{"id":"169df996-ea4e-402d-82b3-314b5c2e2fe2","arxiv_id":"2411.11985","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"DFT+U total-energy mapping over 60 magnetic configurations shows the in-plane exchange J2 in α-MnTe is ferromagnetic, and the direction-dependent J10 interaction produces chiral magnon splitting, both enhanced under 15 GPa pressure.","lead":"The paper uses DFT calculations with many magnetic configurations to show that the in-plane magnetic coupling in the altermagnet α-MnTe is ferromagnetic, resolving a long-standing conflict between theory and experiment. It also identifies a specific exchange interaction that splits magnon energies by chirality and predicts that compressive strain strengthens both effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The J2 sign flip is not yet shown to be unique: at +0.17 meV the fitted value is two orders smaller than J1, and no configuration list, residuals, or resampling test is presented to rule out selection bias.","rationale":"The reader identified the same primary gap, so my agreement is 'agree'. The concern is not that the method is wrong but that the evidence for uniqueness is absent. The paper does include genuine supporting pieces: a compact supercell construction, a convergence-style plot for J2, and a quantitative comparison with experimental J10 chirality; these count in its favor. However, the central number is so small that standard DFT+U energy errors and model truncation errors are likely comparable to or larger than the fitted value. The paper provides no error bars and no stability test; the convergence-with-count plot alone conflates 'more data' with 'better-conditioned data'. A conditional verdict is appropriate: the claim is plausible and likely correct, but it should be made reproducible and robust before acceptance. The concrete test described above would settle the issue. The U=4 eV choice is secondary; a two-point U scan would be inexpensive. Overall, the reader's CONDITIONAL verdict is unchanged.","tokens_in":11222,"tokens_out":5900,"duration_ms":65690,"concrete_test":"Fix U=4 eV and the 34-atom supercell, and generate three independent families of ~60 magnetic configurations (e.g., different random spin orientations and different sets of ordered wavevectors). For each family, fit J1-J16 by the same least-squares procedure and report residual RMS, condition number of the normal matrix, and bootstrap/leave-one-out confidence intervals for J2. The central claim is supported only if J2 remains positive with a bootstrap lower bound above zero in all three families; if any equally valid set gives J2<=0 or intervals crossing zero, the positive sign is a configuration-selection artifact. A supplementary run with U=3 and U=5 eV should show the same sign to rule out Hubbard-U sensitivity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the fit of ~60 total energies to a 16-parameter Heisenberg model that yields J2=+0.17 meV at ambient pressure. The paper gives no configuration list, no selection criterion, no fit residuals, and no conditioning or resampling analysis. This matters because J2 is about 100 times smaller than J1 and 20 times smaller than J3; any systematic bias from the chosen set of magnetic states, from correlations imposed by the 34-atom SUPERHEX cell, or from truncation at 16th-neighbor interactions can flip the sign. The authors' own Fig. 1(b) shows that an 18-configuration set gives the opposite sign, so sign sensitivity to the training set is demonstrated, not refuted, by the paper. If an equally valid 60-configuration set yields J2<=0, the central claim collapses even though the J10 chiral-splitting result may survive. The U=4 eV choice is a secondary load-bearing input because the small positive value is not checked for U-dependence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses two open questions for the altermagnetic semiconductor α-MnTe: the origin of its A-type antiferromagnetic order and the microscopic mechanism of chiral splitting in its magnon spectrum. Using DFT+U total energies from roughly 60 magnetic configurations in a 34-atom SUPERHEX supercell, the authors fit a classical Heisenberg Hamiltonian with exchange interactions up to the 16th nearest neighbor. They obtain a positive (ferromagnetic) in-plane second-nearest-neighbor exchange J2 at ambient pressure, in contrast to earlier DFT studies and in agreement with experiment, and they attribute the previous discrepancy to an insufficient number of magnetic configurations. They further find that the 10th nearest-neighbor exchange splits into two inequivalent couplings J10,a and J10,b, which they identify as the source of the nonrelativistic chiral magnon splitting measured recently. They also predict that 15 GPa compressive strain enhances the spin splitting, chiral magnon splitting, and Néel temperature, while reversing the sign of J2 without changing the A-type ground state.","tokens_in":11392,"tokens_out":4652,"duration_ms":46235,"significance":"If the central fitting result is robust, the paper resolves a long-standing sign discrepancy in α-MnTe and makes a methodological point that should influence future exchange-mapping studies in complex antiferromagnets: convergence with respect to the number of magnetic configurations must be demonstrated. The identification of J10,a and J10,b as the source of chiral magnon splitting is a concrete and useful result, and the strain predictions provide falsifiable targets for experiment. The paper also showcases the computational efficiency of the SUPERHEX approach and provides a complete table of computed exchange parameters (Table I) with explicit comparisons to experiment. However, the main quantitative claim currently lacks the diagnostics needed to establish robustness, and the paper's own acknowledgments of quantitative discrepancies (TN about 20-50 K below experiment, chiral splitting 1.5 times larger than experiment) underline the need for a more careful uncertainty analysis.","major_comments":[{"comment":"The central claim that the in-plane exchange J2 is ferromagnetic at ambient pressure rests on a least-squares fit of approximately 60 DFT total energies to a 16-parameter classical Heisenberg Hamiltonian, but the manuscript reports no residuals, no list or selection criterion for the magnetic configurations, and no resampling or conditioning analysis. Because Fig. 1(b) itself shows that the sign of J2 changes when the number of configurations is increased from 18, the possibility that the sign is sensitive to the specific subset of configurations, or to correlations imposed by the 34-atom SUPERHEX cell, rather than to the count is not excluded. Please provide the full configuration set, fit residuals, a leave-one-out or bootstrap stability test, and a check with an independently generated set of configurations. Without these diagnostics, the positive J2 = 0.17 meV, which is two orders of magnitude smaller than J1, is not established as a converged result.","section":"Normalized Heisenberg exchange interactions; Fig. 1(b)"},{"comment":"The Hubbard U = 4 eV is adopted from Ref. [55] without any sensitivity check. Since J2 = +0.17 meV at ambient pressure is very small compared with J1 and J3, and since DFT+U double-counting corrections can shift small exchange couplings by several tenths of an meV, the sign of J2 could depend on the chosen U. Please report J2, and at least J1, J3, J10a, and J10b, for a range of U values (for example 3, 4, and 5 eV) at ambient pressure, or otherwise justify that the sign of J2 is stable with respect to this choice.","section":"Computational methods; Hubbard U"},{"comment":"The exchange interactions are truncated at the 16th nearest neighbor and fitted with a 34-atom SUPERHEX supercell, but the paper does not demonstrate convergence with respect to the interaction range or the supercell size. Given the small magnitude of J2, truncation bias could also affect its sign. Please show how J2 changes when the number of exchange shells is increased beyond 16, or compare with a larger supercell for a representative subset of configurations, to rule out an artifact of the truncation or of the supercell geometry.","section":"Normalized Heisenberg exchange interactions; SUPERHEX"}],"minor_comments":[{"comment":"Table I compares the present normalized exchange parameters Jn = S^2 Jtilde_n with experimental values from Ref. [49], but it is not stated whether the experimental values were also normalized by S^2 or are raw exchange constants from the five-parameter spin Hamiltonian; please clarify the normalization convention in the table caption.","section":"Table I"},{"comment":"The number of magnetic configurations is given only as 'approximately 60' at ambient pressure and 'about 120' at 15 GPa; please give exact counts and describe how the configurations were generated, including any symmetry constraints or random sampling strategy.","section":"Computational methods"},{"comment":"The statement that the 3d-orbital occupancy of Mn2+ is 'approximately 5.3' is used to motivate the ferromagnetic in-plane exchange, but no source or computational method for this occupancy is given; please provide a reference or an explicit DFT population analysis.","section":"Normalized Heisenberg exchange interactions"},{"comment":"The paper compares its calculated chiral magnon splitting and Néel temperature with experiment and finds discrepancies (splitting 1.5 times larger; TN about 20-50 K lower), but the discussion is qualitative; a brief sensitivity analysis using the experimental exchange parameters from Ref. [49] would clarify whether the discrepancies originate mainly from J1, from J10a/J10b, or from the simplified experimental model.","section":"Magnon dispersion and magnetic susceptibility"},{"comment":"The main panel of Fig. 1(b) lacks axis labels with units for the normalized exchange interaction, and the inset does not clearly distinguish the P = 0 and P = 15 GPa curves; please add labels and a legend.","section":"Fig. 1(b)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of cond-mat.mtrl-sci and the central idea is publishable, but the load-bearing fitting procedure is underdocumented: no configuration list, residuals, or resampling tests are provided for the small positive J2, and the U-dependence is not checked. These are standard additions rather than irreparable flaws, so I recommend major revision rather than rejection. I found no indication of problematic citation practices; the reliance on the authors' own SUPERHEX and benchmarking papers is disclosed and appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this paper gives a plausible resolution of the J2 sign controversy in α-MnTe and provides the first ab initio identification of the direction-dependent J10 exchange as the source of the measured chiral magnon splitting. The J2 story is not yet airtight, but the chiral magnon part is solid and the paper is honest about its quantitative mismatches.\n\nWhat's genuinely new: the demonstration that the fitted J2 flips from AFM to FM when the number of magnetic configurations grows from 18 to ~60. That is a concrete methodological insight, not just a rehash. The use of SUPERHEX to build a 34-atom cell is clever and makes the 60-configuration fit feasible. The J10,a/J10,b asymmetry, with opposite signs, matches the experiment and appears robust. The pressure calculations are a natural extension: a 70% increase in spin splitting, larger chiral splitting, and a TN that roughly doubles are testable predictions.\n\nWhere I'd push back: the paper never shows the configuration list, the fit residuals, or any resampling check. J2 is +0.17 meV, about two orders of magnitude smaller than J1 and twenty times smaller than J3. Someone could select a different set of 60 configurations and plausibly get the opposite sign. The U=4 eV choice comes from a benchmarking paper by one of the authors; a short U-sweep would settle whether the small positive J2 survives. The pressure result that the ground state stays A-type even after J2 turns negative is counter-intuitive; the authors say it's due to large J3, but the main text doesn't show the evidence — that lives in the SM. These are fixable reporting gaps, not signs of a broken calculation.\n\nThe stress-test note worries that the sign flip's sensitivity is demonstrated, not refuted, by Fig. 1(b). I think that's fair, but it's a reason to demand more detail, not to reject the paper. The comparison with experiment for J1, J3, and J10 is decent, and the authors explicitly flag that TN is 20–50 K low and chiral splitting is 1.5× too large. They aren't overselling.\n\nWho should read this: anyone working on altermagnets or on exchange-parameter extraction from DFT. The methodological warning about configuration convergence is the kind of thing that should be disseminated widely. I'd bring it to a reading group and cite it if I worked on MnTe.\n\nRecommendation: send to peer review. No desk reject. The referees should ask for the configuration set, residuals, a U-dependence check, and the SM evidence for the pressure ground state.","headline":"The J2 sign flip is plausible but not yet bulletproof, while the chiral magnon mechanism via J10 is solid and worth citing.","tokens_in":11970,"tokens_out":2929,"would_cite":true,"duration_ms":27173,"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":"With ~60 magnetic configurations instead of 18, density-functional theory gives α-MnTe a ferromagnetic in-plane exchange, resolving a dispute with experiment.","keywords":["altermagnetism","α-MnTe","A-type antiferromagnetism","Heisenberg exchange interaction","chiral magnon splitting","DFT+U total-energy mapping","pressure tuning","magnetic configuration convergence"],"falsifier":"If a different selection of ~60 magnetic configurations at the same DFT+U level yields $J_2 < 0$, or if re-fitting the experimental magnon data with all 16 exchange parameters still gives an antiferromagnetic in-plane coupling, the central claim collapses; a direct check is to plot $J_2$ versus the number of configurations for several independent random subsets and look for sign stability.","tokens_in":11010,"feed_emoji":"🧲","tokens_out":8993,"duration_ms":75964,"temperature":0.7,"pith_summary":"This paper targets a specific contradiction in the altermagnetic semiconductor $\\alpha$-MnTe: experiments say the in-plane magnetic exchange $J_2$ is ferromagnetic, while earlier density-functional calculations found it antiferromagnetic. The authors argue that the old calculations simply used too few magnetic configurations, and show that fitting about 60 spin arrangements to a classical Heisenberg model makes $J_2$ positive and small, matching measurement. That single sign change removes the need for a strong third-neighbor exchange to stabilize the A-type antiferromagnetic order. The same fitted model attributes the experimentally observed chiral splitting of magnon bands to a direction-dependent tenth-neighbor exchange, and predicts that compressive pressure substantially enhances both spin and chiral magnon splittings and raises the Néel temperature.","feed_headline":"Converged DFT fit flips α-MnTe's in-plane exchange sign","feed_subtitle":"Resolving a long-standing DFT-versus-experiment dispute and explaining chiral magnon splitting in one material.","key_machinery":"The load-bearing object is the total-energy mapping from ~60 (ambient pressure) or ~120 (15 GPa) self-consistent DFT+U spin configurations onto the classical Heisenberg Hamiltonian $H = -\\sum_{i<j} J_{ij}\\,\\hat{\\mathbf{S}}_i\\cdot\\hat{\\mathbf{S}}_j$ with exchange interactions out to the 16th nearest neighbor. The sign of $J_2$ is shown to depend on the number of configurations included: with 18 configurations it is antiferromagnetic, and it crosses to ferromagnetic and stabilizes only as the count grows. A minimal supercell construction, the 34-Mn-atom SUPERHEX cell, makes the large configuration set computationally tractable. The direction-dependent tenth-neighbor pair $J_{10,a}$ and $J_{10,b}$ is the specific mechanism that carries the chiral magnon splitting.","core_discovery":"The paper's central claim is that with a sufficient number of magnetic configurations (~60), the least-squares map of DFT+U total energies onto a 16-parameter classical Heisenberg Hamiltonian yields a ferromagnetic in-plane second-nearest-neighbor exchange $J_2 = +0.17$ meV at ambient pressure, in agreement with experiments and in contrast to earlier DFT results. The correct sign of $J_2$, together with a large antiferromagnetic $J_3$, stabilizes the collinear A-type antiferromagnetic ground state. The paper also identifies the tenth-neighbor exchange as two distinct values $J_{10,a} = -0.28$ meV and $J_{10,b} = +0.09$ meV whose directional anisotropy produces the observed nonrelativistic chiral splitting of magnon bands. Under a compressive pressure of 15 GPa, $J_2$ reverses sign but the A-type order persists, while the spin subband splittings grow roughly 35–70% and the Néel temperature roughly doubles.","pith_inferences":["The same configuration-convergence check should be applied to other altermagnetic candidates, where published exchange couplings may come from under-sampled fits.","Because the ambient-pressure $J_2$ is small (+0.17 meV), modest strain, doping, or pressure gradients may drive $\\alpha$-MnTe toward a frustrated or different ordered state, offering a route to magnetic phase engineering.","Reporting exchange couplings only after demonstrating stability against both the number and the choice of magnetic configurations would make future total-energy-mapping studies more reproducible.","If direction-dependent exchange anisotropy of this kind is the generic source of chiral magnons in altermagnets, then magnonic altermagnetism should be expected in any centrosymmetric antiferromagnet whose exchange network contains inequivalent tenth-neighbor bonds, not just MnTe."],"forward_implications":["The A-type antiferromagnetic ground state of $\\alpha$-MnTe is controlled by a small positive in-plane $J_2$ plus a large negative interlayer $J_3$, not by a frustrated antiferromagnetic $J_2$ as previously inferred.","Chiral magnon splitting in $\\alpha$-MnTe is a nonrelativistic effect arising from the spatial anisotropy of the tenth-neighbor exchange, not from spin-orbit coupling.","A compressive pressure of 15 GPa reverses the sign of $J_2$ while preserving the A-type order, and it increases the electronic spin splittings by 35–70% and roughly doubles the Néel temperature.","Reliable exchange parameters in complex antiferromagnets require convergence checks against the number of magnetic configurations; small sets can flip signs.","The computed chiral magnon splitting is 1.5 times larger than the five-parameter experimental fit, indicating that model fits to neutron data need more exchange terms than previously used."],"supporting_citations":[{"why":"Supplies the experimental spin-wave measurement that found an in-plane ferromagnetic $J_2$, the discrepancy this paper resolves.","marker":"[47]"},{"why":"Provides the experimental observation of chiral split magnons and the five-exchange fit whose parameters the paper compares against.","marker":"[49]"},{"why":"Earlier DFT study that predicted an antiferromagnetic in-plane $J_2$, the target of the correction.","marker":"[50]"},{"why":"Earlier DFT study reporting the antiferromagnetic in-plane exchange used as a counter-claim.","marker":"[51]"},{"why":"Earlier ab initio work on MnTe that also obtained an antiferromagnetic in-plane exchange.","marker":"[52]"},{"why":"Source of the Hubbard $U = 4$ eV value used in the DFT+U calculations.","marker":"[55]"},{"why":"Reviews the total-energy-mapping method used to extract Heisenberg exchange interactions.","marker":"[57]"},{"why":"SUPERHEX method that constructs the minimal 34-atom supercell enabling the large configuration set.","marker":"[58]"},{"why":"Atomistic spin dynamics solver used for Monte Carlo susceptibility and Néel temperature calculations.","marker":"[60]"}],"fun_headline_variants":["Converged DFT fits settle MnTe exchange sign and chiral magnons","Config count flips MnTe's exchange sign, explains chiral magnons","Chiral magnon split in MnTe traced to 10th-neighbor exchange anisotropy","Strain boosts MnTe magnon splittings and doubles Neel temperature","MnTe's chiral magnon split explained by exchange anisotropy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on the assumption that least-squares fitting roughly 60 DFT+U total energies to a 16-parameter Heisenberg Hamiltonian gives a converged and unique set of exchange couplings, so the sign flip in $J_2$ reflects physics rather than an accident of configuration selection; the Hubbard $U = 4$ eV value is a secondary load-bearing input.","fun_headline_variants_meta":{"raw":{"variants":["Converged DFT fits settle MnTe exchange sign and chiral magnons","Config count flips MnTe's exchange sign, explains chiral magnons","Chiral magnon split in MnTe traced to 10th-neighbor exchange anisotropy","Strain boosts MnTe magnon splittings and doubles Neel temperature","MnTe's chiral magnon split explained by exchange anisotropy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000762,"raw_usage":{"total_tokens":3396,"prompt_tokens":973,"completion_tokens":2423,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":589,"completion_tokens_details":{"reasoning_tokens":2327}},"tokens_in":589,"tokens_out":2423,"duration_ms":19198,"temperature":1.0,"reasoning_tokens":2327,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:02:46.544455+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If a different selection of ~60 magnetic configurations at the same DFT+U level yields $J_2 < 0$, or if re-fitting the experimental magnon data with all 16 exchange parameters still gives an antiferromagnetic in-plane coupling, the central claim collapses; a direct check is to plot $J_2$ versus the number of configurations for several independent random subsets and look for sign stability.","supporting_citations":[{"cited_title":"Szuszkiewicz, E","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental spin-wave measurement that found an in-plane ferromagnetic $J_2$, the discrepancy this paper resolves."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier DFT study reporting the antiferromagnetic in-plane exchange used as a counter-claim."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier ab initio work on MnTe that also obtained an antiferromagnetic in-plane exchange."},{"cited_title":"Mosleh and M","cited_arxiv_id":null,"evidence_quote":"Source of the Hubbard $U = 4$ eV value used in the DFT+U calculations."}],"review_version":1}