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. 2024 Nov 20;15:10047. doi: 10.1038/s41467-024-54285-z

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© The Author(s) 2024

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. 7 — a Experimental V-amp, V-phase, L-amp, and L-phase PFM images of the pristine state showing a down-convergent domain (panel i), after switching to a metastable state with bubble-like domain (panel ii) and after switching to an up-divergent domain (panel iii). Vertical and lateral PFM amplitudes are given in arbitrary units. b The P-E hysteresis loop of nanoisland switching, showing the simulation results. The numbers correspond to the states to be analyzed. c Distribution of the vertical polarization component, P_z, in the initial (1), intermediate (3, 5), and final switched (8) states. The numbers correspond to the locations of the states on the P-E hysteresis loop. d Dynamics of the polarization vector field during the switching. The blue and red colors correspond to the polarization fluxes in unswitched and switched domains. The switched domain is slightly displaced upwards for the convenience of presentation. Point V is the singular point of the vector field where these fluxes meet. e Topological properties of the singular point V.