- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

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
  • Access by Xinjiang University

First-principles investigation of small polarons in rhombohedral NaNbO3

Mohammad Amirabbasi*, Lorenzo Villa, Elaheh Ghorbani, Jochen Rohrer, and Karsten Albe†

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

Phys. Rev. Materials 10, 115402 – Published 12 November, 2026

DOI: https://doi.org/10.1103/vyp9-s8zs

Abstract

Sodium niobate (NaNbO3) is a perovskite oxide and a key component of emerging lead-free antiferroelectric capacitors for high-energy-density applications. However, its performance can be hindered by irreversible phase transitions and leakage currents associated with low electrical resistivity. Defect and doping engineering offers a potential way to overcome these problems, but its use requires a detailed understanding of electronic, ionic, and polaron charge-compensation mechanisms, where the role of polarons remains largely unexplored. Here, we investigate the stability of small hole and electron polarons in rhombohedral NaNbO3, which is a structurally well-defined model system that avoids lattice-dynamical instabilities. Trapping energies are calculated using density functional theory corrected by a Hubbard U, using the enforced-piecewise-linearity approach including finite-size scaling. For the small hole-polaron centered on O-2p orbital, we find a trapping energy of −0.65 eV and an adiabatic migration barrier of 0.32 eV determined by nudged-elastic-band calculations. In contrast, we show that excess electrons do not self-trap on Nb-4d orbitals, reflecting weak electron-phonon coupling in the conduction band manifold. These results identify oxygen as an intrinsic hole trap in NaNbO3 and highlight the importance of including hole polarons in defect models of NaNbO3-based electroceramics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (94)

  1. T. R. Shrout and S. Zhang, Lead-free piezoelectric ceramics: Alternatives for PZT? J. Electroceram. 19, 185 (2007).
  2. J. Rödel, W. Jo, K. T. P. Seifert, E.-M. Anton, T. Granzow, and D. Damjanovic, Perspective on the development of lead-free piezoceramics, J. Am. Ceram. Soc. 92, 1153 (2009).
  3. A. J. Bell and O. Deubzer, Lead-free piezoelectrics—The environmental and regulatory issues, MRS Bull. 43, 581 (2018).
  4. B. Xu, J. Íñiguez, and L. Bellaiche, Designing lead-free antiferroelectrics for energy storage, Nat. Commun. 8, 15682 (2017).
  5. L. Yang, X. Kong, F. Li, H. Hao, Z. Cheng, H. Liu, J.-F. Li, and S. Zhang, Perovskite lead-free dielectrics for energy storage applications, Prog. Mater. Sci. 102, 72 (2019).
  6. D. Yang, J. Gao, L. Shu, Y.-X. Liu, J. Yu, Y. Zhang, X. Wang, B.-P. Zhang, and J.-F. Li, Lead-free antiferroelectric niobates AgNbO3 and NaNbO3 for energy storage applications, J. Mater. Chem. A 8, 23724 (2020).
  7. Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, and M. Nakamura, Lead-free piezoceramics, Nature (London) 432, 84 (2004).
  8. J. Wu, D. Xiao, and J. Zhu, Potassium-sodium niobate lead-free piezoelectric materials: Past, present, and future of phase boundaries, Chem. Rev. 115, 2559 (2015).
  9. G. Shirane, R. Newnham, and R. Pepinsky, Dielectric properties and phase transitions of NaNbO3 and (Na,K)NbO3, Phys. Rev. 96, 581 (1954).
  10. J. Koruza, H. Liu, M. Höfling, M.-H. Zhang, and P. Veber, (K,Na)NbO3 -based piezoelectric single crystals: Growth methods, properties, and applications, J. Mater. Res. 35, 990 (2020).
  11. D. Fritsch, Electronic and optical properties of sodium niobate: A density functional theory study, Adv. Mater. Sci. Eng. 2018, 6416057 (2018).
  12. Z. Liu, T. Lu, J. Ye, G. Wang, X. Dong, R. Withers, and Y. Liu, Antiferroelectrics for energy storage applications: A review, Adv. Mater. Technol. 3, 1800111 (2018).
  13. J.-F. Li, K. Wang, F.-Y. Zhu, L.-Q. Cheng, and F.-Z. Yao, (K, Na)NbO3-based lead-free piezoceramics: Fundamental aspects, processing technologies, and remaining challenges, J. Am. Ceram. Soc. 96, 3677 (2013).
  14. E. Valdez, C. B. de Araújo, and A. A. Lipovskii, Second harmonic scattered light from a transparent glass-ceramic containing sodium niobate nanocrystals, Appl. Phys. Lett. 89, 031901 (2006).
  15. H. D. Megaw, The seven phases of sodium niobate, Ferroelectrics 7, 87 (1974).
  16. S. Lanfredi, M. H. Lente, and J. A. Eiras, Phase transition at low temperature in NaNbO3 ceramic, Appl. Phys. Lett. 80, 2731 (2002).
  17. L. A. Reznitchenko, A. V. Turik, E. M. Kuznetsova, and V. P. Sakhnenko, Piezoelectricity in NaNbO3 ceramics, J. Phys.: Condens. Matter 13, 3875 (2001).
  18. C. Darlington and H. D. Megaw, The low-temperature phase transition of sodium niobate and the structure of the low-temperature phase, N, Acta Cryst. B 29, 2171 (1973).
  19. A. Glazer and H. Megaw, Studies of the lattice parameters and domains in the phase transitions of NaNbO3, Acta Cryst. A 29, 489 (1973).
  20. A. Glazer and H. D. Megaw, The structure of sodium niobate (T2) at 600C∘, and the cubic-tetragonal transition in relation to soft-phonon modes, Philos. Mag. 25, 1119 (1972).
  21. J. Koruza, J. Tellier, B. Malič, V. Bobnar, and M. Kosec, Phase transitions of sodium niobate powder and ceramics, prepared by solid state synthesis, J. Appl. Phys. 108, 113509 (2010).
  22. N. Luo, L. Ma, G. Luo, C. Xu, L. Rao, Z. Chen, Z. Cen, Q. Feng, X. Chen, F. Toyohisa, Y. Zhu, J. Hong, J.-F. Li, and S. Zhang, Well-defined double hysteresis loop in NaNbO3 antiferroelectrics, Nat. Commun. 14, 1776 (2023).
  23. K. E. Johnston, C. C. Tang, J. E. Parker, K. S. Knight, P. Lightfoot, and S. E. Ashbrook, The polar phase of NaNbO3: A combined study by powder diffraction, solid-state NMR, and first-principles calculations, J. Am. Chem. Soc. 132, 8732 (2010).
  24. C. S. Htet, S. Nayak, A. Manjón-Sanz, J. Liu, J. Kong, D. R. Sørensen, F. Marlton, M. R. V. Jørgensen, and A. Pramanick, Atomic structural mechanism for ferroelectric-antiferroelectric transformation in perovskite NaNbO3, Phys. Rev. B 105, 174113 (2022).
  25. H. Guo, H. Shimizu, Y. Mizuno, and C. A. Randall, Domain configuration changes under electric field-induced antiferroelectric-ferroelectric phase transitions in NaNbO3-based ceramics, J. Appl. Phys. 118, 054102 (2015).
  26. S. Egert, M.-H. Zhang, J. Koruza, P. B. Groszewicz, and G. Buntkowsky, Na23 NMR spectroscopic quantification of the antiferroelectric-ferroelectric phase coexistence in sodium niobate, J. Phys. Chem. C 124, 23852 (2020).
  27. M.-H. Zhang, N. Hadaeghi, S. Egert, H. Ding, H. Zhang, P. B. Groszewicz, G. Buntkowsky, A. Klein, and J. Koruza, Design of lead-free antiferroelectric (1–x)NaNbO3–xSrSnO3 compositions guided by first-principles calculations, Chem. Mater. 33, 266 (2021).
  28. H. Shimizu, H. Guo, S. E. Reyes-Lillo, Y. Mizuno, K. M. Rabe, and C. A. Randall, Lead-free antiferroelectric: xCaZrO3−(1−x)NaNbO3 system (0≤x≤0.10), Dalton Trans. 44, 10763 (2015).
  29. Z. Wang, D. Li, W. Liu, L. He, D. Xu, J. Liu, J. Ren, X. Wang, Y. Liu, G. He, J. Bao, Z. Fang, G. Yan, X. Liang, T. Zhou, W. Zhao, W. Liu, D. Wang, and D. Zhou, Ultra-high energy storage in lead-free NaNbO3-based relaxor ceramics with directional slush-like polar structures design, Nat. Commun. 16, 2892 (2025).
  30. J. Koruza, P. Groszewicz, H. Breitzke, G. Buntkowsky, T. Rojac, and B. Malič, Grain-size-induced ferroelectricity in NaNbO3, Acta Mater. 126, 77 (2017).
  31. Y. Shiratori, A. Magrez, J. Dornseiffer, F.-H. Haegel, C. Pithan, and R. Waser, Polymorphism in micro-, submicro-, and nanocrystalline NaNbO3, J. Phys. Chem. B 109, 20122 (2005).
  32. X. Tan, Z. Xu, X. Liu, and Z. Fan, Double hysteresis loops at room temperature in NaNbO3 -based lead-free antiferroelectric ceramics, Mater. Res. Lett. 6, 159 (2018).
  33. S. Aso, H. Matsuo, and Y. Noguchi, Reversible electric-field-induced phase transition in Ca-modified NaNbO3 perovskites for energy storage applications, Sci. Rep. 13, 6771 (2023).
  34. J. Ye, G. Wang, X. Chen, F. Cao, and X. Dong, Enhanced antiferroelectricity and double hysteresis loop observed in lead-free (1−x)NaNbO3−xCaSnO3 ceramics, Appl. Phys. Lett. 114, 122901 (2019).
  35. F. Ye, H. Cheng, X. Jiang, L. Zhu, W. Shi, and J. Xue, Sn and Ce co-doping regulate phase structure of NaNbO3: Double hysteresis loop and electro-strain, J. Adv. Ceram. 14, 9221119 (2025).
  36. H. Qi, A. Xie, J. Fu, and R. Zuo, Emerging antiferroelectric phases with fascinating dielectric, polarization and strain response in NaNbO3−(Bi0.5Na0.5)TiO3 lead-free binary system, Acta Mater. 208, 116710 (2021).
  37. B. Luo, H. Dong, D. Wang, and K. Jin, Large recoverable energy density with excellent thermal stability in Mn-modified NaNbO3 −CaZrO3 lead-free thin films, J. Am. Ceram. Soc. 101, 3460 (2018).
  38. L. Villa and K. Albe, Role of doping and defect quenching in antiferroelectric NaNbO3 from first principles, Phys. Rev. B 106, 134101 (2022).
  39. W. Sakamoto, Y.-I. Hamazaki, H. Maiwa, M. Moriya, and T. Yogo, Lead-free piezoelectric thin films of Mn-doped NaNbO3−BaTiO3 fabricated by chemical solution deposition, Thin Solid Films 518, 4256 (2010).
  40. M.-H. Zhang, H. Ding, S. Egert, C. Zhao, L. Villa, L. Fulanović, P. B. Groszewicz, G. Buntkowsky, H.-J. Kleebe, K. Albe, A. Klein, and J. Koruza, Tailoring high-energy storage NaNbO3-based materials from antiferroelectric to relaxor states, Nat. Commun. 14, 1525 (2023).
  41. J. T. Devreese, More on polaron theory history, Phys. Today 68(9), 11 (2015).
  42. C. Franchini, M. Reticcioli, M. Setvin, and U. Diebold, Polarons in materials, Nat. Rev. Mater. 6, 560 (2021).
  43. M. I. Dykman and E. I. Rashba, The roots of polaron theory, Phys. Today 68(4), 10 (2015).
  44. A. S. Alexandrov and J. T. Devreese, Advances in polaron physics, Springer Series in Solid-State Sciences (Springer, Berlin and Heidelberg, 2010), Vol. 159.
  45. D. Emin, Polarons (Cambridge University Press, 2012).
  46. T. Holstein, Studies of polaron motion, Ann. Phys. (NY) 8, 343 (1959).
  47. R. I. Eglitis, Ab initio calculations of SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3, PbZrO3 and BaZrO3 (001), (011) and (111) surfaces, as well as F centers, polarons, KTN solid solutions, and Nb impurities therein, Int. J. Mod. Phys. B 28, 1430009 (2014).
  48. H. Fröhlich, H. Pelzer, and S. Zienau, XX. Properties of slow electrons in polar materials, Philos. Mag. 41, 221 (1950).
  49. M.-H. Zhang, L. Fulanović, S. Egert, H. Ding, P. B. Groszewicz, H.-J. Kleebe, L. Molina-Luna, and J. Koruza, Electric-field-induced antiferroelectric to ferroelectric phase transition in polycrystalline NaNbO3, Acta Mater. 200, 127 (2020).
  50. G. Gouget, M. Duttine, E. Durand, A. Villesuzanne, V. Rodriguez, F. Adamietz, T. Le Mercier, M.-D. Braida, and A. Demourgues, Isolating the two room-temperature polymorphs of NaNbO3: Structural features, optical band gap, and reactivity, ACS Appl. Electron. Mater. 1, 513 (2019).
  51. H. Shi and Z. Zou, Photophysical and photocatalytic properties of ANbO3 (A = Na, K) photocatalysts, J. Phys. Chem. Solids 73, 788 (2012).
  52. G.-Z. Wang, H. Chen, G. Wu, A.-L. Kuang, and H.-K. Yuan, Hybrid density functional study on mono- and codoped NaNbO3 for visible-light photocatalysis, ChemPhysChem 17, 489 (2016).
  53. N. Bein, B. Kmet, T. Rojac, A. B. Golob, B. Malič, J. Moxter, T. Schneider, L. Fulanovic, M. Azadeh, T. Frömling, S. Egert, H. Wang, P. van Aken, J. Schwarzkopf, and A. Klein, Fermi energy, electrical conductivity, and the energy gap of NaNbO3, Phys. Rev. Mater. 6, 084404 (2022).
  54. 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).
  55. Y. Hermans, A. Klein, H. P. Sarker, M. N. Huda, H. Junge, T. Toupance, and W. Jaegermann, Pinning of the Fermi level in CuFeO2 by polaron formation limiting the photovoltage for photochemical water splitting, Adv. Funct. Mater. 30, 1910432 (2020).
  56. C. Lohaus, A. Klein, and W. Jaegermann, Limitation of Fermi level shifts by polaron defect states in hematite photoelectrodes, Nat. Commun. 9, 4309 (2018).
  57. T. Tadano and S. Tsuneyuki, Ab initio prediction of structural phase-transition temperature of SrTiO3 from finite-temperature phonon calculation, J. Ceram. Soc. Jpn. 127, 404 (2019).
  58. I. Pallikara, P. Kayastha, J. M. Skelton, and L. D. Whalley, The physical significance of imaginary phonon modes in crystals, Electron. Struct. 4, 033002 (2022).
  59. M. Kotiuga, S. Halilov, B. Kozinsky, M. Fornari, N. Marzari, and G. Pizzi, Microscopic picture of paraelectric perovskites from structural prototypes, Phys. Rev. Res. 4, L012042 (2022).
  60. O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, Electron small polarons and bipolarons in LiNbO3, J. Phys.: Condens. Matter 21, 123201 (2009).
  61. F. Schmidt, A. L. Kozub, T. Biktagirov, C. Eigner, C. Silberhorn, A. Schindlmayr, W. G. Schmidt, and U. Gerstmann, Free and defect-bound (bi)polarons in LiNbO3: Atomic structure and spectroscopic signatures from ab initio calculations, Phys. Rev. Res. 2, 043002 (2020).
  62. S. Sanna, Bound electron polarons in lithium niobate, in 2015 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA) (IEEE, Piscataway, NJ, 2015), pp. 523–527.
  63. A. Sanson, A. Zaltron, N. Argiolas, C. Sada, M. Bazzan, W. G. Schmidt, and S. Sanna, Polaronic deformation at the Fe2+/3+ impurity site in Fe:LiNbO3 crystals, Phys. Rev. B 91, 094109 (2015).
  64. A. Krampf, M. Imlau, Y. Suhak, H. Fritze, and S. Sanna, Evaluation of similarities and differences of LiTaO3 and LiNbO3 based on high-T-conductivity, nonlinear optical fs-spectroscopy and ab initio modeling of polaronic structures, New J. Phys. 23, 033016 (2021).
  65. 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).
  66. 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).
  67. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  68. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  69. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  70. 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).
  71. T. D. Pham and N. A. Deskins, Efficient method for modeling polarons using electronic structure methods, J. Chem. Theory Comput. 16, 5264 (2020).
  72. V. I. Anisimov, J. Zaanen, and O. K. Andersen, Band theory and Mott insulators: Hubbard U instead of Stoner I, Phys. Rev. B 44, 943 (1991).
  73. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
  74. 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).
  75. S. Falletta, J. Wiktor, and A. Pasquarello, Finite-size corrections of defect energy levels involving ionic polarization, Phys. Rev. B 102, 041115(R) (2020).
  76. S. Falletta and A. Pasquarello, Hubbard U through polaronic defect states, npj Comput. Mater. 8, 263 (2022).
  77. R. I. Eglitis, J. Purans, A. I. Popov, R. Jia, and S. P. Kruchinin, B3LYP and B3PW simulations of ABO3 perovskite (001) surfaces, interfaces, and oxygen vacancies therein, Symmetry 18, 550 (2026).
  78. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  79. H. Jónsson, G. Mills, and K. W. Jacobsen, Nudged elastic band method for finding minimum energy paths of transitions, in Classical and Quantum Dynamics in Condensed Phase Simulations (World Scientific, Singapore, 1998), pp. 385–404.
  80. G. Mills, H. Jónsson, and G. K. Schenter, Reversible work transition state theory: Application to dissociative adsorption of hydrogen, Surf. Sci. 324, 305 (1995).
  81. S. K. Mishra, N. Choudhury, S. L. Chaplot, P. S. R. Krishna, and R. Mittal, Competing antiferroelectric and ferroelectric interactions in NaNbO3: Neutron diffraction and theoretical studies, Phys. Rev. B 76, 024110 (2007).
  82. H. H. Nahm and C. H. Park, First-principles study of microscopic properties of the Nb antisite in LiNbO3: Comparison to phenomenological polaron theory, Phys. Rev. B 78, 184108 (2008).
  83. T. You, K. Huang, X. Zhao, A. Yi, C. Chen, W. Ren, T. Jin, J. Lin, Y. Shuai, W. Luo, M. Zhou, W. Yu, and X. Ou, Engineering of self-rectifying filamentary resistive switching in LiNbO3 single crystalline thin film via strain doping, Sci. Rep. 9, 19134 (2019).
  84. J. F. Janak, Proof that ∂E∂ni=ε in density-functional theory, Phys. Rev. B 18, 7165 (1978).
  85. N. A. Deskins and M. Dupuis, Intrinsic hole migration rates in TiO2 from density functional theory, J. Phys. Chem. C 113, 346 (2009).
  86. 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).
  87. F. Schmidt, A. L. Kozub, U. Gerstmann, W. G. Schmidt, and A. Schindlmayr, A density-functional theory study of hole and defect-bound exciton polarons in lithium niobate, Crystals 12, 1586 (2022).
  88. 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).
  89. M. Maiwald and O. F. Schirmer, O-dynamic Jahn-Teller polarons in KTaO3, Europhys. Lett. 64, 776 (2003).
  90. O. F. Schirmer, O-bound small polarons in oxide materials, J. Phys.: Condens. Matter 18, R667 (2006).
  91. P. Herth, T. Granzow, D. Schaniel, T. Woike, M. Imlau, and E. Krätzig, Evidence for light-induced hole polarons in LiNbO3, Phys. Rev. Lett. 95, 067404 (2005).
  92. Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, and I. Tanaka, Band structure diagram paths based on crystallography, Comput. Mater. Sci. 128, 140 (2017).
  93. H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).
  94. S. Kokott, S. V. Levchenko, P. Rinke, and M. Scheffler, First-principles supercell calculations of small polarons with proper account for long-range polarization effects, New J. Phys. 20, 033023 (2018).

Outline

Information

Phys. Rev. Materials 10, 115402– Published 12 November, 2026
  • Received 19 May 2026
  • Accepted 22 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation