{"id":"d2354824-58f8-44cd-884e-63a4b340e1bb","arxiv_id":"2608.13427","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"Monolayer FeTe and FeSe are predicted to host bond-dependent Ising-type Kitaev-like interactions that compete with single-ion anisotropy and produce single-site spin frustration.","lead":"Monolayer sheets of FeTe and FeSe are claimed to contain bond-dependent Kitaev-like magnetic interactions, a type of spin coupling not previously recognized in this tetrahedral structure. If real, this could extend the search for exotic quantum magnetic states beyond the octahedral materials that currently dominate the field.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The extracted Kitaev-like parameters are not uniquely identifiable from the MAE data: the 1NN-only failure that motivates the 2NN terms is an artifact of the assumed Ising-axis geometry, and alternative symmetry-allowed anisotropic models are not tested.","rationale":"The reader's weakest assumption already identifies the Hamiltonian-form post hoc issue: only the assumed Kitaev-like form plus SIA is considered, and the 2NN terms are added when the 1NN-only model fails. My stress-test sharpens this into a concrete identifiability problem: the specific geometric cancellation that makes the BAFM in-plane MAE vanish in the 1NN model is not a robust test of the Kitaev-like interaction; it is a consequence of the chosen Ising axes. Therefore the data do not uniquely select the 2NN Kitaev-like contribution over other symmetry-allowed mechanisms such as DM or distorted-axis anisotropic exchange. This concern is load-bearing because the central claim is the existence and dominance of a Kitaev-like Ising interaction; if an alternative model fits the same data, the quantitative K values lose their physical meaning. The proposed test directly checks whether the alternative model can fit the key BAFM in-plane oscillation. The reader's CONDTIONAL verdict remains appropriate: the qualitative case for bond-dependent anisotropy is plausible, but the quantitative model needs independent validation. I found no reason to move the verdict to ACCEPT or REJECT; the concern supports the existing conditional status. I agree with the reader's weakest_assumption and recommend the same verdict, hence UNCHANGED.","tokens_in":16972,"tokens_out":8729,"duration_ms":97399,"concrete_test":"Re-fit the same DFT MAE data (FM, Néel AFM, BAFM, out-of-plane and in-plane) with an alternative model that keeps SIA and 1NN Kitaev-like terms but replaces the 2NN Kitaev-like terms by a 1NN Dzyaloshinskii-Moriya interaction allowed by the P4/nmm symmetry (or by a 1NN symmetric anisotropic exchange with an unconstrained Ising axis). Compare the least-squares residuals and the resulting parameters. If the alternative model reproduces the nonzero BAFM in-plane MAE oscillation with comparable or better quality, the 2NN Kitaev-like term is not required by the data and the extracted K2/Γ2 values are not identifiable. Independently, evaluate the predicted BAFM easy-axis angle from the reported parameters and check it against the experimental ≈50° tilt.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's quantitative case rests on the assumption that the spin Hamiltonian is exactly the Kitaev-like form in Eq. (1) with Ising axes determined by ideal tetrahedral bond directions, plus a uniaxial SIA, with no DM, biquadratic, or lower-symmetry terms. The data only prove that SIA alone cannot explain the order-dependent MAE; they do not prove the specific Kitaev-like form. The decisive evidence for 2NN interactions is that a 1NN-only Kitaev-like model predicts zero in-plane MAE for BAFM. However, this cancellation is a geometric consequence of the particular choice of Ising axes (w3−w4). A small distortion of the tetrahedra, a slightly different but symmetry-allowed Ising axis, or a 1NN DM term could produce the observed sin²φ in-plane oscillation without any 2NN Kitaev term. The 2NN Kitaev terms were added post hoc, and the fitted curves are evaluated on the same data used for the fit, so the 'perfect match' in Fig. 3 is partly circular. The paper also claims the model explains the experimental 50° BAFM easy-axis tilt but never reports the predicted angle as an independent check. Consequently, the central claim that K1 = −1.63 meV (FeTe) and K1 = −0.37 meV (FeSe) are Kitaev-like Ising parameters is not uniquely established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies monolayer FeTe and FeSe, which have edge-sharing tetrahedral coordination, and proposes that bond-dependent (Kitaev-like) spin interactions coexist with single-ion anisotropy. The authors construct a Hamiltonian with first- and second-neighbor Kitaev-like K and off-diagonal Gamma terms, fit its parameters to DFT+U+SOC magnetic anisotropy energies for ferromagnetic, Néel antiferromagnetic, and bicollinear antiferromagnetic orders, and conclude that a negative nearest-neighbor Kitaev term dominates MAE in FeTe while competing with positive SIA in FeSe. They further propose that the noncollinear local easy axes generate single-site spin frustration, offering a mechanism for magnetic disorder in iron-based parent compounds.","tokens_in":17326,"tokens_out":6813,"duration_ms":64127,"significance":"The qualitative central observation—MAE depends strongly on magnetic order and the BAFM state exhibits in-plane anisotropy that cannot be captured by single-ion anisotropy alone—is convincing and is a useful step toward recognizing bond-dependent anisotropy in tetrahedral magnets. The geometric construction of local Ising axes from Fe-X bond directions is a helpful conceptual contribution. However, the quantitative extraction of K1, K2, Gamma1, Gamma2, and Ak is not uniquely established: the model form is assumed, the parameters are fitted to the same data used for validation, and alternative bond-dependent terms are not tested. The paper's significance depends on strengthening the identifiability of the Kitaev-like parameters.","major_comments":[{"comment":"The data exclude pure SIA, but they do not select the Kitaev-like form of Eq. (1) over other symmetry-allowed bond-dependent terms. A 1NN Dzyaloshinskii-Moriya term, or a small rotation of the assumed Ising axis away from w3-w4, also produces a nonzero in-plane BAFM anisotropy of the observed sin^2(phi) form. Because the fitted values of K1, K2, Gamma1, Gamma2, and Ak are only meaningful if the Hamiltonian is complete, the paper should test at least one alternative decomposition (e.g., including DM terms or allowing the Ising axis to relax) and show that the Kitaev-like model is selected by the data.","section":"Appendix A, Eqs. (4)-(5)"},{"comment":"The validation is circular: the parameters are obtained by least-squares fitting to the same MAE data that the fitted curves are then compared with, so the 'perfect match' in Fig. 3 is expected and carries no independent confirmation. Provide an out-of-sample test, such as calculating MAE for a magnetic order not used in the fit, or quantitatively compare the predicted BAFM easy-axis angle with the experimental 50 degrees mentioned in the text; currently the predicted angle is never reported.","section":"Fig. 3 and the 'self-consistency' statement"},{"comment":"The 2NN Kitaev-like terms were added after the 1NN-only model failed to reproduce the BAFM in-plane MAE. This is a post hoc model extension, and the DOS-based justification ('holds equal status') is qualitative. Report a quantitative model comparison (e.g., residual sum of squares per degree of freedom, or an information criterion) between 1NN-only and 1NN+2NN fits, and state whether the extracted K2 is identifiable from the available MAE curves or degenerate with other parameters.","section":"Main text paragraph introducing 2NN interactions"},{"comment":"The fitted parameters are quoted without uncertainties or a uniqueness check. Given the paper's central quantitative conclusions (K1 = -1.63 meV dominating in FeTe; K1 = -0.37 meV competing with Ak = 0.27 meV in FeSe), report confidence intervals from the least-squares fit and check that the minimum is unique with respect to plausible perturbations of the Hamiltonian.","section":"Fig. 4(a) and parameter values"}],"minor_comments":[{"comment":"The caption lists 'Cr by blue atoms, and I by purple atoms,' species that do not appear in monolayer FeX; this appears to be a leftover from the CrI3 example and should be corrected.","section":"Figure 1 caption"},{"comment":"The acronym GAFM is used without definition; specify that it denotes G-type (Néel) antiferromagnetic order.","section":"Appendix A and Supplemental Material"},{"comment":"There is a typo, 'magneitc anisotropy energy,' and the phrase 'obtained the the full set' has a doubled article; these should be corrected.","section":"Introduction and main text"},{"comment":"The equations are poorly typeset in the submitted text (for example, Eq. (1) and the Appendix A formulas are garbled); please ensure all equations are legible in the final version.","section":"Equations throughout"},{"comment":"The term 'Kitaev-like' is used to include both the K and the off-diagonal Gamma terms; please state explicitly which terms are Ising-type and which are off-diagonal in the model summary.","section":"Model summary"},{"comment":"No residuals or goodness-of-fit values are given; reporting them would help the reader judge the 'perfect match' claim.","section":"Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The paper builds on the same group's earlier Kitaev-interaction methodology for CrTe2 and CrI3, but the tetrahedral geometry is genuinely new and the qualitative evidence for bond-dependent anisotropy is solid. The main risk is the identifiability of the reported Kitaev parameters; if the authors can provide an out-of-sample test or a direct comparison with the experimentally known BAFM easy-axis tilt, the paper would be substantially strengthened. The novelty claims should also be softened, as the 'first time' and 'fiercely competes' phrasing is stronger than the evidence supports."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this is a serious attempt to extend bond-dependent Kitaev-type anisotropy to edge-sharing tetrahedral magnets, and the qualitative claim — that single-ion anisotropy alone cannot explain the MAE differences among FM, Néel AFM, and BAFM orders in monolayer FeTe/FeSe — looks right. The extracted parameters (K1 = −1.63 meV for FeTe, etc.) should not be treated as established values, because the fitting procedure is partly circular and competing terms are not tested.\n\nWhat is actually new: the application of the MAE-mapping method to these tetrahedral systems and the suggestion that local noncollinear Ising axes create single-site spin frustration, which could matter for understanding magnetic disorder in iron-based superconductor parent compounds. The structural derivation of the Kitaev-like model from the tetrahedral bond geometry is careful, and the DFT dataset is exactly the kind of thing that can falsify a pure-SIA picture. If the paper only claimed \"bond-dependent anisotropic exchange is present,\" I would be fairly convinced.\n\nThe soft spots are real but mostly quantitative. The strongest part is the order dependence of the MAE: the trend inversion between FM and Néel AFM and the finite in-plane anisotropy in BAFM are not explainable by SIA. The weak part is the leap from \"SIA is insufficient\" to \"the Hamiltonian is Eq. (1) with these specific K, Γ, Ak values.\" The formulas are defined in terms of the fitted parameters, the 2NN terms are added only after the 1NN model fails, and the \"perfect match\" curves are evaluated on the same data used for the least-squares fit. That is a fitting check, not an independent prediction. There are no error bars, no sensitivity analysis, and no test of DM or biquadratic exchange. The paper also mentions the model explains the 50° easy-axis tilt in FeTe but never reports the predicted angle as an out-of-sample check. I could not verify the algebra from the rendering, and no code or data is provided, so I cannot independently reproduce the fits.\n\nNone of this means the central idea is wrong. It means the quantitative parameters are underdetermined. A serious referee should ask for: a direct comparison of the proposed model against an SIA+DM alternative, error estimates on K, Γ, Ak, and at least one out-of-sample check such as the BAFM easy-axis angle or a spin-wave prediction.\n\nBottom line: this paper is worth a peer-review slot, not a desk reject. With alternative-model tests and out-of-sample checks, it could become a genuinely useful contribution. I would bring it to reading group with caveats.","headline":"A credible qualitative case that bond-dependent anisotropy exists in tetrahedral FeTe/FeSe monolayers, but the quantitative Kitaev-like parameters are not uniquely established by the fitting scheme presented.","tokens_in":17842,"tokens_out":2079,"would_cite":true,"duration_ms":21659,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Monolayer FeTe and FeSe host previously unrecognized bond-dependent Kitaev-like Ising interactions that dominate magnetic anisotropy in FeTe and compete with single-ion anisotropy in FeSe.","keywords":["Kitaev interaction","bond-dependent magnetic anisotropy","magnetic anisotropy energy","edge-sharing tetrahedral magnets","iron-based superconductors","FeTe","FeSe","spin frustration"],"falsifier":"Measure the in-plane magnetic anisotropy of monolayer FeTe in its bicollinear antiferromagnetic (BAFM) state: the model predicts a $\\sin^2\\phi$ oscillation whose amplitude is set by the second-neighbor Kitaev-like parameters, together with an out-of-plane easy axis tilted roughly 50 degrees from c. Observing no such bond-directional anisotropy, or finding that the fitted parameters shift when Dzyaloshinskii-Moriya terms are added to the Hamiltonian, would falsify the Kitaev-like identification.","tokens_in":16718,"feed_emoji":"🧲","tokens_out":14279,"duration_ms":119426,"temperature":0.7,"pith_summary":"The paper sets out to show that bond-dependent, Kitaev-like Ising interactions are not confined to edge-sharing octahedral magnets but also appear in edge-sharing tetrahedral ones, using monolayer FeTe and FeSe as concrete cases. It argues that chalcogen-driven spin-orbit coupling combined with the tetrahedral crystal field produces a measurable bond-directional anisotropy, which it isolates by fitting first-principles magnetic anisotropy energies for ferromagnetic, Néel, and bicollinear antiferromagnetic orders. The fit gives a Kitaev-like term that dominates magnetic anisotropy in FeTe ($K_1 = -1.63$ meV) and competes with an opposite-sign single-ion anisotropy in FeSe ($K_1 = -0.37$ meV vs $A_k = 0.27$ meV). Because the local quantization axes of different bonds cannot be satisfied simultaneously, the paper concludes that these interactions generate intrinsic single-site spin frustration, a possible microscopic mechanism for the magnetic disorder observed in iron-based superconductors.","feed_headline":"Bond-directional Ising term shapes FeTe and FeSe magnetic anisotropy","feed_subtitle":"First-principles mapping isolates a bond-directional Ising term in tetrahedral magnets, extending Kitaev physics beyond octahedra.","key_machinery":"The central object is the Kitaev-like Hamiltonian of Eq. (1), a bond-dependent spin model in which each Fe-Fe pair $i,j$ carries a Kitaev-like coupling $K_{ij}$ and an off-diagonal coupling $\\Gamma_{ij}$, plus a single-ion anisotropy $A_k$. The quantization axes are fixed by the tetrahedral bond vectors $w_p$: for a pair in a given Fe-X-Fe-X plane the Ising axis is the difference of the two out-of-plane bond directions, $w_{p+2}-w_{p+3}$, which is perpendicular to the Fe-Fe bond. The load-bearing machinery is the MAE energy-mapping scheme: out-of-plane and in-plane anisotropy curves are computed from first principles for ferromagnetic, Néel, and bicollinear antiferromagnetic orders, and least-squares fitting to the analytic formulas separates the bond-dependent terms from single-ion anisotropy, which is identical across orders. The nonzero in-plane anisotropy of the BAFM order, which pure single-ion anisotropy forbids, is what forces the inclusion of second-neighbor Kitaev-like terms.","core_discovery":"The paper claims to demonstrate a previously unrecognized bond-dependent Ising-type interaction, of Kitaev form, in monolayer FeTe and FeSe, whose Fe atoms sit in edge-sharing tetrahedra of Te or Se. In the Hamiltonian of Eq. (1), each neighbor pair carries Kitaev-like ($K$) and off-diagonal ($\\Gamma$) couplings whose quantization axes are set by the Fe-X bond geometry; fitting first-principles magnetic anisotropy energies across ferromagnetic, Néel, and bicollinear antiferromagnetic orders yields $K_1=-1.63$ meV for FeTe (with $A_k=-0.73$ meV) and $K_1=-0.37$ meV for FeSe (with $A_k=0.27$ meV). The sign and magnitude comparison shows the Kitaev-like term dominates in FeTe but competes with an opposite-signed single-ion anisotropy in FeSe. Since the local axes for different bonds are mutually noncollinear, the paper concludes these interactions create intrinsic single-site spin frustration, offering a microscopic mechanism for magnetic disorder beyond isotropic exchange models.","pith_inferences":["A direct extension the paper does not compute is to add Dzyaloshinskii-Moriya and biquadratic terms to Eq. (1) and re-fit; if the extracted $K_1$ values shift substantially, the Kitaev-like identification would not be unique.","The same MAE-mapping procedure could be applied to strained or doped FeTe/FeSe; the paper's spin-orbit argument predicts $K_1$ should track the ligand's effective spin-orbit coupling strength.","Because the local axes are noncollinear, classical or quantum Monte Carlo simulations of Eq. (1), which the paper does not report, would show whether the predicted ground state is actually noncollinear and how much degeneracy remains."],"forward_implications":["Bond-directional exchange must be included in any low-energy magnetic model of monolayer FeTe and FeSe; Heisenberg-plus-single-ion models will misassign the anisotropy.","The second-neighbor Kitaev-like terms are directly observable: they produce the in-plane $\\sin^2\\phi$ anisotropy of the BAFM state and the roughly 50-degree tilt of its out-of-plane easy axis.","Single-site spin frustration can arise from noncollinear local easy axes alone, even without geometric frustration of exchange bonds, offering a microscopic route to magnetic disorder in iron-based parent compounds.","Edge-sharing tetrahedral lattices become a legitimate setting for Kitaev-like physics, extending the search beyond honeycomb and octahedral coordination compounds.","The fitted values supply quantitative targets: $K_1=-1.63$ meV for FeTe and $K_1=-0.37$ meV with $A_k=0.27$ meV for FeSe can be checked against spin-wave or inelastic-scattering data."],"supporting_citations":[{"why":"Defines the exactly solvable bond-dependent Kitaev model that the paper extends to tetrahedral coordination.","marker":"[14]"},{"why":"Establishes edge-sharing octahedral $\\alpha$-RuCl$_3$ as the canonical Kitaev material context that this work moves beyond.","marker":"[15]"},{"why":"Supplies the MAE energy-mapping method used to extract Kitaev-like interaction parameters from first-principles energies.","marker":"[21]"},{"why":"Applies the same MAE mapping to a selenide monolayer, giving the methodological baseline for FeSe.","marker":"[22]"},{"why":"Provides the J-K1-Gamma'-K2-Ak interaction-model structure that the tetrahedral Hamiltonian is patterned on.","marker":"[23]"},{"why":"Motivates separating Kitaev interaction from single-ion anisotropy, the central disentangling step of the fitting procedure.","marker":"[25]"},{"why":"Supplies the earlier first-principles identification of the bicollinear antiferromagnetic order used as one of the three magnetic configurations.","marker":"[41]"},{"why":"Documents frustrated magnetic interactions in FeSe, the experimental motivation for the spin-frustration conclusion.","marker":"[45]"}],"fun_headline_variants":["Tetrahedral magnets join the Kitaev family","FeTe and FeSe host hidden bond-dependent Ising term","Kitaev-like physics found in edge-sharing tetrahedra","Bond-directional Ising interaction in iron chalcogenides"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the magnetic anisotropy of FeTe and FeSe is completely captured by single-ion anisotropy plus the Kitaev-like and off-diagonal exchange of the assumed Hamiltonian, with no comparable Dzyaloshinskii-Moriya or biquadratic terms.","fun_headline_variants_meta":{"raw":{"variants":["Tetrahedral magnets join the Kitaev family","FeTe and FeSe host hidden bond-dependent Ising term","Kitaev-like physics found in edge-sharing tetrahedra","Bond-directional Ising interaction in iron chalcogenides"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000608,"raw_usage":{"total_tokens":2864,"prompt_tokens":1010,"completion_tokens":1854,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":1798}},"tokens_in":626,"tokens_out":1854,"duration_ms":14671,"temperature":1.0,"reasoning_tokens":1798,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:15:17.900884+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the in-plane magnetic anisotropy of monolayer FeTe in its bicollinear antiferromagnetic (BAFM) state: the model predicts a $\\sin^2\\phi$ oscillation whose amplitude is set by the second-neighbor Kitaev-like parameters, together with an out-of-plane easy axis tilted roughly 50 degrees from c. Observing no such bond-directional anisotropy, or finding that the fitted parameters shift when Dzyaloshinskii-Moriya terms are added to the Hamiltonian, would falsify the Kitaev-like identification.","supporting_citations":[{"cited_title":"Kitaev, Anyons in an exactly solved model andbeyond,Ann.Phys.321,2–111(2006)","cited_arxiv_id":null,"evidence_quote":"Defines the exactly solvable bond-dependent Kitaev model that the paper extends to tetrahedral coordination."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes edge-sharing octahedral $\\alpha$-RuCl$_3$ as the canonical Kitaev material context that this work moves beyond."},{"cited_title":"Huang, B","cited_arxiv_id":null,"evidence_quote":"Supplies the MAE energy-mapping method used to extract Kitaev-like interaction parameters from first-principles energies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Applies the same MAE mapping to a selenide monolayer, giving the methodological baseline for FeSe."},{"cited_title":"Jiang, C","cited_arxiv_id":null,"evidence_quote":"Provides the J-K1-Gamma'-K2-Ak interaction-model structure that the tetrahedral Hamiltonian is patterned on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Motivates separating Kitaev interaction from single-ion anisotropy, the central disentangling step of the fitting procedure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the earlier first-principles identification of the bicollinear antiferromagnetic order used as one of the three magnetic configurations."},{"cited_title":"The Perdew-Burke-Ernzerhof (PBE) functional[37] was used","cited_arxiv_id":null,"evidence_quote":"Documents frustrated magnetic interactions in FeSe, the experimental motivation for the spin-frustration conclusion."}],"review_version":1}