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REVIEW 4 major objections 5 minor 41 references

Appearance of $c$-axis magnetic moment in odd-parity antiferromagnetic state in CeRh$_2$As$_2$ revealed by $^{75}$As-NMR

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read NMR measurements place the antiferromagnetic order in superconducting CeRh2As2 at a q=0 A-type structure with moments along the c axis, and confirm spin-singlet pairing.

desk verdict Careful NMR study that narrows the CeRh2As2 magnetic structure to a c-axis internal field at As(2), but the q=0 A-type conclusion is provisional rather than nailed down. read the letter →

arxiv 2412.10148 v1 pith:4H42WB4O submitted 2024-12-13 cond-mat.supr-con

Shiki Ogata , Shunsaku Kitagawa , Katsuki Kinjo , Kenji Ishida , Manuel Brando , Elena Hassinger , Christoph Geibel , Seunghyun Khim This is my paper · ORCID
classification cond-mat.supr-con
keywords CeRh2As2heavy-fermionsuperconductorantiferromagneticorderNMRlinewidthKnightshiftspin-singletsuperconductivityodd-paritymultipolemagneticstructure
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

This paper tries to identify the magnetic structure of the antiferromagnetic state that coexists with superconductivity in CeRh2As2, a heavy-fermion superconductor with a field-induced superconducting multiphase. By comparing 75As-NMR linewidths between magnetic fields applied along the c axis and along [110], the authors find that the internal magnetic field at the As(2) site points along the c axis. Combined with the earlier observation that the internal field cancels at the As(1) site, this selects a q=0 A-type antiferromagnet with moments parallel to c. The same data show a reduction of the spin susceptibility in all directions, indicating spin-singlet pairing in the low-field superconducting phase. If correct, this settles a long-open question and connects the magnetism to odd-parity multipolar order.

What carries the argument

The argument rests on comparing NMR linewidth broadening in two field geometries: $H \parallel c$ and $H \parallel [110]$. Since broadening from a staggered internal field is largest when the internal field is parallel to the applied field, the observation that the As(2) site's field distribution is much larger for $H \parallel c$ than for $H \parallel [110]$ locates the internal field along the c axis. To convert linewidth to field distribution in the $H \parallel [110]$ geometry, the paper numerically diagonalizes the nuclear Hamiltonian including quadrupolar coupling, obtaining an effective gyromagnetic ratio for each arsenic site. The q=0 A-type antiferromagnet is the structure in which ferromagnetic planes are antiferromagnetically stacked along c, so the dipolar field cancels at As(1) but not at As(2).

What would settle it

A direct measurement of the ordered moment direction—for example, neutron diffraction or muon spin rotation on the same crystals—that finds a dominant in-plane component, or an NMR measurement at an intermediate field angle that does not show the linewidth anisotropy predicted for a c-axis internal field, would refute the proposed q=0 A-type structure.

Watch

Extended reading notes

Core claim

The paper claims that the internal magnetic field sensed by arsenic nuclei at the As(2) site in the superconducting phase of CeRh2As2 points along the tetragonal c axis. This orientation, together with the previously observed cancellation of the field at the As(1) site, selects the q=0 A-type antiferromagnetic structure with ordered moments parallel to c. From the magnitude of the field distribution, the ordered moment is estimated to be on the order of 0.1 $\mu_B$. The paper also reports a decrease of the spin susceptibility in all measured field directions below the superconducting transition, demonstrating that the low-field superconducting state is spin-singlet.

Load-bearing premise

The conclusion hinges on the assumption that the NMR linewidth increase below the superconducting transition is caused entirely by the staggered internal field, with no comparable contribution from vortex disorder or sample inhomogeneity, and that the two candidate structures from the earlier NQR work are the only possibilities.

Editorial extensions

If this is right

  • The antiferromagnetic order in the low-field superconducting phase has c-axis-oriented moments, resolving the magnetic structure as q=0 A-type.
  • The spin susceptibility decreases in every measured field direction below the superconducting transition, confirming spin-singlet pairing in the low-field superconducting state.
  • The ordered moment is small (about 0.1 $\mu_B$), consistent with the absence of static magnetic scattering in neutron diffraction experiments.
  • The excess Knight-shift reduction at the As(2) site in $H \parallel [110]$ is quantitatively explained by the 16 mT internal field tilting the effective field, rather than by a change in spin susceptibility.
  • The proposed structure corresponds to magnetic monopole order, making CeRh2As2 a rare platform for studying superconductivity coexisting with odd-parity multipoles.

Reading between the lines

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

  • If the q=0 A-type structure is correct, the antiferromagnetic order breaks global inversion symmetry, and CeRh2As2 becomes a testbed for cross-correlated responses such as magnetoelectric effects in a superconductor.
  • The comparison with zero-field NQR data suggests that the ordered moment is suppressed by a c-axis magnetic field; a systematic field-dependence study could map how the moment weakens as the system approaches the high-field superconducting phase.
  • The discrepancy with recent μSR results, which find comparable in-plane and c-axis components, might be resolved by measuring the same high-quality crystals with both techniques, since sample quality and field conditions differ between the two experiments.
  • Extending the Knight-shift measurements to other in-plane field orientations could sharpen the spin-singlet conclusion and test for a possible nodal or anisotropic gap.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript reports 75As-NMR measurements on CeRh2As2 with the magnetic field applied along [110] inside the superconducting phase. By comparing the NMR linewidth at the two As sites with earlier H||c data, the authors find that the excess field distribution below TSC at the As(2) site is much smaller for H||[110] than for H||c, and they interpret this as an internal magnetic field oriented along the c axis with magnitude about 16 mT. Combining this with the As(1)-site cancellation classification of Ref. [20], they propose a q=0 A-type antiferromagnetic structure with moments parallel to c. The paper also uses the Knight-shift decrease to argue for spin-singlet pairing, while noting that a substantial part of the As(2) shift change below TSC is caused by a frequency shift from the internal-field tilt. The authors explicitly acknowledge that recent muSR results on higher-quality samples suggest a different, weakly anisotropic structure, and that the present sample is an early-stage crystal.

Significance. If the proposed magnetic structure is correct, this would be a rare example of an odd-parity magnetic multipole (magnetic monopole) state coexisting with superconductivity, with direct relevance to the field-induced SC multiphase of CeRh2As2. The experimental strategy of comparing linewidths at the same nuclei in two field orientations is sound, and the paper is commendably honest in stating the sample limitations and the conflict with muSR. However, the central structural conclusion is conditional on the attribution of all excess linewidth to a static staggered field, on the exhaustiveness of a classification taken from Ref. [20], and on the representativeness of the early-stage sample; the spin-singlet evidence is also weakened by the internal-field correction to the As(2) Knight shift.

major comments (4)
  1. [IV, Figs. 3(b) and 3(c)] The inference that the internal field at the As(2) site is oriented along the c axis assumes that the entire excess linewidth below TSC is caused by the static staggered internal field. Orientation-dependent contributions from vortex-lattice disorder, SC diamagnetic shielding, or mosaic spread could also differ between H||[110] and H||c, but no quantitative estimate of these effects is provided. Please estimate these contributions or give an additional test (for example, the field dependence of the excess linewidth at fixed temperature) that separates the static staggered-field broadening from other sources.
  2. [IV, Ref. [20]] The step from 'c-axis internal field at As(2)' to 'q=0 A-type AFM with moments parallel to c' relies entirely on the two-structure classification of Ref. [20] and on the cancellation of the internal field at the As(1) site. This classification is cited but not re-derived, and the paper does not demonstrate that no other c-axis-moment structure could also cancel at As(1). If uniqueness is claimed, please include the symmetry enumeration or group-theoretical argument; alternatively, explicitly state that the q=0 A-type structure is the most plausible candidate rather than the uniquely determined one.
  3. [IV, Eq. (3) and following] The spin-singlet claim is weakened by the later analysis in the same section. The observed As(2) Knight-shift reduction of about 0.4% is shown to be largely accounted for by an 11.5 kHz frequency shift arising from the 16 mT c-axis internal field, corresponding to about 0.43% in shift. After this correction, the extracted spin susceptibility reduction at the As(2) site may be comparable to the error bar. Please present the corrected δK_As2 with its uncertainty and state clearly whether spin-singlet pairing is still established without relying on the As(2) shift.
  4. [V, Ref. [26]] The paper acknowledges that muSR on higher-quality crystals detects static magnetic order with comparable in-plane and c-axis components, and that the present NMR sample is an early-stage crystal. This is an honest statement, but it makes the headline structure conditional on sample quality. To strengthen the paper, please discuss which of the NMR constraints would change if the muSR structure were realized, or propose a discriminating measurement (for example, NMR on the higher-quality samples) that could resolve the discrepancy.
minor comments (5)
  1. [Title and abstract] There is a typo in the title: 'sta te' should be 'state'.
  2. [Fig. 2 caption] 'Temeperature' in the caption for Fig. 2(e) should be 'Temperature'.
  3. [Eq. (2)] The formula for Kdia contains an unusual typographical combination 'βλ d√ eξ'; please clarify the expression, e.g., by inserting appropriate parentheses in the logarithm.
  4. [Sec. II] The text uses '3He-4He' with hyphens; please use the standard en-dash notation '3He–4He'.
  5. [Ref. [34]] Reference [34] is listed as 'Phys. Rev. Lett. (unpublished)'; please update it with the arXiv number or provide the publication status.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the c-axis internal-field orientation is inferred from new H||[110] linewidth data compared with prior H||c data, and the prior same-group results used as inputs are independent published measurements.

full rationale

The paper's central claim is that the AFM state coexisting with superconductivity in CeRh2As2 is a q=0 A-type structure with moments along c. The derivation chain is: (1) new 75As-NMR spectra in H||[110] are converted to field distributions using a numerically diagonalized nuclear Hamiltonian and the measured linewidth; (2) comparison with the previously measured H||c field distribution shows the As(2)-site field distribution is larger for H||c, leading to the inference that the internal field is oriented along c; (3) combining this orientation with the As(1)-site cancellation classification from Ref. [20] selects the q=0 A-type structure. Ref. [20], although by heavily overlapping authors, is an independent NQR measurement of As(1) linewidth behavior, not an assumption defined by this paper's target conclusion. The hyperfine coupling constants used to estimate the ordered moment are likewise experimentally determined in prior work. The later use of the 16 mT field to explain the excess Knight-shift reduction at As(2) is a consistency check, not a prediction from fitted parameters. The paper explicitly acknowledges its limitations: the sample is an early-stage crystal, the classification from Ref. [20] is cited rather than re-derived, and recent μSR results on higher-quality samples suggest a different structure. These are honest caveats about robustness, not circular reasoning. No equation in the paper reduces by construction to an input, and no fitted parameter is renamed as a prediction. The self-citations are load-bearing but constitute independent experimental support, so the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on previously measured hyperfine and quadrupole parameters and on the assumption that linewidth broadening is purely magnetic. No new physical entities are introduced, and the only input parameter carried from earlier work is the hyperfine coupling constant.

free parameters (1)
  • Hyperfine coupling constant of As(2) site along c-axis = ~0.27 T/μB
    Taken from Refs [28,29]; used to convert the internal field estimate into an ordered moment of about 0.1 μB. It is an input from earlier work, not fitted in this paper.
assumptions (4)
  • domain assumption The set of possible magnetic structures is limited to the two structures identified in Ref [20]: A-type AFM with c-axis moments or a helical state with in-plane moments.
    This restricts the interpretation of the internal field direction; if other structures exist, the proposed structure is not unique.
  • domain assumption The NMR linewidth increase below TSC arises entirely from the staggered internal field (plus the small SC diamagnetic shift), and the conversion from FWHM to field distribution via the simulated effective gyromagnetic ratios is accurate.
    Any additional field-orientation-dependent broadening would corrupt the inferred direction of the internal field.
  • domain assumption The difference in the field distribution between the As(1) and As(2) sites in H||c reflects the internal field at As(2) because the field at As(1) cancels by symmetry.
    This cancellation is an empirical result from the group's earlier NQR work and is a key input to the structure determination.
  • domain assumption The comparison of the present 0.8 T H||[110] data with the earlier 1.2 T H||c data is valid despite different fields and temperatures.
    The field and temperature differences could in principle change the magnetic structure or the magnitude of the ordered moment, though the field distribution at As(2) is larger in H||c.

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Cite this review

Pith. "Pith review of Appearance of $c$-axis magnetic moment in odd-parity antiferromagnetic state in CeRh$_2$As$_2$ revealed by $^{75}$As-NMR." pith.science (2026). https://pith.science/paper/4H42WB4O

@misc{pith2026241210148,
  author       = {Pith},
  title        = {Pith review of: Appearance of $c$-axis magnetic moment in odd-parity antiferromagnetic state in CeRh$_2$As$_2$ revealed by $^75$As-NMR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4H42WB4O}},
  note         = {Machine review of arXiv:2412.10148}
}
abstract

CeRh$_2$As$_2$ shows the superconducting (SC) multiphase under the $c$-axis magnetic field, which is considered to originate from local inversion symmetry breaking at the Ce site. We reported that the antiferromagnetic (AFM) order is inside the SC phase and that the AFM state disappears at the transition field to the high-field SC phase. However, the magnetic structure in the AFM state has not been clarified yet. In this study, we performed $^{75}$As-NMR measurements in the SC phase in $H\parallel [110]$ to identify the magnetic structure. Comparing the NMR linewidth with $H \parallel c$, we found that the internal magnetic field is oriented to the $c$ axis. This suggests a $q = 0$ $A$-type AFM with the moments parallel to the $c$ axis. We also observed the reduction of the spin susceptibility, which indicates spin-singlet superconductivity in the low-field SC phase. This study provides an important clue to clarify the correlation between the SC multiphase, magnetism, and local inversion symmetry breaking.

Figures

Figures reproduced from arXiv: 2412.10148 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Crystal structure of CeRh [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. NMR measurements in CeRh [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Magnetic field dependence of NMR frequency of each [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The polar angle [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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    P. G. de Gennes: Superconductivity of metals and alloys (CRC Press, 2018)

    2018

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.