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Electron ptychography reveals a ferroelectricity dominated by anion displacements

Nature Materials volume 24, pages 1433–1440 (2025)Cite this article

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Abstract

Sodium niobate, a lead-free ferroic material, hosts delicately balanced, competing order parameters, including ferroelectric states that can be stabilized by epitaxial strain. Here we show that the resulting macroscopic ferroelectricity exhibits an unconventional microscopic structure using multislice electron ptychography. This technique overcomes multiple scattering artefacts limiting conventional electron microscopy, enabling both lateral spatial resolution beyond the diffraction limit and recovery of three-dimensional structural information. These imaging capabilities allow us to separate the ferroelectric interior of the sample from the relaxed surface structure and identify the soft phonon mode and related structural distortions with picometre precision. Unlike conventional ferroelectric perovskites, we find that the polar distortion in this material involves minimal distortions of the cation sublattices and is instead dominated by anion displacements relative to the niobium sublattice. We establish limits on film thickness for interfacial octahedral rotation engineering and directly visualize a random octahedral rotation pattern, arising from the flat dispersion of the associated phonon mode.

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Fig. 1: Schematic of MEP and comparison with conventional STEM techniques.
Fig. 2: Depth sectioning reveals surface relaxation and nanoscale phases in projection.
Fig. 3: Visualizing structural distortions that result in the microscopic dipole moment and characterization of macroscopic polarization.
Fig. 4: Distinguishing octahedral tilt patterns and direct visual evidence of a random tilt pattern.
Fig. 5: Ptychographic imaging and mapping of octahedral tilts across the interface.

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Data availability

The experimental datasets that can be used to reproduce the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.13787851 (ref. 71).

Code availability

The codes for the ptychographic reconstructions are available via Zenodo at https://doi.org/10.5281/zenodo.13787851 (ref. 71).

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Acknowledgements

The authors dedicate the paper to Lena Kourkoutis, who has always been an inspiration. H.K., Y.-T.S. and D.A.M. acknowledge funding from the Department of Defense, Air Force Office of Scientific Research, under award no. FA9550-18-1-0480, which also supported the early stages of NaNbO3 film development. Subsequent work at Stanford/SLAC was supported by the Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract no. DE-AC02-76SF00515. K.P., S.P. and L.B. thank the Grant MURI ETHOS W911NF-21-2-0162 from the Army Research Office (ARO), an ARA Impact Grant 3.0 and the Vannevar Bush Faculty Fellowship (VBFF) grant no. N00014-20-1-2834 from the Department of Defense. This research used resources of the Advanced Photon Source, a US DOE, Office of Science User Facility, operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. C.Z. was supported by the NSF under grant no. PHY-1549132, the Center for Bright Beams. The electron microscopy studies made use of the Cornell Center for Materials Research (CCMR) facilities supported by NSF MRSEC program (DMR-1719875), NSF MIP (DMR-2039380), NSF-MRI-1429155 and NSF (DMR-1539918). Part of this work made use of the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award no. ECCS-2026822. We also thank J. Grazul, M. Silvestry Ramos and M. Thomas for technical support and maintenance of the electron microscopy facilities. We acknowledge the following grants: AFOSR FA9550-18-1-0480 to H.K., R.X., K.J.C., A.K., Y.-T.S., H.Y.H. and D.A.M.; DOE-BES DE-AC02-76SF00515 to R.X., K.J.C., A.K. and H.Y.H.; ARO MURI ETHOS W911NF-21-2-0162 to H.K., K.P., S.P., L.B. and D.A.M.; DOD VBFF N00014-20-1-2834 to K.P., S.P. and L.B.; DOE DE-AC02-06CH11357 to H.Z.; NSF PHY-1549132 to C.Z.; NSF ECCS-2026822 to R.X., K.J.C., A.K. and H.Y.H. We thank the NSF MRSEC program (DMR-1719875), NSF MIP (DMR-2039380), NSF-MRI-1429155 and NSF (DMR-1539918) for the electron microscopy facilities.

Author information

Authors and Affiliations

  1. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Harikrishnan KP, Chenyu Zhang, Yu-Tsun Shao & David A. Muller

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Ruijuan Xu, Kevin J. Crust, Aarushi Khandelwal & Harold Y. Hwang

  3. Department of Applied Physics, Stanford University, Stanford, CA, USA

    Ruijuan Xu, Aarushi Khandelwal & Harold Y. Hwang

  4. Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC, USA

    Ruijuan Xu

  5. Smart Ferroic Materials Center, Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, USA

    Kinnary Patel, Sergey Prosandeev & Laurent Bellaiche

  6. Department of Physics, Stanford University, Stanford, CA, USA

    Kevin J. Crust

  7. X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA

    Hua Zhou

  8. Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, USA

    Yu-Tsun Shao

  9. Department of Materials Science and Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel

    Laurent Bellaiche

  10. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    David A. Muller

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Contributions

H.K., R.X., Y.-T.S. and D.A.M. designed and planned the research. H.K. and Y.-T.S. performed the STEM and MEP characterizations under the supervision of D.A.M. Pulsed laser deposition synthesis of the samples and the X-ray diffraction and PFM characterizations were done by R.X., K.J.C. and A.K. under the supervision of H.Y.H. H.Z. was involved in the synchrotron experiments for the 3D reciprocal-space mapping measurements. K.P. and S.P. performed the DFT calculations under the supervision of L.B. C.Z. wrote the parameter optimization codes for MEP used in this study. H.K. wrote the paper with feedback from all authors.

Corresponding author

Correspondence to David A. Muller.

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Competing interests

Cornell University (D.A.M.) has licensed the EMPAD hardware to Thermo Fisher Scientific. The other authors declare no competing interests.

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Nature Materials thanks Eric Bousquet, Peng Gao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Large field of view comparison of multislice electron ptychography with conventional techniques.

Comparison of images of the NaNbO3/DyScO3 heterostructure acquired with different imaging modalities when viewed along the \({[1\bar{1}0]}_{{\rm{O}}}\) zone axis (top row) and the [001]O zone axis (bottom row) of the DyScO3 substrate.

Extended Data Fig. 2 Comparing ABF images taken at different sample regions.

The contrast of ABF images relies heavily on the details of the diffraction conditions and is most sensitive to the sample’s surface structure. (a-c) show ABF images (inverted contrast) taken at different regions of the NaNbO3/DyScO3 sample. The images show differences in the positions and contrast of the different atoms, arising predominantly from variations in sample thickness. For very thin regions in the sample, ABF might give qualitatively the correct structure as can be seen in (c). But without prior knowledge of the correct structure, ABF images are unreliable as images taken in different regions of the sample can show very different characteristics.

Extended Data Fig. 3 Surface relaxations in NaNbO3 grown on SrTiO3 revealed with depth sectioning.

NaNbO3 thin films grown on SrTiO3 exhibit surface relaxations of a larger magnitude than seen in films grown on DyScO3. a, c, show the depth profiles taken along the white dotted lines in (b). The position of the oxygen atom column in the interior of the sample is marked with a black dotted line in (a) and shows a clear offset from the position of the atoms at the surface of the sample. The Na atoms exhibit much smaller shifts in atomic position at the surface, whereas the Nb atoms stay at the same position throughout the depth of the sample as shown in (c).

Extended Data Fig. 4 Depth sectioning simulations on a modeled sample with surface relaxation.

a, Schematic of a simplified model structure for the surface relaxations seen in the NaNbO3 sample – both surface layers have no octahedral rotation, whereas the interior has a 7° octahedral rotation about the pseudo-cubic axis parallel to the beam direction. b, shows a simulated through-focal series of BF, ABF, iDPC images and different slices from a multislice ptychographic reconstruction. The simulations are infinite-dose and assume an aberration-free probe. For each imaging modality, the image that appears best visually in the defocus series is highlighted with a red border and corresponds to the beam focused near the top surface. The BF and ABF images undergo contrast reversals and show clear atomic contrast only for a limited range of defocus. The contrast in the best ABF and iDPC image is a closer match to the relaxed surface structure than the interior structure, and hence would produce large discrepancies if used for comparisons with other macroscopic measurements. The multislice ptychographic reconstruction is able to capture the relaxed structure at the two surfaces as well as the interior structure accurately. c-f, Depth profiles along the Na-O plane for (c) BF, (d) ABF, (e) iDPC and (f) multislice ptychographic reconstruction. Away from their ideal defocus condition, the BF, ABF and iDPC images do not have the requisite contrast or resolution to unambiguously differentiate the presence of the relaxed surface structure from the bulk structure. Multislice ptychography enables accurate depth sectioning from a single dataset with a clear distinction between the surface and interior structure. We also note that the addition of probe aberrations or small mistilts that are practically unavoidable in an experimental situation will cause severe deterioration in the quality of the BF, ABF and iDPC image. Multislice ptychography can recover the correct probe structure even in the presence of aberrations - an example from an experimental dataset can be seen in Supplementary Fig. 10. Mistilts will produce tilted atomic columns in the depth sectioning, which can easily be corrected by aligning the different slices in a post-processing step. Figure adapted with permission from ref. 43, Oxford Univ. Press.

Extended Data Fig. 5 Crystalline quality and film strain characterized with reciprocal space mapping (RSM) and X-ray diffraction (XRD).

(a) Synchrotron-based 3D RSM taken at the (113)pc peak of DyScO3 with corresponding slices along the (b) H-L, (c) K-L, and (d) H-K reciprocal planes. The H-K plane was sliced aligned with the NaNbO3 peak as shown in (a) and displays four satellite peaks due to the periodic domain structure, as is commonly seen in ferroelectrics. (e, f) Line scan cuts of the H-K plane along the dashed lines from (d), which can be used to extract a domain periodicity of 38 nm along H and 44 nm along K. (g) Synchrotron-based 002-line scan measurement showing strong and clear Laue oscillations, confirming the quality of our NaNbO3 films. (h, i) 2D RSM taken at the (033)pc and (303)pc peaks, respectively, showing that the film is coherently strained along both in-plane directions. From a refinement of these results, we extract lattice parameters for NaNbO3 of a = 5.519 Å, b = 5.516 Å, and c = 15.774 Å and unit cell angles of α = 90°, β = 90°, and γ = 91.3°. We can thus calculate the strain for our NaNbO3 film to be 0.8% tensile along abDSO and 1.6% tensile along cDSO.

Extended Data Fig. 6 Structural distortions in the NaNbO3 films measured for projections along both in-plane pseudo-cubic axes.

Schematic showing the major cation and anion displacements in the NaNbO3 structure for the in-plane \({[{\bf{1}}\bar{{\bf{1}}}{\bf{0}}]}_{{\rm{O}}}\) (top row) and [001]O (bottom row) zone axes (directions in reference to the DyScO3 substrate). The displacements of the different atoms from the reference planes (black dotted lines) are average of the measured values from the regions shown in Extended Data Fig. 8 (a-c, d-f). The Na atoms show anti-polar displacements along both in-plane pseudo-cubic directions, and the Nb atoms show anti-polar displacements in the growth direction. The net displacement magnitude of the oxygen atoms that displace to the left is much larger than for the net displacement to the right and is the major source of the polarization. The small discrepancies (<1 pm) in the displacements in the growth direction for the two projection directions might arise from inhomogeneities in different regions of the sample.

Extended Data Fig. 7 Histogram of oxygen octahedral tilts.

Magnitude of oxygen octahedral tilt in the sodium niobate thin film along the (a) \({[1\bar{1}0]}_{{\rm{O}}}\) and (b) [001]O direction of the DyScO3 substrate.

Extended Data Fig. 8 Atomic displacement maps along both in-plane pseudo-cubic directions.

The vector maps show large displacements of the cation centroids with respect to the centroid of the oxygen anions - (a, d) for Nb atoms and (b, e) for Na atoms, and form the two physical dipoles in the system. The polarization is predominantly in-plane with a small out of plane component. In contrast, the displacement of one cation sublattice with respect to the other (c, f) is much smaller and accounts for a very small fraction of the total polarization. The above displacement maps emphasize the importance of accurately measuring the oxygen atom positions for an accurate characterization of the polarization.

Extended Data Fig. 9 Piezoresponse force microscopy results and schematics.

Piezoresponse force microscopy (PFM) images showing the amplitude (a, b) and phase (c, d) in the vertical and lateral directions, respectively. The lateral direction displays a much clearer domain pattern with stronger PFM signal when compared to the vertical direction, which matches the ptychography result with polarization predominantly oriented along the [110]pc direction. We can also extract an average domain periodicity of 44 nm along [100]pc and 52 nm along [010]pc, which are in rough agreement with the results from X-ray diffraction in Extended Data Fig. 5. Schematics of the domain configurations for the (e) lateral and (f) vertical measurements are also provided. For these measurements, the sample is rotated by 45° with respect to the tip, as polarizations orthogonal to the tip provide the strongest lateral signal and the polarization is known to be mostly along [110]pc. There are four superdomain variants described in these schematics which have been labelled in (a-d). For lateral PFM measurement, the polarization of individual domains will oscillate within a superdomain between pointing along the tip (providing lower amplitude in b and shown in pastel colors in e) and orthogonal to the tip (providing higher amplitude in b and shown in darker colors in e). Superdomains 1 and 3 show the same lateral phase because the PFM tip is torqued in the same direction by the orthogonal domains for these regions (the same is also true for superdomains 2 and 4). For the vertical PFM images, we can see that two superdomain variants (3 and 4) have roughly no net polarization since the polarization of neighboring domains will cancel, and thus the vertical PFM amplitude is low in a. We note that even in these low amplitude regions, oscillating phases can be observed in c as expected from f. However, in regions 1 and 2 the vertical polarizations of neighboring domains are aligned, and so the vertical PFM amplitude is higher in a, and those regions have a single phase in c.

Extended Data Fig. 10 Polarization and oxygen octahedral tilt magnitude for Pc and Cm phases of NaNbO3.

In-plane lattice parameter dependence of (a,c) the polarization and (b,d) tilting of oxygen octahedra at R and M point of the first Brillouin zone for the (a,b) Pc and (c,d) Cm phases of epitaxial (001) NaNbO3 thin films.

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KP, H., Xu, R., Patel, K. et al. Electron ptychography reveals a ferroelectricity dominated by anion displacements. Nat. Mater. 24, 1433–1440 (2025). https://doi.org/10.1038/s41563-025-02205-x

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