{"id":"e9284027-9b38-4b55-9947-3a4e1d745a8a","arxiv_id":"2501.13178","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Muon Knight shift data on molten-salt-flux-grown UTe2 show site-dependent behavior: one muon site preserves heavy-electron Kondo scaling to Tc, while other sites reveal relocalizing U 5f moments below about 12 K.","lead":"Muon measurements on cleaner UTe2 crystals show that the heavy-electron signal follows the universal Kondo-lattice scaling down to low temperature at one muon site, while at other sites the uranium moments relocalize below 12 K. This suggests the normal state holds both itinerant and localized 5f electrons at once, which matters for understanding the exotic superconductivity of UTe2.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Site-assignment inconsistency in §II B is load-bearing: the measured muon-site population ratio matches no DFT/Immm combination, so the K1-vs-K2/K4 coexistence inference lacks a defensible microscopic basis.","rationale":"The raw data are valuable: the MSF crystals are cleaner than CVT, the K1 component's continued scaling to Tc is new, and the comparison between samples is a genuine extension. However, the abstract-level claim that itinerant and localized 5f states coexist spatially rests on treating K1 versus K2/K4 as site-resolved probes of different orbital character. That treatment requires a quantitative muon-site model. The paper's DFT section supplies five candidate sites, but the text explicitly concedes that the measured population ratio cannot be matched to any combination and is incompatible with Immm multiplicities. This is not a disagreement with consensus; it is an internal limitation the authors acknowledge. A wrong site assignment could make the K1/K2 difference a consequence of different hyperfine tensors at chemically equivalent electronic states, or of the misalignment effects they invoke for K4. The reader's conditional verdict is appropriate; the proposed test would decide whether the site-level interpretation can be rescued. I see no basis to reject the paper, but also no basis to upgrade to acceptance without resolving the site assignment.","tokens_in":14703,"tokens_out":8362,"duration_ms":98036,"concrete_test":"Use the DFT candidate-site geometries and energies from the Supplemental Material together with Immm multiplicities to enumerate every possible occupancy combination and compute the expected TF-µSR population ratio; check whether any combination reproduces the measured a1:a2:a3 ratio (and the a4 split). If none does, the site-resolved coexistence claim should be explicitly softened or supported by independent site-assignment evidence, such as field-orientation studies or muon-induced CEF fits.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the assignment of the four muon precession components to distinct crystallographic stopping sites whose Knight shifts reveal different 5f-orbital character. The paper itself, in §II A and §II B, states that the population ratio inferred by TF-µSR for the MSF-grown mosaic does not match any combination of the DFT-computed candidate sites and is incompatible with the multiplicities of positions with the Immm space group. It also argues that K4 is not an independent site but a misalignment-affected version of K2, and it excludes K3 from the universal-scaling analysis because the point-charge CEF model bears little resemblance to the parameters needed to describe the bulk susceptibility. If K1 and K2/K4 cannot be assigned to known U-ladder sites, or if their shifts are dominated by different hyperfine couplings to a single electron fluid, then the central conclusion—coexistence of Kondo hybridization with localized AFM-coupled moments—is not established. The KHF extraction also relies on an assumed T* = 30 K and an unstated K0_HF normalization, but the unresolved site identity is the more fundamental gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports transverse-field muon spin rotation (TF-µSR) measurements on molten salt-flux (MSF) grown UTe2 single crystals with the field along the c axis, and compares the results with previous chemical-vapor-transport (CVT) grown crystals. Four muon precession components are identified. The temperature dependence of the muon Knight shift for the different components is compared with the bulk magnetic susceptibility and with a universal two-fluid scaling function for heavy-fermion materials. The authors find that K1 follows the universal scaling curve down to the superconducting transition, whereas K2 and K4 deviate from this curve below Tr ≈ 12 K. They interpret this deviation as a relocalization of U 5f moments with antiferromagnetic coupling, while the persistence of K1 on the scaling curve indicates coexisting Kondo hybridization and itinerant heavy-electron behavior. The paper concludes that relocalization is an intrinsic property of UTe2 and that localized and itinerant 5f states coexist in the normal state.","tokens_in":14843,"tokens_out":3993,"duration_ms":47087,"significance":"If established, the conclusion that Kondo coherence and localized antiferromagnetically coupled U 5f moments coexist in UTe2 would be an important step toward understanding the normal state from which its unconventional superconductivity emerges. The use of MSF-grown single crystals, which are free of the magnetic clusters found in CVT-grown samples, strengthens the claim that the reported behavior is intrinsic. The comparison with an external universal scaling benchmark from the two-fluid model is a constructive way to test Kondo coherence, and the inclusion of both MSF and CVT data adds useful information. However, the site-resolved interpretation on which the coexistence claim rests is not yet defensible, because the paper itself reports that the muon-site population ratios are incompatible with the DFT-predicted sites and with the Immm space-group multiplicities. The central claim therefore requires additional work.","major_comments":[{"comment":"The manuscript states that the population ratio a1:a2:a3 inferred by TF-µSR 'does not match any combination of the DFT-computed candidate sites, and is incompatible with the multiplicities of positions with the Immm space group.' This is a self-acknowledged unresolved assignment. Because the central conclusion—that K1 and K2/K4 report different local 5f orbital character at distinct crystallographic sites—requires exactly such an assignment, the coexistence inference is not currently established. The authors should either provide a defensible site assignment (e.g., with improved DFT including muon-induced distortions and quantitative relative populations) or explicitly reframe the conclusions as model-dependent on an unverified site identity.","section":"Section II A, Table I"},{"comment":"The paper identifies K4 as not an independent site but a misalignment-affected version of K2, based on the similarity of a2+a4 to a2 in other samples and on linewidth arguments. The spatial-coexistence claim therefore reduces to the difference between K1 and K2. This is acceptable in principle, but the paper does not rule out a simpler alternative: a single electron fluid with different hyperfine couplings at different muon sites could produce different temperature dependencies without any spatial coexistence of itinerant and localized 5f states. No quantitative hyperfine coupling estimates for the candidate muon sites are given, so the orbital-selective interpretation is speculative. A concrete calculation of the contact and dipolar hyperfine fields at the candidate sites would be needed to support the claim.","section":"Section II A, Figs. 2-3"},{"comment":"The universal scaling test assumes T* = 30 K and normalizes each component's KHF by a material-dependent K0_HF. Because K0_HF is an adjustable amplitude per component, Fig. 4 tests only the functional form of Eq. (3), not the absolute magnitude. The paper should report a quantitative goodness-of-fit (e.g., chi-squared per degree of freedom) for K1 and for K2/K4 against Eq. (3), state how K0_HF was determined for each component, and discuss the sensitivity of the Tr ≈ 12 K deviation to the assumed T* and to the choice of high-temperature baseline. As written, the claim that K1 follows the universal curve down to Tc while K2 and K4 deviate relies on visual inspection.","section":"Section II C, Fig. 4 and Eq. (3)"},{"comment":"K3 accounts for 14.4% of the MSF signal and 18% of the CVT signal, yet it is excluded from the two-fluid analysis. The authors justify this by noting that the point-charge CEF model 'bears little resemblance' to the parameters needed to describe the bulk susceptibility. That is an honest caveat, but it means the coexistence conclusion is based on a subset of muon stopping sites. The paper should state explicitly what behavior K3 is expected to show under the proposed site assignments—for example, whether it should obey universal scaling or exhibit relocalization—and how its inclusion or exclusion affects the central claim.","section":"Section II A, discussion of K3"}],"minor_comments":[{"comment":"The word 'latttice' should be corrected to 'lattice'.","section":"Introduction"},{"comment":"The demagnetization and Lorentz corrections are combined in a single term with a factor (1/3 - N). For the mosaic geometry, N is not uniquely defined; the authors should specify how N was determined for the five-crystal mosaic.","section":"Section II A, Eq. (2)"},{"comment":"Panel (g) plots K3 against χa, whereas panels (e), (f), and (h) plot against χc. The caption should state this difference explicitly in the figure caption rather than only in the main text.","section":"Fig. 2 caption"},{"comment":"The notation T* appears without units in several places in Fig. 4; the axis label 'T/T*' should include 'with T* = 30 K' for clarity.","section":"Section II C"}],"recommendation":"major_revision","confidential_remarks":"The paper reports high-quality data on an important material, and the comparison between MSF and CVT samples is valuable. However, the central claim of coexistence of Kondo coherence and localized moments depends on muon-site assignments that the authors themselves admit are inconsistent with their DFT calculations and with the Immm space-group multiplicities. This is a load-bearing gap that cannot be closed by minor edits. I would be willing to reconsider a revised version that either provides a defensible site assignment with quantitative hyperfine calculations or substantially weakens the spatial-coexistence interpretation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real news here is site-resolved: in the cleaner MSF crystals, one muon component (K1) follows the two-fluid scaling curve down to Tc, while K2 and K4 roll away from it below ~12 K. That is a concrete extension of the group’s earlier CVT work and a good argument that the relocalization trend is not just sample-dependent impurity physics. The paper is also honest about its main weakness: the muon stopping-site assignment. Section II B admits the TF-muSR site population matches no combination of DFT candidate sites and is incompatible with Immm multiplicities; K4 is treated as a misalignment-affected version of K2; K3 is excluded through a point-charge CEF model the authors themselves say is unreliable. That matters because the central inference — coexisting itinerant heavy-electron fluid and localized AFM-coupled moments at distinct 5f orbitals — rests on assigning K1 and K2/K4 to sites with different local 5f character. If K1 and K2 are just two hyperfine couplings to the same electron fluid, the site-dependent scaling behavior is still an interesting experimental fact, but it is not evidence of orbital-selective coexistence. The analysis also needs more transparency: T*=30 K is assumed, K0_HF normalization is not stated, and K_HF is obtained by subtracting a linear baseline fit to the same data. Quantitative fit statistics and residuals would let the reader judge whether the sub-Tr deviation is real and whether K1 genuinely tracks the universal curve. None of this is fatal; the data appear to be of good quality and the comparison between MSF and CVT samples is well motivated. The paper deserves a serious referee. A revision should either constrain the site model with better DFT/dipolar calculations or soften the coexistence claim to a site-dependent Knight-shift anomaly. I would cite it for the MSF muon data and would put it on a reading group list for UTe2 people. Send it out.","headline":"Site-resolved muon Knight shift in clean MSF UTe2 makes the relocalization look intrinsic, but the coexistence conclusion leans on muon-site assignments the paper itself admits are shaky.","tokens_in":15543,"tokens_out":3457,"would_cite":true,"duration_ms":36493,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Muon-spin measurements on clean UTe2 crystals show that, just above the superconducting transition, the material's 5f electrons split into an itinerant heavy-electron fluid and localized moments with antiferromagnetic correlations, making…","keywords":["UTe2","muon spin rotation","Knight shift","Kondo lattice","heavy-electron fluid","relocalization","two-fluid model","antiferromagnetic correlations"],"falsifier":"A decisive test would be a site-resolved measurement that fixes the muon stopping sites in the same samples, for example by combining transverse-field muon spin rotation with muon channeling or by matching observed site populations to calculated crystallographic sites: if the K1 signal cannot be tied to a distinct site with persistent Kondo hybridization while K2 and K4 correspond to relocalizing moments, the coexistence claim fails.","tokens_in":14425,"feed_emoji":"🧲","tokens_out":6391,"duration_ms":59054,"temperature":0.7,"pith_summary":"The paper sets out to decide whether the apparent 'relocalization' of uranium 5f electrons in UTe2, previously seen in a chemically-grown crystal, is intrinsic to the material or an artifact of defects. The authors use muon spin rotation on cleaner molten-salt-flux crystals and find both signatures at once: at one muon site the heavy-electron fluid follows a universal two-fluid scaling curve down to the superconducting transition, while at other sites the same quantity departs from that curve below about 12 K, signaling that the moments are becoming localized again and coupled antiferromagnetically. The conclusion is that UTe2's normal state is a coexistence of Kondo hybridization and localized-moment magnetism, and that this coexistence is a genuine property of the clean material preceding superconductivity.","feed_headline":"UTe2 keeps both heavy electrons and local magnets","feed_subtitle":"Clean crystals show 5f electrons split into a heavy Fermi liquid and antiferromagnetic local moments down to Tc.","key_machinery":"The carrying mechanism is the muon Knight shift measured by transverse-field muon spin rotation, decomposed into four precession components assigned to distinct muon stopping sites. The heavy-electron contribution $K_{\\mathrm{HF}}$ to each component is isolated by subtracting the high-temperature linear $K$-versus-susceptibility extrapolation, and is then compared with the two-fluid model's universal scaling function $K_{\\mathrm{HF}}(T) = K^0_{\\mathrm{HF}}(1 - T/T^*)^{3/2}[1 + \\ln(T/T^*)]$, where $T^* \\sim 30$ K is the Kondo-coherence crossover. A component that follows the universal curve is reading a coherent heavy Fermi liquid, while a component that falls below it below $T_r \\sim 12$ K is reading moments that are re-localizing and beginning to interact antiferromagnetically.","core_discovery":"On the paper's own terms, the central discovery is that the normal state of UTe2 supports two electronic populations simultaneously. Transverse-field muon Knight shift data from molten-salt-flux-grown single crystals show that the heavy-electron component $K_{\\mathrm{HF}}(T)$ at one muon site (K1) follows the universal two-fluid scaling function $K_{\\mathrm{HF}} = K^0_{\\mathrm{HF}}(1 - T/T^*)^{3/2}[1 + \\ln(T/T^*)]$ with $T^* \\sim 30$ K all the way down to $T_c$, while at the K2 and K4 sites the same component turns downward below $T_r \\sim 12$ K, indicating a reversal of Kondo hybridization and relocalization of U 5f moments with antiferromagnetic coupling. Because the molten-salt-flux crystals lack the magnetic clusters found in chemically-vapor-transport crystals, the authors argue that this site-dependent behavior cannot be blamed on disorder and is intrinsic. The coexistence of universal scaling at one site and departure from it at others is interpreted as spatially separated, or site-selectively sensed, itinerant and localized 5f states.","pith_inferences":["If the coexistence is real, the superconducting pairing in UTe2 may be favored by the antiferromagnetic fluctuations that develop as localized moments emerge below about 12 K, a connection that could be tested by tracking how $T_c$ and $T_r$ move together under pressure or strain.","The paper's own density-functional-theory muon-site calculations do not reproduce the observed transverse-field muon-spin-rotation site populations, so a decisive test of the spatial-coexistence reading is to identify the K1 and K2 stopping sites experimentally, for example through muon channeling or site-selective spectroscopy.","A natural extension is to apply the same two-fluid scaling analysis to 125Te NMR Knight shift data; if NMR sees no sign of relocalization, the phenomenon may be restricted to muon-probed local environments rather than being a bulk electronic change."],"forward_implications":["Relocalization of U 5f electrons is an intrinsic property of clean UTe2, not a consequence of uranium deficiency, atomic disorder, or magnetic clusters in lower-quality crystals.","The normal state immediately above $T_c$ is a mixed state containing both a heavy-electron fluid and antiferromagnetically correlated local moments, so models of the superconductivity must start from this dual character rather than from a single homogeneous Fermi liquid.","The departure at $T_r \\sim 12$ K places UTe2 in the same class as antiferromagnetic heavy-fermion compounds such as CeRhIn5 and CePt2In7, where Kondo screening partially breaks down before magnetic order, supporting the idea that UTe2 is close to an antiferromagnetic instability at ambient pressure.","The site-dependence of the effect is consistent with orbital-selective Kondo hybridization, in which some U 5f orbitals remain delocalized, as sensed by the K1 muon site, while others relocalize, as sensed by the K2 and K4 sites.","In the chemically-vapor-transport-grown crystal the K1 site did not show the clean universal scaling seen in the molten-salt-flux crystal, suggesting that magnetic clusters in the older crystals disrupt the local Kondo coherence that the clean crystals preserve."],"supporting_citations":[{"why":"Previous muon Knight shift study on a chemically-vapor-transport-grown UTe2 crystal, providing the earlier observation of relocalization and the comparison data used throughout.","marker":"[9]"},{"why":"Supplies the universal two-fluid scaling function that defines the expected heavy-electron contribution to the Knight shift.","marker":"[6]"},{"why":"Zero-field muon study on the same molten-salt-flux crystals, showing no magnetic clusters and supporting the sample quality used to rule out disorder artifacts.","marker":"[16]"},{"why":"Establishes the two-fluid behavior and relocalization in antiferromagnetic heavy-fermion compounds, providing the analogy for interpreting the downturn below $T_r$.","marker":"[8]"},{"why":"Documents magnetic clusters in chemically-vapor-transport-grown UTe2 and gives the initial muon-site calculation that the present work extends.","marker":"[13]"},{"why":"Theoretical work on orbital-selective Kondo hybridization in UTe2, used to explain why different muon sites sense different degrees of localization.","marker":"[50]"},{"why":"Inelastic neutron scattering showing antiferromagnetic fluctuations that saturate near 12 K, supporting the interpretation of $T_r$ as the onset of antiferromagnetic correlations.","marker":"[31]"},{"why":"Evidence for a pressure-induced antiferromagnetic quantum critical point in UTe2, supporting the claim that the material is close to an antiferromagnetic instability at ambient pressure.","marker":"[42]"}],"fun_headline_variants":["UTe2 hosts both heavy electrons and local magnets","Coexisting Kondo and local moments in UTe2's normal state","Muon spin rotation finds dual 5f states in UTe2","UTe2 splits its 5f electrons into two behaviors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each muon precession component comes from a distinct, identifiable crystallographic stopping site whose local surroundings determine whether it senses itinerant or localized 5f electrons, and the paper's own density-functional-theory site calculations do not reproduce the observed muon-site populations, leaving that premise unsecured.","fun_headline_variants_meta":{"raw":{"variants":["UTe2 hosts both heavy electrons and local magnets","Coexisting Kondo and local moments in UTe2's normal state","Muon spin rotation finds dual 5f states in UTe2","UTe2 splits its 5f electrons into two behaviors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000312,"raw_usage":{"total_tokens":1802,"prompt_tokens":1002,"completion_tokens":800,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":618,"completion_tokens_details":{"reasoning_tokens":727}},"tokens_in":618,"tokens_out":800,"duration_ms":8786,"temperature":1.0,"reasoning_tokens":727,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:24:31.025776+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test would be a site-resolved measurement that fixes the muon stopping sites in the same samples, for example by combining transverse-field muon spin rotation with muon channeling or by matching observed site populations to calculated crystallographic sites: if the K1 signal cannot be tied to a distinct site with persistent Kondo hybridization while K2 and K4 correspond to relocalizing moments, the coexistence claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Previous muon Knight shift study on a chemically-vapor-transport-grown UTe2 crystal, providing the earlier observation of relocalization and the comparison data used throughout."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the universal two-fluid scaling function that defines the expected heavy-electron contribution to the Knight shift."},{"cited_title":"Sakai , P","cited_arxiv_id":null,"evidence_quote":"Zero-field muon study on the same molten-salt-flux crystals, showing no magnetic clusters and supporting the sample quality used to rule out disorder artifacts."},{"cited_title":"(3) below a temperature Tr at which AFM cor- relations begin to develop between the partially screened Ce 4f local moments prior to the onset of an AFM phase at lower temperature","cited_arxiv_id":null,"evidence_quote":"Establishes the two-fluid behavior and relocalization in antiferromagnetic heavy-fermion compounds, providing the analogy for interpreting the downturn below $T_r$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents magnetic clusters in chemically-vapor-transport-grown UTe2 and gives the initial muon-site calculation that the present work extends."},{"cited_title":"Giannakis, D","cited_arxiv_id":null,"evidence_quote":"Theoretical work on orbital-selective Kondo hybridization in UTe2, used to explain why different muon sites sense different degrees of localization."},{"cited_title":"Scheie, PyCrystalField: software for calculation, anal- ysis and fitting of crystal electric field Hamiltonians, J","cited_arxiv_id":null,"evidence_quote":"Inelastic neutron scattering showing antiferromagnetic fluctuations that saturate near 12 K, supporting the interpretation of $T_r$ as the onset of antiferromagnetic correlations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Evidence for a pressure-induced antiferromagnetic quantum critical point in UTe2, supporting the claim that the material is close to an antiferromagnetic instability at ambient pressure."}],"review_version":1}