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Long-range symmetry breaking in embedded ferroelectrics


The characteristic functionality of ferroelectric materials is due to the symmetry of their crystalline structure. As such, ferroelectrics lend themselves to design approaches that manipulate this structural symmetry by introducing extrinsic strain. Using in situ dark-field X-ray microscopy to map lattice distortions around deeply embedded domain walls and grain boundaries in BaTiO3, we reveal that symmetry-breaking strain fields extend up to several micrometres from domain walls. As this exceeds the average domain width, no part of the material is elastically relaxed, and symmetry is universally broken. Such extrinsic strains are pivotal in defining the local properties and self-organization of embedded domain walls, and must be accounted for by emerging computational approaches to material design.

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We are grateful to the European Synchrotron for providing beamtime at ID06, and Danscatt for financial assistance related thereto. This work is supported by the ERC Advanced grant ‘d-TXM’ (291321). In addition, H.S. and A.B.H. are supported by individual postdoc grants from the Independent Research Fund Denmark (DFF–4093-00296 and DFF–6111-00440). The work of D.D. has been supported by the Swiss National Science Foundation (grant no. 200021-159603), while J.E.D. acknowledges financial support from the ARC Discovery Projects DP120103968 and DP130100415. The silicon compound refractive lenses used in the experiment were manufactured at DTU Danchip, National Center for Micro- and Nanofabrication.

Author information

A.B.H. and H.S. prepared the samples. H.S., A.C.J., C.D. and M.M. performed the experiments. F.S. developed the X-ray optics for the experiment. S.S. developed the noise-reduction algorithm used in the analysis. H.S. designed the experiment with D.D. and J.E.D. H.S. performed the analysis, then interpreted the data with D.D., J.E.D. and H.F.P. H.S. wrote the article and all authors contributed and commented on the text.

Competing interests

The authors declare no competing interests.

Correspondence to Hugh Simons.

Supplementary information

Supplementary Information

Supplementary Video Captions 1–3, Supplementary Figures 1–2

Supplementary Video 1

Dark-field X-ray microscopy intensity images showing the evolution of a group of domains at a single position in reciprocal space (that is, a single lattice orientation and strain) during in situ electric field application from 0 to 472 V mm–1. Local changes in the observed intensity are due to domain entering and exiting the Bragg condition as their lattice orientation and strain locally changes in response to the applied electric field. The image exposure time is 1 second.

Supplementary Video 2

As above, but during in situ electric field application from 472 V mm–1 to 944 V mm–1. Note the inhomogeneous switching event between 33 and 38 seconds. The image exposure time is 1 second.

Supplementary Video 3

As above, but during the reduction of the in situ electric field from 944 V mm–1 to 0 V mm–1. Note the relatively constant process of domain back-switching during the process. The image exposure time is 1 second.

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Fig. 1: Conventional X-ray diffraction measurement of a single embedded crystallite of BaTiO3.
Fig. 2: Cross-sectional dark-field X-ray microscopy maps of the embedded BaTiO3 grain.
Fig. 3: Local lattice distortions around embedded structural interfaces.
Fig. 4: Changes to the domain topology and orientation distribution in the embedded BaTiO3 grain during the in situ application of a unipolar electric field cycle along the <100> direction.