{"id":"4119e393-bb1d-47f5-a570-5961ff19fb06","arxiv_id":"2509.22303","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Bridgman-grown MnBi2Te4/(Bi2Te3)n crystals form in four growth stages, and the spacing between magnetic septuple layers, set by diffusion-limited MnTe supply, determines whether the material is antiferromagnetic or ferromagnetic.","lead":"This paper shows how magnetic layers inside a special crystal arrange themselves during growth, and how that arrangement decides the crystal's magnetic behavior. It offers a practical way to tune magnetism by controlling the flow of the melted ingredients.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Average Mn concentration is a geometric function of d_SL, so Table 1 cannot independently verify the claimed inverse dependence of SL spacing on melt supersaturation.","rationale":"The reader's conditional verdict is appropriate, and this stress-test sharpens the condition: the central inverse relationship between d_SL and sigma_MnTe is not directly validated because the only available proxy for sigma, the bulk average Mn concentration, is geometrically determined by d_SL itself. The magnetic and structural characterization, including the AFM-to-FM crossover with increased SL separation and the four-stage flow description, is well supported by the data and does not depend on Eq. (1). However, the quantitative growth model and its headline prediction remain conditional until an independent measure of melt supersaturation is provided. This does not move the verdict to rejection; it reinforces the need for additional validation that the paper itself does not supply.","tokens_in":15546,"tokens_out":5936,"duration_ms":59957,"concrete_test":"Compute the geometric prediction for average Mn concentration from the TEM-determined d_SL values and local Mn contents in SLs and QLs (Table 1, Fig. 1), using avg_Mn approximately (Mn_SL * t_SL)/d_SL + Mn_QL. If the predicted values match the EDX averages within uncertainty, Table 1 carries no independent information about sigma_MnTe. Then settle the claim by a controlled stationary-growth series with varied initial MnTe in the charge, and/or by quenching a melt sample at the growth interface and measuring its Mn content directly, checking whether d_SL varies as 1/sigma as required by Eq. (1).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that sigma_MnTe, the supersaturation at the growth interface, be an independent driver of d_SL. In this paper sigma_MnTe is never measured; it is inferred from the spatially averaged Mn concentration in Table 1. That proxy is not independent of the quantity it is supposed to explain. For a layered (MnBi2Te4)/(Bi2Te3)n structure with roughly constant Mn content per SL, the volume-averaged Mn concentration is approximately (Mn_SL * t_SL)/d_SL plus a small QL background. Hence any increase in d_SL automatically lowers the average Mn concentration by geometry, independent of the melt transport model. The comparison of Sample B (avg 7.2 at.%, d_SL = 1-2 QLs) with Sample C (avg 1.14 at.%, d_SL = 7 +/- 2 QLs) is therefore a restatement of the d_SL difference, not a measurement of sigma_MnTe. The same geometric relation also explains the Sample C-D trend without invoking the impurity-ejection argument. What would have to be true for Eq. (1) to be validated is absent: an independent measure of melt supersaturation at the crystallization front, or a controlled series in which the initial MnTe content is varied while flow conditions are fixed. The derivation itself contains a second, separable assumption (neglect of ln(d_SL/a_SL), SI Eq. 4 to Eq. 5), but the empirical gap is the more load-bearing of the two.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a study of Bridgman-grown MnBi2Te4/(Bi2Te3)n crystals, identifying four growth stages (turbulent flow, rapid MnTe precipitation, stationary flow, and flow cessation) and relating these to the observed layer sequences and magnetic properties. The central claim is that the septuple layer spacing d_SL is inversely correlated with MnTe supersaturation sigma_MnTe in the melt, as described by Eq. (1), which combines Chernov's solution-growth model and van der Eerden's step-advance analysis with diffusion-limited MnTe incorporation at layer edges. Structural data from TEM/EDX and magnetic data from SQUID and FMR are used to correlate layer spacing with magnetic ordering: closely spaced SLs give antiferromagnetism, widely spaced SLs give ferromagnetism.","tokens_in":15808,"tokens_out":4131,"duration_ms":35659,"significance":"If the proposed mechanism is correct, it offers a concrete route to tune the layer sequence of a magnetic topological insulator by controlling growth parameters such as melt composition and convection, which is of practical value for bulk synthesis. The paper contains a substantial set of internally consistent experimental data (TEM, EDX, SQUID, FMR) and provides a clear structural typology of the four growth regimes. The identification of a stationary flow regime that supports ordered stacking and the correlation between SL spacing and magnetic phase are useful contributions, even independently of the quantitative model. However, the central quantitative claim linking d_SL to sigma_MnTe is currently supported only indirectly, and the paper's own text marks the key melt-composition inferences as conjectural.","major_comments":[{"comment":"The central claim that d_SL is inversely correlated with sigma_MnTe is not independently verified by the data, because the proxy used for sigma_MnTe—the average Mn concentration in Table 1—is a geometric function of d_SL. For a layered structure with approximately constant Mn content per septuple layer, the volume-averaged Mn concentration scales roughly as t_SL/d_SL (plus a small background from quintuple layers), so any increase in d_SL automatically lowers the average Mn concentration regardless of the transport mechanism. The comparison of Sample B (7.2 at.%, d_SL=1–2 QLs) with Sample C (1.14 at.%, d_SL=7±2 QLs) therefore restates the spacing difference rather than providing an independent measure of sigma_MnTe. To validate Eq. (1), an independent measurement of the MnTe supersaturation at the crystallization front, or a controlled series in which initial MnTe content is varied while flow conditions are fixed, is needed.","section":"Table 1 and Discussion of growth, Eq. (1)"},{"comment":"The empirical support for the inverse relationship rests on only two samples grown in the stationary flow regime, B and C, and the estimated spacing for Sample C has a large uncertainty (7±2 QLs). No intermediate points along the ingot are presented for the stationary regime, so the functional form of the d_SL versus sigma_MnTe relation is not constrained. The model should be tested against additional samples grown with systematically varied melt compositions, or against a spatially resolved map of the superlattice period along the crystal that traces a continuous trend, before a quantitative inverse correlation is asserted.","section":"Discussion of growth, Samples B and C"},{"comment":"The derivation of Eq. (1) in the main text neglects the factor ln(d_SL/a_SL) from van der Eerden's expression, with the statement that preliminary order-of-magnitude estimates give an error below 1% within the observed range. This justification is not shown. Since d_SL varies by roughly sevenfold across the observed range and a_SL is a molecular width, the logarithmic factor is not obviously negligible; the approximation should be quantified with the actual estimates, or the full expression should be retained in Eq. (1), because this approximation is load-bearing for the simple inverse relation.","section":"Supplementary Information, Eq. (4) to Eq. (5)"}],"minor_comments":[{"comment":"The typeset version of Eq. (1) is garbled in the manuscript, rendering the formula unreadable; it should be corrected.","section":"Eq. (1)"},{"comment":"The caption refers to a 'MnBi₂Te₄/Bi₂Te phase'; this should presumably be 'MnBi₂Te₄/Bi₂Te₃'.","section":"Fig. 1 caption"},{"comment":"The word 'respectevely' is a typo for 'respectively'.","section":"Results, magnetic anisotropy"},{"comment":"The manuscript uses phrases such as 'We infer that the distribution of manganese in the melt is not uniform' and 'we propose the following' when discussing impurity ejection and Sample D; these statements are hypotheses and should be explicitly labeled as such in the main text rather than appearing as established conclusions.","section":"Discussion of growth"}],"recommendation":"major_revision","confidential_remarks":"The paper would be strengthened by either adding independent evidence for the supersaturation-spacing relation (e.g., controlled melt-composition series, melt sampling, or in-situ measurements) or by reframing the model as a plausible hypothesis supported by qualitative consistency rather than as a demonstrated quantitative law. The current data are internally consistent, but the main quantitative claim rests on a circular proxy, so the scientific impact as written is lower than the presentation suggests."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a serious experimental study of Bridgman-grown MnBi2Te4/(Bi2Te3)n, and it deserves a proper referee. What is actually new is the four-stage growth narrative—turbulent flow, MnTe precipitation, stationary flow, flow cessation—and the diffusion-limited competition model that yields Eq. (1) for the SL spacing. That model is a genuine attempt to go beyond the empirical description in the authors' earlier work [5], and the TEM, EDX, SQUID, and FMR data are internally consistent and support the AFM/FM phase assignments based on SL separation. I would trust the magnetic characterization.\n\nThe soft spot is the central quantitative claim: d_SL is inversely correlated with melt supersaturation sigma_MnTe. The problem is that sigma_MnTe is never measured. It is inferred from the spatially averaged Mn concentration in the crystal (Table 1). For a layered structure with roughly constant Mn content per SL, that average concentration is approximately t_SL/d_SL times the SL Mn content. So comparing Sample B (7.2 at.%, d_SL = 1–2 QLs) with Sample C (1.14 at.%, d_SL = 7 ± 2 QLs) is largely restating the d_SL difference, not independently testing the transport model. The same geometric relation also explains the Sample C–D trend. To validate Eq. (1) you would need an independent measure of supersaturation at the growth front, or a controlled series where the initial MnTe loading is varied while flow conditions are fixed. The paper has neither. The derivation itself also neglects ln(d_SL/a_SL) in the SI (Eq. 4 to Eq. 5); the authors estimate the error below 1%, which is plausible, but the empirical gap is the load-bearing one.\n\nI would not call this a fatal flaw. The four-stage picture, the magnetic data, and the framing of diffusion-limited competition as a design handle for crystal growers are all worth having. But as it stands, Eq. (1) is a plausible, retrospectively applied model supported by two stationary-regime samples and a proxy that is geometrically coupled to the output. A good referee should push for a direct test or a clear statement that the inverse correlation is currently a hypothesis. I would send it to peer review rather than desk-reject, and I would expect a major revision or a more careful reinterpretation. The paper belongs in a solid materials-science or crystal-growth journal, and I would cite the four-stage picture and the magnetic data even while treating the growth model with caution.","headline":"A careful experimental study with a plausible but under-validated growth model; the central claim rests on a proxy that is geometrically tied to the measured spacing.","tokens_in":16393,"tokens_out":2850,"would_cite":true,"duration_ms":25702,"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":"Septuple layer spacing in MnBi2Te4/(Bi2Te3)n is set by diffusion-limited MnTe incorporation and controls whether the crystal is antiferromagnetic or ferromagnetic.","keywords":["MnBi2Te4","Bridgman growth","septuple layers","quintuple layers","MnTe supersaturation","diffusion-limited growth","magnetic topological insulators","antiferromagnetic-ferromagnetic transition"],"falsifier":"Cool a growing crystal quickly during the stationary regime, slice the frozen melt-crystal interface, and map the MnTe concentration profile next to the growth front; if the measured supersaturation does not correlate inversely with the TEM-observed septuple spacing, Eq. (1) is falsified.","tokens_in":15332,"feed_emoji":"🧲","tokens_out":10587,"duration_ms":90220,"temperature":0.7,"pith_summary":"This paper establishes that the regular stacking of MnBi2Te4 septuple layers inside a Bi2Te3 host is not accidental but is set by diffusion-limited MnTe incorporation during the stationary phase of Bridgman growth. The central result is an inverse correlation between septuple-layer spacing $d_{\\mathrm{SL}}$ and MnTe supersaturation $\\sigma_{\\mathrm{MnTe}}$ in the melt, captured by Eq. (1). Because the magnetism of these crystals switches from antiferromagnetic to ferromagnetic as the spacing widens, the growth model offers a route to tune the magnetic ground state through melt composition and flow conditions. The authors support the claim with TEM/EDX layer-sequence maps of four samples from one ingot, SQUID magnetometry, and X-band magnetic resonance, identifying four growth stages from turbulent flow to diffusive transport. If correct, the result turns a growth nuisance, Mn starvation, into a controllable design parameter for magnetic topological insulators.","feed_headline":"MnTe starvation sets layer spacing in Bridgman-grown crystals","feed_subtitle":"Diffusion-limited MnTe incorporation sets layer spacing, flipping magnetism from antiferro to ferro.","key_machinery":"The argument is carried by Eq. (1), derived from a solution-growth model in which MnTe is the rate-limiting species at MnBi2Te4 layer edges. Each MnBi2Te4 edge acts as a linear sink for MnTe molecules diffusing across an unstirred boundary layer of thickness $\\delta_{\\mathrm{MnTe}}$, and the spacing $d_{\\mathrm{SL}}$ adjusts so that the MnTe flux balances the advance of the surrounding Bi2Te3 quintuple layers; the derivation explicitly equates the septuple and quintuple advance velocities and neglects a logarithmic factor whose contribution the paper estimates as below 1% over the observed spacings. The same machinery links macroscopic flow to nanostructure: turbulent flow thins the boundary layer and favors pure MnBi2Te4, stationary laminar flow produces ordered QL/SL stacks, and flow cessation thickens the diffusion layer and drives Mn depletion and defect formation. An elastic-energy estimate of roughly 5 eV to insert a MnBi2Te4 unit into a perfect Bi2Te3 front explains why new septuple layers need defect sites to nucleate, while the much smaller enthalpy gain keeps spontaneous substitution unfavorable.","core_discovery":"Crystal sections formed in the stationary-flow regime contain MnBi2Te4 septuple layers whose mean separation depends on how starved the melt is for MnTe. Treating each MnBi2Te4 edge as a linear sink for MnTe molecules diffusing through an unstirred boundary layer, and equating the advance velocity of septuple and quintuple layers, yields Eq. (1), which expresses $d_{\\mathrm{SL}}$ in terms of the quintuple-layer velocity $V_{\\mathrm{QL}}$, the septuple-layer width $a_{\\mathrm{SL}}$, the boundary-layer thickness $\\delta_{\\mathrm{MnTe}}$, the MnTe diffusion constant $D_{\\mathrm{MnTe}}$, the equilibrium MnTe concentration $C_{\\mathrm{eq,MnTe}}$, the melt-edge exchange length $\\lambda_{\\mathrm{MnTe}}$, and the supersaturation $\\sigma_{\\mathrm{MnTe}}$. The formula makes $d_{\\mathrm{SL}}$ grow as the boundary layer thickens or supersaturation falls, and shrink as MnTe diffusivity or equilibrium concentration rises. Experimentally, Sample C, with only 1.14 at.% average Mn, shows SLs spaced by 7 ± 2 QLs, while earlier, Mn-richer material packs SLs one or two QLs apart. The magnetic consequences follow: closely spaced, compositionally complete SLs order antiferromagnetically at $T_{\\mathrm{N}}$ = 26 K and 13.5 K in Sample A and 13.5 K in Sample B, while widely spaced, Mn-depleted SLs give ferromagnetic order near 9–11 K, consistent with the earlier result that interlayer exchange becomes negligible beyond two QLs.","pith_inferences":["Editorial inference: if Eq. (1) survives direct measurement of the melt supersaturation, stirring or ampoule rotation becomes a magnetic-property knob, because raising flow velocity shortens $\\delta_{\\mathrm{MnTe}}$ and should tighten SL spacing.","Editorial inference: the same diffusion-limited competition picture should apply to other transition-metal tellurides grown from tellurium-rich melts, where the spacing of magnetic planes could be predicted from the balance of layer-advance velocities.","Editorial inference: a direct quantitative test would be to grow a series of ingots with different starting MnTe fractions and map $d_{\\mathrm{SL}}$ against the measured post-growth Mn profile; the model predicts a monotone curve that a single deviating point would break.","Editorial inference: the paper's four-stage picture implies that the pure MnBi2Te4 phase is a transient, turbulence-assisted product, so scaling up crystal size will require actively maintaining convective mixing rather than only adjusting the nominal composition."],"forward_implications":["Septuple-layer spacing, and therefore the magnetic ground state, can in principle be selected by controlling melt composition, convection, and growth velocity during the stationary regime.","Magnetic phase assignment becomes a structural diagnostic: antiferromagnetic transitions at 26 K and 13.5 K signal closely spaced SLs, while ferromagnetic order near 9–11 K signals spacing of roughly four or more QLs.","The four-stage growth model explains why pure MnBi2Te4 appears only under turbulent mixing and why later growth sections develop increasingly Mn-poor, disorder-prone stacking.","Maintaining constant MnTe supersaturation during growth should preserve a constant SL spacing, giving a route to long-range ordered superlattices over tens of micrometers.","The inverse spacing-supersaturation relation offers a practical calibration rule for Bridgman synthesis of MnBi2Te4/(Bi2Te3)n with targeted layer sequences."],"supporting_citations":[{"why":"Provides the DFT/Monte Carlo layer-resolved magnetism and the 12 K Curie temperature of an isolated MnBi2Te4 layer.","marker":"[2]"},{"why":"Establishes experimental antiferromagnetic ordering and the Néel temperature of MnBi2Te4 and MnBi2Te4/Bi2Te3 used to assign Sample A transitions.","marker":"[3]"},{"why":"Documents how interlayer exchange weakens with SL separation and sets the regime beyond two QLs where ferromagnetic behavior emerges.","marker":"[4]"},{"why":"Supplies earlier MnBi2Te4/(Bi2Te3)n results on Mn depletion, ferromagnetic coupling across QLs, and the anisotropy-field analysis used for $K_1$.","marker":"[5]"},{"why":"Describes the Inverted Vertical Bridgman Method and the turbulent-to-stationary flow transition used to define the growth stages.","marker":"[11]"},{"why":"Reports the preferred c-axis orientation of Bi2Te3 growth fronts that justifies the layer-edge incorporation picture.","marker":"[23]"},{"why":"Gives the formation enthalpies of MnTe and Bi2Te3 used to argue both molecules coexist in the melt and to compare with the SL insertion energy.","marker":"[25]"},{"why":"Supplies the solution-growth model for diffusion-limited advance of MnTe at layer edges.","marker":"[28]"},{"why":"Provides the step-advance velocity expression that the paper combines with the growth model to obtain Eq. (1).","marker":"[31]"},{"why":"Gives the boundary-layer thickness formula linking flow velocity, viscosity, and density to $\\delta_{\\mathrm{MnTe}}$.","marker":"[32]"}],"fun_headline_variants":["MnTe starvation spacing flips magnetic order","Self-organized layer distance switches antiferro to ferro","Diffusion-limited MnTe sets layer spacing, tunes magnetism","MnTe starvation governs spacing, flipping magnetic phase","Bridgman layer spacing set by MnTe supersaturation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that MnTe incorporation at MnBi2Te4 layer edges is rate-limited by diffusion through an unstirred boundary layer, and that the melt supersaturation can be inferred from the crystal's average Mn content; if either assumption fails, the inverse spacing-supersaturation relation is not established, and only two stationary-regime samples (B and C) carry the trend.","fun_headline_variants_meta":{"raw":{"variants":["MnTe starvation spacing flips magnetic order","Self-organized layer distance switches antiferro to ferro","Diffusion-limited MnTe sets layer spacing, tunes magnetism","MnTe starvation governs spacing, flipping magnetic phase","Bridgman layer spacing set by MnTe supersaturation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000542,"raw_usage":{"total_tokens":2710,"prompt_tokens":1171,"completion_tokens":1539,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":787,"completion_tokens_details":{"reasoning_tokens":1463}},"tokens_in":787,"tokens_out":1539,"duration_ms":10566,"temperature":1.0,"reasoning_tokens":1463,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:43:47.981753+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Cool a growing crystal quickly during the stationary regime, slice the frozen melt-crystal interface, and map the MnTe concentration profile next to the growth front; if the measured supersaturation does not correlate inversely with the TEM-observed septuple spacing, Eq. (1) is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the DFT/Monte Carlo layer-resolved magnetism and the 12 K Curie temperature of an isolated MnBi2Te4 layer."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes experimental antiferromagnetic ordering and the Néel temperature of MnBi2Te4 and MnBi2Te4/Bi2Te3 used to assign Sample A transitions."},{"cited_title":"Lamuta, D","cited_arxiv_id":null,"evidence_quote":"Documents how interlayer exchange weakens with SL separation and sets the regime beyond two QLs where ferromagnetic behavior emerges."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies earlier MnBi2Te4/(Bi2Te3)n results on Mn depletion, ferromagnetic coupling across QLs, and the anisotropy-field analysis used for $K_1$."}],"review_version":2}