Letter | Published:

Intrinsic ferroelectric switching from first principles

Nature volume 534, pages 360363 (16 June 2016) | Download Citation


The existence of domain walls, which separate regions of different polarization, can influence the dielectric1, piezoelectric2, pyroelectric3 and electronic properties4,5 of ferroelectric materials. In particular, domain-wall motion is crucial for polarization switching, which is characterized by the hysteresis loop that is a signature feature of ferroelectric materials6. Experimentally, the observed dynamics of polarization switching and domain-wall motion are usually explained as the behaviour of an elastic interface pinned by a random potential that is generated by defects7,8, which appear to be strongly sample-dependent and affected by various elastic, microstructural and other extrinsic effects9,10,11,12. Theoretically, connecting the zero-kelvin, first-principles-based, microscopic quantities of a sample with finite-temperature, macroscopic properties such as the coercive field is critical for material design and device performance; and the lack of such a connection has prevented the use of techniques based on ab initio calculations for high-throughput computational materials discovery. Here we use molecular dynamics simulations13 of 90° domain walls (separating domains with orthogonal polarization directions) in the ferroelectric material PbTiO3 to provide microscopic insights that enable the construction of a simple, universal, nucleation-and-growth-based analytical model that quantifies the dynamics of many types of domain walls in various ferroelectrics. We then predict the temperature and frequency dependence of hysteresis loops and coercive fields at finite temperatures from first principles. We find that, even in the absence of defects, the intrinsic temperature and field dependence of the domain-wall velocity can be described with a nonlinear creep-like region and a depinning-like region. Our model enables quantitative estimation of coercive fields, which agree well with experimental results for ceramics and thin films. This agreement between model and experiment suggests that, despite the complexity of ferroelectric materials, typical ferroelectric switching is largely governed by a simple, universal mechanism of intrinsic domain-wall motion, providing an efficient framework for predicting and optimizing the properties of ferroelectric materials.

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  1. 1.

    , , & Stationary domain wall contribution to enhanced ferroelectric susceptibility. Nat. Commun. 5, 3120 (2014)

  2. 2.

    & Dielectric and piezoelectric response of lead zirconate–lead titanate at high electric and mechanical loads in terms of non-180° domain wall motion. J. Appl. Phys. 90, 5278–5286 (2001)

  3. 3.

    & Pyroelectric properties of polydomain epitaxial Pb(Zr1–x,Tix)O3 thin films. Phys. Rev. B 84, 024102 (2011)

  4. 4.

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

  5. 5.

    et al. Ferroelectric domain wall induced band gap reduction and charge separation in organometal halide perovskites. J. Phys. Chem. Lett. 6, 693–699 (2015)

  6. 6.

    , & Decoding the fingerprint of ferroelectric loops: comprehension of the material properties and structures. J. Am. Ceram. Soc. 97, 1–27 (2014)

  7. 7.

    & Dynamics of interfaces and dislocations in disordered media. J. Phys. C 20, 6149–6158 (1987)

  8. 8.

    , & Creep and depinning in disordered media. Phys. Rev. B 62, 6241–6267 (2000)

  9. 9.

    , , & Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films. Phys. Rev. Lett. 89, 097601 (2002)

  10. 10.

    et al. Nonlinear dynamics of domain-wall propagation in epitaxial ferroelectric thin film. Phys. Rev. Lett. 102, 045701 (2009)

  11. 11.

    , , & Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films. J. Appl. Phys. 100, 051608 (2006)

  12. 12.

    et al. Dynamics of ferroelectric nanodomains in BaTiO3 epitaxial thin films via piezoresponse force microscopy. Nanotechnology 19, 375703 (2008)

  13. 13.

    , , & Reinterpretation of the bond-valence model with bond-order formalism: an improved bond-valence-based interatomic potential for PbTiO3. Phys. Rev. B 88, 104102 (2013)

  14. 14.

    Domain formation and domain wall motions in ferroelectric BaTiO3 single crystals. Phys. Rev. 95, 690–698 (1954)

  15. 15.

    & Mechanism for the sidewise motion of 180° domain walls in barium titanate. Phys. Rev. 117, 1460–1466 (1960)

  16. 16.

    & Ab initio study of ferroelectric domain walls in PbTiO3. Phys. Rev. B 65, 104111 (2002)

  17. 17.

    , , & Nucleation and growth mechanism of ferroelectric domain-wall motion. Nature 449, 881–884 (2007)

  18. 18.

    , & Exploration of the intrinsic inertial response of ferroelectric domain walls via molecular dynamics simulations. Appl. Phys. Lett. 103, 232907 (2013)

  19. 19.

    , , & Domains, domain walls and defects in perovskite ferroelectric oxides: a review of present understanding and recent contributions. Crit. Rev. Solid State Mater. Sci. 37, 243–275 (2012)

  20. 20.

    et al. Atomic-scale mechanisms of ferroelastic domain-wall-mediated ferroelectric switching. Nat. Commun. 4, 2791 (2013)

  21. 21.

    Properties of PZT-based Piezoelectric Ceramics Between −150 and 250°C. Report No. NASA/CR-1998-208708, (NASA, 1998)

  22. 22.

    & 90° domain reorientation and domain wall rearrangement in lead zirconate titanate ceramics characterized by transient current and hysteresis loop measurements. J. Appl. Phys. 89, 5093–5099 (2001)

  23. 23.

    , , & 90° domain wall relaxation and frequency dependence of the coercive field in the ferroelectric switching process. J. Appl. Phys. 95, 2646–2653 (2004)

  24. 24.

    & PZT ceramics formed directly from oxides via reactive sintering. Mater. Lett. 51, 95–100 (2001)

  25. 25.

    et al. ac dynamics of ferroelectric domains from an investigation of the frequency dependence of hysteresis loops. Phys. Rev. B 82, 174125 (2010)

  26. 26.

    & Effect of the ac field level on the aging of the dielectric response in polycrystalline BaTiO3. J. Am. Ceram. Soc. 75, 3385–3389 (1992)

  27. 27.

    et al. Epitaxial BiFeO3 multiferroic thin film heterostructures. Science 299, 1719–1722 (2003)

  28. 28.

    et al. Reduced coercive field in BiFeO3 thin films through domain engineering. Adv. Mater. 23, 669–672 (2011)

  29. 29.

    , & Strain controlled ferroelectric switching time of BiFeO3 capacitors. Appl. Phys. Lett. 101, 242908 (2012)

  30. 30.

    Greater Functionality of Bismuth and Lead Based Perovskites. PhD thesis, Univ. Pennsylvania, (2005)

  31. 31.

    , , & Development of a bond-valence molecular-dynamics model for complex oxides. Phys. Rev. B 71, 054104 (2005)

  32. 32.

    et al. Asymmetric response of ferroelastic domain-wall motion under applied bias. ACS Appl. Mater. Interfaces 8, 2935–2941 (2016)

  33. 33.

    & Ferroelectric transitions at ferroelectric domain walls found from first principles. Phys. Rev. Lett. 112, 247603 (2014)

  34. 34.

    et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008)

  35. 35.

    , & Phase transition energetics and thermodynamic properties of ferroelectric PbTiO3. J. Mater. Res. 13, 3197–3206 (1998)

  36. 36.

    , , & Domain walls in a perovskite oxide with two primary structural order parameters: first-principles study of BiFeO3. Phys. Rev. B 87, 024102 (2013)

  37. 37.

    et al. Ferroelectric domains in multiferroic BiFeO3 films under epitaxial strains. Phys. Rev. Lett. 110, 187601 (2013)

  38. 38.

    et al. BiFeO3 domain wall energies and structures: a combined experimental and density functional theory + U study. Phys. Rev. Lett. 110, 267601 (2013)

  39. 39.

    & Construction of a generalized gradient approximation by restoring the density-gradient expansion and enforcing a tight Lieb–Oxford bound. J. Chem. Phys. 128, 184109 (2008)

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S.L. was supported by the NSF through Grant DMR-1124696, Grant CBET-1159736, and the Carnegie Institution for Science. I.G. was supported by the US ONR under Grant N00014-12-1-1033. A.M.R. was supported by the US DOE under Grant DE-FG02-07ER46431. Computational support was provided by the US DOD through a Challenge Grant from the HPCMO, and by the US DOE through computer time at NERSC.

Author information


  1. Geophysical Laboratory, Carnegie Institution for Science, Washington DC 20015, USA

    • Shi Liu
  2. The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

    • Ilya Grinberg
    •  & Andrew M. Rappe
  3. Department of Chemistry, Bar-Ilan University, Ramat Gan 5290002 Israel

    • Ilya Grinberg


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S.L., I.G. and A.M.R. designed and analysed the simulation approaches. S.L. performed the molecular dynamics simulations. All authors discussed the results and implications of the work and commented on the manuscript at all stages.

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The authors declare no competing financial interests.

Corresponding authors

Correspondence to Shi Liu or Andrew M. Rappe.

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