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Cooperative elastic fluctuations provide tuning of the metal–insulator transition


Metal-to-insulator transitions1 driven by strong electronic correlations occur frequently in condensed matter systems, and are associated with remarkable collective phenomena in solids, including superconductivity and magnetism. Tuning and control of the transition holds the promise of low-power, ultrafast electronics2, but the relative roles of doping, chemistry, elastic strain and other applied fields have made systematic understanding of such transitions difficult. Here we show that existing data3,4,5 on the tuning of metal-to-insulator transitions in perovskite transition-metal oxides through ionic size effects provides evidence of large systematic effects on the phase transition owing to dynamical fluctuations of the elastic strain, which have usually been neglected6. We illustrate this using a simple yet quantitative statistical mechanical calculation in a model that incorporates cooperative lattice distortions coupled to the electronic degrees of freedom. We reproduce the observed dependence of the transition temperature on the cation radius in the well studied manganite7 and nickelate8 materials. Because elastic couplings are generally strong, we anticipate that these conclusions will generalize to all metal-to-insulator transitions that couple to a change in lattice symmetry.

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Fig. 1: Perovskite lattices.
Fig. 2: Lattice distortions and strain responses.
Fig. 3: Effective elastic energy.
Fig. 4: Comparison to experiments.

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

    Article  CAS  ADS  Google Scholar 

  2. Yang, Z., Ko, C. & Ramanathan, S. Oxide electronics utilizing ultrafast metal-insulator transitions. Annu. Rev. Mater. Res. 41, 337–367 (2011).

    Article  CAS  ADS  Google Scholar 

  3. Torrance, J. B., Lacorre, P., Nazzal, A. I., Ansaldo, E. J. & Niedermayer, Ch. Systematic study of insulator-metal transitions in perovskites RNiO3 (R = Pr, Nd, Sm, Eu) due to closing of charge-transfer gap. Phys. Rev. B 45, 8209–8212 (1992).

    Article  CAS  ADS  Google Scholar 

  4. Hwang, H. Y., Cheong, S.-W., Radaelli, P. G., Marezio, M. & Batlogg, B. Lattice effects on the magnetoresistance in doped LaMnO3. Phys. Rev. Lett. 75, 914–917 (1995).

    Article  CAS  ADS  Google Scholar 

  5. Rodriguez-Martinez, L. M. & Attfield, J. P. Cation disorder and size effects in magnetoresistive manganese oxide perovskites. Phys. Rev. B 54, R15622(R) (1996).

    Article  ADS  Google Scholar 

  6. Khomskii, D. I. Transition Metal Compounds (Cambridge University Press, 2014).

  7. Tokura, Y. Critical features of colossal magnetoresistive manganites. Rep. Prog. Phys. 69, 797–851 (2006).

    Article  CAS  ADS  Google Scholar 

  8. Catalano, S. et al. Rare-earth nickelates RNiO3: thin films and heterostructures. Rep. Prog. Phys. 81, 046501 (2018).

    Article  CAS  ADS  Google Scholar 

  9. Katsufuji, T., Taguchi, Y. & Tokura, Y. Transport and magnetic properties of a Mott–Hubbard system whose bandwidth and band filling are both controllable: R1−xCaxTiO3+y/2. Phys. Rev. B 56, 10145–10153 (1997).

    Article  CAS  ADS  Google Scholar 

  10. Sarma, D. D., Shanthi, N. & Mahadevan, P. Electronic structure and the metal-insulator transition in LnNiO3(Ln = La, Pr, Nd, Sm and Ho): bandstructure results. J. Cond. Matt. Phys. 6, 10467–10474 (1994).

    Article  CAS  ADS  Google Scholar 

  11. Radaelli, P. G. et al. Structural effects on the magnetic and transport properties of perovskite A1−xAxMnO3 (x = 0.25, 0.30). Phys. Rev. B 56, 8265–8276 (1997).

    Article  CAS  ADS  Google Scholar 

  12. Medarde, M., Lacorre, P., Conder, K., Fauth, F. & Furrer, A. Giant 16 O-18 O isotope effect on the metal-insulator transition of RNiO3 perovskites (R = rare earth). Phys. Rev. Lett. 80, 2397–2400 (1998).

    Article  CAS  ADS  Google Scholar 

  13. Varignon, J., Grisolia, M. N., Íñiguez, J., Barthélémy, A. & Bibes, M. Complete phase diagram of rare-earth nickelates from first-principles. npj Quant. Mater. 2, 21 (2017).

    Google Scholar 

  14. Fujimori, A. Electronic structure of metallic oxides: band-gap closure and valence control. J. Phys. Chem. Solids 53, 1595–1602 (1992).

    Article  CAS  ADS  Google Scholar 

  15. Pavarini, E., Yamasaki, A., Nuss, J. & Andersen, O. K. How chemistry controls electron localization in 3d 1 perovskites: a Wannier-function study. New J. Phys. 7, 188 (2005).

    Article  ADS  Google Scholar 

  16. Han, Q. & Millis, A. Lattice energetics and correlation-driven metal-insulator transitions: the case of Ca2RuO4. Phys. Rev. Lett. 121, 067601 (2018).

    Article  CAS  ADS  Google Scholar 

  17. Rondinelli, J. M., May, S. J. & Freeland, J. W. Control of octahedral connectivity in perovskite oxide heterostructures: an emerging route to multifunctional materials discovery. MRS Bull. 37, 261–270 (2012).

    Article  CAS  Google Scholar 

  18. Millis, A. J., Littlewood, P. B. & Shraiman, B. I. Double exchange alone does not explain the resistivity of La1−xSrxMnO3. Phys. Rev. Lett. 74, 5144–5147 (1995).

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Kartha, S., Krumhansl, J. A., Sethna, J. P. & Wickham, L. K. Disorder-driven pretransitional tweed pattern in martensitic transformations. Phys. Rev. B 52, 803 (1995).

    Article  CAS  ADS  Google Scholar 

  21. Ahn, K. H., Lookman, T. & Bishop, A. R. Strain-induced metal-insulator phase coexistance in perovskite manganites. Nature 428, 401–404 (2004).

    Article  CAS  ADS  Google Scholar 

  22. Ahn, K. H., Seman, T. F., Lookman, T. & Bishop, A. R. Role of complex energy landscapes and strains in multiscale inhomogeneities in perovskite manganites. Phys. Rev. B 88, 144415 (2013).

    Article  ADS  Google Scholar 

  23. Millis, A. J. Cooperative Jahn–Teller effect and electron-phonon coupling in La1−xAxMnO3. Phys. Rev. B 53, 8434–8441 (1996)

    Article  CAS  ADS  Google Scholar 

  24. Jaramillo, R. et al. Origins of bad-metal conductivity and the insulator–metal transition in the rare-earth nickelates. Nat. Phys. 10, 304–307 (2014).

    Article  CAS  Google Scholar 

  25. Attfield, J. P., Kharlanov, A. L. & McAllister, J. A. Cation effects in doped La2CuO4 superconductors. Nature 394, 157–159 (1998).

    Article  CAS  ADS  Google Scholar 

  26. Balachandran, P. V., Broderick, S. R. & Rajan, K. Identifying the inorganic gene for high-temperature piezoelectric perovskites through statistical learning. Proc. R. Soc. A 467, 2271–2290 (2011).

    Article  CAS  ADS  Google Scholar 

  27. Zadik, R. H. et al. Optimized unconventional superconductivity in a molecular Jahn–Teller metal. Sci. Adv. 1, e1500059 (2015).

    Article  ADS  Google Scholar 

  28. Obradors, X. et al. Pressure dependence of the metal-insulator transition in the charge-transfer oxides RNiO3 (R = Pr, Nd, Nd0.7La0.3). Phys. Rev. B 47, 12353–12356 (1993).

    Article  CAS  ADS  Google Scholar 

  29. Fontcuberta, J., Laukhin, V. & Obradors, X. Local disorder effects on the pressure dependence of the metal-insulator transition in manganese perovskites. Appl. Phys. Lett. 72, 2607–2609 (1998).

    Article  CAS  ADS  Google Scholar 

  30. Liu, J. et al. Heterointerface engineered electronic and magnetic phases of NdNiO3 thin films. Nat. Commun. 4, 2714 (2013).

    Article  ADS  Google Scholar 

  31. Guzmán-Verri, G. G., Littlewood, P. B. & Varma, C. M. Paraelectric and ferroelectric states in a model for relaxor ferroelectrics. Phys. Rev. B 88, 134106 (2013).

    Article  ADS  Google Scholar 

  32. Zaghrioui, M., Bulou, A., Lacorre, P. & Laffez, P. Electron diffraction and Raman scattering evidence of a symmetry breaking at the metal-insulator transition of NdNiO3. Phys. Rev. B 64, 081102 (2001).

    Article  ADS  Google Scholar 

  33. Martín-Carrón, L., de Andrés, A., Martínez-Lope, M. J., Casais, M. T. & Alonso, J. A. Raman phonons as a probe of disorder, fluctuations, and local structure in doped and undoped orthorhombic and rhombohedral manganites. Phys. Rev. B 66, 174303 (2002).

    Article  ADS  Google Scholar 

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We acknowledge discussions with G. Lonzarich, H. Park and F. Ballar-Trigueros. Work at Argonne National Laboratory is supported by the US Department of Energy, Materials Science Division, Office of Basic Energy Sciences under contract number DE-AC02-06CH11357. G.G.G.-V. acknowledges support from the Vice-rectory for Research (project number 816-B7-601), and the Office of International Affairs at the University of Costa Rica, the Royal Society International Exchanges programme (grant number IES\R3\170025), Churchill College (University of Cambridge). G.G.G.-V. thanks the Department of Materials Science and Metallurgy and the Cavendish Laboratory at the University of Cambridge (where part of this work was done) for hospitality. R.T.B. acknowledges support from the Yale Prize Postdoctoral Fellowship and Homerton College (University of Cambridge).

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P.B.L. conceived the study. G.G.G.-V. and R.T.B. performed the calculations. All authors constructed the model, wrote the manuscript, discussed the results and implications at all stages.

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Correspondence to G. G. Guzmán-Verri or P. B. Littlewood.

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R.T.B. is currently an editor at Nature Communications.

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Peer review information Nature thanks Mona Berciu, Paolo Radaelli and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended Data Table 1 Model parameters

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Supplementary information

This file contains Supplementary Notes 1–3, including Supplementary Figures 1, 2 and Supplementary References.

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Guzmán-Verri, G.G., Brierley, R.T. & Littlewood, P.B. Cooperative elastic fluctuations provide tuning of the metal–insulator transition. Nature 576, 429–432 (2019).

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