Spin dynamics and orbital-antiphase pairing symmetry in iron-based superconductors

Journal name:
Nature Physics
Year published:
Published online

The symmetry of the wavefunction describing the Cooper pairs is one of the most fundamental quantities in a superconductor, but for iron-based superconductors it has proved to be problematic to determine, owing to their complex multi-band nature1, 2, 3. Here we use a first-principles many-body method, including the two-particle vertex function, to study the spin dynamics and the superconducting pairing symmetry of a large number of iron-based compounds. Our results show that these high-temperature superconductors have both dispersive high-energy and strong low-energy commensurate or nearly commensurate spin excitations, which play a dominant role in Cooper pairing. We find three closely competing types of pairing symmetries, which take a very simple form in the space of active iron 3d orbitals, and differ only in the relative quantum mechanical phase of the xz, yz and xy orbital components of the Cooper pair wavefunction. The extensively discussed s+− symmetry appears when contributions from all orbitals have equal sign, whereas a novel orbital-antiphase s+− symmetry emerges when the xy orbital has an opposite sign to the xz and yz orbitals. This orbital-antiphase pairing symmetry agrees well with the angular variation of the superconducting gaps in LiFeAs (refs 4, 5).

At a glance


  1. Dynamic spin structure factor S(q, [omega]) in iron pnictides, chalcogenides and MgFeGe.
    Figure 1: Dynamic spin structure factor S(q, ω) in iron pnictides, chalcogenides and MgFeGe.

    S(q, ω) is plotted along the high-symmetry path (H, K, L = 1) in the first Brillouin zone of the single-iron unit cell. The intensity varies substantially across these compounds, hence the maximum value of the intensity was adjusted to emphasize the dispersion most clearly. The maximum value of the intensity in each compound is shown in the top-right corner. The colour coding corresponds to the theoretical calculations for (a) BaFe2P2 (TCmax < 2K); (b) LiFeP (TC = 6 K); (c) LaFePO (TC = 7 K); (d) SrFe2As2 (TCmax = 37 K); (e) LaFeAsO (TCmax = 43 K); (f) BaFe2As2 (TCmax = 39 K); (g) LiFeAs (TC = 18 K); (h) FeSe (TCmax = 37 K); (i) MgFeGe (TCmax = 0 K); (j) FeTe (TCmax = 0 K); (k) BaFe1.7Ni0.3As2 (TC < 2 K); (l) BaFe1.9Ni0.1As2 (TC = 20 K); (m) Ba0.6K0.4Fe2As2 (TC = 39 K); (n) KFe2As2 (TC = 3.5 K); (o) KFe2Se2. The experimental data are shown as black dots with error bars in f,g,l and m, digitized from refs 10, 11, 12, 13. r.l.u., reciprocal lattice units.

  2. Dynamic spin structure factor S(q, [omega]) in iron pnictides, chalcogenides and MgFeGe.
    Figure 2: Dynamic spin structure factor S(q, ω) in iron pnictides, chalcogenides and MgFeGe.

    S(q, ω) is plotted in the 2D plane (H, K) at constant ω = 5 meV for the same materials as in Fig. 1. The maximum intensity scale for each compound is marked as a number in the top-right corner of each subplot. The momentum dependence in the kz direction is weak in most compounds, hence we show only the cut at L = 1. In MgFeGe and phosphorus compounds, we instead show the L = 0 plane to emphasize the tendency towards ferromagnetism in these compounds. r.l.u., reciprocal lattice units.

  3. Fermi surfaces, pairing symmetries and the basic building blocks.
    Figure 3: Fermi surfaces, pairing symmetries and the basic building blocks.

    Top row: the original and unfolded two-dimensional Fermi surfaces in the Γ plane for the representative compound LaFeAsO in the paramagnetic state, shown in the first Brillouin zone of the single-iron unit cell. On the top right, the Fermi surfaces are further decomposed into the dominating Fe-t2g (xz,yz, and xy) characters. The next three rows, from top to bottom, show respectively the conventional s+−, the orbital-antiphase s+− and the d-wave pairing symmetries of the superconducting order parameter. The left column shows the Fermi surfaces, coloured with the strength of the diagonal order parameter in the band basis (i is the band index), while the right columns decompose the order parameter in orbital space—that is, (α runs over Fe-t2g orbitals: xz,yz, and xy). Note that the order parameter is not constant on each of the Fermi surfaces in the conventional s+− state. Whereas the diagonal order parameter in the band basis has nodes on the electron Fermi surfaces in the orbital-antiphase s+− state, the spectral superconducting gap can be nodeless as a result of interband pairing (see text and Fig. 4).

  4. Superconducting pairing symmetry and gap function anisotropy in LiFeAs.
    Figure 4: Superconducting pairing symmetry and gap function anisotropy in LiFeAs.

    a,b, The superconducting gaps on the Fermi surfaces are obtained by diagonalizing the Bogoliubov quasiparticle Hamiltonian, with the orbital-antiphase s+− (a) and conventional s+− pairing symmetries (b). The red and blue colours denote the different signs of the superconducting gaps. cf, Angular dependences of the superconducting gaps for the orbital-antiphase s+− (c,d) and conventional s+− (e,f) states on the three-hole Fermi surfaces (c,e) and the two electron Fermi surfaces (d,f), respectively. The solid lines correspond to theoretical results and the symbols denote the experimental measurements from ref. 4. Note that we rescaled the whole gap function such that the computed superconducting gap on the inner hole pocket matches the experimental value4.


  1. Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 15891652 (2011).
  2. Hirschfeld, P. J., Korshunov, M. M. & Mazin, I. I. Gap symmetry and structure of Fe-based superconductors. Rep. Prog. Phys. 74, 124508 (2011).
  3. Dai, P., Hu, J. & Dagotto, E. Magnetism and its microscopic origin in iron-based high-temperature superconductors. Nature Phys. 8, 709718 (2012).
  4. Borisenko, S. V. et al. One-sign order parameter in iron based superconductor. Symmetry 4, 251264 (2012).
  5. Umezawa, K. et al. Unconventional anisotropic s-wave superconducting gaps of the LiFeAs iron-pnictide superconductor. Phys. Rev. Lett. 108, 037002 (2012).
  6. Mazin, I. I., Singh, D. J., Johannes, M. D. & Du, M. H. Unconventional superconductivity with a sign reversal in the order parameter of LaFeAsO1−xFx. Phys. Rev. Lett. 101, 057003 (2008).
  7. Haule, K. & Kotliar, G. Coherence–incoherence crossover in the normal state of iron-oxypnictides and importance of the Hund’s rule coupling. New J. Phys. 11, 025021 (2009).
  8. Yin, Z. P., Haule, K. & Kotliar, G. Magnetism and charge dynamics in iron pnictides. Nature Phys. 7, 294297 (2011).
  9. Yin, Z. P., Haule, K. & Kotliar, G. Kinetic frustration and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides. Nature Mater. 10, 932935 (2011).
  10. Harriger, L. W. et al. Nematic spin fluid in the tetragonal phase of BaFe2As2. Phys. Rev. B 84, 054544 (2011).
  11. Wang, M. et al. Antiferromagnetic spin excitations in single crystals of nonsuperconducting Li1−xFeAs. Phys. Rev. B 83, 220515(R) (2011).
  12. Liu, M. S. et al. Nature of magnetic excitations in superconducting BaFe1.9Ni0.1As2. Nature Phys. 8, 376381 (2012).
  13. Wang, M. et al. Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides. Nature Commun. 4, 2874 (2013).
  14. Yin, Z. P., Haule, K. & Kotliar, G. Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations. Phys. Rev. B 86, 195141 (2012).
  15. Margadonna, S. et al. Pressure evolution of the low-temperature crystal structure and bonding of the superconductor FeSe (Tc = 37 K). Phys. Rev. B 80, 064506 (2009).
  16. Ikeda, H., Arita, R. & Kunes̆, J. Doping dependence of spin fluctuations and electron correlations in iron pnictides. Phys. Rev. B 82, 024508 (2010).
  17. Rhee, H. B. & Pickett, W. E. Contrast of LiFeAs with isostructural, isoelectronic, and non-superconducting MgFeGe. J. Phys. Soc. Jpn 82, 034714 (2013).
  18. Jeschke, H. O., Mazin, I. I. & Valenti, R. Why MgFeGe is not a superconductor. Phys. Rev. B 87, 241105(R) (2013).
  19. Bao, W. et al. Incommensurate magnetic order in the α-Fe(Te, Se) superconductor systems. Phys. Rev. Lett. 102, 247001 (2009).
  20. Scalapino, D. J. A common thread: The pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 13831417 (2012).
  21. Lee, C. H. et al. Incommensurate spin fluctuations in hole-overdoped superconductor KFe2As2. Phys. Rev. Lett. 106, 067003 (2011).
  22. Bao, W. et al. A novel large moment antiferromagnetic order in K0.8Fe1.6Se2 Superconductor. Chin. Phys. Lett. 28, 086104 (2011).
  23. Wang, Y. et al. Superconducting gap in LiFeAs from three-dimensional spin-fluctuation pairing calculations. Phys. Rev. B 88, 174516 (2013).
  24. Platt, C., Thomale, R. & Hanke, W. Superconducting state of the iron pnictide LiFeAs: A combined density-functional and functional-renormalization-group study. Phys. Rev. B 84, 235121 (2011).
  25. Khodas, M. & Chubukov, A. V. Interpocket pairing and gap symmetry in Fe-based superconductors with only electron pockets. Phys. Rev. Lett. 108, 247003 (2012).
  26. Zhang, P. et al. Observation of momentum-confined in-gap impurity state in Ba0.6K0.4Fe2As2: Evidence for anti-phase s± pairing. Phys. Rev. X 4, 031001 (2014).
  27. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865951 (2006).
  28. Park, H., Haule, K. & Kotliar, G. Magnetic excitation spectra in BaFe2As2: A two-particle approach within a combination of the density functional theory and the dynamical mean-field theory method. Phys. Rev. Lett. 107, 137007 (2011).
  29. Kutepov, A., Haule, K., Savrasov, S. Y. & Kotliar, G. Self consistent GW determination of the interaction strength: Application to the iron arsenide superconductors. Phys. Rev. B 82, 045105 (2010).
  30. De’ Medici, L., Giovannetti, G. & Capone, M. Selective Mott physics as a key to iron superconductors. Phys. Rev. Lett. 112, 177001 (2014).

Download references

Author information


  1. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

    • Z. P. Yin,
    • K. Haule &
    • G. Kotliar


Z.P.Y. carried out the calculations. K.H. developed the DMFT code. Z.P.Y., K.H. and G.K. analysed the results and wrote the paper. Z.P.Y. led the project.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (560KB)

    Supplementary Information

Additional data