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Anisotropic superconducting gap probed by $^{125}$Te NMR in noncentrosymmetric Sc$_6M$Te$_2$ ($M$ = Fe, Co)

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read 125Te NMR shows the superconducting gap in noncentrosymmetric Sc6MTe2 (M = Fe, Co) is anisotropic, with a Knight shift that stays finite and a nuclear spin-lattice relaxation rate that follows a T^3 power law below Tc.

desk verdict A careful first NMR look at a new noncentrosymmetric superconductor family, with a plausible but not proven nodal-gap claim that rests on single-field relaxation data. read the letter →

arxiv 2506.02484 v1 pith:IL5Y7U2E submitted 2025-06-03 cond-mat.supr-con

Kanako Doi , Hayase Takei , Yusaku Shinoda , Yoshihiko Okamoto , Daigorou Hirai , Koshi Takenaka , Taku Matsushita , Yoshiaki Kobayashi
show 1 more author
Yasuhiro Shimizu
This is my paper
classification cond-mat.supr-con
keywords superconductivityNMRKnightshiftnuclearspin-latticerelaxationnoncentrosymmetricsuperconductorlinenodespairingsymmetryscandiumtelluride125Te
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper uses 125Te NMR to determine the symmetry of the superconducting gap in two noncentrosymmetric compounds, Sc6FeTe2 and Sc6CoTe2. It finds that below Tc the Knight shift, which measures the local spin susceptibility, is suppressed but remains finite down to about 0.4 K, and that the nuclear spin-lattice relaxation rate 1/T1 falls as a power law T^n with n ≈ 3, with no coherence peak. These observations are taken as evidence for line nodes in the quasiparticle excitation gap, possibly accompanied by a spin-triplet admixture or a residual density of states. The result matters because it constrains the pairing symmetry in a strongly correlated material where strong electron-phonon coupling has also been predicted.

What carries the argument

The central measurements are the 125Te Knight shift K and the nuclear spin-lattice relaxation rate 1/T1. K probes the local spin susceptibility at the tellurium site; its change across Tc distinguishes spin-singlet pairing, which would suppress the spin susceptibility, from a spin-triplet admixture. 1/T1 probes the low-energy quasiparticle spectrum; its temperature dependence below Tc (power law versus exponential) diagnoses whether the gap has nodes. The analysis also relies on the Korringa relation between 1/T1T and $K^{2}$ to establish the normal-state baseline and to evaluate the orbital contribution to the Knight shift, and on the stretched-exponential recovery of nuclear magnetization below Tc, which the authors take as an indication of a residual normal-state component.

What would settle it

Measure 1/T1 and the Knight shift on single crystals of Sc6FeTe2 and Sc6CoTe2 at fields well below Hc2 (for example 0.1–0.5 T) where vortex overlap is negligible. If the power-law exponent n increases toward an exponential form or the residual Knight shift disappears, the proposed line-node gap would be an artifact of the measurement field; conversely, observing a Knight-shift anisotropy between field directions parallel and perpendicular to the proposed d-vector would confirm a spin-triplet admixture.

Watch

Extended reading notes

Core claim

In both Sc6FeTe2 and Sc6CoTe2, 125Te NMR at a magnetic field of 2.57 T reveals that the Knight shift decreases below the superconducting transition temperature but does not vanish even at the lowest measured temperature, and that 1/T1 drops steeply below Tc and then follows a power law ~ T^n with n approximately 3. The absence of a coherence peak and the power-law relaxation are inconsistent with an isotropic s-wave gap, and the authors interpret them as evidence for line nodes in the quasiparticle excitation gap. The residual Knight shift is attributed either to a spin-triplet admixture arising from the broken inversion symmetry or to a residual density of states under the applied magnetic field.

Load-bearing premise

The NMR data at 2.57 T—about 30% of the upper critical field—are assumed to reflect the intrinsic quasiparticle gap structure rather than being dominated by vortex-core quasiparticles or a residual normal-state fraction.

Editorial extensions

If this is right

  • If the gap is nodal, specific-heat and magnetic-penetration-depth measurements on these compounds should also show power-law temperature dependences at low temperatures rather than activated behavior.
  • The finite Knight shift below Tc implies either a spin-triplet component or a residual density of states; a spin-triplet component would produce a Knight-shift anisotropy for field directions parallel versus perpendicular to the d-vector, testable on single crystals.
  • The observed T^3 relaxation law and the absence of a coherence peak provide a quantitative benchmark that candidate order parameters for the noncentrosymmetric point group must reproduce.
  • Lower-field measurements should exhibit a smaller residual Knight shift and a sharper power law if the residual contributions are vortex-related, sharpening the intrinsic-gap determination.
  • The normal-state Korringa ratio near unity indicates weak spin fluctuations, suggesting that the anisotropic pairing, if intrinsic, is likely driven by strong electron-phonon coupling rather than magnetic fluctuations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The apparent T^3 law could in part be a vortex-core effect: if the relaxation at 2.57 T is dominated by quasiparticles localized in vortex cores, the line-node conclusion would be weakened, and a direct test is to measure 1/T1 at fields well below 30% of Hc2.
  • The two different orbital-shift baselines (0.02–0.05% from the Korringa plot versus 0.29–0.48% from the K–chi plot) imply that the absolute change in spin susceptibility across Tc is uncertain; reconciling this discrepancy would sharpen whether the residual shift is a spin-triplet signature or a normal-state artifact.
  • The structural spectral splitting observed in Sc6CoTe2 near 150 K indicates a symmetry-lowering transition; if superconductivity emerges in the low-temperature phase, the nodal structure could be a consequence of the lower symmetry rather than the high-temperature P-62m structure.
  • Since a finite Sommerfeld coefficient γ0 exists even in zero field, some normal-state fraction is always present; separating this extrinsic contribution from the intrinsic 1/T1 signal will be necessary before the exact exponent n can be trusted.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper reports 125Te NMR measurements on polycrystalline Sc6MTe2 (M = Fe, Co) in the normal and superconducting states. The Knight shift is negative and scales with bulk susceptibility, indicating negative hyperfine coupling; below Tc the peak shifts positive, which the authors interpret as a suppression of spin susceptibility with a finite residual value down to about 0.4 K. The spin-lattice relaxation rate 1/T1, measured at a single field of 2.57 T, shows no coherence peak and follows an approximate T^3 power law. In the normal state, 1/T1T versus K approximately satisfies Korringa scaling. The authors conclude that the superconducting gap is anisotropic, possibly with line nodes, and discuss singlet-triplet admixture. They also report a spectral splitting in Sc6CoTe2 below about 150 K attributed to a structural mirror-symmetry breaking. The abstract itself hedges the low-temperature behavior as 'pairing admixture or a residual density of states under magnetic field,' but the text and conclusion make a stronger claim of evidence for nodal gap.

Significance. If the nodal-gap conclusion were firmly established, Sc6MTe2 would be a valuable addition to the small family of noncentrosymmetric superconductors with possible mixed-parity pairing and nodal structure. The paper also provides useful normal-state Korringa analysis and identifies a structural transition in the Co compound. Strengths include the explicit discussion of residual normal-state contributions, the site-resolved Knight shift in Sc6CoTe2, and the internal consistency of the raw qualitative features: no coherence peak, power-law 1/T1, and positive ΔK below Tc with negative hyperfine coupling. However, the current single-field data and the baseline ambiguity for the orbital shift prevent the strong claim from being fully supported, so the significance is conditional on the requested revision.

major comments (2)
  1. [Section III (Figs. 3 and 4)] The superconducting-state Knight shift and 1/T1 data were obtained at a single field H = 2.57 T, approximately 30% of Hc2(0) for Sc6FeTe2, while the paper itself reports that the recovery becomes a stretched exponential with β = 0.8–1 below Tc, 'indicating the residual normal state under the magnetic field,' and that a finite γ0 persists even at zero field and grows with field. A vortex-core or normal-state fraction contributes a finite density of states at the Fermi level, which can produce a residual Knight shift and a 1/T1 power law with an effective exponent near 3 even in an s-wave superconductor. Consequently, the absence of a coherence peak and the T^3 dependence do not uniquely establish line nodes, and the finite low-temperature Knight shift does not uniquely establish spin-triplet admixture. The authors should either quantify and subtract this extrinsic contribution (e.g., via field-dependent 1/T1 at fixed temperature, two-component recovery analysis, or vortex-core relaxation models) or restrict the conclusion to 'consistent with an anisotropic or nodal gap' as the abstract already does.
  2. [Appendix A and Fig. 3(c)] The choice of orbital shift baseline is load-bearing: the paper adopts Korb = 0.02% (Fe) and 0.05% (Co) from the Korringa-plot extrapolation, whereas the K–χ plot in Fig. 6 yields Korb = 0.29% and 0.48%, an order-of-magnitude difference. Because the reported ΔK below Tc is only 0.04% (Fe) and 0.02% (Co), the inferred residual spin susceptibility and the discussion of parity mixing are extremely sensitive to this choice. The explanation that the K–χ plot has a constant offset from magnetic impurities is plausible but not quantitatively supported; the authors should provide an independent estimate (e.g., from band-structure calculations of the orbital shift) or a sensitivity analysis showing the robustness of the conclusions.
minor comments (6)
  1. [Section III, Fig. 4] The dashed and solid curves for the full-gap and line-node calculations are not described in the text or caption; the gap function, parameters, and calculation method should be given so the comparison can be reproduced.
  2. [Section II] In the sentence '125Te (125I = 1/2) NMR', the isotope notation is redundant; it should read '125Te (I = 1/2)'.
  3. [Section III] The text refers to Fig. 1(b) for the spectral splitting in Sc6CoTe2, but the splitting is shown in Fig. 1(c); the citation should be corrected.
  4. [Fig. 4] No error bars are shown for 1/T1, and the T^3 line is presented as a guide; a quantitative fit with uncertainties for the exponent n would strengthen the power-law claim.
  5. [Section III] The spelling 'Korriga's relation' appears once; it should read 'Korringa's relation'.
  6. [Section III] The paper does not report the lower critical field Hc1 or the exact Hc2 for Sc6CoTe2, which would help the reader assess how deep the measurement field is relative to the superconducting phase boundary.

Circularity Check

1 steps flagged · score 2.0 of 10

Main gap conclusions are data-driven; only the Korringa-consistency statement is circular by construction.

  1. fitted input called prediction [Section III (Knight-shift analysis and Fig. 5 discussion; Appendix A)]
    "Assuming Korringa’s relation described in the following, the orbital part Korb is evaluated from the K-(T1T )−0.5 plot as Korb = 0.02% for Sc6FeTe2 and Korb = 0.05% for Sc6CoTe2 (See Appendix A). ... Therefore, Korriga’s relation, 1 /T1T ∝ K 2 s , holds in both compounds (See also the Appendix A)."

    Korb is obtained as the intercept of a linear fit of K versus (T1T)^-0.5. That fit presupposes Ks ∝ (T1T)^-0.5, i.e., Korringa scaling. After subtracting the fitted Korb, the statement that 1/T1T ∝ Ks^2 holds is therefore an algebraic consequence of the fitting procedure, not an independent empirical check. The paper’s wording (“Assuming ... evaluated ... Therefore ... holds”) makes the circularity explicit. This affects only the normal-state Korringa characterization and does not enter the superconducting-gap conclusions, which rely on the raw Knight-shift shift and the T^3 relaxation.

full rationale

The central claims — Knight-shift suppression below Tc with a finite residual value, and 1/T1 following T^3 without a coherence peak — are qualitative features of the raw NMR data and do not depend on any fitted parameter. The interpretation in terms of line nodes is a comparison with standard theoretical curves, not a parameter extraction from those curves. The one circular element is the Korringa-scaling statement: the orbital shift Korb is extracted by assuming Ks ∝ sqrt(1/T1T), and the subsequent assertion that 1/T1T ∝ Ks^2 holds is just restating that assumed linearity. However, this step is peripheral to the superconducting-gap conclusion and is also supported qualitatively by the parallel T-dependence of 1/T1T and K in Fig. 5. The authors’ explicit caveats about single-field measurements, stretched-exponential recovery, and residual normal-state contributions bear on interpretation but are not circularity. Overall the derivation chain is largely self-contained, with only this minor by-construction consistency check.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities and no new fitting parameters beyond standard experimental calibration; the numbers that drive the central claims are the orbital-shift baseline Korb (with two inconsistent determinations), the fitted relaxation exponent n ~ 3, the stretched-exponential index beta, and the hyperfine coupling constants. The central axioms are the standard BCS/Yosida and Korringa frameworks, plus the material-specific assumption that the 150 K spectral splitting in Sc6CoTe2 is structural in origin. The main burden is the self-consistency loop in the Korb extraction: the Korringa relation is assumed to separate Ks from Korb and is then verified by the constancy of Kalpha.

free parameters (4)
  • Orbital Knight shift Korb (baseline for spin susceptibility) = 0.02% (Fe), 0.05% (Co) via Korringa plot; alternative K-chi values 0.29% and 0.48%
    Chosen by extrapolation in the K vs (T1T)^-0.5 plot assuming Korringa scaling; sets the scale of Ks and therefore of Kalpha and of the claimed residual spin susceptibility. The alternative K-chi determination differs by about an order of magnitude (Appendix A).
  • Power-law exponent n in 1/T1 ~ T^n = n ~ 3
    Fitted to the superconducting-state 1/T1 data at H = 2.57 T; shown as a guide line in Fig. 4 with no uncertainty estimate.
  • Stretched-exponential exponent beta = 0.8-1 below Tc
    Fitted to magnetization-recovery curves below Tc; quantifies inhomogeneous relaxation and residual normal-state weight, which affects the reliability of the T^3 determination.
  • Hyperfine coupling constants Hhf = -0.8(2) T/muB (Fe), -3.4(3) T/muB (Co)
    Fitted from the linearity of the K-chi plot; converts Knight shift into spin susceptibility. Standard NMR calibration, not central to the claim, but its sign convention underlies the interpretation of DeltaK.
assumptions (5)
  • domain assumption Korringa relation 1/T1T ~ Ks^2 holds in the normal state and is used to separate spin and orbital Knight shifts
    Used in Appendix A to extrapolate the K vs (T1T)^-0.5 plot and set Korb; the reported Kalpha ~ 1.0-1.3 then confirms the same relation, a mild self-consistency loop.
  • standard math The Knight shift change below Tc equals the spin-susceptibility change through the same hyperfine coupling (Yosida picture)
    Standard BCS/Yosida framework (Ref [36]); needed to interpret the positive DeltaK for negative Hhf as spin-susceptibility suppression.
  • domain assumption 1/T1 for line-node and full-gap superconductors follows the standard Hebel-Slichter and BCS model with assumed gap structures
    The comparison curves in Fig. 4 assume specific gap geometries whose parameters are not independently fixed; the T^3 guide line is a fit, not a parameter-free prediction.
  • domain assumption Tc at H = 2.57 T is 3.4 K (Fe) and 2.5 K (Co), taken from prior self-cited work [24]
    Used to normalize the superconducting-state temperature range; a slightly different Tc (3.3 and 2.2 K) appears later in the same text.
  • ad hoc to paper The 125Te NMR spectral splitting below T* ~ 150 K in Sc6CoTe2 indicates a structural mirror-symmetry breaking
    Inferred solely from the NMR line shape showing Te-site doubling; no diffraction or thermodynamic confirmation is presented.

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Cite this review

Pith. "Pith review of Anisotropic superconducting gap probed by $^{125}$Te NMR in noncentrosymmetric Sc$_6M$Te$_2$ ($M$ = Fe, Co)." pith.science (2026). https://pith.science/paper/IL5Y7U2E

@misc{pith2026250602484,
  author       = {Pith},
  title        = {Pith review of: Anisotropic superconducting gap probed by $^125$Te NMR in noncentrosymmetric Sc$_6M$Te$_2$ ($M$ = Fe, Co)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IL5Y7U2E}},
  note         = {Machine review of arXiv:2506.02484}
}
abstract

The superconducting gap symmetry is investigated by $^{125}$Te NMR measurements on Sc$_6M$Te$_2$ ($M$ = Fe, Co) without spatial inversion symmetry. The spin susceptibility obtained from the Knight shift $K$ is suppressed below the superconducting transition temperature, while leaving a finite value down to the lowest temperature ($\simeq 0.4$ K). The nuclear spin-lattice relaxation rate $1/T_1$ follows a power law against temperature $T$ without showing a coherence peak characteristic of the isotropic gap. The result implies a pairing admixture or a residual density of states under magnetic field. The normal metallic state has a Korringa scaling relation between $1/T_1T$ and the Knight shift, reflecting a weak electron correlation.

Figures

Figures reproduced from arXiv: 2506.02484 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Crystal structure of Sc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Temperature dependence of 1 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Nuclear spin-lattice relaxation rate divided by tem [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Knight shift vs bulk magnetic susceptibility as an [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Knight shift [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

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