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.

Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5

Abstract

Electronic nematic materials are characterized by a lowered symmetry of the electronic system compared to the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals1. Such nematic phases appear in the copper- and iron-based high-temperature superconductors2,3,4, and their role in establishing superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of fluctuating nematic character in a heavy-fermion superconductor, CeRhIn5 (ref. 5). We observe a magnetic-field-induced state in the vicinity of a field-tuned antiferromagnetic quantum critical point at Hc ≈ 50 tesla. This phase appears above an out-of-plane critical field H* ≈ 28 tesla and is characterized by a substantial in-plane resistivity anisotropy in the presence of a small in-plane field component. The in-plane symmetry breaking has little apparent connection to the underlying lattice, as evidenced by the small magnitude of the magnetostriction anomaly at H*. Furthermore, no anomalies appear in the magnetic torque, suggesting the absence of metamagnetism in this field range. The appearance of nematic behaviour in a prototypical heavy-fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be common among correlated materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: CeRhIn5 microstructured devices for measurements of in-plane resistivity anisotropy.
Figure 2: Broken tetragonal symmetry in the high-field state.
Figure 3: Temperature dependence of resistivity anisotropy.
Figure 4: Nematic character of CeRhIn5.

References

  1. 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)

    ADS  CAS  Article  Google Scholar 

  2. 2

    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)

    ADS  Article  CAS  PubMed  Google Scholar 

  3. 3

    Kasahara, S. et al. Electronic nematicity above the structural and superconducting transition in BaFe2(As1−xPx)2 . Nature 486, 382–385 (2012)

    ADS  CAS  PubMed  Article  Google Scholar 

  4. 4

    Fernandes, R. M. & Millis, A. J. Nematicity as a probe of superconducting pairing in iron-based superconductors. Phys. Rev. Lett. 111, 127001 (2013)

    ADS  PubMed  Article  CAS  Google Scholar 

  5. 5

    Hegger, H. et al. Pressure-induced superconductivity in quasi-2D CeRhIn5 . Phys. Rev. Lett. 84, 4986–4989 (2000)

    ADS  CAS  PubMed  Article  Google Scholar 

  6. 6

    Fisher, R. A. et al. Specific heat of CeRhIn5: pressure-driven evolution of the ground state from antiferromagnetism to superconductivity. Phys. Rev. B 65, 224509 (2002)

    ADS  Article  CAS  Google Scholar 

  7. 7

    Shishido, H., Settai, R., Harima, H. & Onuki, Y. A drastic change of the Fermi surface at a critical pressure in CeRhIn5: dHvA study under pressure. J. Phys. Soc. Jpn 74, 1103–1106 (2005)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Jiao, L. et al. Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5 . Proc. Natl Acad. Sci. USA 112, 673–678 (2015)

    ADS  CAS  PubMed  Article  Google Scholar 

  9. 9

    Moll, P. J. W. et al. Field-induced density wave in the heavy-fermion compound CeRhIn5 . Nat. Commun. 6, 6663 (2015)

    ADS  CAS  PubMed  Article  Google Scholar 

  10. 10

    Christianson, A., Lacerda, A., Hundley, M., Pagliuso, P. & Sarrao, J. Magnetotransport of CeRhIn5 . Phys. Rev. B 66, 054410 (2002)

    ADS  Article  CAS  Google Scholar 

  11. 11

    Park, T. et al. Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5 . Nature 440, 65–68 (2006)

    ADS  CAS  PubMed  Article  Google Scholar 

  12. 12

    Bao, W. et al. Incommensurate magnetic structure of CeRhIn5 . Phys. Rev. B 62, R14621–R14624 (2000)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Raymond, S. E., Knebel, G., Aoki, D. & Flouquet, J. Magnetic structure of CeRhIn5 under magnetic field. J. Phys. Condens. Matter 19, 242204 (2007)

    ADS  CAS  PubMed  Article  Google Scholar 

  14. 14

    Takeuchi, T., Inoue, T., Sugiyama, K. & Aoki, D. Magnetic and thermal properties of CeIrIn5 and CeRhIn5 . J. Phys. Soc. Jpn. 70, 877–883 (2001)

    ADS  CAS  Article  Google Scholar 

  15. 15

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

    ADS  CAS  PubMed  Article  Google Scholar 

  16. 16

    Pan, W. et al. Strongly anisotropic electronic transport at Landau level filling factor ν=9/2 and ν=5/2 under a tilted magnetic field. Phys. Rev. Lett. 83, 820–823 (1999)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Eisenstein, J. P. Two-dimensional electrons in excited Landau levels: evidence for new collective states. Solid State Commun. 117, 123–131 (2001)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Lester, C. et al. Field-tunable spin-density-wave phases in Sr3Ru2O7 . Nat. Mater. 14, 373–378 (2015)

    ADS  CAS  PubMed  Article  Google Scholar 

  19. 19

    Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014)

    CAS  Article  Google Scholar 

  20. 20

    Gegenwart, P., Weickert, F., Perry, R. S. & Maeno, Y. Low-temperature magnetostriction of Sr3Ru2O7 . Physica B 378–380, 117–118 (2006)

    ADS  Article  CAS  Google Scholar 

  21. 21

    Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Rost, A. W. et al. Thermodynamics of phase formation in the quantum critical metal Sr3Ru2O7 . Proc. Natl Acad. Sci. USA 108, 16549–16553 (2011)

    ADS  CAS  PubMed  Article  Google Scholar 

  23. 23

    Capriotti, L. & Sachdev, S. Low-temperature broken-symmetry phases of spiral antiferromagnets. Phys. Rev. Lett. 93, 257206 (2004)

    ADS  PubMed  Article  CAS  Google Scholar 

  24. 24

    Chandra, P., Coleman, P. & Larkin, A. I. Ising transition in frustrated Heisenberg models. Phys. Rev. Lett. 64, 88–91 (1990)

    ADS  CAS  PubMed  Article  Google Scholar 

  25. 25

    Das, P. et al. Magnitude of the magnetic exchange interaction in the heavy-fermion antiferromagnet CeRhIn5 . Phys. Rev. Lett. 113, 246403 (2014)

    ADS  PubMed  Article  CAS  Google Scholar 

  26. 26

    Bauer, E. D. et al. Antiferromagnetic quantum critical point in CeRhIn5−xSnx . Physica B 378–380, 142–143 (2006)

    ADS  Article  CAS  Google Scholar 

  27. 27

    Chu, J.-H., Kuo, H.-H., Analytis, J. G. & Fisher, I. R. Divergent nematic susceptibility in an iron arsenide superconductor. Science 337, 710–712 (2012)

    ADS  CAS  PubMed  Article  Google Scholar 

  28. 28

    Zhong, R., Winn, B. L., Gu, G., Reznik, D. & Tranquada, J. M. Evidence for a nematic phase in La1.75Sr0.25NiO4 . Phys. Rev. Lett. 118, 177601 (2017)

    ADS  PubMed  Article  Google Scholar 

  29. 29

    Park, T. et al. Textured superconducting phase in the heavy fermion CeRhIn5 . Phys. Rev. Lett. 108, 077003 (2012)

    ADS  PubMed  Article  CAS  Google Scholar 

  30. 30

    Park, T. & Thompson, J. D. Magnetism and superconductivity in strongly correlated CeRhIn5 . New J. Phys. 11, 055062 (2009)

    ADS  Article  CAS  Google Scholar 

  31. 31

    Park, T. et al. Isotropic quantum scattering and unconventional superconductivity. Nature 456, 366–368 (2008)

    ADS  CAS  PubMed  Article  Google Scholar 

  32. 32

    Graf, D. et al. High magnetic field induced charge density wave state in a quasi-one-dimensional organic conductor. Phys. Rev. Lett. 93, 076406 (2004)

    ADS  CAS  PubMed  Article  Google Scholar 

  33. 33

    Rotter, M., Pangerl, M., Tegel, M. & Johrendt, D. Superconductivity and crystal structures of (Ba(1−x)Kx)Fe2As2 (x=0–1). Angew. Chem. Int. Ed. 47, 7949–7952 (2008)

    CAS  Article  Google Scholar 

  34. 34

    Pomeranchuk, I. I. On the stability of a Fermi liquid. Sov. Phys. J. Exp. Theor. Phys. 35, 524–525 (1958); J. Exp. Theor. Phys. 8, 361–362 (1959) [transl.]

    Google Scholar 

  35. 35

    Fil, D. V. Piezoelectric mechanism for the orientation of stripe structures in two-dimensional electron systems. Low Temp. Phys. 26, 581–585 (2000)

    ADS  CAS  Article  Google Scholar 

  36. 36

    Gerber, S. et al. Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields. Science 350, 949–952 (2015)

    CAS  PubMed  Article  Google Scholar 

  37. 37

    Grüner, G. The dynamics of spin-density waves. Rev. Mod. Phys. 66, 1–24 (1994)

    ADS  Article  Google Scholar 

  38. 38

    Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 32, 11–25 (1988)

    Google Scholar 

  39. 39

    Coppersmith, S. N. & Littlewood, P. B. Pulse-duration memory effect and deformable charge-density waves. Phys. Rev. B 36, 311–317 (1987)

    ADS  CAS  Article  Google Scholar 

  40. 40

    Dumas, J. & Schlenker, C. Charge density wave transport in the blue bronzes K0.30MoO3 and Rb0.30MoO3: metastability, hysteresis and memory effects. Lect. Notes Phys. 217, 439–448 (1985)

    ADS  CAS  Article  Google Scholar 

  41. 41

    Gill, J. C. Thermally initiated phase-slip in the motion and relaxation of charge-density waves in niobium triselenide. J. Phys. C 19, 6589–6604 (1986)

    ADS  CAS  Article  Google Scholar 

  42. 42

    Daou, R. et al. High resolution magnetostriction measurements in pulsed magnetic fields using fiber Bragg gratings. Rev. Sci. Instrum. 81, 033909 (2010)

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  43. 43

    Jaime, M. et al. Magnetostriction and magnetic texture to 100.75 Tesla in frustrated SrCu2(BO3)2 . Proc. Natl Acad. Sci. USA 109, 12404–12407 (2012)

    ADS  CAS  Article  Google Scholar 

  44. 44

    Kim, J. W. et al. Successive magnetic-field-induced transitions and colossal magnetoelectric effect in Ni3TeO6 . Phys. Rev. Lett. 115, 137201 (2015)

    ADS  PubMed  Article  CAS  Google Scholar 

  45. 45

    Grachtrup, D. S. et al. Field induced Lifshitz transition in UPt2Si2: Fermi surface under extreme conditions. Phys. Rev. B 95, 134422 (2017)

    ADS  Article  Google Scholar 

  46. 46

    Cornelius, A. L., Pagliuso, P. G., Hundley, M. F. & Sarrao, J. L. Field-induced magnetic transitions in the quasi-two-dimensional heavy-fermion antiferromagnets. Phys. Rev. B 64, 144411 (2001)

    ADS  Article  CAS  Google Scholar 

  47. 47

    Shishido, H. et al. Fermi surface, magnetic and superconducting properties of LaRhIn5 and CeTIn5 (T: Co, Rh and Ir). J. Phys. Soc. Jpn 71, 162–173 (2002)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank A. Mackenzie, B. Batlogg, S. Kivelson, E. Fradkin, C. Geibel and J. Thompson for discussions. We also thank B. Zeng for supporting the torque measurements. L.B. is supported by DOE-BES through award DE-SC0002613. The project was supported by the Max Planck Society and funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — MO 3077/1-1. Work at Los Alamos National Laboratory was performed under the auspices of the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Work at the National High Magnetic Field Laboratory was supported by National Science Foundation Cooperative Agreement no. DMR-1157490, the State of Florida, and the US DOE. M.J. acknowledges support from the IMS Rapid Response program at LANL. M.K.C. was supported by funds from US DOE BES ‘Science at 100T’.

Author information

Affiliations

Authors

Contributions

P.J.W.M. and F.R. designed the experiment. P.J.W.M., K.R.S., T.H. and M.D.B. fabricated the microstructured devices. P.J.W.M., T.H., M.K.C., B.J.R., R.D.M. and F.F.B. performed the pulsed field experiments and P.J.W.M., K.R.S. and L.B. the dc-field experiments. E.D.B. and F.R. grew the crystals. M.J. performed the magnetostriction measurements and their analysis. All authors contributed to the manuscript.

Corresponding author

Correspondence to P. J. W. Moll.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

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

Extended data figures and tables

Extended Data Figure 1 Sketch of the focussed ion beam fabrication process.

a, Precutting of the lamella from the large single crystal. Red arrow in all panels shows the position of the focussed ion beam (FIB). b, Undercutting the lamella to disconnect it from the crystal for the ex situ transfer. c, Transfer of the lamella onto a silicon substrate and electric contacting with gold (Au). d, Final fine structuring into the shapes shown in Fig. 1.

Extended Data Figure 2 Quantum critical transport.

a, In-plane resistivity as a function of field H || [010] for different temperatures (labels on curves, in K). The transition into the AFM state is clearly visible as a kink in the curve moving to higher fields at lower temperatures. At the lowest temperatures, the signature turns into a step-like transition. b, Temperature dependence of in-plane resistivity at fixed field (see key: Hc, critical field) extracted from the data in a. Whereas the resistivity above and below Hc cannot be described by a simple power law, at Hc a slightly sublinear power law ρ ≈ T0.91 describes the measured resistivity over a temperature range up to 10 K.

Extended Data Figure 3 Angle dependence of the anisotropy.

Main panel, measurements of the field angle dependence of in-plane resistivity in a static field (35 T applied along the c direction to ensure the sample is in the high-field phase) and at fixed temperature (300 mK). The samples were rotated in the field towards 20° at which the maximum anisotropy occurs. Two different samples were used to probe this anisotropy. The triangular one shown in Fig. 1 probes the anisotropy developing along the [110], channel (dashed line; also shown in Fig. 2), while a second similar sample featuring resistance bars along [100], [010] probed the other orientation (solid line). The emergent anisotropy of the two devices with similar dimensions is remarkably similar. The field configuration during the rotation is sketched on the right. The top sketch indicates the rotation of the magnetic field towards one in-plane direction (red arrow) while the orthogonal in-plane direction defines the axis of rotation (blue). The same colour-code is used consistently in the main panel. The middle (bottom) sketch indicates the configuration for the concrete case of the [110], ([100], [010]) device. Owing to the off-axis field during the rotation, an in-plane field Bip emerges and its direction in the individual devices is indicated by the green arrow.

Extended Data Figure 4 Lattice response to temperature and magnetic field.

a, Measured zero field coefficient of thermal expansion α(T) of CeRhIn5 in 3He gas. The lambda-type anomaly at the second order AFM phase transition is evident (TN, Néel temperature). b, Magnetostriction ΔL/L(H) measured along the c direction in pulsed magnetic fields at 510 mK. The pulsed field measurement was performed on the same needle-like crystal of CeRhIn5 that is shown in the zero-field measurement in a. The high-field measurement was taken using the same experimental set-up as the temperature-dependent measurement. The crystal was immersed in liquid 3He with the magnetic field applied 11° off the c axis. These raw data show a typical smooth and roughly quadratic behaviour in the magnetic field. Both pulse upsweep (red) and downsweep (blue) overlap well and are barely distinguishable in the raw data. c, Same magnetostriction ΔL/L as in b but after subtraction of a smooth background. In the downsweep, a small but sharp feature appears at H ≈ 30 T that may indicate c-axis shrinkage as the sample transitions into the nematic phase.

PowerPoint slides

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ronning, F., Helm, T., Shirer, K. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017). https://doi.org/10.1038/nature23315

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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