Examination of permittivity for depolarization field of ferroelectric by ab initio calculation, suggesting hidden mechanisms

1. Kittel, C. Physical theory of ferromagnetic domains. Rev. Mod. Phys. 21, 541–583 (1949).

2. Kalinin, S. V. & Bonnell, D. Domain polarity and temperature induced potential inversion on the B

­ aTiO3 (100) surface. J. Appl.

Phys. 91, 3816 (2002).

3. Batra, I. P., Wurfel, P. & Silverman, B. D. Phase transition, stability, and depolarization field in ferroelectric thin films. Phys. Rev.

B. 8, 3257–3265 (1973).

4. Mehta, R. R., Silverman, B. D. & Jacobs, J. T. Depolarization fields in thin ferroelectric films. J. Appl. Phys. 44, 3379–3385 (1973).

5. Black, C. T., Farrell, C. & Licata, T. J. Suppression of ferroelectric polarization by an adjustable depolarization field. Appl. Phys.

Lett. 71, 2041–2043 (1997).

6. Zhao, D. et al. Depolarization of multidomain ferroelectric materials. Nat. Commun. 10, 2547-1–11 (2019).

7. Tian, J. et al. Depolarization-field-induced retention loss in ferroelectric diodes. Phys. Rev. Appl. 11, 024058-1–15 (2019).

8. Kim, D. J. et al. Polarization relaxation induced by a depolarization field in ultrathin ferroelectric B

­ aTiO3 capacitors. Phys. Rev.

Lett. 95, 237602-1–4 (2005).

9. Jo, J. Y., Kim, Y. S., Noh, T. W., Yoon, J.-G. & Song, T. K. Coercive fields in ultrathin ­BaTiO3 capacitors. Appl. Phys. Lett. 89, 2329091–3 (2006).

10. Schroeder, U., Lomenzo, P. D., Toriumi, A. & Mikolajick, T. Impact of depolarization fields on the ferroelectric switching behavior

in doped H

­ fO2. Ext. Abst. Fundament. Phys. Ferroelectr. Relat. Mater. 2020, 21–22 (2020).

11. Polanco, M. A. M. et al. Stabilization of highly polarized P

­ bTiO3 nanoscale capacitors due to in-plane symmetry breaking at the

interface. Phys. Rev. B 85, 214107-1–7 (2012).

12. Watanabe, Y. Proper permittivity for depolarization field in perfectly insulating ferroelectric and examination of background

permittivity. Ferroelectrics 461, 38–43 (2014).

13. Watanabe, Y. Proper permittivity for depolarization field and its implication to universal instability of insulating ferroelectric: A

note. J. Phys. Soc. Jpn. 79, 034713-1–5 (2010) (Especially, Eqs. (4)–(10)).

14. Watanabe, Y., Okano, M. & Masuda, A. Surface conduction on insulating B

­ aTiO3 crystal suggesting an intrinsic surface electron

layer. Phys. Rev. Lett. 86, 332–335 (2001).

15. Watanabe, Y. Theoretical stability of the polarization in a thin semiconducting ferroelectric. Phys. Rev. B 57, 789–804 (1998).

16. Jiang, B. et al. Barium titanate at the nanoscale: Controlled synthesis and dielectric and ferroelectric properties. Chem. Soc. Rev.

48, 1194–1228 (2019).

17. You, W.-X. & Su, P. Depolarization field in ferroelectric nonvolatile memory considering minor loop operation. IEEE Electron

Device Lett. 40, 1415–1418 (2019).

18. Watanabe, Y. Electrostatics liberating restrictions on ferroelectric by unification of polar discontinuity e−h+ layers and criteria of

intrinsicality. Ferroelectrics 556, 29–36 (2020).

19. Watanabe, Y. Ferroelectricity of stress-free and strained pure S­ rTiO3 revealed by ab initio calculations with hybrid and density

functionals. Phys. Rev. B 99, 064107-1–14 (2019).

20. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558R (1993).

21. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).

22. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave

basis set. J. Comput. Mater. Sci. 6, 15–50 (1996).

23. Blöchel, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

24. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

25. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406-1–4

(2008).

26. Resta, R. Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Rev. Mod. Phys. 66, 899–915 (1994).

27. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

28. Liechtenstein, A. I., Anisimov, V. I. & Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in MottHubbard insulators. Phys. Rev. B 52, 5467R-5470R (1995).

29. Watanabe, Y. Breakdown of ion-polarization-correspondence and born effective charges: Algebraic formulas of accurate polarization under field. Phys. Rev. Mater. 4, 104405-1–11 (2020).

30. Heine, V. Theory of surface states. Phys. Rev. A 138, 1689–1696 (1965).

31. Li, Y. L., Cross, L. E. & Chen, L. Q. A phenomenological thermodynamic potential for ­BaTiO3 single crystals. J. Appl. Phys. 98,

06410114 (2005) (For examples of standard GLD theories).

32. Cross, L. E. & Pohanka, R. C. Ferroelectricity in bismuth oxide type layer structure compounds. Mater. Res. Bull. 6, 939–949 (1971).

33. Känzig, W. Ferroelectrics and antiferroelectrics. In Solid State Physics Vol. 4 (eds Seitz, E. & Turnbull, D.) 1–197 (Academic, New

York, 1957).

34. Haun, M. J., Furman, E., Jang, S. J., McKinstry, H. A. & Cross, L. E. Thermodynamic theory of P

­ bTiO3. J. Appl. Phys. 62, 3331–3338

(1987).

35. Tagantsev, A. K. Landau expansion for ferroelectrics: Which variable to use?. Ferroelectrics 375, 19–27 (2008).

36. Boni, G. A. et al. Low value for the static background dielectric constant in epitaxial PZT thin films. Sci. Rep. 9, 14698 (2019).

37. Watanabe, Y. Calculation of strained B

­ aTiO3 with different exchange correlation functionals examined with criterion by Ginzburg–Landau theory, uncovering expressions by crystallographic parameters. J. Chem. Phys. 148, 194702 (2018).

38. Garrity, K. F., Rabe, K. M. & Vanderbilt, D. Hyperferroelectrics: Proper ferroelectrics with persistent polarization. Phys. Rev. Lett.

112, 27601-1–5 (2014).

39. Liu, S. & Cohen, R. E. Stable charged antiparallel domain walls in hyperferroelectrics. J. Phys. Condens. Matter 29, 244003 (2017).

40. Krčmar, M. & Fu, C. L. Structural and electronic properties of B

­ aTiO3 slabs: Mechanism for surface conduction. Phys. Rev. B 68,

115404-1–7 (2003).

41. Sai, N., Fennie, C. J. & Demkov, A. A. Absence of critical thickness in an ultrathin improper ferroelectric film. Phys. Rev. Lett. 102,

107601 (2009).

42. Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87–90 (2019).

43. Ievlev, A. V. et al. Chemical state evolution in ferroelectric films during tip-induced polarization and electroresistive switching.

Appl. Mater. Interfaces 8, 29588–29593 (2016).

44. Fong, D. D. et al. Stabilization of monodomain polarization in ultrathin P

­ bTiO3films. Phys. Rev. Lett. 91, 127601-1–4 (2006).

Scientific Reports |

Vol:.(1234567890)

(2021) 11:2155 |

https://doi.org/10.1038/s41598-021-81237-0

10

www.nature.com/scientificreports/

45. Deleuze, P.-M., Domenichini, B. & Dupont, C. Ferroelectric polarization switching induced from water adsorption in ­BaTiO3

ultrathin films. Phys. Rev. B 101, 075410 (2020).

46. Banieck, J. D. et al. Photoemission and quantum chemical study of S­ rTiO3 (001) surfaces and their interaction with C

­ O2. Phys.

Rev. B 78, 195415-1–12 (2008).

47. De Souza, R. A., Metlenko, V., Park, D. & Weirich, T. E. Behavior of oxygen vacancies in single-crystal S­ rTiO3: Equilibrium distribution and diffusion kinetics. Phys. Rev. B 85, 174109-1–11 (2012) (For example).

48. Su, C.-P. et al. Impact of strain-field interference on the coexistence of electron and hole gases in ­SrTiO3/LaAlO3/SrTiO3. Phys.

Rev. Mater. 3, 075003-1–10 (2019) (For example).

49. Hacene, M. et al. Accelerating VASP electronic structure calculations using graphic processing units. J. Comput. Chem. 33, 2581–

2589 (2012).

50. Hutchinson, M. & Widom, M. VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron.

Comput. Phys. Commun. 7, 1422–1426 (2011).

51. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

Acknowledgements

Dr. P. Blöchel and Dr. M. Takashige for discussions, Dr. R. R. Mehta for his questions and discussions about

Ref.13, and the support JSPS KAKENHI no. JP19K21853 are acknowledged.

Author contributions

Y.W. did this work.

Competing interests The author declares no competing interests.

Additional information

Correspondence and requests for materials should be addressed to Y.W.

Reprints and permissions information is available at www.nature.com/reprints.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and

institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International

License, which permits use, sharing, adaptation, distribution and reproduction in any medium or

format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the

Creative Commons licence, and indicate if changes were made. The images or other third party material in this

article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the

material. If material is not included in the article’s Creative Commons licence and your intended use is not

permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from

the copyright holder. To view a copy of this licence, visit http://creat​iveco​mmons​.org/licen​ses/by/4.0/.

© The Author(s) 2021

Scientific Reports |

(2021) 11:2155 |

https://doi.org/10.1038/s41598-021-81237-0

11

Vol.:(0123456789)

...