{"id":"f3ff29fc-858e-41a6-b652-cb4763d59373","arxiv_id":"2506.09675","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"First-principles calculations show that breaking mirror symmetry in a non-Janus altermagnet monolayer Fe2WS2Se2 spontaneously lifts valley degeneracy, a mechanism the authors call type III valley polarization.","lead":"This paper predicts a new mechanism for spontaneous valley polarization, called type III, in a two-dimensional antiferromagnet called Fe2WS2Se2, by breaking a mirror symmetry of the crystal. A smart generalist might read it because it expands valleytronics beyond magnetic and ferroelectric mechanisms and suggests a route to high-density information storage in atomically thin materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 2.27 meV VBM valley splitting without SOC is the linchpin of the type III claim; no U-dependence or k-mesh convergence is shown, so the central result may be numerical noise rather than a symmetry-generated spontaneous polarization.","rationale":"The reader's weakest assumption and my stress-test converge on the same point: the headline mechanism is quantitatively anchored by a meV-scale eigenvalue splitting from a single PBE+U calculation, and no numerical robustness evidence is provided. The symmetry argument in Section A justifies that a nonzero splitting is allowed, but it cannot prove that the computed 2.27 meV at the VBM is physically meaningful. The 8.40 meV CBM splitting is larger and less likely to be pure noise, but the abstract and Section C emphasize the no-SOC VBM splitting as the demonstration of the new type III mechanism. If a U-scan or denser-k calculation removes or strongly shifts that 2.27 meV value, the central novelty loses its quantitative support. Other weaknesses, such as the schematic AVHE and lack of data/code deposition, are real but secondary: they concern a derived transport claim and reproducibility, while the type III concept itself would survive if the no-SOC splitting were robust. The paper has independent support from phonon-stability calculations and a clear symmetry analysis of the Janus versus Non-Janus structures, which should be credited. My recommendation is therefore to keep the reader's conditional verdict: the mechanism is plausible and worth publishing in a form that demands the missing numerical-convergence evidence.","tokens_in":14875,"tokens_out":6306,"duration_ms":71775,"concrete_test":"Recompute the non-SOC band structure of Non-Janus Fe2WS2Se2 for Ueff = 0, 2, 3, 4, and 5 eV and for k-meshes of 12x12, 20x20, and 28x28, extracting the VBM and CBM splittings at X and Y with identical convergence criteria. If the 2.27 meV VBM splitting changes sign, vanishes below ~1 meV, or varies by more than a factor of two across this set, the central claim of spontaneous type III valley polarization is not established; additionally, compare smearing methods (tetrahedron versus Methfessel-Paxton) to confirm the splitting is not a numerical ghost.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Abstract and Section C rest the central claim that Non-Janus Fe2WS2Se2 spontaneously generates valley splitting without SOC on the no-SOC Kohn-Sham eigenvalue differences: 2.27 meV at the VBM and 8.40 meV at the CBM (Fig. 3a). The Methods specify a single PBE+U calculation with Ueff = 3 eV and a 20x20x1 k-mesh. Symmetry analysis shows only that the X/Y degeneracy may be lifted once [C2||Mxy] is broken; it does not determine the magnitude or sign of the splitting. At the meV scale, Kohn-Sham eigenvalue differences from a single Hubbard-U choice are not automatically physical. Without a U-dependence study or k-mesh convergence check, the 2.27 meV VBM splitting, in particular, is within the range of typical numerical uncertainty for PBE+U calculations, and could be an artifact of Ueff = 3 eV or of the collinear spin-polarized treatment in which spin-up and spin-down channels are decoupled. Because the type III label depends on this no-SOC splitting being a real, spontaneous symmetry-breaking effect, the absence of numerical robustness data is the most load-bearing gap. The anomalous valley Hall effect being schematic (Fig. 7) and the lack of deposited code/structures are secondary concerns; they affect the AVHE claim and reproducibility, but do not undercut the proposed mechanism as directly as the numerical fragility of the linchpin splitting.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a third mechanism for spontaneous valley polarization, named ‘type III’, based on breaking the mirror symmetry Mxy in a collinear antiferromagnet, and claims its realization in monolayer Non-Janus Fe2WS2Se2. Using PBE+U calculations, the authors find a Néel-type AFM ground state, direct band gaps, a biaxial magnetic anisotropy in the xy plane, a no-SOC valley splitting of 2.27 meV (VBM) and 8.40 meV (CBM) in the Non-Janus structure, and a variety of SOC-induced valley splittings for both Non-Janus and Janus phases. The paper also reports strain and magnetization-direction tuning of the splittings and presents schematic anomalous valley Hall effects.","tokens_in":15174,"tokens_out":9164,"duration_ms":99688,"significance":"The proposed mechanism is conceptually interesting and, if the meV-scale splittings are numerically robust, would expand the known routes to valley polarization beyond time-reversal-breaking and inversion-breaking systems. The symmetry arguments are clean, and the predicted strain and magnetization dependencies are falsifiable. The phonon stability and magnetic ground-state calculations are useful supporting results. The main reservation is that the central quantitative result rests on a single DFT+U parameter set and the anomalous valley Hall effect is not backed by Berry curvature calculations; the significance is therefore conditional on the missing numerical robustness tests.","major_comments":[{"comment":"The central claim of spontaneous type III valley polarization rests on the 2.27 meV no-SOC VBM splitting and the 8.40 meV CBM splitting. These are Kohn-Sham eigenvalue differences from a single PBE+U calculation with Ueff = 3 eV and a 20×20×1 k-mesh. At this energy scale, eigenvalue differences are sensitive to the Hubbard U and to k-mesh convergence, and the paper reports no U-dependence study, no k-mesh convergence test, and no comparison with an alternative functional. The symmetry analysis proves only that the X/Y degeneracy may be lifted; it does not establish that the mean-field eigenvalue difference is converged or physical. Without such tests, the type III classification is not yet established.","section":"§C, Fig. 3(a), Methods"},{"comment":"The anomalous valley Hall effect is presented only as a schematic, with no Berry curvature, Chern number, or anomalous Hall conductivity calculation. Since the sign of the valley Hall response is determined by the Berry curvature around the X and Y valleys, the assignment of spin-up electrons to the left boundary and spin-down holes to the right boundary is not demonstrated by the band-structure data alone. A Berry curvature calculation, or at least a symmetry-constrained argument for the Berry curvature, is needed to support the AVHE claims.","section":"§F, Fig. 7"},{"comment":"The title and abstract describe both Non-Janus and Janus Fe2WS2Se2 as altermagnets, but §B states that the Janus structure has the [C2||Mxy] spin symmetry and possesses d-wave altermagnet characteristics, while the Non-Janus structure has no such spin symmetry. If the Non-Janus structure lacks a spin-space symmetry connecting the two Fe sublattices, its classification as an altermagnet needs to be justified explicitly, or the central claim should be reframed as a broken-mirror-symmetry mechanism in a Néel antiferromagnet rather than an altermagnetic mechanism.","section":"§A, §B, title/abstract"}],"minor_comments":[{"comment":"The opening sentence beginning ‘Due to its unparalleled advantages’ is a sentence fragment; please revise for clarity.","section":"Introduction"},{"comment":"The caption contains a corrupted symbol ‘[C /g3671||Mxy]’; this should be printed as [C2||Mxy].","section":"Fig. 1 caption"},{"comment":"The strain definition sentence contains a missing symbol: ‘where a0 and represent the lattice constant’ should be ‘where a0 and a represent the lattice constant’.","section":"§D"},{"comment":"The code availability statement is ungrammatical (‘The codes are available from the findings of this study are available from the corresponding author on reasonable request’); in addition, depositing the input structures, pseudopotential settings, and analysis scripts would substantially aid reproducibility.","section":"Methods, Data and Code availability"},{"comment":"The main text repeatedly refers to Tables SI–SVII and SX–SXI, but these supplementary tables are not included in the provided manuscript; the authors should ensure that all cited tables are present and consistent.","section":"Supplementary material"},{"comment":"The MAE values are of order 1 meV, and the angular plots in Fig. 2 are presented without any numerical uncertainty estimate; a brief statement of k-mesh and Ueff convergence for the MAE would strengthen the biaxial anisotropy claim.","section":"§B, Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern is on point: the no-SOC VBM splitting is the central result and is not yet shown to be robust against changes in Ueff and k-mesh. I would not require experimental validation, but I would require U and k-mesh convergence tests and a Berry curvature calculation for the AVHE before the quantitative claims can be accepted. The paper has a heavy self-citation cluster, and the editor may wish to check the novelty of the ‘type III’ label against the preprints cited as refs. 17 and 18; this is a novelty-assessment issue rather than a circularity issue, since the valley splitting is an output of the calculations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The interesting thing here is conceptual: they propose a third route to spontaneous valley polarization in altermagnets by breaking the Mxy mirror symmetry with a non-Janus atomic arrangement, and support it with a symmetry analysis that is independent of the DFT numbers. That part holds up. The problem is the central quantitative evidence: the zero-field, no-SOC valley splitting that defines 'type III' is 2.27 meV at the VBM and 8.40 meV at the CBM, from a single PBE+U calculation with Ueff = 3 eV and a 20x20x1 mesh. No U-dependence or k-mesh convergence is shown. At that energy scale, Kohn-Sham eigenvalue differences are within typical numerical uncertainty, so the linchpin may be noise. This is not a fatal flaw—the symmetry argument says the splitting must exist—but the magnitude and even the sign need to be established more robustly before the 'type III' label carries weight.\n\nWhat the paper does well: the non-Janus design is genuinely new, and the contrast with the Janus structure gives a clean symmetry-controlled comparison. The phonon spectra show dynamical stability, the magnetic ground state analysis is standard and seems solid, and the four-leaf clover biaxial MAE is a nice find. The strain and magnetization-direction maps of valley splitting are thorough, though they inherit the same numerical robustness question.\n\nSoft spots, in order: (1) the missing U/k-mesh tests on the no-SOC splitting; (2) the anomalous valley Hall effect is only a schematic—no Berry curvature, no anomalous Hall conductivity; (3) no deposited structures or code, so the numbers are not independently checkable. The self-citation pattern is noticeable but not abusive; the central claim does not depend on it.\n\nWho is this for: the altermagnet/valleytronics DFT community. A serious referee should look at it, but with a clear request for convergence data and a computed Berry curvature.\n\nRecommendation: send to peer review, and in the review ask for the robustness tests. The concept deserves the referee time; the current evidence does not yet justify the strength of the abstract's claim.","headline":"Plausible symmetry-based mechanism for type III valley polarization, but the meV-scale linchpin splitting needs convergence proof.","tokens_in":15723,"tokens_out":1998,"would_cite":false,"duration_ms":19124,"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":"Breaking a mirror symmetry alone separates the valleys of a 2D altermagnet, no spin-orbit coupling needed.","keywords":["valley polarization","altermagnetism","type III valley polarization","valley Hall effect","magnetic anisotropy","two-dimensional materials","spin-orbit coupling","density functional theory"],"falsifier":"Recompute the non-SOC band structure of Non-Janus Fe$_2$WS$_2$Se$_2$ with $U_\\text{eff}$ varied from 0 to 6 eV and k-meshes from 12×12×1 to 24×24×1: if the X–Y valence splitting changes sign or drops below about 0.5 meV at any reasonable parameter set, the claimed intrinsic type III mechanism collapses.","tokens_in":14677,"feed_emoji":"🧲","tokens_out":7169,"duration_ms":68216,"temperature":0.7,"pith_summary":"The paper proposes and tests a third mechanism for spontaneous valley polarization, which it calls type III. Existing routes separate valleys by breaking time-reversal symmetry with magnetism or inversion symmetry with ferroelectricity; this one breaks a mirror symmetry, $M_{xy}$, that connects the two antiferromagnetic sublattices of an altermagnet. First-principles calculations on monolayer Non-Janus Fe$_2$WS$_2$Se$_2$ find that removing this symmetry alone lifts the degeneracy of the X and Y valleys, giving 2.27 meV valence and 8.40 meV conduction splittings even with spin-orbit coupling switched off. If the calculation is right, valley polarization becomes an intrinsic, nonrelativistic property of certain altermagnets, tunable by strain and magnetization direction, with an anomalous valley Hall effect for readout.","feed_headline":"Valley splitting without spin-orbit coupling in a 2D altermagnet","feed_subtitle":"Fe2WS2Se2 separates X and Y valleys by structure alone, opening a third route to valleytronics.","key_machinery":"The load-bearing object is the mirror symmetry $M_{xy}$ (and the combined spin-space symmetry $[C_2\\parallel M_{xy}]$) that pairs the two Fe sublattices in the altermagnet. In the Janus Fe$_2$WS$_2$Se$_2$ monolayer this symmetry keeps the X and Y valleys degenerate; in the Non-Janus structure, with S and Se placed differently relative to the two Fe sites, it is absent, and the inequivalence of the two sublattices appears as a valley splitting. The mechanism is nonrelativistic, since it operates with SOC turned off, and the altermagnetic spin splitting supplies the spin-valley locking that leads to the anomalous valley Hall effect once carriers are doped.","core_discovery":"In its own terms, the paper's central discovery is that valley polarization can be intrinsic to a crystal rather than imposed by magnetic or electric order. In monolayer Non-Janus Fe$_2$WS$_2$Se$_2$, the two Fe sublattices are not connected by the combined symmetry $[C_2\\parallel M_{xy}]$ that exists in the Janus structure, so the X and Y valleys are no longer degenerate: the valence-band splitting is 2.27 meV and the conduction-band splitting 8.40 meV without SOC. With SOC the same material shows larger, direction-dependent splittings, and the Janus Fe$_2$WS$_2$Se$_2$, which preserves that symmetry, needs both magnetism and SOC to valley-split. The paper also reports a rare biaxial magnetic anisotropy with four equivalent in-plane easy directions, and shows that biaxial strain and magnetization orientation can tune the magnitude and sign of the valley polarization, enabling an anomalous valley Hall effect.","pith_inferences":["A testable extension is to scan other Non-Janus altermagnets with two different chalcogen heights: if the mechanism is generic, the without-SOC valley splitting should scale with the structural asymmetry between the two sublattices rather than with atomic spin-orbit strength.","Because the splitting appears without SOC, it should also survive in light-element isostructural compounds where spin-orbit coupling is weak, which would separate this mechanism cleanly from type I in experiment.","Computing the Berry curvature and intrinsic anomalous Hall conductivity would put the schematic anomalous valley Hall effect on quantitative footing; the paper stops at a schematic diagram.","If the 2.27 meV without-SOC splitting is confirmed at higher $U$ values and denser k-meshes, the mechanism implies that valley degeneracy in altermagnets is not protected by time reversal alone, revising the usual symmetry classification of valleytronic materials."],"forward_implications":["Non-Janus Fe$_2$WS$_2$Se$_2$ is a dynamically stable, direct-gap N\\'eel antiferromagnet whose X and Y valleys are spontaneously split by 2.27 meV (valence) and 8.40 meV (conduction) with SOC off.","Biaxial strain from -5% to +5% preserves the AFM1 ground state and the out-of-plane easy axis while tuning valley splitting by tens of meV, and reversing magnetization from x to y reverses the splitting signs.","Both Non-Janus and Janus Fe$_2$WS$_2$Se$_2$ display an anomalous valley Hall effect: under in-plane electric field, spin-up and spin-down carriers from inequivalent valleys accumulate on opposite sample edges.","The four-leaf-clover in-plane magnetic anisotropy gives four equivalent easy axes, which could encode four logic states in a biaxial magnetic tunnel junction.","The Janus structure, by contrast, exhibits type I valley polarization only when SOC and in-plane magnetization break the $[C_2\\parallel M_{xy}]$ symmetry, so the two structures bracket the type III/type I distinction in one material family."],"supporting_citations":[{"why":"Defines altermagnets as collinear antiferromagnets with nonrelativistic spin splitting and zero net magnetization, the host class for the proposed mechanism.","marker":"[12–18]"},{"why":"Shows the X/Y valley degeneracy in altermagnets is protected by mirror symmetry, so breaking $M_{xy}$ is the lever for valley splitting.","marker":"[37, 38]"},{"why":"Documents the piezovalley route where uniaxial strain breaks mirror symmetry; the paper's design aims to make that breaking intrinsic rather than external.","marker":"[16, 17, 37, 39]"},{"why":"Establishes the type I (magnetism/time-reversal) and type II (ferroelectricity/inversion) valley polarization categories that the new type III mechanism is contrasted against.","marker":"[5–11]"},{"why":"Supplies the fourth-order single-ion anisotropy Hamiltonian used to describe the biaxial four-leaf-clover magnetic anisotropy.","marker":"[45]"},{"why":"Provides the plane-wave DFT methods (VASP, PBE functional) behind all electronic-structure and total-energy results.","marker":"[46–49]"},{"why":"Justifies the GGA+U treatment with $U_\\text{eff} = 3$ eV for Fe 3d electrons, the correlation scheme that determines the reported meV splittings.","marker":"[50–53]"},{"why":"Underpins the phonon calculations used to establish dynamical stability of the predicted monolayers.","marker":"[54]"}],"fun_headline_variants":["Valley splitting by mirror symmetry breaking in altermagnet","No SOC needed: altermagnet splits valleys by structure","Type III valley polarization from mirror symmetry loss","Fe2WS2Se2: valley split without spin-orbit coupling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim stands on a first-principles calculation that uses a tuned electron-correlation parameter ($U_\\text{eff}=3$ eV) to get meV-scale energy differences, with no test of how those differences vary when that parameter or the numerical grid is changed.","fun_headline_variants_meta":{"raw":{"variants":["Valley splitting by mirror symmetry breaking in altermagnet","No SOC needed: altermagnet splits valleys by structure","Type III valley polarization from mirror symmetry loss","Fe2WS2Se2: valley split without spin-orbit coupling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000247,"raw_usage":{"total_tokens":1597,"prompt_tokens":1053,"completion_tokens":544,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":669,"completion_tokens_details":{"reasoning_tokens":477}},"tokens_in":669,"tokens_out":544,"duration_ms":6287,"temperature":1.0,"reasoning_tokens":477,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:42:32.709767+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the non-SOC band structure of Non-Janus Fe$_2$WS$_2$Se$_2$ with $U_\\text{eff}$ varied from 0 to 6 eV and k-meshes from 12×12×1 to 24×24×1: if the X–Y valence splitting changes sign or drops below about 0.5 meV at any reasonable parameter set, the claimed intrinsic type III mechanism collapses.","supporting_citations":[{"cited_title":"Z., & Li, P","cited_arxiv_id":null,"evidence_quote":"Supplies the fourth-order single-ion anisotropy Hamiltonian used to describe the biaxial four-leaf-clover magnetic anisotropy."},{"cited_title":"D., Zhang, L., Zhang, Y., Li, P., & Wang, G","cited_arxiv_id":null,"evidence_quote":"Underpins the phonon calculations used to establish dynamical stability of the predicted monolayers."}],"review_version":1}