{"id":"a73fb99c-fa0c-4705-bfaf-04c41b1211b6","arxiv_id":"2505.14589","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Epitaxial MnTe films show a spontaneous anomalous Hall effect and anisotropic magnetoresistance whose angular dependence fits 2φ, 3φ, 4φ, and 6φ Fourier components, linking the transport response to the Néel vector orientation and hexagonal crystal symmetry.","lead":"This paper reports magnetotransport measurements on epitaxial thin films of the altermagnet MnTe, showing that both the anomalous Hall effect and the anisotropic magnetoresistance change with the angle between the applied field, the current, and the crystal axes. The work demonstrates that crystal symmetry and altermagnetic order jointly control the electronic transport, which matters for designing future altermagnet-based spintronic devices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central attribution to altermagnetism rests on unmeasured full spin compensation; a parasitic weak moment could mimic the observed 2φ/3φ/6φ transport.","rationale":"The paper provides solid structural evidence for epitaxial hexagonal MnTe and carefully measured angular transport data with symmetry-motivated fits. However, the headline claim is causal: altermagnetic order, not a net magnetic moment, produces the anomalous Hall effect and the observed AMR harmonics. Because MnTe is known to exhibit weak magnetization in some samples (ref. 27), the assumption of perfect compensation cannot be inherited without direct characterization of these specific films. The reader's conditional accept is therefore appropriate; magnetization measurement is the missing decisive control. If the check passes, the paper's interpretation is substantially supported; if it fails, the central claim would need to be reframed as conventional weak-ferromagnet transport. I agree with the reader's weakest assumption and would keep the verdict unchanged.","tokens_in":10991,"tokens_out":6670,"duration_ms":66832,"concrete_test":"Measure magnetization of an identically grown MnTe(0001) film (same thickness and capping) with SQUID-VSM at 175 K, with field in-plane along [01-10] and [2-1-10] up to ±13 T and the same field history as in Fig. 2; report the remanent moment per Mn. If the remanent moment is below ~10^-3 μB/Mn and the saturation curve shows no ferromagnetic component, the altermagnetic attribution remains viable. If a weak moment is found, quantitatively fit the measured 2φ, 3φ, and 6φ amplitudes against this moment to test whether conventional weak-ferromagnet AHE/AMR can account for them.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract and summary claim that the angular dependence of ρxx and ρxy is governed by the interplay of altermagnetic order and hexagonal crystal symmetry. This requires the films to be fully compensated altermagnets with zero net magnetization. No magnetization, neutron, or XMCD measurement is presented for the grown films; the only cited evidence for compensated order comes from prior work on other MnTe samples. Ref. 27 explicitly reports weak magnetization coexisting with the anomalous Hall effect in nominally collinear MnTe, so a parasitic or canted moment in these 40-nm films is a concrete alternative. With a weak ferromagnetic moment, conventional AMR and AHE models can produce 2φ and, through hexagonal magnetocrystalline anisotropy, higher-order angular harmonics, making the fits in Fig. 3 and Fig. 4 insufficient to uniquely identify altermagnetism. The absence of magnetization data is therefore load-bearing: if a net moment exists, the central attribution is not established. Separately, the S2 odd-Hall isolation formula writes ρodd = [ρ(H)+ρ(−H)]/2, which is the symmetric rather than antisymmetric component; even if this is typographical, the extraction must be clarified for the AHE data to be reproducible.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports magnetotransport measurements on MBE-grown epitaxial (0001) MnTe thin films on InP(111), and claims that both longitudinal and transverse resistivities depend on the relative orientation of the applied current, the Néel vector, and the hexagonal crystal symmetry. The authors observe hysteretic ρxx(B) and ρxy(B) below a Néel temperature of about 200 K, attribute the hysteresis to spin-flop transitions and a spontaneous anomalous Hall effect, fit angular sweeps in three geometries to symmetry-motivated 2φ, 3φ, 4φ, and 6φ Fourier forms, and report a zero-field circular-device transverse signal that scales as sin(2ψ). The central attribution is that these responses arise from altermagnetic order with fully compensated spins.","tokens_in":11096,"tokens_out":4376,"duration_ms":44805,"significance":"If the central attribution holds, the paper provides a useful systematic symmetry-based characterization of magnetotransport in epitaxial MnTe, separating a magnetic twofold component from crystalline sixfold and threefold components. The internal consistency between the zero-field circular-device signal and the in-plane 2φ transverse term is a genuine strength, and the symmetry-motivated fitting procedure is transparent and falsifiable. The main limitation is that no direct magnetic characterization (magnetometry, neutron diffraction, or XMCD) is presented for the measured films, so the significance is conditional on establishing that the films are fully compensated and that a parasitic or canted magnetic moment does not explain the angular dependence.","major_comments":[{"comment":"The central attribution to altermagnetism presupposes fully compensated order with zero net magnetization, but no magnetometry, neutron, or XMCD data are presented for these 40-nm films. Given that Ref. 27 reports weak magnetization coexisting with the anomalous Hall effect in nominally collinear MnTe, a parasitic or canted moment is a concrete alternative that could produce similar 2φ and higher-order angular harmonics through conventional ferromagnetic AMR and AHE models. Please add a direct magnetic characterization of these films (for example, a SQUID or MOKE magnetization loop with sensitivity adequate to detect a weak moment, or XMCD), and use that data to support the compensated-altermagnet attribution; otherwise the claims in the abstract and summary should be correspondingly weakened.","section":"Introduction and interpretation of Figs. 2e and 3"},{"comment":"The stated odd-Hall isolation formula ρodd_xy = [ρ(H) + ρ(−H)]/2 is the symmetric average, not the antisymmetric component used to isolate an odd-in-field Hall contribution. If the implemented procedure actually used [ρ(H) − ρ(−H)]/2, Eq. (1) must be corrected; if not, the AHE extraction is invalid. Please also specify the high-field range used for the linear ordinary-Hall background subtraction and describe how the background slope was determined, so that the reported AHE values are reproducible.","section":"Supplementary S2, Eq. (1)"},{"comment":"The two displayed expressions for ρxy are inconsistent at face value for φI = 0: substituting φI = 0 into ρxy = −ρ2 sin(2φI − 2φ) − ρ4 sin(2φI + 4φ) gives +ρ2 sin(2φ) − ρ4 sin(4φ), whereas the high-field expression is written as −ρ2 sin(2φ) + ρ3 sin(3φ) − ρ4 sin(4φ). The sign of the ρ2 term differs between the two forms. Please resolve this sign/phase convention explicitly before the fitted signs of the Fourier amplitudes in Fig. S4 are interpreted.","section":"Results, in-plane xy fits"},{"comment":"The sentence stating that in the low-field regime 'the Néel vector does not change (for B = 0) or fully rotate with the magnetic field (for B = 1T)' appears to contain a missing 'not' before 'fully rotate', since the authors then conclude that no substantial angular dependence is observed. As written, the statement is self-contradictory and obscures the interpretation of the low-field data.","section":"Results, low-field regime discussion"}],"minor_comments":[{"comment":"The label 'corresponding longitudinal resistance (Rxy)' should read 'transverse resistance' or 'Hall resistance', and the units on the vertical axis should be specified explicitly.","section":"Fig. 4c"},{"comment":"There are several typographical errors, including 'Thesesymmetryproperties' (missing spaces), 'flim' in the Fig. 1e caption, and 'altermganetic' in Supplementary S2. These should be corrected during revision.","section":"Throughout"},{"comment":"The term 'spontaneous AHE' should be defined precisely: it is used for a zero-field remanent-like signal in the circular device, but also for the zero-field intercept of field-cycled hysteresis loops. Clarifying the definition would help readers distinguish the remanent response from the antisymmetric Hall intercept.","section":"Fig. 2e and Summary"},{"comment":"The Néel temperature is inferred from the peak in ρxx(T); since magnetic characterization is absent, please state whether this TN assignment is based on a direct comparison with literature values or an independent measurement.","section":"Fig. 2c"}],"recommendation":"major_revision","confidential_remarks":"The absence of direct magnetic characterization is the key correctness risk. If the authors cannot provide magnetometry or equivalent data, the manuscript could be reframed as a symmetry-based transport characterization that does not claim to establish compensated altermagnetic order. The sign inconsistency in the ρxy fitting expressions and the incorrect odd-Hall isolation formula in S2 should also be fixed before the paper is reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this paper if you track MnTe transport. The headline is that the paper provides the cleanest angular-resolved magnetotransport data so far for epitaxial MnTe, including a zero-field 12-contact circular device that shows a sin2ψ transverse response, and it decomposes ρxx and ρxy into 2φ, 3φ, and 6φ components in three field-rotation planes. Those are genuinely new measurements, not in the cited references. The crystal quality is well documented (XRD, RHEED, AFM), and the fits are internally consistent: the zero-field circular-device signal mirrors the in-plane 2φ term measured at high field.\n\nThe paper's main claim is that these angular dependencies reveal the interplay between altermagnetic order and hexagonal crystal symmetry. That attribution stands only if the films are fully compensated with zero net magnetization. The authors do not measure magnetization, neutron, or XMCD on these films. They cite ref. 27, which explicitly reports weak magnetization coexisting with the anomalous Hall effect in nominally collinear MnTe. So a parasitic or canted moment is a concrete alternative that could generate 2φ and, via hexagonal anisotropy, higher harmonics. This is a load-bearing gap, not a cosmetic one, though it is addressable.\n\nTwo smaller technical issues. The supplementary S2 formula for isolating the \"odd\" Hall signal writes ρodd = [ρ(H)+ρ(−H)]/2, which is the symmetric combination; if that is a typo, it needs fixing, otherwise the AHE extraction is wrong. The ordinary Hall subtraction uses a linear high-field background, which can bias the spontaneous AHE estimate. The figures lack error bars and multi-device statistics, and raw data are not deposited; for a transport paper with small signals, that matters.\n\nAll of this is fixable. The work is a solid, incremental experimental contribution that deserves a serious referee. My honest verdict: conditional accept, not full accept, until the compensation assumption is checked with magnetization data or a control experiment, and the S2 formula is corrected. If the authors close that gap, this will be a useful reference for MnTe device work.","headline":"A genuinely careful angular magnetotransport study of MnTe, but the central altermagnetism attribution rests on an unmeasured full-compensation assumption and a likely sign error in the odd-Hall isolation.","tokens_in":11815,"tokens_out":2242,"would_cite":true,"duration_ms":20899,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["75.47.-m","72.20.My"],"model":"deepseek-v4-flash","headline":"The paper claims that in epitaxial MnTe, both longitudinal and transverse transport responses are set by the relative orientation of the applied current, the Néel vector, and the hexagonal crystal axes, with the anomalous Hall effect…","keywords":["altermagnetism","MnTe thin films","anomalous Hall effect","anisotropic magnetoresistance","crystal symmetry","Néel vector","hexagonal NiAs structure","magnetotransport"],"falsifier":"A direct magnetization measurement on the same 40-nm MnTe films with SQUID or vibrating-sample magnetometry would settle the attribution: if a net moment large enough to account for the anomalous Hall amplitude is present, conventional ferromagnetic anisotropic magnetoresistance and anomalous Hall models could reproduce the angular data without invoking altermagnetic order.","tokens_in":10664,"feed_emoji":"🧲","tokens_out":8219,"duration_ms":65123,"temperature":0.7,"pith_summary":"Altermagnets are magnetic materials with fully compensated antiparallel spins whose crystal symmetry still lifts the spin degeneracy of the electronic bands, giving them ferromagnet-like behavior with no net magnetization. This paper studies 40-nm epitaxial MnTe films and demonstrates that the longitudinal resistivity $\\rho_{xx}$ and the transverse Hall resistivity $\\rho_{xy}$ both depend on the angle between the applied current and the Néel vector, and on the orientation of the hexagonal crystal axes. When a magnetic field strong enough to align the Néel vector is rotated in the basal plane, the angular data decompose into a $2\\varphi$ magnetic part, a $6\\varphi$ crystalline part in $\\rho_{xx}$, and a $3\\varphi$ anomalous Hall part in $\\rho_{xy}$ — the signature of altermagnetic order. The authors also observe a spontaneous anomalous Hall effect at zero field whose sign and magnitude are controlled by the Néel-vector direction, as demonstrated in a circular device with current injected along different crystal axes. The paper concludes that the interplay of altermagnetic order and crystal symmetry governs the magnetotransport of MnTe, offering a basis for devices that read or control the Néel vector through electrical transport.","feed_headline":"MnTe's transport angles match both spin and crystal order","feed_subtitle":"Rotating the field splits resistivity into 2φ magnetic, 6φ crystal, and 3φ altermagnetic Hall parts.","key_machinery":"The central object is the angular-harmonic decomposition of the resistivities under rotation of the Néel vector within the basal plane. For MnTe, with its hexagonal NiAs structure and two Mn sublattices related by crystal rotation symmetry, the symmetry analysis reduces the angular dependence to $\\rho_{xx} = \\rho_2\\cos(2\\varphi) + \\rho_4\\cos(4\\varphi) + \\rho_6\\cos(6\\varphi)$ and $\\rho_{xy} = -\\rho_2\\sin(2\\varphi) + \\rho_3\\sin(3\\varphi) - \\rho_4\\sin(4\\varphi)$, which separates the twofold non-crystalline magnetic anisotropy from the four- and sixfold crystalline terms and from the threefold anomalous-Hall term that requires altermagnetic order. In the high-field regime above the spin-flop transition the Néel vector tracks the field, so $\\varphi$ becomes the field angle; in the circular-device measurement the Néel vector is pinned to a crystal axis and only the current angle $\\psi$ is varied, giving the same relative-orientation control.","core_discovery":"The central claim is that the magnetotransport of epitaxial MnTe is set by the relative orientation of the current, the Néel vector, and the hexagonal crystal lattice, and that the altermagnetic order contributes a measurable anomalous Hall term. Below the Néel temperature, the films show a spontaneous anomalous Hall effect whose hysteresis closes at a spin-flop transition, and the angular dependence in three rotation planes is fitted by the symmetry-allowed harmonics: $\\rho_{xx} = \\rho_2\\cos(2\\varphi) + \\rho_4\\cos(4\\varphi) + \\rho_6\\cos(6\\varphi)$ and $\\rho_{xy} = -\\rho_2\\sin(2\\varphi) + \\rho_3\\sin(3\\varphi) - \\rho_4\\sin(4\\varphi)$, where $\\varphi$ is the in-plane field angle relative to the current. The dominant $2\\varphi$ terms are magnetic, the $6\\varphi$ term reflects the hexagonal basal-plane symmetry, and the $3\\varphi$ Hall term is the fingerprint of the altermagnetic anomalous Hall effect. A zero-field circular device yields a transverse response scaling as $\\sin(2\\psi)$ with the current direction $\\psi$, confirming that the current–Néel-vector relative orientation controls the response without an applied field.","pith_inferences":["A direct magnetization measurement on these films would strengthen or revise the central attribution, since a weak net moment could mimic the observed angle dependence through conventional ferromagnetic mechanisms.","The same three-plane angular scans could be adopted as a standard protocol to map the full anisotropy landscape of hexagonal altermagnets, including the out-of-plane orbital-magnetization contribution hinted at in the z-axis scans.","A testable extension is to compare the $3\\varphi$ Hall amplitude between the two non-equivalent in-plane current directions, checking whether its sign flips as expected if the anomalous Hall coefficient is tied to a specific Néel-vector orientation."],"forward_implications":["The $3\\varphi$ Hall component provides a transport-only fingerprint for detecting and tracking Néel-vector reorientation in altermagnetic MnTe.","Angle-dependent magnetotransport can act as an electrical detwinning probe, since rotating the field selects and reorients Néel domains below the spin-flop field.","Interface or memory devices can encode information in the zero-field transverse response, whose sign and magnitude follow the relative angle between current and crystal axes.","The harmonic decomposition transfers to other hexagonal altermagnets, giving a scheme to separate magnetic and crystalline anisotropy contributions in their transport."],"supporting_citations":[{"why":"The baseline observation of a spontaneous anomalous Hall effect in an unconventional compensated magnetic phase, which this paper reproduces and extends to angle-resolved transport.","marker":"[23]"},{"why":"The cited coexistence of anomalous Hall effect and weak magnetization in MnTe, which motivates the paper's altermagnetic attribution and its limits.","marker":"[27]"},{"why":"Supports the predicted dependence of the anomalous Hall effect on Néel-vector orientation relative to crystal axes, which the in-plane angular scans test.","marker":"[31]"},{"why":"Supplies the sixfold crystalline anisotropic magnetoresistance decomposition used to fit the longitudinal resistivity.","marker":"[37]"},{"why":"The prior anisotropic magnetoresistance study of altermagnetic MnTe that the angular-harmonic analysis builds on.","marker":"[38]"},{"why":"The general model of twofold non-crystalline anisotropic magnetoresistance used for the magnetic component.","marker":"[39]"},{"why":"Earlier demonstration of multiple-stable anisotropic magnetoresistance memory in MnTe, connecting the observed angle dependence to device functionality.","marker":"[22]"},{"why":"Experimental observation of giant altermagnetic band splitting in MnTe, establishing the material background for the transport interpretation.","marker":"[24]"}],"fun_headline_variants":["Spontaneous anomalous Hall effect observed in altermagnet MnTe","MnTe transport depends on current, Neel vector, and crystal symmetry","Altermagnetic MnTe's transport reveals symmetry interplay","MnTe's anomalous Hall effect depends on Neel vector orientation","Crystal and spin symmetries both shape MnTe's transport"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The films are assumed to be fully compensated altermagnets with zero net magnetization, so the observed anomalous Hall effect and anisotropic magnetoresistance are attributed to altermagnetic spin splitting and Berry curvature rather than to a parasitic ferromagnetic moment.","fun_headline_variants_meta":{"raw":{"variants":["Spontaneous anomalous Hall effect observed in altermagnet MnTe","MnTe transport depends on current, Neel vector, and crystal symmetry","Altermagnetic MnTe's transport reveals symmetry interplay","MnTe's anomalous Hall effect depends on Neel vector orientation","Crystal and spin symmetries both shape MnTe's transport"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001389,"raw_usage":{"total_tokens":5657,"prompt_tokens":1014,"completion_tokens":4643,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":4557}},"tokens_in":630,"tokens_out":4643,"duration_ms":31926,"temperature":1.0,"reasoning_tokens":4557,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:31:41.151854+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct magnetization measurement on the same 40-nm MnTe films with SQUID or vibrating-sample magnetometry would settle the attribution: if a net moment large enough to account for the anomalous Hall amplitude is present, conventional ferromagnetic anisotropic magnetoresistance and anomalous Hall models could reproduce the angular data without invoking altermagnetic order.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The baseline observation of a spontaneous anomalous Hall effect in an unconventional compensated magnetic phase, which this paper reproduces and extends to angle-resolved transport."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The cited coexistence of anomalous Hall effect and weak magnetization in MnTe, which motivates the paper's altermagnetic attribution and its limits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the predicted dependence of the anomalous Hall effect on Néel-vector orientation relative to crystal axes, which the in-plane angular scans test."},{"cited_title":"K.; Agireen, I.; Maniv, E.; Goldstein, M.; Dagan, Y","cited_arxiv_id":null,"evidence_quote":"Supplies the sixfold crystalline anisotropic magnetoresistance decomposition used to fit the longitudinal resistivity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The prior anisotropic magnetoresistance study of altermagnetic MnTe that the angular-harmonic analysis builds on."},{"cited_title":"Anisotropic magnetoresistance: materials, models and applications","cited_arxiv_id":null,"evidence_quote":"The general model of twofold non-crystalline anisotropic magnetoresistance used for the magnetic component."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier demonstration of multiple-stable anisotropic magnetoresistance memory in MnTe, connecting the observed angle dependence to device functionality."},{"cited_title":"Observation of a giant band splitting in altermagnetic MnTe","cited_arxiv_id":null,"evidence_quote":"Experimental observation of giant altermagnetic band splitting in MnTe, establishing the material background for the transport interpretation."}],"review_version":1}