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REVIEW 4 major objections 6 minor 36 references

Absence of ferromagnetic instability and weak spin-orbit coupling effect in AV$_3$Sb$_5$ (A = Cs, Rb, and K)

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The pristine phase of the kagome metals AV$_3$Sb$_5$ (A = Cs, Rb, K) is nonmagnetic, and a previously reported ferromagnetic state is an artifact of an insufficient k-point mesh.

desk verdict A useful, mostly convincing computational correction to the claimed magnetism in AV3Sb5; the k-mesh artifact explanation holds up, though 'definitively' overreaches the two-mesh evidence. read the letter →

arxiv 2412.07190 v1 pith:BEZUE5SI submitted 2024-12-10 cond-mat.mtrl-sci cond-mat.supr-con

Chongze Wang , Shichang Yao , Shuyuan Liu , Bing Wang , Liangliang Liu , Yu Jia , Jun-Hyung Cho This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.supr-con
keywords kagomemetalsAV3Sb5ferromagneticinstabilityStonercriterionspin-orbitcouplingk-pointmeshconvergencePauliparamagnetismdensityfunctionaltheory
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 argues that the pristine phase of the kagome superconductors AV$_3$Sb$_5$ (A = Cs, Rb, K) has a nonmagnetic ground state, and that the ferromagnetic state reported in a recent first-principles study is an artifact of an insufficiently dense k-point mesh. With a coarse $5\times5\times3$ mesh the authors reproduce the ferromagnetic solution, but a dense $18\times18\times12$ mesh makes spin-polarized calculations converge to a nonmagnetic state whose paramagnetic susceptibility matches the Pauli-like response measured in single crystals. They also find that spin-orbit coupling changes the geometry and band structure only slightly, opening a gap of less than about 20 meV at the Dirac points, and that the DFT bands align closely with angle-resolved photoemission data, indicating weak electron correlations. If the conclusion holds, magnetism, strong spin-orbit effects, and strong correlations drop out of the explanation of the charge-density-wave physics in these materials.

What carries the argument

The key mechanism is the Stoner criterion $I\cdot D(E_F) > 1$, evaluated using the density of states at the Fermi level and an exchange parameter $I$ estimated from the ratio of exchange splitting to magnetic moment. The paper demonstrates that this criterion is sensitive to Brillouin-zone sampling: the coarse $5\times5\times3$ mesh inflates $D(E_F)$ (to 10.97, 8.66, and 7.85 states/eV per unit cell), producing $I\cdot D(E_F)$ values of 1.82, 1.44, and 1.21 and a spurious ferromagnetic minimum, while the dense $18\times18\times12$ mesh gives $I\cdot D(E_F)$ below 1 and a nonmagnetic minimum. The fixed-spin-moment method is the supporting tool, tracing total energy as a function of magnetization for both meshes and yielding a paramagnetic susceptibility consistent with Pauli paramagnetism.

What would settle it

A spin-polarized DFT calculation with the same functional but a denser mesh (for example $24\times24\times16$) that recovers a ferromagnetic or antiferromagnetic solution with nonzero V moments would falsify the central claim, as would a measurement on ultra-clean single crystals showing an intrinsic Curie-Weiss magnetic susceptibility that cannot be attributed to impurity spins.

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Extended reading notes

Core claim

The central claim is that the ground state of pristine AV$_3$Sb$_5$ (A = Cs, Rb, K) is nonmagnetic, contradicting a recent DFT+DMFT+SOC study that predicted local moments on V atoms. The paper shows that a $5\times5\times3$ k-point mesh overestimates the density of states at the Fermi level, pushing the Stoner product $I\cdot D(E_F)$ above 1 and stabilizing a ferromagnetic state, whereas an $18\times18\times12$ k-mesh yields $D(E_F)$ values of 6.58, 6.42, and 6.16 states/eV per unit cell for CsV$_3$Sb$_5$, RbV$_3$Sb$_5$, and KV$_3$Sb$_5$ and no ferromagnetic solution. Total-energy versus magnetization curves from the fixed-spin-moment method confirm a nonmagnetic minimum with the dense mesh. Spin-orbit coupling produces geometry changes below 0.01 \AA\ and a Dirac-point gap smaller than about 20 meV. The DFT band structures reproduce the van Hove singularities and Dirac points measured by ARPES, which the paper interprets as evidence against strong correlations and against the notion that magnetism, spin-orbit coupling, and correlations drive the charge-density wave.

Load-bearing premise

The load-bearing premise is that the PBE exchange-correlation functional with the DFT-D3 dispersion correction and an $18\times18\times12$ k-mesh correctly captures the magnetic ground state, untested against antiferromagnetic orders, Hubbard U, hybrid functionals, or intermediate k-mesh densities.

Editorial extensions

If this is right

  • Charge-density-wave and superconductivity models for AV$_3$Sb$_5$ should proceed without intrinsic V moments, shifting weight to orbital or loop-current mechanisms.
  • Published first-principles results for AV$_3$Sb$_5$ obtained with a $5\times5\times3$ k-mesh should be re-examined, since the magnetic ground state flips with Brillouin-zone sampling.
  • The SOC-induced gap at the Dirac points is bounded by about 20 meV, constraining topological or Berry-curvature effects that rely on this splitting.
  • Standard PBE band structures, without Hubbard U or DMFT corrections, adequately describe the normal-state bands near the Fermi level.

Reading between the lines

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

  • The same k-mesh artifact could affect other narrow-band or van Hove metals where a coarse sampling inflates the Fermi-level DOS; a mesh-convergence test should precede any Stoner-based magnetism claim.
  • The calculated susceptibility (roughly $6.5\text{--}8.5 \times 10^{-4}$ emu/mol) overshoots the experimental Pauli value by about a factor of two; a finite-temperature treatment of spin fluctuations within the same framework could test whether that gap closes.
  • If the nonmagnetic ground state is correct, the anomalous Hall effect and chiral charge order reported in these kagome metals likely arise from nonmagnetic time-reversal-symmetry-breaking mechanisms associated with the CDW itself, rather than from local V moments.
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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 / 6 minor

Summary. The paper reports DFT and DFT+SOC calculations for the kagome metals AV3Sb5 (A = Cs, Rb, K). The authors show that the previously reported ferromagnetic (FM) state, obtained with a 5×5×3 k-mesh, is not reproduced with a denser 18×18×12 k-mesh: spin-polarized calculations converge to a nonmagnetic (NM) solution, fixed-spin-moment curves decrease monotonically to M = 0, and the coarse-mesh FM instability is attributed to an artificial enhancement of the density of states at the Fermi level satisfying the Stoner criterion. They further find that spin-orbit coupling (SOC) has a minor effect on the band structure, opening gaps of less than approximately 20 meV at the Dirac points, and that their DFT bands agree well with ARPES data, supporting weak electron correlations. They conclude that the pristine phase is nonmagnetic and that magnetism, SOC, and correlations do not play the decisive role in the CDW physics claimed by Hasan et al.

Significance. If correct, the paper resolves a current controversy by showing that a high-profile theoretical prediction of FM order in AV3Sb5 is a numerical artifact of insufficient k-point sampling. The two-mesh comparison and fixed-spin-moment curves are a useful diagnostic, and the comparison with ARPES and magnetic susceptibility provides external validation. The paper also reinforces the weak-correlation picture for these kagome metals. However, the strength of the conclusion is not fully matched by the evidence: the k-mesh convergence is not established, only one exchange-correlation functional is used, and antiferromagnetic configurations are not considered.

major comments (4)
  1. [§II–III, Fig. 3, Table I] The central claim that the pristine phase is 'definitively NM' is supported only by a comparison between two k-meshes (5×5×3 and 18×18×12), with no systematic convergence study. The density of states at the Fermi level changes dramatically between these meshes (e.g., from 10.97 to 6.58 states/eV for CsV3Sb5 in Section III), which shows that neither mesh is demonstrably converged for this quantity. The fixed-spin-moment curves in Fig. 3 show a monotonic decrease of E(M) for the dense mesh, but they do not rule out the possibility that an even denser mesh or a different smearing/tetrahedron integration scheme would restore a magnetic solution. The authors should provide intermediate k-meshes (e.g., 9×9×6, 12×12×8, 15×15×10) and specify the Brillouin-zone integration method, or soften the 'definitively NM' claim.
  2. [§III, first paragraph; Abstract] The statement that 'any initial configuration of magnetic moments quickly converges to a NM solution' is only verified for collinear FM starting states. The abstract's broader claim of a 'nonmagnetic pristine phase' would require testing of antiferromagnetic (AFM) and possibly noncollinear spin configurations, which are not reported. Since the title is limited to the 'absence of ferromagnetic instability,' the authors should either test AFM orders or explicitly restrict their conclusion to the FM instability.
  3. [§III, Stoner criterion paragraph] The Stoner product I·D(EF) is quoted only for the 5×5×3 mesh (1.82, 1.44, and 1.21 for CVS, RVS, and KVS, respectively). The corresponding values for the 18×18×12 mesh are not given, so the reader cannot verify that the dense mesh is on the nonmagnetic side of the Stoner criterion. Moreover, the Stoner parameter I is estimated from the exchange splitting and magnetic moment of the self-consistent FM state at the coarse mesh; this quantity may itself be mesh-dependent. Providing D(EF) and I at the dense mesh would complete the quantitative argument.
  4. [§II, §III] The conclusion is based exclusively on the PBE exchange-correlation functional. While PBE is an appropriate choice for comparing with the previous PBE-based claim, the paper's broader statement that the pristine phase 'possesses a NM ground state' (Summary) goes beyond the evidence. A test with PBE+U or a hybrid functional, or at minimum a caveat that the result is functional-dependent, would make the claim robust.
minor comments (6)
  1. [§II] Typo: 'ad DFT' should be 'and DFT'.
  2. [§III] Typo: 'tough' should be 'though' in the sentence 'rough their predicted magnetic moment...'.
  3. [Fig. 2 caption] The definition of exchange splitting is convoluted; it should be stated directly as the difference between the spin-up and spin-down Kohn-Sham eigenvalues at the same k-point or as an average.
  4. [§II] The Brillouin-zone integration scheme (e.g., Methfessel-Paxton smearing, tetrahedron method with Blöchl corrections) and the smearing width are not specified; this matters for the DOS(EF) values in Table I and the text.
  5. [References] The placeholder URL for the Supplemental Material (Ref. [31]) should be replaced with the actual link.
  6. [§III] The phrase 'definitively NM' is too informal; consider 'nonmagnetic within the present DFT approach' or similar.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NM ground-state claim is an independent DFT result benchmarked against external experiments, not a fit or self-citation chain.

full rationale

The paper's central claim is that the pristine phase of AV3Sb5 is nonmagnetic when computed with an 18x18x12 k-mesh, and that the previously reported ferromagnetic state arises from a coarse 5x5x3 mesh that artificially inflates DOS(EF) and satisfies the Stoner criterion. This is a direct DFT result: the input is the PBE functional, DFT-D3 correction, and a chosen k-mesh, and the output is the total energy as a function of magnetization from fixed-spin-moment calculations. No parameter is fitted to the experimental quantities the paper claims to explain. The comparison with Pauli susceptibility is post-hoc and explicitly overestimated, not used to constrain the calculation. The reproduction of the FM state with the coarse mesh uses the same DFT machinery, so it is not a fitted-input-then-predicted construction. The self-citations [23-26] are used only as precedents for computational parameters (e.g., k-mesh and cutoff for CDW studies) and do not carry the magnetic ground-state conclusion. External benchmarks (ARPES data, muon spin rotation, magnetization measurements) are independent of the DFT calculations. The lack of a systematic k-mesh convergence study beyond two meshes, and the absence of AFM or noncollinear calculations, are correctness or convergence risks, not evidence of circular reasoning. Therefore the derivation is self-contained with respect to its inputs, and no circular step can be exhibited from the paper's own equations or citations.

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

No new physical entities or fitted constants are introduced. The load-bearing inputs are standard DFT settings plus three modeling assumptions: PBE adequacy, k-mesh convergence, and the fixed-spin-moment susceptibility interpretation. These are reasonable but not independently certified.

assumptions (4)
  • domain assumption PBE plus DFT-D3 adequately describes the electronic and magnetic ground state of AV3Sb5.
    Section II: all central conclusions use this functional; no U, hybrid, or DMFT benchmark is given.
  • domain assumption The 18x18x12 mesh is sufficiently dense to converge the magnetic ground state.
    Section III uses this mesh for the NM conclusion; no explicit convergence test beyond comparison with 5x5x3 is provided.
  • domain assumption Fixed-spin-moment energy curvature gives a meaningful estimate of magnetic susceptibility.
    Section III: chi is derived from d^2E/dM^2 and compared with measured Pauli susceptibility; spin fluctuations are neglected.
  • domain assumption ARPES band positions validate the DFT band structure and therefore imply weak correlations.
    Section III uses ARPES comparison to dismiss DMFT+SOC results; ARPES is a surface-sensitive probe and the comparison is qualitative.

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Pith. "Pith review of Absence of ferromagnetic instability and weak spin-orbit coupling effect in AV$_3$Sb$_5$ (A = Cs, Rb, and K)." pith.science (2026). https://pith.science/paper/BEZUE5SI

@misc{pith2026241207190,
  author       = {Pith},
  title        = {Pith review of: Absence of ferromagnetic instability and weak spin-orbit coupling effect in AV$_3$Sb$_5$ (A = Cs, Rb, and K)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BEZUE5SI}},
  note         = {Machine review of arXiv:2412.07190}
}
abstract

A family of V-based kagome metals AV$_3$Sb$_5$ (A = Cs, Rb, K) presents an intriguing platform for exploring the interplay of time-reversal symmetry breaking, nontrivial topological bands, and electron correlations, resulting in a range of exotic quantum states, including the anomalous Hall effect, unconventional charge density waves, and superconductivity. These features prompt critical questions regarding the roles of magnetism and spin-orbit coupling (SOC) in these systems. Our density functional theory (DFT) calculations demonstrate a notable sensitivity of the magnetic properties to the choice of $k$-point mesh used in Brillouin zone integrations. Specifically, we find that using a dense $k$-point mesh yields a nonmagnetic pristine phase characterized by paramagnetic susceptibility, consistent with the recently observed Pauli paramagnetic behavior in single crystalline samples at high temperatures. In contrast, a coarser $k$-point mesh significantly increases the density of states at the Fermi level, inducing a ferromagnetic instability that satisfies the Stoner criterion. Moreover, our results show that the effect of SOC on both the geometric and electronic structures is minimal, with only a slight gap opening at the Dirac points, indicating a weak SOC influence in these materials. Importantly, our DFT band structure calculations closely align with angle-resolved photoemission spectroscopy data, reinforcing the notion of weak electron correlations in these kagome metals. This refined understanding challenges recent theoretical assertions that the interplay of magnetism, SOC, and electron correlations is essential for determining the nature of charge density waves in AV$_3$Sb$_5$.

Figures

Figures reproduced from arXiv: 2412.07190 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Optimized structure of the pristine phase of CsV [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Calculated FM band structures of (a) CsV [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Comparison of the DFT and DFT + SOC band structures [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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