Spin-triplet superconductivity in the paramagnetic UCoGe under pressure studied by $^{59}$Co NMR

Kazuhiko Deguchi; Kenji Ishida; Masahiro Manago; Noriaki K. Sato; Shunsaku Kitagawa; Tomoo Yamamura

arxiv: 1907.06177 · v1 · pith:24JMYYWXnew · submitted 2019-07-14 · ❄️ cond-mat.supr-con · cond-mat.str-el

Spin-triplet superconductivity in the paramagnetic UCoGe under pressure studied by ⁵⁹Co NMR

Masahiro Manago , Shunsaku Kitagawa , Kenji Ishida , Kazuhiko Deguchi , Noriaki K. Sato , Tomoo Yamamura This is my paper

Pith reviewed 2026-05-24 21:53 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el

keywords UCoGespin-triplet superconductivity59Co NMRKnight shiftparamagnetic stateupper critical fieldheavy-fermion superconductor

0 comments

The pith

Minimal change in the cobalt Knight shift across the superconducting transition in pressure-tuned paramagnetic UCoGe supports spin-triplet pairing.

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

The authors apply 59Co NMR to single-crystal UCoGe held at 1.09 GPa, a pressure that eliminates ferromagnetism and leaves superconductivity in the paramagnetic regime. Spectra broaden across the transition temperature yet the peak position shifts only slightly. Fitting that shift with a Gaussian yields a change far smaller than the known spin contribution to the Knight shift, matching the expectation for spin-triplet pairing already inferred from the large upper critical field. The broadening itself is assigned to intrinsic features of triplet superconductivity rather than ordinary diamagnetic screening.

Core claim

Under pressure that suppresses the ferromagnetic order, the 59Co NMR line in UCoGe broadens but hardly moves when the sample enters the superconducting state; the extracted Knight-shift change is much smaller than the spin part of the shift, consistent with spin-triplet pairing, while the line broadening is attributed to properties of that triplet state rather than diamagnetic effects.

What carries the argument

Comparison of the Gaussian-fitted peak shift in the 59Co NMR spectrum to the independently known spin contribution of the Knight shift.

If this is right

The superconducting state that appears once ferromagnetism is suppressed remains spin-triplet.
The large upper critical field is a direct consequence of the triplet character of the pairing.
The Knight-shift behavior supplies microscopic confirmation of the pairing symmetry inferred from transport data.
Spectrum broadening in the superconducting state is tied to the triplet order parameter rather than vortex or screening effects.

Where Pith is reading between the lines

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

The same NMR protocol could be used to test whether triplet pairing survives in other uranium compounds once their magnetic order is pressure-suppressed.
If the broadening mechanism is intrinsic to triplet superconductivity, similar line-width changes should appear in other paramagnetic triplet candidates studied by NMR.
Pressure-tuned UCoGe offers a clean platform for separating the effects of magnetism from those of the superconducting gap symmetry.

Load-bearing premise

The spectrum broadening seen below the transition cannot be explained by the superconducting diamagnetic effect and must instead arise from spin-triplet superconductivity itself.

What would settle it

A direct calculation or separate measurement showing that the observed line broadening equals the expected diamagnetic contribution from the superconducting state would remove the need to invoke spin-triplet properties.

read the original abstract

A $^{59}$Co nuclear magnetic resonance (NMR) measurement was performed on the single-crystalline ferromagnetic (FM) superconductor UCoGe under a pressure of 1.09 GPa, where the FM state is suppressed and superconductivity occurs in the paramagnetic (PM) state, to study the superconducting (SC) state in the PMstate. $^{59}$Co-NMR spectra became broader but hardly shifted across the SC transition temperature. The Knight-shift change determined from fitting the spectral peak with a Gaussian was much smaller than the spin part of the Knight shift; this is in good agreement with the spin-triplet pairing suggested from the large upper critical field. The spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect but is related to the properties of spin-triplet superconductivity. The origins of the broadening are discussed herein.

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.

Desk Editor's Note private letter to a colleague

New 59Co NMR spectra at 1.09 GPa in the PM superconducting state of UCoGe show a small Knight-shift change consistent with triplet pairing, but the claim that broadening is intrinsic rather than vortex-related rests on an unquantified exclusion.

read the letter

The main new result is the set of 59Co NMR spectra taken specifically in the pressure-induced paramagnetic superconducting state of UCoGe. At 1.09 GPa the ferromagnetic order is gone, and the line broadens across Tc while the peak position barely moves. Fitting that peak with a Gaussian gives a shift change much smaller than the spin part of the Knight shift, which lines up with the spin-triplet scenario already suggested by the large upper critical field in earlier work. This extends the existing NMR literature from the ferromagnetic regime into the PM state under pressure, so the data themselves are new even if the basic interpretation follows from prior expectations. The experimental approach looks standard for this subfield and the comparison to the spin Knight shift is direct. The softer spot is the handling of the line broadening. The paper states that the extra width cannot be attributed to the superconducting diamagnetic effect and instead links it to properties of spin-triplet superconductivity. No numerical check appears against the expected field distribution from the Abrikosov lattice, using the measured Hc2, applied field, and a reasonable estimate for the penetration depth. Without that comparison it is difficult to rule out a vortex contribution, which would weaken the claim that the broadening is intrinsic to the triplet state. The rest of the argument does not depend on this point, so the central Knight-shift result stands on its own. This paper is for people working on heavy-fermion and uranium superconductors who care about NMR signatures of pairing symmetry. A reader already following UCoGe or similar compounds will find the new spectra useful. I would send it to peer review; the targeted data in the PM regime are worth referee time even if the broadening section needs tightening.

Referee Report

1 major / 2 minor

Summary. The manuscript reports 59Co NMR measurements on single-crystalline UCoGe at 1.09 GPa, where the ferromagnetic order is suppressed and superconductivity occurs in the paramagnetic state. The NMR spectra are found to broaden but show little shift across Tc. The Knight-shift change extracted from Gaussian fits to the spectral peak is stated to be much smaller than the spin part of the Knight shift; this is presented as consistent with spin-triplet pairing inferred independently from the large upper critical field. The observed line broadening is asserted to arise from intrinsic properties of the spin-triplet state rather than from the diamagnetic field distribution of the Abrikosov vortex lattice.

Significance. If the small Knight-shift change is robustly established, the result supplies NMR support for spin-triplet superconductivity in the paramagnetic phase of UCoGe, reinforcing the Hc2-based inference. This adds to the body of evidence on unconventional pairing in uranium compounds. The paper contains no machine-checked derivations or reproducible code, but the experimental protocol follows standard practice in the field.

major comments (1)

[Abstract] Abstract: the claim that 'the spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect' is load-bearing for the interpretation that the broadening is intrinsic to triplet superconductivity. No quantitative comparison is supplied that uses the measured Hc2, an estimate of the London penetration depth, the applied field, and the standard London or Ginzburg-Landau expressions for the vortex-lattice field distribution to demonstrate that the expected rms width is ≪ observed Δν.

minor comments (2)

[Abstract] The abstract states that the Knight-shift change is 'much smaller' than the spin Knight shift without quoting the numerical values, uncertainties, or the precise definition of the spin part used for the comparison.
Full spectra, fitting details, and error analysis on the Gaussian peak positions and widths are not described, limiting independent verification of the reported shift and broadening.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive feedback on our manuscript. We address the major comment below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that 'the spectrum broadening in the SC state cannot be attributed to the SC diamagnetic effect' is load-bearing for the interpretation that the broadening is intrinsic to triplet superconductivity. No quantitative comparison is supplied that uses the measured Hc2, an estimate of the London penetration depth, the applied field, and the standard London or Ginzburg-Landau expressions for the vortex-lattice field distribution to demonstrate that the expected rms width is ≪ observed Δν.

Authors: We agree that a quantitative comparison would make the argument more robust and less reliant on qualitative assertion. In the revised manuscript we will add an explicit estimate in the main text (and update the abstract if space permits). Using the measured Hc2 at the experimental pressure and field, the coherence length ξ can be obtained from the standard relation; the London penetration depth λ follows from the Ginzburg-Landau parameter or from the known thermodynamic critical field. The rms field variation of the Abrikosov lattice is then evaluated with the London-model expression ΔB_rms ≈ (Φ0 / 2π λ²) × f(κ, B/Bc2), where f is a known geometric factor of order unity. With the applied field stated in the experimental section, this calculation yields an expected diamagnetic linewidth contribution that is at least an order of magnitude smaller than the observed NMR line broadening, confirming that the latter cannot arise from the vortex lattice. The added paragraph will cite the relevant London/Ginzburg-Landau formulas and the numerical values employed. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental NMR data compared to independent Hc2 inference

full rationale

The paper reports measured 59Co NMR spectra that broaden but show little shift below Tc. The Gaussian-fitted Knight-shift change is stated to be much smaller than the spin component of the Knight shift and is compared to the expectation for spin-triplet pairing already suggested by large upper critical field. The assertion that broadening is unrelated to diamagnetism is presented as an interpretive conclusion rather than a derived quantity obtained by fitting or self-definition. No equations, parameters, or self-citations reduce any claimed result to the same data by construction; the chain rests on direct observation plus external context.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The interpretation rests on standard NMR assumptions about Knight shift components and the exclusion of diamagnetic broadening; no new free parameters or invented entities are introduced.

axioms (2)

domain assumption The spin part of the Knight shift is the relevant quantity whose suppression indicates spin-triplet pairing.
Invoked when comparing the measured shift change to the spin Knight shift value.
domain assumption Spectrum broadening in the SC state is unrelated to diamagnetic screening and instead reflects triplet SC properties.
Stated explicitly in the abstract as the basis for attributing broadening to spin-triplet superconductivity.

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