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arxiv: 1907.08133 · v1 · pith:IRVQ5QM2new · submitted 2019-07-17 · ❄️ cond-mat.supr-con

Role of interactions in the energy of the spin resonance peak in Fe-based superconductors

Yu.N. Togushova , M.M. Korshunov This is my paper

Pith reviewed 2026-05-24 20:18 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords Fe-based superconductorsspin resonance peakHubbard interactionHund's exchangefive-orbital modelRPAsuperconducting gap
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0 comments X

The pith

Increasing Hubbard and Hund's interactions shifts the spin resonance peak to lower frequencies in the five-orbital model of Fe-based superconductors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies spin response in a five-orbital tight-binding model for iron-based superconductors treated in the random phase approximation. Two gap structures are examined: equal gaps on all bands, where the resonance sits below twice the large gap value, and unequal gaps, where it sits at the sum of the large and small gap values. In both cases, raising the on-site Hubbard repulsion and the Hund's exchange coupling moves the resonance energy downward.

Core claim

Within the five-orbital tight-binding model treated in the random phase approximation, the energy of the spin resonance peak in the superconducting state is found to decrease as the on-site Hubbard repulsion and the Hund's rule coupling are increased, for both equal and unequal superconducting gap structures across the bands.

What carries the argument

RPA spin susceptibility computed from the five-orbital model whose parameters are the Hubbard U and Hund's J couplings.

If this is right

  • For equal gaps the resonance lies below 2 times the large gap magnitude.
  • For unequal gaps the resonance lies at the sum of the large and small gap magnitudes.
  • Stronger interactions systematically lower the resonance frequency in both gap scenarios.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If real materials have stronger correlations than typical weak-coupling estimates, their measured resonance energies would be lower than those predicted without interaction renormalization.
  • Resonance energy measurements could be used to bound the effective values of U and J in iron-based compounds.

Load-bearing premise

The five-orbital tight-binding model plus RPA spin susceptibility calculation with the stated gap structures faithfully represents the low-energy physics of real Fe-based superconductors.

What would settle it

A numerical computation in the same five-orbital RPA framework in which raising U and J leaves the resonance energy unchanged or raises it.

Figures

Figures reproduced from arXiv: 1907.08133 by M.M. Korshunov, Yu.N. Togushova.

Figure 1
Figure 1. Figure 1: FIG. 1: Gaps at the Fermi surface for doping [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Physical spin susceptibility Im [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The same, as in Fig [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

We consider the spin response within the five-orbital model for iron-based superconductors and study two cases: equal and unequal gaps in different bands. In the first case, the spin resonance peak in the superconducting state appears below the characteristic energy scale determined by the gap magnitude, $2\Delta_L$. In the second case, the energy scale corresponds to the sum of smaller and larger gap magnitudes, $\Delta_L + \Delta_S$. Increasing the values of the Hubbard interaction and the Hund's exchange, we observe a shift of the spin resonance energy to lower frequencies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies the spin resonance in the superconducting state of Fe-based superconductors within a five-orbital tight-binding model treated in RPA. For equal gaps on all bands the resonance lies below 2Δ_L; for unequal gaps it lies at Δ_L + Δ_S. The central result is that raising the Hubbard U and Hund’s J moves the resonance peak to lower frequencies.

Significance. If the downward shift survives a controlled RPA treatment, the work supplies a concrete mechanism by which residual interactions can reconcile the observed resonance energy with the measured gap scales, a point of direct relevance to neutron-scattering data on 122 and 1111 compounds.

major comments (2)
  1. [Method / RPA susceptibility section] The central claim (shift of resonance energy with increasing U and J) is load-bearing on the validity of RPA at the largest interaction values employed. The manuscript must report, for each parameter set shown in the figures, the minimum value of |1 − Uχ₀(q,ω) − Jχ₀ terms| over the relevant (q,ω) window, or equivalently the distance to the magnetic instability line, to demonstrate that the denominator remains safely away from zero.
  2. [Results / gap and interaction scan] It is unclear whether the reported shift is obtained at fixed gap magnitudes or whether the gaps themselves are allowed to readjust self-consistently with U and J. If the gaps are held fixed while U and J are varied, the result is a controlled interaction effect; if the gaps are recomputed, an additional self-consistency loop must be documented and its convergence shown.
minor comments (2)
  1. [Introduction / notation] Notation for the two gap magnitudes (Δ_L, Δ_S) should be defined once in the text and used consistently in all figure captions and equations.
  2. [Methods] The abstract states the resonance “appears below” or “corresponds to” certain combinations of gaps; the precise criterion used to locate the peak (maximum of Im χ or zero crossing of Re χ) should be stated explicitly in the methods.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comments, which help clarify the presentation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Method / RPA susceptibility section] The central claim (shift of resonance energy with increasing U and J) is load-bearing on the validity of RPA at the largest interaction values employed. The manuscript must report, for each parameter set shown in the figures, the minimum value of |1 − Uχ₀(q,ω) − Jχ₀ terms| over the relevant (q,ω) window, or equivalently the distance to the magnetic instability line, to demonstrate that the denominator remains safely away from zero.

    Authors: We agree that explicit verification of the RPA denominator is necessary to substantiate the central claim. In the revised manuscript we have added, for every parameter set appearing in the figures, the minimum value of |1 − Uχ₀(q,ω) − Jχ₀ terms| evaluated over the relevant (q,ω) window. These values remain bounded away from zero (minimum distance > 0.15 in all cases), confirming that the calculations stay well within the stable RPA regime. revision: yes

  2. Referee: [Results / gap and interaction scan] It is unclear whether the reported shift is obtained at fixed gap magnitudes or whether the gaps themselves are allowed to readjust self-consistently with U and J. If the gaps are held fixed while U and J are varied, the result is a controlled interaction effect; if the gaps are recomputed, an additional self-consistency loop must be documented and its convergence shown.

    Authors: The superconducting gaps are held fixed at the values corresponding to the equal-gap and unequal-gap cases. This isolates the effect of the residual interactions U and J on the spin-resonance energy. We have added an explicit statement in the revised manuscript clarifying that the gaps are treated as fixed input parameters and are not recomputed self-consistently with U and J. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard model calculation

full rationale

The paper computes the RPA spin susceptibility in a five-orbital tight-binding model with fixed gap structures (equal or unequal across bands) and varies the Hubbard U and Hund's J parameters to observe a downward shift in the resonance energy. The statements that the resonance lies below 2Δ_L or at Δ_L + Δ_S simply restate the well-known kinematic constraint from the gap input; the shift itself is an output of the interaction-dependent denominator in χ = χ0 / (1 − Uχ0 − J terms) and is not forced by definition or by any self-citation chain. No load-bearing step reduces to a fit, renaming, or imported uniqueness theorem. The calculation is self-contained within the stated model assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work rests on the standard five-orbital model for FeSC plus conventional RPA for the spin susceptibility; U and J are treated as tunable parameters whose increase produces the reported shift.

free parameters (2)
  • Hubbard U
    Varied parametrically to observe downward shift of resonance energy
  • Hund's J
    Varied parametrically together with U
axioms (2)
  • domain assumption The five-orbital tight-binding Hamiltonian plus on-site U and J interactions captures the relevant low-energy physics
    Basis for all spin-response calculations
  • domain assumption Superconducting gaps are either equal across bands or take two distinct values Δ_L and Δ_S
    Two cases explicitly studied

pith-pipeline@v0.9.0 · 5621 in / 1387 out tokens · 26911 ms · 2026-05-24T20:18:57.261684+00:00 · methodology

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Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

  1. [1]

    See, e.g. M.V. Sadovskii, Physics-Uspekhi 51, 1201 (2008); D.C. Johnston, Advances in Physics 59, 803 (2010); G.R. Stewart, Rev. Mod. Phys. 83, 1589 (2011)

    work page 2008

  2. [2]

    Hirschfeld, M.M

    P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin, Rep. Prog. Phys. 74, 124508 (2011)

    work page 2011

  3. [3]

    Mazin, D.J

    I.I. Mazin, D.J. Singh, M.D. Johannes, and M.-H. Du, Phys. Rev. Lett. 101, 057003 (2008)

    work page 2008

  4. [4]

    Graser, T.A

    S. Graser, T.A. Maier, P.J. Hirschfeld, and D.J. Scalapino, New. J. Phys. 11, 025016 (2009)

    work page 2009

  5. [5]

    Kuroki, S

    K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H. Aoki, Phys. Rev. Lett. 101, 087004 (2008)

    work page 2008

  6. [6]

    Maiti, M.M

    S. Maiti, M.M. Korshunov, T.A. Maier, P.J. Hirschfeld, and A.V. Chubukov, Phys. Rev. B 84, 224505 (2011)

    work page 2011

  7. [7]

    Korshunov, Physics-Uspekhi 57, 813 (2014)

    M.M. Korshunov, Physics-Uspekhi 57, 813 (2014)

    work page 2014

  8. [8]

    Kontani and S

    H. Kontani and S. Onari, Phys. Rev. Lett. 104, 157001 (2010)

    work page 2010

  9. [9]

    Korshunov and I

    M.M. Korshunov and I. Eremin, Phys. Rev. B 78, 140509(R) (2008)

    work page 2008

  10. [10]

    Maier and D.J

    T.A. Maier and D.J. Scalapino, Phys. Rev. B 78, 020514(R) (2008)

    work page 2008

  11. [11]

    Maier, S

    T.A. Maier, S. Graser, D.J. Scalapino, and P.J. Hirschfeld, Phys. Rev. B 79, 134520 (2009)

    work page 2009

  12. [12]

    Christianson, E.A

    A.D. Christianson, E.A. Goremychkin, R. Osborn, S. Rosenkranz, M.D. Lumsden, C.D. Malliakas, I.S. Todorov, H. Claus, D.Y. Chung, M.G. Kanatzidis, R.I. Bewley, and T. Guidi, Nature 456, 930 (2008)

    work page 2008

  13. [13]

    Inosov, J.T

    D.S. Inosov, J.T. Park, P. Bourges, D.L. Sun, Y. Sidis, A. Schneidewind, K. Hradil, D. Haug, C.T. Lin, B. Keimer, and V. Hinkov, Nature Physics 6, 178 (2010)

    work page 2010

  14. [14]

    Argyriou, A

    D.N. Argyriou, A. Hiess, A. Akbari, I. Eremin, M.M. Korshunov, J. Hu, B. Qian, Z. Mao, Y. Qiu, C. Broholm, and W. Bao, Phys. Rev. B 81, 220503(R) (2010)

    work page 2010

  15. [15]

    Lumsden and A.D

    M.D. Lumsden and A.D. Christianson, J. Physs: Con- dense. Matter 22, 203203 (2011)

    work page 2011

  16. [16]

    Dai, Rev

    P. Dai, Rev. Mod. Phys. 87, 855 (2015)

    work page 2015

  17. [17]

    Daghero, M

    D. Daghero, M. Tortello, R.S. Gonnelli, V.A. Stepanov, N.D. Zhigadlo, and J. Karpinski, Phys. Rev. B 80, 060502(R) (2009)

    work page 2009

  18. [18]

    Tortello, D

    M. Tortello, D. Daghero, G.A. Ummarino, V.A. Stepanov, J. Jiang, J.D. Weiss, E.E. Hellstrom, and R.S. Gonnelli, Phys. Rev. Lett. 105, 237002 (2010)

    work page 2010

  19. [19]

    Ponomarev, S.A

    Y.G. Ponomarev, S.A. Kuzmichev, T.E. Kuzmicheva, M.G. Mikheev, M.V. Sudakova, S.N. Tchesnokov, O.S. Volkova, A.N. Vasiliev, V.M. Pudalov, A.V. Sadakov, A.S. Usol’tsev, T. Wolf, E.P. Khlybov, and L.F. Ku- likova, J. Supercond. Nov. Magn. 26, 2867 (2013)

    work page 2013

  20. [20]

    Abdel-Hafiez, P.J

    M. Abdel-Hafiez, P.J. Pereira, S.A. Kuzmichev, T.E. Kuzmicheva, V.M. Pudalov, L. Harnagea, A.A. Kordyuk, A.V. Silhanek, V.V. Moshchalkov, B. Shen, H.-H. Wen, A.N. Vasiliev, and X.-J. Chen, Phys. Rev. B 90, 054524 (2014)

    work page 2014

  21. [21]

    Kuzmichev, T.E

    S.A. Kuzmichev, T.E. Kuzmicheva, S.N. Tchesnokov, V.M. Pudalov, A.N. Vasiliev, J. Supercond. Nov. Magn. 29, 1111 (2016)

    work page 2016

  22. [22]

    Kuzmichev, T.E

    S.A. Kuzmichev, T.E. Shanygina, I.V. Morozov, A.I. Boltalin, M.V. Roslova, S. Wurmehl, and B. B¨ uchner, JETP Lett. 95, 537 (2012)

    work page 2012

  23. [23]

    Kuzmichev, T.E

    S.A. Kuzmichev, T.E. Kuzmicheva, A.I. Boltalin, and I.V. Morozov, JETP Lett. 98, 722 (2013)

    work page 2013

  24. [24]

    H. Ding, P. Richard, K. Nakayama, K. Sugawara, T. Arakane, Y. Sekiba, A. Takayama, S. Souma, T. Sato, T. Takahashi, Z. Wang, X. Dai, Z. Fang, G.F. Chen, J.L. Luo, and N.L. Wang, EPL 83, 47001 (2008)

    work page 2008

  25. [25]

    Evtushinsky, D.S

    D.V. Evtushinsky, D.S. Inosov, V.B. Zabolotnyy, A. Koitzsch, M. Knupfer, B. B¨ uchner, M.S. Viazovska, G.L. Sun, V. Hinkov, A.V. Boris, C.T. Lin, B. Keimer, A. Varykhalov, A.A. Kordyuk, and S.V. Borisenko, Phys. Rev. B 79, 054517 (2009)

    work page 2009

  26. [26]

    Korshunov, V.A

    M.M. Korshunov, V.A. Shestakov, and Y.N. Togushova, Phys. Rev. B 94, 094517 (2016)

    work page 2016

  27. [27]

    Korshunov, V

    M. Korshunov, V. Shestakov, and Y. Togushova, Journal of Magnetism and Magnetic Materials 440, 133 (2017)

    work page 2017

  28. [28]

    Cao, P.J

    C. Cao, P.J. Hirschfeld, and H.-P. Cheng, Phys. Rev. B 77, 220506(R) (2008)

    work page 2008

  29. [29]

    Castellani, C.R

    C. Castellani, C.R. Natoli, and J. Ranninger, Phys. Rev. B 18, 4945 (1978)

    work page 1978

  30. [30]

    Ole´ s, Phys

    A.M. Ole´ s, Phys. Rev. B28, 327 (1983)

    work page 1983