{"id":"fe7b8696-d6c4-40d0-8905-17610208ae0b","arxiv_id":"2506.02484","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"125Te NMR on noncentrosymmetric Sc6MTe2 (M = Fe, Co) shows a suppressed but finite spin susceptibility below Tc and a T^3-like relaxation rate without a coherence peak, indicating an anisotropic or nodal superconducting gap.","lead":"Using 125Te NMR, the authors measured how the superconducting state of two noncentrosymmetric superconductors, Sc6FeTe2 and Sc6CoTe2, loses spin susceptibility and relaxes nuclear magnetization below their transition temperatures. The data show a power-law relaxation without the classic coherence peak, pointing to an anisotropic, possibly nodal, superconducting gap, though residual signals leave room for alternative explanations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The nodal-gap conclusion rests on a single-field (H = 2.57 T) 1/T1 measurement whose own stretched-exponential recovery indicates residual normal-state/vortex-core contributions; until these are separated, the T^3 law does not uniquely establish line nodes.","rationale":"I agree with the Reader's weakest assumption. The single most dangerous point is not the Korb ambiguity, which changes the normalization of Ks but not the observed positive shift below Tc, but rather the vortex/normal-state contamination of 1/T1: it is the only channel that would make the central 'line nodes' assertion collapse. The paper is unusually candid about this limitation, including the failed attempts at lower fields due to Meissner shielding; that candor is evidence, but it also means the decisive control is absent. The measured facts: no coherence peak, T^n with n about 3, and a small residual shift, are each separately compatible with vortex-core and impurity effects, as the paper's own references [40-43] note. Therefore the conditional verdict is appropriate; I would not move it to a harsher verdict because the authors do hedge several claims in the body text, the raw observations are reported with stated caveats, and the proposed low-field or modeling checks are the correct next step rather than a demonstration of internal inconsistency. The conclusion does overstate the body by presenting parity mixing as an implication of the residual shift, but that is a rhetorical excess within an otherwise careful experimental report. The single proposed check, a two-channel fit or a lower-field comparison, would settle whether the T^3 law is intrinsic or an artifact of the field-induced normal-state fraction.","tokens_in":10372,"tokens_out":6062,"duration_ms":66794,"concrete_test":"Re-fit the low-temperature 1/T1 data in Fig. 4 with 1/T1(T) = a T + b T^3, where the T-linear term is the vortex/normal-state channel, and fix its coefficient from the measured residual gamma(H) and the stretched-exponential beta; then test whether the T^3 term is required. If the T-linear term alone fits the points below about 1.5 K, the line-node claim is not established. As an independent check, measure 1/T1 on an aligned single crystal or small-particle sample at H about 1 T (where the rf field can penetrate after field cooling) and compare the exponent; an intrinsic nodal gap should keep n about 3 nearly H-independent, whereas a vortex-contaminated signal will show n depending on H and beta moving further from 1.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is that the relaxation data below Tc (Fig. 4) reflect the quasiparticle gap of the homogeneous superconducting phase. All such data were taken at one field, H = 2.57 T, roughly 30% of Hc2(0) for the Fe compound, and the paper itself reports that recovery becomes a stretched exponential with beta = 0.8-1 below Tc, 'indicating the residual normal state under the magnetic field.' It also cites the finite zero-field gamma0 that grows with field and the known suppression of the coherence peak by field and impurities. A vortex-core or normal-state fraction therefore contributes a finite density of states and can produce or mimic a power-law 1/T1 with an exponent near 3, so the absence of a coherence peak and the T^3 dependence are not uniquely attributable to line nodes. The abstract itself hedges the companion claim as 'pairing admixture or a residual density of states under magnetic field.' The line-node assertion in the text is stronger than what the single-field data can support.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":10497,"tokens_out":6772,"duration_ms":64161,"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":[{"comment":"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.","section":"Section III (Figs. 3 and 4)"},{"comment":"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.","section":"Appendix A and Fig. 3(c)"}],"minor_comments":[{"comment":"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.","section":"Section III, Fig. 4"},{"comment":"In the sentence '125Te (125I = 1/2) NMR', the isotope notation is redundant; it should read '125Te (I = 1/2)'.","section":"Section II"},{"comment":"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.","section":"Section III"},{"comment":"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.","section":"Fig. 4"},{"comment":"The spelling 'Korriga's relation' appears once; it should read 'Korringa's relation'.","section":"Section III"},{"comment":"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.","section":"Section III"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for cond-mat.supr-con, and the experimental data appear honestly reported. My recommendation of major revision rests on two load-bearing issues: the single-field/vortex-core contamination of the superconducting-state data and the ambiguity in the orbital-shift baseline. Both are addressable in revision, so I would not reject. The authors have been transparent about the residual normal-state problem, which strengthens their credibility but also means the strong nodal-gap conclusion requires additional analysis or a softening of the language."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth reading: it is the first 125Te NMR study of the Sc6MTe2 superconductors, and it reports genuinely new observations — suppressed but finite spin susceptibility below Tc, a T^3-like 1/T1 with no coherence peak, a site-dependent superconducting shift in the Co member, and a 150 K spectral splitting that suggests a structural transition. The normal-state Korringa scaling is a useful constraint on the pairing mechanism. The authors are also honest about their limitations: they note the single field (2.57 T, roughly a third of Hc2), the stretched-exponential recovery below Tc that they attribute to a residual normal state, the failed attempts at lower fields due to Meissner shielding, and the need for single-crystal work.\n\nThe stress-test concern is real and lands where it should. The T^3 relaxation and missing coherence peak are qualitative patterns, not fit-parameter artifacts, so they are not circular in the usual sense. But the single-field measurement cannot separate intrinsic quasiparticle dynamics from vortex-core or normal-state contributions, and the paper's own stretched-exponent statement makes that contamination likely. So the line-node conclusion is plausible, not established. The abstract says \"pairing admixture or a residual density of states\" — that is the right level of certainty. The conclusion's \"evidence for nodal gap\" pushes further than the data support.\n\nThe Korb ambiguity is a genuine soft spot: two standard extraction methods give baselines that differ by an order of magnitude (0.02–0.05% vs 0.29–0.48%), which directly affects the magnitude of the spin-susceptibility drop. The authors mention magnetic impurities as a likely cause, but the discrepancy is not resolved. This matters for the parity-mixing claim, less so for the gap-symmetry claim, which relies on 1/T1.\n\nThis is not a flawed paper; it is a solid experimental study with an interpretation that is appropriately hedged in most places. The new data are useful and the reporting is careful. A serious referee should be asked to justify or soften the nodal conclusion and to model the vortex-core contribution, but the work does not deserve rejection. It is a good candidate for publication with revision, and I would cite it if I worked on noncentrosymmetric superconductors.","headline":"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.","tokens_in":11189,"tokens_out":1515,"would_cite":true,"duration_ms":18027,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["superconductivity","NMR Knight shift","nuclear spin-lattice relaxation","noncentrosymmetric superconductor","line nodes","pairing symmetry","scandium telluride","125Te NMR"],"falsifier":"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.","tokens_in":10037,"feed_emoji":"🔬","tokens_out":4614,"duration_ms":42188,"temperature":0.7,"pith_summary":"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.","feed_headline":"NMR finds T^3 relaxation and a nodal gap in Sc6MTe2","feed_subtitle":"125Te Knight shift stays finite while 1/T1 scales as T^3, pointing to anisotropic pairing in noncentrosymmetric superconductors.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Discovery of superconductivity in the Sc6MTe2 series; supplies Tc, upper critical field, specific-heat jump, and the finite zero-field γ0 used for comparison.","marker":"[24]"},{"why":"Hebel–Slichter BCS calculation for the nuclear relaxation rate in a full-gap superconductor; provides the coherence-peak and exponential baseline that the observed T^3 law is contrasted against.","marker":"[37]"},{"why":"Theory of spin susceptibility in noncentrosymmetric superconductors with a d-vector; frames the interpretation of the residual Knight shift as a possible triplet admixture.","marker":"[35]"},{"why":"Ab initio study proposing strong electron-phonon coupling and a rattling mode in Sc6MTe2; used to interpret the absence of a coherence peak and the strong-coupling character.","marker":"[38]"},{"why":"Reference for the suppression of the NMR coherence peak by magnetic impurities and magnetic field, which the authors invoke to caution that the missing peak may be extrinsic.","marker":"[40]"},{"why":"Source of the K–(T1T)^-0.5 method used to evaluate the orbital Knight shift, one of the two baselines that determines the size of the spin-susceptibility suppression.","marker":"[45]"}],"fun_headline_variants":["125Te NMR reveals anisotropic gap in noncentrosymmetric Sc6MTe2","Power-law 1/T1 and finite Knight shift point to nodal gap in Sc6MTe2","125Te NMR: no coherence peak, power-law relaxation in Sc6MTe2","Knight shift persists below Tc while 1/T1 ~ T^3 in Sc6MTe2","Anisotropic pairing in Sc6MTe2 from residual spin susceptibility"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["125Te NMR reveals anisotropic gap in noncentrosymmetric Sc6MTe2","Power-law 1/T1 and finite Knight shift point to nodal gap in Sc6MTe2","125Te NMR: no coherence peak, power-law relaxation in Sc6MTe2","Knight shift persists below Tc while 1/T1 ~ T^3 in Sc6MTe2","Anisotropic pairing in Sc6MTe2 from residual spin susceptibility"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000651,"raw_usage":{"total_tokens":2937,"prompt_tokens":850,"completion_tokens":2087,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":466,"completion_tokens_details":{"reasoning_tokens":1973}},"tokens_in":466,"tokens_out":2087,"duration_ms":15340,"temperature":1.0,"reasoning_tokens":1973,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:24:27.569767+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Shinoda, Y","cited_arxiv_id":null,"evidence_quote":"Discovery of superconductivity in the Sc6MTe2 series; supplies Tc, upper critical field, specific-heat jump, and the finite zero-field γ0 used for comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Hebel–Slichter BCS calculation for the nuclear relaxation rate in a full-gap superconductor; provides the coherence-peak and exponential baseline that the observed T^3 law is contrasted against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Theory of spin susceptibility in noncentrosymmetric superconductors with a d-vector; frames the interpretation of the residual Knight shift as a possible triplet admixture."},{"cited_title":"Jiang, R","cited_arxiv_id":null,"evidence_quote":"Ab initio study proposing strong electron-phonon coupling and a rattling mode in Sc6MTe2; used to interpret the absence of a coherence peak and the strong-coupling character."},{"cited_title":"Masuda and M","cited_arxiv_id":null,"evidence_quote":"Reference for the suppression of the NMR coherence peak by magnetic impurities and magnetic field, which the authors invoke to caution that the missing peak may be extrinsic."},{"cited_title":"Harada, J","cited_arxiv_id":null,"evidence_quote":"Source of the K–(T1T)^-0.5 method used to evaluate the orbital Knight shift, one of the two baselines that determines the size of the spin-susceptibility suppression."}],"review_version":1}