Coexistence of Kondo Coherence and Localized Magnetic Moments in the Normal State of Molten Salt-Flux Grown UTe2

B. M. Huddart; E. Mun; J. D. Thompson; J. E. Sonier; M. M. Bordelon; M. Yakovlev; N. Azari; O. P. Uzoh; P. F. S. Rosa; S. J. Blundell

REVIEW 4 major objections 4 minor 52 references

Coexistence of Kondo Coherence and Localized Magnetic Moments in the Normal State of Molten Salt-Flux Grown UTe2

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2501.13178 v1 pith:TKF254EO submitted 2025-01-22 cond-mat.supr-con

N. Azari , M. Yakovlev , S. R. Dunsiger , O. P. Uzoh , E. Mun , B. M. Huddart , S. J. Blundell , M. M. Bordelon

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S. M. Thomas J. D. Thompson P. F. S. Rosa J. E. Sonier

This is my paper · ORCID

classification cond-mat.supr-con

keywords UTe2muonspinrotationKnightshiftKondolatticeheavy-electronfluidrelocalizationtwo-fluidmodelantiferromagneticcorrelations

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper 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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the 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.

Referee Report

4 major / 4 minor

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.

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 (4)

[Section II A, Table I] 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 II A, Figs. 2-3] 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 II C, Fig. 4 and Eq. (3)] 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 II A, discussion of K3] 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.

minor comments (4)

[Introduction] The word 'latttice' should be corrected to 'lattice'.
[Section II A, Eq. (2)] 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.
[Fig. 2 caption] 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 II C] 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.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the universal-scaling comparison is an external two-fluid benchmark, and the MSF muon-Knight-shift data independently reproduce the relocalization seen in the authors' prior CVT study.

full rationale

The derivation chain is: (i) fit TF-muSR spectra to multiple precession components; (ii) convert frequencies to K_i via Eq. (2); (iii) isolate the heavy-electron contribution by subtracting a linear baseline fitted to K_i versus chi above T*; (iv) compare KHF/K0_HF to Eq. (3), the two-fluid universal scaling function from Yang et al. (2008); and (v) interpret departures below Tr ~ 12 K at sites K2/K4 as relocalization, while K1 continuing to follow Eq. (3) as coexistence. Step (iv) is the only place where a prediction is tested, and it is not circular by construction: Eq. (3) is an external, parameter-free shape; K0_HF is an amplitude normalization and T* is assumed from the observed crossover, but the residual KHF is not algebraically forced to equal Eq. (3). The relocalization claim is supported by new MSF data (K2, K4 departures) rather than by the authors' prior CVT paper alone; the self-citation to Ref. [9] supplies complementary data and the previously noted T* value, but it is not load-bearing because the clean MSF sample independently reproduces the effect. The paper itself flags a genuine limitation in Sections II A and II B: the muon-site population ratio inferred by TF-muSR does not match any DFT candidate-site combination and is incompatible with Immm multiplicities, so the spatial assignment of K1 versus K2/K4 to distinct 5f-orbital environments is not microscopically established. This is an assumption and validity risk, not a circularity, and it limits confidence in the coexistence interpretation. Overall, no load-bearing step reduces to its inputs; the score of 2 reflects only the minor self-citation and the standard baseline-subtraction normalization caveat.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the two-fluid model's universal scaling curve, on a fitted baseline subtraction, on assumed muon-site identities, and on an analogy with Ce-based heavy-fermion compounds. No new particles, fields, or conserved quantities are introduced. The most fragile inputs are T* = 30 K and the K0_HF amplitude, both material-dependent and not independently derived here.

free parameters (3)

T* (Kondo coherence crossover temperature) = 30 K (assumed)
Used to scale all data in Fig. 4; the paper states 'assuming T*=30 K' and does not fit it afresh, but it is a material-dependent input, not a derived quantity.
K0_HF heavy-electron Knight shift amplitude per muon component = not reported
Eq. (3) contains a material-dependent K0_HF; the paper plots K_HF/K0_HF but does not state how the normalization is obtained, so the collapse to the universal curve is partly a fitted amplitude.
High-T linear K-chi baseline slope and intercept for each muon component = not reported
K_HF is defined by subtracting a linear extrapolation of K_i versus chi_c fitted over 30 K < T < 150 K; the fit range and resulting slope and intercept set the anomaly and therefore the scaling comparison.

assumptions (5)

domain assumption Two-fluid model of the Kondo lattice with universal scaling Eq. (3) applies to UTe2.
Invoked in Section II C as the benchmark for K_HF; the model is from Refs. [6,7] and was developed for Ce- and Yb-based heavy fermions, and its applicability to UTe2's 5f system is assumed.
domain assumption High-temperature linear K-chi scaling can be extrapolated below T*.
K_HF is obtained by subtracting a linear baseline fitted above T*; this assumes the same hyperfine coupling and local susceptibility continue below T* in the absence of the heavy-electron fluid.
domain assumption The four muon precession components correspond to distinct, fixed muon stopping sites with known local hyperfine couplings.
The site-resolved interpretation requires this; the paper notes the DFT candidate site populations do not match the measured amplitudes in Section II B.
domain assumption Deviation of K_HF below the universal curve indicates reversal of Kondo hybridization and AFM correlations between relocalized moments.
This interpretive step is taken by analogy with CeRhIn5, CePt2In7, and UPd2Al3; it is not directly measured in UTe2.
domain assumption Bulk susceptibility chi_c used in the K-chi plots is representative of these crystals and includes no spurious low-field cluster contribution.
The MSF crystals were previously shown to lack magnetic clusters in Ref. [16], but the bulk chi data used for scaling are not re-measured in this paper.

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Cite this review

Pith. "Pith review of Coexistence of Kondo Coherence and Localized Magnetic Moments in the Normal State of Molten Salt-Flux Grown UTe2." pith.science (2026). https://pith.science/paper/TKF254EO

@misc{pith2026250113178,
  author       = {Pith},
  title        = {Pith review of: Coexistence of Kondo Coherence and Localized Magnetic Moments in the Normal State of Molten Salt-Flux Grown UTe2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TKF254EO}},
  note         = {Machine review of arXiv:2501.13178}
}

read the original abstract

The development of Kondo lattice coherence in UTe2 leads to the formation of a heavy Fermi liquid state from which superconductivity emerges at lower temperature. In Kondo lattice systems, the nuclear magnetic resonance (NMR) and muon Knight shift have proven to be particularly sensitive to the properties of the developing heavy-electron fluid. Here we report muon Knight shift measurements on high-quality UTe2 single crystals grown by a molten salt-flux method. Together with previous data from a single crystal grown by a chemical-vapor transport method, our results show the contribution of the heavy-electron liquid to the muon Knight shift increases below a crossover temperature T* ~ 30 K in accord with a universal scaling function of T/T* for heavy-fermion materials. An observed departure from this universal scaling below a temperature T ~ 12 K at certain muon stopping sites signifies a reversal of the Kondo hybridization and a relocalization of U 5f moments with an antiferromagnetic coupling. The preservation of universal scaling at a different muon site demonstrates a coexistence of itinerant and localized 5f electron states preceding the superconducting phase transition.

Figures

Figures reproduced from arXiv: 2501.13178 by the authors.

**Figure 1.** shows a comparison of the Fourier transforms of a TF-µSR asymmetry spectrum in the previously studied CVT-grown single crystal and the MSF-grown single crystal mosaic recorded at a temperature well above Tc and for a field H = 20 kOe applied parallel to the c axis. Although two peaks are observed in the Fourier transform for the CVT-grown single crystal, fits in the time domain reveal that the left peak is compris… view at source ↗

**Figure 2.** FIG. 2. (a)-(d) Temperature dependence of the four [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Comparison of the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Plot of the normalized heavy-electron fluid contri [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Pith tools

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(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

and CePt2In7 [36], KHF determined by NMR deviates from Eq. (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. By analogy it appears that short- range AFM interactions between relocalizing U 5 f local moments in UTe 2 commence at...

work page