Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Two-dimensional overdamped fluctuations of the soft perovskite lattice in CsPbBr3

Abstract

Lead halide perovskites exhibit structural instabilities and large atomic fluctuations thought to impact their optical and thermal properties, yet detailed structural and temporal correlations of their atomic motions remain poorly understood. Here, these correlations are resolved in CsPbBr3 crystals using momentum-resolved neutron and X-ray scattering measurements as a function of temperature, complemented with first-principles simulations. We uncover a striking network of diffuse scattering rods, arising from the liquid-like damping of low-energy Br-dominated phonons, reproduced in our simulations of the anharmonic phonon self-energy. These overdamped modes cover a continuum of wave vectors along the edges of the cubic Brillouin zone, corresponding to two-dimensional sheets of correlated rotations in real space, and could represent precursors to proposed two-dimensional polarons. Further, these motions directly impact the electronic gap edge states, linking soft anharmonic lattice dynamics and optoelectronic properties. These results provide insights into the highly unusual atomic dynamics of halide perovskites, relevant to further optimization of their optical and thermal properties.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Structural distortions and cubic phonon dispersions.
Fig. 2: Diffuse scattering revealing network of rods from overdamped phonons.
Fig. 3: Overdamping of phonon modes along M–R in the cubic and tetragonal phases.
Fig. 4: Damping of anharmonic phonons and their effect on the electronic structure.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

References

  1. Huang, J., Yuan, Y., Shao, Y. & Yan, Y. Understanding the physical properties of hybrid perovskites for photovoltaic applications. Nat. Rev. Mater. 2, 17042 (2017).

    Article  CAS  Google Scholar 

  2. Snaith, H. J. Present status and future prospects of perovskite photovoltaics. Nat. Mater. 17, 372–376 (2018).

    Article  CAS  Google Scholar 

  3. Stoumpos, C. C. et al. Crystal growth of the perovskite semiconductor CsPbBr3: a new material for high-energy radiation detection. Cryst. Growth Des. 13, 2722–2727 (2013).

    Article  CAS  Google Scholar 

  4. He, Y. et al. High spectral resolution of gamma-rays at room temperature by perovskite CsPbBr3 single crystals. Nat. Commun. 9, 1609 (2018).

    Article  Google Scholar 

  5. Lee, W. et al. Ultralow thermal conductivity in all-inorganic halide perovskites. Proc. Natl Acad. Sci. USA 114, 8693–8697 (2017).

    Article  CAS  Google Scholar 

  6. Xie, H. et al. All-inorganic halide perovskites as potential thermoelectric materials: dynamic cation off-centering induces ultralow thermal conductivity. J. Am. Chem. Soc. 142, 9553–9563 (2020).

    Article  CAS  Google Scholar 

  7. Jeon, N. J. et al. A fluorene-terminated hole-transporting material for highly efficient and stable perovskite solar cells. Nat. Energy 3, 682–689 (2018).

    Article  CAS  Google Scholar 

  8. Jiang, Q. et al. Surface passivation of perovskite film for efficient solar cells. Nat. Photon. 13, 460–466 (2019).

    Article  CAS  Google Scholar 

  9. Herz, L. M. How lattice dynamics moderate the electronic properties of metal-halide perovskites. J. Phys. Chem. Lett. 9, 6853–6863 (2018).

    Article  CAS  Google Scholar 

  10. Xing, G. et al. Long-range balanced electron- and hole-transport lengths in organic–inorganic CH3NH3PbI3. Science 342, 344–347 (2013).

    Article  CAS  Google Scholar 

  11. Whalley, L. D., Frost, J. M., Jung, Y.-K. & Walsh, A. Perspective: Theory and simulation of hybrid halide perovskites. J. Chem. Phys. 146, 220901 (2017).

    Article  Google Scholar 

  12. Miyata, K., Atallah, T. L. & Zhu, X.-Y. Lead halide perovskites: crystal–liquid duality, phonon glass electron crystals, and large polaron formation. Sci. Adv. 3, e1701469 (2017).

    Article  Google Scholar 

  13. Katan, C., Mohite, A. D. & Even, J. Entropy in halide perovskites. Nat. Mater. 17, 377–379 (2018).

    Article  CAS  Google Scholar 

  14. Gehrmann, C. & Egger, D. A. Dynamic shortening of disorder potentials in anharmonic halide perovskites. Nat. Commun. 10, 3141 (2019).

    Article  Google Scholar 

  15. Bertolotti, F. et al. Coherent nanotwins and dynamic disorder in cesium lead halide perovskite nanocrystals. ACS Nano 11, 3819–3831 (2017).

    Article  CAS  Google Scholar 

  16. Sakata, M., Harada, J., Cooper, M. & Rouse, K. A neutron diffraction study of anharmonic thermal vibrations in cubic CsPbX3. Acta Crystallogr. A 36, 7–15 (1980).

    Article  Google Scholar 

  17. Simoncelli, M., Marzari, N. & Mauri, F. Unified theory of thermal transport in crystals and glasses. Nat. Phys. 15, 809–813 (2019).

    Article  CAS  Google Scholar 

  18. Li, X. et al. All-inorganic CsPbBr3 perovskite solar cells with 10.45% efficiency by evaporation-assisted deposition and setting intermediate energy levels. ACS Appl. Mater. Interfaces 11, 29746–29752 (2019).

    Article  CAS  Google Scholar 

  19. Bechtel, J. S. & Van der Ven, A. Octahedral tilting instabilities in inorganic halide perovskites. Phys. Rev. Mater. 2, 025401 (2018).

    Article  CAS  Google Scholar 

  20. Yang, R. X., Skelton, J. M., Da Silva, E. L., Frost, J. M. & Walsh, A. Spontaneous octahedral tilting in the cubic inorganic cesium halide perovskites CsSnX3 and CsPbX3 (X = F, Cl, Br, I). J. Phys. Chem. Lett. 8, 4720–4726 (2017).

    Article  CAS  Google Scholar 

  21. Prasanna, R. et al. Band gap tuning via lattice contraction and octahedral tilting in perovskite materials for photovoltaics. J. Am. Chem. Soc. 139, 11117–11124 (2017).

    Article  CAS  Google Scholar 

  22. Oksenberg, E. et al. Large lattice distortions and size-dependent bandgap modulation in epitaxial halide perovskite nanowires. Nat. Commun. 11, 489 (2020).

    Article  CAS  Google Scholar 

  23. Li, W., Vasenko, A. S., Tang, J. & Prezhdo, O. V. Anharmonicity extends carrier lifetimes in lead halide perovskites at elevated temperatures. J. Phys. Chem. Lett. 10, 6219–6226 (2019).

    Article  CAS  Google Scholar 

  24. Rakita, Y. et al. Low-temperature solution-grown CsPbBr3 single crystals and their characterization. Cryst. Growth Des. 16, 5717–5725 (2016).

    Article  CAS  Google Scholar 

  25. Mayers, M. Z., Tan, L. Z., Egger, D. A., Rappe, A. M. & Reichman, D. R. How lattice and charge fluctuations control carrier dynamics in halide perovskites. Nano Lett. 18, 8041–8046 (2018).

    Article  CAS  Google Scholar 

  26. Beecher, A. N. et al. Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide perovskite. ACS Energy Lett. 1, 880–887 (2016).

    Article  CAS  Google Scholar 

  27. Comin, R. et al. Lattice dynamics and the nature of structural transitions in organolead halide perovskites. Phys. Rev. B 94, 094301 (2016).

    Article  Google Scholar 

  28. Gold-Parker, A. et al. Acoustic phonon lifetimes limit thermal transport in methylammonium lead iodide. Proc. Natl Acad. Sci. USA 115, 11905–11910 (2018).

    Article  CAS  Google Scholar 

  29. Songvilay, M. et al. Lifetime-shortened acoustic phonons and static order at the Brillouin zone boundary in the organic–inorganic perovskite CH3NH3PbCl3. Phys. Rev. Mater. 2, 123601 (2018).

    Article  CAS  Google Scholar 

  30. Songvilay, M. et al. Common acoustic phonon lifetimes in inorganic and hybrid lead halide perovskites. Phys. Rev. Mater. 3, 093602 (2019).

    Article  CAS  Google Scholar 

  31. Ferreira, A. et al. Direct evidence of weakly dispersed and strongly anharmonic optical phonons in hybrid perovskites. Commun. Phys. 3, 48 (2020).

    Article  Google Scholar 

  32. Fujii, Y., Hoshino, S., Yamada, Y. & Shirane, G. Neutron-scattering study on phase transitions of CsPbCl3. Phys. Rev. B 9, 4549 (1974).

    Article  CAS  Google Scholar 

  33. Ma, H. et al. Experimental phonon dispersion and lifetimes of tetragonal CH3NH3PbI3 perovskite crystals. J. Phys. Chem. Lett. 10, 1–6 (2018).

    Article  Google Scholar 

  34. Manley, M. et al. Giant isotope effect on phonon dispersion and thermal conductivity in methylammonium lead iodide. Sci. Adv. 6, eaaz1842 (2020).

    Article  CAS  Google Scholar 

  35. Maughan, A. E. et al. Anharmonicity and octahedral tilting in hybrid vacancy-ordered double perovskites. Chem. Mater. 30, 472–483 (2018).

    Article  CAS  Google Scholar 

  36. Mozur, E. M. et al. Orientational glass formation in substituted hybrid perovskites. Chem. Mater. 29, 10168–10177 (2017).

    Article  CAS  Google Scholar 

  37. Li, B. et al. Polar rotor scattering as atomic-level origin of low mobility and thermal conductivity of perovskite CH3NH3PbI3. Nat. Commun. 8, 16086 (2017).

    Article  CAS  Google Scholar 

  38. Yaffe, O. et al. Local polar fluctuations in lead halide perovskite crystals. Phys. Rev. Lett. 118, 136001 (2017).

    Article  Google Scholar 

  39. Guo, Y. et al. Interplay between organic cations and inorganic framework and incommensurability in hybrid lead-halide perovskite CH3NH3PbBr3. Phys. Rev. Mater. 1, 042401 (2017).

    Article  Google Scholar 

  40. Sharma, R. et al. Elucidating the atomistic origin of anharmonicity in tetragonal CH3NH3PbI3 with Raman scattering. Phys. Rev. Mater. 4, 092401 (2020).

    Article  CAS  Google Scholar 

  41. Wu, X. et al. Light-induced picosecond rotational disordering of the inorganic sublattice in hybrid perovskites. Sci. Adv. 3, e1602388 (2017).

    Article  Google Scholar 

  42. Miyata, K. et al. Large polarons in lead halide perovskites. Sci. Adv. 3, e1701217 (2017).

    Article  Google Scholar 

  43. Hirotsu, S., Harada, J., Iizumi, M. & Gesi, K. Structural phase transitions in CsPbBr3. J. Phys. Soc. Jpn 37, 1393–1398 (1974).

    Article  CAS  Google Scholar 

  44. Glazer, A. The classification of tilted octahedra in perovskites. Acta Crystallogr. B 28, 3384–3392 (1972).

    Article  CAS  Google Scholar 

  45. Laurita, G., Fabini, D. H., Stoumpos, C. C., Kanatzidis, M. G. & Seshadri, R. Chemical tuning of dynamic cation off-centering in the cubic phases of hybrid tin and lead halide perovskites. Chem. Sci. 8, 5628–5635 (2017).

    Article  CAS  Google Scholar 

  46. Nield, V. M. et al. Diffuse Neutron Scattering from Crystalline Materials Vol. 14 (Oxford Univ. Press, 2001).

  47. Bruce, A. D. & Cowley, R. Structural phase transitions III. Critical dynamics and quasi-elastic scattering. Adv. Phys. 29, 219–321 (1980).

    Article  CAS  Google Scholar 

  48. Bansal, D. et al. Magnetically driven phonon instability enables the metal–insulator transition in h-FeS. Nat. Phys. 16, 669–675 (2020).

  49. He, X. et al. Anharmonic eigenvectors and acoustic phonon disappearance in quantum paraelectric SrTiO3. Phys. Rev. Lett. 124, 145901 (2020).

    Article  CAS  Google Scholar 

  50. Swainson, I. et al. Soft phonon columns on the edge of the Brillouin zone in the relaxor PbMg1/3Nb2/3O3. Phys. Rev. B 79, 224301 (2009).

    Article  Google Scholar 

  51. Boehme, S. C. et al. Phonon-mediated and weakly size-dependent electron and hole cooling in CsPbBr3 nanocrystals revealed by atomistic simulations and ultrafast spectroscopy. Nano Lett. 20, 1819–1829 (2020).

    Article  CAS  Google Scholar 

  52. Mannino, G. et al. Temperature dependent optical band gap in CsPbBr3, MAPbBr3 and FAPbBr3 single crystals. J. Phys. Chem. Lett. 11, 2490–2496 (2020).

  53. Cinquanta, E. et al. Ultrafast THz probe of photoinduced polarons in lead-halide perovskites. Phys. Rev. Lett. 122, 166601 (2019).

    Article  CAS  Google Scholar 

  54. Thouin, F. et al. Phonon coherences reveal the polaronic character of excitons in two-dimensional lead halide perovskites. Nat. Mater. 18, 349–356 (2019).

    Article  CAS  Google Scholar 

  55. Chu, W., Zheng, Q., Prezhdo, O. V., Zhao, J. & Saidi, W. A. Low-frequency lattice phonons in halide perovskites explain high defect tolerance toward electron–hole recombination. Sci. Adv. 6, eaaw7453 (2020).

    Article  CAS  Google Scholar 

  56. Krogstad, M. J. et al. Reciprocal space imaging of ionic correlations in intercalation compounds. Nat. Mater. 19, 63 (2020).

    Article  CAS  Google Scholar 

  57. Ehlers, G., Podlesnyak, A., Niedziela, J., Iverson, E. & Sokol, P. The new cold neutron chopper spectrometer at the Spallation Neutron Source: design and performance. Rev. Sci. Instrum. 82, 085108 (2011).

  58. Arnold, O. et al. Mantid—data analysis and visualization package for neutron scattering and μSR experiments. Nucl. Instrum. Methods Phys. Res. A 764, 156–166 (2014).

    Article  CAS  Google Scholar 

  59. Ewings, R. et al. Horace: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods Phys. Res. A 834, 132–142 (2016).

    Article  CAS  Google Scholar 

  60. Abernathy, D. L. et al. Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source. Rev. Sci. Instrum. 83, 015114 (2012).

    Article  CAS  Google Scholar 

  61. Lahnsteiner, J., Kresse, G., Heinen, J. & Bokdam, M. Finite-temperature structure of the MAPbI3 perovskite: comparing density functional approximations and force fields to experiment. Phys. Rev. Mater. 2, 073604 (2018).

    Article  CAS  Google Scholar 

  62. Perez-Osorio, M. A., Champagne, A., Zacharias, M., Rignanese, G.-M. & Giustino, F. Van der Waals interactions and anharmonicity in the lattice vibrations, dielectric constants, effective charges, and infrared spectra of the organic–inorganic halide perovskite CH3NH3PbI3. J. Phys. Chem. C 121, 18459–18471 (2017).

    Article  CAS  Google Scholar 

  63. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

    Article  CAS  Google Scholar 

  64. Natarajan, M. & Prakash, B. Phase transitions in ABX3 type halides. Phys. Status Solidi A 4, K167–K172 (1971).

    Article  CAS  Google Scholar 

  65. Rodová, M., Brožek, J., Knížek, K. & Nitsch, K. Phase transitions in ternary caesium lead bromide. J. Therm. Anal. Calorim. 71, 667–673 (2003).

    Article  Google Scholar 

  66. Hellman, O., Steneteg, P., Abrikosov, I. A. & Simak, S. I. Temperature dependent effective potential method for accurate free energy calculations of solids. Phys. Rev. B 87, 104111 (2013).

    Article  Google Scholar 

  67. Hellman, O., Abrikosov, I. & Simak, S. Lattice dynamics of anharmonic solids from first principles. Phys. Rev. B 84, 180301 (2011).

    Article  Google Scholar 

  68. Hellman, O. & Abrikosov, I. A. Temperature-dependent effective third-order interatomic force constants from first principles. Phys. Rev. B 88, 144301 (2013).

    Article  Google Scholar 

  69. Squires, G. L. Introduction to the Theory of Thermal Neutron Scattering (Courier, 1996).

  70. Cowley, R. Anharmonic crystals. Rep. Prog. Phys. 31, 123 (1968).

    Article  CAS  Google Scholar 

  71. Maradudin, A. & Fein, A. Scattering of neutrons by an anharmonic crystal. Phys. Rev. 128, 2589 (1962).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank D. Mitzi and V. Blum for discussions. We thank O. Hellman for providing access to the TDEP software package. T.L.-A. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0019299. X.H. and O.D. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0019978. Initial support of T.L.-A. by Duke Energy Initiative seed funds is acknowledged. Work at Argonne (synthesis, characterization and X-ray and neutron scattering measurements) is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The use of Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. We acknowledge the support of the National Institute of Standards and Technology, US Department of Commerce, in providing the neutron research facilities used in this work. Theoretical calculations were performed using resources of the National Energy Research Scientific Computing Center, a US Department of Energy Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231.

Author information

Authors and Affiliations

Authors

Contributions

Neutron scattering measurements and analysis were performed by T.L.-A., R.O., M.J.K., X.H., S.R. and O.D., with support from D.M.P., D.L.A., G.N.M.N.X. and Z.X. X-ray scattering measurements were performed by M.J.K., S.R. and R.O. and were analysed by M.J.K. Sample synthesis was performed by D.-Y.C. X.H. performed the first-principles simulations. T.L.-A., X.H. and O.D. wrote the manuscript and all authors commented on it.

Corresponding authors

Correspondence to R. Osborn or O. Delaire.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks Felix Fernandez-Alonso, Antonietta Guagliardi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–34, Discussion and Tables 1–4.

Supplementary Video 1

Animation for M-mode soft phonon.

Supplementary Video 2

Animation for R-mode soft phonon.

Source data

Source Data Fig. 1

Source data for graphs in Fig. 1.

Source Data Fig. 2

Source data for graphs in Fig. 2.

Source Data Fig. 3

Source data for graphs in Fig. 3.

Source Data Fig. 4

Source data for graphs in Fig. 4.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lanigan-Atkins, T., He, X., Krogstad, M.J. et al. Two-dimensional overdamped fluctuations of the soft perovskite lattice in CsPbBr3. Nat. Mater. 20, 977–983 (2021). https://doi.org/10.1038/s41563-021-00947-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-021-00947-y

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing