Abstract
Polar skyrmions have demonstrated rich physics and exotic properties for developing novel functionalities. However, so far, skyrmion nanodomains exist only in a few material systems, such as ferroelectric/dielectric superlattices, free-standing PbTiO3/SrTiO3 epitaxial bilayers and ultrathin Pb(Zr,Ti)O3/SrTiO3/Pb(Zr,Ti)O3 sandwiches. These heterostructures are fabricated with elaborately designed boundary conditions to meet the delicate energy balance for stabilizing topological phases. This requirement limits the broad applications of skyrmions in electronic devices. Here we show widespread skyrmion nanodomains in ferroelectric–antiferroelectric solid solutions, composed of ferroelectric PbTiO3 and one antiferroelectric PbSnO3 (Pb(Ti1–xSnx)O3), PbHfO3 (Pb(Ti1–xHfx)O3) or PbZrO3 (Pb(Ti1–xZrx)O3). The skyrmionic textures are formed by engineering dipole–dipole and antiferrodistortive–dipole couplings in competition between ferroelectric and antiferroelectric polar orderings, allowing the stabilization of topological phases. A phase diagram is built for the three solid solution series, revealing the stabilization regions of skyrmion nanodomains. In addition, the non-trivial domains also exhibit improved switching character, reversible writing/erasure and long-term retention for the electrical manipulation of polar configurations. These findings open an avenue for the investigation and exploitation of polar skyrmions in ferroelectric-based materials, providing opportunities in topological electronics.
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Data availability
The data that support this work are available via figshare at https://doi.org/10.6084/m9.figshare.28450781 (ref. 52).
Code availability
The effective Hamiltonian fitting and simulation are performed using the ALFE-H package, which is available at https://obeyond.nju.edu.cn/Code/index.html after registration. Other code or mathematical algorithm files in this paper are available from the corresponding authors upon reasonable request.
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Acknowledgements
Z.W. acknowledges support from the Natural Science Foundation of China (grant number 52372113) and the Taishan Scholar Program of Shandong Province (grant number tstp20240511). Y.Y. acknowledges support from the Natural Science Foundation of China (grant numbers 12274201 and 52232001) and the National Key R&D Program of China (grant numbers 2022YFB3807601 and 2020YFA0711504). Y.D. acknowledges support from the Natural Science Foundation of China (grant number 12274202). L.B. thanks the Vannevar Bush Faculty Fellowship (VBFF; grant number N00014-20-1-2834) from the Department of Defense, the Army Research Office (ARO) grant number W911NF-21-1-0113, grant number MURI ETHOS W911NF-21-2-0162 from ARO, and the MonArk NSF Quantum Foundry supported by the National Science Foundation Q-AMASE-i Program under NSF Award Number DMR-1906383. Y.N. acknowledges support from the National Natural Science Foundation of China (grant number 12434002) and Natural Science Foundation of Jiangsu Province (grant number BK20233001).
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Z.W. conceived this work. Z.W. and W.Z. designed the experiments. Y.Y. and X.M. designed the calculations. W.Z. fabricated the samples and carried out the PFM characterizations under the supervision of Z.W. X.M. carried out the effective Hamiltonian simulations under the supervision of Y.Y. Z.P. and Y.R. carried out the STEM characterizations and analyses under the supervision of Y.D. W.Z. and J.X. carried out the X-ray diffraction characterizations. Z.W., Y.Y., Y.D., W.Z., X.M., Z.P., H.C., C.Z., J.L., X.L., Y.N., D.W. and L.B. analysed the experimental and simulation results. Z.W., Y.Y., Y.D., W.Z., X.M. and L.B. wrote the paper. All authors discussed the data and contributed to the paper.
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Extended data
Extended Data Fig. 1 Skyrmion nanodomains in PTS thin films.
a, XRD pattern of the PTSx=0.25/SrRuO3/GdScO3 thin-film heterostructure. The 80 nm-thick PTSx=0.25 thin film is epitaxial on the (001)pc-oriented GdScO3 substrate by pulsed laser deposition, buffered with metallic SrRuO3 as the bottom electrode. The * and # symbols denote the Bragg reflections of the GdScO3 and the SrRuO3, respectively. The insets show AFM surface topographies of the GdScO3 substrate, the SrRuO3 bottom electrode, and the PTSx=0.25 thin film, respectively, exhibiting atomically-smooth surfaces. b, c, Vector PFM images measured at the azimuth angle of 0° and 90°, respectively, in which one can find that the centre-convergent skyrmionic textures with the core polarization downwards are formed in the upward-polarized matrix with the domain walls always following the azimuth angle.
Extended Data Fig. 2 Construction of the in-plane (IP) piezoresponse vector map.
a, Schematic of the LPFM measurement. LPFM detects the torsional motion of the cantilever to sense the IP oscillations of the underneath sample. b, The amplitude and phase signals of the fitting curve, which determine the amplitude and direction of the IP piezoresponse vector. LPFM real part signal was collected experimentally as a function of tip orientation angle φ and then the amplitude and the phase delay were determined by trigonometric curve fitting. c, IP piezoresponse vector map for a center-convergent dipole textures in the PTSx=0.25 solid solution. d, The trigonometric curve fitting for four representative points that are denoted as red spots in (c).
Extended Data Fig. 3 Quantified analyses of the polar textures.
HAADF images (left panels) and color-scale mappings of the vector displacements (right panels) for (a) centre-divergent and (b) centre-convergent skyrmionic textures, respectively. In HAADF images, thick red circles indicate skyrmion nanodomains and the dashed white circles indicate the divided concentric-ring regions labeled with the number 1~4 for estimating averaged displacements. c, A sketch for a skyrmionic texture in top view. The thick yellow arrow denotes a polar vector (its length is defined as the |D|). The dashed lines denote the radial direction of dipoles in ideal conditions, in which the arrows define the positive directions that are against the center. The Dr is the radial displacement, that is, the projection of |D| on the radial direction. d, e plot averaged Dr and |D| of the four regions for the two types of polar textures, respectively, in which the error bars are s.d. from more than 12 data points for each region. For the centre-divergent (centre-convergent) texture, all the Dr are positive (negative), conforming the divergent (convergent) character of the dipoles along the radial directions. In addition, both the averaged |Dr| and |D| are increasing with region number from centric to outer. These results correspond to the feature of skyrmionic texture where the dipoles in the core are almost out-of-plane arranged and they are whirling from the core to the outside, resulting in the increase in the in-plane displacement components.
Extended Data Fig. 4 The calculation of effective Hamiltonian parameters of the PTSx=0.25 by the active learning approach.
a, Bayesian error. The dashed line in denotes the threshold to perform first-principles calculations. b, Potential energy. The blue and orange lines in denote the potential energy predicted by the effective Hamiltonian model during the fitting process and using the parameters obtained after the fitting, respectively. The open circles in denote the potential energy obtained from the first-principles calculations. c, Local dipolar mode. The active learning is performed on 2 × 2 × 2 supercell of the perovskite unit-cell (40 atoms). The Bayesian error (a) exhibits a sharp drop at the beginning of fitting, with first principles calculations called frequently. After about 5000 steps, the Bayesian error threshold (a) remains basically unchanged, and first-principles calculations are less frequently called, indicating that the fitting is approaching convergence. The potential energy values predicted by the effective Hamiltonian are close to those obtained from first principles calculations (b). The local dipolar mode (c) shows one nonzero average value during the whole fitting process, characterizing a macroscopic tetrahedral ferroelectric phase.
Extended Data Fig. 5 Simulated domain configuration of the PTSx=0.25 ceramic.
a, Simulated domain configuration in top view. b, Topology charge density. c, d, Cross-sectional views along x and y directions, respectively.
Extended Data Fig. 6 Skyrmion nanodomains with different lateral sizes.
a, The HAADF images with overlay of polar displacement vectors, in which the skyrmionic textures with lateral size of ~3.0 and ~8.0 nm are observed. b, Vector PFM characterizations of the skyrmion nanodomains. The smallest skyrmion nanodomains observed by the PFM are ~15 nm in lateral. For skyrmions smaller than 15 nm, clear dipole textures cannot be detected because of the limitation of the tip diameter (see Methods for the details of tips).
Extended Data Fig. 7 Raman spectra of the ceramics.
a, PTSx=0.25. b, PTHx=0.25. c, PTZx=0.25. d, PbTiO3. e, Enlarged views of the Raman spectra in 30~100 cm−1 region for the PTSx=0.25, PTHx=0.25, and PTZx=0.25 solid solutions with the intensity of E(TO1) mode normalized to 1.0 and f, The PbTiO3. In the Raman spectra, the AFD mode appears at ~45 cm−1, on the left side of the E(TO1) mode (e, f). To facilitate the comparison, the intensities of the E(TO1) modes are normalized to 1.0, as indicated by the horizontal dashed lines. As shown, at the same antiferroelectric concentration of x = 0.25, the PTSx=0.25 exhibits the strongest AFD mode intensity and the AFD mode intensity decreases successively from PTSx=0.25 to PTHx=0.25 and then to PTZx=0.25. For PbTiO3, there is no AFD mode.
Extended Data Fig. 8 PFM hysteresis loops of the solid-solution ceramics.
a, PTSx=0.25. b, PTHx=0.50. c, PTZx=0.67. The PFM phase (red) and amplitude (blue) loops are plotted by the out-of-plane piezoresponse signals by setting the AC frequency of readout to the vertical resonance peak in the DART mode. The tips adopted have force constant of 0.5~9.5 N/m (Nanosensors PPP-EFM). With the skyrmionic textures, the imprint effects are reduced and the coercive voltages are lowered. The coercive voltages, determined by the amplitude minima of the butterfly-type amplitude loops, are plotted in Fig. 6b in the main text.
Extended Data Fig. 9 The evolution of skyrmion nanodomains during switching.
a–c, Vector PFM characterizations of the skyrmion nanodomains for the pristine state and after applying +4.0 and +8.0 V. The skyrmion gradually shrinks and finally annihilates. d–f, Vector PFM characterizations of the skyrmion nanodomains after applying −4.0 and −8.0 V. The skyrmion is created by switching the area (the dashed blue circle) upwards and then becomes larger with increasing negative DC bias. During these erasure/writing processes, the skyrmion nanodomain always keeps its isotropy in in-plane polarization component.
Extended Data Fig. 10 Vector PFM characterizations for the electrical writing of skyrmion arrays.
a, Skyrmion arrays written on PTSx=0.25 ceramic, where the nanodomains can be written in the regions where there already exist skyrmions in the ceramic. b, Skyrmion arrays written on PTSx=0.25 thin film. The nanodomains can be written anywhere on the 80 nm-thick PTSx=0.25/SrRuO3/GdScO3 heterostructure.
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Zheng, W., Ma, X., Pang, Z. et al. Skyrmion nanodomains in ferroelectric–antiferroelectric solid solutions. Nat. Mater. 24, 1424–1432 (2025). https://doi.org/10.1038/s41563-025-02216-8
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DOI: https://doi.org/10.1038/s41563-025-02216-8
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