{"id":"6051dcfc-ddf4-43d9-baa6-476af90877e4","arxiv_id":"2608.08741","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In CrSb thin films, altermagnetic spin splitting is controlled by long-range inter-unit-cell coplanar Cr-Sb hopping, whose suppression explains why some surface orientations lose the splitting.","lead":"This paper uses density functional theory and Wannier tight-binding models to explain why altermagnetic spin splitting in CrSb thin films depends on surface orientation, with only certain surfaces keeping the splitting. A generalist should care because thin-film altermagnets could power new spintronic devices, and the result gives a surface-engineering rule for controlling their spin properties.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The universal 'requires long-range Cr-Sb hopping' claim is underdetermined: it is tested only for one slab, and even there the ablation shows Sb-Sb hopping alone can produce splitting.","rationale":"The paper's core evidence is real: the Wannier ablation in the (2-1-10) slab shows that intra-unit-cell hopping alone yields degenerate bands, while adding inter-unit-cell Cr-Sb and Sb-Sb hopping reproduces the spin splitting, with Cr-Sb playing the dominant role. That is a meaningful microscopic result. The reader's concern about the unsupported generalization to (0001) and (10-10) is valid: the universal claim rests on geometric inference, not a direct hopping analysis of those slabs. I add a second, more internal issue: the abstract's 'requires ... Cr-Sb hopping' is stronger than the data, since Fig. 3(b) demonstrates that Sb-Sb inter-cell hopping alone is already sufficient to induce splitting. Thus the attack is not that the mechanism is wrong, but that the stated central claim overreaches the shown evidence in two distinct ways. A focused Wannier ablation of the degenerate surfaces, plus a quantitative report of long-range Cr-Sb matrix elements, would settle whether the surface-dependence mechanism is correct. The recommended verdict remains conditional: the paper is plausible and partly supported, but the central claim should be revised or further substantiated before acceptance as stated.","tokens_in":9446,"tokens_out":5669,"duration_ms":63680,"concrete_test":"Perform the same Wannier hopping ablation for the (0001) and (10-10) slabs as was done for (2-1-10): construct truncated Hamiltonians from the Wannier fits with (i) intra-unit-cell terms only, (ii) plus inter-unit-cell Cr-Sb, (iii) plus inter-unit-cell Sb-Sb, and (iv) the full Hamiltonian. Compute the maximum spin splitting along the same low-symmetry k-path in each case, and also report the largest inter-cell |t_Cr-Sb| matrix elements for all three slabs. If adding inter-cell Cr-Sb does not restore splitting in (0001)/(10-10), the geometric suppression claim is wrong; if Sb-Sb alone already restores splitting in (2-1-10), the abstract's 'requires Cr-Sb' must be weakened to 'requires inter-cell hopping, dominated by Cr-Sb.'","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim has two linked weak spots. First, the Wannier hopping ablation is performed only for the (2-1-10) slab; the statement that the degenerate (0001) and (10-10) slabs lack splitting because long-range Cr-Sb hopping is suppressed is inferred from geometry (Cr and Sb at different depths) rather than from the Wannier fits for those slabs. The paper does not report the relevant long-range Cr-Sb matrix elements for (0001) and (10-10), so the 'preservation or suppression of pathways' mechanism is not directly verified where it is needed most. Second, even within the (2-1-10) slab, Fig. 3(b) shows that adding only inter-unit-cell Sb-Sb hopping is sufficient to induce momentum-dependent spin splitting. This contradicts the abstract's wording that thin-film splitting 'requires long-range inter-unit-cell coplanar Cr-Sb hopping'; the displayed data support only 'some long-range inter-unit-cell hopping is indispensable, with Cr-Sb dominant and Sb-Sb contributing.' If the stronger 'requires Cr-Sb' is retained, that conclusion is not established by the reported ablation. The conflict with ARPES observations of splitting in 10-30 nm films is also unresolved, but the internal logical gap is the more immediate obstacle to accepting the mechanism as stated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript investigates the microscopic origin of surface-dependent altermagnetic spin splitting in CrSb thin films using DFT and Wannier tight-binding analysis. The authors find that (2-1-10) and (11-2-4) slabs retain pronounced spin splitting while (0001) and (10-10) slabs show nearly spin-degenerate bands, despite all slabs preserving altermagnetic spin-group symmetry. Through a Wannier hopping ablation for the (2-1-10) slab, they argue that intra-unit-cell hopping alone is insufficient and that long-range inter-unit-cell Cr-Sb hopping is the dominant mechanism, with Sb-Sb hopping contributing additionally. The paper concludes that dimensional reduction fundamentally changes the microscopic origin of altermagnetic splitting relative to bulk CrSb.","tokens_in":9679,"tokens_out":5271,"duration_ms":56663,"significance":"If the central claim is established, the paper provides a useful design principle for engineering altermagnetic spin splitting in thin films through surface orientation, a topic of active experimental and theoretical interest. The Wannier ablation in Fig. 3 is a clean and instructive decomposition for the (2-1-10) slab, and the inclusion of two additional slab orientations as validation is a strength. However, the universal claim that thin films 'require' Cr-Sb hopping is not actually supported by the reported ablation, and the extension to other surfaces is based on geometric inference rather than direct Wannier evidence. These issues undermine the strongest conclusions in the abstract and summary, so the manuscript needs substantial revision before it can be accepted.","major_comments":[{"comment":"The abstract and summary claim that altermagnetic spin splitting in thin films 'requires long-range inter-unit-cell coplanar Cr-Sb hopping,' but Fig. 3(b) shows that including only inter-unit-cell Sb-Sb hopping is sufficient to induce momentum-dependent spin splitting. The ablation therefore establishes only that some long-range inter-unit-cell hopping is indispensable and that Cr-Sb is the dominant contributor, not that Cr-Sb is required. The central claim should be reworded to avoid this logical contradiction, or an additional ablation should be provided that isolates the necessity of Cr-Sb specifically.","section":"Abstract and Fig. 3(b)"},{"comment":"The paper attributes the absence of splitting in the (0001) and (10-10) slabs to suppression of long-range Cr-Sb hopping, but no Wannier fits are reported for those slabs. The only evidence is the geometric argument that Cr and Sb lie at different depths and the qualitatively described enhancement of Cr-Cr_perp hopping in Fig. 2(e). To support the universal mechanism, the authors should report the actual Wannier hopping parameters for the (0001) and (10-10) slabs and demonstrate directly that the long-range Cr-Sb matrix elements are suppressed relative to the (2-1-10) case.","section":"Hopping analysis of the (2-1-10) slab, Figs. 2(e), 2(c), 2(d)"},{"comment":"The calculations use ultrathin slabs with a 15 Å vacuum, whereas the cited ARPES experiments observe sizable splitting in CrSb (0001) and (10-10) films with thicknesses of 10-30 nm. The manuscript does not address how the proposed mechanism scales with thickness, which leaves the practical relevance of the central claim unclear. The authors should either restrict the claim to the ultrathin limit or include a thickness-convergence study connecting to the experimentally relevant regime.","section":"Comparison with experiments in the Introduction"}],"minor_comments":[{"comment":"The manuscript states that VASP was used but does not specify the exchange-correlation functional, any Hubbard U parameter, plane-wave cutoff, k-point sampling, or the number of atomic layers in each slab; these details should be provided in the text or supplement.","section":"Computational methods"},{"comment":"Figures 2(c)-(f) are described as schematic illustrations, and the text refers to hopping amplitudes 'decreasing rapidly' or 'increasing significantly' without reporting numerical values; please include a quantitative plot or table of the fitted Wannier hopping parameters.","section":"Figs. 2(c)-(f)"},{"comment":"There are several typographical errors, including 'Reimerset al.' (should be 'Reimers et al.'), 'measurment' (should be 'measurement'), and 'V ASP' (should be 'VASP').","section":"Typographical issues"},{"comment":"The assertion that all three slab models preserve the altermagnetic spin-group symmetry is not accompanied by the explicit spin group or magnetic space group of each slab; specifying these groups would strengthen the symmetry argument.","section":"Spin-group statement"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a timely topic and contains a useful hopping analysis for one slab orientation, but the overstatement of the central claim and the lack of direct Wannier evidence for the other surfaces are significant. I believe the authors can address these points with a focused revision, so I do not recommend rejection at this stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper’s real contribution is the Wannier ablation for the (2-1-10) slab. It cleanly shows that intra-unit-cell hopping alone gives no spin splitting, that adding inter-unit-cell Sb-Sb hopping brings splitting back, and that Cr-Sb hopping alone nearly reproduces the full DFT band structure. That is a concrete step beyond the earlier surface-dependence reports, and it gives people something to test.\n\nThe soft spots are real but not fatal. The abstract says thin films 'require' long-range coplanar Cr-Sb hopping, but their own Fig. 3(b) shows Sb-Sb hopping alone is sufficient to induce momentum-dependent splitting. The accurate statement is that some inter-unit-cell hopping is indispensable, with Cr-Sb dominant. That overclaim should be fixed. Second, the explanation for why (0001) and (10-10) slabs are degenerate is inferred from geometry, not shown from the Wannier fits for those slabs. They report hopping evolutions for (0001) but not the specific Cr-Sb matrix elements that are claimed to be suppressed. A referee should ask for that direct evidence. Third, no computational parameters (cutoffs, k-grids) are given, which is a minor but avoidable reproducibility gap. Finally, the experiments on 10–30 nm films show splitting on the very surfaces where these ultrathin slabs are degenerate; the paper doesn't reconcile that, and it should at least comment on thickness.\n\nThe central mechanism is plausible and the core ablation holds up. The universal claim is broader than the demonstrated results, but that's a revision issue, not a desk-reject issue. I'd send it to peer review and ask for the direct Wannier evidence in the degenerate slabs and a softened abstract. The paper is aimed at the altermagnetic thin-film and spintronics crowd, and it deserves their attention.","headline":"A clean Wannier ablation for one slab, an overstated universal claim, and a plausible mechanism worth testing.","tokens_in":10219,"tokens_out":2510,"would_cite":true,"duration_ms":26728,"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":"This paper establishes that in CrSb thin films the momentum-dependent spin splitting characteristic of altermagnetism is governed by the survival of long-range, inter-unit-cell, coplanar Cr–Sb hopping, with Sb–Sb hopping secondary, rather…","keywords":["altermagnetism","CrSb thin films","spin splitting","surface orientation","Wannier tight-binding","hopping pathways","spin-group symmetry","first-principles calculations"],"falsifier":"Compute the Wannier-interpolated long-range Cr–Sb hopping amplitudes in the $(0001)$ and $(10\\bar{1}0)$ slabs: if these matrix elements are as large as in the $(2\\bar{1}\\bar{1}0)$ slab while the bands are spin-degenerate, the claim that suppression of this hopping causes the degeneracy is falsified.","tokens_in":9236,"feed_emoji":"🧲","tokens_out":8772,"duration_ms":87706,"temperature":0.7,"pith_summary":"The paper asks why altermagnetic spin splitting—the momentum-dependent band splitting into opposite spins in a zero-net-magnetization magnetic phase—depends so strongly on which surface terminates CrSb, and it answers with a hopping-based microscopic mechanism. First-principles calculations on ultrathin slabs show that the $(2\\bar{1}\\bar{1}0)$ and $(11\\bar{2}\\bar{4})$ faces retain pronounced momentum-dependent spin splitting, while the $(0001)$ and $(10\\bar{1}0)$ faces become nearly spin-degenerate, even though all slabs satisfy the spin-group symmetries of altermagnetism. By switching hopping channels on and off in a Wannier tight-binding Hamiltonian, the authors show that in the thin-film limit the splitting requires long-range inter-unit-cell coplanar Cr–Sb hopping, with Sb–Sb hopping as an additional contribution; retaining only intra-unit-cell terms or the bulk-relevant Cr–Cr third-neighbor hopping leaves the bands degenerate. The preservation or suppression of these hopping pathways by the surface geometry explains the orientation dependence. This gives surface engineering a concrete target: maintain or restore coplanar Cr–Sb connectivity to keep the splitting.","feed_headline":"CrSb films lose spin splitting when Cr–Sb hops vanish","feed_subtitle":"Surface geometry decides which hopping paths survive; (0001) and (10-10) faces go degenerate while (2-1-10) keeps the split.","key_machinery":"The central object is the Wannier tight-binding Hamiltonian of a slab, truncated so that only selected classes of hopping terms are retained while the altermagnetic spin-group symmetry is held fixed. This which-hoppings-can-you-delete construction isolates the microscopic channels that generate spin splitting: long-range inter-unit-cell coplanar Cr–Sb hopping is the dominant carrier, Sb–Sb inter-unit-cell hopping is secondary, and short-range intra-unit-cell or third-neighbor Cr–Cr terms are not enough. A companion vacuum-spacing sweep tunes the slabs continuously from the three-dimensional bulk limit toward the isolated two-dimensional film, showing that the relevant inter-slab and inter-unit-cell couplings die out over a length scale comparable to the Cr–Sb hopping range.","core_discovery":"The central discovery is that dimensional reduction changes the microscopic origin of altermagnetic spin splitting in CrSb. In bulk CrSb the splitting had been attributed to third-nearest-neighbor Cr–Cr hopping, but a truncated Wannier Hamiltonian of the $(2\\bar{1}\\bar{1}0)$ slab that includes that channel produces no significant splitting; the splitting appears only when inter-unit-cell Cr–Sb hopping between neighboring unit cells is restored, and Sb–Sb inter-unit-cell hopping adds a smaller correction. The authors generalize this by showing that the deciding geometric condition is whether Cr and Sb atoms form coplanar layers parallel to the surface: the $(11\\bar{2}\\bar{4})$ surface, which preserves such coplanar paths, keeps the splitting, while the $(0001)$ surface, where Cr and Sb sit at different depths, loses it. Because all slabs keep altermagnetic-compatible spin-group symmetry, the mechanism must be energetic rather than purely symmetry-based.","pith_inferences":["If the geometric coplanarity criterion is general, then intentional engineering—capping layers, epitaxial strain, or substrate selection that restores Cr–Sb connectivity on a $(0001)$ surface—could recover spin splitting on otherwise degenerate faces.","The mechanism implies defect sensitivity specific to films: Sb-site substitution or Sb vacancies should degrade the spin splitting in thin films more strongly than in bulk, because the long-range Cr–Sb channels become load-bearing.","The same reasoning might extend to other NiAs-type altermagnets or to altermagnets whose ligands mediate inter-unit-cell hopping, making surface-dependent spin splitting predictable from the crystal structure alone.","A direct test would be thickness-resolved photoemission on $(2\\bar{1}\\bar{1}0)$ and $(0001)$ films: the splitting should disappear on $(0001)$ below a thickness scale set by the Cr–Sb hopping range, while $(2\\bar{1}\\bar{1}0)$ should keep it down to the monolayer limit."],"forward_implications":["Surface orientation, not just spin-group symmetry, determines whether altermagnetic spin splitting survives in CrSb films; $(0001)$ and $(10\\bar{1}0)$ terminations should show nearly spin-degenerate bands, while $(2\\bar{1}\\bar{1}0)$ and $(11\\bar{2}\\bar{4})$ terminations retain it.","The microscopic design rule for low-dimensional CrSb is to preserve coplanar Cr–Sb connectivity; surfaces or interfaces that place Cr and Sb in the same plane parallel to the film keep the splitting, and those that separate them by depth suppress it.","Thin-film altermagnetism in CrSb is not captured by bulk models centered on Cr–Cr third-neighbor hopping; calculations of films should include long-range Cr–Sb and Sb–Sb inter-unit-cell channels.","For a $(0001)$ film, reducing vacuum spacing (or, equivalently, re-introducing inter-film coupling) can partially restore spin splitting, indicating that the suppression is a coupling-range effect rather than a magnetic-moment collapse."],"supporting_citations":[{"why":"Attributes bulk CrSb altermagnetic splitting to third-nearest-neighbor Cr–Cr hopping, the baseline hypothesis the slab truncation tests and displaces.","marker":"[40]"},{"why":"Demonstrates in isostructural NiS that hopping involving nonmagnetic atoms can dominate altermagnetic splitting, motivating the analysis of Cr–Sb and Sb–Sb channels.","marker":"[41]"},{"why":"Reports the surface-orientation dependence of altermagnetic splitting in CrSb slabs, the empirical pattern the paper's microscopic mechanism explains.","marker":"[32]"},{"why":"Supplies the symmetry-checking tool used to verify that all considered slabs preserve spin-group symmetries compatible with altermagnetism.","marker":"[37]"},{"why":"Provides the Wannier interpolation method used to construct the slab tight-binding Hamiltonians and to selectively retain hopping channels.","marker":"[39]"}],"fun_headline_variants":["CrSb films: spin split only with inter-cell Cr–Sb hops","Surface orientation dictates CrSb film spin splitting","CrSb thin films: inter-cell Cr–Sb hops control spin split","Spin split in CrSb films requires Cr–Sb inter-unit hops"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that in the non-splitting slabs the long-range coplanar Cr–Sb hopping is actually suppressed by the surface geometry; if those matrix elements remain comparable to the splitting-preserving surfaces while the bands stay degenerate, the proposed mechanism would not hold.","fun_headline_variants_meta":{"raw":{"variants":["CrSb films: spin split only with inter-cell Cr–Sb hops","Surface orientation dictates CrSb film spin splitting","CrSb thin films: inter-cell Cr–Sb hops control spin split","Spin split in CrSb films requires Cr–Sb inter-unit hops"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000573,"raw_usage":{"total_tokens":2730,"prompt_tokens":988,"completion_tokens":1742,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":1670}},"tokens_in":604,"tokens_out":1742,"duration_ms":11973,"temperature":1.0,"reasoning_tokens":1670,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:25:08.954700+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the Wannier-interpolated long-range Cr–Sb hopping amplitudes in the $(0001)$ and $(10\\bar{1}0)$ slabs: if these matrix elements are as large as in the $(2\\bar{1}\\bar{1}0)$ slab while the bands are spin-degenerate, the claim that suppression of this hopping causes the degeneracy is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Attributes bulk CrSb altermagnetic splitting to third-nearest-neighbor Cr–Cr hopping, the baseline hypothesis the slab truncation tests and displaces."},{"cited_title":"Mandal, A","cited_arxiv_id":null,"evidence_quote":"Demonstrates in isostructural NiS that hopping involving nonmagnetic atoms can dominate altermagnetic splitting, motivating the analysis of Cr–Sb and Sb–Sb channels."},{"cited_title":"Smolyanyuk, L","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetry-checking tool used to verify that all considered slabs preserve spin-group symmetries compatible with altermagnetism."}],"review_version":1}