{"id":"839950fb-529c-4d88-9a17-8702014d07fc","arxiv_id":"2501.06829","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Starting from the PT-antiferromagnet CrC2S6, the paper predicts that Janus engineering gives an altermagnet and isovalent alloying gives fully-compensated ferrimagnets.","lead":"This paper predicts that a single 2D magnetic material, CrC2S6, can be switched between three types of zero-magnetization magnets by swapping atoms or applying an electric field. If correct, it gives researchers a concrete platform for comparing altermagnets and fully-compensated ferrimagnets in spintronics.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The material-realization claim rests on a single Hubbard-U value (3.00 eV for Cr and Mo) with no sensitivity test; a U sweep is needed to confirm the AFM1 ground state and spin-splitting survive.","rationale":"The reader's weakest_assumption identifies the PBE+U parametrization, and I agree that this is the load-bearing point. The symmetry relationships underlying the transition scheme are generic and likely correct; the novelty is the concrete material family. The paper provides phonon, AIMD, and elastic-constant stability checks, which support the structural claims. However, the central claim is a materials prediction, and the absence of a U-sensitivity analysis leaves a real gap: U at 3.00 eV is imported from a prior study of a related but not identical compound, and it directly controls the d-state localization and magnetic exchange. A U sweep is the natural falsification check: if the qualitative physics is robust, the claim holds; if not, the specific compounds do not realize the PT-antiferromagnet-to-altermagnet-to-fully-compensated-ferrimagnet sequence. Other limitations, such as synthesis feasibility and the exact i-wave symmetry label, are secondary and can be addressed separately. Therefore, the reader's CONDITIONAL verdict remains appropriate, and no change is needed.","tokens_in":9960,"tokens_out":15048,"duration_ms":157940,"concrete_test":"Recompute the total-energy differences of Figure 3(b) and the spin-polarized band structures of Figure 4 for Cr2C2S3Se3 and CrMoC2S6 using U=2.0, 4.0, and 5.0 eV (plus U=0 as a PBE reference), keeping all other settings identical. If AFM1 is no longer the lowest collinear configuration, if a noncollinear calculation lowers the energy further, or if the gap closes and the altermagnetic/ferrimagnetic splitting pattern disappears, the material realization of the proposed transition is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that Cr2C2S6, Cr2C2S3Se3, CrMoC2S6 and CrMoC2S3Se3 each adopt the AFM1 collinear state as the ground state and exhibit the claimed spin-splitting symmetries (i-wave altermagnet, s-wave fully-compensated ferrimagnet). These results come from a single DFT+U parametrization: U=3.00 eV for both Cr and Mo d-orbitals, taken from Ref. [40] in the Computational detail. The paper reports no U-dependence. U directly controls the relative energy of FM versus AFM orders and the position of d-states near the gap. A modest change (for example, 2.0 or 4.0 eV) could make FM or AFM2 lower than AFM1, destroying the net-zero magnetization and the PT symmetry that underpin the classification; alternatively, if the gap closes, the insulating net-zero-magnetization phases and their spin-splitting would no longer be realized. The ground-state search is also limited to four collinear configurations (Figure 3), leaving noncollinear spin textures untested. Because the paper's own mode of verification is 'by first-principles calculations, the proposed transitions can be verified in these compounds', this single U value is the least secure element of the materials realization. This is a correctness risk, not a consensus dispute: the symmetry-breaking scheme is plausible, but the specific examples are conditional on U.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a symmetry-based framework for transitions among three classes of net-zero-magnetization magnets—PT-antiferromagnets, altermagnets, and fully-compensated ferrimagnets—and claims first-principles verification in a single 2D materials family: PT-antiferromagnetic Cr2C2S6, altermagnetic Cr2C2S3Se3 (via Janus engineering), and fully-compensated ferrimagnetic CrMoC2S6 and CrMoC2S3Se3 (via isovalent alloying). DFT+U calculations are used to establish the AFM1 ground state, stability (phonons, AIMD, elastic constants), spin-splitting symmetries, and Berry-curvature-based anomalous valley Hall effect. The central conceptual message is that breaking P (and C/M) symmetries of a parent PT-antiferromagnet transforms the spin-splitting symmetry from degenerate to i-wave (altermagnet) or s-wave (fully-compensated ferrimagnet).","tokens_in":10265,"tokens_out":4350,"duration_ms":43707,"significance":"If the material realization is robust, the paper provides a clear and conceptually useful demonstration of how symmetry-breaking operations connect three important classes of net-zero-magnetization magnets within one 2D family. The proposed Cr2C2S6-derived compounds would constitute a promising platform for exploring momentum-dependent versus global spin splitting, and for potential spintronic and valleytronic applications. The paper includes several commendable elements: symmetry arguments tied to magnetic space groups, explicit collinear magnetic configuration searches, phonon/AIMD/elastic stability checks, and Berry-curvature illustrations of the anomalous valley Hall effect. However, the material-specific predictions rest on a single DFT+U parametrization, and the paper would be significantly strengthened by demonstrating robustness of the magnetic ground state and spin-splitting with respect to the Hubbard U and to noncollinear magnetic order.","major_comments":[{"comment":"The central material-realization claim depends on AFM1 being the magnetic ground state for all four compounds, yet this is established only at a single PBE+U value, U=3.00 eV for both Cr and Mo, taken from Ref. [40]. No U-dependence is reported. Since U directly controls the relative energies of FM, AFM2, AFM3, and AFM1, and can also alter the d-orbital ordering near the gap, the paper should provide a U-sweep (for example, U = 2.0 to 4.0 eV) for the energy differences in Figure 3(b), and ideally verify that the AFM1 ground state and the reported spin-splitting patterns survive across this range. In addition, only four collinear configurations are considered; noncollinear spin arrangements are not tested, leaving an unexamined possibility for an even lower-energy state. These checks are load-bearing because the paper's mode of validation is explicitly first-principles verification in these specific compounds.","section":"Computational detail and Figure 3"},{"comment":"The external-electric-field route is used to argue that a PT-antiferromagnet can be turned into an altermagnet, with Cr2C2S6 at E = 0.30 V/Å shown as the example. The computational implementation of the field is not described: the paper does not state whether a sawtooth potential, dipole-correction scheme, or other method is used in the periodic slab, nor whether the field strength is large enough to be realistic while remaining below dielectric breakdown. Because the external field is one of the three proposed symmetry-breaking methods in the abstract and introduction, these details matter for reproducibility and for assessing whether the reported spin-splitting is a genuine field effect rather than a numerical artifact. Please specify the implementation and add a field-strength dependence (e.g., E = 0.1–0.5 V/Å) for the band structure.","section":"Material realization, Figure 4(e)"}],"minor_comments":[{"comment":"The chemical formulas are inconsistent: the abstract uses CrC2S6, CrC2S3Se3, CrMoC2S6, and CrMoC2S3Se3, while the main text uses Cr2C2S6, Cr2C2S3Se3, CrMoC2S6, and CrMoC2S3Se3. Please unify the notation, as the two-Cr formula is the one supported by the structure and stoichiometry.","section":"Abstract and main text"},{"comment":"There is a typo in 'anomalous Halll/Nernst effect'; 'Halll' should be 'Hall'.","section":"Introduction"},{"comment":"The phrase 'confirming thier mechanical stabilities' contains a typo ('thier' should be 'their').","section":"Stability paragraph"},{"comment":"The symbols C2, C/M, and P are used in the caption but not defined there; define them (two-fold rotation in spin space, rotation/mirror symmetry in lattice space, inversion) so the figure is self-contained.","section":"Figure 1 caption"},{"comment":"The abbreviations 'V ASP' and 'PA W' contain spacing artifacts; they should read 'VASP' and 'PAW'.","section":"Computational detail"},{"comment":"The energy differences are described only as positive; providing numerical values or a table would make the ground-state assignment more quantitative and would strengthen the paper.","section":"Figure 3(b)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on the authors' prior work, particularly Refs. [7] and [29–33], and Ref. [11] is listed as 'under review'. The editor may wish to verify that the present results are sufficiently distinct from these prior papers and that Ref. [11] does not overlap with the fully-compensated ferrimagnet claims here. This is a scope and novelty concern rather than a technical error."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Net-zero-magnetization magnets are an active area, and this paper does a useful thing: it takes one parent PT-AFM (CrC2S6) and shows, with symmetry arguments plus DFT+U, how Janus engineering and isovalent alloying produce an altermagnet (Cr2C2S3Se3) and two fully-compensated ferrimagnets (CrMoC2S6, CrMoC2S3Se3). The specific compounds are new predictions, and the band-structure symmetries from the text match what the symmetry classification expects: i-wave splitting in the Janus case, s-wave splitting in the alloyed cases. The phonon, AIMD, and elastic-constant checks are appropriate. The Berry curvature and valley splitting numbers (7.4 and 3.3 meV) are reasonable and consistent with the MAE values.\n\nThe soft spot, as you flagged, is the single Hubbard U. All four ground states come from U=3.00 eV on both Cr and Mo, taken from a prior paper. There is no U sweep, and the energy differences in Figure 3(b) are reported without absolute scale, so we can't see how close the competing orders are. It's entirely possible that a different U (or a noncollinear configuration) changes the ground state, which would undo the specific material claims. This is not a fatal flaw in the symmetry story — the point-group argument is independent of U — but it is load-bearing for the material realization. A referee should ask for a U sensitivity test (2–4 eV) and at least a check of noncollinear orders before publication.\n\nTwo smaller points: the external-field calculation is described only briefly, so I'd like to see how the field is applied in the slab and whether the 0.30 V/Å result is a proper response or just an order-of-magnitude estimate. And the paper leans heavily on the authors' own prior definitions of fully-compensated ferrimagnets; that's not a problem in itself, but it makes the paper less self-contained for someone new to the terminology.\n\nOverall, I think the paper is a solid, modest contribution. It doesn't redefine the field, but it gives a clean concrete example of transitions among three classes of net-zero-magnetization magnets, with plausible (not proven) material candidates. I would send it to review, with the U-sensitivity request as a condition. For a reading group, it's a reasonable way to get into the altermagnet/fully-compensated ferrimagnet discussion, but I wouldn't call it essential.","headline":"A clean symmetry-based demonstration of PT-AFM to altermagnet to fully-compensated ferrimagnet transitions in one 2D family, but the material realization rests on a single Hubbard U value with no sensitivity test.","tokens_in":10823,"tokens_out":2778,"would_cite":true,"duration_ms":26231,"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":"Symmetry breaking in a single monolayer family produces the full sequence of net-zero-magnetization magnets, from PT-antiferromagnet through altermagnet to fully-compensated ferrimagnet, with the expected spin-splitting symmetries.","keywords":["net-zero-magnetization magnets","altermagnetism","fully-compensated ferrimagnet","PT-antiferromagnet","Janus engineering","isovalent alloying","spin splitting","anomalous valley Hall effect"],"falsifier":"Compute the CrC2S6 family with a different Hubbard U (or a hybrid functional) and with noncollinear spin arrangements; if the AFM1 order ceases to be the ground state, or the band structures lose the i-wave/s-wave spin splitting, the paper's central claim is refuted. Experimentally, growing the monolayer and performing spin-resolved ARPES or magnetic circular dichroism on Cr2C2S3Se3 and CrMoC2S6 would directly test whether the splitting symmetries match the predictions.","tokens_in":9758,"feed_emoji":"🧲","tokens_out":8398,"duration_ms":67359,"temperature":0.7,"pith_summary":"The paper claims that the three kinds of net-zero-magnetization magnets — PT-antiferromagnets, altermagnets, and fully-compensated ferrimagnets — are connected by symmetry breaking, and that one can walk through the whole sequence in a single two-dimensional material family. Starting from a PT-antiferromagnetic CrC2S6 monolayer with both inversion and mirror symmetry, the authors show by density functional theory that replacing one sulfur layer with selenium (Janus engineering) breaks inversion while keeping the mirror, yielding an altermagnet with i-wave spin splitting, while substituting one chromium by molybdenum (isovalent alloying) breaks both symmetries, yielding fully-compensated ferrimagnets with s-wave splitting. The same altermagnetic splitting is reproduced by an external electric field on the parent compound, making the symmetry-breaking route reversible and voltage-tunable. If correct, this gives a clear material playground for comparing and exploiting the distinct spin-splitting symmetry classes and for anomalous valley Hall transport in zero-moment magnets.","feed_headline":"A single 2D monolayer hosts all three zero-magnet magnetic phases","feed_subtitle":"Janus engineering and alloying turn PT-antiferromagnetic CrC2S6 into an altermagnet and a compensated ferrimagnet.","key_machinery":"The organizing device is the symmetric-connection classification of the two oppositely polarized magnetic sublattices: [C2∥P] (inversion-connected, PT-antiferromagnet), [C2∥C/M] (rotation/mirror-connected, altermagnet), and [C2∥Null] (asymmetrically connected, fully-compensated ferrimagnet). The paper's specific strategy is to start from a PT-antiferromagnet that carries both P and a mirror (C/M) symmetry, so that breaking just one symmetry toggles the class: P-breaking with C/M intact gives momentum-dependent (d/g/i-wave) splitting, and breaking both gives s-wave splitting. In the CrC2S6 example the symmetry operations are concrete: parent P-31m with P and Mxy; Janus CrC2S3Se3 in P31m without P but with Mxy; alloyed CrMoC2S6/CrMoC2S3Se3 in P312/P3 without either. The machinery is what makes the transitions predictable and the spin-splitting symmetry diagnosable from the space group alone.","core_discovery":"Starting from a collinear PT-antiferromagnet whose opposite-spin sublattices are connected simultaneously by inversion P and a mirror Mxy, breaking only P (keeping Mxy) converts the material into an altermagnet with momentum-dependent, i-wave spin splitting; breaking both P and Mxy converts it into a fully-compensated ferrimagnet with global s-wave splitting. In the CrC2S6 monolayer, these two breakings are realized chemically: Janus substitution of one S layer by Se gives CrC2S3Se3 (altermagnet), and isovalent Cr-to-Mo substitution gives CrMoC2S6 and CrMoC2S3Se3 (fully-compensated ferrimagnets with out-of-plane easy axis and valley polarization of opposite sign at the two valleys). The parent remains a 2.31 eV bandgap semiconductor with strictly zero total moment, and the derived phases retain zero net moment while showing the predicted spin-splitting symmetries and, in the ferrimagnets, a large orbital-mismatch-driven splitting near the Fermi level and an anomalous valley Hall effect. An external electric field of 0.30 V/Å on the parent reproduces the altermagnetic splitting, with the splitting order reversing when the field reverses.","pith_inferences":["The symmetry criterion is parameter-free: any collinear PT-antiferromagnet with the same P+C/M group constraints should show the same transitions, so the specific Hubbard U value matters for quantitative band gaps and moments but not for the existence of the splitting symmetries.","If the altermagnetic CrC2S3Se3 and ferrimagnetic CrMoC2S6 monolayers can be exfoliated or grown, spin-resolved angle-resolved photoemission should directly image the contrasting i-wave vs s-wave spin splitting, and a Hall-bar measurement should detect the predicted transverse voltage.","The external-field route on the parent suggests a reversible, non-volatile two-state switch between spin-degenerate and spin-split regimes, and combining Janus and alloying could yield lateral heterostructures with a built-in interface between altermagnet and ferrimagnet.","Because only four collinear magnetic configurations were checked, the authors' identification of AFM1 as the ground state could be tested by noncollinear spin-spiral calculations; if a noncollinear order wins, the predicted net-zero phases in these exact compounds would not form, though the symmetry rationale would survive."],"forward_implications":["The same symmetry recipe — start from a PT-antiferromagnet with P plus rotation/mirror, then break P, or P and mirror — should generate altermagnets and fully-compensated ferrimagnets from other honeycomb PT-AFM parents, not only CrC2S6.","Reversing the external electric field reverses the order of spin-splitting in the altermagnetic phase, which the paper identifies as a handle for tuning spin currents in spintronic devices.","The fully-compensated ferrimagnets exhibit spontaneous valley polarization with opposite Berry curvature at K and -K, so shifting the Fermi level between valleys produces an anomalous valley Hall effect in a zero-moment magnet.","A single material family now allows direct comparison of properties that otherwise live in unrelated compounds: PT-AFM spin degeneracy, altermagnetic d/i-wave splitting, and ferrimagnetic s-wave splitting under the same lattice and magnetic ordering."],"supporting_citations":[{"why":"defines the altermagnetic class and its momentum-dependent spin-splitting symmetry, the classification this paper starts from.","marker":"[5]"},{"why":"supplies the conceptual distinction between altermagnetism and conventional PT-antiferromagnetism.","marker":"[6]"},{"why":"shows that placing opposite-spin magnetic atoms in different environments produces spin splitting, the mechanism behind Janus and alloying.","marker":"[7]"},{"why":"establishes two-dimensional fully-compensated ferrimagnetism and its global s-wave spin splitting.","marker":"[11]"},{"why":"provides the parent CrMoC2S6 compound and the U=3.00 eV Hubbard values used for Cr and Mo.","marker":"[40]"},{"why":"gives the rotationally invariant Hubbard correction scheme in which the DFT+U calculations are performed.","marker":"[41]"},{"why":"derives momentum-dependent spin splitting in collinear antiferromagnets, underpinning the i-wave symmetry assignment.","marker":"[12]"}],"fun_headline_variants":["Symmetry breaking flips zero-magnet phases in one monolayer","One 2D material hosts all three zero-magnet magnetic orders","From PT-antiferromagnet to altermagnet and ferrimagnet in one monolayer","Janus engineering and alloying switch between zero-magnet phases","Electric field alone can induce altermagnetic spin-splitting in 2D magnet"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central assumption is that the density-functional calculations with the chosen Hubbard U correction (3 eV on chromium and molybdenum) and the four collinear spin arrangements tested actually find the true magnetic ground state; if a noncollinear ordering or a different U value changes which magnetic order wins, the predicted altermagnet and fully-compensated ferrimagnet phases in these specific compounds would not form as described.","fun_headline_variants_meta":{"raw":{"variants":["Symmetry breaking flips zero-magnet phases in one monolayer","One 2D material hosts all three zero-magnet magnetic orders","From PT-antiferromagnet to altermagnet and ferrimagnet in one monolayer","Janus engineering and alloying switch between zero-magnet phases","Electric field alone can induce altermagnetic spin-splitting in 2D magnet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000796,"raw_usage":{"total_tokens":3601,"prompt_tokens":1140,"completion_tokens":2461,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":756,"completion_tokens_details":{"reasoning_tokens":2364}},"tokens_in":756,"tokens_out":2461,"duration_ms":16030,"temperature":1.0,"reasoning_tokens":2364,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:49:50.203719+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the CrC2S6 family with a different Hubbard U (or a hybrid functional) and with noncollinear spin arrangements; if the AFM1 order ceases to be the ground state, or the band structures lose the i-wave/s-wave spin splitting, the paper's central claim is refuted. Experimentally, growing the monolayer and performing spin-resolved ARPES or magnetic circular dichroism on Cr2C2S3Se3 and CrMoC2S6 would directly test whether the splitting symmetries match the predictions.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"establishes two-dimensional fully-compensated ferrimagnetism and its global s-wave spin splitting."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the parent CrMoC2S6 compound and the U=3.00 eV Hubbard values used for Cr and Mo."},{"cited_title":"Hayami, Y","cited_arxiv_id":null,"evidence_quote":"derives momentum-dependent spin splitting in collinear antiferromagnets, underpinning the i-wave symmetry assignment."}],"review_version":1}