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Metal–ferroelectric supercrystals with periodically curved metallic layers


Simultaneous manipulation of multiple boundary conditions in nanoscale heterostructures offers a versatile route to stabilizing unusual structures and emergent phases. Here, we show that a stable supercrystal phase comprising a three-dimensional ordering of nanoscale domains with tailored periodicities can be engineered in PbTiO3–SrRuO3 ferroelectric–metal superlattices. A combination of laboratory and synchrotron X-ray diffraction, piezoresponse force microscopy, scanning transmission electron microscopy and phase-field simulations reveals a complex hierarchical domain structure that forms to minimize the elastic and electrostatic energy. Large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO3 layers with curvatures up to 107 m−1. Our results show that multidomain ferroelectric systems can be exploited as versatile templates to induce large curvatures in correlated materials, and present a route for engineering correlated materials with modulated structural and electronic properties that can be controlled using electric fields.

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Fig. 1: Reciprocal space view of the 3D domain structure.
Fig. 2: PFM characterization of flux-closure domains.
Fig. 3: Electron microscopy characterization of the supercrystal phase.
Fig. 4: Supercrystal structure in PbTiO3–SrTiO3 hierarchical superlattices.
Fig. 5: Phase-field simulations.
Fig. 6: Mapping the curvature of periodically modulated SrRuO3 layers.

Data availability

The STEM dataset and analysis used for calculating the curvature of the SrRuO3 layers can be found at Other datasets supporting the findings of this study are available from the corresponding authors upon reasonable request.


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We thank V. Tileli for preliminary TEM characterization and ESRF for provision of synchrotron radiation facilities. Parts of this work were supported by the EPSRC through grant nos. EP/M007073/1 (P.Z. and M.H.) and EP/S010769/1 (P.Z., Y.L. and E.Z.), the China Scholarship Council (Y.L.), UCL-ESRF Impact scholarship (E.Z.) and the A. G. Leventis Foundation (M.H.). J.H. and P.O. acknowledge support from the Czech Science Foundation (project 19-28594X). M.C., K.M., E.N.O’C. and U.B. acknowledge financial support from Science Foundation Ireland (SFI 16/US/3344). M.C. acknowledges funding from SFI Industry Fellowship (18/IF/6282).

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Authors and Affiliations



Sample growth and laboratory diffraction measurements were carried out by M.H. and Y.L. Synchrotron experiments were carried out by M.H., E.Z., G.A.C. and S.L. The results were analysed and interpreted by M.H. and P.Z. PFM measurements were carried out by Y.L. STEM sample preparation, measurements and analysis were performed by M.C., K.M., E.N.O’C. and U.B. Phase-field simulations were performed by P.O., P.M. and J.H. M.H. and P.Z. conceived the project and drafted the manuscript with input from all authors.

Corresponding authors

Correspondence to Marios Hadjimichael or Pavlo Zubko.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Oleg Shpyrko and the other, anonymous, reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–14, Table 1 and refs. 1–4.

Supplementary Video 1

Synchrotron XRD 3D reciprocal space map.

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Hadjimichael, M., Li, Y., Zatterin, E. et al. Metal–ferroelectric supercrystals with periodically curved metallic layers. Nat. Mater. 20, 495–502 (2021).

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