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arxiv: 2604.13576 · v1 · submitted 2026-04-15 · ❄️ cond-mat.str-el

Revisiting 9Be Nuclear Magnetic Resonance in UBe13: Itinerant-Localized Duality and Possible Fermi Surface Reconstruction at High Magnetic Field

Rintaro Matsuki , Shoko Minami , Hisashi Kotegawa , Hisatomo Harima , Yoshinori Haga , Etsuji Yamamoto , Yoshichika Onuki , Hideki Tou This is my paper

Pith reviewed 2026-05-10 12:43 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords 9Be NMRUBe13Knight shiftFermi surface reconstructionheavy fermionitinerant-localized dualitymagnetic field dependencenon-symmorphic structure
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The pith

Anomalies in the Knight shift of 9Be in UBe13 around 6 T indicate a partial reconstruction of the multiple Fermi surfaces at high magnetic fields.

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

This study revisits 9Be nuclear magnetic resonance measurements on single-crystal UBe13, a heavy fermion superconductor, to address inconsistencies in high-field NMR spectra that previous parameters could not explain. By conducting field-dependent measurements from 0.5 to 8 T and angle-dependent studies at low and high fields, combined with detailed simulations accounting for the non-symmorphic crystal structure, the authors establish new NMR parameters that fit the complex line profiles. These parameters highlight the important contribution of classical dipolar fields and enable a comparison showing the itinerant-localized duality of electrons in the material. The Knight shift displays anomalies near 6 T, which the work links to a reconstruction of part of the Fermi surfaces in strong fields.

Core claim

New 9Be-NMR data on UBe13 show that the Knight shift varies anomalously with magnetic field around 6 T. This observation, obtained after determining an improved set of Knight shift and electric field gradient parameters that incorporate classical dipolar interactions and the non-symmorphic space group, provides supporting evidence for an itinerant-localized duality and indicates that part of the multiple Fermi surfaces undergoes reconstruction in the high magnetic field region.

What carries the argument

The updated NMR parameters for the Knight shift and electric field gradient, derived from simulations that include classical dipolar fields in the non-symmorphic structure of UBe13.

If this is right

  • The observed Knight shift anomalies are interpreted as signs of Fermi surface reconstruction above 6 T.
  • Classical dipolar fields play a significant role in the high-field NMR spectra of UBe13.
  • The electron system in UBe13 exhibits both itinerant and localized character as evidenced by the Knight shift analysis.
  • Previous low-field NMR parameters are insufficient to describe behavior at fields up to 8 T.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the reconstruction is confirmed, it may explain field-induced changes in the superconducting or normal state properties of UBe13.
  • This duality could be a general feature in other uranium-based heavy fermion compounds.
  • Band structure calculations under high magnetic fields might reveal the specific Fermi surface sheets affected.

Load-bearing premise

The anomalies in the Knight shift around 6 T result from a Fermi surface reconstruction rather than from field-induced changes in hyperfine coupling or other effects.

What would settle it

A lack of corresponding changes in quantum oscillation frequencies across the 6 T field would indicate that the Knight shift anomalies do not arise from Fermi surface reconstruction.

Figures

Figures reproduced from arXiv: 2604.13576 by Etsuji Yamamoto, Hideki Tou, Hisashi Kotegawa, Hisatomo Harima, Rintaro Matsuki, Shoko Minami, Yoshichika Onuki, Yoshinori Haga.

Figure 2
Figure 2. Figure 2: (Color online) Magnetic field-angle dependence of the 9Be NMR spectra, measured at 1.75 K, for applied magnetic fields of (a) µ0H = 0.5 T and (b) 6 T. The field angle was varied from the [001] to [110] crystallo￾graphic direction. The red solid lines are calculations with the nuclear spin Hamiltonian (see text). 3. Results 3.1 9Be-NMR spectra under different magnetic field orien￾tations Figures 2(a) and 2(… view at source ↗
Figure 1
Figure 1. Figure 1: (Color online) (a) Schematic view of the crystal structure of UBe13. (b) The direction of applied magnetic field in crystal axis coordinate frame Σ c using polar angles (θ, ϕ). (c) Arrangements of Be12 and Be′ 12 cages. For example, legends, A1 and A′ 1 correspond to the BeII(A1) and the BeII(A′ 1 ) sites, respectively. tial and α, β = x, y,z. The single crystalline sample used for the 9Be NMR measurements… view at source ↗
Figure 3
Figure 3. Figure 3: (Color online) Magnetic field dependence of 9Be NMR spectra for (a) H∥[001] and (b) H∥[111]. Triangle symbols indicate the resonance fre￾quency of the BeI site. The red solid lines are calculations with the nuclear spin Hamiltonian (see text). 3.3 9Be-nuclear spin Hamiltonian In order to reproduce the complex NMR line profiles at high magnetic fields, simulation calculations were performed by precisely dia… view at source ↗
Figure 4
Figure 4. Figure 4: (Color online) Magnetic field dependence of the linewidth of the convolution function for BeI and BeII NMR lines. sults of simulations thus obtained are shown by the red solid lines in Figs. 2 and 3. 3.5 9Be-NMR spectral analysis above 2T Above 2 T, both K iso II and K iso I become dependent on the magnetic field strength and its angle, and cannot be re￾produced using the parameters derived in the low-fiel… view at source ↗
Figure 5
Figure 5. Figure 5: (Color online) Magnetic field dependences of the field-induced components the KS, (a) K ind II for BeII site and (b) K ind I for BeI site. Blue closed and red open circles are data for H∥[001] and H∥[111], respectively. Here, K iso II = 0.095 % and K iso I = −0.08 %. (c) Magnetic field dependence of the Wilson ratio R calculated using Eq.(9). 6 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (Color online) Magnetic field angle dependences of the field￾induced component of the KS for (a) BeII site and for (b) BeI site. (c) Mag￾netic field angle dependence of the Wilson ratio R(θ) from H∥[001] to [111]. 4.3 Emergence of the field induced magnetic correlation around HK Finally, we address the field-orientation-dependence of K ind at 6 T [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

We report on new results of 9Be nuclear magnetic resonance (NMR) measurements conducted on a single crystal of the heavy fermion superconductor UBe13. Our previous 2007 study [J. Phys. Soc. Jpn. 76 204705 (2007)] determined NMR and electric field gradient (EFG) parameters that successfully reproduced the NMR spectra at low magnetic fields. However, these parameters did not accurately describe the angular dependence of the NMR spectra at high magnetic fields. To address this discrepancy, we have now performed a more comprehensive investigation, measuring the magnetic field dependence of the 9Be-NMR spectra across a field range of 0.5 T to 8 T, as well as the magnetic field angle dependence at 0.5 T and 6 T. Through detailed simulations that take into account the non-symmorphic space group of UBe13, we have determined a new set of parameters capable of reproducing the complex NMR line profiles observed at high magnetic fields. Notably, our analysis reveals the significant influence of classical dipolar fields. A comparison between the Knight shift (KS) and the classical dipolar shift provides microscopic supporting evidence for the nature of an itinerant-localized duality in UBe13. Furthermore, the magnetic field dependence of the KS exhibits anomalies around 6 T, suggesting a reconstruction of a part of the multiple Fermi surfaces in the high magnetic field region.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript reports new 9Be NMR measurements on a UBe13 single crystal over 0.5–8 T, including angular dependence at 0.5 T and 6 T. Updated NMR/EFG parameters, incorporating the non-symmorphic space group and classical dipolar fields, are shown via simulations to reproduce the high-field spectra better than the 2007 set. Comparison of the extracted Knight shift with the classical dipolar shift is presented as microscopic evidence for itinerant-localized duality, while anomalies in the field-dependent Knight shift near 6 T are interpreted as indicating partial reconstruction of the multiple Fermi surfaces.

Significance. If the central interpretation holds, the work supplies useful microscopic constraints on the electronic structure and duality in the heavy-fermion superconductor UBe13, with potential relevance to its unconventional superconductivity. The technical advance of a new parameter set that successfully models the angular dependence at high fields, together with the explicit inclusion of dipolar contributions, strengthens the experimental foundation for field-dependent studies in this material.

major comments (1)
  1. [magnetic field dependence of the Knight shift] The claim that Knight-shift anomalies around 6 T indicate partial Fermi-surface reconstruction (abstract and the magnetic-field-dependence section) is load-bearing for the paper’s interpretive conclusion yet rests on qualitative observation alone. No quantitative modeling of the expected shift change from a reconstructed Fermi surface is provided, nor are explicit checks reported (e.g., field-dependent hyperfine-tensor fits or estimates of quadrupolar-relaxation contributions) that would exclude alternative sources of apparent shift variation in the 0.5–8 T range.
minor comments (1)
  1. A side-by-side table comparing the 2007 and new NMR/EFG parameter values would improve clarity and allow readers to assess the magnitude of the revisions directly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback on the interpretive section. We address the major comment point by point below.

read point-by-point responses

  1. Referee: The claim that Knight-shift anomalies around 6 T indicate partial Fermi-surface reconstruction (abstract and the magnetic-field-dependence section) is load-bearing for the paper’s interpretive conclusion yet rests on qualitative observation alone. No quantitative modeling of the expected shift change from a reconstructed Fermi surface is provided, nor are explicit checks reported (e.g., field-dependent hyperfine-tensor fits or estimates of quadrupolar-relaxation contributions) that would exclude alternative sources of apparent shift variation in the 0.5–8 T range.

    Authors: We agree that the interpretation of the Knight-shift anomalies as evidence for partial Fermi-surface reconstruction is based on observation rather than quantitative modeling, and we acknowledge that this limits the strength of the claim. The anomalies are identified in the field dependence of the isotropic Knight shift after spectral fitting with the updated parameters (including non-symmorphic symmetry and classical dipolar contributions) that reproduce the angular dependence at 0.5 T and 6 T. We have performed field-dependent fits of the hyperfine tensor and find it consistent within experimental uncertainty across the measured range; quadrupolar contributions to the central transition are accounted for in the simulations and do not produce the observed step-like feature. A full quantitative calculation of the shift change expected from partial reconstruction would require field-dependent band-structure and hyperfine-coupling computations that are beyond the scope of this experimental work. We will revise the manuscript to (i) qualify the language in the abstract and discussion as suggestive rather than definitive, (ii) explicitly state the checks performed on the hyperfine tensor and quadrupolar effects, and (iii) note the absence of quantitative modeling as a limitation to be addressed by future theory. revision: partial

Circularity Check

1 steps flagged

Minor self-citation to 2007 parameters; central claims rest on new measurements and independent fits

specific steps
  1. self citation load bearing [Abstract and Introduction (paragraph 1)]
    "Our previous 2007 study [J. Phys. Soc. Jpn. 76 204705 (2007)] determined NMR and electric field gradient (EFG) parameters that successfully reproduced the NMR spectra at low magnetic fields. However, these parameters did not accurately describe the angular dependence of the NMR spectra at high magnetic fields."

    The citation is used only to motivate the new data collection and re-fitting; the new parameters and the KS anomalies are determined from the fresh measurements and simulations, not derived from or forced by the 2007 result.

full rationale

The derivation chain consists of new 0.5–8 T field-dependent and angle-dependent 9Be NMR spectra on a single crystal, followed by simulations that incorporate the non-symmorphic space group and classical dipolar fields to extract a revised set of NMR/EFG parameters. These parameters are shown to reproduce the high-field line profiles better than the 2007 set. Knight-shift values are then extracted and compared directly to the computed dipolar shift; anomalies near 6 T are interpreted as possible partial Fermi-surface reconstruction. The only self-citation is to the authors’ own 2007 work, used solely to document that the prior parameter set fails at high fields; it does not supply any load-bearing uniqueness theorem, ansatz, or fitted quantity that is renamed as a prediction. No equation reduces to a self-definition, and the duality/reconstruction statements remain interpretive comparisons outside the fitting procedure itself.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard NMR theory plus the assumption that classical dipolar fields can be calculated from the known crystal structure without significant quantum corrections. No new particles or forces are postulated.

free parameters (2)
  • Electric field gradient tensor components and asymmetry parameter
    Fitted to reproduce the observed quadrupolar splitting at multiple fields and angles.
  • Knight shift tensor components
    Adjusted to match the field- and angle-dependent resonance positions after subtracting dipolar contributions.
axioms (2)
  • standard math The non-symmorphic space group of UBe13 determines the symmetry-allowed EFG and dipolar field orientations at the Be sites.
    Invoked to constrain the allowed parameter space in the spectral simulations.
  • domain assumption Classical dipolar fields from neighboring U and Be moments can be computed from the known lattice positions and added linearly to the hyperfine shift.
    Central to the revised fitting procedure that resolves the high-field discrepancy.

pith-pipeline@v0.9.0 · 5601 in / 1462 out tokens · 31039 ms · 2026-05-10T12:43:12.017077+00:00 · methodology

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Reference graph

Works this paper leans on

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