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. 2023 Jul 10;14:4091. doi: 10.1038/s41467-023-39744-3

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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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — a Schematic illustration of phase transition. b XRD results of CSCM and CCM, with or without exposure to the external magnetic field. c Enlarged image of β-phase change of XRD results. d Schematic diagram of the time points for detection of XRD and residual polarization intensity. Created with BioRender.com. e The semi-quantitative relative area of β-phase change, according to the loaded conditions of the external magnetic field. f The residual polarization intensity (P_r) of CSCM was changed according to the loaded conditions of the external magnetic field. (n = 5 independent membrane samples; mean ± SEM) g Schematic diagram of interface polarization. h Phase-field simulation of surface potential change before and after magnetic field exposure. The surface potential values along the diagonal represent the interfacial polarization with the addition of a magnetic field. i Without (left) and with (right) magnetic field loading, the SKPM images of interface polarization and relative surface potential. Comparison of mean values of the surface potential within the detection range (scan size = 1.5 μm) and ΔSP, which represents the difference of surface potential between the interface and the matrix (ΔSP = SP_Interface - SP_Matrix). Source data are provided as a Source Data file.