{"id":"a95893ab-2627-44a1-9953-fb724bb1b103","arxiv_id":"2507.22172","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Zero-field circular and vortex-beam dichroism of the 0.85 THz magnon doublet is reported in h-Lu0.6Sc0.4FeO3 and interpreted as evidence for altermagnetic A2 ordering.","lead":"Terahertz and Raman measurements of hexagonal ferrite h-Lu0.6Sc0.4FeO3 reveal magnon modes near 0.85 and 1.2 THz, including a doublet that splits at zero magnetic field and responds differently to left- and right-circularly polarized light. The authors attribute this zero-field circular dichroism to the altermagnetic A2 spin structure, a candidate mechanism for THz nonreciprocal optics in multiferroics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The altermagnetic attribution is not supported because the zero-field splitting (Δ≈0.06 THz, Eq. 1, Fig. 4) may be a standard DMI effect of the canted A2 order; the paper's M_R comparison does not rule this out.","rationale":"The paper reports a substantial body of new experimental data—THz magnon spectra, circular and vortex-beam dichroism, Raman phonons, and ellipsometry with DFT+eDMFT—and the magnon doublet and dichroism are credible observations. The problem is the attribution. The strongest claim requires that the 0.06 THz zero-field splitting is a signature of the altermagnetic property of the A2 phase. To establish this, the authors must exclude the conventional explanation in which the non-collinear A2 order itself, via the DM interaction, gives rise to the splitting and the circular dichroism. Their attempt at exclusion is the comparison between the splitting expressed as g μB B_eff ≈ 1.4 T and the measured net moment of 0.01 μB/f.u. This comparison is not physically valid: in weak ferromagnets the DM exchange field sets the magnon gap and can be much larger than the field corresponding to the net magnetization; the net moment is only the small canting resultant, not the internal field strength. The paper even states that 'the large zero-field magnon splitting should be additionally clarified with elaborate spin-structure calculations' and that the VVB data may contain systematic errors. Because no spin-wave or DM calculation is provided, the altermagnetic conclusion is not established. This is exactly the reader's weakest assumption, so the conditional verdict stands. I would not move to reject because the data and the phenomenology remain valuable; the appropriate action is to reframe the altermagnetic claim as a hypothesis and either supply the calculation or soften the conclusion.","tokens_in":18899,"tokens_out":6854,"duration_ms":80113,"concrete_test":"Perform a linear spin-wave calculation for the A2 spin structure of h-Lu0.6Sc0.4FeO3 using exchange, Dzyaloshinskii-Moriya, single-ion anisotropy, and magnetoelectric parameters consistent with T_N≈160 K and the measured weak-ferromagnetic moment of 0.01 μB/f.u. (e.g., from Ref. 3 or fitted to the magnon frequencies at 0.85/1.2 THz and the g-factor 3.0). Compute the zero-field magnon eigenfrequencies for k||c and their circular-polarization selection rules. If the model produces a splitting ≈0.06 THz with opposite circular polarizations, the altermagnetic/Berry-phase mechanism is not needed and the central claim is refuted. If the splitting cannot be reproduced within a standard canted-AFM DMI model, the altermagnetic hypothesis is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the zero-field magnon doublet splitting and circular dichroism are unique to an altermagnetic A2 phase with Berry-phase spin chirality. The paper's only explicit argument against a conventional interpretation is the estimate that Δ=0.06 THz, converted via g=3.0 (Eq. 1 and Fig. 4), corresponds to an effective field of ~1.4 T, whereas the measured remnant magnetization is only 0.01 μB/f.u. (Ref. 3). This comparison is not valid for a canted antiferromagnet: the zero-field magnon splitting in a weak ferromagnet is set by the Dzyaloshinskii-Moriya (DM) exchange field, which can be of order 1 T or more while the net canting moment remains ~10^-2 μB. The DM interaction is symmetry-allowed in the A2 phase and is already the accepted origin of the canted moment; no microscopic spin-wave or DMI calculation is presented to show it cannot reproduce Δ≈0.06 THz. Indeed, the paper states the needed 'elaborate spin-structure calculations' are left for future work, and the VVB data are explicitly limited by possible axicon-alignment artifacts. Without excluding the standard DMI mechanism, the attribution to altermagnetism is an unsupported hypothesis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a multi-technique optical study of hexagonal Lu0.6Sc0.4FeO3 single crystals, including THz transmission with circular polarizations and vector vortex beams, Raman scattering, infrared ellipsometry, and visible-UV ellipsometry combined with DFT+eDMFT calculations. The authors observe two magnon modes (M1 at ~0.8 THz and M2 at ~1.2 THz), an electromagnon, phonons, and electronic transitions. The central claim is that the M1 magnon appears as a doublet split by about 0.06 THz at zero external field, with opposite circular polarizations selecting the two branches, and that this zero-field dichroism is evidence for altermagnetic A2 spin ordering with broken P·T symmetry. Additional results include a fitted Fe3+ g-factor of 3.0, a nonreciprocal reorientation field asymmetry at low temperature, a Fano asymmetric phonon at 115 cm-1, and a DFT+eDMFT interpretation of the electronic spectra.","tokens_in":19195,"tokens_out":5614,"duration_ms":63479,"significance":"If the altermagnetic interpretation is correct, the paper would provide a valuable zero-field optical signature of an insulating multiferroic altermagnet and predict a large magneto-optical Kerr effect below 160 K. The experimental data set is rich and the internal consistency of the THz transmission fits, the temperature and field dependencies, and the ellipsometry/DFT+eDMFT comparison is a clear strength. However, the central attribution of the zero-field magnon splitting to altermagnetism is an interpretation rather than a derivation; the manuscript explicitly defers the needed spin-structure calculations. The observed zero-field doublet splitting and circular dichroism are significant experimental facts regardless of the interpretation, but the paper's title and conclusions currently overstate the evidence.","major_comments":[{"comment":"The inference that Δ≈0.06 THz (2 cm-1) cannot be explained by the weak ferromagnetic moment is not justified. In a canted antiferromagnet, the zero-field magnon splitting is controlled by the Dzyaloshinskii-Moriya (DM) exchange field, which can be of order 1 T or more while the net canting moment remains ~0.01 μB/f.u. The manuscript's comparison of the effective field 1.4 T with the measured remnant magnetization 0.01 μB/f.u. (Ref. 3) does not rule out the conventional DM mechanism because the two quantities are not directly related. The text itself states that 'elaborate spin-structure calculations that includes the Dzyaloshinskii-Moriya interaction' are left for future work. Without a spin-wave or DMI calculation showing that the standard canted-A2 mechanism cannot produce the observed splitting, the altermagnetic attribution is an unsupported hypothesis rather than a demonstrated conclusion.","section":"Experimental Results, A (Eq. 1 and following paragraph)"},{"comment":"The VVB data are presented as corroborating evidence for the zero-field dichroism, but the paper explicitly states that 'there are no strong arguments to relate the magnon line shape to the specifics of the ferroelectric domains or magnetic spin structure' and that the observed asymmetry is 'more reasonable to assign ... to systematic errors due to imperfect alignment of the axicon optics.' This self-acknowledged artifact limitation should be stated in the abstract and conclusions, and the VVB results should be treated as preliminary. The conventional circular-polarization transmission data remain the primary evidence, but they alone do not establish the altermagnetic mechanism.","section":"Experimental Results, A (vector vortex beam paragraph)"},{"comment":"The manuscript notes that A1 and A2 spin structures coexist as micron-sized domains below 60 K, while the THz beam footprint is mm-sized, so the transmission averages over many domains. The analysis does not address how A1/A2 domain averaging affects the observed zero-field doublet splitting and the circular-polarization selection rules. If the A1 and A2 domains have different magnon frequencies, the apparent doublet could be a superposition of domain responses rather than an intrinsic splitting of a single A2 domain. This issue is load-bearing for the central claim and needs to be addressed, for example by estimating the domain fractions from the spectroscopic data or by measuring a single-domain sample.","section":"Introduction and Experimental Results, A (domain coexistence)"},{"comment":"The g-factor of 3.0±0.5 is extracted from a two-parameter empirical fit using Eq. (1), and the zero-field splitting Δ appears both as a fitted parameter and as an input to the effective-field estimate. The manuscript does not report the fit residuals, the correlation between Δ and g, or the statistical basis for the quoted uncertainty. Since the 1.4 T estimate depends directly on the product g·Δ, a proper error propagation is needed before using this value to argue against the conventional weak-ferromagnetic explanation.","section":"Experimental Results, A (Eq. 1 and g-factor fit)"}],"minor_comments":[{"comment":"The phrase 'applied long the c axis' should be 'applied along the c axis' in the abstract and in the main text.","section":"Abstract and text"},{"comment":"The caption contains a typo: 'thee electromagnon' should be 'the electromagnon'.","section":"Table I caption"},{"comment":"The phrase 'back town to T=6 K' should be 'back down to T=6 K'.","section":"Experimental Results, A (temperature cycling)"},{"comment":"The text refers to 'Fe3+ ions having nominal S=3/2' when estimating the effective field, but later the manuscript expects high-spin Fe3+ with S=5/2 and the DFT+eDMFT section argues for Fe valence 2.5+ with effective spin closer to S=2. Please ensure a consistent spin value is used in the g-factor and effective-field estimates.","section":"Introduction (spin value)"},{"comment":"The magnetic point group is written as '6/'m mm' with garbled symbols; please use a clear notation such as 6/m'mm' or 6/mm'm' and define the symbols.","section":"Introduction (magnetic point group)"},{"comment":"The caption says '(c) Temperature dependence of the magnetization reversal field BR' but the text refers to Fig. 4(d) for BR(T) and Fig. 4(c) for low-field magnon frequencies; the caption and figure panel labels need to be reconciled.","section":"Fig. 4 caption"},{"comment":"Equation (1) is typeset with missing symbols; the intended form appears to be Ω±(B,T) = Ω0(T) ± 1/2 sqrt(Δ² + (g μB B)²), but the displayed formula is garbled and should be rewritten clearly.","section":"Eq. (1)"},{"comment":"The reference list contains duplicate entries: Ref. 4 and Ref. 8 are the same paper, and Ref. 6 and Ref. 10 are the same paper. These should be consolidated.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The experimental work is substantial and likely publishable, but the title and the abstract overstate the altermagnetic attribution relative to the evidence actually presented. The authors should either provide a microscopic DMI-based calculation that excludes the conventional weak-ferromagnetic origin of the zero-field splitting, or substantially soften the claim (e.g., 'consistent with altermagnetic A2 ordering') and move the strong altermagnetic statement to a discussion section. The VVB data limitation is acknowledged in the text but not in the conclusions, which weakens the paper's internal consistency. I recommend major revision rather than rejection because the experimental observations are novel and the interpretive gap appears fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper delivers real new data: first THz and Raman magnon spectra in h-Lu0.6Sc0.4FeO3, including a zero-field split magnon doublet (Δ≈0.06 THz) with circular dichroism and a vector-vortex-beam counterpart. The temperature dependence, field evolution, g-factor ~3.0, and the nonreciprocal reorientation-field asymmetry are interesting and seem internally consistent. The phonon and ellipsometry work is also solid, and the DFT+eDMFT electronic-structure part is a genuine bonus.\n\nBut the central attribution—that this dichroism is a strong altermagnetic effect—is not established. The stress-test concern hits the load-bearing point: for a canted antiferromagnet with DMI-allowed A2 order, a zero-field magnon splitting of 0.06 THz can be an ordinary DM exchange-field effect even when the net moment is only 0.01 μB/f.u. The paper's comparison of the splitting to an effective 1.4 T internal field against a 0.01 μB remnant moment does not rule that out; the two quantities are not in tension for a weak ferromagnet. There is no microscopic spin-wave or DMI calculation to exclude the conventional mechanism. The paper itself concedes these calculations are left for future work and that the VVB lineshape may be affected by axicon alignment. So the altermagnetic conclusion should be treated as a hypothesis, not a derivation.\n\nNone of this makes the experiment bad. The observation is credible and independent of the classification; the altermagnetic label is applied, not fitted. The A1/A2 domain coexistence is mentioned and the interpretation is reasonably cautious in places. The main fix is to reframe the conclusion and add either a quantitative DMI/spin-wave calculation or an explicit discussion of why weak-ferromagnet canting cannot produce the splitting.\n\nWho this is for: THz magnonics, multiferroic hexaferrites, and altermagnetism people. They will want the data even if they push back on the interpretation. It deserves a serious referee; I would not desk reject. Recommend major revision with the interpretation reframed and the DMI alternative addressed.","headline":"Solid first data on LSFO magnons with a real zero-field dichroism, but the altermagnetic attribution is unproven and the DMI alternative must be answered.","tokens_in":19926,"tokens_out":2122,"would_cite":true,"duration_ms":24374,"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":"Terahertz measurements show that the antiferromagnetic magnon doublet in h-Lu0.6Sc0.4FeO3 is split by about 0.06 THz at zero applied field, evidence the authors attribute to its altermagnetic A2 spin structure.","keywords":["h-Lu0.6Sc0.4FeO3","altermagnetism","magnon dichroism","terahertz spectroscopy","vector vortex beams","A2 spin structure","multiferroics"],"falsifier":"A decisive check would be to compute the zero-field magnon splitting from a spin Hamiltonian whose exchange, single-ion, and Dzyaloshinskii-Moriya parameters are fixed by the measured remanent magnetization, the g-factor, and the reorientation field: if the splitting computed from the weak ferromagnetic canting alone is much smaller than $0.06$ THz, and the splitting persists in a fully poled single A2-domain crystal measured with high polarization purity, the altermagnetic interpretation is confirmed; if the splitting collapses or scales with the ordinary magnetization, it is not.","tokens_in":18708,"feed_emoji":"🧲","tokens_out":14922,"duration_ms":155066,"temperature":0.7,"pith_summary":"Terahertz spectroscopy of the hexagonal ferrite h-Lu0.6Sc0.4FeO3 finds that its antiferromagnetic spin excitation (a magnon) is already split at zero applied magnetic field into two circularly polarized components, separated by about $0.06$ THz. The paper attributes this zero-field 'magnon dichroism' to the A2 spin structure, a canted non-collinear arrangement of Fe$^{3+}$ moments that breaks both parity and time-reversal symmetry and is therefore classified as a strong altermagnetic phase, even though the crystal's net magnetization is only about $0.01\\,\\mu_B$ per formula unit. If correct, the compound becomes an insulating multiferroic altermagnet whose hidden magnetic order can be read out optically at terahertz frequencies, and the dichroism becomes a general probe for altermagnetism in materials with nearly zero net magnetization. The paper also reports a magnon g-factor of $g=3.0$ for Fe$^{3+}$, nonreciprocal light propagation below 10 K, Fano-broadened optical phonons, and a DFT+eDMFT description of the electronic transitions.","feed_headline":"Magnetic resonance split at zero field exposes altermagnetic order","feed_subtitle":"In h-Lu0.6Sc0.4FeO3, terahertz circular dichroism marks the A2 phase as an insulating multiferroic altermagnet.","key_machinery":"The load-bearing object is the A2 spin structure, in which Fe$^{3+}$ moments on the trimerized triangular lattice form a nearly $120^\\circ$ non-collinear pattern with a small c-axis canting that couples a weak ferromagnetic moment to the electric polarization. Because this structure breaks parity and time reversal together, it is classified as a 'strong altermagnetic' phase, a compensated magnetic order whose simultaneous P and T breaking allows spin-dependent optical responses without net magnetization. The observable that carries the argument is the M1 magnon doublet: its zero-field splitting $\\Delta\\approx0.06$ THz, the opposite circular-polarization selection rules of its two branches, and the sign reversal with magnetic field and with the orbital angular momentum of vector vortex beams. The paper invokes the finite scalar spin chirality $S_1\\cdot(S_2\\times S_3)$ and the associated Berry phase as the mechanism generating the effective internal field that splits the magnons.","core_discovery":"The central discovery is a strong circular dichroism of the antiferromagnetic magnon doublet at zero external field: the M1 magnon near $0.85$ THz splits into two branches, separated by about $0.06$ THz, that are active in opposite circular polarizations of terahertz light. The same splitting is reproduced with terahertz vector vortex beams carrying orbital angular momentum $\\ell=\\pm1$, and its sign can be reversed by reversing either the applied magnetic field or the beam vorticity. The authors interpret this as the zero-field optical signature of the A2 spin structure with broken PT symmetry, a 'strong altermagnetic' phase, and estimate that the splitting corresponds to an effective internal field of about $1.4$ T acting on the Fe$^{3+}$ spins, far larger than the $0.01\\,\\mu_B$ per formula unit remanent moment would produce. In applied fields along the c axis the doublet splitting gives a g-factor of $g=3.0$ for Fe$^{3+}$, and below 10 K the field needed to reorient the remanent magnetization depends on the light propagation direction, demonstrating nonreciprocal propagation.","pith_inferences":["Because the paper finds that A1 domains grow below 60 K while the reported zero-field splitting stays roughly constant, a natural test is to measure the splitting across that crossover: an exclusive A2 origin should make the dichroism weaken as the A1 fraction grows.","If the Berry-phase spin-chirality mechanism is correct, the sign of the zero-field splitting should follow the handedness of the non-collinear spins, the sign of $S_1\\cdot(S_2\\times S_3)$, so circular-dichroism imaging could map the vortex-antivortex ferroelectric domain structure with terahertz light.","The same circular-dichroism probe could be applied to other hexagonal ferrites or manganites with A1/A2 competition, predicting that zero-field magnon dichroism appears only where the canted A2 phase dominates."],"forward_implications":["Below $T_N=160$ K, h-Lu0.6Sc0.4FeO3 becomes a candidate insulating multiferroic altermagnet in which electric polarization, weak ferromagnetism, and zero-field terahertz circular dichroism coexist.","Zero-field magnon dichroism, seen with both circular polarization and vector vortex beams, can serve as a spectroscopic fingerprint that distinguishes the altermagnetic A2 phase from the non-altermagnetic A1 phase in hexagonal ferrites and related multiferroics.","The measured g-factor of $g=3.0$ for Fe$^{3+}$ and the reorientation field of about $0.25$ T give quantitative constraints that any microscopic spin Hamiltonian of the A2 phase must reproduce.","The nonreciprocal light propagation below 10 K implies that the c axis of an A2-ordered crystal acts as a one-way channel for terahertz light, with the preferred direction set by the electric polarization and the remanent magnetization.","The paper predicts a large magneto-optical Kerr effect in h-Lu0.6Sc0.4FeO3 below 160 K, extending altermagnetic optics from metals to an insulating ferroelectric compound."],"supporting_citations":[{"why":"Supplies the same LSFO crystals, the A2 weak-ferromagnetic domain behavior, and the 0.01 μB per formula unit zero-field magnetization that the altermagnetic interpretation must outstrip.","marker":"[3]"},{"why":"Establishes the A2 magnetic structure of hexagonal LuFeO3 that the magnon dichroism is assigned to.","marker":"[1]"},{"why":"Provides the Landau-theory framework in which A1 and A2 spin orders compete, framing the domain coexistence in the samples.","marker":"[10]"},{"why":"Defines altermagnetism with non-collinear spins and the PT-symmetry criterion that classes the A2 structure as altermagnetic.","marker":"[13]"},{"why":"Introduces the terahertz vector vortex beam technique used to confirm the dichroism with orbital angular momentum.","marker":"[18]"},{"why":"Provides the negative control of zero-field magnon splitting in B2-type hexagonal manganites, making the LSFO splitting distinctive.","marker":"[22]"},{"why":"Supplies the Mn3Sn analogy of large zero-field magneto-optical effects with nearly zero remanent magnetization, supporting the altermagnetic reading.","marker":"[23]"},{"why":"Provides the Berry-phase and spin-chirality mechanism that the paper invokes to generate the effective 1.4 T internal field from non-collinear spins.","marker":"[26]"}],"fun_headline_variants":["Zero-field magnon dichroism exposes altermagnetic order","Altermagnetic A2 phase revealed by strong THz dichroism","Magnon split at zero field: altermagnetic signature in ferrite","Terahertz circular dichroism marks altermagnetic A2 spin structure","Nonreciprocal magnon dichroism from altermagnetic A2 ordering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim rests on the assumption that the $0.06$ THz zero-field splitting of the magnon doublet is too large to be explained by the crystal's tiny measured ferromagnetic moment of $0.01\\,\\mu_B$ per formula unit, so it must come from an effective internal field of about $1.4$ T generated by altermagnetic order or by spin chirality.","fun_headline_variants_meta":{"raw":{"variants":["Zero-field magnon dichroism exposes altermagnetic order","Altermagnetic A2 phase revealed by strong THz dichroism","Magnon split at zero field: altermagnetic signature in ferrite","Terahertz circular dichroism marks altermagnetic A2 spin structure","Nonreciprocal magnon dichroism from altermagnetic A2 ordering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000329,"raw_usage":{"total_tokens":1889,"prompt_tokens":1050,"completion_tokens":839,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":666,"completion_tokens_details":{"reasoning_tokens":757}},"tokens_in":666,"tokens_out":839,"duration_ms":9006,"temperature":1.0,"reasoning_tokens":757,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T12:00:22.736674+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to compute the zero-field magnon splitting from a spin Hamiltonian whose exchange, single-ion, and Dzyaloshinskii-Moriya parameters are fixed by the measured remanent magnetization, the g-factor, and the reorientation field: if the splitting computed from the weak ferromagnetic canting alone is much smaller than $0.06$ THz, and the splitting persists in a fully poled single A2-domain crystal measured with high polarization purity, the altermagnetic interpretation is confirmed; if the splitting collapses or scales with the ordinary magnetization, it is not.","supporting_citations":[{"cited_title":"Adjusted oscillator strength matching for hybrid magnetic and electric excitations in Dy3Fe5O12 garnet","cited_arxiv_id":null,"evidence_quote":"Supplies the same LSFO crystals, the A2 weak-ferromagnetic domain behavior, and the 0.01 μB per formula unit zero-field magnetization that the altermagnetic interpretation must outstrip."},{"cited_title":"Geometric ferroelectricity in rare-earth compounds RGaO3 and RInO3","cited_arxiv_id":null,"evidence_quote":"Establishes the A2 magnetic structure of hexagonal LuFeO3 that the magnon dichroism is assigned to."},{"cited_title":"Spin dynamics and magnetic excitations of quasi-1D spin chain Ca$_3$ZnMnO$_6$","cited_arxiv_id":"2502.04919","evidence_quote":"Provides the Landau-theory framework in which A1 and A2 spin orders compete, framing the domain coexistence in the samples."}],"review_version":1}