{"id":"58e16b0b-9fe4-4dab-85c8-ce64688a9c9a","arxiv_id":"2608.00210","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"In ErMn6Sn6, planar magnetic anisotropy breaks the symmetry that separates left- and right-handed magnons, forcing them to hybridize and reverse chirality with momentum; in TbMn6Sn6 the crossing remains protected.","lead":"Magnons in two rare-earth magnets either cross without mixing or repel and swap their handedness depending on how magnetic symmetry breaks the spin precession. The result shows a new way to switch magnon chirality in a bulk material by changing magnetic anisotropy.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Chirality reversal rests on model-dependent conversion of σ_ch to SAM; the raw sign change could be a structure-factor effect","rationale":"The reader's weakest assumption—that the conversion of σ_ch into a mode-SAM/chirality statement relies on the linear spin-wave model and previously fitted parameters—is the same load-bearing concern I identify. The central symmetry argument (U(1) protection in Tb166 vs. broken U(1) in Er166) is well supported by the clear difference in the unpolarized dispersions: the Tb166 data show a crossing while the Er166 data show an avoided crossing. That part of the claim is robust and does not depend on the precise CEF parameters. However, the more specific and novel claim—that the chirality within a single band reverses with momentum—is an interpretation of the chiral neutron signal. As the authors themselves note, σ_ch is not a direct measure of mode SAM; it is weighted by eigenvectors and structure factors. The data demonstrate a sign change in σ_ch, but the sign of σ_ch can change for reasons unrelated to SAM reversal, as explicitly shown in Fig. 1(f) near H=1. The only way the paper connects the measured σ_ch sign change to the asserted chirality reversal is through the linear spin-wave eigenvectors computed from a Hamiltonian whose anisotropy parameters (notably B6^6 and B0^4) are taken from earlier unpolarized fits without error bars. The SI sensitivity analysis varies B6^6 and shows the gap closes at ~5× its nominal value, but it does not examine whether the total SAM of the lower branch still crosses zero over a realistic parameter range, nor does it vary B0^4. Therefore the chirality-reversal claim is conditional on the model being quantitatively accurate in just the parameter combination that controls magnon mixing. This does not overturn the paper's central symmetry-based mechanism, but it does mean the headline 'chirality reversal in a single band' is not yet established beyond the model. The reader's CONDITIONAL verdict is appropriate; no verdict change is needed.","tokens_in":13679,"tokens_out":6020,"duration_ms":68891,"concrete_test":"Recompute the total SAM S_ν(k) of the acoustic/optic branches along (H,0,0) using the same linear spin-wave code (sunny.jl) while independently varying B6^6 and B0^4 over the ranges consistent with the fits in Refs. [29,30]—for example, ±50% of the Table S1 values and the 0.8–3× B6^6 window used in Fig. S4. For each parameter set that still reproduces the measured unpolarized dispersions to within the experimental resolution, determine whether the wavevector at which the total SAM of the lower branch crosses zero shifts by more than a few percent or disappears entirely. If the zero crossing is absent for some allowed parameters, then the measured σ_ch reversal cannot be uniquely attributed to chirality reversal, and the central claim would need to be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that the gapped modes in ErMn6Sn6 have k-dependent chirality and that the chirality reverses within a single band—requires that the measured chiral neutron cross-section sign change near the avoided crossing be interpreted as a reversal of the mode spin angular momentum. But σ_ch in Eq. (1) is weighted by the magnon eigenvector and the magnetic structure factor, so its sign can flip between Brillouin zones or near a crossing simply because the dominant sublattice weight shifts, even if the intrinsic SAM of the mode does not reverse. The paper itself acknowledges this for H near 1 in Fig. 1(f): 'both modes in Fig. 1(f) appear to be left-handed near H=1, but this arises from a reduced contribution of the Mn structure factor to the chiral cross-section in this Brillouin zone.' The measured σ_ch reversal in Fig. 2(c–d) is therefore not by itself definitive evidence of chirality reversal. The mode SAM is computed from Eqs. (4)–(7) using the linear spin-wave model with Hamiltonian parameters from Table S1, fitted to unpolarized data in Refs. [29,30]. The relevant parameters—especially B6^6 and B0^4, which set the difference (K_Ryy − K_Rzz) that controls mixing—have no quoted uncertainties. The SI sensitivity scan (Fig. S4) varies B6^6 and shows the gap closes at ~5× the nominal value, but it does not test whether the total SAM of the lower branch still crosses zero over the allowed parameter range, nor does it vary B0^4. If those CEF parameters are inaccurate, the computed zero-crossing and reversal of the total SAM could be an artifact, even though the raw σ_ch sign change and the avoided crossing are real.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports polarized and unpolarized inelastic neutron scattering on the collinear ferrimagnets TbMn6Sn6 and ErMn6Sn6, together with linear spin-wave calculations, and proposes a symmetry-based mechanism for chiral magnon mixing. In TbMn6Sn6, where the easy-axis magnetic order preserves an effective U(1) symmetry, the acoustic and optic magnon bands cross without hybridizing and the two modes retain pure opposite chirality. In ErMn6Sn6, the easy-plane order breaks U(1) and the crossing develops a gap; the gapped modes are elliptically polarized superpositions of the SAM eigenstates, and the authors claim that the lower band's chirality reverses with momentum near the hybridization point. The central experimental observations are the crossing in Tb166, the gap in Er166, and a sign change in the half-polarized chiral neutron cross-section near the avoided crossing. The mode-resolved chirality reversal is inferred from linear spin-wave eigenvectors computed with Hamiltonian parameters taken from prior work.","tokens_in":14155,"tokens_out":4174,"duration_ms":51790,"significance":"If the central claim is correct, the paper identifies a new and potentially useful mechanism for manipulating magnon chirality in ferrimagnets: the anisotropy-driven symmetry breaking that turns protected band crossings into hybridized gaps with momentum-dependent chirality. This is relevant to chiral magnonics and to the broader family of RMn6Sn6 kagome magnets, where spin-reorientation transitions could switch the chirality by temperature or field. The manuscript is strengthened by the use of new half-polarized INS data on ErMn6Sn6, an explicit symmetry argument for the Tb/Er difference, and a clearly described model calculation. The data are openly available, and the LSWT framework is standard. However, the quantitative support for the headline chirality-reversal claim is currently limited: no error bars are shown on the chiral maps, no quantitative data-model comparison is reported, and the SAM reversal relies on model eigenvectors whose parameters carry no quoted uncertainties. These gaps are load-bearing because the raw chiral cross-section sign is not by itself a direct measure of the mode SAM.","major_comments":[{"comment":"The statement that the half-polarized data 'confirm the predicted reversal of the magnon handedness' is supported only by qualitative color maps in Fig. 2(c-d). No error bars, statistical uncertainties, or background-subtraction details are given for the extracted σ_ch, and no quantitative comparison is made between the measured and calculated sign-change wavevector or the magnitude of the hybridization gap. Because σ_ch is an antisymmetric difference of two large scattering channels, small systematic errors (flipper efficiency, incomplete polarization, background) can create apparent sign changes. The authors should provide line cuts of σ_ch with uncertainties, show the sign-change point quantitatively, and state how well the model reproduces it. This is central to the paper's main claim.","section":"Fig. 2 and §Experimental results"},{"comment":"The chirality reversal within a single band is not measured directly; it is obtained from the linear spin-wave eigenvectors using the Hamiltonian parameters in Table S1, which are taken from earlier fits (Refs. [29,30]) with no reported uncertainties. As the paper itself notes near Fig. 1(f), the sign of σ_ch can change because of the magnetic structure factor even when the intrinsic mode SAM does not reverse. Thus the observed σ_ch sign change near the avoided crossing could in principle result from a shift of sublattice weight rather than from an actual reversal of the total mode SAM. To make the central claim convincing, the authors should demonstrate that the measured σ_ch profile tracks the calculated SAM sign (not merely the calculated σ_ch), and should perform a robustness analysis of the total-SAM zero crossing over the credible parameter ranges, including B0^4 as well as B6^6. T","section":"§Mode chiralities, Eq. (1), and SI Table S1/Fig. S4"},{"comment":"The symmetry argument for why Tb166 has a protected crossing while Er166 does not is clear and plausible. However, the paper states that the hybridization gap is proportional to the net yz anisotropy, yet Fig. S4 shows the gap as a function of B6^6 only, not of K_Ryy − K_Rzz, and the relationship to B0^4 is not tested. Since the difference (K_Ryy − K_Rzz) is the quantity that controls mixing per Eq. (3), the authors should either give the analytic dependence or plot the gap versus the anisotropy difference over a parameter range that includes the values where the gap closes (e.g., the 5×B6^6 point in Fig. S4). This would strengthen the claimed connection between crystal-field anisotropy and chiral hybridization.","section":"§Magnetic symmetry and SI Sec. SII(C)"}],"minor_comments":[{"comment":"The term 'R166' is used without definition in the abstract and introduction; define it at first use for readers outside the RMn6Sn6 community.","section":"Abstract/Introduction"},{"comment":"The displayed chiral cross-section formula has a typographically awkward 'i[...]' and missing angular brackets in the time correlation; please clean up the notation so that the antisymmetric correlation is unambiguous.","section":"Eq. (1)"},{"comment":"The text says the gap closes when B6^6 is increased by 'five times' while the caption says 'four times'; reconcile these numbers.","section":"SI Fig. S4 caption and text"},{"comment":"Reference [33] has a malformed author name ('N. L, T. Victa Trevisan'); please correct.","section":"Reference list"},{"comment":"The calculated chiral scattering in Fig. 1(f) is difficult to read near the crossing and near H=1; larger panels or separate color-scale plots for the two modes would clarify the predicted sign change versus the structure-factor effect.","section":"Fig. 1(f)"}],"recommendation":"major_revision","confidential_remarks":"The work is potentially significant and the qualitative data are compelling, but the central chirality-reversal claim is currently overreaching relative to the quantitative evidence and model robustness. I would support publication after the authors add error bars/uncertainty analysis, a quantitative data-model comparison, and a parameter-sensitivity study of the SAM zero crossing. The manuscript's scope is appropriate for the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper reports that in easy-plane ErMn6Sn6 the acoustic and optic magnon branches hybridize and the mode chirality reverses with momentum, while in easy-axis TbMn6Sn6 the crossing is U(1)-protected. The new piece is the symmetry mechanism: planar anisotropy breaks the U(1) that separates right/left magnons, so they mix and a gap opens. That is a neat, generalizable argument, and it is well supported by the data.\n\nThe half-polarized INS on Er is a demanding measurement, and the data look convincing: a clean avoided crossing in σ_M and a sign change in σ_ch near the gap. The Tb/Er contrast is a good control. The paper is also honest about the structure-factor caveat in the H=1 zone, which shows care. The LSWT calculations reproduce the main features using parameters from earlier work, and the sensitivity scan on B6^6 is a start.\n\nThe soft spots are real but not fatal. The conversion from measured σ_ch to a statement about mode spin angular momentum is model-dependent. The paper itself notes σ_ch is weighted by eigenvector and structure factor, so a sign change alone does not prove chirality reversal. In Fig. 2 the measured reversal happens at the crossing where the gap opens, which is suggestive, but it could in principle be a Brillouin-zone effect. What is missing: error bars on the chiral maps, a quantitative cut comparing data to model, and a robustness check that varies B0^4 as well as B6^6 and tracks whether the total SAM zero-crossing survives. Without that, the \"reversal\" claim is conditional, even though the raw observations are solid.\n\nAlso, the parameters come from previous fits. If the CEF parameters are off, the inferred chirality reversal could be wrong even though the avoided crossing and σ_ch sign change are real. That is a fair concern, but it does not undermine the core symmetry argument; it just means the interpretation needs stronger uncertainties.\n\nThis paper is for the magnonics/spintronics community and for anyone interested in symmetry-controlled band hybridization. It deserves a serious referee. The main revisions should be about uncertainty quantification and model robustness, not about the core observation. Send it to review, and ask for error bars and a sensitivity analysis on the chirality reversal.","headline":"A clean symmetry-driven story about chiral magnon hybridization in a bulk ferrimagnet; the central observation is robust, but the chirality-reversal claim leans on model parameters that deserve a robustness pass.","tokens_in":14700,"tokens_out":2200,"would_cite":true,"duration_ms":25332,"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":"In easy-plane ErMn6Sn6, breaking U(1) spin-rotation symmetry hybridizes right- and left-handed magnon bands at their crossing, making magnon chirality reverse with momentum.","keywords":["Chiral magnons","Ferrimagnets","Magnon hybridization","Spin angular momentum","Polarized inelastic neutron scattering","RMn6Sn6","U(1) symmetry breaking","Magnon chirality"],"falsifier":"Measure the hybridization gap in ErMn6Sn6 as an applied magnetic field drives the moments from easy-plane to easy-axis: if the gap persists when U(1) symmetry is restored, the symmetry-breaking mechanism is wrong.","tokens_in":13621,"feed_emoji":"🧲","tokens_out":4931,"duration_ms":50447,"temperature":0.7,"pith_summary":"This paper claims that in the collinear ferrimagnet ErMn6Sn6, easy-plane magnetic anisotropy breaks the U(1) symmetry that normally keeps right- and left-handed magnons independent, allowing the acoustic and optic magnon bands to hybridize where they cross. The hybridized bands carry elliptical, mixed-chirality excitations whose net spin angular momentum passes through zero and reverses sign: each band's dynamical chirality becomes momentum-dependent. In TbMn6Sn6, whose uniaxial order preserves U(1), the same crossing stays a protected nodal line. Using polarized inelastic neutron scattering, the authors measure the chiral neutron cross-section and show the sign reversal predicted by their linear spin-wave model. The result matters because it gives a symmetry-based knob—field, temperature, or rare-earth substitution—to switch magnon handedness in a single material.","feed_headline":"Magnon chirality reverses inside one band in ErMn6Sn6","feed_subtitle":"Polarized neutrons show easy-plane anisotropy hybridizes handed magnons, a control knob for magnonic devices","key_machinery":"The central object is the U(1) spin-rotation symmetry around the net magnetization direction. When preserved, the right/left circular magnon polarizations carry quantized SAM S_z = ∓ℏ and do not mix. Easy-plane anisotropy of the form V = K_yy S_y^2 + K_zz S_z^2 breaks U(1); its off-diagonal matrix elements coupling the |±> SAM states are proportional to |K_yy - K_zz|, so the hybridization gap at the band crossing is set by the net yz anisotropy. The chiral neutron scattering cross-section σ_ch(Q,ω), which measures antisymmetric spin correlations weighted by the magnon eigenvectors and magnetic structure factor, provides the observable, while the mode spin angular momentum S_ν = W_R S_R + W_M","core_discovery":"The central discovery is that the chirality of magnons in a ferrimagnet is not fixed by the sublattice compensation; it can be mixed and reversed within a single band when the magnetic structure's spin-rotation symmetry is broken. In ErMn6Sn6 the planar magnetic order has only twofold rotational symmetry, and the rare-earth crystalline-electric-field anisotropy (terms of the form K_yy S_y^2 + K_zz S_z^2) couples the right- and left-handed SAM basis states |±>. The resulting off-diagonal matrix elements ⟨±|V|∓⟩ ∝ |K_yy - K_zz| open a hybridization gap at the acoustic-optic crossing. The two gapped modes are elliptically polarized superpositions whose total spin angular momentum (summed over M","pith_inferences":["The mechanism is likely generic: any collinear ferrimagnet with easy-plane anisotropy and a finite-momentum acoustic–optic crossing should exhibit analogous chiral mixing; searching other R166 compounds or rare-earth–transition-metal ferrimagnets with easy-plane order would test this.","The intra-band zero-chirality point, where the two sublattices precess with opposite handedness and cancel, is a magnonic analogue of linear polarization and could serve as a basis for interference or decoherence-resistant states, though the paper does not explore this.","A practical caution follows from the paper's own analysis: the raw chiral cross-section sign can flip between Brillouin zones because of the structure factor, so experimentally confirming chirality reversal requires eigenvector-based SAM extraction, not just sign of σ_ch.","Applying this symmetry-breaking logic to antiferromagnets with weak anisotropy suggests a way to engineer hybridization gaps without an applied field, but that extension goes beyond the present data."],"forward_implications":["In ErMn6Sn6, each hybridized magnon band carries momentum-dependent chirality: the total spin angular momentum changes sign across the avoided crossing, enabling handedness encoding within a single band.","The symmetry of the ferrimagnetic order controls whether the magnon crossing is a protected nodal line (TbMn6Sn6) or a gapped hybridization (ErMn6Sn6), so spin-reorientation transitions—via field or temperature—switch the mechanism on and off.","Because the hybridization gap scales with the net anisotropy difference |K_yy - K_zz|, tuning the rare-earth crystal-field parameters (e.g., B6^6, B0^4) tunes the gap and can drive the system from gapped back to crossing.","The measured chiral cross-section sign change in ErMn6Sn6 matches calculations, establishing a neutron-scattering signature for chiral magnon mixing.","This provides a new mechanism for manipulating magnon chirality that complements compensation-temperature and field-driven reversal, relevant for chirality-based quantum magnonics."],"fun_headline_variants":["Magnon chirality flips inside one band in ErMn6Sn6","Symmetry-breaking hybridizes chiral magnons in ErMn6Sn6","ErMn6Sn6 magnons swap handedness at a crossing","Rare-earth anisotropy controls magnon chiral mixing","Chiral magnons get k-dependent handedness in ErMn6Sn6"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The central claim depends on the fitted spin-wave Hamiltonian—especially the rare-earth crystal-field coefficients that set the easy-plane anisotropy—being accurate enough that the eigenvector-derived spin angular momentum, and not just the raw chiral cross-section sign, correctly identifies the mode chirality and its reversal.","fun_headline_variants_meta":{"raw":{"variants":["Magnon chirality flips inside one band in ErMn6Sn6","Symmetry-breaking hybridizes chiral magnons in ErMn6Sn6","ErMn6Sn6 magnons swap handedness at a crossing","Rare-earth anisotropy controls magnon chiral mixing","Chiral magnons get k-dependent handedness in ErMn6Sn6"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000229,"raw_usage":{"total_tokens":1306,"prompt_tokens":725,"completion_tokens":581,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":469,"completion_tokens_details":{"reasoning_tokens":503}},"tokens_in":469,"tokens_out":581,"duration_ms":6633,"temperature":1.0,"reasoning_tokens":503,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T00:59:59.767329+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the hybridization gap in ErMn6Sn6 as an applied magnetic field drives the moments from easy-plane to easy-axis: if the gap persists when U(1) symmetry is restored, the symmetry-breaking mechanism is wrong.","supporting_citations":[],"review_version":1}