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. 2019 Apr 10;10:1661. doi: 10.1038/s41467-019-09650-8

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© The Author(s) 2019

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. 2 — PFM imaging artefacts. a, b Vertical (a) and lateral (b) PFM phase images of the 180° domains in a microscale (001)-oriented Pb(Zr,Ti)O₃ capacitor. Lateral PFM contrast in b arises due to the changes of the top electrode morphology induced by the vertical expansion and contraction of the antiparallel 180° domains causing torsional movement of the cantilever, which changes its direction with the change in the surface slope sign. c, d Any asymmetry in the tip–sample system, for example, due to the surface slope, asymmetric tip apex, local variations in sample stoichiometry, or dielectric or elastic constants, may cause imaging artifacts especially pronounced in lateral PFM. c Atomic force microscopic topography and d lateral PFM images of the (001)-oriented Pb(Zr,Ti)O₃ nanograins showing strong variations in the lateral electron microscopic response, which are not related to the in-plane polarization (c, d are adapted from ref. ⁹⁹, with the permission of AIP Publishing)