Skip to main content
×
×
Home

3D polarization texture of a symmetric 4-fold flux closure domain in strained ferroelectric PbTiO3 films

  • Y.L. Tang (a1), Y.L. Zhu (a1), Z.J. Hong (a2), E.A. Eliseev (a3), A.N. Morozovska (a4), Y.J. Wang (a1), Y. Liu (a1), Y.B. Xu (a1), B. Wu (a1), L.Q. Chen (a2), S.J. Pennycook (a5) and X.L. Ma (a1)...
Abstract

Although the strong coupling of polarization to spontaneous strain in ferroelectrics would impart a flux-closure with severe disclination strains, recent studies have successfully stabilized such a domain via a nano-scaled multi-layer growth. Nonetheless, the detailed distributions of polarizations in three-dimensions (3D) and how the strains inside a flux closure affect the structures of domain walls are still less understood. Here we report a 3D polarization texture of a 4-fold flux closure domain identified in tensile strained ferroelectric PbTiO3/SrTiO3 multilayer films. Ferroelectric displacement analysis based on aberration-corrected scanning transmission electron microscopic imaging reveals highly inhomogeneous strains with strain gradient above 107/m. These giant disclination strains significantly broaden the 90° domain walls, while the flexoelectric coupling at 180° domain wall is less affected. The present observations are helpful for understanding the basics of topological dipole textures and indicate novel applications of ferroelectrics through engineering strains.

Copyright
Corresponding author
a) Address all correspondence to this author. e-mail: xlma@imr.ac.cn
Footnotes
Hide All

Contributing Editor: Rafal E. Dunin-Borkowski

Footnotes
References
Hide All
1. Shinjo, T., Okuno, T., Hassdorf, R., Shigeto, K., and Ono, T.: Magnetic vortex core observation in circular dots of permalloy. Science 289, 930 (2000).
2. Rößler, U.K., Bogdanov, A.N., and Pfleiderer, C.: Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797 (2006).
3. Uchida, M., Onose, Y., Matsui, Y., and Tokura, Y.: Real-space observation of helical spin order. Science 311, 359 (2006).
4. Yu, X.Z., Onose, Y., Kanazawa, N., Park, J.H., Han, J.H., Matsui, Y., Nagaosa, N., and Tokura, Y.: Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901 (2010).
5. Romming, N., Hanneken, C., Menzel, M., Bickel, J.E., Wolter, B., von Bergmann, K., Kubetzka, A., and Wiesendanger, R.: Writing and deleting single magnetic skyrmions. Science 341, 636 (2013).
6. Nagaosa, N. and Tokura, Y.: Topological properties and dynamics of magnetic skyrmions. Nature Nanotech. 8, 899 (2013).
7. Catalan, G., Seidel, J., Ramesh, R., and Scott, J.F.: Domain wall nanoelectronics. Rev. Mod. Phys. 84, 119 (2012).
8. Cohen, R.E.: Origin of ferroelectricity in perovskite oxides. Nature 358, 136 (1992).
9. Scott, J.F.: Applications of modern ferroelectrics. Science 315, 954 (2007).
10. Spaldin, N.A.: Analogies and differences between ferroelectrics and ferromagnets. In Physics of Ferroelectrics a Modern Perspective. Topics in Applied Physics, Vol. 105, Rabe, K.M., Ahn, C.H. and Triscone, J-M. eds.; Springer-Verlag, Berlin Heidelberg, 2007; pp. 175218.
11. Naumov, I.I., Bellaiche, L., and Fu, H.: Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737 (2004).
12. Prosandeev, S. and Bellaiche, L.: Characteristics and signatures of dipole vortices in ferroelectric nanodots: First-principles-based simulations and analytical expressions. Phys. Rev. B: Condens. Matter Mater. Phys. 75, 094102 (2007).
13. Aguado-Puente, P. and Junquera, J.: Ferromagnetic like closure domains in ferroelectric ultrathin films: First-principles simulations. Phys. Rev. Lett. 100, 177601 (2008).
14. Chen, W.J., Zheng, Y., and Wang, B.: Vortex domain structure in ferroelectric nanoplatelets and control of its transformation by mechanical load. Sci. Rep. 2(796), 00796 (2012).
15. Zhou, Z.D. and Wu, D.Y.: Domain structures of ferroelectric films under different electrical boundary conditions. AIP Adv. 5, 107206 (2015).
16. Kittel, C.: Physical theory of ferromagnetic domains. Rev. Mod. Phys. 21, 541 (1949).
17. Schilling, A., Byrne, D., Catalan, G., Webber, K.G., Genenko, Y.A., Wu, G.S., Scott, J.F., and Gregg, J.M.: Domains in ferroelectric nanodots. Nano Lett. 9, 3359 (2009).
18. McGilly, L.J., Schilling, A., and Gregg, J.M.: Domain bundle boundaries in single crystal BaTiO3 lamellae: Searching for naturally forming dipole flux-closure/quadrupole chains. Nano Lett. 10, 4200 (2010).
19. McQuaid, R.G.P., McGilly, L.J., Sharma, P., Gruverman, A., and Gregg, J.M.: Mesoscale flux-closure domain formation in single-crystal BaTiO3 . Nat. Commun. 2(404), 1413 (2011).
20. McGilly, L.J. and Gregg, J.M.: Polarization closure in PbZr(0.42)Ti(0.58)O3 nanodots. Nano Lett. 11, 4490 (2011).
21. Chang, L-W., Nagarajan, V., Scott, J.F., and Gregg, J.M.: Self-similar nested flux closure structures in a tetragonal ferroelectric. Nano Lett. 13, 2553 (2013).
22. Jia, C.L., Urban, K.W., Alexe, M., Hesse, D., and Vrejoiu, I.: Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric Pb(Zr,Ti)O3 . Science 331, 1420 (2011).
23. Nelson, C.T., Winchester, B., Zhang, Y., Kim, S-J., Melville, A., Adamo, C., Folkman, C.M., Baek, S-H., Eom, C-B., Schlom, D.G., Chen, L-Q., and Pan, X.: Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11, 828 (2011).
24. Tang, Y.L., Zhu, Y.L., Ma, X.L., Borisevich, A.Y., Morozovska, A.N., Eliseev, E.A., Wang, W.Y., Wang, Y.J., Xu, Y.B., Zhang, Z.D., and Pennycook, S.J.: Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 films. Science 348, 547 (2015).
25. Yadav, A.K., Nelson, C.T., Hsu, S.L., Hong, Z., Clarkson, J.D., Schlepütz, C.M., Damodaran, A.R., Shafer, P., Arenholz, E., Dedon, L.R., Chen, D., Vishwanath, A., Minor, A.M., Chen, L.Q., Scott, J.F., Martin, L.W., and Ramesh, R.: Observation of polar vortices in oxide superlattices. Nature 530, 198 (2016).
26. Catalan, G., Lubk, A., Vlooswijk, A.H.G., Snoeck, E., Magen, C., Janssens, A., Rispens, G., Rijnders, G., Blank, D.H.A., and Noheda, B.: Flexoelectric rotation of polarization in ferroelectric thin films. Nat. Mater. 10, 963967 (2011).
27. Anthony, S.M. and Granick, S.: Image analysis with rapid and accurate two-dimensional Gaussian fitting. Langmuir 25, 81528160 (2009).
28. Jia, C-L., Nagarajan, V., He, J-Q., Houben, L., Zhao, T., Ramesh, R., Urban, K., and Waser, R.: Unit-cell scale mapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films. Nat. Mater. 6, 64 (2007).
29. Li, Y.L., Hu, S.Y., Liu, Z.K., and Chen, L.Q.: Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films. Acta Mater. 50, 395 (2002).
30. Chen, L.Q.: Phase-field method of phase transitions/domain structures in ferroelectric thin films: A review. J. Am. Ceram. Soc. 91, 18351844 (2008).
31. Li, Y.L., Hu, S.Y., Liu, Z.K., and Chen, L.Q.: Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Appl. Phys. Lett. 81, 427429 (2002).
32. Haun, M.J.: Ph.D Thesis, The Pennsylvania State University, 1988.
33. Sheng, G., Li, Y.L., Zhang, J.X., Choudhury, S., Jia, Q.X., Gopalan, V., Schlom, D.G., Liu, Z.K., and Chen, L.Q.: A modified Landau–Devonshire thermodynamic potential for strontium titanate. Appl. Phys. Lett. 96, 232902 (2010).
34. Wang, J.J., Ma, X.Q., Li, Q., Britson, J., and Chen, L.Q.: Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity. Acta Mater. 61, 75917603 (2013).
35. Chen, L.Q. and Shen, J.: Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Commun. 108, 147158 (1998).
36. Hÿtch, M.J., Snoeck, E., and Kilaas, R.: Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 74, 131146 (1998).
37. Tang, Y.L., Zhu, Y.L., and Ma, X.L.: On the benefit of aberration-corrected HAADF-STEM for strain determination and its application to tailoring ferroelectric domain patterns. Ultramicroscopy 160, 5763 (2016).
38. Kittel, C.: Theory of the structure of ferromagnetic domains in films and small particles. Phys. Rev. 70, 965 (1946).
39. Srolovitz, D.J. and Scott, J.F.: Clock-model description of incommensurate ferroelectric films and of nematic-liquid-crystal films. Phys. Rev. B: Condens. Matter Mater. Phys. 34, 1815 (1986).
40. Balke, N., Choudhury, S., Jesse, S., Huijben, M., Chu, Y.H., Baddorf, A.P., Chen, L.Q., Ramesh, R., and Kalinin, S.V.: Deterministic control of ferroelastic switching in multiferroic materials. Nat. Nanotechnol. 4, 868875 (2009).
41. Slutsker, J., Artemev, A., and Roytburd, A.: Phase-field modeling of domain structure of confined nanoferroelectrics. Phys. Rev. Lett. 100, 087602 (2008).
42. Lee, D., Lu, H., Gu, Y., Choi, S-Y., Li, S-D., Ryu, S., Paudel, T.R., Song, K., Mikheev, E., Lee, S., Stemmer, S., Tenne, D.A., Oh, S.H., Tsymbal, E.Y., Wu, X., Chen, L-Q., Gruverman, A., and Eom, C.B.: Emergence of room-temperature ferroelectricity at reduced dimensions. Science 349, 1314 (2015).
43. Tagantsev, A.K., Cross, L.E., and Fousek, J.: Chapter 6. In Domains in Ferroic Crystals and Thin Films. (Springer, New York, 2010); pp. 300304.
44. Yudin, P.V., Tagantsev, A.K., Eliseev, E.A., Morozovska, A.N., and Setter, N.: Bichiral structure of ferroelectric domain walls driven by flexoelectricity. Phys. Rev. B: Condens. Matter Mater. Phys. 86, 134102 (2012).
45. Eliseev, E.A., Yudin, P.V., Kalinin, S.V., Setter, N., Tagantsev, A.K., and Morozovska, A.N.: Structural phase transitions and electronic phenomena at 180-degree domain walls in rhombohedral BaTiO3 . Phys. Rev. B: Condens. Matter Mater. Phys. 87, 054111 (2013).
46. Meyer, B. and Vanderbilt, D.: Ab initio study of ferroelectric domain walls in PbTiO3 . Phys. Rev. B: Condens. Matter Mater. Phys. 65, 104111 (2002).
47. Nye, J.F.: Physical Properties of Crystals: Their Representation by Tensors and Matrices (Clarendon Press, Oxford, 1985).
48. Roitburd, A.L.: Equilibrium structure of epitaxial layers. Phys. Status Solidi A 37, 329 (1976).
49. Tagantsev, A.K., Gerra, G., and Setter, N.: Short-range and long-range contributions to the size effect in metal-ferroelectric-metal heterostructures. Phys. Rev. B: Condens. Matter Mater. Phys. 77, 174111 (2008).
50. Chandra, P. and Littelwood, P.B.: A landau primer for ferroelectrics. In Physics of Ferroelectrics a Modern Perspective, Topics Applied Physics, Vol. 105, Rabe, K.M., Ahn, C.H. and Triscone, J-M. eds.; Springer-Verlag, Berlin Heidelberg, 2007; pp. 69116.
51. Chopra, H.D. and Wuttig, M.: Non-Joulian magnetostriction. Nature 521, 340 (2015).
52. McQuaid, R.G., Gruverman, A., Scott, J.F., and Gregg, J.M.: Exploring vertex interactions in ferroelectric flux-closure domains. Nano Lett. 14, 42304237 (2014).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed