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. 2023 Apr 20;14:2274. doi: 10.1038/s41467-023-38055-x

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© The Author(s) 2023

Open Access This 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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Fig. 3 — a M-H diagrams of BFO/STO, BFO/SAO/STO, and freestanding BFO films transferred onto STO (001) substrates. b, c Schematic diagrams of the non-collinear G-type cycloid antiferromagnetic order in the freestanding BFO films with low strain and that in BFO/STO films with high strain, respectively. d Schematic diagram of the relationship between polarization P and cycloidal vectors k without the magnetic field. e Schematic diagram of the relationship between polarization P and cycloidal vectors k′ with the magnetic field. f–h Room temperature RA-SHG measurements of BFO/STO, BFO/SAO/STO, and freestanding BFO films without magnetic field, respectively. i–k Magnetic field-dependent SHG of BFO/STO, BFO/SAO/STO, and freestanding BFO films in the p-p polarization configuration, respectively. l–n Magnetic field dependent SHG of freestanding BFO films at 200, 250, and 300 K, respectively.