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The transport–structural correspondence across the nematic phase transition probed by elasto X-ray diffraction

Nature Materials volume 20, pages 1519–1524 (2021)Cite this article

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Abstract

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and X-ray diffraction measurements with in-situ tunable strain (elasto X-ray diffraction) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of Ba(Fe0.96Co0.04)2As2. The ratio of transport to structural quantities is nearly temperature independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto X-ray diffraction is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of the mean-field description reveals the intertwined nature of nematicity.

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Fig. 1: Nematic-elastic-transport coupling.
Fig. 2: Shear modulus and elastoresistivity.
Fig. 3: Spontaneous resistivity anisotropy and orthorhombicity.
Fig. 4: Transport–structural ratio equivalence.

Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information. Raw X-ray data are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

  1. Fradkin, E., Kivelson, S. A., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).

    Article  CAS  Google Scholar 

  2. Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).

    Article  CAS  Google Scholar 

  3. Du, R. R. et al. Strongly anisotropic transport in higher two-dimensional Landau levels. Solid State Commun. 109, 389–394 (1999).

    Article  CAS  Google Scholar 

  4. Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7. Science 315, 214–217 (2007).

    Article  CAS  Google Scholar 

  5. Fernandes, R. M. et al. Effects of nematic fluctuations on the elastic properties of iron arsenide superconductors. Phys. Rev. Lett. 105, 157003 (2010).

    Article  CAS  Google Scholar 

  6. Chu, J.-H. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).

    Article  CAS  Google Scholar 

  7. Hinkov, V. et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45. Science 319, 597–600 (2008).

    Article  CAS  Google Scholar 

  8. Ando, Y., Segawa, K., Komiya, S. & Lavrov, A. N. Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002).

    Article  CAS  Google Scholar 

  9. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

    Article  CAS  Google Scholar 

  10. Shapiro, M. C., Hristov, A. T., Palmstrom, J. C., Chu, J. & Fisher, I. R. Measurement of the B1g and B2g components of the elastoresistivity tensor for tetragonal materials via transverse resistivity configurations. Rev. Sci. Instrum. 87, 063902 (2016).

    Article  CAS  Google Scholar 

  11. Ishida, S. et al. Anisotropy of the in-plane resistivity of underdoped Ba(Fe1–xCox)2As2 superconductors induced by impurity scattering in the antiferromagnetic orthorhombic phase. Phys. Rev. Lett. 110, 207001 (2013).

    Article  CAS  Google Scholar 

  12. Gastiasoro, M. N., Paul, I., Wang, Y., Hirschfeld, P. J. & Andersen, B. M. Emergent defect states as a source of resistivity anisotropy in the nematic phase of iron pnictides. Phys. Rev. Lett. 113, 127001 (2014).

    Article  CAS  Google Scholar 

  13. Fernandes, R. M., Abrahams, E. & Schmalian, J. Anisotropic in-plane resistivity in the nematic phase of the iron pnictides. Phys. Rev. Lett. 107, 217002 (2011).

    Article  CAS  Google Scholar 

  14. Kuo, H. H. & Fisher, I. R. Effect of disorder on the resistivity anisotropy near the electronic nematic phase transition in pure and electron-doped BaFe2As2. Phys. Rev. Lett. 112, 227001 (2014).

    Article  CAS  Google Scholar 

  15. Lederer, S., Schattner, Y., Berg, E. & Kivelson, S. A. Enhancement of superconductivity near a nematic quantum critical point. Phys. Rev. Lett. 114, 097001 (2015).

    Article  CAS  Google Scholar 

  16. Chen, X., Maiti, S., Fernandes, R. M. & Hirschfeld, P. J. Nematicity and superconductivity: competition versus cooperation. Phys. Rev. B 102, 184512 (2020).

    Article  CAS  Google Scholar 

  17. Kuo, H. H., Chu, J. H., Palmstrom, J. C., Kivelson, S. A. & Fisher, I. R. Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors. Science 352, 958–962 (2016).

    Article  CAS  Google Scholar 

  18. Yoshizawa, M. et al. Structural quantum criticality and superconductivity in iron-based superconductor Ba(Fe1–xCox)2As2. J. Phys. Soc. Jpn 81, 024604 (2012).

    Article  CAS  Google Scholar 

  19. Tanatar, M. A. et al. Uniaxial-strain mechanical detwinning of CaFe2As2 and BaFe2As2 crystals: optical and transport study. Phys. Rev. B 81, 184508 (2010).

    Article  CAS  Google Scholar 

  20. Nandi, S. et al. Anomalous suppression of the orthorhombic lattice distortion in superconducting Ba(Fe1–xCox)2As2 single crystals. Phys. Rev. Lett. 104, 057006 (2010).

    Article  CAS  Google Scholar 

  21. Kim, M. G. et al. Character of the structural and magnetic phase transitions in the parent and electron-doped BaFe2As2 compounds. Phys. Rev. B 83, 134522 (2011).

    Article  CAS  Google Scholar 

  22. Fujii, C. et al. Anisotropic Grüneisen parameter and diverse order parameter fluctuations in iron-based superconductor Ba(Fe1–xCox)2As2. J. Phys. Soc. Jpn 87, 074710 (2018).

    Article  Google Scholar 

  23. Hicks, C. W., Barber, M. E., Edkins, S. D., Brodsky, D. O. & Mackenzie, A. P. Piezoelectric-based apparatus for strain tuning. Rev. Sci. Instrum. 85, 065003 (2014).

    Article  CAS  Google Scholar 

  24. Böhmer, A. E. et al. Nematic susceptibility of hole-doped and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements. Phys. Rev. Lett. 112, 047001 (2014).

    Article  CAS  Google Scholar 

  25. Carpenter, M. et al. Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2. J. Phys. Condens. Matter 31, 155401 (2019).

    Article  CAS  Google Scholar 

  26. Palmstrom, J. C., Hristov, A. T., Kivelson, S. A., Chu, J. H. & Fisher, I. R. Critical divergence of the symmetric (A1g) nonlinear elastoresistance near the nematic transition in an iron-based superconductor. Phys. Rev. B 96, 205133 (2017).

    Article  Google Scholar 

  27. Analytis, J. G. et al. Quantum oscillations in the parent pnictide BaFe2As2: itinerant electrons in the reconstructed state. Phys. Rev. B 80, 064507 (2009).

    Article  CAS  Google Scholar 

  28. Shimojima, T. et al. Orbital-dependent modifications of electronic structure across the magnetostructural transition in BaFe2As2. Phys. Rev. Lett. 104, 057002 (2010).

    Article  CAS  Google Scholar 

  29. Nakajima, M. et al. Unprecedented anisotropic metallic state in undoped iron arsenide BaFe2As2 revealed by optical spectroscopy. Proc. Natl Acad. Sci. USA 108, 12238–12242 (2011).

    Article  CAS  Google Scholar 

  30. Watson, M. D. et al. Probing the reconstructed Fermi surface of antiferromagnetic BaFe2As2 in one domain. npj Quantum Mater. 4, 36 (2019).

    Article  CAS  Google Scholar 

  31. Tanatar, M. A. et al. Direct imaging of the structural domains in the iron pnictides AFe2As2 (A = Ca,Sr,Ba). Phys. Rev. B 79, 180508(R) (2009).

    Article  CAS  Google Scholar 

  32. Tanatar, M. A. et al. Origin of the resistivity anisotropy in the nematic phase of FeSe. Phys. Rev. Lett. 117, 127001 (2016).

    Article  CAS  Google Scholar 

  33. Liu, L. et al. In-plane electronic anisotropy in the antiferromagnetic orthorhombic phase of isovalent-substituted Ba(Fe1–xRux)2As2. Phys. Rev. B 92, 094503 (2015).

    Article  CAS  Google Scholar 

  34. Blomberg, E. C. et al. In-plane anisotropy of electrical resistivity in strain-detwinned SrFe2As2. Phys. Rev. B 83, 134505 (2011).

    Article  CAS  Google Scholar 

  35. Fisher, I. R., Degiorgi, L. & Shen, Z. X. In-plane electronic anisotropy of underdoped ‘122’ Fe-arsenide superconductors revealed by measurements of detwinned single crystals. Rep. Prog. Phys. 74, 124506 (2011).

    Article  CAS  Google Scholar 

  36. Paul, I. & Garst, M. Lattice effects on nematic quantum criticality in metals. Phys. Rev. Lett. 118, 227601 (2017).

    Article  CAS  Google Scholar 

  37. Ikeda, M. S. et al. Elastocaloric signature of nematic fluctuations. Preprint at https://arxiv.org/abs/2101.00080 (2020).

  38. Hong, X. et al. Evolution of the nematic susceptibility in LaFe1-xCoxAsO. Phys. Rev. Lett. 125, 067001 (2020).

    Article  CAS  Google Scholar 

  39. Hosoi, S. et al. Nematic quantum critical point without magnetism in FeSe1–xSx superconductors. Proc. Natl Acad. Sci. USA 113, 8139–8143 (2016).

    Article  CAS  Google Scholar 

  40. Breitkreiz, M., Brydon, P. M. R. & Timm, C. Resistive anisotropy due to spin-fluctuation scattering in the nematic phase of iron pnictides. Phys. Rev. B 90, 121104 (2014).

    Article  CAS  Google Scholar 

  41. Kissikov, T. et al. Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2. Nat. Commun. 9, 1058 (2018).

    Article  CAS  Google Scholar 

  42. Fernandes, R. M., Orth, P. P. & Schmalian, J. Intertwined vestigial order in quantum materials: nematicity and beyond. Annu. Rev. Condens. Matter Phys. 10, 133–154 (2019).

    Article  Google Scholar 

  43. Andrade, E. F. et al. Visualizing the nonlinear coupling between strain and electronic nematicity in the iron pnictides by elasto-scanning tunneling spectroscopy. Preprint at https://arxiv.org/abs/1812.05287 (2018).

  44. Bartlett, J. et al. Relationship between transport anisotropy and nematicity in FeSe. Phys. Rev. X 33, 021038 (2021).

    Google Scholar 

  45. Schmidt, J. et al. Nematicity in the superconducting mixed state of strain detwinned underdoped Ba(Fe1–xCox)2As2. Phys. Rev. B 99, 064515 (2019).

    Article  CAS  Google Scholar 

  46. Pfau, H. et al. Detailed band structure of twinned and detwinned BaFe2As2 studied with angle-resolved photoemission spectroscopy. Phys. Rev. B 99, 035118 (2019).

    Article  CAS  Google Scholar 

  47. Zheng, X. Y., Feng, R., Ellis, D. S. & Kim, Y. J. Bulk-sensitive imaging of twin domains in La2–xSrxCuO4 under uniaxial pressure. Appl. Phys. Lett. 113, 071906 (2018).

    Article  CAS  Google Scholar 

  48. Kim, H. H. et al. Uniaxial pressure control of competing orders in a high-temperature superconductor. Science 362, 1040–1044 (2018).

    Article  CAS  Google Scholar 

  49. Ikeda, M. S. et al. Symmetric and antisymmetric strain as continuous tuning parameters for electronic nematic order. Phys. Rev. B 98, 245133 (2018).

    Article  CAS  Google Scholar 

  50. Dhital, C. et al. Effect of uniaxial strain on the structural and magnetic phase transitions in BaFe2As2. Phys. Rev. Lett. 108, 087001 (2012).

    Article  CAS  Google Scholar 

  51. Lu, X. et al. Nematic spin correlations in the tetragonal state of uniaxial-strained BaFe2–xNixAs2. Science 345, 657–660 (2014).

    Article  CAS  Google Scholar 

  52. Malinowski, P. et al. Suppression of superconductivity by anisotropic strain near a nematic quantum critical point. Nat. Phys. https://doi.org/10.1038/s41567-020-0983-9 (2020).

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Acknowledgements

We thank C. Xu, J.-Y. Chen, R. Fernandes, A. V. Andreev and M. Ikeda for discussions. This work was mainly supported by National Science Foundation’s Materials Research Science and Engineering Center at the University of Washington (DMR-1719797) and the Air Force Office of Scientific Research under grant FA9550-17-1-0217 and grant FA9550-21-1-0068. J.-H.C. acknowledges the support of the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF6759 to J.-H.C.; the David and Lucile Packard Foundation; the Alfred P. Sloan Foundation; and the Clean Energy Institute funded by the state of Washington. J.L. acknowledges support from the National Science Foundation under grant no. DMR-1848269. This research used resources of the Advanced Photon Source, a US Department of Energy Office of Science User Facility operated for the Department of Energy Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. J.J.S. was partially supported by the US Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research programme, administered by the Oak Ridge Institute for Science and Education for the Department of Energy. Oak Ridge Institute for Science and Education is managed by Oak Ridge Associated Universities under contract no. DE-SC0014664.

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Authors and Affiliations

  1. Department of Physics, University of Washington, Seattle, WA, USA

    Joshua J. Sanchez, Paul Malinowski, Joshua Mutch & Jiun-Haw Chu

  2. Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA

    Jian Liu

  3. Advanced Photon Source, Argonne National Laboratories, Lemont, IL, USA

    J.-W. Kim & Philip J. Ryan

  4. School of Physical Sciences, Dublin City University, Dublin, Ireland

    Philip J. Ryan

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Contributions

J.M. grew the samples. J.J.S. and P.M. did the experiments. P.J.R., J.-W.K. and J.L. helped conceive and design the X-ray diffraction measurements at the Advanced Photon Source. J.J.S. analysed the data. J.-H.C. supervised the project. All authors contributed extensively to the interpretation of the data and the writing of the manuscript.

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Correspondence to Jiun-Haw Chu.

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Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–10 and Discussion.

Supplementary Video

X-ray diffraction data of detwinning process.

Source data

Source Data Fig. 1

The x–T phase diagram data.

Source Data Fig. 2

Lattice constant and resistivity data versus strain and orthorhombicity, and extracted shear modulus and elastoresistivity coefficients.

Source Data Fig. 3

X-ray diffraction images of in-line lattice constant across temperature and applied strain; and corresponding resistivity and domain population changes with detwinning, extracted spontaneous resistivity anisotropy and spontaneous orthorhombicity.

Source Data Fig. 4

Extracted spontaneous elastoresistivity proportionality ratios versus temperature; and shear modulus and elastoresistivity Curie–Weiss coefficient data versus doping.

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Sanchez, J.J., Malinowski, P., Mutch, J. et al. The transport–structural correspondence across the nematic phase transition probed by elasto X-ray diffraction. Nat. Mater. 20, 1519–1524 (2021). https://doi.org/10.1038/s41563-021-01082-4

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