{"id":"8901c105-7622-43ef-a64e-1937b621f8fe","arxiv_id":"2505.19615","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using two crystallographically distinct Te sites to cancel the superconducting diamagnetic shift, the authors show that the spin susceptibility along the b and c axes decreases in the superconducting state of ultraclean UTe2, implying a d-vector with components along all three crystal axes.","lead":"This paper measures tiny changes in the NMR Knight shift along two crystal axes of the superconductor UTe2 in its superconducting state, and shows that the changes reflect a real decrease in spin susceptibility rather than a mundane magnetic shielding effect. The result helps pin down the spin-triplet pairing symmetry of UTe2, a leading candidate for topological superconductivity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The c-axis spin-susceptibility decrease rests on a two-peak fit of heavily overlapping 125Te NMR lines below Tc; the authors concede Kc,I may be overestimated, and no error bars are given for the differences, so the interval decrease could be a fitting artifact.","rationale":"After reading the paper carefully, the cleanest way to establish the central claim would be a robust c-axis difference. The manuscript's own acknowledgment of possible overestimation of Kc,I is a manuscript-stated limitation (Sec. III), and the absence of error bars in Fig. 5 makes the drop in Kc,I - Kc,II hard to evaluate. The site-independence of K_dia, though assumed, is physically well-justified by the long vortex-lattice length scale relative to the unit cell, so I do not think that is the most dangerous point. The b-axis data support a spin-susceptibility decrease along b, but the all-three-components conclusion requires the c-axis evidence. A constrained refit with error propagation would settle whether the c-axis interval decrease is real. Since the reader already returned a conditional verdict, my recommendation remains conditional (UNCHANGED), with the requested reanalysis as a condition.","tokens_in":11685,"tokens_out":6950,"duration_ms":71737,"concrete_test":"Reanalyze the raw H || c spectra below Tc with a constrained two-peak fit: fix the relative intensities to 1:1 (equal Te site populations) and constrain the linewidths to values calibrated from the normal-state spectra, allowing only the peak positions to vary. Compute pointwise 68% and 95% confidence intervals for Kc,I - Kc,II (e.g., via Monte Carlo or bootstrapping of residuals). If the low-temperature difference is consistent with the normal-state value within 2 sigma, the c-axis spin-susceptibility decrease is not established; if the decrease remains significant, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that spin susceptibility decreases along the c axis depends on the observed decrease of Kc,I - Kc,II in Fig. 5. In H || c (Sec. III), the two Te NMR peaks are partially overlapped and become 'unclear' below Tc due to broadening and a larger decrease of the Te(I) shift. The peak positions are extracted from a two-peak Lorentzian fit, and the authors explicitly state that 'the decrease in Kc,I may have been overestimated due to this fitting uncertainty.' If Kc,I is overestimated downward, the interval Kc,I - Kc,II decreases even if the true spin susceptibility is unchanged, producing exactly the signature claimed as evidence. The manuscript provides no error bars for the fitted positions or for the differences plotted in Fig. 5, so the significance of the drop cannot be evaluated. The b-axis result is comparatively clean, but the d-vector conclusion (components along all three axes) specifically requires the c-axis interval decrease to be real. The reader's alternate concern about site-independence of the diamagnetic shift is less severe: in the mixed state at ~0.8 T the vortex-lattice field varies on a scale (~50 nm) much larger than the unit cell, so both Te sites should indeed experience essentially the same diamagnetic local field.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports 125Te NMR Knight-shift measurements on an ultraclean UTe2 single crystal with Tc = 2.1 K, for H applied along the b and c axes, resolved at the two crystallographically distinct Te sites. The authors observe small decreases of Kb and Kc below Tc that are comparable in size to the expected superconducting diamagnetic shift. To remove the diamagnetic contribution, they use the difference between the two Te-site Knight shifts, arguing that the diamagnetic shift is site-independent. They report a decrease of this difference for both H || b and H || c, which, combined with the previously reported large a-axis Knight-shift decrease, leads them to conclude that the spin susceptibility decreases along all three axes and that the d-vector has components along all three crystal axes. They also analyze the b-axis spin shift using full-gap, point-node, and line-node gap models, finding that the line-node model can be ruled out while full-gap and point-node scenarios cannot be distinguished.","tokens_in":11961,"tokens_out":7858,"duration_ms":75445,"significance":"If the c-axis result is quantitatively secure, this is an important experimental constraint on the UTe2 superconducting order parameter: it would imply a spin-triplet d-vector with components along all three axes, favoring an Au-type state or f-wave pairing and distinguishing the ultraclean 2.1 K sample from earlier lower-Tc samples. The b-axis part of the paper is convincing: the two Te resonances are well separated, the site-difference method cancels the common-mode diamagnetic shift, and the authors are appropriately cautious about auxiliary model fits. The paper also has the strength of using a disorder-free sample and of transparently acknowledging the limitations of the c-axis fit and of the Kdia_c determination. However, the central all-axes conclusion depends on a c-axis difference whose statistical and systematic uncertainties are not quantified, and the wording 'unambiguously decreases' is stronger than the presented evidence.","major_comments":[{"comment":"The conclusion that the spin susceptibility decreases along the c axis rests entirely on the temperature dependence of Kc,I − Kc,II. In the same section the authors state that the two peaks are 'partially overlapped,' that the separation between the two peaks becomes 'unclear' in the superconducting state, and that 'the decrease in Kc,I may have been overestimated due to this fitting uncertainty.' No error bars are reported for the fitted peak positions or for the differences plotted in Fig. 5. Because a downward bias in the fitted Kc,I directly produces a spurious decrease in Kc,I − Kc,II, the observed drop cannot currently be distinguished from an artifact of the two-peak Lorentzian fit. To support the central d-vector claim, the authors should provide error propagation from the fits, show representative fitted spectra with residuals at several temperatures, and test the robustness of the decrease under alternative fitting choices (for example, fixed linewidths, different line shapes, or constraints from the normal-state peak separation). If such an analysis is not possible, the c-axis conclusion should be moderated.","section":"Section III, Fig. 5"},{"comment":"The extraction of ΔK_spin_b,II depends on Γb, on K_dia_b(0), and on the assumed temperature form K_dia_b(T) = K_dia_b(0)[1 − (T/Tc)^2]. The manuscript reports Γb = 1.32 ± 0.01 but does not propagate the uncertainty of the linear fit or of K_dia_b(0) into ΔK_spin_b,II or into the gap-model comparison. The stated agreement between ΔK_spin_b,II and the b-axis site difference is not an independent check, since both quantities are derived from the same raw Knight-shift data. In addition, the 1 − (T/Tc)^2 form is introduced without justification for a type-II superconductor in the mixed state at 0.8 T. This analysis does not affect the qualitative difference-based conclusion, but it does affect the quantitative claims about the magnitude and temperature dependence of the spin susceptibility and the subsequent gap-structure discussion; those claims need uncertainty estimates and a justification of the temperature form.","section":"Section III, Eq. (1) and Fig. 6"}],"minor_comments":[{"comment":"The sentence 'Figure 5 shows Kb,II − Kb,I for H ∥ b and Kc,I − Kb,II for H ∥ c' contains a typo: the second quantity should be Kc,I − Kc,II.","section":"Section III, text near Fig. 5"},{"comment":"The word 'Lorentian' appears instead of 'Lorentzian' in the description of the two-peak fit.","section":"Fig. 1 caption and Section III"},{"comment":"The phrase 'the large reduction in the quantized a axis' is unclear; it should likely read 'the large reduction in the a-axis Knight shift' or similar.","section":"Section III, near the end"},{"comment":"The caption says 'in (a) H ∥ b and H ∥ c below 4 K'; it should specify '(a) H ∥ b and (b) H ∥ c' to match the two panels.","section":"Fig. 3 caption"},{"comment":"Given the acknowledged c-axis fitting uncertainty, the word 'unambiguously' in the abstract and conclusion is too strong unless quantitative error analysis is added; 'is consistent with' would be more precise at the present level of evidence.","section":"Abstract and Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a direct extension of the same group's prior UTe2 NMR work, and the novelty lies in applying the site-difference method to the ultraclean 2.1 K sample and in reporting the c-axis result. The main risk is that the c-axis fit uncertainty could invalidate the three-axis d-vector conclusion; I would press for quantitative error analysis and robustness tests before publication. The b-axis result alone would be a solid but narrower contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The genuinely new thing is the b/c-axis Knight shift measurement on the Tc = 2.1 K sample with the two-Te-site subtraction. The b-axis result is clean: the two peaks are well separated, Kb,II - Kb,I clearly drops below Tc, and the drop survives a model-free subtraction of any common-mode diamagnetic shift. That is real evidence for a spin-susceptibility decrease along b, and it makes the earlier a-axis result more credible. The authors also give a reasonable consistency check by extracting Kdia_b and showing the resulting spin shift tracks the site-difference curve.\n\nThe c-axis leg is softer. The two 125Te lines overlap, the fit becomes unclear below Tc, and the authors admit Kc,I may be overestimated. Since Fig. 5 has no error bars, the size and even the existence of the c-axis interval decrease is hard to judge. The stress-test note is right: if Kc,I is biased downward by the fit, part or all of the apparent c-axis spin decrease could be an artifact. That matters because the all-three-axes d-vector conclusion, and the Au-state suggestion, lean on the c-axis being real. I don't think this is fatal—the paper flags the problem—but it needs to be addressed with error bars, a constrained or blinded fit, or independent c-axis data before I'd call the central claim airtight.\n\nThe site-independence of the diamagnetic shift, which the reader flagged, is less of a worry. At 0.8 T in the mixed state the vortex field varies on a scale much larger than the Te-Te separation, so a common-mode shift is a reasonable assumption. The b-axis diamagnetic separation does use a fitted Kdia_b(0) and assumes Gamma_b from the normal state carries over, but that is a secondary estimate, not the load-bearing evidence.\n\nThe gap-structure discussion is appropriately tentative: they can rule out the line-node model but cannot distinguish full-gap from point-node, and they call for 1/T1 measurements. The paper is honest, well cited, and the authors don't hide the c-axis weakness. It is a meaningful step in a contested problem. I'd send it to a serious referee; the right referee will ask for error bars and a more robust c-axis analysis, but the b-axis result and the subtraction method deserve publication.","headline":"Good b-axis evidence for a spin-susceptibility drop in clean UTe2; the c-axis leg needs error bars before the all-three-axes d-vector conclusion is secure.","tokens_in":12583,"tokens_out":3258,"would_cite":true,"duration_ms":129097,"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 establishes that the spin susceptibility of UTe2 drops along all three crystallographic axes in the superconducting state, not just the a axis, by cancelling the superconducting diamagnetic background with a difference of…","keywords":["UTe2","spin-triplet superconductivity","Knight shift","125Te NMR","d-vector","spin susceptibility","heavy-fermion superconductor"],"falsifier":"Repeat the b- and c-axis Knight-shift measurements at a second applied field well above Hc1 (for example 1.5 T) and check whether Kb,II − Kb,I and Kc,I − Kc,II show the same drop below Tc; a field-dependent drop would mean the diamagnetic shielding affects the two Te sites differently, and the spin-susceptibility conclusion would collapse.","tokens_in":11485,"feed_emoji":"🧲","tokens_out":6407,"duration_ms":60478,"temperature":0.7,"pith_summary":"The paper aims to settle whether the tiny drops in the b- and c-axis Knight shifts of the spin-triplet superconductor UTe2 below its 2.1 K transition come from a real loss of spin susceptibility or merely from the superconducting diamagnetic shielding. The authors measure 125Te NMR at two crystallographically distinct Te sites and subtract one site's shift from the other, which cancels any site-independent diamagnetic background. They find that the difference Kb,II − Kb,I and Kc,I − Kc,II clearly drops at Tc, proving the spin susceptibility falls along both axes. Combined with the previously reported large a-axis drop, this establishes that the d-vector has finite components along all three crystal axes, an important constraint on the pairing state.","feed_headline":"Knight shifts show UTe2 spin drops on all three axes","feed_subtitle":"Subtracting two tellurium-site shifts cancels the diamagnetic background and reveals a true spin drop along b and c.","key_machinery":"The central object is the difference of 125Te Knight shifts measured at the two crystallographically distinct Te sites, Te(I) and Te(II), for each field direction. Because the orbital shift is temperature-independent and the superconducting diamagnetic shift is assumed to be site-independent, the subtraction Kα,II − Kα,I cancels the diamagnetic term and leaves only the spin contribution proportional to (Aα,II − Aα,I)χspin(T). A supplementary Γ-ratio analysis, using the linear relation between the two site shifts below 20 K, estimates the diamagnetic shift K_dia for the b axis and confirms that the spin part is consistent with the direct site-difference result.","core_discovery":"This work reports 125Te Knight-shift measurements along the b and c axes of an ultraclean UTe2 single crystal with Tc = 2.1 K, down to 70 mK. In the superconducting state, the raw b- and c-axis Knight shifts decrease by only about 3% of their normal-state values, comparable to the estimated diamagnetic shielding, so the paper cannot rely on those raw changes alone. The decisive step is to take the difference of the Knight shifts measured at the two crystallographically distinct Te sites; because the diamagnetic shift is assumed identical at both sites, it cancels in the difference, leaving only the spin part. The difference drops below Tc for both field directions, showing that the spin susceptibility along the b and c axes genuinely decreases. Together with the large a-axis reduction reported earlier, the paper concludes that the d-vector has components along all three crystal axes, consistent with an Au odd-parity pairing state or an f-wave state, and that the superconducting gap is likely anisotropic full-gap or point-node, not line-node.","pith_inferences":["If the site-independence of the diamagnetic shift is generic, the same two-site subtraction could be applied to other multi-site superconductors with small Knight-shift changes, converting the diamagnetic background into a built-in null reference.","The c-axis analysis is the least certain because the two Te peaks overlap and Γc is close to 1; a measurement at higher field or on a differently oriented sample that resolves the two peaks could tighten the c-axis spin-drop claim.","The nearly temperature-independent spin susceptibility below 1 K leaves open a finite residual density of states; low-temperature 1/T1 measurements would test whether the gap is truly full.","If the d-vector truly has all three components, rotating the field in the bc and ab planes should reveal field-induced d-vector reorientation, connecting these results to the field-reinforced superconducting phases of UTe2."],"forward_implications":["The spin susceptibility of UTe2 decreases along the a, b, and c axes in the superconducting state, so the d-vector has nonzero components along all three axes.","The single-component B3u scenario, which has no a-axis spin reduction, is ruled out for the ultraclean 2.1 K sample.","The gap is not line-nodal; the low-temperature spin susceptibility is compatible with a full gap or point nodes only if 2Δ(0)/kBTc exceeds the BCS value of 3.5.","The absence of Pauli depairing near the estimated Pauli limit, despite the large a-axis spin drop, supports spin-triplet pairing with field-aligned spins.","The difference-of-sites method provides a way to extract spin susceptibility changes even when the raw diamagnetic shift is of the same size as the spin effect."],"supporting_citations":[{"why":"Reports the large a-axis Knight-shift reduction in the same 2.1 K sample, providing the a-axis input for the three-axis conclusion.","marker":"[23]"},{"why":"Shows the earlier apparent a-axis invariance came from a non-superconducting fraction, motivating the use of the ultraclean sample.","marker":"[21]"},{"why":"Describes the molten-salt flux growth that produced the ultraclean Tc = 2.1 K crystals.","marker":"[22]"},{"why":"Establishes that the two Te-site Knight shifts scale with bulk susceptibility, the basis for the site-difference analysis.","marker":"[27]"},{"why":"Supplies lower-critical-field values used to estimate the diamagnetic shift for comparison.","marker":"[33]"},{"why":"Proposes the Au odd-parity pairing state with d-vector components along all three axes, the main candidate consistent with the result.","marker":"[40]"},{"why":"Calculates paramagnetic effects that agree with the large a-axis reduction and support the triplet interpretation.","marker":"[41]"},{"why":"Assigns the two Te sites and documents the anisotropic spin-susceptibility response, establishing the site labeling used here.","marker":"[15]"}],"fun_headline_variants":["UTe2 spin susceptibility drops along all three axes","Knight shift reveals UTe2 spin drop on all three axes","Distinct Te sites expose UTe2 spin drop along all axes","Subtle Knight shift change confirms UTe2 spin drop on all axes","Te-site difference proves UTe2 spin drop along all axes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the superconducting diamagnetic shift is exactly the same at the two Te sites, so that subtracting one Knight shift from the other removes it entirely; if the mixed-state field distribution at 0.8 T shifts the two sites differently, the observed difference drop could be diamagnetic rather than spin.","fun_headline_variants_meta":{"raw":{"variants":["UTe2 spin susceptibility drops along all three axes","Knight shift reveals UTe2 spin drop on all three axes","Distinct Te sites expose UTe2 spin drop along all axes","Subtle Knight shift change confirms UTe2 spin drop on all axes","Te-site difference proves UTe2 spin drop along all axes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000711,"raw_usage":{"total_tokens":3209,"prompt_tokens":965,"completion_tokens":2244,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":2156}},"tokens_in":581,"tokens_out":2244,"duration_ms":16561,"temperature":1.0,"reasoning_tokens":2156,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:11:38.454463+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the b- and c-axis Knight-shift measurements at a second applied field well above Hc1 (for example 1.5 T) and check whether Kb,II − Kb,I and Kc,I − Kc,II show the same drop below Tc; a field-dependent drop would mean the diamagnetic shielding affects the two Te sites differently, and the spin-susceptibility conclusion would collapse.","supporting_citations":[{"cited_title":"Matsumura, H","cited_arxiv_id":null,"evidence_quote":"Reports the large a-axis Knight-shift reduction in the same 2.1 K sample, providing the a-axis input for the three-axis conclusion."},{"cited_title":"Kitagawa, K","cited_arxiv_id":null,"evidence_quote":"Shows the earlier apparent a-axis invariance came from a non-superconducting fraction, motivating the use of the ultraclean sample."},{"cited_title":"Aoki, Molten Salt Flux Liquid Transport Method for Ultra Clean Single Crystals UTe2, J","cited_arxiv_id":null,"evidence_quote":"Describes the molten-salt flux growth that produced the ultraclean Tc = 2.1 K crystals."},{"cited_title":"Tokunaga, H","cited_arxiv_id":null,"evidence_quote":"Establishes that the two Te-site Knight shifts scale with bulk susceptibility, the basis for the site-difference analysis."},{"cited_title":"Ishihara, M","cited_arxiv_id":null,"evidence_quote":"Supplies lower-critical-field values used to estimate the diamagnetic shift for comparison."},{"cited_title":"Ishizuka, S","cited_arxiv_id":null,"evidence_quote":"Proposes the Au odd-parity pairing state with d-vector components along all three axes, the main candidate consistent with the result."},{"cited_title":"Hiranuma and S","cited_arxiv_id":null,"evidence_quote":"Calculates paramagnetic effects that agree with the large a-axis reduction and support the triplet interpretation."},{"cited_title":"Nakamine, K","cited_arxiv_id":null,"evidence_quote":"Assigns the two Te sites and documents the anisotropic spin-susceptibility response, establishing the site labeling used here."}],"review_version":1}