Skip to main content

Thank you for visiting 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.

Intermittency, quasiperiodicity and chaos in probe-induced ferroelectric domain switching


Memristive materials and devices, which enable information storage and processing on one and the same physical platform, offer an alternative to conventional von Neumann computation architectures. Their continuous spectra of states with intricate field-history dependence give rise to complex dynamics, the spatial aspect of which has not been studied in detail yet. Here, we demonstrate that ferroelectric domain switching induced by a scanning probe microscopy tip exhibits rich pattern dynamics, including intermittency, quasiperiodicity and chaos. These effects are due to the interplay between tip-induced polarization switching and screening charge dynamics, and can be mapped onto the logistic map. Our findings may have implications for ferroelectric storage, nanostructure fabrication and transistor-less logic.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: LiNbO3 sample overview and domain writing schematics.
Figure 2: Evolution of domain morphologies in a single chain as a function of writing conditions.
Figure 3: Evolution of the domain patterns.
Figure 4: Modelling domain writing.
Figure 5: Numerical solutions for various conditions.
Figure 6: Comparison of experimental and modelled results.


  1. 1

    Gleick, J. Chaos: Making a New Science (Penguin Books, 2008).

    Google Scholar 

  2. 2

    Strogatz, S. H. Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Westview, 2001).

    Google Scholar 

  3. 3

    Bunde, A. & Havlin, S. Fractals and Disordered Systems (Springer, 2012).

    Google Scholar 

  4. 4

    Havlin, D. Diffusion and Reactions in Fractals and Disordered Systems (Cambridge Univ. Press, 2005).

    Google Scholar 

  5. 5

    Barabasi, A-L. & Stanley, H. E. Fractal Concepts in Surface Growth (Cambridge Univ. Press, 1995).

    Google Scholar 

  6. 6

    Abarbanel, H. D. I., Brown, R., Sidorowich, J. J. & Tsimring, L. S. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65, 1331–1392 (1993).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7

    Ott, E., Grebogi, C. & Yorke, J. A. Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8

    Garstecki, P., Fuerstman, M. J. & Whitesides, G. M. Oscillations with uniquely long periods in a microfluidic bubble generator. Nature Phys. 1, 168–171 (2005).

    ADS  Article  Google Scholar 

  9. 9

    Gruverman, A. & Kholkin, A. Nanoscale ferroelectrics: Processing, characterization and future trends. Rep. Prog. Phys. 69, 2443–2474 (2006).

    ADS  Article  Google Scholar 

  10. 10

    Kalinin, S. V., Morozovska, A. N., Chen, L. Q. & Rodriguez, B. J. Local polarization dynamics in ferroelectric materials. Rep. Prog. Phys. 73, 056502 (2010).

    ADS  Article  Google Scholar 

  11. 11

    Rodriguez, B. J. et al. Domain growth kinetics in lithium niobate single crystals studied by piezoresponse force microscopy. Appl. Phys. Lett. 86, 012906 (2005).

    ADS  Article  Google Scholar 

  12. 12

    Woo, J. et al. Quantitative analysis of the bit size dependence on the pulse width and pulse voltage in ferroelectric memory devices using atomic force microscopy. J. Vac. Sci. Technol. B 19, 818–824 (2001).

    Article  Google Scholar 

  13. 13

    Tybell, T., Paruch, P., Giamarchi, T. & Triscone, J. M. Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films. Phys. Rev. Lett. 89, 097601 (2002).

    ADS  Article  Google Scholar 

  14. 14

    Bonnell, D. A., Kalinin, S. V., Kholkin, A. L. & Gruverman, A. Piezoresponse force microscopy: A window into electromechanical behavior at the nanoscale. MRS Bull. 34, 648–657 (2009).

    Article  Google Scholar 

  15. 15

    Tanaka, K. et al. Scanning nonlinear dielectric microscopy nano-science and technology for next generation high density ferroelectric data storage. Jpn J. Appl. Phys. 47, 3311–3325 (2008).

    ADS  Article  Google Scholar 

  16. 16

    Shen, J. et al. Study of asymmetric charge writing on Pb(Zr,Ti)O3thin films by Kelvin probe force microscopy. Appl. Surf. Sci. 252, 8018–8021 (2006).

    ADS  Article  Google Scholar 

  17. 17

    Franke, K., Besold, J., Haessler, W. & Seegebarth, C. Modification and detection of domains on ferroelectric PZT films by scanning force microscopy. Surf. Sci. 302, L283–L288 (1994).

    ADS  Article  Google Scholar 

  18. 18

    Morozovska, A. N. et al. Piezoresponse force spectroscopy of ferroelectric-semiconductor materials. J. Appl. Phys. 102, 114108 (2007).

    ADS  Article  Google Scholar 

  19. 19

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

    Google Scholar 

  20. 20

    Kalinin, S. V. & Bonnell, D. A. Screening phenomena on oxide surfaces and its implications for local electrostatic and transport measurements. Nano Lett. 4, 555–560 (2004).

    ADS  Article  Google Scholar 

  21. 21

    Kumar, A. et al. Probing surface and bulk electrochemical processes on the LaAlO3–SrTiO3 interface. ACS Nano 6, 3841–3852 (2012).

    Article  Google Scholar 

  22. 22

    Watanabe, Y., Okano, M. & Masuda, A. Surface conduction on insulating BaTiO3 crystal suggesting an intrinsic surface electron layer. Phys. Rev. Lett. 86, 332–335 (2001).

    ADS  Article  Google Scholar 

  23. 23

    Fridkin, V. M. Ferroelectric Semiconductors (Springer, 1980).

    Google Scholar 

  24. 24

    Kalinin, S. V. & Bonnell, D. A. Local potential and polarization screening on ferroelectric surfaces. Phys. Rev. B 63, 125411 (2001).

    ADS  Article  Google Scholar 

  25. 25

    Kalinin, S. V., Johnson, C. Y. & Bonnell, D. A. Domain polarity and temperature induced potential inversion on the BaTiO3(100) surface. J. Appl. Phys. 91, 3816–3823 (2002).

    ADS  Article  Google Scholar 

  26. 26

    Son, J. Y., Kyhm, K. & Cho, J. H. Surface charge retention and enhanced polarization effect on ferroelectric thin films. Appl. Phys. Lett. 89, 092907 (2006).

    ADS  Article  Google Scholar 

  27. 27

    Kim, Y., Hong, S., Kim, S. H. & No, K. Surface potential of ferroelectric domain investigated by Kelvin force microscopy. J. Electroceram. 17, 185–188 (2006).

    Article  Google Scholar 

  28. 28

    Rodriguez, B. J., Jesse, S., Baddorf, A. P., Kim, S. H. & Kalinin, S. V. Controlling polarization dynamics in a liquid environment: From localized to macroscopic switching in ferroelectrics. Phys. Rev. Lett. 98, 247603 (2007).

    ADS  Article  Google Scholar 

  29. 29

    Rodriguez, B. J., Jesse, S., Baddorf, A. P. & Kalinin, S. V. High resolution electromechanical imaging of ferroelectric materials in a liquid environment by piezoresponse force microscopy. Phys. Rev. Lett. 96, 237602 (2006).

    ADS  Article  Google Scholar 

  30. 30

    Morozovska, A. N., Eliseev, E. A. & Kalinin, S. V. The piezoresponse force microscopy of surface layers and thin films: Effective response and resolution function. J. Appl. Phys. 102, 074105 (2007).

    ADS  Article  Google Scholar 

  31. 31

    Morozovska, A. N., Eliseev, E. A., Bravina, S. L. & Kalinin, S. V. Resolution-function theory in piezoresponse force microscopy: Wall imaging, spectroscopy, and lateral resolution. Phys. Rev. B 75, 174109 (2007).

    ADS  Article  Google Scholar 

  32. 32

    Kalinin, S. V. et al. Quantitative determination of tip parameters in piezoresponse force microscopy. Appl. Phys. Lett. 90, 212905 (2007).

    ADS  Article  Google Scholar 

  33. 33

    Eliseev, E. A., Kalinin, S. V., Jesse, S., Bravina, S. L. & Morozovska, A. N. Electromechanical detection in scanning probe microscopy: Tip models and materials contrast. J. Appl. Phys. 102, 014109 (2007).

    ADS  Article  Google Scholar 

  34. 34

    Molotskii, M. I. & Shvebelman, M. M. Dynamics of ferroelectric domain formation in an atomic force microscope. Phil. Mag. 85, 1637–1655 (2005).

    ADS  Article  Google Scholar 

  35. 35

    Aravind, V. R. et al. Correlated polarization switching in the proximity of a 180 degrees domain wall. Phys. Rev. B 82, 024111 (2010).

    ADS  Article  Google Scholar 

  36. 36

    Di Ventra, M. & Pershin, Y. V. The parallel approach. Nature Phys. 9, 200–202 (2013).

    ADS  Article  Google Scholar 

  37. 37

    Pershin, Y. V. & Di Ventra, M. Memory effects in complex materials and nanoscale systems. Adv. Phys. 60, 145–227 (2011).

    ADS  Article  Google Scholar 

  38. 38

    Spaldin, N. A. & Fiebig, M. The renaissance of magnetoelectric multiferroics. Science 309, 391–392 (2005).

    Article  Google Scholar 

  39. 39

    Wu, W. D., Horibe, Y., Lee, N., Cheong, S. W. & Guest, J. R. Conduction of topologically protected charged ferroelectric domain walls. Phys. Rev. Lett. 108, 077203 (2012).

    ADS  Article  Google Scholar 

  40. 40

    Seidel, J. et al. Conduction at domain walls in oxide multiferroics. Nature Mater. 8, 229–234 (2009).

    ADS  Article  Google Scholar 

Download references


A part of this research (S.J., E.S., A.K., S.V.K.) was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. A.V.I. and V.Y.S. acknowledge CNMS user proposal, RFBR (Grants 11-02-91066-CNRS-a, 13-02-01391-a, 13-02-96041-r-Ural-a), Ministry of Education and Science (Contract 14.513.12.0006). Y.V.P. was supported by National Science Foundation grant ECCS-1202383. The authors gratefully acknowledge Y. Wu (Tufts University) for posting the original version of the chaos analysis codes on the MathWorks website. A.N.M. and E.A.E. acknowledge the support through the bilateral SFFR-NSF project (US National Science Foundation under NSF-DMR-1210588 and State Fund of Fundamental State Fund of Fundamental Research of Ukraine, grant UU48/002). We gratefully acknowledge A. K. Tagantsev (EPFL) for valuable advice on the role of screening phenomena on ferroelectric phase stability, and B. Sumpter and S. Pennycook (ORNL) for illuminating discussions. S.V.K. and V.Y.S. would like to acknowledge many useful discussions with the late Y. D. Tretyakov (Moscow State University, Russia), who introduced them to the field of chaos and fractals in solid-state systems and inspired this work, and dedicate this paper to him in memoriam.

Author information




A.V.I. obtained and analysed the experimental data. S.V.K. proposed the concept and wrote (with A.N.M. and A.V.I.) the paper. E.S. and A.K. assisted in development of the experimental set-up and development of modelling codes. A.N.M. and E.A.E. developed theoretical analysis of the screening process and derived recursive formulae for domains in the chain. S.J. wrote the codes for simulating chaotic dynamics. Y.V.P. analysed the applications of the observed phenomena in information technology. S.V.K. and V.Y.S. directed the research.

Corresponding authors

Correspondence to V. Ya. Shur or S. V. Kalinin.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1408 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ievlev, A., Jesse, S., Morozovska, A. et al. Intermittency, quasiperiodicity and chaos in probe-induced ferroelectric domain switching. Nature Phys 10, 59–66 (2014).

Download citation

Further reading


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