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Coupled polarization and nanodomain evolution underpins large electromechanical responses in relaxors


Understanding the evolution and role of nanoscale polar structures during polarization rotation in relaxor ferroelectrics is a long-standing challenge in materials science and condensed-matter physics. These nanoscale polar structures are characterized by polar nanodomains, which are believed to play a key role in enabling the large susceptibilities of relaxors. Using epitaxial strain, we stabilize the intermediate step during polarization rotation in epitaxial films of a prototypical relaxor and study the co-evolution of polarization and polar nanodomains. Our multimodal approach allows for a detailed examination of correlations between polarization and polar nanodomains; illuminates the effect of local chemistry, strain and electric field on their co-evolution; and reveals the underappreciated role of strain in enabling the large electromechanical coupling in relaxors. As the strain increases, the competition between chemistry-driven disorder and strain-driven order of the polar units intensifies, which is manifested in the coexistence of inclined and elongated polar nanodomains in the intermediate step of polarization rotation. Our findings establish that structural transitions between polar nanodomain configurations underpins the polarization rotation and large electromechanical coupling of relaxors.

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Fig. 1: Reciprocal-space characterizations of the –0.75% heterostructures.
Fig. 2: Real-space characterizations of the –0.75% heterostructures.
Fig. 3: In operando μXRD under applied electric field.
Fig. 4: Analysis of in operando μXRD under applied electric field.

Data availability

All data supporting the findings of this study are available within the Article and its Supplementary Information. Additional data are available from the corresponding author upon request. Source data are provided with this paper.

Code availability

Custom Python scripts used to analyse the STEM images are available from the corresponding author upon request.


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J.K. acknowledges support from the Army Research Office under grant W911NF-21-1-0118. J.M.L. and A.K. acknowledge support for this work from the John Chipman Career Development Professorship and the NVIDIA Corporation for supplying a Titan Xp graphics processing unit for STEM image simulations. A.F. acknowledges support from the National Science Foundation under grant DMR-2102895. Z.T. acknowledges support from the Army Research Office under grant W911NF-21-1-0126. A.M.R. acknowledges support from the Office of Naval Research under grant N00014-20-1-2701. Y.Q. acknowledges the center for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award No. DE-SC0021118, including the extension of bond-valence molecular dynamics modeling to thin films. Y.Q., H.T., A.M.R., J.M.L. and L.W.M. also acknowledge support from the Army Research Laboratory via the Collaborative for Hierarchical Agile and Responsive Materials (CHARM) under cooperative agreement W911NF-19-2-0119. Use of the Advanced Photon Source, an Office of Science User Facility operated for the US Department of Energy (DOE), Office of Science, by Argonne National Laboratory (ANL), was supported by the US DOE under contract no. DE-AC02-06CH11357. The authors acknowledge computational support from the High-Performance Computing Modernization Office (HPCMO) of the US Department of Defense (DOD) and National Energy Research Scientific Computing Center (NERSC), a US Department of Energy, Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network (NNIN) and part of Harvard University, supported by the National Science Foundation under award no. ECS-0335765. This work was performed in part in the MIT.nano Characterization Facilities.

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Authors and Affiliations



J.K. and L.W.M. conceived this study. J.K. synthesized the films and performed the structural characterizations. J.K., A.F. and Z.T. fabricated the devices for in operando synchrotron diffraction. J.K. and D.M. performed the synchrotron diffraction measurements. A.K. and J.M.L. performed the STEM studies. Y.Q., H.T. and A.M.R. performed the molecular dynamics simulation studies. P.J.R. and J.-W.K. developed the in operando synchrotron diffraction setup. J.K., D.M., Z.T., P.J.R. and J.-W.K. performed the in operando synchrotron diffraction measurements. J.K. and A.K. wrote the initial draft of the manuscript. J.K., A.K., Y.Q., H.T., A.M.R., J.M.L. and L.W.M. revised the manuscript. All the authors discussed the results and edited the manuscript.

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Correspondence to Lane W. Martin.

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Nature Physics thanks Dawei Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9 and refs. 1–4.

Source data

Source Data Fig. 3

Electric-field-dependent XRD data.

Source Data Fig. 4

XRD fitting results and electric-field-dependent XRD data.

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Kim, J., Kumar, A., Qi, Y. et al. Coupled polarization and nanodomain evolution underpins large electromechanical responses in relaxors. Nat. Phys. 18, 1502–1509 (2022).

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