{"id":"e409cf04-77f5-4f89-881a-352e6738a28d","arxiv_id":"2501.07906","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In collinear Kagome and honeycomb ferromagnets, Dzyaloshinskii-Moriya interactions give thermally excited magnons a spin texture that produces a finite scalar spin chirality at finite temperature.","lead":"The authors show that thermally excited magnons can create scalar spin chirality in ferromagnets whose ground state is collinear, a class of magnets previously thought to have no chirality. This extends spin chirality physics to common collinear magnets and proposes measurable signatures in Kagome and honeycomb materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantitative comparability claim in Sec. II C is not controlled: reaching chi~0.045 requires magnon densities ~30%, where quadratic Holstein-Primakoff theory has no error estimate.","rationale":"The reader's acceptance is well founded for the qualitative existence result: the symmetry argument, the explicit Holstein-Primakoff expansion, and the consistency of Eq. (12) and Eq. (23) with the numerics establish that DMI can induce a finite thermal SSC in collinear ferromagnets. The concern I raise is specifically about the quantitative 'comparable to non-coplanar systems' claim, which is a central part of the abstract and conclusion. To reach |chi| ~ 0.045 for the Kagome material parameters, the system must be at a temperature where the magnon density is roughly a third of a boson per site; for S = 1/2 this means the quadratic spin-wave expansion is not quantitatively controlled. The paper does not estimate the size of 1/S or interaction corrections, and the low-temperature analytic formula is itself used beyond its stated validity range because the gap 2KS + g mu_B H is only about 0.07 K for K = 0, H = 0.05 T. These are not fatal to the core mechanism, but they leave the headline magnitude unverified. A one-loop interacting spin-wave calculation is a concrete, decisive check: if the correction is small, the comparability claim stands; if it is large, the authors should either provide a controlled calculation or restrict their claim to the low-temperature dilute regime. Hence a conditional acceptance is appropriate: accept the scientific result, but require the interaction estimate or a qualified claim about the magnitude before publication.","tokens_in":12933,"tokens_out":23655,"duration_ms":251800,"concrete_test":"Using the same parameters as Fig. 3(a) (S = 1/2, J = 0.6 meV, K = 0, H = 0.05 T, D_z = 0.09 meV), include the quartic Holstein-Primakoff terms and compute the one-loop Hartree-Fock correction to the thermal average of the SSC operator at T = 3 K and T = 4 K, where Eq. (12) gives |chi| ~ 0.025-0.05. If the corrected value differs from Eq. (12) by more than 30%, the claim in Sec. II C that the induced SSC is comparable to chi_KAFM ~ 0.045 is not quantitatively supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The symmetry-based existence of a finite thermal scalar spin chirality in collinear DMI ferromagnets is well supported by the analytic and numerical agreement. The load-bearing weak point is the paper's quantitative claim (Sec. II C and abstract) that the magnon-induced SSC can be comparable to non-coplanar systems (chi_KAFM ~ 0.045). For the Cu(1,3-bdc) parameters (S = 1/2, J = 0.6 meV, K = 0, H = 0.05 T), Eq. (12) reaches |chi_eq| ~ 0.045 only at T ~ 3-4 K (for D_z = 0.09 meV), where k_B T is comparable to J and the thermal magnon density n = sum_k 1/(exp(beta(J S k^2 + Delta)) - 1) is roughly 25-35%. Since the quadratic Holstein-Primakoff truncation, Eq. (4), is a dilute-gas expansion in n/(2S), and 1/(2S) = 1 for S = 1/2, corrections of order n are uncontrolled; the paper provides no 1/S or interaction estimate. In addition, the derivation of Eq. (12) in Appendix A uses Li3(e^{-beta Delta}) approx e^{-beta Delta}, which requires beta(2KS + g mu_B H) >> 1; for K = 0 and H = 0.05 T, this gap corresponds to about 0.07 K, yet Fig. 3(b) shows agreement below 1 K. This does not invalidate the qualitative mechanism, but it weakens the headline experimental-feasibility claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies two-dimensional ferromagnets on the kagome and honeycomb lattices described by a Heisenberg Hamiltonian with easy-axis anisotropy, out-of-plane Dzyaloshinskii-Moriya interactions, and an applied magnetic field. It argues that although the classical ground state is collinear and the zero-temperature scalar spin chirality vanishes, thermally excited magnons in the DMI-broken magnon Hamiltonian generate a finite SSC at finite temperatures. Using a Holstein-Primakoff expansion truncated at quadratic order, the authors derive analytic low-temperature formulas for the SSC in the kagome case, Eq. (12), and in the honeycomb case, Eq. (23), and support them with numerical band-structure and SSC-profile calculations. They then use material parameters for Cu(1,3-bdc) and CrBr3 to claim that the induced SSC can be comparable in magnitude to the SSC of non-coplanar kagome antiferromagnets.","tokens_in":13196,"tokens_out":10410,"duration_ms":106214,"significance":"If the result is correct, the paper establishes a simple and potentially general mechanism for finite-temperature scalar spin chirality in collinear magnets, with consequences for electron and phonon transport. The symmetry argument is robust: without DMI the chirality profile is odd in momentum and the thermal sum vanishes, while DMI breaks the effective time-reversal symmetry of the magnon Hamiltonian and gives a nonzero result. The low-temperature analytic derivations in Appendix A are transparent, and the numerical and analytic results agree in the appropriate low-temperature regime (Figs. 3(b) and 5(b)). The predictions are falsifiable: the SSC scales linearly with D_z, vanishes with the exponential of the anisotropy/field gap, and follows T^3 (kagome) and T^4 (honeycomb) power laws. The main weakness is that the quantitative comparison to non-coplanar kagome antiferromagnets is made in a temperature regime where the quadratic Holstein-Primakoff truncation has no controlled error estimate.","major_comments":[{"comment":"The claim that the magnon-induced SSC is comparable to that of non-coplanar kagome antiferromagnets (χKAFM ~ 0.045) rests on evaluating Eq. (12) at T around 4–5 K for the Cu(1,3-bdc) parameters. At these temperatures the results lie outside the dilute-magnon regime: with S = 1/2 and k_B T ~ 0.3–0.4 meV comparable to J = 0.6 meV, the thermal magnon density is of order 0.3 per site, so the quadratic Holstein-Primakoff truncation in Eq. (4) has no small parameter. The paper provides no estimate of 1/S or magnon-magnon interaction corrections. I therefore do not consider the quantitative comparability claim to be established, although the qualitative mechanism is sound. Please add a controlled estimate of the corrections, for example a next-order 1/S calculation or a classical Monte Carlo benchmark at these temperatures, or soften the headline claim.","section":"Sec. II C and Abstract"},{"comment":"The derivations replace polylogarithms by their leading exponential: Li3(e^{-βΔ}) ≈ e^{-βΔ} and similarly for Li4. This requires β(2KS + gμB H) ≫ 1. For the kagome parameters used in Fig. 3(b), K = 0 and H = 0.05 T give a gap of only about 0.07 K, so over the plotted range 0.1–1 K the argument of the polylogarithm is not small; the approximation has an estimated error of 10–20%. The same concern applies to Eq. (23) for CrBr3, where the gap 2KS is also small on the temperature scale of Fig. 5(b). The analytic comparison should either use the exact polylogarithm expression, or the stated agreement should be restricted to temperatures where the exponential approximation is controlled, or the validity condition in the text should be revised accordingly.","section":"Appendix A, Eqs. (12) and (23), Figs. 3(b) and 5(b)"}],"minor_comments":[{"comment":"The text says that in Fig. 2(b) and Fig. 4(b) the SSC profile is an odd function of k; the panels showing SSC profiles are actually Fig. 2(c)/(d) and Fig. 4(c)/(d), while Fig. 2(b) and Fig. 4(b) show band structures with DMI. Please correct the panel references.","section":"Sec. II C and Sec. III C, Figs. 2 and 4"},{"comment":"There are small typographical errors in Appendix A: 'focucing' should be 'focusing' and 'Brilluin zone' should be 'Brillouin zone'.","section":"Appendix A"},{"comment":"The text states k_BT ⪅ 2KS + gμB H as the low-temperature limit for Eq. (12); for the parameters of Fig. 3 this inequality is satisfied only below about 0.1 K, so the stated regime should be made consistent with the polylogarithm approximation discussed above.","section":"Sec. II B, Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"The central symmetry-based mechanism appears sound and the paper is a good candidate for publication once the quantitative extrapolation is either backed by an error estimate or appropriately softened. The main risk is that the abstract and Sec. II C overstate the experimental feasibility claim relative to the controlled regime of the calculation. I do not see a reason to reject, but the comparability claim needs to be made rigorous or qualified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core result holds up: thermally excited magnons do generate scalar spin chirality in collinear ferromagnets with DMI. The symmetry argument is clean—DMI breaks the effective time-reversal symmetry of the magnon Hamiltonian, and the SSC operator is odd under that symmetry, so a thermal average becomes nonzero. The analytic formulas (12) and (23) are a genuine asset, and the numerical diagonalization matches them at low T. The kagome (T^3) and honeycomb (T^4) scaling is a nice physical contrast.\n\nTwo soft spots, in proportion. First, the Li3(z) ≈ z approximation in Appendix A requires beta times the gap to be large; for the kagome parameters with H = 0.05 T, that gap is only about 0.07 K, yet the comparison with numerics in Fig. 3(b) extends to 1 K. The fact that the numbers still agree is encouraging, but the analytic formula is being used outside its controlled limit. Second, the comparability claim in Sec. II C is the real weak point. Reaching |χ| ~ 0.045 at T ~ 3–4 K for S = 1/2 implies a thermal magnon density around 25–30%, where quadratic Holstein-Primakoff theory is a dilute-gas expansion with expansion parameter n/(2S) ~ 0.3. No 1/S or interaction estimate is provided. So the specific number is plausible but not quantitatively controlled. The mechanism itself does not depend on that number, so I would not let this sink the paper, but the referee should push for a toned-down claim or a simple interaction estimate.\n\nThe citation pattern is fine: Ref. [33] from the same group provides the SSC formalism, and the earlier paramagnetic-phase result in Ref. [32] is properly distinguished. This paper is for anyone working on magnon transport, spin chirality, or two-dimensional magnets. It deserves a serious referee, and I would bring it to the reading group. I would cite it.","headline":"A real new mechanism—thermal magnons producing scalar spin chirality in collinear DMI ferromagnets—but the quantitative comparability claim is softer than the abstract suggests.","tokens_in":13802,"tokens_out":2923,"would_cite":true,"duration_ms":30315,"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":"Thermally excited magnons create a nonzero scalar spin chirality in collinear ferromagnets on Kagome and honeycomb lattices when Dzyaloshinskii-Moriya interactions are present.","keywords":["scalar spin chirality","magnon","Kagome lattice","honeycomb lattice","Dzyaloshinskii-Moriya interaction","collinear ferromagnet","thermal Hall effect","Holstein-Primakoff transformation"],"falsifier":"Compute the scalar spin chirality in the same spin model including the next-order 1/S Holstein-Primakoff corrections; if the correction is comparable in magnitude to the quadratic result, or changes its sign, at temperatures where Eqs. (12) and (23) predict chirality about 0.01, the quantitative claim collapses. Alternatively, measure the temperature dependence of the chirality via the topological Hall effect in Cu(1,3-bdc) below 1 K and look for the predicted $T^{3}$ scaling; its absence would falsify the mechanism.","tokens_in":12673,"feed_emoji":"🧲","tokens_out":5194,"duration_ms":49300,"temperature":0.7,"pith_summary":"The paper claims that thermally excited magnons can induce a finite scalar spin chirality even in two-dimensional ferromagnets whose ground state is collinear, contrary to the usual assumption that chirality requires noncoplanar spin textures. The mechanism is the Dzyaloshinskii-Moriya interaction (DMI), which breaks the effective time-reversal symmetry of the magnon Hamiltonian and makes the momentum-space chirality profile no longer odd, so the Bose-weighted sum over the Brillouin zone does not vanish. The authors derive analytic low-temperature expressions for the chirality in Kagome and honeycomb lattices, Eqs. (12) and (23), showing it grows with temperature and DMI strength, and they estimate that for realistic materials the magnitude can rival chirality values found in noncoplanar magnets. This matters because it broadens the class of materials where chiral physics and chirality-driven transport can be expected.","feed_headline":"Thermal magnons induce spin chirality in collinear ferromagnets","feed_subtitle":"DMI lets heat-generated magnons create scalar spin chirality, rivaling non-coplanar magnets.","key_machinery":"The key machinery is the momentum-space scalar spin chirality matrix chi-hat_k, whose expectation value in magnon band eigenstates is weighted by the Bose distribution function. Under time reversal the magnon Hamiltonian transforms as h_k -> h*_{-k}, while the chirality matrix obeys chi-hat_k = -chi-hat*_{-k}, so in a time-reversal-symmetric system the chirality profile is odd in momentum and the Brillouin-zone sum vanishes. The DMI breaks this symmetry and introduces an even component near the band bottom; the analytic results follow from expanding the lowest-band eigenstate and the chirality profile near the Gamma point and integrating the thermal factor with $k^{4}$ (Kagome) or $k^{6}$ (honeycomb) weight.","core_discovery":"The central discovery is that collinear ferromagnets with DMI acquire a nonzero thermal expectation value of the scalar spin chirality, chi_eq, at finite temperatures. In the Kagome case, the paper finds chi_eq approximately equal to minus $\\sqrt$(3) D_z divided by (9 pi $\\sqrt$($J^{2}$ + $D_z^{2}$) S), times exp(-$\\beta$(2KS + g mu_B H)) over ($\\beta$ J S)^3, while in the honeycomb case the leading term is $\\sqrt$(3) D_z over (pi J S) times exp(-$\\beta$(2KS + g mu_B H)) over ($\\beta$ J S)^4. Both expressions show the chirality is proportional to the perpendicular DMI component D_z and increases with temperature; numerically, using material parameters for Cu(1,3-bdc) and CrBr3, the predicted chirality reaches values on the order of 0.1, comparable to the chirality of noncoplanar Kagome antiferromagnets with canting angles around one degree.","pith_inferences":["A general principle suggested by this work is that any collinear magnet whose magnon Hamiltonian has a Berry curvature and broken time-reversal symmetry should also exhibit thermal scalar spin chirality, linking the magnon thermal Hall effect to a spontaneous chiral spin texture in momentum space.","A testable extension is to measure the temperature dependence of the topological Hall contribution in collinear ferromagnets and check whether it follows the predicted T^3 or T^4 scaling rather than the exponential activation alone.","The quadratic Holstein-Primakoff truncation likely sets the limit of validity; including 1/S corrections at higher temperatures may shift the magnitude, and comparing such a calculation with the analytic formula would delineate where the effect is robust."],"forward_implications":["Collinear ferromagnets with DMI should exhibit a measurable scalar spin chirality at low temperatures, with magnitude comparable to noncoplanar magnets, making them candidate platforms for chirality-driven phenomena.","The chirality follows distinct power laws in temperature, T^3 for Kagome and T^4 for honeycomb, which provides a sharp experimental signature.","The result implies that collinear spin systems can host chirality-induced transport, such as a topological Hall effect for conduction electrons or a phonon thermal Hall effect via skew scattering.","Candidate materials include the Kagome ferromagnet Cu(1,3-bdc) and honeycomb ferromagnets such as CrBr3, CrI3, CrSiTe3, and CrGeTe3.","The DMI is strictly necessary: in its absence the chirality vanishes exactly, so the effect is tied to broken time-reversal symmetry in the magnon sector."],"supporting_citations":[{"why":"Supplies the DMI-induced time-reversal breaking in the magnon Hamiltonian and the eigenstate expansion near the band bottom used in the analytic derivation.","marker":"[11]"},{"why":"Shows that the DMI does not alter the collinear ferromagnetic ground state on the Kagome lattice, justifying the starting assumption.","marker":"[27]"},{"why":"Further supports the collinearity of the ground state and provides the context of topological magnon bands on Kagome lattices.","marker":"[28]"},{"why":"Provides the experimental material parameters for Cu(1,3-bdc) and evidence of the magnon thermal Hall effect in this Kagome ferromagnet.","marker":"[29]"},{"why":"Establishes the magnon Hamiltonian for honeycomb ferromagnets with DMI, the two-band model used in the honeycomb analysis.","marker":"[30]"},{"why":"Gives the honeycomb topological magnon insulator model, supporting the definition of SSC on next-nearest-neighbor triangles.","marker":"[31]"},{"why":"Reports Monte Carlo evidence of chiral spin fluctuations in Kagome lattices, consistent with the finite chirality found here.","marker":"[32]"},{"why":"Supplies the formalism relating scalar spin chirality to magnon operators and the chirality matrix used in Eqs. (8)-(9).","marker":"[33]"},{"why":"Provides the expression for scalar spin chirality in non-coplanar Kagome antiferromagnets used to benchmark the magnitude of the magnon-induced chirality.","marker":"[35]"},{"why":"Supplies the material parameters for CrBr3 used in the honeycomb numerical calculations.","marker":"[37]"}],"fun_headline_variants":["Heat-driven magnons twist collinear spins into chiral order","Collinear magnets get chiral via DMI and heat","Magnon heat turns collinear magnets chiral","Heat makes collinear magnets rival non-coplanar chirality"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation treats magnons as non-interacting by cutting the spin-wave expansion at quadratic order in the Holstein-Primakoff bosons, so the results stand or fall on magnon-magnon interactions being negligible in the temperature range where the chirality becomes sizable.","fun_headline_variants_meta":{"raw":{"variants":["Heat-driven magnons twist collinear spins into chiral order","Collinear magnets get chiral via DMI and heat","Magnon heat turns collinear magnets chiral","Heat makes collinear magnets rival non-coplanar chirality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001598,"raw_usage":{"total_tokens":6394,"prompt_tokens":996,"completion_tokens":5398,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":5343}},"tokens_in":612,"tokens_out":5398,"duration_ms":35848,"temperature":1.0,"reasoning_tokens":5343,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:31:36.228226+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the scalar spin chirality in the same spin model including the next-order 1/S Holstein-Primakoff corrections; if the correction is comparable in magnitude to the quadratic result, or changes its sign, at temperatures where Eqs. (12) and (23) predict chirality about 0.01, the quantitative claim collapses. Alternatively, measure the temperature dependence of the chirality via the topological Hall effect in Cu(1,3-bdc) below 1 K and look for the predicted $T^{3}$ scaling; its absence would falsify the mechanism.","supporting_citations":[{"cited_title":"Chirality-driven anomalous Hall effect in weak coupling regime,","cited_arxiv_id":null,"evidence_quote":"Supplies the DMI-induced time-reversal breaking in the magnon Hamiltonian and the eigenstate expansion near the band bottom used in the analytic derivation."},{"cited_title":"Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators,","cited_arxiv_id":null,"evidence_quote":"Shows that the DMI does not alter the collinear ferromagnetic ground state on the Kagome lattice, justifying the starting assumption."},{"cited_title":"Thermal Hall effect of magnons in magnets with dipolar interaction,","cited_arxiv_id":null,"evidence_quote":"Further supports the collinearity of the ground state and provides the context of topological magnon bands on Kagome lattices."},{"cited_title":"Magnon Hall effect and topology in kagome lattices: A theoretical investigation,","cited_arxiv_id":null,"evidence_quote":"Provides the experimental material parameters for Cu(1,3-bdc) and evidence of the magnon thermal Hall effect in this Kagome ferromagnet."},{"cited_title":"Edge states in topological magnon insulators,","cited_arxiv_id":null,"evidence_quote":"Establishes the magnon Hamiltonian for honeycomb ferromagnets with DMI, the two-band model used in the honeycomb analysis."},{"cited_title":"Thermal Hall effect of spin excita- tions in a kagome magnet,","cited_arxiv_id":null,"evidence_quote":"Gives the honeycomb topological magnon insulator model, supporting the definition of SSC on next-nearest-neighbor triangles."},{"cited_title":"Realization of the Haldane- Kane-Mele model in a system of localized spins,","cited_arxiv_id":null,"evidence_quote":"Reports Monte Carlo evidence of chiral spin fluctuations in Kagome lattices, consistent with the finite chirality found here."},{"cited_title":"A first theoretical realization of honeycomb topological magnon insulator,","cited_arxiv_id":null,"evidence_quote":"Supplies the formalism relating scalar spin chirality to magnon operators and the chirality matrix used in Eqs. (8)-(9)."},{"cited_title":"Magnon ther- mal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions,","cited_arxiv_id":null,"evidence_quote":"Supplies the material parameters for CrBr3 used in the honeycomb numerical calculations."}],"review_version":1}