• Mon - Sat 8:00 - 6:30, Sunday - CLOSED

Ferroelectric incommensurate spin crystals | Nature Close banner Close banner

Ferroelectric incommensurate spin crystals | Nature Close banner Close banner

Naturevolume 602, pages 240–244 (2022)Cite this article

Subjects

Abstract

Ferroics, especially ferromagnets, can form complex topological spin structures such as vortices1 and skyrmions2,3 when subjected to particular electrical and mechanical boundary conditions. Simple vortex-like, electric-dipole-based topological structures have been observed in dedicated ferroelectric systems, especially ferroelectric–insulator superlattices such as PbTiO3/SrTiO3, which was later shown to be a model system owing to its high depolarizing field4,5,6,7,8. To date, the electric dipole equivalent of ordered magnetic spin lattices driven by the Dzyaloshinskii–Moriya interaction (DMi)9,10 has not been experimentally observed. Here we examine a domain structure in a single PbTiO3 epitaxial layer sandwiched between SrRuO3 electrodes. We observe periodic clockwise and anticlockwise ferroelectric vortices that are modulated by a second ordering along their toroidal core. The resulting topology, supported by calculations, is a labyrinth-like pattern with two orthogonal periodic modulations that form an incommensurate polar crystal that provides a ferroelectric analogue to the recently discovered incommensurate spin crystals in ferromagnetic materials11,12,13. These findings further blur the border between emergent ferromagnetic and ferroelectric topologies, clearing the way for experimental realization of further electric counterparts of magnetic DMi-driven phases.

Access through your institutionBuy or subscribe

This is a preview of subscription content

Access options

Access through your institutionAccess through your institutionChange institutionBuy or subscribe

Subscribe to nature+

Get immediate online access to the entire Nature family of 50+ journals

$29.99

monthly

Subscribe

Subscribe to Journal

Get full journal access for 1 year

$199.00

only $3.90 per issue

Subscribe

All prices are NET prices. VAT will be added later in the checkout.Tax calculation will be finalised during checkout.

Buy article

Get time limited or full article access on ReadCube.

$32.00

Buy

All prices are NET prices.

Data availability

The data that support the findings of this study are available at the University of Warwick open access research repository (http://wrap.warwick.ac.uk/159776/) or from the corresponding author on reasonable request.

References

  1. Wachowiak, A. et al. Direct observation of internal spin structure of magnetic vortex cores. Science 298, 577–580 (2002).

    ADS CAS PubMed Google Scholar

  2. Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).

    ADS CAS PubMed Google Scholar

  3. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    ADS CAS PubMed Google Scholar

  4. Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).

    ADS CAS PubMed Google Scholar

  5. Hsu, S.-L. et al. Emergence of the vortex state in confined ferroelectric heterostructures. Adv. Mater. 31, 1901014–1901022 (2019).

    Google Scholar

  6. Shafer, P. et al. Emergent chirality in the electric polarization texture of titanate superlattices. Proc. Natl Acad. Sci. USA 115, 915–920 (2018).

    ADS CAS PubMed PubMed Central Google Scholar

  7. Gruverman, A. et al. Vortex ferroelectric domains. J. Phys. Condens. Matter 20, 4 (2008).

    Google Scholar

  8. Nelson, C. T. et al. Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11, 828–834 (2011).

    ADS CAS PubMed Google Scholar

  9. Dzyaloshinsky, I. Thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).

    ADS CAS Google Scholar

  10. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).

    ADS CAS Google Scholar

  11. Kurumaji, T. et al. Néel-type skyrmion lattice in the tetragonal polar magnet VOSe2O5. Phys. Rev. Lett. 119, 237201–237205 (2017).

    ADS PubMed Google Scholar

  12. Kurumaji, T. et al. Direct observation of cycloidal spin modulation and field-induced transition in Néel-type skyrmion-hosting VOSe2O5. J. Phys. Soc. Jpn 90, 024705 (2021).

    ADS Google Scholar

  13. Seddon, S. D. et al. Real-space observation of ferroelectrically induced magnetic spin crystal in SrRuO3. Nat. Commun. 12, 2007 (2021).

    ADS CAS PubMed PubMed Central Google Scholar

  14. Hong, Z. et al. Stability of polar vortex lattice in ferroelectric superlattices. Nano Lett. 17, 2246–2252 (2017).

    ADS CAS PubMed Google Scholar

  15. Damodaran, A. R. et al. Phase coexistence and electric-field control of toroidal order in oxide superlattices. Nat. Mater. 16, 1003–1009 (2017).

    ADS CAS PubMed Google Scholar

  16. Stoica, V. A. et al. Optical creation of a supercrystal with three-dimensional nanoscale periodicity. Nat. Mater. 18, 377–383 (2019).

    ADS CAS PubMed Google Scholar

  17. Li, X. et al. Atomic-scale observations of electrical and mechanical manipulation of topological polar flux closure. Proc. Natl Acad. Sci. USA 117, 18954–18961 (2020).

    ADS CAS PubMed PubMed Central Google Scholar

  18. Ponomareva, I., Naumov, I. I. & Bellaiche, L. Low-dimensional ferroelectrics under different electrical and mechanical boundary conditions: atomistic simulations. Phys. Rev. B 72, 214118 (2005).

    ADS Google Scholar

  19. Sanchez-Santolino, G. et al. Resonant electron tunnelling assisted by charged domain walls in multiferroic tunnel junctions. Nat. Nanotechnol. 12, 655–662 (2017).

    ADS CAS PubMed Google Scholar

  20. Penthorn, N. E., Hao, X., Wang, Z., Hua, Y. & Jiang, H. W. Experimental observation of single skyrmion signatures in a magnetic tunnel junction. Phys. Rev. Lett. 122, 257201 (2019).

    ADS CAS PubMed Google Scholar

  21. Peters, J. J. P., Apachitei, G., Beanland, R., Alexe, M. & Sanchez, A. M. Polarization curling and flux closures in multiferroic tunnel junctions. Nat. Commun. 7, 13484 (2016).

    ADS CAS PubMed PubMed Central Google Scholar

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

    ADS CAS PubMed Google Scholar

  23. Li, S. et al. Periodic arrays of flux-closure domains in ferroelectric thin films with oxide electrodes. Appl. Phys. Lett. 111, 052901 (2017).

    ADS Google Scholar

  24. Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019).

    ADS CAS PubMed Google Scholar

  25. Yi, S. D., Onoda, S., Nagaosa, N. & Han, J. H. Skyrmions and anomalous Hall effect in a Dzyaloshinskii-Moriya spiral magnet. Phys. Rev. B 80, 054416–054421 (2009).

    ADS Google Scholar

  26. Zhao, H. J., Chen, P., Prosandeev, S., Artyukhin, S. & Bellaiche, L. Dzyaloshinskii–Moriya-like interaction in ferroelectrics and antiferroelectrics. Nat. Mater. 20, 341–345 (2021).

    ADS CAS PubMed Google Scholar

  27. Aguado-Puente, P. & Junquera, J. Ferromagnetic-like closure domains in ferroelectric ultrathin films: first-principles simulations. Phys. Rev. Lett. 100, 177601–177604 (2008).

    ADS PubMed Google Scholar

  28. Dürr, H. A. et al. Chiral magnetic domain structures in ultrathin FePd films. Science 284, 2166–2168 (1999).

    PubMed Google Scholar

  29. Ahn, C. H. et al. Ferroelectric field effect in ultrathin SrRuO3 films. Appl. Phys. Lett. 70, 206–208 (1997).

    ADS CAS Google Scholar

  30. Jia, C.-L. et al. Atomic-scale study of electric dipoles near charged and uncharged domain walls in ferroelectric films. Nat. Mater. 7, 57–61 (2008).

    ADS CAS PubMed Google Scholar

  31. Naumov, I., Bellaiche, L. & Fu, H. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737–740 (2004).

    ADS CAS PubMed Google Scholar

  32. Junquera, J. & Ghosez, P. Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422, 506–509 (2003).

    ADS CAS PubMed Google Scholar

  33. Nahas, Y. et al. Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics. Nat. Commun. 11, 5779 (2020).

    ADS CAS PubMed PubMed Central Google Scholar

  34. Nahas, Y. et al. Inverse transition of labyrinthine domain patterns in ferroelectric thin films. Nature 577, 47–51 (2020).

    ADS CAS PubMed Google Scholar

  35. Carter, C. B. & Williams, D. B. Transmission Electron Microscopy: Diffraction, Imaging, and Spectrometry (Springer, 2016).

  36. Bode, M. et al. Chiral magnetic order at surfaces driven by inversion asymmetry. Nature 447, 190–193 (2007).

    ADS CAS PubMed Google Scholar

  37. Udalov, O. G., Beloborodov, I. S. & Sapozhnikov, M. V. Magnetic skyrmions and bimerons in films with anisotropic interfacial Dzyaloshinskii-Moriya interaction. Phys. Rev. B 103, 174416 (2021).

    ADS CAS Google Scholar

  38. Chen, J., Zhang, D. W. & Liu, J. M. Exotic skyrmion crystals in chiral magnets with compass anisotropy. Sci. Rep. 6, 29126 (2016).

    ADS CAS PubMed PubMed Central Google Scholar

  39. Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216 (2017).

    ADS CAS PubMed PubMed Central Google Scholar

  40. Tsesses, S. et al. Optical skyrmion lattice in evanescent electromagnetic fields. Science 361, 993–996 (2018).

    ADS MathSciNet CAS PubMed MATH Google Scholar

  41. Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

    CAS PubMed Google Scholar

  42. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    PubMed Google Scholar

  43. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    ADS CAS PubMed Google Scholar

  44. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).

    ADS MathSciNet Google Scholar

  45. Zhang, Y., Sun, J., Perdew, J. P. & Wu, X. Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA. Phys. Rev. B 96, 035143 (2017).

    ADS Google Scholar

  46. Kolpak, A. M., Sai, N. & Rappe, A. Short-circuit boundary conditions in ferroelectric PbTiO3 thin films. Phys. Rev. B 74, 054112–054117 (2006).

    ADS Google Scholar

  47. Leferovich, R. P. & Mitchell, R. H. A structural study of ternary lanthanide orthoscandate perovskites. J. Solid State Chem. 177, 2188–2197 (2004).

    ADS Google Scholar

  48. Longo, V. M. et al. On the photoluminescence behavior of samarium-doped strontium titanate nanostructures under UV light. A structural and electronic understanding. Phys. Chem. Chem. Phys. 12, 7566–7579 (2010).

    CAS PubMed Google Scholar

  49. Bansal, C., Kawanaka, H., Takahashi, R. & Nishihara, Y. Metal–insulator transition in Fe-substituted SrRuO3 bad metal system. J. Alloys Compd. 360, 47–53 (2003).

    CAS Google Scholar

  50. Kuroiwa, Y., Aoyagi, S. & Sawada, A. Evidence for Pb-O covalency in tetragonal PbTiO3. Phys. Rev. Lett. 87, 217601–217605 (2001).

    ADS CAS PubMed Google Scholar

  51. Jones, L. et al. Smart Align—a new tool for robust non-rigid registration of scanning microscope data. Adv. Struct. Chem. Imaging 1, 8 (2015).

    Google Scholar

  52. Li, Q. et al. Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. Nat. Commun. 8, 1468 (2017).

    ADS CAS PubMed PubMed Central Google Scholar

  53. Aso, R., Kan, D., Shimakawa, Y. & Kurata, H. Octahedral tilt propagation controlled by A-site cation size at perovskite oxide heterointerfaces. Cryst. Growth Des. 14, 2128–2132 (2014).

    CAS Google Scholar

  54. Peters, J. J. P. et al. Polarization screening mechanisms at La0.7Sr0.3MnO3–PbTiO3 interfaces. ACS Appl. Mater. Interfaces 12, 10657–10663 (2020).

    CAS PubMed Google Scholar

  55. Sanchez-Santolino, G. et al. Oxygen octahedral distortions in LaMO3/SrTiO3 superlattices. Microsc. Microanal. 20, 825–831 (2014).

    ADS CAS PubMed Google Scholar

  56. Rondinelli, J. M. & Spaldin, N. A. Structure and properties of functional oxide thin films: insights from electronic-structure calculations. Adv. Mater. 23, 3363–3381 (2011).

    CAS PubMed Google Scholar

  57. Sepliarsky, M., Stachiotti, M. G. & Migoni, R. L. Surface reconstruction and ferroelectricity in PbTiO3 thin films. Phys. Rev. B 72, 014110–014116 (2005).

    ADS Google Scholar

  58. Zhang, S. et al. Polarization rotation in ultrathin ferroelectrics tailored by interfacial oxygen octahedral coupling. ACS Nano 12, 3681–3688 (2018).

    CAS PubMed Google Scholar

Download references

Acknowledgements

This work was partly supported by the EPSRC (UK) through grant nos. EP/P031544/1 and EP/P025803/1. M.A. acknowledges the Theo Murphy Blue Skies Award of the Royal Society. This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science user facility, operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. We also acknowledge the technical support from M. Crosbie. We would like to acknowledge the University of Warwick Research Technology Platform for assistance in the research described in this paper.

Author information

Affiliations

  1. Department of Physics, University of Warwick, Coventry, UK

    Dorin Rusu, Jonathan J. P. Peters, Thomas P. A. Hase, James A. Gott, Samuel D. Seddon, Richard Beanland, Ana M. Sanchez & Marin Alexe

  2. School of Physics, Trinity College Dublin, Dublin, Ireland

    Jonathan J. P. Peters

  3. Diamond Light Source, Didcot, UK

    Gareth A. A. Nisbet

  4. Argonne National Laboratory, Lemont, IL, USA

    Jörg Strempfer & Daniel Haskel

Authors
  1. Dorin RusuView author publications

    You can also search for this author inPubMed Google Scholar

  2. Jonathan J. P. PetersView author publications

    You can also search for this author inPubMed Google Scholar

  3. Thomas P. A. HaseView author publications

    You can also search for this author inPubMed Google Scholar

  4. James A. GottView author publications

    You can also search for this author inPubMed Google Scholar

  5. Gareth A. A. NisbetView author publications

    You can also search for this author inPubMed Google Scholar

  6. Jörg StrempferView author publications

    You can also search for this author inPubMed Google Scholar

  7. Daniel HaskelView author publications

    You can also search for this author inPubMed Google Scholar

  8. Samuel D. SeddonView author publications

    You can also search for this author inPubMed Google Scholar

  9. Richard BeanlandView author publications

    You can also search for this author inPubMed Google Scholar

  10. Ana M. SanchezView author publications

    You can also search for this author inPubMed Google Scholar

  11. Marin AlexeView author publications

    You can also search for this author inPubMed Google Scholar

Contributions

M.A. conceived the idea. D.R., M.A. and A.M.S. designed the experiments. D.R. prepared the samples, performed DFT and DF-TEM experiments and analysed the data. J.J.P.P. and J.A.G. performed the STEM experiments and analysis. G.A.A.N., J.S., D.H. and D.R. collected the synchrotron data. T.P.A.H. and D.R. analysed the XRD data. R.B. performed the two-beam diffraction contrast simulations. All authors contributed to the discussions. All authors wrote the manuscript.

Corresponding author

Correspondence toMarin Alexe.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review information

Peer review information

Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Structure characterization.

a, AFM topography of the surface of our (SrRuO3)11/(PbTiO3)13/(SrRuO3)11 trilayer sample. b, Low-magnification cross-sectional STEM of the sample. The scale bar is 10 nm.

Extended Data Fig. 2 RSM data.

a, 3D reciprocal space map around the DSO 002pc Bragg peak. The side panels show the 2D projected intensity of the recorded scatter. b, RSM around the asymmetric reflection (103)pc. c, Reciprocal space map Qz versus Qx. d, Comparison plot of the extracted Qz scan at Qx = 0 and Qx = 0.07 Å−1. e, Integrated (boxed area) line profile showing the first-order and second-order satellite peaks and their widths. f, Reciprocal space map Qz versus Qy. g, The integrated (boxed area) line profile shows weak first-order satellite peaks corresponding to a periodicity of about 8.05 nm. h, Plan-view projection into a Qx versus Qy RSM map with extracted line scans showing the in-plane distribution of the satellite peaks.

Extended Data Fig. 3 Cross-sectional DF-TEM.

a, Image of a (100)pc cross section taken under the g = 020pc excitation condition. b, Image of the same (100)pc cross section taken under the g = 002pc excitation. c, Image of a (010)pc cross section (that is, cut at 90° from a and b) taken using g = 002pc. The scale bars are 20 nm.

Extended Data Fig. 4 Plan-view DF-TEM.

a, Low-magnification plan view of the complex domain pattern take under the g1 = 110pc condition. The figure inset shows the enlarged boxed area. b, Plan-view dark-field image taken under g2 = 100pc. c, Plan-view diffraction contrast taken under g3 = 010pc excitation. The scale bars are 100 nm for a and 30 nm for b and c.

Extended Data Fig. 5 Noise filter.

a, 2D Fourier transform of the plan-view image taken under g1 = 110 excitation. b, Bandpass filter that removes the noise and retains the signal for |Q| −1. c, Bandpass filter that also removes the central spot and the signal for |Q| −1. The scale bar is 30 nm.

Extended Data Fig. 6 Filtered/unfiltered plan-view DF-TEM.

a, The bandpass filter improves the signal-to-noise ratio without introducing artefacts. Both the filtered and unfiltered images show, apart from the labyrinth pattern, a periodic modulation in the contrast along the individual domains. b, The second modulation permeates the labyrinth pattern.

Extended Data Fig. 7 Diffraction contrast simulations.

Left, experimental plan-view DF-TEM images of the vortex array. Note that the g = 110pc image is at higher magnification and Bragg filtered. Right, two-beam Howie–Whelan diffraction contrast simulations of the contrast arising from the strain fields of a 2D array of vortices as described in the main text (deviation parameter s = 0.01 nm). The scale bars are 30 nm for g = 010, 30 nm for g = 100 and 10 nm for g = 110.

Extended Data Fig. 8 Tilt map.

Left, oxygen tilt behaviour along a row of unit cells. Right, tilt map throughout the PTO layer.

Extended Data Fig. 9 Cross-sectional polar maps.

a, Polarization maps along the ordered [010]pc direction. The projection of a cycloidal and helical modulated vortex array into the [001]pc–[010]pc plane shows that the domain topology is retained. b, The projection of the modulated vortex array into the [001]pc–[100]pc plane shows that the cycloidal modulation allows the polar vector to rotate in plane, similar to the experimental polar map, whereas the helical modulation does not.

Extended Data Fig. 10 X-ray CD data.

a, [100]pc//[001]o in the scattering plane. b, [010]pc//[−110]o in the scattering plane. The first row presents the sum of the dichroic signal, (I+ + I)/2, in which I± refers to the measured intensity for opposite helicities of the incoming light and the second row shows the CD signal, (I+ − I)/(I+ + I), and its behaviour on 180° rotation of the sample. The third panel shows the dichroic signal, (CDϕ1 − CDϕ2)/2, associated with a rotation of the sample by 180°, demonstrating a weak signal at the ± satellites in a, which is absent in b. In c and d, we show the dichroism under sample rotation when [100]pc//[001]o is in the scattering plane (c) and when the [010]pc//[−110]o direction is in the scattering plane (d). The upper panels of c and d plot the data from the two satellites onto a common axis, with the lower panels showing their average.

Supplementary information

Supplementary Information

This file contains Supplementary Text, Supplementary Figures 1–10 and Supplementary References.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rusu, D., Peters, J.J.P., Hase, T.P.A. et al. Ferroelectric incommensurate spin crystals.Nature 602, 240–244 (2022). https://doi.org/10.1038/s41586-021-04260-1

Download citation

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.