Coexistence of Commensurate and Incommensurate Antiferromagnetic Groundstates in Co$_x$NbSe$_2$ Single Crystal

Alicia Manj\'on-Sanz; Efrain E. Rodriguez; H. Cein Mandujano; Huibo Cao; Peter Y. Zavalij

REVIEW 3 major objections 6 minor 57 references

Coexistence of Commensurate and Incommensurate Antiferromagnetic Groundstates in Co$_x$NbSe$_2$ Single Crystal

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A single Co0.28NbSe2 crystal hosts two coexisting antiferromagnetic phases, one at 169 K and one at 28 K.

desk verdict First magnetic structure solution for Co1/3NbSe2 is solid, but the claim of both ground states coexisting in the Co0.28 single crystal rests on bulk anomalies and a structural model, not on magnetic diffraction in that crystal. read the letter →

arxiv 2501.00591 v1 pith:D6J37OKU submitted 2024-12-31 cond-mat.mtrl-sci cond-mat.str-el

H. Cein Mandujano , Peter Y. Zavalij , Alicia Manjón-Sanz , Huibo Cao , Efrain E. Rodriguez This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.str-el

keywords cobalt-intercalatedniobiumdiselenideA-typeantiferromagnetismdouble-qmagneticstructurecommensurateandincommensurateorderP6322chiralsuperlatticecoexistenceneutrondiffractiontransitionmetaldichalcogenides

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 argues that in $\mathrm{Co}_x\mathrm{NbSe}_2$, the cobalt concentration picks out one of two crystal symmetries, and each symmetry carries its own magnetic ground state: $x\approx 1/4$ produces the centrosymmetric $P6_3/mmc$ structure and a collinear A-type antiferromagnet at $T_N^A=169$ K, while $x\approx 1/3$ produces the chiral $P6_3 22$ structure and a lower-temperature order at $T_N^S=28$ K. For single crystals with intermediate composition $x=0.28$, the paper claims both structural sublattices coexist inside one $2\sqrt{3}a_h\times 2\sqrt{3}a_h$ superlattice, and bulk measurements show both magnetic transitions in the same crystal. Single-crystal neutron diffraction solves the high-temperature phase as a $\Gamma_7$ antiferromagnet with moments along $c$; neutron powder diffraction of the $x=1/3$ compound reveals a double-$q$ low-temperature structure combining a commensurate wave vector $q_1=(0,1/3,0)$ and an incommensurate wave vector $q_2=(0,1/3,0.048(4))$. If correct, the paper establishes that a single intercalated dichalcogenide crystal can host two structurally and magnetically distinct ground states, with implications for altermagnetism and chiral magnetism in the same material.

What carries the argument

The central object is the $2\sqrt{3}a_h\times2\sqrt{3}a_h$ superlattice in the chiral space group $P6_3 22$, whose cell is twice the $\sqrt{3}a_h\times\sqrt{3}a_h$ sublattice along each direction; the Miller-index transformation connecting this supercell to the host lattice is given explicitly in the paper. This supercell is the structural device that accommodates both cobalt sublattices at once, so it is what makes the coexistence claim physically concrete. The argument runs on two further pieces of machinery: irreducible representation analysis of the magnetic structures, which assigns the high-temperature order to $\Gamma_7$ with the moment along $c$, and a two-wave-vector refinement of the powder data, which separates the commensurate $q_1$ and incommensurate $q_2$ components of the low-temperature order.

What would settle it

A single-crystal neutron diffraction experiment at temperatures below 28 K with long counting at the predicted positions $q_1=(0,1/3,0)$ and $q_2=(0,1/3,0.048(4))$ would settle the coexistence claim: if no magnetic satellites appear, the low-temperature order is not present in the same crystal volume, and the claim reduces to a two-sample comparison between powder and crystal.

Watch

Extended reading notes

Core claim

Working with $\mathrm{Co}_{0.28}\mathrm{NbSe}_2$ single crystals, the paper reports that two magnetic transitions coexist: a $169$ K transition tied to the $x\sim 1/4$ sublattice and a $28$ K transition tied to the $x\sim 1/3$ sublattice. The structural basis for coexistence is a superlattice with cell dimensions $a_{2S}=11.9622(3)$ Å built from satellite reflections indexed by the nuclear propagation vector $(1/3,1/3,0)$ with respect to the host lattice; in this $P6_3 22$ supercell, cobalt sites are allocated so that both the $2a_h\times2a_h$ and $\sqrt{3}a_h\times\sqrt{3}a_h$ sublattices are present, either in the same layer or stacked between layers. Magnetic susceptibility, specific heat, and resistivity all detect the two transitions, with only the high-temperature phase producing a clear resistivity anomaly. Single-crystal neutron diffraction shows that below $T_N^A$ the magnetic reflections overlap nuclear reflections, corresponding to $q_m=(0,0,0)$; representation analysis selects the antiferromagnetic $\Gamma_7$ representation with moments along $c$ and a refined moment of $1.5(4)\,\mu_B/\mathrm{Co}^{2+}$. In powder samples of $\mathrm{Co}_{1/3}\mathrm{NbSe}_2$, the ground state is a double-$q$ structure: a commensurate $q_1=(0,1/3,0)$ component with moments mostly along $c$ ($1.2(2)\,\mu_B$) and an incommensurate $q_2=(0,1/3,0.048(4))$ sine wave with moments in the $ab$-plane ($2.9(2)\,\mu_B$), spanning roughly 255 Å.

Load-bearing premise

The central claim depends on the assumption that the 28 K transition seen in the single-crystal bulk measurements is the same magnetic order solved in the powder sample of $\mathrm{Co}_{1/3}\mathrm{NbSe}_2$, and that the proposed $2\sqrt{3}a_h\times2\sqrt{3}a_h$ superlattice correctly describes how cobalt atoms are arranged in the crystal.

Editorial extensions

If this is right

Bulk measurements on $\mathrm{Co}_{0.28}\mathrm{NbSe}_2$ must be read as the sum of two magnetic order parameters, not one; the 169 K and 28 K anomalies are separate phase transitions with separate symmetries.
The high-temperature phase is a $c$-axis collinear A-type antiferromagnet, the same structure class proposed for altermagnetism in $\mathrm{Co}_{1/4}\mathrm{NbSe}_2$, so altermagnetic order can coexist with a second, lower-temperature magnetic phase in one crystal.
The low-temperature phase of $\mathrm{Co}_{1/3}\mathrm{NbSe}_2$ is a double-$q$ ground state whose incommensurate component is a long-period ($\approx 255$ Å) $ab$-plane sine wave, consistent with Dzyaloshinskii-Moriya interactions in the non-centrosymmetric structure.
A single structural superlattice with a $(1/3,1/3,0)$ nuclear propagation vector can host both Co site orderings, meaning phase coexistence in these intercalates need not be chemical segregation into separate crystals.
Intercalating cobalt into $2H$-NbSe$_2$ suppresses its charge-density wave and superconductivity while introducing these two magnetic orders, changing the low-temperature phase diagram of the host.

Reading between the lines

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

If the coexistence is controlled by the average cobalt concentration, then compositions between $x=1/4$ and $x=1/3$ should allow continuous tuning of the volume fractions of the two magnetic phases; the paper does not map that phase diagram, but its $x=0.28$ result sits in the tunable window.
The absence of low-temperature magnetic satellites in the single-crystal neutron data leaves open the possibility that the 28 K order is a minority phase in the crystal or lives in regions not sampled by that diffraction condition; a dedicated search for $q_1$ and $q_2$ satellites below 28 K would test whether both orders occupy the same crystal volume.
The incommensurate component $q_2=(0,1/3,0.048(4))$ may lock to a commensurate value at lower temperature or under applied field, which would turn the reported double-$q$ state into a single commensurate multi-$q$ ground state; the paper flags this as an open question.
Because the same host lattice can be intercalated with Fe or Cr, the $2\sqrt{3}a_h\times2\sqrt{3}a_h$ superlattice motif may be a general route to engineering coexisting commensurate and incommensurate magnetic orders across the $M_x$NbSe$_2$ family, though only Co is tested here.

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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

Here's the short version. The paper solves the magnetic structure of Co1/3NbSe2 for the first time—a double-q structure with a commensurate q1=(0,1/3,0) and an incommensurate q2=(0,1/3,0.048) component—and that part is solid. The headline, however, that both the x≈1/4 A-type and x≈1/3 double-q ground states coexist in the same Co0.28NbSe2 single crystal, is not directly demonstrated. The single-crystal neutron diffraction shows only the high-T A-type order (q=0, Γ7, TN=169 K); no low-T magnetic satellites were observed, which the authors state openly. The 28 K anomaly in bulk data and the (1/3,1/3,0) structural superlattice from X-ray are suggestive, but the identification of that anomaly with the powder-solved P6322 double-q phase is inference, not observation.

What's genuinely good: the high-T magnetic structure is solved cleanly from single-crystal neutron data with representation analysis, and the Γ7 choice follows from susceptibility anisotropy. The powder refinements of the double-q phase look reasonable, including the ~255 Å incommensurate modulation. The paper is honest about its main limitation.

Soft spots, in proportion: the superlattice structural model is not quantitatively refined in the main text (no Co occupancies or domain fractions), so it supports but doesn't confirm the coexistence picture. The link between the single-crystal 28 K transition and the powder phase would be much stronger with even a weak magnetic peak in the crystal data; without it, an extrinsic or minority-phase origin can't be excluded. The critical exponent β=0.38(3) is a single fit with several free parameters, consistent with Heisenberg but not a strong test. None of these are fatal, but they are real.

Who gets value from this: anyone working on intercalated TMD magnetism or altermagnetism. The new powder structure is a useful data point, and the high-T solution adds confirmation. But the central coexistence claim should be read as a motivated hypothesis.

Recommendation: yes, send to peer review. A referee can push for quantitative refinement of the superlattice and a clearer separation of direct vs. inferred evidence. The paper deserves a serious look.

Referee Report

3 major / 6 minor

Summary. The paper investigates CoxNbSe2 for compositions near x = 1/4 and x = 1/3. It reports that single crystals of Co0.28NbSe2 exhibit two magnetic transitions, at 169 K and 28 K, assigned to the x ~ 1/4 and x ~ 1/3 phases, respectively. The high-temperature magnetic structure is solved from single-crystal neutron diffraction as a Γ7 A-type antiferromagnet with the moment along c. The low-temperature phase is solved from neutron powder diffraction of Co1/3NbSe2 as a double-q structure with a commensurate vector q1 = (0, 1/3, 0) and an incommensurate vector q2 = (0, 1/3, 0.048). Single-crystal X-ray diffraction shows satellite reflections at q2S = (1/3, 1/3, 0), leading to a 2√3a × 2√3a superlattice model in P6322 that accommodates both the 2a×2a (x ≈ 1/4) and √3a×√3a (x ≈ 1/3) cobalt sublattices. The central claim is the coexistence of both magnetic ground states in a single crystal.

Significance. If verified, the coexistence of a centrosymmetric A-type antiferromagnet and a non-centrosymmetric double-q phase in one single crystal would be a notable contribution to the phase-coexistence literature in intercalated transition-metal dichalcogenides and relevant to altermagnetism. The paper's strengths include the single-crystal neutron solution of the high-temperature phase with representation analysis, the first powder neutron solution of the low-temperature double-q structure, a critical exponent β = 0.38(3) that is close to the Heisenberg value, and the combined use of X-ray and neutron diffraction as complementary probes. The main weakness is that the low-temperature magnetic order is not directly observed in the same single crystal that displays both transitions; the coexistence claim rests on an indirect assignment that is not supported by the magnetic diffraction data presented.

major comments (3)

[Section 3 (Fig. 3), Section 4 (Fig. 4)] The central claim of coexistence is not directly supported by the magnetic diffraction data. In the single-crystal neutron experiment on Co0.28NbSe2, the authors state that 'no satellite reflections were observed' and that 'all magnetic reflections correspond exclusively to TN_A' (Section 3). The low-temperature P6322 double-q magnetic structure was solved only in Co1/3NbSe2 powder (Section 4). Since the 28 K anomaly in the single crystal has no magnetic diffraction counterpart, the identification of this anomaly with the powder-solved double-q phase is an assumption, not a demonstrated result. The paper should either provide single-crystal magnetic evidence for the low-T order (e.g., longer counting at the predicted q1/q2 positions, or a powder sample of Co0.28), or explicitly restate the coexistence claim as a hypothesis.
[Section 2 (Fig. 2)] The 2√3a × 2√3a superlattice model in P6322 is used to argue for structural coexistence of the aA and aS sublattices, but no quantitative refinement of this model is presented in the main text. In particular, the refined Co site occupancies, the domain fraction of each motif, the reliability factors, and the comparison against alternative models (e.g., a P63/mmc average structure with occupational modulation) are not reported. Without these details, the structural coexistence remains a plausible interpretation of the satellite reflections rather than an established result.
[Section 2 and Section 1] The proposed 2√3a × 2√3a superlattice must be consistent with the measured composition Co0.28NbSe2. The text does not state the total Co content implied by the model or how the coexistence of a 2a×2a (x = 1/4) motif and a √3a×√3a (x = 1/3) motif yields an average x = 0.28. The authors should provide the refined composition from the superlattice model and discuss how it compares with the EDS/SXD-determined stoichiometry; otherwise, the structural model may be internally inconsistent.

minor comments (6)

[Section 2] The transformation matrix between the a2S and host-lattice Miller indices is stated without derivation; please define the basis vectors and verify the determinant. Also, '2√3a' is ambiguous—specify whether it is 2 × √3 × a or another combination.
[Section 3] The order-parameter fit to I = I0 + A(1 - T/TN)^{2β} should report the refined TN value, the fitted background I0, and the goodness of fit; currently only β is quoted.
[Section 4] The use of 'double-q' for the combination of q1 = (0, 1/3, 0) and q2 = (0, 1/3, 0.048) should be justified, since the two vectors are not symmetry-related in the conventional sense.
[Figure 2 caption] 'c-diretion' is a typo; also the blue arrows labeling the 2ah×2ah cell are not introduced in the caption text.
[References] The supplemental material is cited as reference [37] without a DOI or URL; the manuscript should provide a stable link or state that it is available with the arXiv posting.
[Abstract] The abstract claims 'we report the coexistence of both substructures within a superlattice' more strongly than the evidence warrants; consider softening to 'we propose' or 'our data are consistent with'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: magnetic and structural refinements use measured intensities, and the coexistence claim rests on independent bulk and diffraction evidence rather than on fitted inputs.

full rationale

The derivation chain is self-contained with respect to the measured data. The high-temperature magnetic structure is solved from single-crystal neutron intensities via irreducible representation analysis, with the moment direction constrained by observed susceptibility anisotropy; this is a standard physical constraint, not a back-fit of the result. The low-temperature double-q structure is refined from neutron powder data on the separately synthesized Co1/3NbSe2 sample, not from the same crystal used to claim coexistence. The coexistence claim in Co0.28NbSe2 rests on directly observed bulk anomalies (susceptibility and specific heat) plus X-ray satellite reflections indexed by q2S=(1/3,1/3,0); the assignment of TN_S to the x~1/3 phase is calibrated on isolated powder samples and is an empirical fingerprint rather than a quantity fitted from the same data. The paper explicitly acknowledges the evidential limitation that no TN_S satellite reflections were observed in the single-crystal neutron experiment ('no satellite reflections were observed', 'all magnetic reflections correspond exclusively to TN_A'), and it pivots to powder diffraction for that phase; acknowledging a gap is not circular. The only self-citation load-bearing candidates are comparative (e.g., ref. [44] citing the same group's Co1/4TaSe2 work for the P6'3/m'm'c magnetic space group), but they are not used to define or derive the present refinements. No equation or fitted parameter is defined in terms of the result it is claimed to produce, and no prediction is renamed from an input. Therefore no circular step is present.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim depends on the modeled supercell and on the assignment of the two bulk transitions to the two Co sublattices. No new particles or forces are introduced. Fitted magnetic moments and propagation vectors are measurements, not theoretical parameters, but they anchor the structural model.

free parameters (6)

Magnetic moment of high-temperature phase = 1.5(4) mu_B/Co
Refined from single-crystal neutron diffraction intensities using Mag2Pol; central to the magnetic structure solution.
Magnetic moment of q1 commensurate phase = 1.2(2) mu_B/Co
Refined from neutron powder diffraction data for Co1/3NbSe2.
Magnetic moment of q2 incommensurate phase = 2.9(2) mu_B/Co
Refined from neutron powder diffraction data; supports the sine-wave model.
Incommensurate component of q2 = 0.048(4) r.l.u.
Refined from the position of the side peaks in the low-Q triplet.
Critical exponent beta = 0.38(3)
Fit to the temperature dependence of the (101) reflection; used to claim Heisenberg-like critical behavior.
Debye-Einstein background parameters = not reported
Used to subtract lattice contribution from specific heat; values not given in the main text.

assumptions (4)

domain assumption The structural model in P6_3 22 with a 2*sqrt(3)a x 2*sqrt(3)a supercell correctly represents the Co site ordering in Co0.28NbSe2.
The superlattice model is used to claim coexistence of both Co sublattices; no explicit site-occupancy refinement is shown in the main text.
domain assumption The 28 K transition in the single crystal corresponds to the same magnetic order solved in Co1/3NbSe2 powder.
Single-crystal neutron diffraction did not observe the low-temperature magnetic reflections, so the assignment relies on bulk measurements and powder results.
domain assumption The magnetic easy axis inferred from susceptibility is the c-axis for the high-temperature phase, which selects Gamma_7 among the twelve possible representations.
This reasoning is stated in the section on single-crystal neutron diffraction and is used to constrain the magnetic structure solution.
standard math Standard crystallographic and representation-analysis tools (SHELX, GSAS-II, Mag2Pol) give reliable results.
The paper relies on these established programs for all structure solutions and refinements.

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Cite this review

Pith. "Pith review of Coexistence of Commensurate and Incommensurate Antiferromagnetic Groundstates in Co$_x$NbSe$_2$ Single Crystal." pith.science (2026). https://pith.science/paper/D6J37OKU

@misc{pith2026250100591,
  author       = {Pith},
  title        = {Pith review of: Coexistence of Commensurate and Incommensurate Antiferromagnetic Groundstates in Co$_x$NbSe$_2$ Single Crystal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D6J37OKU}},
  note         = {Machine review of arXiv:2501.00591}
}

abstract

In Co$_x$NbSe$_2$, crystal symmetry, and cobalt site occupation drive the formation of two distinct magnetic phases. At $x = 1/4$, the centrosymmetric structure ($P$6$_3$/$mmc$) promotes Co-Co interactions leading to the formation of an $A$-type antiferromagnetic structure phase with a transition temperature of $T_N^A$ = 169 K. At $x = 1/3$, the non-centrosymmetric structure ($P$6$_3$22) induces a lower-temperature magnetic phase with $T_N^S$ = 28 K. We report the coexistence of both substructures within a superlattice, with a nuclear propagation vector of (1/3, 1/3, 0) relative to the host lattice. Single crystals of Co$_{0.28}$NbSe$_2$ exhibit both magnetic transitions, with $T_N^A$ corresponding to the $x \sim 1/4$ phase and $T_N^S$ corresponding to the $x \sim 1/3$ phase. Magnetic susceptibility and specific heat measurements confirm these transitions, although only the high-temperature $T_N^A$ phase significantly affects resistivity. We successfully isolate each phase in powder samples, while single crystals with an intercalation ratio of $x = 0.28$ display the coexistence of both phases in a single sample. Using single-crystal neutron diffraction, we solved the magnetic structure of the high-temperature centrosymmetric phase ($T_N^A$), and neutron powder diffraction revealed the double-$q$ magnetic structure of the low-temperature noncentrosymmetric phase ($T_N^S$)

Figures

Figures reproduced from arXiv: 2501.00591 by the authors.

**Figure 3.** FIG. 3. Single crystal neutron diffraction results. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** FIG. 4. Neutron powder diffraction of Co [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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This intensity growth observed between 200 K and 50 K, is consistent with the TN A transition, but no further changes were detected down to 5 K

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