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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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Electronic structures of La-doped BaTiO₃films. Band structure of La-doped BTO calculated at various La concentrations, x, for the non-polar (polar) structure in the upper (lower) panel. The energy separations of bands caused by crystal field splitting and spin orbit interactions are by Δ_CFSand Δ_SOI, respectively. For the polar cases, red and blue colours represent the opposite spin states of the bands (red: spins pointing out of the page; blue: spins pointing inward). The shaded area denotes the energy range within which states are occupied. E _CBMcorresponds to the energy level of the conduction band minimum.