{"id":"6262b8f7-6ada-45ad-b4e9-35e5659ebeec","arxiv_id":"2608.11356","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"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 monolayers couple weakly to strain.","lead":"This paper computes how stretching two atom-thin magnetic crystals, NiPS3 and CrPS4, changes their magnetic order and mechanical stiffness. It predicts that CrPS4 responds strongly to strain, switching between spiral and aligned magnetic states, which could make it useful for strain-controlled magnetic devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The most load-bearing concern is that CrPS4's spin-spiral magnetoelastic predictions are built from exchange derivatives extracted in the collinear FM state, with no test of transferability to the noncollinear state (Sec. IV).","rationale":"The reader's weakest_assumption correctly identifies the CrPS4 FM-to-spiral transferability problem, and my read of the full text agrees that this is the most load-bearing assumption. The formal derivation in Sec. II is coherent, the shell-convergence checks for A in Figs. 6 and 11 are useful, and the NiPS3 results are less exposed because the DFT reference state is the actual zigzag ground state. However, for CrPS4 the manuscript itself states that the true spiral ground state was not used in DFT, and the same FM-derived exchange derivatives are used both for Monte Carlo phase stability and for the SS magnetostrictive tensors. If those derivatives are state-dependent, the central quantitative predictions for CrPS4 — the strain-driven spiral-to-FM transitions, the SS-phase T_c enhancement, and the ~0.1% magnetostrictive jump — could change substantially. I also note that the paper's isotropic-exchange-only construction of A and B and the absence of released data are secondary concerns; they affect quantitative precision but do not threaten the overall framework as directly as the FM-to-SS transferability does. The proposed generalized Bloch theorem test is a concrete, feasible way to settle whether the assumption holds. Since the paper is already CONDITIONAL and the reader's concern matches mine, no verdict change is needed; the condition should explicitly require the spiral-state transferability check before the CrPS4 magnitudes are relied upon.","tokens_in":16158,"tokens_out":6653,"duration_ms":72078,"concrete_test":"Perform spin-spiral DFT calculations using the generalized Bloch theorem for CrPS4 at the relaxed FM-optimized geometry and at two representative strains (e.g., ε_y = −1% and +1%), constraining the spiral vector q=(0,2π/λ,0) with λ≈6.9b, and extract the exchange parameters J_N and their strain derivatives by fitting the energy dispersion E(q) with the same long-range Heisenberg Hamiltonian used in the paper. Compare the resulting b_μ and a_μν against Table III. If the SS-derived A_SS and B_SS differ from the FM-derived values by more than ~20%, the transferability assumption is falsified and the quantitative phase diagram and magnetostriction claims for CrPS4 should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section IV the authors state that the true CrPS4 ground state is a spin-spiral with propagation vector q=(0,q,0) and wavelength λ≈6.9b, and that this state is 'computationally inaccessible within conventional first-principles calculations.' Consequently, 'all DFT calculations were performed for the collinear FM state with spins aligned along the z direction.' The strain-dependent exchange parameters J_N(ε), and hence the first and second strain derivatives b_μ and a_μν in Table III, are therefore obtained from FM-constrained DFT. These parameters are then used to predict (i) the spin-spiral phase stability and strain-driven phase diagram in Fig. 8, (ii) the strain-dependent critical temperatures in Fig. 10, and (iii) the SS magnetoelastic tensors A_SS and B_SS through the phase factor e_i·e_j = cos(q·r_ij), leading to the magnetostrictive strains in Eq. (13). All of these steps assume J_ij and its strain derivatives are identical in the noncollinear spiral state and in the collinear FM reference. In a superexchange-dominated semiconductor such as CrPS4, the FM and spiral states can differ in self-consistent charge/orbital occupations and spin-orbit-induced exchange anisotropy, so this transferability is not guaranteed. If b_μ or a_μν differ by even 20–30% in the SS state, the predicted SS magnetostriction and the nearly 0.1% magnetostrictive jump across the FM–SS transition would shift proportionally, and the phase-boundary locations in Fig. 8 could move. The paper provides no cross-check of this assumption, leaving the central quantitative claim for CrPS4 unverified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript develops a first-principles framework for magnetoelasticity in two-dimensional magnets, in which the first and second strain derivatives of Heisenberg exchange interactions define a generalized magnetoelastic force B and a magnetic correction A to the elastic tensor. The authors apply this framework to monolayer NiPS3 and CrPS4, combining DFT with a long-range exchange mapping and Monte Carlo simulations. They conclude that NiPS3 has weak, nearly isotropic spin-lattice coupling with magnetostrictive strains around 0.01–0.02%, while CrPS4 shows strong anisotropic coupling, a strain-driven spiral-to-ferromagnetic phase diagram, and a magnetostrictive jump of nearly 0.1% at the FM–SS transition. The framework is general, and the shell-resolved convergence analyses for A and B are a useful contribution.","tokens_in":16450,"tokens_out":12223,"duration_ms":110313,"significance":"If correct, this work provides a practical first-principles route to compute magnetostrictive strains and magnetic elastic renormalizations from strain-dependent exchange interactions, complementing existing spin-phonon treatments. The explicit tabulation of exchange derivatives, the convergence checks with interaction shells (Figs. 6 and 11), and the contrasting material predictions are valuable and likely to guide experiments on strain engineering in CrPS4. The central physical distinction between weak coupling in NiPS3 and strong, anisotropic coupling in CrPS4 is plausible. However, the quantitative claims, especially for CrPS4, rest on a sign issue, an incomplete subtraction of magnetic contributions, and an untested transferability assumption, as detailed below.","major_comments":[{"comment":"There is a sign error in the definition of the magnetostrictive strain. Minimizing E_tot = (V/2) ε^T C ε + B^T ε + (1/2) ε^T A ε with respect to ε gives ε_eq = −(VC + A)^−1 B, because ∂E/∂ε = (VC + A)ε + B = 0. Equation (9) instead defines ε_M = +(VC + A)^−1 B, which has the opposite sign. Since Eq. (8) writes the elastic energy as (V/2)(ε + ε_M)^T C_M (ε + ε_M) + ΔE_ms, the equilibrium strain is actually −ε_M. The manuscript nevertheless reports the values obtained from Eq. (9) as the magnetostrictive strains in Eqs. (12)–(13). Consequently the sign of every reported magnetostrictive strain, and the direction of the magnetostrictive jump across the FM–SS transition, is reversed. This is not a harmless convention choice: inserting the value from Eq. (9) into the derivative of Eq. (8) gives a nonzero force. The sign convention must be corrected and all numerical predictions re-evaluated.","section":"§II.B, Eqs. (8)–(10)"},{"comment":"The subtraction C = C_M − A/V does not yield a genuinely bare nonmagnetic elastic tensor. The DFT total energies from which C_M is obtained are computed in the spin-polarized magnetic state, so C_M contains the strain response of all magnetic interactions, including exchange anisotropy, Dzyaloshinskii–Moriya terms, and single-ion anisotropy. The tensor A in Eq. (6), however, includes only the isotropic Heisenberg exchange contribution. Subtracting A/V therefore removes only part of the magnetic contribution and leaves all non-isotropic magnetic terms inside the quantity called 'bare' C. This is numerically unimportant for NiPS3, where A/V components are of order 1 meV/Ų against C components of order 5000 meV/Ų, but for CrPS4 the A_22/V component is about 50 meV/Ų against C_22 ≈ 2500 meV/Ų, so an omitted magnetic contribution of comparable magnitude would change the extracted C and hence the magnetostrictive strains in Eq. (13). The paper should either compute a non-spin-polarized reference tensor or include the full magnetic interaction tensor in A and B.","section":"§II.B, Eq. (11), and the extraction of the 'bare' tensor in §§III–IV"},{"comment":"The spin-spiral predictions for CrPS4 are built from exchange couplings and strain derivatives extracted from DFT calculations constrained to the collinear ferromagnetic state, as stated in Sec. IV. These parameters are then weighted by the phase factor cos(q·r_ij) to construct A_SS and B_SS, and they are used to predict the strain-driven SS–FM phase boundaries, the SS critical temperatures, and the SS magnetostrictive strains in Eq. (13). The text acknowledges that the true ground state is the SS, but no test is provided of whether the FM-constrained J_N(ε), b_μ, and a_μν transfer to the noncollinear state. Changes of 20–30% in these parameters, which are plausible given that the FM and SS states may differ in self-consistent charge and orbital occupations, would shift the phase boundaries and the reported ≈0.1% magnetostrictive jump proportionally. I request a concrete transferability test: for example, compute exchange couplings for a commensurate shorter-period spiral at one or two representative strains and compare with the FM values, or compare a direct DFT FM–SS total-energy difference with the model prediction. If such a test is not computationally feasible, the SS-specific quantitative claims should be presented as model extrapolations rather than as robust predictions.","section":"§IV, Fig. 8, Eq. (13), and Table III"}],"minor_comments":[{"comment":"The caption reads 'Converge of the magnetic elastic contributions'; this should be 'Convergence of the magnetic elastic contributions'.","section":"Fig. 11 caption"},{"comment":"The statement that magnetic contributions are 'already included at the electronic-structure level and must not be added separately' is confusing because A is later subtracted to obtain the bare tensor. Please rewrite this paragraph to clarify what is subtracted and why only the isotropic-exchange part is used.","section":"§II.B, paragraph after Eq. (11)"},{"comment":"Reference [21] (Bonca et al., spin-stiffness calculation) does not appear related to strain-induced phase transitions or noncollinear spin textures; please verify that this citation is intended in that context.","section":"Introduction, Refs. [20]–[21]"},{"comment":"The text states that the difference between the zigzag and stripy magnetostrictive strains is 'below 0.01%', but the values in Eq. (12) differ by about 0.003% in x and 0.007% in y; consider stating the actual differences to avoid ambiguity.","section":"§III, magnetostrictive strains"}],"recommendation":"major_revision","confidential_remarks":"The manuscript depends heavily on the companion paper arXiv:2607.20631 for the exchange interactions, magnetic ground states, and strain-independent phase diagrams. Since the present paper's original contribution is the strain dependence and the magnetoelastic formalism, the editor may wish to confirm that the companion paper is available and peer-reviewed. The sign error in Eq. (9) is straightforward to fix, but the SS transferability issue for CrPS4 may require additional calculations or a careful restatement of the status of the SS predictions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Plain take: this is a useful material-specific application of the known Lu–Xiang magnetoelastic framework, not a paradigm shift. The new value is in the working comparison: NiPS3 shows weak, nearly isotropic spin–lattice coupling; CrPS4 shows strong, anisotropic coupling with a strain-driven spiral-to-FM transition. The shell-resolved convergence checks for the A and B sums are a genuine methodological addition.\n\nThe main soft spot is in Section IV. All CrPS4 DFT is done in the collinear FM state, and those J_N and their strain derivatives are used to predict the spin-spiral phase stability, T_c, and the SS magnetoelastic tensors through the cos(q·r) phase factor. That transferability is assumed, not shown. The paper does recover the spiral ground state at zero strain, which gives some confidence, but the quantitative SS magnetostriction and the ~0.1% jump across the FM–SS transition could shift by tens of percent if the derivatives change in the noncollinear state. A sensitivity estimate or a constrained noncollinear calculation would settle this.\n\nSecond issue: A and B are built from isotropic exchange only, while the DFT elastic tensor C_M contains all magnetic interactions. Subtracting A_iso/V to get the 'bare' tensor leaves the anisotropic, DM, and single-ion contributions inside it. So calling that C the bare nonmagnetic tensor is an overstatement. It is fine for displaying the isotropic contribution, but the interpretation should be softened.\n\nMinor: no error bars on the DFT fits or MC, and no released code or data. That makes the specific magnitudes hard to audit independently. The citation pattern is fine; leaning on the companion paper [23] for parameters is normal.\n\nFor the right reader—anyone working on strain engineering of 2D magnets, especially experimentalists eyeing CrPS4—this paper is worth engaging with. It deserves peer review. The referee should ask for a transferability check on the CrPS4 spiral state and a clearer statement of what C actually represents after the isotropic subtraction. I would engage with it.","headline":"Useful material-specific magnetoelastic study of NiPS3 and CrPS4; the CrPS4 spiral-state numbers rest on an untested FM-to-spiral transferability.","tokens_in":17073,"tokens_out":3262,"would_cite":true,"duration_ms":31086,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A first-principles strain-dependent Heisenberg model predicts that monolayer CrPS4 switches between spin-spiral and ferromagnetic order under a few percent strain, accompanied by a nearly 0.1% magnetostrictive jump.","keywords":["two-dimensional magnets","magnetoelastic coupling","magnetostriction","strain engineering","spin-spiral magnetism","monolayer CrPS4","monolayer NiPS3","Heisenberg exchange"],"falsifier":"Measure the in-plane lattice parameters of a CrPS4 monolayer as it is driven through the spiral-to-ferromagnetic transition by magnetic field or strain: the framework predicts a jump of about 0.08\\% in the y-axis magnetostrictive strain, from roughly -0.103\\% in the spiral state to -0.187\\% in the ferromagnetic state. A lattice change an order of magnitude smaller would falsify the predicted strong anisotropic magnetoelastic coupling.","tokens_in":15948,"feed_emoji":"🧲","tokens_out":6036,"duration_ms":73491,"temperature":0.7,"pith_summary":"The paper develops a first-principles route from electronic structure to magnetoelastic response in two-dimensional magnets. It shows that the first and second strain derivatives of the exchange interactions in a Heisenberg model directly yield the magnetostrictive strain and the magnetic renormalization of the elastic tensor, quantities that previously had to be fitted separately. Applied to two monolayer phosphorus chalcogenides, the approach identifies two distinct regimes: NiPS3 with weak, nearly isotropic spin-lattice coupling, and CrPS4 with strong, anisotropic coupling, strain-driven spin-spiral to ferromagnetic transitions, a strain-tunable critical temperature, and a nearly 0.1% magnetostrictive jump at the transition. If correct, this gives a general route to predict and design strain-controlled magnetic order in flexible two-dimensional devices.","feed_headline":"Strain flips CrPS4's magnetic order from spiral to ferromagnet","feed_subtitle":"A first-principles model ties exchange couplings to elasticity, predicting a measurable 0.1 percent length jump.","key_machinery":"The load-bearing object is the strain-dependent Heisenberg Hamiltonian with isotropic exchange, Dzyaloshinskii-Moriya, and single-ion anisotropy terms, whose exchange couplings are computed by density functional theory as functions of applied Voigt strain and fitted quadratically. The machinery is the pair of strain derivatives: first derivatives form the magnetoelastic force $B$, second derivatives form the magnetic stiffness correction $A$, both weighted by spin products $\\mathbf{e}_i\\cdot\\mathbf{e}_j$, summed over neighbor shells, and combined with the bare elastic tensor $C$ to give the magnetostrictive strain and the effective tensor $C_M$. This makes the magnetic-state dependence explicit and allows shell-by-shell convergence of the magnetoelastic response.","core_discovery":"The paper argues that a strain-dependent classical Heisenberg Hamiltonian, with isotropic exchange $J_{ij}(\\varepsilon)$ expanded to second order in strain, is enough to capture magnetoelasticity. The first strain derivatives form a generalized magnetoelastic force $B_\\mu = \\sum_{i,j} (\\partial J_{ij}/\\partial \\varepsilon_\\mu)\\, \\mathbf{e}_i\\cdot\\mathbf{e}_j$, which sets the magnetostrictive strain $\\varepsilon_M = (VC + A)^{-1} B$, while the second derivatives form $A_{\\mu\\nu} = \\sum_{i,j} (\\partial^2 J_{ij}/\\partial \\varepsilon_\\mu \\partial \\varepsilon_\\nu)\\, \\mathbf{e}_i\\cdot\\mathbf{e}_j$, which renormalizes the elastic tensor through $C_M = C + A/V$. Applying this to monolayers, the paper finds that NiPS3 has magnetostrictive strains of only about 0.01\\% to 0.02\\%, whereas CrPS4 shows strains of order 0.05\\% to 0.19\\% and a change of nearly 0.1\\% between the spin-spiral and ferromagnetic states, making the magnetoelastic effect experimentally detectable.","pith_inferences":["Extension: because the framework attributes the strong anisotropy to first-neighbor Cr-S-Cr exchange pathways along the chain direction, the same pathways should dominate spin-phonon coupling in CrPS4; Raman or inelastic neutron measurements across the ordering temperature could test this directly.","Extension: the second-derivative sums predict magnetic-order-dependent sound velocities, so ultrasonic or Brillouin measurements on CrPS4 should show a change in the chain-direction longitudinal mode when the spiral orders.","Extension: by using strain along the b direction as a control parameter, the roughly 0.1\\% magnetostrictive jump could act as a strain-actuated structural switch without an applied magnetic field, provided the spiral-to-ferromagnetic transition is reversible."],"forward_implications":["For monolayer NiPS3, strain of a few percent switches the zigzag propagation direction between the 0 degrees and ±120 degrees states and can drive a transition to stripy antiferromagnetic order near 3\\% biaxial tension, with the critical temperature changing by more than 10\\%.","For monolayer CrPS4, strain along the b direction reduces the dimerization of the first-neighbor exchange interactions, destabilizes the spin-spiral state, and stabilizes an out-of-plane ferromagnet, with a magnetic-anisotropy sign reversal near 0.6\\% strain.","The magnetostrictive strain in CrPS4 is roughly an order of magnitude larger than in NiPS3, and the magnetic renormalization of the elastic tensor reaches about 2\\% along the chain direction, so the structural change across the spiral-to-ferromagnetic transition should be observable.","Because $A$ and $B$ depend on the magnetic configuration through the factors $\\mathbf{e}_i\\cdot\\mathbf{e}_j$, the elastic tensor and magnetostriction are magnetic-state dependent, giving a microscopic explanation for why different magnetic phases have different lattice responses."],"supporting_citations":[{"why":"Supplies the microscopic starting point: strain-dependent exchange interactions as the origin of magnetoelastic coupling.","marker":"[8]"},{"why":"Establishes that spin-lattice coupling renormalizes the elastic tensor and phonons in two-dimensional magnets, which the second-derivative term generalizes.","marker":"[12]"},{"why":"Companion study that provides the magnetic ground states, exchange shells, and critical temperatures of the same two monolayers.","marker":"[23]"},{"why":"Prior first-principles study of exchange interactions in strained CrPS4 monolayers, used as a comparison for the exchange and strain behavior.","marker":"[22]"},{"why":"Density-functional method used to compute the electronic structure and energy-strain curves for both materials.","marker":"[33]"},{"why":"Method used to map the Kohn-Sham results onto the relativistic Heisenberg model, yielding the exchange and anisotropy parameters.","marker":"[38]"}],"fun_headline_variants":["Strain flips CrPS4 spiral to ferromagnet","0.1% strain flips CrPS4's magnetic order","Spiral to ferromagnet: strain reorders CrPS4","CrPS4's magnetic phase toggled by strain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For CrPS4, the exchange constants and their strain derivatives are extracted from density functional calculations in the collinear ferromagnetic state, then used to predict the spin-spiral phase and its magnetoelastic coefficients; the transferability of these couplings to the spiral state is assumed.","fun_headline_variants_meta":{"raw":{"variants":["Strain flips CrPS4 spiral to ferromagnet","0.1% strain flips CrPS4's magnetic order","Spiral to ferromagnet: strain reorders CrPS4","CrPS4's magnetic phase toggled by strain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000789,"raw_usage":{"total_tokens":3488,"prompt_tokens":963,"completion_tokens":2525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":579,"completion_tokens_details":{"reasoning_tokens":2453}},"tokens_in":579,"tokens_out":2525,"duration_ms":17346,"temperature":1.0,"reasoning_tokens":2453,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:13:06.331615+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the in-plane lattice parameters of a CrPS4 monolayer as it is driven through the spiral-to-ferromagnetic transition by magnetic field or strain: the framework predicts a jump of about 0.08\\% in the y-axis magnetostrictive strain, from roughly -0.103\\% in the spiral state to -0.187\\% in the ferromagnetic state. A lattice change an order of magnitude smaller would falsify the predicted strong anisotropic magnetoelastic coupling.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the microscopic starting point: strain-dependent exchange interactions as the origin of magnetoelastic coupling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes that spin-lattice coupling renormalizes the elastic tensor and phonons in two-dimensional magnets, which the second-derivative term generalizes."},{"cited_title":"Magnetic ground states of CrPS$_4$ and NiPS$_3$ monolayers from long-range exchange interactions","cited_arxiv_id":"2607.20631","evidence_quote":"Companion study that provides the magnetic ground states, exchange shells, and critical temperatures of the same two monolayers."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior first-principles study of exchange interactions in strained CrPS4 monolayers, used as a comparison for the exchange and strain behavior."},{"cited_title":"Mart´ ınez-Carracedo, L","cited_arxiv_id":null,"evidence_quote":"Method used to map the Kohn-Sham results onto the relativistic Heisenberg model, yielding the exchange and anisotropy parameters."}],"review_version":1}