temperature T _Cas a function of the in-plane strain εof non-doped and La-doped BTO films on GSO, of non-doped BTO films on GSO and of DSO²⁶with a theoretical line based on the phase-field simulation³².