Probing the polarisation configuration of ferroelectric domain walls using x-ray diffraction

Marios Hadjimichael ¹ Petr Ondrejkovic ² Céline Lichtensteiger ¹ Edoardo Zatterin ³ Ludovica Tovaglieri ¹ Steven Leake ³ Pavlo Zubko ⁴ Jirka Hlinka ² Jean-Marc Triscone ¹

¹Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland
²Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
³Beamline ID01, ESRF—The European Synchrotron, Grenoble, France
⁴Department of Physics and Astronomy, University College London, London, UK

Non-trivial polarisation textures in ferroelectric thin films and multilayers have been of great interest recently, as evidenced by the observation of ordered flux-closure domains [1], polar skyrmions[2] and polar merons[3] in PbTiO₃ multilayers. So far, the techniques used for these observations have been invasive and/or destructive for the studied samples. Conversely, some non-invasive techniques were used to unravel the structure of ferroelectric domain walls (DWs), but they were restricted by their spatial resolution, and thus were appropriate for ferroelectrics with a minimum domain size[4-6]. To study systems with nanoscale periodic domain structures without limitations in the minimum domain size, as well as systems with buried domains, x-ray diffraction (XRD) is the most appropriate tool[7]. However, its use to elucidate the properties and structure of ferroelectric DWs has been limited.

Here, we show that it is possible to use XRD to investigate the structure of nanoscale 180° ferroelectric DWs in PbTiO₃/SrTiO₃ superlattices. We show that characteristic diffraction patterns arise in the diffuse scattering around specific Bragg peaks, due to the interaction of the scattering vector with polar atomic displacements at the DWs. Using phase-field modelling in combination with diffuse scattering calculations we show that this diffraction pattern arises due to the in-plane polarisation configuration at the DWs of the PbTiO₃ layers. Our results show that this is a general technique that can be used to probe different materials and to study various types of DWs in ferroelectric systems.

References
[1] Tang et al., Science 348, 547-551 (2015)
[2] Das et al., Nature 568, 368-372 (2019)
[3] Wang et al., Nat. Mater. 19, 881-886 (2020)
[4] Cherifi-Hertel et al., Nat. Commun. 8, 15768 (2017)
[5] Hadjimichael et al., Nat. Mater. 20, 495-502 (2021)
[6] Lu et al., Nature 603, 63-67 (2022)
[7] Streiffer et al., Phys. Rev. Lett. 89, 067601 (2002)