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Magnetic ground states of CrPS$_4$ and NiPS$_3$ monolayers from long-range exchange interactions

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper shows that the magnetic ground states of CrPS4 and NiPS3 monolayers are set by long-range exchange interactions, not by the few nearest-neighbor couplings used in earlier models: CrPS4 becomes a spin spiral and NiPS3's zigzag ord

desk verdict CrPS4 spin-spiral rests on a ferromagnetically relaxed lattice; the NiPS3 J5 result is solid — worth a serious referee, but the CrPS4 conclusion needs more work. read the letter →

arxiv 2607.20631 v1 pith:CQMN3SLF submitted 2026-07-22 cond-mat.mtrl-sci

Balazs Nagyfalusi , Ritesh Das , Alvaro Bermejillo-Seco , Herr S. J. van der Zant , Yaroslav M. Blanter , Amador Garcia-Fuente , Jaime Ferrer This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords CrPS4monolayerNiPS3spinspiralzigzagantiferromagnetismlong-rangeexchangeinteractionsfrustrationtwo-dimensionalvanderWaalsmagnetsMonteCarlomodel
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 sets out to show that the standard practice of truncating magnetic exchange interactions after the first few neighbor shells fails for two thiophosphate monolayers. By extracting exchange tensors directly from density functional theory and pushing the interaction range until the results converge, the authors find that CrPS4's true ground state is a long-wavelength spin spiral rather than the ferromagnet predicted by short-range models, and that NiPS3's experimentally observed zigzag order appears only when fifth-neighbor couplings are included. If right, these results mean that quantitatively predictive spin models for two-dimensional van der Waals magnets must include long-range exchange, and that earlier short-range predictions for CrPS4's ordering and transition temperature were qualitatively wrong.

What carries the argument

The central object is the set of tensorial exchange interactions extracted directly from the electronic structure rather than fitted to total energies; the isotropic part of each pair's exchange tensor is included shell by shell until ground state and critical temperature converge. In CrPS4, the decisive coupling is the fourth-shell antiferromagnetic interaction J4, which opposes the ferromagnetic first-neighbor bonds along the b-direction; combined with a structural dimerization that splits the first-neighbor couplings into two inequivalent values, it drives the spin spiral. In NiPS3, the decisive coupling is the fifth-shell antiferromagnetic interaction J5 ≈ 2 J1, which supplies the frustr

What would settle it

Relax the CrPS4 monolayer lattice self-consistently in the spin-spiral magnetic state and recompute the exchange tensors and Monte Carlo transition temperature; if the spiral and the ~21 K Tc do not survive this relaxation, the paper's central claim for CrPS4 fails.

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Extended reading notes

Core claim

The paper claims that in monolayer CrPS4, a fourth-neighbor antiferromagnetic exchange couples second neighbors along the b-direction and competes directly with the ferromagnetic first-neighbor couplings, frustrating the collinear ferromagnet and stabilizing a spin spiral with a wavelength of about 6.9 lattice constants. When exchange interactions are extended to numerical convergence (about the tenth shell), the Monte Carlo critical temperature settles near 21 K, matching the experimental value around 23 K. In monolayer NiPS3, the paper finds that a model truncated at the third shell produces a staggered antiferromagnetic state; the experimentally observed zigzag order appears only when the

Load-bearing premise

For CrPS4, the entire spin-spiral picture rests on a lattice that was relaxed in a ferromagnetic four-atom unit cell, which cannot represent the spiral state; if the true spiral equilibrium has different bond lengths, the exchange tensors, wavevector, and transition temperature could shift.

Editorial extensions

If this is right

  • Monolayer CrPS4 is predicted to be a spin spiral at zero field, with a critical temperature of about 21 K; the experimentally reported ~23 K transition is reproduced only when exchange interactions are included out to the tenth shell.
  • The (B,T) phase diagram of monolayer CrPS4 contains a spin-spiral phase, a canted spin-spiral phase with a net out-of-plane moment, and a field-induced ferromagnetic phase, so magnetic fields can be used to switch between non-collinear orders.
  • Monolayer NiPS3 requires exchange interactions up to the fifth shell to obtain the experimentally observed zigzag antiferromagnetic order; a three-shell model gives the wrong (staggered) ground state, while the five-shell model is sufficient and yields Tc ≈ 61 K.
  • The spin-wave spectra computed from the full long-range models reproduce the main measured magnon features for both materials, whereas truncating the exchange range or averaging out the structural dimerization in CrPS4 degrades the agreement.

Reading between the lines

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

  • If the CrPS4 spiral is real, zero-field experiments that reported out-of-plane ferromagnetism may have been probing the field-polarized state; a zero-field local probe (spin-polarized scanning tunneling microscopy, for instance) could directly image the spiral and its ~6.9-unit-cell wavelength.
  • The paper's finding that CrPS4's spiral unwinds when the dimerization is artificially removed suggests uniaxial strain along the b-direction could tune the spiral pitch or suppress it entirely, a testable extension.
  • The systematic failure of short-range fitted models in these two compounds implies that apparent discrepancies in other 2D magnets may also trace back to omitted long-range exchange, not to missing anisotropy or interlayer coupling; applying the same convergence protocol to those materials could resolve similar puzzles.
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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

3 major / 5 minor

Summary. The paper investigates monolayer CrPS4 and NiPS3 using DFT with the LKAG formalism to extract tensorial exchange interactions, then uses Monte Carlo to determine ground states and critical temperatures as a function of the number of exchange shells. For CrPS4, the authors claim that including long-range exchange (beyond third shell) destabilizes the previously predicted ferromagnetic state and stabilizes a spin spiral, reducing Tc to ~21 K, in agreement with experiments. For NiPS3, they claim that the experimentally observed zigzag antiferromagnetic order only emerges when fifth-shell interactions are included. The central methodological claim is that conventional three-shell Heisenberg models fitted to total energies are insufficient for these thiophosphate monolayers, and that LKAG-derived exchange tensors with convergence in the number of shells are required.

Significance. If correct, the results would establish that short-range Heisenberg models are qualitatively inadequate for two important 2D magnetic semiconductors, providing a broader lesson for first-principles spin-model construction. The use of LKAG without total-energy fitting, systematic shell-number convergence checks, and Monte Carlo with demonstrated finite-size control are explicit strengths. The NiPS3 result—fifth-shell exchange providing the frustration for zigzag order—appears robust and is a valuable contribution. The CrPS4 spin-spiral claim, however, rests on an acknowledged but unresolved structural inconsistency: the exchange tensors are extracted from a ferromagnetically relaxed unit cell that cannot accommodate the spiral, and the Hubbard U is chosen to match the very Tc later quoted as agreement. These issues do not invalidate the methodology but leave the most dramatic claim not yet established.

major comments (3)
  1. [Sec. III, Eq. (3)] The CrPS4 exchange tensors are obtained from a DFT calculation whose structural relaxation was restricted to a four-Cr ferromagnetic unit cell, which the authors state 'cannot accommodate the long-wavelength spin-spiral state identified below.' Since the spiral is stabilized by the dimerization (reducing J1a/J1b splitting unwinds the spiral, per Eq. (3)), the FM-relaxed lattice may not be representative of the spiral ground state. If the true spiral has a different magnetostrictive distortion, J1a, J1b, J4, and higher shells all change, potentially altering q and Tc or destroying the spiral. The authors acknowledge the limitation but do not perform a self-consistent relaxation of the spiral state or a robustness check with respect to the lattice. This is load-bearing for the central claim; I request either a spiral-state relaxation in a sufficiently large cell or a controlled test showin
  2. [Sec. III, 'U=0 provides the best agreement...'] The Hubbard U for CrPS4 was selected as U=0 because it reproduces the experimental Tc~23 K, and then the computed Tc≈21 K is quoted as 'excellent agreement.' This is partially circular: the agreement is built into the parameter choice. The paper does not report how the exchange interactions, spiral wavevector, or Tc vary with U∈{1,2} eV, even though the authors state they tested U=0–2 eV. A robustness scan over U (or a U determined from an independent observable such as the magnon spectrum or band gap) is needed to support the claim that the long-range-exchange mechanism is not an artifact of the U selection.
  3. [Sec. III, Fig. 3(a)] The transition from FM to spin-spiral is stated to occur when interactions up to the seventh shell are included, and Tc converges only at the tenth shell. However, the figure appears to show the ground-state switch at N_s=7 with Tc still decreasing substantially beyond that. Since the central claim involves both the ground-state symmetry and the quantitative Tc, the convergence criterion for 'numerical convergence' should be specified explicitly (e.g., change in Tc below a threshold) rather than inferred from the figure. This is a presentation issue, but it bears on the reproducibility of the claimed convergence.
minor comments (5)
  1. [Sec. II, Eq. (1)] The definition of J_ij as the isotropic coupling (1/3 trace) should be stated more prominently; currently it appears only in text after the Hamiltonian. Also, the single-ion anisotropy tensor A_i is not defined in the equation explicitly (it is clear from context).
  2. [Sec. III, Fig. 4] The phase diagram labels SS and SS' but the reader must infer the field/temperature ranges from the text. Adding dashed lines or annotations to mark the 0.45 T and 1.3 T boundaries would improve readability.
  3. [Sec. IV, Fig. 11] The Tc values for N_s=3 and N_s=5 are close (68 K vs 61 K), and the figure error bars are not defined. Please indicate whether these differences are within Monte Carlo uncertainty, especially since 'the fifth-neighbor interaction stabilizes the zigzag phase' but Tc changes modestly.
  4. [General] The phrase 'parameter-free exchange tensors' in Sec. III is overstated: the LKAG extraction avoids fitting total energies, but the results still depend on the choice of XC functional and Hubbard U. Suggest rephrasing to 'fit-free' or 'not fitted to total energies.'
  5. [References] Ref. [45] is dated 2026 and Ref. [46] is dated 2025; please verify these are published or give preprint DOIs. Several references to 'in preparation' (Ref. [25]) should be flagged as such.

Circularity Check

2 steps flagged · score 6.0 of 10

Quantitative 'agreement' claims for Tc and magnon bandwidth are partly fitted through Hubbard-U selection; the qualitative shell-convergence results remain independent.

  1. fitted input called prediction [Sec. III, CrPS4 results, U selection and Tc comparison]
    "Among these values, U=0 provides the best agreement with the experimentally reported transition temperature of approximately 23 K for monolayer CrPS4 [14] and is therefore adopted throughout this section. ... The resulting transition temperature of 21 K is in excellent agreement with the experimentally reported value for monolayer CrPS4 [14]."

    The Hubbard U is an input parameter of the DFT+U calculation that controls the exchange tensors entering the spin Hamiltonian. The paper explicitly selects U=0 because it reproduces the experimental Tc≈23 K, and then presents the Monte Carlo result Tc≈21 K as 'excellent agreement.' The agreement is therefore not an independent test: the Hamiltonian was tuned to the very observable later quoted as a prediction. The FM-to-spiral shell-convergence is not itself a fit, but the quantitative Tc claim is partly by construction, and no robustness of the spiral against U=1–2 eV is reported.

  2. fitted input called prediction [Sec. IV, NiPS3 results, U selection and magnon comparison]
    "To determine the optimal Hubbard parameter, we compared the calculated electronic gap and spin-wave spectrum with the available experimental data [37]. We found that U=4 eV provides the best overall agreement with the measured magnon dispersion ... U=4 eV provides the best overall agreement with the experimental dispersion."

    The Hubbard U is chosen by fitting the computed magnon dispersion to the experimental neutron-scattering data, and the same experimental dispersion is then cited as validation of the model. The reproduced magnon bandwidth is thus an input-adjusted outcome rather than an independent prediction. The separate qualitative result that the fifth-shell interaction stabilizes the zigzag ground state is less affected, since U=0 structural relaxations already give zigzag as the lowest-energy configuration, but the quantitative spin-wave agreement is by construction.

full rationale

The paper's central qualitative claims—that long-range exchange interactions destabilize the ferromagnetic state in CrPS4 in favor of a spin spiral and that the fifth-neighbor interaction is required for the zigzag ground state in NiPS3—are not circular in the narrow sense. The exchange tensors are obtained from LKAG/DFT rather than fitted to total energies or to the target magnetic orders, and the Monte Carlo simulations are self-contained. However, two quantitative 'agreement' claims are weakened by parameter fitting. For CrPS4, U=0 is explicitly adopted because it best matches the experimental Tc≈23 K, and the resulting Tc≈21 K is then reported as excellent agreement; this is a fitted-input-called-prediction pattern for the Tc claim. For NiPS3, U=4 eV is chosen by comparing the computed magnon spectrum to the measured dispersion, and the same agreement is later invoked as validation. These steps do not make the shell-convergence conclusions themselves fitted, but they do make the quantitative agreements partially by construction. The self-citations to the in-house codes grogu and Magnopy are tool citations and are not load-bearing circularity. A separate consistency limitation, noted by the authors in Sec. III, is that the CrPS4 structural relaxation was performed in a four-Cr ferromagnetic cell 'which cannot accommodate the long-wavelength spin-spiral state identified below'; this is a robustness/self-consistency concern rather than a definitional circularity, and it should be weighed as a correctness risk. Overall, the paper has substantial independent content, but the two fitted quantitative agreements justify a partial-circularity score of 6.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central results rest on two tuned Hubbard U values, one per material, each selected to reproduce the very experimental quantity later quoted as agreement. The LKAG method and the classical spin Hamiltonian are standard, but no independent benchmark for the long-range exchange tensors is provided, and the CrPS4 spiral is modeled on a lattice relaxed in a ferromagnetic state. No new physical entities are introduced.

free parameters (2)
  • Hubbard U (CrPS4) = 0 eV
    Adopted because it 'provides the best agreement with the experimentally reported transition temperature of approximately 23 K' (Sec. III), i.e., selected to match the experiment later used as validation.
  • Hubbard U (NiPS3) = 4 eV
    Chosen to match measured magnon dispersion (Sec. IV): 'U=4 eV provides the best overall agreement with the measured magnon dispersion'.
assumptions (4)
  • domain assumption LKAG linear-response formalism provides quantitatively reliable exchange tensors in these gapped magnetic insulators.
    The entire second-principles model rests on this mapping (Refs. 22–23); no external benchmark is given for the long-range tensors.
  • domain assumption The classical bilinear Heisenberg + DM + single-ion anisotropy Hamiltonian (Eq. 1) is complete for these systems.
    Higher-order spin terms and magnetoelastic couplings are neglected; used throughout Secs. III–IV.
  • ad hoc to paper For CrPS4, the structure relaxed in the ferromagnetic phase is representative of the spin-spiral ground state.
    The 4-Cr cell cannot host the spiral; authors state this explicitly ('structural relaxations were performed using the four-Cr-atom unit cell ... which cannot accommodate the long-wavelength spin-spiral state'). The dimerization from the FM state is used as input to the spiral model.
  • domain assumption PBE(+U) with in-house norm-conserving pseudopotentials fitted to ELK is an adequate electronic-structure description.
    Underlies all DFT inputs; method choice affects gap and exchange magnitudes.

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Cite this review

Pith. "Pith review of Magnetic ground states of CrPS$_4$ and NiPS$_3$ monolayers from long-range exchange interactions." pith.science (2026). https://pith.science/paper/CQMN3SLF

@misc{pith2026260720631,
  author       = {Pith},
  title        = {Pith review of: Magnetic ground states of CrPS$_4$ and NiPS$_3$ monolayers from long-range exchange interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CQMN3SLF}},
  note         = {Machine review of arXiv:2607.20631}
}
abstract

We investigate the magnetic properties of monolayer CrPS$_4$ and NiPS$_3$ by combining first-principles calculations, second-principles spin models, and Monte Carlo simulations. Unlike conventional approaches that truncate exchange interactions after only a few shells and determine them by fitting total energies, we extract the magnetic exchange tensors directly from density functional theory using the LKAG formalism and include interactions until numerical convergence is achieved. We show that long-range exchange interactions qualitatively modify the magnetic behavior of both materials. In CrPS$_4$, they destabilize the previously predicted ferromagnetic ground state and stabilize a spin-spiral phase, reducing the critical temperature to about 21\,K, in agreement with available experiments. The resulting magnetic phase diagram contains multiple collinear and non-collinear phases that can be tuned by temperature and external magnetic fields. In NiPS$_3$, the experimentally observed zigzag antiferromagnetic order only emerges when exchange interactions up to the fifth shell are included. These results demonstrate that quantitatively predictive spin models for thiophosphate monolayers require long-range exchange interactions and provide a predictive framework for accurately describing two-dimensional van der Waals magnets.

Figures

Figures reproduced from arXiv: 2607.20631 by the authors.

Figure 1
Figure 1. FIG. 1. Optimized crystal structure of a CrPS [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) First five shells defining the isotropic exchange in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Critical temperature [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Magnetic phase diagram of a CrPS [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Specific heat [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Average out-of-plane magnetization [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Optimized crystal structure of a NiPS [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Linear spin-wave spectrum of a CrPS [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Geometry of the first three exchange shells in a [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Symmetry-equivalent zigzag magnetic configu [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Critical temperature [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strain-controlled magnetism and magnetoelasticity in monolayer NiPS$_3$ and CrPS$_4$

    cond-mat.mtrl-sci 2026-08 conditional novelty 6.0 of 10

    A strain-dependent spin model built from DFT exchange interactions predicts that CrPS4 monolayers have strong anisotropic magnetoelastic coupling with strain-driven spiral-to-ferromagnetic transitions, while NiPS3 mon...

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