Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Electron polaron at neutral 180∘ domain wall in PbTiO3: Stability, trapping energies, and transverse polarization

Mohammad Amirabbasi*, Jochen Rohrer, and Karsten Albe†

  • *Contact author: amirabbasi@mm.tu-darmstadt.de
  • †Contact author: albe@mm.tu-darmstadt.de

Phys. Rev. Materials 10, 104409 – Published 13 October, 2026

DOI: https://doi.org/10.1103/fpsj-5g81

Abstract

We use density functional theory with a Hubbard correction to investigate Ti-centered electron polarons at neutral PbO-centered 180∘ domain walls in tetragonal PbTiO3. The Hubbard parameter for Ti 3d states is determined using the finite-size-corrected polaronic energy-level alignment procedure, yielding stable electron-polaron formation in bulk PbTiO3 with a trapping energy of −0.06eV. In the domain-wall supercell, the excess electron localizes on a Ti site and forms a Ti3+ center with an occupied in-gap dxy state. Comparison of bulk-like and near-wall Ti sites shows that their trapping energies differ by only about 0.01 eV, indicating that this neutral domain wall does not provide a significant thermodynamic driving force for electron-polaron segregation. While the Ising-like reversal of the out-of-plane polarization is preserved, the localized electron induces a finite transverse polarization component normal to the wall, enhancing a local Néel-like distortion that is strongest when the polaron is located at the wall. These results show that neutral 180∘ domain walls in PbTiO3 do not substantially alter the stability of Ti-centered electron polarons, but they can couple to the polaron-induced lattice distortion through a localized transverse polarization response.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (82)

  1. J. F. Scott, Applications of modern ferroelectrics, Science 315, 954 (2007).
  2. M. Acosta, N. Novak, V. Rojas, S. Patel, R. Vaish, J. Koruza, G. A. Rossetti, Jr., and J. Rödel, BaTiO3-based piezoelectrics: Fundamentals, current status, and perspectives, Appl. Phys. Rev. 4, 041305 (2017).
  3. P. Muralt, PZT thin films for microsensors and actuators: Where do we stand?, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 47, 903 (2002).
  4. A. K. Tagantsev, L. E. Cross, and J. Fousek, Domains in FERROIC Crystals and Thin Films (Springer, New York, 2010).
  5. E. K. Salje, Domain boundary engineering – recent progress and many open questions, Phase Trans. 86, 2 (2013).
  6. D. Meier and S. M. Selbach, Ferroelectric domain walls for nanotechnology, Nat. Rev. Mater. 7, 157 (2022).
  7. D. Lee, H. Xu, V. Dierolf, V. Gopalan, and S. R. Phillpot, Shape of ferroelectric domains in LiNbO3 and LiTaO3 from defect/domain-wall interactions, Appl. Phys. Lett. 98, 092903 (2011).
  8. G. F. Nataf, M. Guennou, J. M. Gregg, D. Meier, J. Hlinka, E. K. H. Salje, and J. Kreisel, Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials, Nat. Rev. Phys. 2, 634 (2020).
  9. A. Chandrasekaran, D. Damjanovic, N. Setter, and N. Marzari, Defect ordering and defect–domain-wall interactions in PbTiO3: A first-principles study, Phys. Rev. B 88, 214116 (2013).
  10. A. Bencan, G. Drazic, H. Ursic, M. Makarovic, M. Komelj, and T. Rojac, Domain-wall pinning and defect ordering in BiFeO3 probed on the atomic and nanoscale, Nat. Commun. 11, 1762 (2020).
  11. A. J. Klomp, R. Khachaturyan, T. Wallis, K. Albe, and A. Grünebohm, Thermal stability of nanoscale ferroelectric domains by molecular dynamics modeling, Phys. Rev. Mater. 6, 104411 (2022).
  12. P. Marton, M. Paściak, M. A. P. Gonçalves, O. Novák, J. Hlinka, R. Beanland, and M. Alexe, Pyramidal charged domain walls in ferroelectric BiFeO3, Commun. Mater. 6, 161 (2025).
  13. G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, Domain wall nanoelectronics, Rev. Mod. Phys. 84, 119 (2012).
  14. D. Meier, Functional domain walls in multiferroics, J. Phys.: Condens. Matter 27, 463003 (2015).
  15. P. Maksymovych, J. Seidel, Y. H. Chu, P. Wu, A. P. Baddorf, L.-Q. Chen, S. V. Kalinin, and R. Ramesh, Dynamic conductivity of ferroelectric domain walls in BiFeO3, Nano Lett. 11, 1906 (2011).
  16. G. Tian, W. Yang, X. Song, D. Zheng, L. Zhang, C. Chen, P. Li, H. Fan, J. Yao, D. Chen, Z. Fan, Z. Hou, Z. Zhang, S. Wu, M. Zeng, X. Gao, and J.-M. Liu, Manipulation of conductive domain walls in confined ferroelectric nanoislands, Adv. Funct. Mater. 29, 1807276 (2019).
  17. Y. Zuo, Y. A. Genenko, and B.-X. Xu, Charge compensation of head-to-head and tail-to-tail domain walls in barium titanate and its influence on conductivity, J. Appl. Phys. 116, 044109 (2014).
  18. T. Sluka, A. K. Tagantsev, D. Damjanovic, M. Gureev, and N. Setter, Enhanced electromechanical response of ferroelectrics due to charged domain walls, Nat. Commun. 3, 748 (2012).
  19. J. Seidel, L. W. Martin, Q. He, Q. Zhan, Y.-H. Chu, A. Rother, M. E. Hawkridge, P. Maksymovych, P. Yu, M. Gajek, N. Balke, S. V. Kalinin, S. Gemming, F. Wang, G. Catalan, J. F. Scott, N. A. Spaldin, J. Orenstein, and R. Ramesh, Conduction at domain walls in oxide multiferroics, Nat. Mater. 8, 229 (2009).
  20. N. S. Bein, P. Machado, M. Coll, F. Chen, M. Makarovic, T. Rojac, and A. Klein, Electrochemical reduction of undoped and cobalt-doped BiFeO3 induced by water exposure: Quantitative determination of reduction potentials and defect energy levels using photoelectron spectroscopy, J. Phys. Chem. Lett. 10, 7071 (2019).
  21. T. Rojac, A. Bencan, G. Drazic, N. Sakamoto, H. Ursic, B. Jancar, G. Tavcar, M. Makarovic, J. Walker, B. Malic, and D. Damjanovic, Domain-wall conduction in ferroelectric BiFeO3 controlled by accumulation of charged defects, Nat. Mater. 16, 322 (2017).
  22. C. Franchini, M. Reticcioli, M. Setvin, and U. Diebold, Polarons in materials, Nat. Rev. Mater. 6, 560 (2021).
  23. A. Klein, K. Albe, N. Bein, O. Clemens, K. A. Creutz, P. Erhart, M. Frericks, E. Ghorbani, J. P. Hofmann, B. Huang, B. Kaiser, U. Kolb, J. Koruza, C. Kübel, K. N. S. Lohaus, J. Rödel, J. Rohrer, W. Rheinheimer, R. A. De Souza, V. Streibel, et al., The Fermi energy as common parameter to describe charge compensation mechanisms: A path to Fermi level engineering of oxide electroceramics, J. Electroceram. 51, 147 (2023).
  24. J. B. Varley, A. Janotti, C. Franchini, and C. G. Van de Walle, Role of self-trapping in luminescence and p-type conductivity of wide-band-gap oxides, Phys. Rev. B 85, 081109(R) (2012).
  25. B. Faust, H. Müller, and O. Schirmer, Free small polarons in LiNbO3, Ferroelectrics 153, 297 (1994).
  26. F. Ambrosio, J. Wiktor, F. De Angelis, and A. Pasquarello, Origin of low electron–hole recombination rate in metal halide perovskites, Energy Environ. Sci. 11, 101 (2018).
  27. M. Friedrich, W. G. Schmidt, A. Schindlmayr, and S. Sanna, Polaron optical absorption in congruent lithium niobate from time-dependent density-functional theory, Phys. Rev. Mater. 1, 054406 (2017).
  28. O. F. Schirmer, O− bound small polarons in oxide materials, J. Phys.: Condens. Matter 18, R667 (2006).
  29. O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, Electron small polarons and bipolarons in LiNbO3, J. Phys.: Condens. Matter 21, 123201 (2009).
  30. V. S. Vikhnin, R. I. Eglitis, S. E. Kapphan, G. Borstel, and E. A. Kotomin, Polaronic-type excitons in ferroelectric oxides: Microscopic calculations and experimental manifestation, Phys. Rev. B 65, 104304 (2002).
  31. F. Ambrosio and J. Wiktor, Strong hole trapping due to oxygen dimers in BiVO4: Effect on the water oxidation reaction, J. Phys. Chem. Lett. 10, 7113 (2019).
  32. Y. Xu, P. Sharma, H. Wen, D. Zhang, C. Kong, Z. Yan, S. L. Y. Chang, and J. Seidel, Electronic properties of W'twin walls in ferroelastic BiVO4, Adv. Funct. Mater. 34, 2400420 (2024).
  33. S. Körbel, J. Hlinka, and S. Sanvito, Electron trapping by neutral pristine ferroelectric domain walls in BiFeO3, Phys. Rev. B 98, 100104(R) (2018).
  34. S. Y. Xiao, T. Kämpfe, Y. M. Jin, A. Haußmann, X. M. Lu, and L. M. Eng, Dipole-tunneling model from asymmetric domain-wall conductivity in LiNbO3 single crystals, Phys. Rev. Appl. 10, 034002 (2018).
  35. M. Schröder, A. Haußmann, A. Thiessen, E. Soergel, T. Woike, and L. M. Eng, Conducting domain walls in lithium niobate single crystals, Adv. Funct. Mater. 22, 3936 (2012).
  36. D. Meier, J. Seidel, A. Cano, K. Delaney, Y. Kumagai, M. Mostovoy, N. A. Spaldin, R. Ramesh, and M. Fiebig, Anisotropic conductance at improper ferroelectric domain walls, Nat. Mater. 11, 284 (2012).
  37. E. A. Eliseev, A. N. Morozovska, G. S. Svechnikov, P. Maksymovych, and S. V. Kalinin, Domain wall conduction in multiaxial ferroelectrics, Phys. Rev. B 85, 045312 (2012).
  38. F. Kluibenschedl, G. M. Koutentakis, R. Alhyder, and M. Lemeshko, Domain-wall ferroelectric polarons in a two-dimensional rotor lattice model, Phys. Rev. Lett. 134, 096302 (2025).
  39. N. Sicron, B. Ravel, Y. Yacoby, E. A. Stern, F. Dogan, and J. J. Rehr, Nature of the ferroelectric phase transition in PbTiO3, Phys. Rev. B 50, 13168 (1994).
  40. A. M. Glazer and S. A. Mabud, Powder profile refinement of lead zirconate titanate at several temperatures. II. Pure PbTiO3, Acta Cryst. B 34, 1065 (1978).
  41. A. García and D. Vanderbilt, First-principles study of stability and vibrational properties of tetragonal PbTiO3, Phys. Rev. B 54, 3817 (1996).
  42. R. J. Nelmes, R. O. Piltz, W. F. Kuhs, Z. Tun, and R. Restori, Order-disorder behaviour in the transition of PbTiO3, Ferroelectrics 108, 165 (1990).
  43. M. D. Fontana, H. Idrissi, and K. Wojcik, Displacive to order-disorder crossover in the cubic-tetragonal phase transition of PbTiO3, Europhys. Lett. 11, 419 (1990).
  44. G. Burns and B. A. Scott, Lattice modes in ferroelectric perovskites: PbTiO3, Phys. Rev. B 7, 3088 (1973).
  45. D. I. Bilc, R. Orlando, R. Shaltaf, G.-M. Rignanese, J. Íñiguez, and P. Ghosez, Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides, Phys. Rev. B 77, 165107 (2008).
  46. R. Schafranek, S. Li, F. Chen, W. Wu, and A. Klein, PbTiO3/SrTiO3 interface: Energy band alignment and its relation to the limits of Fermi level variation, Phys. Rev. B 84, 045317 (2011).
  47. K. van Benthem, C. Elsässer, and R. H. French, Bulk electronic structure of SrTiO3: Experiment and theory, J. Appl. Phys. 90, 6156 (2001).
  48. J. Joseph, T. M. Vimala, V. Sivasubramanian, and V. R. K. Murthy, Structural investigations on Pb(ZrxTi1−x)O3 solid solutions using the X-ray Rietveld method, J. Mater. Sci. 35, 1571 (2000).
  49. W. Dmowski, T. Egami, L. Farber, and P. K. Davies, Structure of Pb(Zr,Ti)O3 near the morphotropic phase boundary, AIP Conf. Proc. 582, 33 (2001).
  50. J. A. Rodriguez, A. Etxeberria, L. González, and A. Maiti, Structural and electronic properties of PbTiO3, PbZrO3, and PbZr0.5Ti0.5O3: First-principles density-functional studies, J. Chem. Phys. 117, 2699 (2002).
  51. T. Yamanaka, Y. Nakamoto, M. Ahart, and H. K. Mao, Pressure dependence of electron density distribution and dp−π hybridization in titanate perovskite ferroelectrics, Phys. Rev. B 97, 144109 (2018).
  52. B. Meyer and D. Vanderbilt, Ab initio study of ferroelectric domain walls in PbTiO3, Phys. Rev. B 65, 104111 (2002).
  53. R. K. Behera, C. W. Lee, D. Lee, A. N. Morozovska, S. B. Sinnott, A. Asthagiri, V. Gopalan, and S. R. Phillpot, Structure and energetics of 180∘ domain walls in PbTiO3 by density functional theory, J. Phys.: Condens. Matter 23, 175902 (2011).
  54. S. Pöykkö and D. J. Chadi, Ab initio study of 180° domain wall energy and structure in PbTiO3, Appl. Phys. Lett. 75, 2830 (1999).
  55. K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
  56. R. I. Eglitis, E. A. Kotomin, V. A. Trepakov, S. E. Kapphan, and G. Borstel, Quantum chemical modelling of electron polarons and ‘green’ luminescence in PbTiO3 perovskite crystals, J. Phys.: Condens. Matter 14, L647 (2002).
  57. E. Ghorbani, L. Villa, P. Erhart, A. Klein, and K. Albe, Self-consistent calculations of charge self-trapping energies: A comparative study of polaron formation and migration in PbTiO3, Phys. Rev. Mater. 6, 074410 (2022).
  58. D. Windsor and H. Xu, Treating interactions between polarons and oxygen vacancies in perovskite oxides, Phys. Rev. Mater. 8, 094406 (2024).
  59. P. Erhart, A. Klein, D. Åberg, and B. Sadigh, Efficacy of the DFT+U formalism for modeling hole polarons in perovskite oxides, Phys. Rev. B 90, 035204 (2014).
  60. M. Cococcioni and S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the LDA+U method, Phys. Rev. B 71, 035105 (2005).
  61. S. Falletta, J. Wiktor, and A. Pasquarello, Finite-size corrections of defect energy levels involving ionic polarization, Phys. Rev. B 102, 041115(R) (2020).
  62. S. Falletta and A. Pasquarello, Hubbard U through polaronic defect states, npj Comput. Mater. 8, 263 (2022).
  63. G. Kresse and J. Furthmüller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  64. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  65. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  66. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  67. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  68. J. P. Allen and G. W. Watson, Occupation matrix control of d-and f-electron localisations using DFT+U, Phys. Chem. Chem. Phys. 16, 21016 (2014).
  69. C. Freysoldt, J. Neugebauer, and C. G. Van de Walle, Fully ab initio finite-size corrections for charged-defect supercell calculations, Phys. Rev. Lett. 102, 016402 (2009).
  70. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, First-principles calculations for point defects in solids, Rev. Mod. Phys. 86, 253 (2014).
  71. C. M. Foster, Z. Li, M. Grimsditch, S.-K. Chan, and D. J. Lam, Anharmonicity of the lowest-frequency A1(TO) phonon in PbTiO3, Phys. Rev. B 48, 10160 (1993).
  72. N. Österbacka, P. Erhart, S. Falletta, A. Pasquarello, and J. Wiktor, Small electron polarons in CsPbBr3: Competition between electron localization and delocalization, Chem. Mater. 32, 8393 (2020).
  73. W. Zhong, R. D. King-Smith, and D. Vanderbilt, Giant LO-TO splittings in perovskite ferroelectrics, Phys. Rev. Lett. 72, 3618 (1994).
  74. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related materials (Oxford University Press, Oxford, 2001).
  75. T. Abe, S. Kim, C. Moriyoshi, Y. Kitanaka, Y. Noguchi, H. Tanaka, and Y. Kuroiwa, Visualization of spontaneous electronic polarization in Pb ion of ferroelectric PbTiO3 by synchrotron-radiation x-ray diffraction, Appl. Phys. Lett. 117, 252905 (2020).
  76. E. Tadmor, U. Waghmare, G. Smith, and E. Kaxiras, Polarization switching in PbTiO3: An ab initio finite element simulation, Acta Mater. 50, 2989 (2002).
  77. G. Sághi-Szabó, R. E. Cohen, and H. Krakauer, First-principles study of piezoelectricity in PbTiO3, Phys. Rev. Lett. 80, 4321 (1998).
  78. M. Kingsland, K. A. Lynch, S. Lisenkov, X. He, and I. Ponomareva, Comparative study of Minnesota functionals performance on ferroelectric BaTiO3 and PbTiO3, Phys. Rev. Mater. 4, 073802 (2020).
  79. Y. Zhang, J. Sun, J. P. Perdew, and X. Wu, Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA, Phys. Rev. B 96, 035143 (2017).
  80. U. Petralanda, M. Kruse, H. Simons, and T. Olsen, Oxygen vacancies nucleate charged domain walls in ferroelectrics, Phys. Rev. Lett. 127, 117601 (2021).
  81. S. Tomoda, T. Shimada, T. Ueda, J. Wang, and T. Kitamura, Hybrid functional study on the ferroelectricity of domain walls with O-vacancies in PbTiO3, Mech. Eng. J. 2, 15-00037 (2015).
  82. L. He and D. Vanderbilt, First-principles study of oxygen-vacancy pinning of domain walls in PbTiO3, Phys. Rev. B 68, 134103 (2003).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation