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Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2

Abstract

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc (ref. 1). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. 2), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction3. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations3, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity6. Indeed, UTe2, which has a Tc ≈ 1.6 K (refs. 7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability7,8,9,10,11,12,13,14, although it also has antiferromagnetic (AF) spin fluctuations15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled to a sharp magnetic excitation, termed resonance17,18,19,20,21,22,23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability17,18,19,20,21,22,23, its observation in UTe2 suggests that AF spin fluctuations may also induce spin-triplet pairing24 or that electron pairing in UTe2 has a spin-singlet component.

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Fig. 1: Crystal structure, heat capacity and a summary of INS results.
Fig. 2: The wavevector, energy and temperature dependence of the scattering function S(Q, E) in the [H, K, O] plane.
Fig. 3: The wavevector and energy dependence of the scattering below and above Tc.
Fig. 4: The wavevector, energy and temperature dependence of the scattering at Brillouin zone boundary points.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  2. Scalapino, D. J. A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383–1417 (2012).

    Article  ADS  CAS  Google Scholar 

  3. Mackenzie, A. P. & Maeno, Y. The superconductivity of Sr2RuO2 and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003).

    Article  ADS  CAS  Google Scholar 

  4. Sato, M. & Ando, Y. Topological superconductors: a review. Rep. Prog. Phys. 80, 076501 (2017).

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  5. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Usp. 44, 131–136 (2001).

    Article  ADS  Google Scholar 

  6. Aoki, D., Ishida, K. & Flouquet, J. Review of U-based ferromagnetic superconductors: comparison between UGe2, URhGe, and UCoGe. J. Phys. Soc. Jpn. 88, 022001 (2019).

    Article  ADS  Google Scholar 

  7. Ran, S. et al. Nearly ferromagnetic spin-triplet superconductivity. Science 365, 684–687 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Aoki, D. et al. Unconventional superconductivity in heavy fermion UTe2. J. Phys. Soc. Jpn. 88, 043702 (2019).

    Article  ADS  Google Scholar 

  9. Ran, S. et al. Extreme magnetic field-boosted superconductivity. Nat. Phys. 15, 1250–1254 (2019).

    Article  CAS  Google Scholar 

  10. Knebel, G. et al. Field-reentrant superconductivity close to a metamagnetic transition in the heavy-fermion superconductor UTe2. J. Phys. Soc. Jpn. 88, 063707 (2019).

    Article  ADS  Google Scholar 

  11. Sundar, S. et al. Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor UTe2. Phys. Rev. B 100, 140502 (2019).

    Article  ADS  CAS  Google Scholar 

  12. Jiao, L. et al. Chiral superconductivity in heavy-fermion metal UTe2. Nature 579, 523–527 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Nakamine, G. et al. Anisotropic response of spin susceptibility in the superconducting state of UTe2 probed with 125Te–NMR measurement. Phys. Rev. B 103, L100503 (2021).

    Article  ADS  CAS  Google Scholar 

  14. Hayes, I. M. et al. Multicomponent superconducting order parameter in UTe2. Science 373, 797–801 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Thomas, S. M. et al. Evidence for a pressure-induced antiferromagnetic quantum critical point in intermediate-valence UTe2. Sci. Adv. 6, eabc8709 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  16. Duan, C. et al. Incommensurate spin fluctuations in the spin-triplet superconductor candidate UTe2. Phys. Rev. Lett. 125, 237003 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Rossat-Mignod, J. et al. Neutron scattering study of the YBa2Cu3O6+x system. Physica C 185–189, 86–92 (1991).

    Article  ADS  Google Scholar 

  18. Wilson, S. D. et al. Resonance in the electron-doped high-transition-temperature superconductor Pr0.88LaCe0.12CuO4−δ. Nature 442, 59–62 (2006).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Dai, P. Antiferromagnetic order and spin dynamics in iron-based superconductors. Rev. Mod. Phys. 87, 855–896 (2015).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Sato, N. K. et al. Strong coupling between local moments and superconducting ‘heavy’ electrons in UPd2Al3. Nature 410, 340–343 (2001).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Bernhoeft, N. Superconductor order parameter symmetry in UPd2Al3. Eur. Phys. J. B 13, 685–694 (2000).

    Article  ADS  CAS  Google Scholar 

  22. Stock, C., Broholm, C., Hudis, J., Kang, H. J. & Petrovic, C. Spin resonance in the d-wave superconductor CeCoIn5. Phys. Rev. Lett. 100, 087001 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Stockert, O. et al. Magnetically driven superconductivity in CeCu2Si2. Nat. Phys. 7, 119–124 (2011).

    Article  CAS  Google Scholar 

  24. Kuwabara, T. & Ogata, M. Spin-triplet superconductivity due to antiferromagnetic spin-fluctuation in Sr2RuO4. Phys. Rev. Lett. 85, 4586–4589 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Eschrig, M. The effect of collective spin-1 excitations on electronic spectra in high-Tc superconductors. Adv. Phys. 55, 47–183 (2006).

    Article  ADS  CAS  Google Scholar 

  26. Yu, G., Li, Y., Motoyama, E. M. & Greven, M. A universal relationship between magnetic resonance and superconducting gap in unconventional superconductors. Nat. Phys. 5, 873–875 (2009).

    Article  CAS  Google Scholar 

  27. Huxley, A. D., Raymond, S. & Ressouche, E. Magnetic excitations in the ferromagentic superconductor UGe2. Phys. Rev. Lett. 91, 207201 (2003).

    Article  ADS  CAS  PubMed  Google Scholar 

  28. Stock, C. et al. Anisotropic critical magnetic fluctuations in the ferromagnetic superconductor UCoGe. Phys. Rev. Lett. 107, 187202 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Kunkemöller, S. et al. Absence of a large superconductivity-induced gap in magnetic fluctuations of Sr2RuO4. Phys. Rev. Lett. 118, 147002 (2017).

    Article  ADS  PubMed  Google Scholar 

  30. Steffens, P. et al. Spin fluctuations in Sr2RuO4 from polarized neutron scattering: implications for superconductivity. Phys. Rev. Lett. 122, 047004 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Pustogow, A. et al. Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance. Nature 574, 72–75 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Joynt, R. & Taillefer, L. The superconducting phases of UPt3. Rev. Mod. Phys. 74, 235–294 (2002).

    Article  ADS  CAS  Google Scholar 

  33. Aeppli, G. et al. Magnetic order and fluctuations in superconducting UPt3. Phys. Rev. Lett. 60, 615–618 (1988).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Gannon, W. J. et al. Spin susceptibility of the topological superconductor UPt3 from polarized neutron diffraction. Phys. Rev. B 96, 041111(R) (2017).

    Article  ADS  Google Scholar 

  35. Song, Y. et al. Nature of the spin resonance mode in CeCoIn5. Commun. Phys. 3, 98 (2020).

    Article  CAS  Google Scholar 

  36. Zwicknagl, G. & Fulde, P. The dual nature of 5f electrons and the origin of heavy fermions in U compounds. J. Phys. Condens. Matter 15, S1911–S1916 (2003).

    Article  ADS  CAS  Google Scholar 

  37. Fujimori, S. et al. Core-level photoelectron spectroscopy study of UTe2. J. Phys. Soc. Jpn. 90, 015002 (2021).

    Article  ADS  Google Scholar 

  38. Ishizuka, J. & Yanase, Y. Periodic Anderson model for magnetism and superconductivity in UTe2. Phys. Rev. B 103, 094504 (2021).

    Article  ADS  CAS  Google Scholar 

  39. Wang, M. et al. Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides. Nat. Commun. 4, 2874 (2013).

    Article  ADS  PubMed  Google Scholar 

  40. Miao, L. et al. Low energy band structure and symmetries of UTe2 from angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 124, 076401 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Kim, J. S., Tam, G. N. & Stewart, G. R. Universal scaling law for the condensation energy across a broad range of superconductor classes. Phys. Rev. B 92, 224509 (2015).

    Article  ADS  Google Scholar 

  42. Ehlers, G., Podlesnyak, A. A., Niedziela, J. L., Iverson, E. B. & Sokol, P. E. The new Cold Neutron Chopper Spectrometer at the Spallation Neutron Source: design and performance, Rev. Sci. Instrum. 82, 085108 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Ewings, R. A. et al. Horace: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Meth. Phys. Res. A 834, 132–142 (2016).

    Article  ADS  CAS  Google Scholar 

  44. Nica, E. N. & Si, Q. Multiorbital singlet pairing and d + d superconductivity. npj Quantum Mater. 6, 3 (2021).

    Article  ADS  CAS  Google Scholar 

  45. Nica, E. M., Yu, R. & Si, Q. Orbital-selective pairing and superconductivity in iron selenides. npj Quantum Mater. 2, 24 (2017).

    Article  ADS  Google Scholar 

  46. Pang, G. M. et al. Fully gapped d-wave superconductivity in CeCu2Si2. Proc. Natl Acad. Sci. USA 115, 5343–5347 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  47. Amorese, A. et al. Possible multiorbital ground state in CeCu2Si2. Phys. Rev. B 102, 245146 (2020).

    Article  ADS  CAS  Google Scholar 

  48. Shick, A. B. & Pickett, W. E. Spin–orbit coupling induced degeneracy in the anisotropic unconventional superconductor UTe2. Phys. Rev. B 100, 134502 (2019).

    Article  ADS  CAS  Google Scholar 

  49. Shick, A. B., Fujimori, S. & Pickett, W. E. UTe2: a nearly insulating half-filled \(j=\frac{5}{2}5{f}^{3}\) heavy-fermion metal. Phys. Rev. B 103, 125136 (2021).

    Article  ADS  CAS  Google Scholar 

  50. Koster, G. F. et al. The Properties of the Thirty-Two Point Groups (MIT Press, 1963).

  51. Pixley, J. H., Deng, L., Ingersent, K. & Si, Q. Pairing correlations near a Kondo-destruction quantum critical point. Phys. Rev. B 91, 201109(R) (2015).

    Article  ADS  Google Scholar 

  52. Nguyen, D. H. et al. Superconductivity in an extreme strange metal. Nat. Commun. 12, 4341 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

P.D. thanks D. Natelson, W. P. Halperin, N. Butch and J. Paglione for discussions. E.M.N. and Q.S. acknowledge discussions with H. Hu, S. Paschen and J.-X. Zhu. The INS work at Rice is supported by the US DOE, BES under grant no. DE-SC0012311 (P.D.). Part of the material characterization efforts at Rice is supported by the Robert A. Welch Foundation grant nos C-1839 (P.D.). Work performed by R.E.B. at the National High Magnetic Field Laboratory was supported by National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida. Synthesis of crystalline materials and measurements by R.E.B. were supported by the Center for Actinide Science and Technology (CAST), an Energy Frontier Research Center (EFRC) funded by the US DOE, BES, under grant no. DE-SC0016568. Research at UC San Diego was supported by the US DOE, BES under grant no. DEFG02-04-ER46105 (single-crystal growth) and US NSF under grant no. DMR-1810310 (characterization of physical properties). The theory work at Rice has primarily been supported by the US DOE, BES under award no. DE-SC0018197, with travel support provided by the Robert A. Welch Foundation grant no. C-1411. Q.S. acknowledges the hospitality of the Aspen Center for Physics, which is supported by NSF grant no. PHY-1607611. E.M.N. was supported by an ASU startup grant. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by ORNL.

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Authors and Affiliations

Authors

Contributions

P.D. and M.B.M. conceived the project. R.E.B. grew the single crystals and made specific-heat measurements on the crystals. The single crystals of UTe2 were aligned using Laue X-ray diffraction by C.D., Y.D., C.M. and A.J.B. and characterized by means of powder X-ray diffraction by C.M., A.J.B. and Y.D. at UCSD. The INS experiments were carried out by A.P. in remote discussion with C.D. and P.D. The data analysis was carried out by C.D. and P.D. E.M.N. and Q.S. contributed to the theoretical idea that AF spin fluctuations may facilitate spin-triplet superconductivity. The paper was written by P.D., C.D., R.E.B., E.M.N and Q.S., and all coauthors made comments on the paper.

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Correspondence to Pengcheng Dai.

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Extended data figures and tables

Extended Data Fig. 1 Pictures of the UTe2 single crystals used in the INS experiment.

a, A typical piece of UTe2 single crystal of 10 mm by 3 mm by 3 mm in size. The direction of the longest edge is the intersection of [1, 1, 0] plane and [0, 0, 1] plane. b, c, 27 pieces of UTe2 single crystals co-aligned on two oxygen-free Cu sample plates. The total mass is 0.9 grams.

Extended Data Fig. 2 Summary of temperature-dependent heat capacity C/T for single-crystal specimens of UTe2.

a, Comparison of C/T versus T for two representative crystals of UTe2. One crystal shows a single superconducting phase transition whereas the other shows two features. Several other crystals were measured, which all show similar behavior. b, The electronic component of the heat capacity Ce/T, which was obtained by subtracting the low temperature phonon heat capacity βT2, which was obtained by fitting the data for T > Tc using the expression C/T = γ + βT2. The normal state electronic coefficient of the heat capacity γ is indicated by the horizontal dotted blue line. An equal entropy construction is also indicated by dotted blue lines to determine Tc and the ideal size of the heat-capacity jump ΔC/Tc.

Extended Data Fig. 3 X-ray Laue pattern of the [0, 0, 1] plane of UTe2.

Pattern is shown for one of the samples used in the experiment.

Extended Data Fig. 4 Unsymmetrized raw data in the [H, K, 0] plane with Ei = 3.32 meV.

al, Constant-energy cuts of the unsymmetrized S(Q, E) with Ei = 3.32 meV at (a) 0.0 ± 0.1 meV and BT, (b) 0.0 ± 0.1 meV and 2 K, (c) 0.4 ± 0.1 meV and BT, (d) 0.4 ± 0.1 meV and 2 K, (e) 0.7 ± 0.1 meV and BT, (f) 0.7 ± 0.1 meV and 2 K, (g) 1.0 ± 0.1 meV and BT, (h) 1.0 ± 0.1 meV and 2 K, (i) 1.5 ± 0.1 meV and BT, (j) 1.5 ± 0.1 meV and 2 K, (k) 2.0 ± 0.1 meV and BT, (l) 2.0 ± 0.1meV and 2 K. The bin size is 0.035 r.l.u. along both H and K. The integration range is ±0.2 r.l.u. in L, and ±0.1 meV in E. The unit of the colour bars in Extended Data Figs. 4, 5, 6 is the same as that of Fig. 2b.

Extended Data Fig. 5 Unsymmetrized raw data in the [H, K, 0] plane with Ei = 12 meV.

ad, Constant energy cuts of the unsymmetrized S(Q, E) with Ei = 12 meV and BT at (a) 0.0 ± 0.5 meV, (b) 3.25 ± 0.25 meV, (c) 5.25 ± 0.25 meV, (d) 7.25 ± 0.25 meV. The bin size is 0.04 r.l.u. along both H and K. The integration range is ±0.2 r.l.u. in L, and ±0.25 meV in E. The rings of scattering in a are from the nuclear (1, 1, 1) and (2, 0, 0) Bragg peaks of the Cu sample holder.

Extended Data Fig. 6 Unsymmetrized raw data, EQ plots and one-dimensional energy cuts with Ei = 2.5 meV.

ad, Constant energy cuts of the unsymmetrized S(Q, E) with Ei = 2.5 meV at (a) 0.25 to 0.3 meV and BT, (b) 0.25 to 0.3 meV and 3.5 K, (c) 1.05 to 1.1 meV and BT, (d) 1.05 to 1.1 meV and 3.5 K. The bin size is 0.02 r.l.u. along H and 0.03 r.l.u. along K. The integration range is ±0.3 r.l.u. in L. e, f, EQ plots of the scattering function S(Q, E) with Ei = 2.5 meV at BT (e) and 3.5 K (f), respectively. The integration range is ±0.08 r.l.u. in H and ±0.3 r.l.u. in L, the bin size along K is 0.03 r.l.u., and the E step is 0.03 meV. g, One-dimensional cuts of the scattering function S(Q) with high temperature data (SHT(Q)) subtracted. The cuts are taken at Y1 along E taken at BT (blue), 0.4 K (red), 0.8 K (yellow), 1.2 K (purple), and 1.5 K (green) with Ei = 2.5 meV. The high-temperature data are taken at 3.5 K. At low energy the excitation at Y1 is not fully covered with this Ei, which causes the gap feature between 0.2 to 0.7 meV to be hard to observe in the subtracted one-dimensional data. Different temperature data in g are artificially shifted, with the dashed black line representing the base line for each temperature. The integration ranges in g are: ±0.08 r.l.u. in H, ±0.15 r.l.u. in K, and ±0.3 r.l.u. in L. The bin size in E is 0.04 meV.

Extended Data Fig. 7 Temperature dependence of the excitations at different Q positions.

a, b, One-dimensional cuts of S(E) with Ei = 3.32 meV at Bragg peak (1, −1, 0) along E at BT and 2 K, respectively. Incoherent background scattering integrated at Qbkg is plotted in green triangles. There are no FM spin fluctuation signals observed above the background. The broad peak around E = 0.7 meV is powder ring of scattering not associated with UTe2 (see Extended Data Fig. 4e, g). (c) One-dimensional cuts of S(E) with Ei = 3.32 meV at Y1 along E at 1.5, 1.8, and 2 K. There is no significant change in the quasielastic energy range for temperature close to and above Tc. d, e, One-dimensional cuts of S(E) with Ei = 3.32 meV (d) and 2.5 meV (e), respectively. The subtle increase of S(E) above Tc near 1.4 meV with Ei = 3.32 meV is just above one standard deviation, and is not observed with Ei = 2.5 meV. The integration ranges of the one-dimensional data in d, e are: ±0.1 r.l.u. in H, ±0.15 r.l.u. in K, and ±0.3 r.l.u. in L. The bin size in E is 0.04 meV.

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Duan, C., Baumbach, R.E., Podlesnyak, A. et al. Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2. Nature 600, 636–640 (2021). https://doi.org/10.1038/s41586-021-04151-5

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