{"id":"d11f2a68-9285-45fa-9af4-733fab32aa82","arxiv_id":"2607.13400","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"First-principles calculations predict hexagonal NiS is a compensated altermagnetic semimetal whose Dirac-like crossings produce large spin and anomalous Hall conductivities and ~1700% magnetoresistance at 30 T.","lead":"This paper uses computer simulations to predict that the magnetic semimetal NiS combines several sought-after quantum effects: a large spin Hall response, a symmetry-allowed anomalous Hall effect, and giant magnetoresistance. It also derives the magnetic interactions from first principles and compares the resulting ordering temperature to experiment.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"All transport predictions rest on a single untested LSDA+U parametrization; near-perfect compensation and SOC-gapped Berry curvature are not symmetry-protected against U/functional shifts.","rationale":"The Reader's weakest assumption identified the U=2.3 eV LSDA+U sensitivity, and I think that is the most load-bearing concern in the paper. The paper's own method section states the U value is imported from Ref. [18] without benchmarking, and the claimed high sensitivity of SHC to chemical potential (Fig. 3) makes the lack of a U/functional scan a concrete correctness risk rather than a generic DFT caveat. The central claim—'model platform where compensation, altermagnetism, Berry-curvature transport coexist'—would survive if different U choices preserved compensation and the large SHC; it would not survive if small parameter changes destroy compensation or flip the sign of the SHC. I agree with CONDITIONAL as the verdict; my pass does not move it. The paper does contain other issues (the abstract's MR 'exceeding 10000 percent' vs '10^3%' in the text; the TN 446 K vs 265 K comparison; absence of a topological invariant for the 'Dirac' label), but those are secondary or partially typographical compared with the missing parameter-robustness evidence. No machine-checked proof or deposited code is available, so an independent numerical recheck is the appropriate test.","tokens_in":17037,"tokens_out":12166,"duration_ms":128772,"concrete_test":"Recompute the full Wannier-based transport pipeline (bands, n_e/n_h, SOC gaps at K/A, σ^y_xz(E_F), AHC(E_F), MR at 30 T) for U = 0, 2.0, 2.7, 3.5 eV and for at least one alternative functional (e.g., PBE+U or SCAN). If the compensated carrier densities and the SHC/AHC at E_F remain within ~20% with unchanged sign, the U choice is not the load-bearing weakness; if they change substantially or compensation is lost, the quantitative central claim must be reclassified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claims—SHC σ^y_xz(E_F)=−171 (ℏ/e) S/cm, the symmetry-allowed AHC, and MR~1.7×10^3%—are all computed from DFT band structures obtained with LSDA+U+SOC at U=2.3 eV, adopted from Ref. [18] without revalidation (SM: 'The value of U=2.3 eV was adopted based on earlier studies of NiS [18]'). The Fermi surface is claimed to be nearly perfectly compensated (n_e≈n_h≈2.73×10^20 cm^−3), but carrier compensation is an accidental band-gradient property, not a symmetry-enforced invariant. Likewise, the SOC-induced avoided crossings α–δ that produce the spin Berry curvature depend on the delicate energy separation of the e1g/e2g manifolds near E_F, exactly the quantity LSDA+U is most sensitive to. No U scan, no alternative exchange-correlation functional, and no comparison with measured quantum oscillations or ARPES is provided to pin the Fermi-surface volumes. Given the strong energy dependence shown in Fig. 3, a modest shift of E_F or band position can change the SHC by hundreds of S/cm or reverse its sign, and the AHC at E_F—already near zero—could become nonzero or remain zero for reasons unrelated to the claimed symmetry. The magnetic-side check (T_N≈446 K vs the 265 K transition discussed in the same text) is a separate unresolved inconsistency, but even setting it aside, the transport claims lack robustness evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to establish hexagonal NiS as a compensated 3d altermagnetic semimetal in which altermagnetic symmetry, SOC-gapped Dirac-like crossings, Berry-curvature transport, and carrier compensation coexist. Using LSDA+U+SOC band structures, Wannier-based Kubo/Boltzmann transport, and LKAG-derived spin Hamiltonians with sLLG simulations, the authors report a large spin Hall conductivity, a symmetry-allowed but numerically small anomalous Hall conductivity at the Fermi level, a nearly compensated Fermi surface with MR ~1.7e3% at 30 T, and a calculated Néel temperature of ~446 K that is described as agreeing with experiment. The paper combines standard, well-established computational methods and presents dense k-mesh results, but several internal inconsistencies and robustness gaps affect the central quantitative claims.","tokens_in":17403,"tokens_out":4128,"duration_ms":48172,"significance":"If the claims are correct, NiS would be a valuable 3d platform in which altermagnetic order, SOC-induced Berry-curvature responses, and semimetallic carrier compensation coexist in a chemically simple material. The calculation pipeline is standard and reproducible in principle, and the SHC values, momentum-resolved Berry curvature, and FS compensation are concrete, falsifiable predictions. However, because the quantitative predictions are extremely sensitive to details of the band structure near EF, the lack of robustness tests and the internal inconsistencies described below must be resolved before the central claims can be taken as established.","major_comments":[{"comment":"The entire transport and compensation picture rests on a single LSDA+U parametrization with U=2.3 eV, 'adopted based on earlier studies of NiS [18]'. No U scan, no alternative exchange-correlation functional, and no comparison with measured Fermi-surface or ARPES data are provided. Since the SHC and AHC in Fig. 3 change by hundreds of S/cm over an energy window of a few tenths of an eV, and the claimed near-perfect electron-hole compensation is an accidental band-gradient property rather than a symmetry invariant, the robustness of the central quantitative predictions to moderate U variations is a load-bearing concern. A U scan (for example, 2.0–3.0 eV) and/or a GGA+U or hybrid-functional cross-check is needed to establish that the altermagnetic gaps, Berry-curvature hot spots, and carrier densities are not artifacts of this one choice.","section":"SM: LSDA+U+SOC calculations; Electronic structure"},{"comment":"The paper states in the Electronic Structure section that NiS undergoes a first-order transition at T_t ≈ 265 K to an A-type antiferromagnetic semimetal, but the spin-dynamics section reports T_N ≈ 446 K from the first-principles spin Hamiltonian and calls this 'excellent agreement with experiment [39]'. These two statements are mutually inconsistent: 446 K is ~1.7 times larger than 265 K. Either the experimental reference for T_N is different from the transition temperature discussed throughout the paper, or the sLLG model overestimates T_N. This discrepancy must be reconciled; as written, the magnetic-side claim is not internally consistent.","section":"Spin Hamiltonian; Fig. 5(b); Table I"},{"comment":"The abstract states that the magnetoresistance exceeds 10000%, while the main text reports MR_zz ≈ 1.7×10^3% at 30 T and compares this with experimental MR ~1500% (Ref. [21]). A factor-of-six discrepancy between the abstract and the body undermines the headline claim. Please correct the abstract or state clearly that 10000% is an extrapolated or upper-bound estimate; if the latter, specify the field and model assumptions used for the extrapolation.","section":"Abstract vs. 'Fermi-surface topology and large magnetoresistance'"},{"comment":"The text describes 'a sizable intrinsic AHC' and an 'anomalous Hall response despite zero net magnetization,' but the calculated AHC at E_F is explicitly stated to be 'close to zero' (Fig. 3(b)), with the nonzero values of order 15–20 S/cm occurring at -0.5 eV and +0.8 eV. If the measurable AHC at E_F is essentially zero, the headline claim of a finite anomalous Hall response is misleading. The authors should clearly separate the symmetry-allowed statement from the numerical value at E_F, and should state whether any finite AHC at E_F is actually predicted at the doping level relevant to experiments.","section":"Spin and anomalous Hall conductivity; Fig. 3(b)"},{"comment":"The title and abstract use 'Dirac topology,' but the crossings labeled α–δ are fourfold degenerate in the absence of SOC and are split or gapped once SOC is included; no topological invariant or surface-state signature is computed. In the conclusion the authors call the material a 'Dirac semimetal.' This overstates the topological classification. The manuscript should either compute and report a topological invariant (e.g., Z2 indices, mirror Chern numbers, or surface states) or consistently use the more cautious 'Dirac-like crossings' terminology throughout, including the title.","section":"Electronic structure; title and conclusion"}],"minor_comments":[{"comment":"The magnetotransport discussion repeatedly refers to 'Fig. S8(d)–(f)' and insets, but the main text also has a 'Fig. 4' with the same panels. Please synchronize the numbering and remove the duplicate/incorrect citations.","section":"Figure references"},{"comment":"In the abstract, 'nonsaturating magnetoresistance exceeding 10000 percent' should be reconciled with the body value. Also, 'sizable intrinsic AHC' should be replaced by a statement that the AHC is symmetry-allowed but numerically near zero at E_F.","section":"Abstract and text wording"},{"comment":"The sentence 'Thus, the first-principles derived spin Hamiltonian quantitatively reproducing the experimental Néel temperature' is grammatically incomplete; please revise.","section":"Spin Hamiltonian section"},{"comment":"There are typographical errors, e.g., 'properti es,' 'volet' should be 'violet,' and 'T y p' in the references. Also, Eq. (S6) has the relaxation time appearing on the left side in a way that is dimensionally confusing; please clarify the definition of σ(n)_ij(B).","section":"Supplemental Material"},{"comment":"Ref. [4] appears to be mis-formatted ('Bohm-Jung Yang, Classification...'); the author list should be corrected. Please also ensure Refs. [25] and [31] include complete titles and page/article numbers.","section":"Reference formatting"},{"comment":"The data-availability statement says data are available from the authors upon request. Given the quantitative nature of the predictions, please consider depositing the Wannier Hamiltonians, input files, and spin-model parameters in a public repository to strengthen reproducibility.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The manuscript uses U=2.3 eV from Ref. [18], a paper with overlapping authorship, without an independent sensitivity analysis. The T_N inconsistency (446 K vs the 265 K transition described in the text) and the abstract/body MR discrepancy are likely fixable but currently undermine the paper's central quantitative narrative. The AHC claim is also weaker than the abstract implies. I recommend major revision with a mandatory U/functional robustness study and a consistent set of headline numbers."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on the NiS paper. The genuinely new content is the transport tensor: the spin Hall conductivity with its strong energy dependence, the symmetry-allowed but numerically small AHC, and the Boltzmann-transport MR estimate, all computed from a DFT band structure with SOC. The exchange-tensor and sLLG analysis is also new and mostly well done. That part is worth publishing.\n\nCredit where due: the k-meshes are dense (885 k in the IBZ for the self-consistent calculation, 251^3 for Berry curvature), the Wannier interpolation is checked against the DFT bands, and the LKAG/KKR machinery is standard. The claim that NiS has large altermagnetic splitting is consistent with Ref [20], and the compensation picture matches the existing experimental MR, so nothing here is off-the-wall.\n\nSoft spots. First, the internal numbers don't line up. The abstract states MR exceeding 10000%, while the main text reports ~1.7x10^3% at 30 T; the experimental comparison [21] is ~1500%. That is a factor of 6 difference and needs correction. Second, the sLLG calculation gives TN≈446 K, which the text says is in excellent agreement with experiment, but the same paper earlier quotes the 265 K magnetostructural transition. There is no experimental 446 K transition cited; Coey and Brusetti [39] measure the heat capacity anomaly around 265 K. This is not a minor typo—it undercuts the claim of quantitative agreement.\n\nThird, and most substantive, the entire transport prediction rests on a single LSDA+U calculation with U=2.3 eV taken from a prior paper by the same group, with no U dependence study. The large SHC comes from SOC-gapped crossings near EF, and as Fig. 3 shows the SHC varies by hundreds of S/cm over ±0.3 eV. A small shift in band positions or U could change the sign or magnitude. The authors should provide a U scan or a comparison with ARPES/quantum oscillations to pin the Fermi surface. They also don't compute a topological invariant; the 'Dirac topology' wording is loose because the crossings gap out under SOC and are not symmetry-protected Dirac points in the sense of the cited refs.\n\nFinally, the AHC at EF is explicitly close to zero in Fig. 3(b) yet the text calls it 'sizable.' That is a descriptive error, though the symmetry-allowed point stands.\n\nOverall: the paper is a good computational contribution with correct methods, but it is overhyped in its present form. The fixes needed are calibrating the abstract and TN references, adding a U sensitivity check (even a two-point scan would help), and toning down 'Dirac topology.' None of that requires new physics, just careful revision.\n\nWho is this for? Computational condensed matter people working on altermagnets and Berry-curvature transport. I'd bring it to a reading group as an example of a promising but not yet bulletproof ab initio prediction. It deserves a serious referee; I would not desk-reject it. Send it to referees, but expect the internal consistency issues to require a revision.","headline":"Solid computational study with real new transport predictions for NiS, but the headline claims are oversold and the paper has internal inconsistencies (MR, Néel temperature) that need fixing before the numbers are trusted.","tokens_in":17908,"tokens_out":4007,"would_cite":false,"duration_ms":39446,"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":"Hexagonal NiS is a compensated 3d altermagnetic semimetal in which SOC-gapped Dirac-like crossings generate intense Berry curvature, a large intrinsic spin Hall conductivity, a symmetry-allowed anomalous Hall response, and nonsaturating mag","keywords":["altermagnetism","Dirac semimetal","spin Hall effect","anomalous Hall effect","magnetoresistance","NiS","Berry curvature","carrier compensation"],"falsifier":"Angle-resolved photoemission on single-crystal NiS along L–Γ: if the predicted ~0.7 eV momentum-dependent spin splitting with opposite spin orderings in the two planes is not observed, the altermagnetic band structure on which the Hall and magnetoresistance predictions rest is incorrect.","tokens_in":16905,"feed_emoji":"🧲","tokens_out":9871,"duration_ms":97852,"temperature":0.7,"pith_summary":"The paper argues that low-temperature NiS is a three-dimensional altermagnetic semimetal: its A-type antiferromagnetic order has zero net magnetization, yet the rotational symmetry of the NiAs lattice produces momentum-dependent spin splitting of up to about 0.7 eV. When spin–orbit coupling is included, fourfold Dirac-like crossings open small gaps and act as Berry-curvature hot spots, yielding a spin Hall conductivity of about −171 (ℏ/e) S/cm at the Fermi level and a finite anomalous Hall effect even though the material is compensated and collinear. The same band structure has nearly equal electron and hole pockets (about 2.7×10^20 cm^-3 each), which drives nonsaturating magnetoresistance of order 10^3%, matching earlier measurements. A first-principles spin Hamiltonian with dominant long-range superexchange reproduces the experimental Néel temperature near 446 K, so magnetism and transport are traced to the same symmetry framework. The payoff is a chemically simple 3d platform where altermagnetism, Dirac-like topology, carrier compensation, and strong magnetotransport coexist.","feed_headline":"NiS: a 3d altermagnetic semimetal with 10^3% magnetoresistance","feed_subtitle":"The same symmetry framework yields large spin Hall, allowed anomalous Hall, and compensated electron-hole pockets in one 3d compound.","key_machinery":"The load-bearing object is the magnetic symmetry group: preserved inversion P, the antiunitary S=Tτ_{1/2}, and the rotational coset of the NiAs lattice relating the two spin sublattices. This combination defines the altermagnetic state and lets Berry curvature survive despite zero net magnetization. The main electronic ingredients are the fourfold Dirac-like crossings enforced by the non-symmorphic P6_3/mmc space group; with spin–orbit coupling they become gapped avoided crossings that act as Berry-curvature hot spots. Kubo–Berry linear response turns those hot spots into large spin and anomalous Hall conductivities, and semiclassical Boltzmann transport turns the nearly compensated Fermi su","core_discovery":"The paper establishes hexagonal NiS as a compensated 3d altermagnetic semimetal. Its A-type antiferromagnetic order preserves inversion and S=Tτ_{1/2} while relating the two spin sublattices by rotation, so time reversal is broken without a net moment. That symmetry permits momentum-dependent spin splitting and nonzero Berry curvature. SOC gaps at the symmetry-enforced Dirac-like crossings (at K and along L–A) act as Berry-curvature hot spots, producing a large intrinsic spin Hall conductivity (≈−171 (ℏ/e) S/cm at E_F), a sign-reversing anomalous Hall effect, and nonsaturating magnetoresistance of order 10^3% from near-perfect electron–hole compensation. A first-principles spin Hamiltonian r","pith_inferences":["The symmetry mechanism should be generic: extended to other NiAs-type 3d chalcogenides and pnictides with A-type order, the same rotational-coset symmetry may yield compensated altermagnetic semimetals with comparable transport responses—a testable materials search.","The computed anomalous Hall sign reversal with chemical potential suggests that electrostatic gating or chemical substitution could switch Hall polarity in devices, turning NiS into a tunable Hall switch; the paper does not propose this application.","Because the spin and anomalous Hall effects arise specifically from SOC-gapped Dirac crossings, strain or uniaxial pressure that moves those crossings relative to E_F should strongly modulate the Hall conductivities—a concrete prediction that can be checked before full device work.","If the ~0.7 eV altermagnetic splitting is confirmed by ARPES, NiS may also serve as a spin-splitter or spin-filter material even in a nominally antiferromagnetic, zero-magnetization state, though that functionality is not discussed in the paper."],"forward_implications":["NiS is a 3d antiferromagnet with an intrinsic spin Hall conductivity comparable to 4d/5d metals, so spin-current generation can be achieved in a light, chemically simple compound without a net magnetic moment.","Moderate doping or gating can tune the spin Hall conductivity from roughly −282 to +314 (ℏ/e) S/cm and drive the anomalous Hall conductivity through sign changes, making the Hall response electrically controllable.","The nearly perfect electron–hole compensation produces nonsaturating magnetoresistance of order 10^3%, matching measured values and placing NiS alongside established compensated semimetals such as WTe2.","The first-principles spin Hamiltonian quantitatively reproduces the experimental Néel temperature (≈446 K), so the magnetic model underlying the altermagnetic state is consistent with thermodynamic data.","Finite anomalous Hall conductivity in a collinear compensated antiferromagnet follows from altermagnetic symmetry alone, removing the usual requirement of noncollinearity or net magnetization."],"fun_headline_variants":["NiS: altermagnetic semimetal with 10^4% magnetoresistance","Altermagnetic NiS: zero-net-moment Hall and 10^4% MR","Carrier-compensated altermagnet NiS: giant MR and Hall","3d altermagnet NiS: 10^4% MR and anomalous Hall","NiS altermagnet: Berry-curvature hot spots drive Hall and MR"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The calculations assume that LSDA+U with a single Hubbard U of 2.3 eV (taken from earlier studies of NiS) accurately captures the low-energy Ni-3d bands, including the near-perfect electron–hole compensation and the SOC-induced gaps; if correlation effects shift those bands, the quantitative values of the Hall conductivities, magnetoresistance, and Néel temperature would change.","fun_headline_variants_meta":{"raw":{"variants":["NiS: altermagnetic semimetal with 10^4% magnetoresistance","Altermagnetic NiS: zero-net-moment Hall and 10^4% MR","Carrier-compensated altermagnet NiS: giant MR and Hall","3d altermagnet NiS: 10^4% MR and anomalous Hall","NiS altermagnet: Berry-curvature hot spots drive Hall and MR"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001139,"raw_usage":{"total_tokens":4584,"prompt_tokens":783,"completion_tokens":3801,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":527,"completion_tokens_details":{"reasoning_tokens":3691}},"tokens_in":527,"tokens_out":3801,"duration_ms":27488,"temperature":1.0,"reasoning_tokens":3691,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T05:16:51.155018+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Angle-resolved photoemission on single-crystal NiS along L–Γ: if the predicted ~0.7 eV momentum-dependent spin splitting with opposite spin orderings in the two planes is not observed, the altermagnetic band structure on which the Hall and magnetoresistance predictions rest is incorrect.","supporting_citations":[],"review_version":1}