Letter | Published:

Observation of room-temperature polar skyrmions

Abstract

Complex topological configurations are fertile ground for exploring emergent phenomena and exotic phases in condensed-matter physics. For example, the recent discovery of polarization vortices and their associated complex-phase coexistence and response under applied electric fields in superlattices of (PbTiO3)n/(SrTiO3)n suggests the presence of a complex, multi-dimensional system capable of interesting physical responses, such as chirality, negative capacitance and large piezo-electric responses1,2,3. Here, by varying epitaxial constraints, we discover room-temperature polar-skyrmion bubbles in a lead titanate layer confined by strontium titanate layers, which are imaged by atomic-resolution scanning transmission electron microscopy. Phase-field modelling and second-principles calculations reveal that the polar-skyrmion bubbles have a skyrmion number of +1, and resonant soft-X-ray diffraction experiments show circular dichroism, confirming chirality. Such nanometre-scale polar-skyrmion bubbles are the electric analogues of magnetic skyrmions, and could contribute to the advancement of ferroelectrics towards functionalities incorporating emergent chirality and electrically controllable negative capacitance.

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Acknowledgements

S.D. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, under grant GBMF5307. Funding for the synthesis and characterization work (to A.B.M., D.G.S. and R.R.) was also provided by the Army Research Office under grant W911NF-16-1-0315. Y.L.T. and R.R. acknowledge support by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract number DE-AC02-05-CH11231 (Quantum Materials program KC2202) for detailed polarization vector analysis. M.R.M. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant number DGE-1106400. M.A.P.G. and J.Í. are funded by the Luxembourg National Research Fund through the CORE programme (grant FNR/C15/MS/10458889 NEWALLS). Z.H. acknowledges support from the National Science Foundation (DMR-1210588). F.G.-O., P.G.-F. and J.J. acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through grant number FIS2015-64886-C5-2-P, and P.G.-F. acknowledges support from Ramón y Cajal grant number RyC-2013-12515. L.Q.C. is supported by the US DOE, Office of Basic Energy Sciences under award FG02-07ER46417. V.A.S. acknowledges support from the US DOE, Office of Science, Office of Basic Energy Sciences, under award number DE-SC- 0012375. M.R.M. and S.D. acknowledges use of the Advanced Photon Source, which was supported by the US DOE, Office of Science, Office of Basic Energy Science (DE-AC02-06CH11357), for the synchrotron-based reciprocal space map studies of samples at the Sector 33-BM-C and 7-ID-C beamline. This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility, under contract number DE-AC02-05CH11231. L.W.M. acknowledges support from the US DOE, Office of Science, Office of Basic Energy Sciences, under award number DE-SC-0012375 for the development of novel ferroic heterostructures. Electron microscopy of superlattice structures was performed at the Molecular Foundry, LBNL, supported by the Office of Science, Office of Basic Energy Sciences, US DOE (DE-AC02-05CH11231). STEM and phase-field analysis and visualization performed by C.T.N. was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. EMPAD-STEM polar mapping at the Cornell Center for Materials Research was funded by the US DOE, grant DE-SC0002334. The Cornell EM Facility is supported by the Cornell Center for Materials Research through the National Science Foundation MRSEC programme, award #DMR DMR-1719875.

Reviewer information

Nature thanks Marty Gregg, Sergey Prosandeev and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

S.D., Y.L.T. and R.R. designed the experiments. S.D. carried out the synthesis and characterization of the trilayers and superlattice samples via RHEED-assisted pulsed-laser deposition; A.B.M. synthesized trilayers and superlattice samples by molecular-beam epitaxy with advice from D.G.S. Y.L.T. performed TEM characterization of the samples, along with detailed polarization vector analysis. K.X.N. performed polarization mapping on superlattice films using EMPAD-STEM, supervised by D.A.M. C.T.N. performed STEM and phase-field analysis and visualization. M.A.P.G., F.G.-O., P.G.-F., J.Í. and J.J. completed the second-principles simulations. Z.H. performed phase-field calculations for these samples with strain. M.R.M., S.D. and V.A.S. carried out the reciprocal space map studies of these samples using synchrotron X-ray diffraction. S.D., M.R.M. and C.K. performed synchrotron X-ray circular-dichroism measurements on these films with P.S. and E.A.’s assistance. R.R., L.W.M., S.D., Y.L.T., Z.H., M.R.M., L.Q.C., P.G.-F., J.Í. and J.J. analysed the data and co-wrote the manuscript. R.R., L.W.M., L.Q.C. and J.J. supervised the research. All authors contributed to the discussions and manuscript preparation.

Competing interests

The authors declare no competing interests.

Correspondence to S. Das or R. Ramesh.

Extended data figures and tables

  1. Extended Data Fig. 1 Three-dimensional reciprocal space mapping.

    af, RSM of the specular peak for the [(PbTiO3)16/(SrTiO3)16]8 superlattice (SL; a and b) and the (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayer (c and d) on a SrTiO3 (001) substrate and for the [(PbTiO3)16/(SrTiO3)16]8 superlattice on a DyScO3 (110) substrate (ef). Near the (003) diffraction condition in a and c, satellite peaks, assigned to polar ordering in PbTiO3, are detected along the in-plane directions, and their lateral characteristic size is about 8 nm and proportional to 1/Qx at the satellite position. b, d, In-plane RSM cuts (taken at the dashed black line in a and c) show a preferential fourfold intensity distribution along the cubic directions of the substrate, which overlaps with a diffuse scattering ring—a pattern that is more intense in the superlattice sample compared to the trilayer sample. g, In-plane line scan data from the dashed lines in b and d are plotted together for the superlattice and trilayer samples. h, Gaussian line profile analyses of the satellite peaks (fitting functions are plotted as black lines) provide peak positions and peak widths at the half intensity maximum (∆Qx), which are found to be similar in the superlattice and trilayer samples grown on the SrTiO3 (001) substrate. The similar sizes of the diffuse-scattering rings (about 8 nm) and the in plane-widths, as well as the same vertical position (Qz) of the diffuse-scattering patterns in the superlattice and trilayer samples, show that the polar-ordering states have common origin in these samples. By contrast, the reciprocal space maps of the polar-vortex structure in the [(PbTiO3)16/(SrTiO3)16]8 superlattice on DyScO3 (110) shown in e around the (003)pc (pc, pseudo-cubic) peak exhibit highly anisotropic in-plane peak satellites, including higher-order peak satellites, which correspond to vortex array ordering with periodicity of about 11 nm, as shown in more detail in the in-plane cut from f, which is taken at the Qz value indicated by the dashed line in e.

  2. Extended Data Fig. 2 Under-focus STEM imaging of polar-skyrmion bubbles across the entire [(PbTiO3)16/(SrTiO3)16]8 superlattice.

    a, The full image. b–d, Magnifications of areas I, II and III labelled in a, showing that the skyrmion bubbles formed in all of the PbTiO3 layers.

  3. Extended Data Fig. 3 Planar-view dark-field STEM imaging.

    a, c, Planar-view dark-field STEM images of (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayers (a) and the [(PbTiO3)16/(SrTiO3)16]8 superlattice (c) on SrTiO3 (001), showing the widespread occurrence of nanometre-size skyrmion bubbles and elongated-skyrmion-like features along the [100] and [010] directions. b, d, Planar-view dark-field STEM images of (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayers (b) and the [(PbTiO3)16/(SrTiO3)16]8 superlattice (d) on DyScO3 (110), showing the long-range in-plane ordering associated with the clockwise–counterclockwise vortex stripe along \({\left[\bar{1}00\right]}_{{\rm{pc}}}\) and confirming the widespread occurrence of these vortex stripes in the trilayers and superlattice films on DyScO3 (110) substrates.

  4. Extended Data Fig. 4 Phase-field simulation of topological polar structure of (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayer and [(PbTiO3)16/(SrTiO3)16]m (m = 3–8) superlattices with different total film thickness.

    ad, Planar view of the (STO)16/(PTO)16/(STO)16 trilayer (a), showing that skyrmion bubbles (diameter of about 8 nm) coexist with elongated skyrmions (length, about 40 nm; diameter, about 8 nm)—long closed vortex-line-like structures. By increasing the number of PTO layers to the [(PbTiO3)16/(SrTiO3)16]3 (b) and [(PbTiO3)16/(SrTiO3)16]5 (c) superlattices, it is observed that the elongated skyrmions become smaller and the skyrmion-bubble density increases. The density of skyrmion bubbles continues to increase until it reaches almost 100% for the [(PbTiO3)16/(SrTiO3)16]8 superlattice (d). Interestingly, the size of the skyrmion bubbles in all these systems barely changes. This is a demonstration of a thickness-driven Rayleigh–Plateau instability, where the longer vortex-line like structure decomposes into small skyrmion bubbles. These features closely match the experimental observations. The blue markers represent in-plane polarization (Pip), whereas the white regions have out-of-plane polarization (Pop). Here, the interior of the skyrmion has Pop out of the page, which rotates in-plane (Pip) to the edge of the skyrmion. eg, Phase-field simulation of the central plane in a PbTiO3 layer. e, The out-of-plane polarization (Pz) of the skyrmion bubble in the PbTiO3 layer at 0 K under various in-plane (ε11) and out-of-plane (ε33) strain states. f, The in-plane polarization distribution for different strain states in the selected region (black solid rectangle) of e reveals the finite Bloch component. g, The out-of-plane polarization (Pz) of the skyrmion bubble in the PbTiO3 layer at 298 K under various strain states. h, The in-plane polarization distribution of different strain states in the selected region (black dashed rectangle) of g reveals the finite Bloch component.

  5. Extended Data Fig. 5 Pontryagin density distribution from phase-field simulations of skyrmion bubbles and elongated skyrmions for the [(PbTiO3)16/(SrTiO3)16]3 superlattice.

    a, Planar view of the [(PbTiO3)16/(SrTiO3)16]3 superlattice, showing coexistence of skyrmion bubbles with elongated-skyrmion features. b, The corresponding Pontryagin density calculation. Skyrmion bubbles have a circular shape, indicating a radial distribution of the polar texture, whereas the elongated-skyrmion features have larger density in the two ends and both positive and negative values in the middle. The surface integration gives a topological charge value of +1 for both the skyrmion bubbles and the elongated skyrmions, so the elongated-skyrmion features and the skyrmion bubbles are topologically equivalent structures.

  6. Extended Data Fig. 6 High-resolution HAADF-STEM imaging.

    a, Atomically resolved plane-view HAADF-STEM image of the (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayer. b, Enlarged PbTiO3 unit cells around the circular domain, showing the Ti shifts directly, as marked by yellow boxes in a. We note the diverging Ti-displacement vector configuration marked with a box. The domain walls are roughly sketched in a (marked by white lines) according to the Ti-displacement map. c, False-colour representations of a. The enhanced contrast facilitates the visualization of the skyrmion bubble and domain walls because of the remnant diffraction contrast, where the ferroelectric domain walls can be seen by the naked eye. dg, Ti-cation-displacement vector maps based on the plane-view HAADF-STEM images showing the domain walls. d, Atomically resolved HAADF-STEM image. White lines denote domain walls. e, A false-colour representation of d. The enhanced contrast facilitates the visualization of the domain walls because of the remnant diffraction contrast, where the ferroelectric domain walls can be seen by the naked eye. f, Superposition of Ti-shift vectors with the HAADF image of the area in d marked with a red box. Dashed lines denote the domain walls. g, An enlarged area of the Ti-shift mapping in f (marked by a blue box), showing the domain walls. Yellow arrows denote Ti-displacement directions. The displacement of Ti cations at the ferroelectric domain walls can be seen clearly.

  7. Extended Data Fig. 7 Electron beam channelling along a column of Sr atoms in SrTiO3.

    a, High-angle ADF signal (50–200 mrad) I(z) for a 300-keV electron beam centred on the Sr site as a function of depth, z, into the crystal, with a 17.2-mrad convergence angle, similar to that used in the HAADF experiments to resolve individual atoms. b, The derivative of the HAADF signal, showing that the peak signal is generated at 3.9 nm or about 10 unit cells into the SrTiO3. The signal is close to the minimum at 16 unit cells, indicating a strong dechannelling at the point where PbTiO3 would begin in a multilayer structure. c, The HAADF signal for a 1.7-mrad convergence angle, similar to that used in the EMPAD experiments to separate diffraction disks. d, From the derivative dI/dz, the signal is still channelling efficiently at the point where the PbTiO3 would begin in a multilayer structure. Thus, the EMPAD setup couples more efficiently to the PbTiO3. The yellow box shows the thickness of 16 unit cells of SrTiO3, the thickness of the repeated cell in the 16 × 16 multilayer.

  8. Extended Data Fig. 8 Chiral textures of the polarization.

    a, b, Three-dimensional cross-sectional view of a polar-skyrmion bubble (a) and chiral polar-vortex structures3 (b). c, The cross-section in the middle of the polar-skyrmion bubble (from the black box in a), where the green and purple colouring represents the in-plane component along the positive and negative y direction, respectively. df, An expanded view of the polarization at the centre of the skyrmion bubble (marked by black lines in c), showing how the polarization rotates in a helical (Bloch-like) fashion along the in-plane direction (d). This is virtually identical to the helical rotation of the polarization (e, f) that is observed at the centre (marked by the black line in b) of chiral polar-vortex structures.

  9. Extended Data Fig. 9 RSXD for a trilayer sample.

    a, Spectra of right- (red) and left- (blue) circularly polarized light at the satellite diffraction peak. b, The same spectra for the trilayer sample after background fluorescence is subtracted. c, The difference of the spectra (XCD) shown in b, which shows strong dichroism at the L3 t2g edge. d, The intensity difference of two CCD images measured at the t2g resonance with opposite circular polarizations. The result clearly shows the circular dichroism at the satellite peak. This localization of dichroism at the diffraction peak indicates that the dichroism comes from periodic chiral structures in the sample. Data for the peak and background were measured at the regions marked in magenta and white, respectively.

  10. Extended Data Fig. 10 RSXD polarization-averaged intensity for a [(PbTiO3)16/(SrTiO3)16]8 superlattice.

    a, Scattering of right- (red) and left- (blue) circularly polarized X-rays from polar skyrmions. The diffraction data were collected along the in-plane (Qy) direction at the third-order superlattice reflection (Qz = 0.16 Å−1). These peaks are the (013) and \(\left(0\bar{1}3\right)\) peaks of the skyrmion lattice. b, The polarization-averaged intensity from RSXD studies reveals an asymmetry in the (013) and \(\left(0\bar{1}3\right)\) diffraction peaks. The asymmetry of the scattered intensity indicates that the polar structures are chiral and consistent with an in-plane Bloch component. c, RSXD images for a superlattice. Images from the two-dimensional CCD used to collect diffraction data for right- (top row) and left- (middle row) circularly polarized light. A strong enhancement in diffraction intensity is observed around 457.2 eV, at the L3 t2g resonance, particularly for right-circularly polarized light. The XCD can be visualized by the difference of the images of right- and left-circularly polarized light (bottom row).

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Fig. 1: Observation of ordered polar structure.
Fig. 2: Second-principles calculations of the skyrmion structure in a PbTiO3–SrTiO3 superlattice.
Fig. 3: Observation of polar-skyrmion structure.
Fig. 4: RSXD circular dichroism.
Extended Data Fig. 1: Three-dimensional reciprocal space mapping.
Extended Data Fig. 2: Under-focus STEM imaging of polar-skyrmion bubbles across the entire [(PbTiO3)16/(SrTiO3)16]8 superlattice.
Extended Data Fig. 3: Planar-view dark-field STEM imaging.
Extended Data Fig. 4: Phase-field simulation of topological polar structure of (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayer and [(PbTiO3)16/(SrTiO3)16]m (m = 3–8) superlattices with different total film thickness.
Extended Data Fig. 5: Pontryagin density distribution from phase-field simulations of skyrmion bubbles and elongated skyrmions for the [(PbTiO3)16/(SrTiO3)16]3 superlattice.
Extended Data Fig. 6: High-resolution HAADF-STEM imaging.
Extended Data Fig. 7: Electron beam channelling along a column of Sr atoms in SrTiO3.
Extended Data Fig. 8: Chiral textures of the polarization.
Extended Data Fig. 9: RSXD for a trilayer sample.
Extended Data Fig. 10: RSXD polarization-averaged intensity for a [(PbTiO3)16/(SrTiO3)16]8 superlattice.

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