Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Flexoelectric rotation of polarization in ferroelectric thin films

Nature Materials volume 10, pages 963–967 (2011)Cite this article

Subjects

Abstract

Strain engineering enables modification of the properties of thin films using the stress from the substrates on which they are grown. Strain may be relaxed, however, and this can also modify the properties thanks to the coupling between strain gradient and polarization known as flexoelectricity. Here we have studied the strain distribution inside epitaxial films of the archetypal ferroelectric PbTiO3, where the mismatch with the substrate is relaxed through the formation of domains (twins). Synchrotron X-ray diffraction and high-resolution scanning transmission electron microscopy reveal an intricate strain distribution, with gradients in both the vertical and, unexpectedly, the horizontal direction. These gradients generate a horizontal flexoelectricity that forces the spontaneous polarization to rotate away from the normal. Polar rotations are a characteristic of compositionally engineered morphotropic phase boundary ferroelectrics with high piezoelectricity; flexoelectricity provides an alternative route for generating such rotations in standard ferroelectrics using purely physical means.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Piezo-response force microscopy image of a twinned ferroelectric film.
Figure 2: X-ray diffraction data revealing a correlated distribution of tetragonality and twin angles.
Figure 3: Direct imaging of strain gradients.
Figure 4: Sketch of stresses, strain gradients and polar vectors in the twinned film.
Figure 5: Direct observation of polarization rotations.

Similar content being viewed by others

References

  1. Rossetti, G. A., Cross, L. E. & Kushida, K. Stress induced shift of the Curie point in epitaxial PbTiO3 thin films. Appl. Phys. Lett. 59, 2524–2526 (1991).

    Article  CAS  Google Scholar 

  2. Pertsev, N. A., Zembilgotov, A. G. & Tagantsev, A. K. Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. 80, 1988–1991 (1998).

    Article  CAS  Google Scholar 

  3. Canedy, C. L. et al. Dielectric properties in heteroepitaxial Ba0.6Sr0.4TiO3 thin films: Effect of internal stresses and dislocation-type defects. Appl. Phys. Lett. 77, 1695–1697 (2000).

    Article  CAS  Google Scholar 

  4. Sinnamon, L. J., Bowman, R. M. & Gregg, J. M. Thickness-induced stabilization of ferroelectricity in SrRuO3/Ba0.5Sr0.5TiO3/Au thin film capacitors. Appl. Phys. Lett. 81, 889–891 (2002).

    Article  CAS  Google Scholar 

  5. Choi, K. J. et al. Enhancement of ferroelectricity in strained BaTiO3 thin films. Science 306, 1005–1009 (2004).

    Article  CAS  Google Scholar 

  6. Haeni, J. H. et al. Room-temperature ferroelectricity in strained SrTiO3 . Nature 430, 758–761 (2004).

    Article  CAS  Google Scholar 

  7. Catalan, G., Sinnamon, L. J. & Gregg, J. M. The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films. J. Phys. Condens. Matter 16, 2253–2264 (2004).

    Article  CAS  Google Scholar 

  8. Catalan, G., Noheda, B., McAneney, J., Sinnamon, L. J. & Gregg, J. M. Strain gradients in epitaxial ferroelectrics. Phys. Rev. B 72, 020102 (2005).

    Article  Google Scholar 

  9. Majdoub, M. S., Maranganti, R. & Sharma, P. Understanding the origins of the intrinsic dead layer effect in nanocapacitors. Phys. Rev. B 79, 115412 (2009).

    Article  Google Scholar 

  10. Kogan, V. D. Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov. Phys. Solid State 5, 2069–2070 (1964).

    Google Scholar 

  11. Bursian, E. V. & Zaikovskii, O. I. Changes in the curvature of a ferroelectric film due to polarization. Sov. Phys. Solid State 10, 1121–1124 (1968).

    Google Scholar 

  12. Cross, L. E. Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients. J. Mater. Sci. 41, 53–63 (2006).

    Article  CAS  Google Scholar 

  13. Zhu, W., Fu, J. Y., Li, N. & Cross, L. Piezoelectric composite based on the enhanced flexoelectric effects. Appl. Phys. Lett. 89, 192904 (2006).

    Article  Google Scholar 

  14. Ma, W. A study of flexoelectric coupling associated internal electric field and stress in thin film ferroelectrics. Phys. Status Solidi B 245, 761–768 (2008).

    Article  CAS  Google Scholar 

  15. Majdoub, M. S., Sharma, P. & Çağin, T. Dramatic enhancement in energy harvesting for a narrow range of dimensions in piezoelectric nanostructures. Phys. Rev. B 78, 121407 (2008).

    Article  Google Scholar 

  16. Tagantsev, A. K., Meunier, V. & Sharma, P. Novel electromechanical phenomena at the nanoscale: Phenomenological theory and atomistic modeling. MRS Bull. 34, 643–647 (2009).

    Article  CAS  Google Scholar 

  17. Zubko, P., Catalan, G., Welche, P. R. L., Buckley, A. & Scott, J. F. Strain-gradient-induced polarization in SrTiO3 single crystals. Phys. Rev. Lett. 99, 167601 (2007).

    Article  CAS  Google Scholar 

  18. Maranganti, R. & Sharma, P. Atomistic determination of flexoelectric properties of crystalline dielectrics. Phys. Rev. B 80, 054109 (2009).

    Article  Google Scholar 

  19. Hong, J., Catalan, G., Scott, J. F. & Artacho, E. The flexoelectricity of barium and strontium titanates from first principles. J. Phys. Condens. Matter 22, 112201 (2010).

    Article  Google Scholar 

  20. Gruverman, A. et al. Mechanical stress effect on imprint behavior of integrated ferroelectric capacitors. Appl. Phys. Lett. 83, 728–730 (2003).

    Article  CAS  Google Scholar 

  21. Tagantsev, A. K., Cross, L. E. & Fousek, J. Domains in Ferroelectric Crystals and Thin Films 637 (Springer, 2010).

    Book  Google Scholar 

  22. Lee, D. et al. Giant flexoelectric effect in ferroelectric epitaxial thin films. Phys. Rev. Lett. 107, 057602 (2011).

    Article  CAS  Google Scholar 

  23. Vrejoiu, I. et al. Intrinsic ferroelectric properties of strained tetragonal PbZr0.2Ti0.8O3 obtained on layer-by-layer grown, defect-free single-crystalline films. Adv. Mater. 18, 1657–1661 (2006).

    Article  CAS  Google Scholar 

  24. Catalan, G. et al. Polar domains in lead titanate films under tensile strain. Phys. Rev. Lett. 96, 127602 (2006).

    Article  CAS  Google Scholar 

  25. Pompe, W., Gong, X., Suo, Z. & Speck, J. S. Elastic energy release due to domain formation in the strained epitaxy of ferroelectric and ferroelastic films. J. Appl. Phys. 74, 6012–6019 (1993).

    Article  CAS  Google Scholar 

  26. Zeches, R. J. et al. A strain-driven morphotropic phase boundary in BiFeO3 . Science 326, 977–980 (2009).

    Article  CAS  Google Scholar 

  27. Qiu, Q. Y., Nagarajan, V. & Alpay, S. P. Film thickness versus misfit strain phase diagrams for epitaxial PbTiO3 ultrathin ferroelectric films. Phys. Rev. B 78, 064117 (2008).

    Article  Google Scholar 

  28. Bellaiche, L., Garcia, A. & Vanderbilt, D. Finite-temperature properties of Pb(Zr1−xTix)O3 alloys from first principles. Phys. Rev. Lett. 84, 5427–5430 (2000).

    Article  CAS  Google Scholar 

  29. Fu, H. & Cohen, R. E. Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature 403, 281–283 (2000).

    Article  CAS  Google Scholar 

  30. Guo, R. et al. Origin of the high piezoelectric response in PbZr1−xTixO3 . Phys. Rev. Lett. 84, 5423–5426 (2000).

    Article  CAS  Google Scholar 

  31. Speck, J. S. & Pompe, W. Domain configurations due to multiple misfit relaxation mechanisms in epitaxial ferroelectric thin films. I. Theory. J. Appl. Phys. 76, 466–476 (1994).

    Article  CAS  Google Scholar 

  32. Pertsev, N. A. & Zembilgotov, A. G. Energetics and geometry of 90° domain structures in epitaxial ferroelectric and ferroelastic films. J. Appl. Phys. 78, 6170–6180 (1995).

    Article  CAS  Google Scholar 

  33. Vlooswijk, A. H. G. et al. Smallest 90° domains in epitaxial ferroelectric films. Appl. Phys. Lett 91, 112901 (2007).

    Article  Google Scholar 

  34. Kwak, B. S. et al. Strain relaxation by domain formation in epitaxial ferroelectric thin films. Phys. Rev. Lett. 68, 3733–3736 (1992).

    Article  CAS  Google Scholar 

  35. Kwak, B. S. et al. Domain formation and strain relaxation in epitaxial ferroelectric heterostructures. Phys. Rev. B 49, 14865–14879 (1994).

    Article  CAS  Google Scholar 

  36. Ivry, Y., Chu, D. P. & Durkan, C. Bundles of polytwins as meta-elastic domains in the thin polycrystalline simple multi-ferroic system PZT. Nanotechnology 21, 065702 (2010).

    Article  Google Scholar 

  37. Pietsch, U., Holy, V. & Baumbach, T. High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures (Springer, 2004).

    Book  Google Scholar 

  38. Walker, D., Thomas, P. A. & Collins, S. R. A comprehensive investigation of the structural properties of ferroelectric PbZr0.2Ti0.8O3 thin films grown by PLD. Phys. Status Solidi A 206, 1799–1803 (2009).

    Article  CAS  Google Scholar 

  39. Nellist, P. D. et al. Direct sub-angstrom imaging of a crystal lattice. Science 305, 1741 (2004).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  41. Hytch, M. J., Snoeck, E. & Kilaas, R. Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 74, 131–146 (1998).

    Article  CAS  Google Scholar 

  42. GPA Phase plug-in for DigitalMicrograph (Gatan) (HREM Research Inc.) available at: http://www.hremresearch.com.

  43. Ma, W. & Cross, L. E. Strain-gradient-induced electric polarization in lead zirconate titanate ceramics. Appl. Phys. Lett. 82, 3293–3295 (2003).

    Article  CAS  Google Scholar 

  44. Hellwege, K-H. & Hellwege, A. M. (eds) Landolt–Bornstein: Numerical Data and Functional Relationships in Science and Technology (New Series—Group III, Vol. 16a, Springer, 1981).

  45. Cohen, R. E. Origin of ferroelectricity in perovskite oxides. Nature 358, 136–138 (1992).

    Article  CAS  Google Scholar 

  46. Jia, C-L. et al. Unit-cell scalemapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films. Nature Mater. 6, 64–69 (2007).

    Article  CAS  Google Scholar 

  47. Muralt, P. The emancipation of ferroelectricity. Nature Mater. 6, 8–9 (2007).

    Article  CAS  Google Scholar 

  48. Rossetti, G. A. Jr, Zhang, W. & Khachaturyan, A. G. Phase coexistence near the morphotropic phase boundary in lead zirconate titanate (PbZrO3–PbTiO3) solid solutions. Appl. Phys. Lett. 88, 072912 (2006).

    Article  Google Scholar 

  49. Noheda, B. & Cox, D. E. Bridging phases at the morphotropic boundaries of lead oxide solid solutions. Phase Transit. 79, 5–20 (2006).

    Article  CAS  Google Scholar 

  50. Davis, M. Picturing the elephant: Giant piezoelectric activity and the monoclinic phases of relaxor-ferroelectric single crystals. J. Electroceramics 19, 23–45 (2007).

    Article  CAS  Google Scholar 

  51. Ahn, S. J., Kim, J-J., Kim, J-H. & Choo, W-K. Origin of polar domains in ferroelectric relaxors. J. Korea Phys. Soc. 42, S1009–S1011 (2003).

    CAS  Google Scholar 

  52. Nagarajan, V. et al. Dynamics of ferroelastic domains in ferroelectric thin films. Nature Mater. 2, 43–47 (2003).

    Article  CAS  Google Scholar 

  53. Koster, G., Kropman, B. L., Rijnders, G. J. H. M., Blank, D. H. A. & Rogalla, H. Quasi-ideal strontium titanate crystal surfaces through formation of strontium hydroxide. Appl. Phys. Lett. 73, 2920–2922 (1998).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

W. Caliebe is gratefully acknowledged for his help at the W1 beamline. This work is part of research programme 04PR2359 of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). G.C., A.H.G.V. and B.N. also acknowledge financial support from the NWO-Vidi grant 700.54.426, and from the Explora grant MAT2010-10067-E (G.C.). A.L. and E.S. acknowledge financial support from the European Union under the Framework 6 program under a contract for an Integrated Infrastructure Initiative. Reference 026019 ESTEEM.

Author information

Authors and Affiliations

  1. Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands

    G. Catalan, A. H. G. Vlooswijk, G. Rispens & B. Noheda

  2. ICREA and CIN2, Campus Universitat Autonoma de Barcelona, Bellaterra 08193, Barcelona, Spain

    G. Catalan

  3. CEMES-CNRS, 29, rue Jeanne-Marvig, 31055 Toulouse, France

    A. Lubk & E. Snoeck

  4. Transpyrenean Associated Laboratory for Electron Microscopy, CEMES—INA, CNRS—University of Zaragoza, Spain

    E. Snoeck & C. Magen

  5. and Departamento de Física de la Materia Condensada, Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA)–ARAID, Universidad de Zaragoza, 50018 Zaragoza, Spain

    C. Magen

  6. MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands

    A. Janssens, G. Rijnders & D. H. A. Blank

Authors
  1. G. Catalan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Lubk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. H. G. Vlooswijk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. Snoeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Magen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. Janssens
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. G. Rispens
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. G. Rijnders
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. D. H. A. Blank
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. B. Noheda
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.C. and B.N. have devised, designed and organized the work; A.H.G.V. and A.J. have grown the films under the supervision of G.R. and D.H.A.B.; A.H.G.V., G.C., G.R. and B.N. have carried out the X-ray experiments and analysed the X-ray data; A.L., E.S. and C.M. have designed, carried out and organized the electron microscopy experiments and analysed the data. All the authors have contributed to the discussions.

Corresponding authors

Correspondence to G. Catalan or B. Noheda.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Catalan, G., Lubk, A., Vlooswijk, A. et al. Flexoelectric rotation of polarization in ferroelectric thin films. Nature Mater 10, 963–967 (2011). https://doi.org/10.1038/nmat3141

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3141

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing