Magnetically driven phonon instability enables the metal–insulator transition in h-FeS


Hexagonal iron sulfide exhibits a fascinating coexistence of metal–insulator, structural and magnetic transitions, reflecting an intimate interplay of its spin, phonon and charge degrees of freedom. Here, we show how a subtle competition of energetic and entropic free-energy components governs its thermodynamics and the sequence of phase transitions it undergoes upon cooling. By means of comprehensive neutron and X-ray scattering measurements, and supported by first-principles electronic structure simulations, we identify the critical role of the coupling between antiferromagnetic ordering and instabilities of anharmonic phonons in the metallic phase in driving the metal–insulator transition. The antiferromagnetic ordering enables the emergence of two zone-boundary soft phonons, whose coupling to a zone-centre mode drives the lattice distortion opening the electronic bandgap. Simultaneously, spin–lattice coupling opens a gap in the magnon spectrum that controls the entropy component of the metal–insulator transition free energy. These results reveal the importance of spin–phonon coupling to tune anharmonic effects, thus opening new avenues to design novel technologically important materials harbouring the metal–insulator transition and magnetoelectric behaviours.

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Fig. 1: Structural and magnetic phase transition and lattice distortions.
Fig. 2: Lattice instabilities enabled by AFM ordering.
Fig. 3: Phonon instabilities measured using IXS and INS.
Fig. 4: Magnon bandgap and in-plane triangular cluster excitation from INS.
Fig. 5: Thermodynamics of the MIT.

Data availability

Source data for Figs. 15 are provided with the paper. Other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


  1. 1.

    Peierls, R. More Surprises in Theoretical Physics (Princeton Univ. Press, 1991).

  2. 2.

    Slater, J. Magnetic effects and the Hartree-Fock equation. Phys. Rev. 82, 538–541 (1951).

    ADS  Google Scholar 

  3. 3.

    Mott, N. The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. A 62, 416–422 (1949).

    ADS  Google Scholar 

  4. 4.

    Mott, N. Metal-Insulator Transitions (Taylor and Francis, 1990).

  5. 5.

    Pustogow, A. et al. Quantum spin liquids unveil the genuine Mott state. Nat. Mater. 17, 773–777 (2018).

    ADS  Google Scholar 

  6. 6.

    Liang, Y., Yuan, X., Gao, Y., Zhang, W. & Zhang, P. Phonon-assisted crossover from a nonmagnetic Peierls insulator to a magnetic Stoner metal. Phys. Rev. Lett. 113, 176401 (2014).

    ADS  Google Scholar 

  7. 7.

    Munoz, J., Aranda, M., Alonso, J. & Lope, M. Structure and charge order in the antiferromagnetic band-insulating phase of NdNiO3. Phys. Rev. B 79, 134432 (2009).

    ADS  Google Scholar 

  8. 8.

    Mercy, A., Bieder, J., Iniguez, J. & Ghosez, P. Structurally triggered metal-insulator transition in rare-earth nickelates. Nat. Commun. 8, 1677 (2017).

    ADS  Google Scholar 

  9. 9.

    Asamitsu, A., Moritomo, Y., Tomioka, Y., Arima, T. & Tokura, Y. A structural phase transition induced by an external magnetic field. Nature 373, 407–409 (1995).

    ADS  Google Scholar 

  10. 10.

    Imada, M., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).

    ADS  Google Scholar 

  11. 11.

    Cui, Q. et al. Slater insulator in iridate perovskites with strong spin-orbit coupling. Phys. Rev. Lett. 117, 176603 (2016).

    ADS  Google Scholar 

  12. 12.

    Cheong, S. W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007).

    ADS  Google Scholar 

  13. 13.

    Ramesh, R. & Spaldin, N. A. Multiferroics: progress and prospects in thin films. Nat. Mater. 6, 21–29 (2007).

    ADS  Google Scholar 

  14. 14.

    Fiebig, M., Lottermoder, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 16046 (2016).

    ADS  Google Scholar 

  15. 15.

    Benedek, N. A. & Fennie, C. J. Hybrid improper ferroelectricity: a mechanism for controllable polarization-magnetization coupling. Phys. Rev. Lett. 106, 107204 (2011).

    ADS  Google Scholar 

  16. 16.

    Murakami, M. Anisotropy of electrical conduction in iron sulfide single crystal. J. Phys. Soc. Jpn 16, 187–192 (1961).

    ADS  Google Scholar 

  17. 17.

    Andresen, A. & Torbo, P. Phase transitions in FexS (x = 0.90–1.00) studied by neutron diffraction. Acta Chem. Scandinavica 21, 2841–2848 (1967).

    Google Scholar 

  18. 18.

    Pearce, C., Pattrick, A. & Vaughan, D. Electrical and magnetic properties of sulfides. Rev. Mineral. Geochem. 61, 127–180 (2006).

    Google Scholar 

  19. 19.

    Ricci, F. & Bousquet, E. Unveiling the room-temperature magnetoelectricity of troilite FeS. Phys. Rev. Lett. 116, 227601 (2016).

    ADS  Google Scholar 

  20. 20.

    Hirahara, E. & Murakami, M. Magnetic and electrical anisotropies of iron sulfide single crystals. J. Phys. Chem. Solids 7, 281–289 (1958).

    ADS  Google Scholar 

  21. 21.

    King, H. & Prewitt, C. High-pressure and high-temperature polymorphism of iron sulfide FeS. Acta Cryst. B38, 1877–1887 (1982).

    Google Scholar 

  22. 22.

    Li, F. & Franzen, H. Phase transitions in near stoichiometric iron sulfide. J. Alloys Compound. 238, 73–80 (1996).

    Google Scholar 

  23. 23.

    Kusaba, K., Syono, Y., Kikegawa, T. & Shimomura, O. High pressure and temperature behavior of FeS. J. Phys. Chem. Solids 59, 945–950 (1998).

    ADS  Google Scholar 

  24. 24.

    Andresen, A. Magnetic phase transition in stoichiometric FeS studied by means of neutron diffraction. Acta Chem. Scandinavica 14, 919–926 (1960).

    Google Scholar 

  25. 25.

    Adachi, K. Magnetic anisotropy energy in nickel arsenide type crystals. J. Phys. Soc. Jpn 16, 2187–2206 (1961).

    ADS  Google Scholar 

  26. 26.

    Adachi, K. & Sato, K. Origin of magnetic anisotropy energy of Fe7S8 and Fe7Se8. J. Appl. Phys. 39, 1343–1344 (1968).

    ADS  Google Scholar 

  27. 27.

    Sakkopoulos, S. Antiferromagnetism and metal-semiconductor transition in iron sulfides FeSx, 1≤x<1.25. J. Appl. Phys. 59, 3540–3542 (1986).

    ADS  Google Scholar 

  28. 28.

    Takele, S. & Hearne, G. Electrical transport, magnetism, and spin-state configurations of high-pressure phases of FeS. Phys. Rev. B 60, 4401–4403 (1999).

    ADS  Google Scholar 

  29. 29.

    Kobayashi, H., Takeshita, N., Mori, N., Takahashi, H. & Kamimura, T. Pressure-induced semiconductor-metal-semiconductor transitions in FeS. Phys. Rev. B 63, 115203 (2001).

    ADS  Google Scholar 

  30. 30.

    Trahan, J., Goodrich, R. & Watkins, S. X-ray diffraction measurements on metallic and semiconducting hexagonal NiS. Phys. Rev. B 2, 2859–2863 (1970).

    ADS  Google Scholar 

  31. 31.

    Panda, S., Dasgupta, I., Sasioglu, E., Blugel, S. & Sarma, D. NiS—an unusual self-doped, nearly compensated antiferromagnetic metal. Sci. Rep. 3, 2995 (2013).

    ADS  Google Scholar 

  32. 32.

    Shimada, K. et al. Spin-integrated and spin-resolved photoemission study of Fe chalcogenides. Phys. Rev. B 57, 8845–8853 (1998).

    ADS  Google Scholar 

  33. 33.

    Rueff, J.-P. et al. Pressure-induced high-spin to low-spin transition in FeS evidenced by X-ray emission spectroscopy. Phys. Rev. Lett. 82, 3284–3287 (1999).

    ADS  Google Scholar 

  34. 34.

    Nesbitt, H., Schaufuss, A., Bancroft, G. & Szargan, R. Crystal orbital contributions to the pyrrhotite valence band with XPS evidence for weak Fe–Fe π bond formation. Phys. Chem. Minerals 29, 72–77 (2002).

    ADS  Google Scholar 

  35. 35.

    Goodenough, J. Cation-cation three-membered ring formation. J. Appl. Phys. 33, 1197–1199 (1962).

    ADS  Google Scholar 

  36. 36.

    Bertaut, E. On sulfides and pnictides. Pure Appl. Chem. 52, 73–92 (1979).

    Google Scholar 

  37. 37.

    Sakkopoulos, S., Vitoratos, E. & Argyreas, T. Energy band diagram for pyrrhotite. J. Phys. Chem. Solids 45, 923–928 (1984).

    ADS  Google Scholar 

  38. 38.

    Craco, L. & Faria, J. Electronic localization and bad-metallicity in pure and electron-doped troilite: a local-density-approximation plus dynamical-mean-field-theory study of FeS for lithium-ion batteries. J. Appl. Phys. 119, 085107 (2016).

    ADS  Google Scholar 

  39. 39.

    Craco, L., Faria, J. & Leoni, S. Electronic reconstruction of hexagonal FeS: a view from density functional dynamical mean-field theory. Mater. Res. Express 4, 036303 (2017).

    ADS  Google Scholar 

  40. 40.

    Orobengoa, D., Capillas, C., Aroyo, M. I. & Perez-Mato, J. M. AMPLIMODES: symmetry-mode analysis on the Bilbao Crystallographic Server. J. Appl. Cryst. A42, 820–833 (2009).

    Google Scholar 

  41. 41.

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

    ADS  Google Scholar 

  42. 42.

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

    ADS  Google Scholar 

  43. 43.

    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).

    ADS  Google Scholar 

  44. 44.

    Fennie, C. J. & Rabe, K. M. Ferroelectric transition in YMnO3 from first principles. Phys. Rev. B 72, 100103(R) (2005).

    ADS  Google Scholar 

  45. 45.

    Bansal, D. et al. Momentum-resolved observations of the phonon instability driving geometric improper ferroelectricity in yttrium manganite. Nat. Commun. 9, 15 (2018).

    ADS  Google Scholar 

  46. 46.

    Robie, R. A. & Waldbaum, D. R. Thermodynamic Properties of Minerals and Related Substances at 298.15 K (25.0 °C) and One Atmosphere (1.013 Bars) Pressure and at Higher Temperatures (US Govt. Printing Office, 1968).

  47. 47.

    Benedek, N. A., Rondinelli, J. M., Djani, H., Ghosez, P. & Lightfoot, P. Understanding ferroelectricity in layered perovskites: new ideas and insights from theory and experiments. Dalton Trans. 44, 10543–10558 (2015).

    Google Scholar 

  48. 48.

    Toellner, T., Alatas, A. & Said, A. Six reflection meV-monochromator for synchrotron radiation. J. Synchrotron Radiat. 18, 605–611 (2011).

    Google Scholar 

  49. 49.

    Said, A., Sinn, H. & Divan, R. New developments in fabrication of high-energy-resolution analyzers for inelastic X-ray spectroscopy. J. Synchrotron Radiat. 18, 492–496 (2011).

    Google Scholar 

  50. 50.

    Lovesey, S. Theory of Neutron Scattering from Condensed Matter (Clarendon Press, 1984).

  51. 51.

    Stone, M. et al. A comparison of four direct geometry time-of-flight spectrometers at the Spallation Neutron Source. Rev. Sci. Instruments 85, 045113 (2014).

    ADS  Google Scholar 

  52. 52.

    Arnold, O. et al. Mantid–data analysis and visualization package for neutron scattering and μSR experiments. Nuclear Instruments Meth. Phys. Res. Sect. A 764, 156–166 (2014).

    ADS  Google Scholar 

  53. 53.

    Bansal, D. et al. Electron-phonon coupling and thermal transport in the thermoelectric compound Mo3Sb7−xTex. Phys. Rev. B 92, 214301 (2015).

    ADS  Google Scholar 

  54. 54.

    Wallace, D. Thermodynamics of Crystals (John Wiley & Sons Inc., 1972).

  55. 55.

    Fultz, B. Vibrational thermodynamics of materials. Prog. Mater. Sci. 55, 247–352 (2010).

    Google Scholar 

  56. 56.

    Bansal, D. et al. Phonon anharmonicity and negative thermal expansion in SnSe. Phys. Rev. B 94, 054307 (2016).

    ADS  Google Scholar 

  57. 57.

    Wallace, D. Statistical Physics of Crystals and Liquids: A Guide to Highly Accurate Equations of State (World Scientific Pub. Co. Inc., 2003).

  58. 58.

    Grimvall, G. Thermophysical Properties of Materials (Elsevier, 1999).

  59. 59.

    Blundell, S. Magnetism in Condensed Matter (Oxford Univ. Press, 2001).

  60. 60.

    Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    ADS  Google Scholar 

  61. 61.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    ADS  Google Scholar 

  62. 62.

    Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Google Scholar 

  63. 63.

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

    ADS  Google Scholar 

  64. 64.

    Dudarev, S., Botton, G., Savrasov, S., Humphreys, C. & Sutton, A. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).

    ADS  Google Scholar 

  65. 65.

    Gosselin, J., Townsend, M. & Tremblay, R. Electric anomalies at the phase transition in FeS. Solid State Commun. 19, 799–803 (1976).

    ADS  Google Scholar 

  66. 66.

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

    Google Scholar 

  67. 67.

    Toth, S. & Lake, B. Linear spin wave theory for single-Q incommensurate magnetic structures. J. Phys. Condens. Matter 27, 166002 (2015).

    ADS  Google Scholar 

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We thank O. Hellman for providing access to and support with the TDEP software. Neutron and X-ray scattering measurements were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under the Early Career award no. DE-SC0016166. Analysis of results and writing of the manuscript was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under award no. DE-SC0019978. H.Z. (sample synthesis) thanks the support from NSF-DMR-1350002. The use of Oak Ridge National Laboratory’s Spallation Neutron Source and High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US DOE. This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. Theoretical calculations were performed using resources of the National Energy Research Scientific Computing Center, a DOE 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




D.B., J.L.N., O.D., S.C., D.L.A. and A.I.K. performed the neutron scattering experiments. D.B. and A.H.S. performed the IXS measurements. T.L.-A. and D.B. performed the calorimetry measurements. S.C. analysed the neutron diffraction data. D.B. analysed the INS and IXS data, and performed spin-wave and phonon simulations. R.R. and H.Z. synthesized the samples. D.B. and O.D. wrote the manuscript and all authors commented on it. O.D. supervised the project.

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Correspondence to Dipanshu Bansal or Olivier Delaire.

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Supplementary Information

Supplementary Figs. 1–25 and Discussion.

Source data

Source Data Fig. 1

Numerical data for cartesian plots in Fig. 1.

Source Data Fig. 2

Numerical data for cartesian plots in Fig. 2.

Source Data Fig. 3

Numerical data for cartesian plots in Fig. 3.

Source Data Fig. 4

Numerical data for cartesian plots in Fig. 4.

Source Data Fig. 5

Numerical data for cartesian plots in Fig. 5.

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

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