{"id":"8ae6c05b-805f-4cbc-9f6e-f4a8ff969a1b","arxiv_id":"2506.12449","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"NbTaOs2 is a new non-centrosymmetric α-Mn superconductor (Tc ≈ 2.4 K) with evidence for a fully gapped state and, from zero-field muon spin relaxation, a small spontaneous field below Tc suggestive of time-reversal symmetry breaking.","lead":"Researchers synthesized the new non-centrosymmetric superconductor NbTaOs2 and measured its properties with resistivity, magnetization, specific heat, and muon spin rotation. The data suggest a fully gapped superconducting state and a small spontaneous internal field below Tc, which would indicate time-reversal symmetry breaking in a rhenium-free α-Mn alloy for the first time.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ZF-μSR evidence for TRSB rests on a 0.008 μs⁻¹ relaxation increase whose separation from the nuclear-dipolar rate is degenerate; the fixed-ΔZ fit and 5 mT decoupling cannot exclude impurity static fields, so the central claim is underdetermined.","rationale":"The paper's most important and novel claim is TRSB in a Re-free α-Mn superconductor, supported by a small ZF-μSR relaxation-rate enhancement. My analysis identifies the same load-bearing assumption as the reader: that the increase in Λ is not an artifact of the fitting procedure or of static impurity fields. The equation-level errors (Eq. 17 inversion, reversed Brandt condition, negative phonon term) are likely typographical and affect derived parameters, not the central TRSB claim directly. However, the ZF-μSR analysis has a genuine underdetermination: two Gaussian relaxation channels are fit with one fixed by normal-state data. The 5 mT decoupling is a standard test for static fields but does not rule out dilute magnetic impurities, a known background in polycrystalline alloys. My proposed reanalysis of the raw spectra with free ΔZ would settle the question. If the global fit still requires a Λ increase below Tc, the TRSB claim would be substantially strengthened; if not, the conclusion should be tempered. Thus I recommend no change to the reader's CONDITIONAL verdict, but the TRSB claim requires this additional verification before it can be accepted at face value.","tokens_in":15241,"tokens_out":6618,"duration_ms":78501,"concrete_test":"Reanalyze the existing ZF-μSR spectra without fixing ΔZ: perform a global fit of all temperatures (0.25–6 K) with A(t) = Ai GKT(t) exp(−(Λt)^β) + Abg, allowing ΔZ, Ai, Abg, and β to vary freely, and test whether a model with Λ(T) constant is rejected by the data. If the data are equally well described without a low-T Λ increase, the TRSB evidence collapses.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central TRSB claim depends entirely on the 0.008(1) μs⁻¹ increase in the additional relaxation rate Λ below Tc in the zero-field μSR analysis (Section III.E, Eq. (19), Fig. 5(b)). Because both the Kubo-Toyabe term GKT(t) (Eq. (20)) and the added term exp(−Λt)^β (with β ≈ 2) are Gaussian-type decays in the measured time window, the two rates ΔZ and Λ are strongly degenerate. The authors fix ΔZ, Ai, and Abg to their normal-state values and then attribute all residual relaxation to Λ. Any temperature dependence of the true nuclear dipolar width ΔZ (from muon diffusion, thermal contraction, or dilute magnetic moments) will therefore be misattributed to a spontaneous internal field. The 5 mT longitudinal-field decoupling at 0.25 K only shows that the relaxation is static; it does not discriminate between TRSB-generated fields and static fields from magnetic impurities or a spurious magnetic transition, both of which would be fully decoupled by 50 G. The internal field Bint = 0.094(5) G is obtained from Eq. (21) using δΛ, so the conclusion that NbTaOs2 is the first Re-free α-Mn TRSB superconductor is not uniquely established by the presented data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the synthesis of the ternary non-centrosymmetric α-Mn-type compound NbTaOs2 and characterizes its superconductivity through resistivity, magnetization, specific heat, transverse-field muon spin rotation, and zero-field muon spin relaxation. The authors find bulk type-II superconductivity at Tc≈2.4 K, a fully gapped moderately coupled s-wave-like state with Δ(0)/kBTc≈2.1–2.2 from both specific heat and TF-μSR, and a small (0.008(1) μs⁻¹) increase in the zero-field muon relaxation rate below Tc that they attribute to spontaneous internal fields and hence to time-reversal symmetry breaking. On this basis they claim NbTaOs2 is the first Re-free α-Mn-type compound with TRSB.","tokens_in":15555,"tokens_out":9171,"duration_ms":112335,"significance":"If confirmed, the TRSB claim is significant because the established TRSB cases in α-Mn-type superconductors are mostly Re-based; a Re-free counterexample would sharpen the debate about the role of Re, antisymmetric spin-orbit coupling, and disorder. The fully gapped moderate-coupling s-wave conclusion is well supported: the gap ratios from two independent probes (specific heat: 2.22(1); TF-μSR: 2.02(1) when Eq. (17) is corrected) agree within uncertainties, and the TF-μSR analysis uses standard BCS formulas. The paper is also commendable for reporting detailed raw measurements and fits. The main weakness is that the TRSB evidence rests on one very small relaxation-rate change extracted under fixed nuclear-width parameters, and the analysis does not yet rule out static impurity fields as the source of the extra relaxation.","major_comments":[{"comment":"The central TRSB claim depends on the 0.008(1) μs⁻¹ increase in Λ below Tc. Because the Kubo-Toyabe term and the added Gaussian term are both (near-)Gaussian over the measured time window, ΔZ and Λ are strongly correlated; the authors' decision to fix ΔZ, Ai, and Abg at their normal-state values means that any temperature dependence of the nuclear dipolar width—from thermal contraction, muon diffusion, or dilute static moments—would be absorbed into Λ. The 5 mT longitudinal-field decoupling only establishes that the relaxation is static; it does not discriminate between a TRSB spontaneous field and static impurity fields or a weak magnetic transition, both of which also decouple at 50 G. The manuscript should fit ΔZ as a free parameter with reported correlation contours, provide an independent determination of the nuclear dipolar width, or include control measurements on a non-superconducting analog before the 'first Re-free α-Mn TRSB' claim can be considered established.","section":"III.E, Eq. (19), Eq. (21), Fig. 5(b)"},{"comment":"Eq. (17) as written equates σ_fll⁻²(T)/σ_fll⁻²(0) to λ⁻²(T)/λ⁻²(0), but Eq. (16) implies σ_fll ∝ λ⁻², so σ_fll⁻² ∝ λ⁴ and the left side is λ⁴(T)/λ⁴(0), which rises as T approaches Tc and cannot describe the plotted λ⁻²(T) that decreases toward Tc. The intended dirty-limit BCS relation is σ_fll(T)/σ_fll(0) = λ⁻²(T)/λ⁻²(0) = (Δ(T)/Δ(0)) tanh(Δ(T)/2kBT). The equation should be corrected, and the quoted Δ(0)/kBTc = 2.02(1) should be verified with the correct expression.","section":"III.E, Eq. (17)"}],"minor_comments":[{"comment":"The λe−ph calculation uses Tc = 2.25(3) K, while Tc values quoted elsewhere are 2.40(2) K from magnetization and specific heat and 2.90(3) K from resistivity; please state the origin of 2.25(3) K and assess the sensitivity of λe−ph (and of the Uemura ratio) to this choice.","section":"III.D, Eq. (10)"},{"comment":"The text says the simplified Brandt formula applies under the condition H/Hc2 ≫ 1, but the correct regime is H/Hc2 ≪ 1; at the applied field of 40 mT with Hc2(0) ≈ 4.5 T, H/Hc2 ≈ 0.009, so the text should read H/Hc2 ≪ 1.","section":"III.E, text after Eq. (16)"},{"comment":"The convention for Λ in Eq. (19) should be stated explicitly: with β = 2 the extra term is exp(−Λ²t²), which differs from the conventional Gaussian relaxation form exp(−σ²t²/2) used in the Kubo-Toyabe term; if the conventional form is intended, the conversion Bint = δΛ/γμ in Eq. (21) may need a √2 factor.","section":"III.E, Eq. (19) and Eq. (21)"},{"comment":"The compound is incorrectly written as NbTaO2 in the text near Fig. 2(a) and again in Section IV; it should be NbTaOs2.","section":"III.C and IV"},{"comment":"The statement that 'the absence of oscillatory components in the LF spectra confirms the absence of magnetic ordering' is too strong; the data show no evidence of long-range magnetic order, but dilute static moments would also fail to produce coherent oscillations.","section":"III.E, ZF-μSR discussion"}],"recommendation":"major_revision","confidential_remarks":"This is a competently executed materials characterization paper whose headline claim is the TRSB observation. I recommend that the revised version be reviewed by a muon-spin specialist, because the statistical treatment and physical interpretation of the ZF-μSR fits is the decisive issue. The paper does not appear to misrepresent prior work, and the novelty claim is appropriately framed in the introduction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, quick take on arXiv:2506.12449. The genuinely new thing here is the compound itself: NbTaOs2 is a rhenium-free α-Mn non-centrosymmetric superconductor, and the paper gives a solid bulk characterization. Resistivity, magnetization, specific heat, and TF-μSR line up: Tc ~2.4 K, type-II, fully gapped moderate-coupling s-wave state with Δ(0)/kBTc ≈ 2.0–2.2 from two independent probes, and a Uemura ratio that puts it outside the unconventional region. That part is credible and useful. The citation pattern is fine too—the α-Mn TRSB literature is small and mostly from the same groups, and the prior NbOs2/TaOs papers are the right comparisons.\n\nThe soft spot is the headline claim, TRSB. The ZF-μSR evidence is a 0.008(1) μs⁻¹ increase in an additional relaxation rate Λ below Tc, with ΔZ, Ai, and Abg fixed to normal-state values. The Gaussian Kubo-Toyabe and exp(−Λt)^β forms overlap in the measured time window, so those parameters are degenerate; any temperature drift in the nuclear-dipolar width or a dilute static impurity contribution would be absorbed into Λ. The 5 mT longitudinal-field decoupling only shows the field is static; it does not distinguish a TRSB internal field from impurity or spurious magnetic fields. The abstract says \"suggesting,\" but the conclusion calls it \"the first observation of TRSB in a Re-free α-Mn compound\"—that is an overstatement relative to the evidence.\n\nThere are also several small analysis errors: Eq. (17) mismatches exponents (σ⁻² ratio set equal to λ⁻² ratio, which is dimensionally wrong); the Brandt condition is stated as H/Hc2 ≫ 1 when it should be ≪ 1; and C_ph is printed with a minus sign. None of these are load-bearing if the underlying fits used the correct forms, but they need fixing.\n\nThe data and the compound warrant a serious referee. The authors should deposit raw μSR spectra, correct the typos, and either strengthen the TRSB case—e.g., show that ΔZ is temperature independent in the normal state across the same range, check multiple samples, or report an impurity-sensitive measurement—or soften the conclusion to \"suggestive of TRSB.\" As it stands, the paper is a solid materials-oriented study with an under-supported central claim. I'd send it to review with a clear request for those revisions.","headline":"NbTaOs2 is a genuinely new rhenium-free α-Mn superconductor with solid bulk characterization, but the TRSB headline rests on a tiny relaxation increase whose analysis is underdetermined, and the conclusion overstates the evidence.","tokens_in":16185,"tokens_out":3853,"would_cite":true,"duration_ms":43707,"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":"This paper argues that the new ternary superconductor NbTaOs2 breaks time-reversal symmetry in its superconducting state, making it the first rhenium-free α-Mn compound with this signature.","keywords":["time-reversal symmetry breaking","non-centrosymmetric superconductor","alpha-Mn structure","muon spin relaxation","NbTaOs2","superconducting gap","antisymmetric spin-orbit coupling","type-II superconductor"],"falsifier":"A decisive check would be a zero-field muon experiment on a series of NbTaOs2 samples with controlled purity: if the extra relaxation below Tc disappears or scales with impurity concentration rather than with the superconducting fraction, the assignment to time-reversal symmetry breaking fails. A second check is to measure the same relaxation increase in a sample with a muon site shifted by chemical substitution, since TRSB fields should follow the superconducting order parameter rather than the local defect environment.","tokens_in":14987,"feed_emoji":"🧲","tokens_out":3736,"duration_ms":40878,"temperature":0.7,"pith_summary":"This paper reports a new ternary superconductor, NbTaOs2, and argues that its superconducting ground state breaks time-reversal symmetry. The compound crystallizes in the non-centrosymmetric α-Mn structure, and zero-field muon spin relaxation shows a small extra relaxation rate appearing only below the transition temperature, which the authors interpret as a spontaneous internal field of about 0.1 G. If correct, this is the first rhenium-free α-Mn superconductor to show time-reversal symmetry breaking, a status previously associated mainly with rhenium-based members of the family. The same measurements also indicate a fully gapped, moderately coupled pairing state, so the material combines a conventional-looking gap with an unconventional symmetry-breaking signature.","feed_headline":"Rhenium-free superconductor breaks time-reversal symmetry","feed_subtitle":"Muon data in NbTaOs2 show a spontaneous internal field below Tc, first for a Re-free α-Mn superconductor.","key_machinery":"The central object is the zero-field muon spin relaxation function A(t) = Ai G_KT(t) exp(−(Λt)^β) + Abg, where G_KT is the static Kubo-Toyabe function describing randomly oriented nuclear dipoles. The additional Gaussian relaxation rate Λ is the probe: when Tc is crossed, Λ increases by 0.008(1) μs−1 while the nuclear term is held fixed, and the increase is converted to an internal field through Bint = δΛ/γμ. The structural carrier of the effect is the non-centrosymmetric α-Mn lattice with mixed Nb/Ta 4d/5d sites, which the authors argue enhances antisymmetric spin-orbit coupling.","core_discovery":"The central claim is that NbTaOs2 is an unconventional superconductor in which time-reversal symmetry is broken in the superconducting state. This is inferred from zero-field muon spin relaxation: a static Gaussian Kubo-Toyabe relaxation is observed at all temperatures, and an additional relaxation rate Λ grows below Tc = 2.4 K, corresponding to a spontaneous static field Bint ≈ 0.094 G. Specific heat and transverse-field muon data show a single isotropic nodeless gap with Δ(0)/kBTc ≈ 2.2 and moderate electron-phonon coupling, and the upper critical field reaches the Pauli limit. The authors conclude that NbTaOs2 is the first Re-free α-Mn non-centrosymmetric superconductor with time-reversal symmetry breaking.","pith_inferences":["If the time-reversal symmetry breaking is intrinsic, theory would predict a two-component order parameter such as s+is or s+id for NbTaOs2; a low-temperature specific-heat or Josephson-phase measurement could distinguish such pairing from a single-component state.","The disorder-versus-intrinsic question could be settled by comparing the size of the Λ increase with the residual resistivity ratio in samples with different annealing histories, following the idea that disorder alone can induce TRSB.","A natural extension is to scan neighboring Re-free α-Mn ternaries, for example substituting Os with other 5d elements, to map which 4d/5d site combinations produce time-reversal symmetry breaking.","The same material may exhibit a field-free superconducting diode effect; a transport measurement with an in-plane current and no applied magnetic field would be a direct test."],"forward_implications":["The first Re-free α-Mn superconductor with time-reversal symmetry breaking weakens the idea that rhenium content is required for TRSB in this structure family.","A fully gapped, moderately coupled superconductor with broken time-reversal symmetry provides a concrete candidate for the intrinsic superconducting diode effect.","The spontaneous field scale of about 0.1 G is comparable to other TRSB non-centrosymmetric superconductors, so similar α-Mn ternaries become promising targets for muon-based searches.","The closeness of the upper critical field to the Pauli limit suggests antisymmetric spin-orbit coupling is active, linking the broken inversion symmetry to the measured properties."],"supporting_citations":[{"why":"Shows TRSB detection in Re6Zr by muon spin spectroscopy, the benchmark this paper extends to a Re-free compound.","marker":"[29]"},{"why":"Reports TRSB in Re6Hf, one of the rhenium-based α-Mn cases that motivated the question of whether Re is critical.","marker":"[30]"},{"why":"Provides the Re6Ti TRSB study and the relation Bint = δΛ/γμ used to estimate the internal field.","marker":"[31]"},{"why":"Gives the NbOs2 muon study of a Re-free α-Mn superconductor without TRSB, the direct comparator.","marker":"[38]"},{"why":"Reports nodeless s-wave superconductivity in TaOs without TRSB, another Re-free comparator.","marker":"[39]"},{"why":"Systematic study of TRSB across Re-based superconductors that frames the rhenium-dependence question.","marker":"[43]"},{"why":"Brandt's vortex-lattice formula used to convert transverse-field muon relaxation into the magnetic penetration depth.","marker":"[65]"},{"why":"Defines the static Kubo-Toyabe function used to model zero-field relaxation from nuclear moments.","marker":"[68]"},{"why":"Proposes disorder-driven TRSB, the alternative scenario the paper argues against for NbTaOs2.","marker":"[70]"}],"fun_headline_variants":["Re-free superconductor breaks time-reversal","Time-reversal broken in new Re-free superconductor","First Re-free α-Mn superconductor with broken time-reversal","NbTaOs2: α-Mn superconductor with broken time-reversal","Broken time-reversal in Re-free α-Mn superconductor"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument relies on the assumption that the muon's nuclear-dipolar relaxation, the initial asymmetry, and the background contribution are exactly the same above and below the superconducting transition, so the small extra relaxation must come from new static internal fields rather than from impurities or a spurious magnetic transition.","fun_headline_variants_meta":{"raw":{"variants":["Re-free superconductor breaks time-reversal","Time-reversal broken in new Re-free superconductor","First Re-free α-Mn superconductor with broken time-reversal","NbTaOs2: α-Mn superconductor with broken time-reversal","Broken time-reversal in Re-free α-Mn superconductor"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001124,"raw_usage":{"total_tokens":4629,"prompt_tokens":855,"completion_tokens":3774,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":471,"completion_tokens_details":{"reasoning_tokens":3684}},"tokens_in":471,"tokens_out":3774,"duration_ms":33356,"temperature":1.0,"reasoning_tokens":3684,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:50:08.324758+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be a zero-field muon experiment on a series of NbTaOs2 samples with controlled purity: if the extra relaxation below Tc disappears or scales with impurity concentration rather than with the superconducting fraction, the assignment to time-reversal symmetry breaking fails. A second check is to measure the same relaxation increase in a sample with a muon site shifted by chemical substitution, since TRSB fields should follow the superconducting order parameter rather than the local defect environment.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows TRSB detection in Re6Zr by muon spin spectroscopy, the benchmark this paper extends to a Re-free compound."},{"cited_title":"Singh, J","cited_arxiv_id":null,"evidence_quote":"Reports TRSB in Re6Hf, one of the rhenium-based α-Mn cases that motivated the question of whether Re is critical."},{"cited_title":"Singh, K","cited_arxiv_id":null,"evidence_quote":"Provides the Re6Ti TRSB study and the relation Bint = δΛ/γμ used to estimate the internal field."},{"cited_title":"Singh, K","cited_arxiv_id":null,"evidence_quote":"Gives the NbOs2 muon study of a Re-free α-Mn superconductor without TRSB, the direct comparator."},{"cited_title":"Singh, K","cited_arxiv_id":null,"evidence_quote":"Reports nodeless s-wave superconductivity in TaOs without TRSB, another Re-free comparator."},{"cited_title":"Shang, M","cited_arxiv_id":null,"evidence_quote":"Systematic study of TRSB across Re-based superconductors that frames the rhenium-dependence question."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Brandt's vortex-lattice formula used to convert transverse-field muon relaxation into the magnetic penetration depth."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes disorder-driven TRSB, the alternative scenario the paper argues against for NbTaOs2."}],"review_version":1}