{"id":"0186c4ee-f146-494d-8119-cc88bd03e9ab","arxiv_id":"2502.10018","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Spontaneous in-plane anomalous Hall effect at zero field is observed in (111)-oriented SrRuO3 ultrathin films, coupled to in-plane spin magnetization.","lead":"Strontium ruthenate thin films with magnetization lying in the film plane show a spontaneous Hall voltage at zero magnetic field, a response that can be switched by rotating the in-plane magnetization. This extends the in-plane anomalous Hall effect from nonmagnetic and soft magnets to a conventional hard ferromagnet, pointing to new ways to control Hall transport.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Nuclear claim rests on excluding out-of-plane canting, but the zero-field polar scan (Fig. 4A) actually shows a large ρyx plateau around out-of-plane [111], leaving no independent magnetization check that the remanent state is strictly in-plane.","rationale":"The reader identified the same weakest assumption: the zero-field remanent magnetization is inferred to be strictly in-plane from transport only, with no direct magnetization measurement. In my reading of Fig. 4A, the issue is even sharper: the polar scan of ρyx,0T shows a large plateau around θ=0° ([111]) as well as near θ=90° ([112]), and the paper's own description says the plateau structure appears 'not only around the out-of-plane [111]... but also over the range including the in-plane [112].' If after polarizing at θ=0 the film retains a nonzero out-of-plane moment, the zero-field Hall signal at θ=0 would be conventional out-of-plane AHE, and the 'spontaneous in-plane' claim would not follow. The closed hysteresis around in-plane [112] shows that the remanence direction after in-plane polarization is not the out-of-plane easy axis, but it does not quantitatively exclude a partial out-of-plane component or a multi-domain state. Additional weaknesses: the higher-order-term analysis (Eqs. 1-2 and Fig. 4D) is a qualitative symmetry expansion, not a fit or first-principles calculation, so it cannot independently establish the mechanism; and the claim of 'out-of-plane orbital ferromagnetism' is inferred indirectly through the transport response without direct orbital magnetization measurement. These are not fatal—the observation of a reproducible, hysteretic, temperature-dependent zero-field Hall signal with threefold azimuthal symmetry is a solid experimental finding—but they justify a conditional verdict pending direct magnetization checks and a more quantitative model comparison. I agree with the reader's CONDITIONAL assessment and with their identification of the weakest assumption; my concrete test sharpens the required check to a quantitative remanent out-of-plane magnetization measurement and a polar-angle remanence protocol.","tokens_in":9207,"tokens_out":1967,"duration_ms":17826,"concrete_test":"Measure remanent magnetization of the same (111) SrRuO3 films at 2 K with SQUID or MOKE after in-plane 9 T polarization along [112]; if Mz/M is nonzero (>5%) at zero field, the transport zero-field signal cannot be attributed to pure in-plane AHE. Complement with a transport-only test: polar-angle remanence protocol—polarize at θ=90°, return to zero, then measure ρyx,0T as a function of subsequent polar angle; a strictly in-plane remanent state should yield ρyx,0T(θ) following the closed-loop behavior around θ=90° with zero out-of-plane plateau at θ=0°, whereas canting predicts nonzero ρyx,0T(0°).","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that the zero-field Hall signal is an in-plane AHE coupled to in-plane spin magnetization, not a conventional out-of-plane AHE from canting. The paper's only stated evidence against canting is the closed hysteresis around in-plane [112] in Fig. 4A and supporting S4. But Fig. 4A itself shows a broad, nonzero ρyx,0T plateau near the out-of-plane [111] direction: after a 9 T polarizing field at θ≈0, the remanent magnetization can include a substantial out-of-plane component, and the measured θ≈0 remanent ρyx is comparable in magnitude to the in-plane value. A hard ferromagnet with coercivity indicated by hysteretic loops can retain a partially out-of-plane remanent domain population even when easy axes are nominally in-plane, and SrRuO3 has ⟨111⟩ magnetocrystalline anisotropy that competes with shape anisotropy. Without direct magnetization data (SQUID/MOKE) or an angle-dependent remanence measurement that quantitatively shows zero out-of-plane moment, the 'spontaneous in-plane AHE at zero field' could be a conventional out-of-plane AHE from a canted or multi-domain remanent state. The claim is not disproven; it is under-supported at the most load-bearing point. Also note that Eq. (1)-(2) expansion is qualitative; the trigonal-distortion term B[100]B[010]B[001] is invoked without a parameter-free derivation or fit, so the interpretation rests even more heavily on the magnetization-direction assignment.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports magnetotransport measurements on (111)-oriented SrRuO3 ultrathin films (4.1 and 7.0 nm) at low temperature. It shows that Hall resistivity measured under an in-plane magnetic field is nonzero and hysteretic, has threefold azimuthal symmetry, and persists at zero field after in-plane polarization; the zero-field signal disappears near the Curie temperature and is reproduced in two samples and for two current directions. The authors interpret this as a spontaneous in-plane anomalous Hall effect coupled to the in-plane spin magnetization through higher-order terms allowed by trigonal distortion, and they support this with polar-angle scans that show a nonmonotonic θ dependence and a sign change near [11-1].","tokens_in":9492,"tokens_out":5299,"duration_ms":52273,"significance":"If confirmed, the observation would be the first spontaneous in-plane anomalous Hall effect in a hard ferromagnet, extending the recently studied field-induced in-plane AHE to a hysteretic material with a zero-field response. The experimental data are internally consistent: the zero-field signal tracks ferromagnetic order, appears in two samples and two current directions, and the azimuthal angular dependence matches the C3 symmetry of the (111) SrRuO3 film. The interpretation uses a standard symmetry expansion without fitted parameters. The main weakness is that the attribution of the zero-field signal to in-plane magnetization, rather than to a conventional out-of-plane AHE from a canted remanent state, is not backed by a direct magnetization measurement.","major_comments":[{"comment":"The central claim that the zero-field Hall signal is a spontaneous in-plane AHE rests on excluding out-of-plane canting of the remanent magnetization. The only evidence presented is the closed hysteresis loop near the in-plane [112] direction and the inference of in-plane easy axes from transport data. Fig. 4A itself shows a substantial ρyx,0T plateau for polarization near the out-of-plane [111] direction, with magnitude comparable to the in-plane value; for a hard ferromagnet with competing ⟨111⟩ magnetocrystalline and shape anisotropies, this is the signature expected if a partially out-of-plane remanent component survives. A direct vector magnetization measurement (SQUID or MOKE) at remanence, or an angle-resolved remanent-moment determination, is required to rule out a conventional out-of-plane AHE contribution from a canted or multi-domain remanent state. This is load-bearing for the title and abstract claims.","section":"§4, Fig. 4A and Supplementary Note S4"},{"comment":"The higher-order term B[100]B[010]B[001], introduced to explain the sign change near [11-1], is an ad hoc symmetry-allowed term: it is not derived from the trigonal distortion parameters of the film and no fit or quantitative comparison with the measured ρyx(θ) is shown. Because the agreement in Fig. 4D is only qualitative, the statement that the zero-field response is shaped by this term is plausible but not quantitatively supported. The central claim does not depend on this term alone, but the interpretation would be substantially strengthened by a comparison of the calculated curves with the data, with stated magnitudes or an estimate of the relative weight of the linear and third-order terms.","section":"Discussion, Eqs. (1)-(2) and Fig. 4D"}],"minor_comments":[{"comment":"The notation is ambiguous: B is used both as a vector (B = B α_i e_i) and as a magnitude in the prefactors B, B^3, and B^5. Using B_i or m_i for vector components would make the expansion and the terms B^3_[100] etc. easier to follow.","section":"Eqs. (1)-(2)"},{"comment":"The caption for the right panel of Fig. 2 appears to label the geometry as \"B // [111]\", which is the out-of-plane configuration shown in panel A; the in-plane configuration in panel B should be labeled with the in-plane field direction to avoid confusion.","section":"Fig. 2 caption"},{"comment":"The antisymmetrization ρyx(ϕ) = (ρyx,raw(ϕ) − ρyx,raw(ϕ+180°))/2 is used repeatedly but never explained; the text should state that this removes even-in-field longitudinal and planar-Hall contributions and isolates the odd Hall response.","section":"§3, antisymmetrization procedure"},{"comment":"The phrase \"out-of-plane orbital ferromagnetism\" is used as a conclusion, but no direct measurement of orbital magnetization is presented. It would be helpful to define the term operationally and to distinguish the inferred out-of-plane orbital moment from the measured transport signal.","section":"Abstract and Discussion"}],"recommendation":"major_revision","confidential_remarks":"The paper is of genuine interest to the Hall-effect and oxide-community readership, and I do not see a circularity problem: the observation is not defined in terms of the symmetry model, and the model is a standard expansion without fitted free parameters. The decisive risk is the absence of magnetization data at remanence. If the authors can add vector magnetometry or a quantitative angle-resolved remanent-moment measurement showing zero out-of-plane component, the central claim would be much stronger. I would not reject the manuscript on the current evidence, but the load-bearing point needs to be addressed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper reports a genuinely new transport observation — a spontaneous, hysteretic, threefold-symmetric Hall signal at zero field in (111) SrRuO3 films after in-plane polarization. The observation appears solid: it is reproducible across two samples and two current directions, tracks the ferromagnetic ordering, and the azimuthal angle dependence matches the C3 symmetry expected for the trigonal distortion. The weak spot is the interpretation. The authors attribute the zero-field signal to an in-plane AHE coupled to in-plane spin magnetization, and they rule out conventional out-of-plane canting using transport data alone. Their own Fig. 4A shows a substantial plateau in the zero-field polar scan near the out-of-plane [111] direction, which could be a conventional out-of-plane AHE from a partially out-of-plane remanent magnetization. A hard ferromagnet with competing ⟨111⟩ magnetocrystalline and shape anisotropy can retain out-of-plane domains even when the nominal easy axes are in-plane. The paper needs a direct magnetization measurement, such as SQUID or MOKE, or an angle-dependent remanence measurement that quantitatively shows zero out-of-plane moment. Without that, the central claim of a pure in-plane AHE is under-supported, though not disproven. The higher-order term analysis is also qualitative; the trigonal-distortion term B[100]B[010]B[001] is invoked to explain the sign change in the polar scans without a parameter-free derivation or a quantitative fit. That is a secondary concern. Overall, this is a careful experimental paper with a clear, novel observation. The missing magnetization data is the load-bearing gap. It deserves a serious referee, and the referee should ask for direct magnetization data before the claim is fully accepted. The paper will be of interest to experimentalists in magnetotransport and oxide thin films, and I would bring it to a reading group, though I would not build on the in-plane AHE interpretation until the remanence question is settled.","headline":"Genuinely new zero-field Hall observation in SrRuO3, but the in-plane AHE interpretation hinges on an untested assumption about strictly in-plane remanence.","tokens_in":10050,"tokens_out":2859,"would_cite":false,"duration_ms":29620,"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":"Spontaneous anomalous Hall voltage observed at zero field in a ferromagnetic oxide.","keywords":["anomalous Hall effect","in-plane magnetization","SrRuO3 thin films","spontaneous Hall response","trigonal distortion","orbital ferromagnetism","zero-field transport","ferromagnetic oxide"],"falsifier":"Perform SQUID or polar-MOKE magnetometry at 2 K on the same films using the exact 9 T in-plane polarization protocol, and compare the measured out-of-plane remanent moment with the threshold needed to produce the observed zero-field $\\rho_{yx}$ through the out-of-plane anomalous Hall hysteresis of Fig. 2A. If the out-of-plane remanence exceeds that threshold, the spontaneous in-plane interpretation fails; if it is negligible, the claim is supported.","tokens_in":8990,"feed_emoji":"🧲","tokens_out":13981,"duration_ms":125714,"temperature":0.7,"pith_summary":"This paper reports that (111)-oriented SrRuO3 ultrathin films, whose magnetization prefers to lie in the film plane, produce a spontaneous anomalous Hall voltage at zero magnetic field. The signal is hysteretic, switches sign when the in-plane magnetization direction is rotated by 60 degrees, and vanishes at the Curie temperature, so it is tied to the ferromagnetic order itself. The authors interpret it as an off-diagonal transport response: the in-plane spin magnetization generates an out-of-plane orbital ferromagnetic moment through higher-order terms that trigonal distortion makes allowed. If correct, this is the first demonstration of a spontaneous, switchable in-plane anomalous Hall effect in a hard ferromagnet, and it opens a way to engineer Hall responses without applying any magnetic field.","feed_headline":"In-plane spins produce a spontaneous Hall voltage","feed_subtitle":"The (111)-oriented oxide keeps a switchable Hall signal after the in-plane field is turned off.","key_machinery":"The load-bearing object is a symmetry-based expansion of the Hall conductivity on the Hall plane in powers of the field or magnetization direction cosines. For a cubic crystal on a (111) plane, the leading term is proportional to $B_{[100]}+B_{[010]}+B_{[001]}$, which vanishes when $B$ lies in the plane and therefore cannot produce the observed in-plane signal. The paper argues that trigonal distortion of the film, which breaks the threefold rotations about the three other $\\langle111\\rangle$ directions, allows third-order terms such as $B_{[100]}B_{[010]}B_{[001]}$; this term has the right polar-angle shape, including a local maximum at $[11\\bar{1}]$ with sign opposite to $[111]$. Replacing $B$ by the magnetization $M$ in the same expansion explains why a spontaneous Hall response survives at zero field. The machinery is therefore a phenomenological higher-order coupling between the in-plane field or spin direction and an out-of-plane Hall vector.","core_discovery":"On (111)-oriented SrRuO3 films with thicknesses of 4.1 and 7.0 nm, the Hall resistivity $\\rho_{yx}$ measured while sweeping an in-plane field reaches values comparable to the conventional out-of-plane anomalous Hall effect, and it remains finite and hysteretic after the field is returned to zero. The zero-field Hall resistivity follows a square-wave pattern with threefold symmetry as the in-plane polarizing-field direction is rotated, and it disappears above the Curie temperature. Because the films have in-plane easy axes, the authors rule out the conventional explanation through an out-of-plane magnetization canting and instead attribute the response to out-of-plane orbital ferromagnetism off-diagonally coupled to the in-plane spin magnetization. The polar-angle scans show a nonmonotonic dependence with a sign change between $[111]$ and $[11\\bar{1}]$, which in their analysis requires higher-order terms such as $B_{[100]}B_{[010]}B_{[001]}$ that become allowed under trigonal distortion.","pith_inferences":["Editorial extension: if the higher-order $M$-term mechanism is general, other trigonally distorted ferromagnetic films with in-plane easy axes and Berry-curvature-rich band structures should show the same spontaneous in-plane Hall effect, making it a design handle rather than an SrRuO3-specific accident.","Editorial extension: the paper treats the higher-order terms phenomenologically and does not quantify their relative weights, so a first-principles calculation of the anomalous Hall conductivity as a function of in-plane magnetization direction is the natural next test.","Editorial extension: the remanent, switchable Hall voltage suggests a magnetic-field-free Hall memory, but the paper does not address switching speed, cycling endurance, or whether the threefold pattern survives in patterned device geometries."],"forward_implications":["A zero-field Hall state with memory exists in a conventional ferromagnetic oxide: polarizing along an in-plane easy direction leaves a large $\\rho_{yx}$ that persists until the field is reapplied or the temperature approaches $T_C$.","The sign of the spontaneous Hall voltage is set by the in-plane magnetization direction, so a 60-degree rotation of the writing field reverses the output without requiring any out-of-plane field.","The trigonal-distortion analysis predicts a threefold-symmetric angular pattern for the in-plane anomalous Hall effect, and this pattern is observed in both the azimuthal and polar scans.","The response disappears at the Curie temperature and its magnitude follows the ferromagnetic hysteresis, indicating that it is intrinsic to the magnetic order rather than a field-geometry artifact."],"supporting_citations":[{"why":"Provide the symmetry-based requirement for Hall conductivity under an in-plane field and the in-plane AHE theory that the paper uses to identify the allowed threefold-symmetric higher-order terms.","marker":"[21, 22]"},{"why":"Earlier observations of field-induced in-plane AHE with threefold symmetry in kagome and Weyl magnets, which the paper extends from a field-induced response to a spontaneous zero-field response.","marker":"[5, 6, 7]"},{"why":"Band-structure results showing Weyl point pairs near the Fermi level in SrRuO3, used to motivate why SrRuO3 should host a large in-plane AHE.","marker":"[23, 24]"},{"why":"Previous studies of (111) SrRuO3 thin films that supply the expected Curie temperature and out-of-plane hysteresis behavior against which the present films are checked.","marker":"[26, 27, 28]"}],"fun_headline_variants":["Spontaneous Hall voltage from in-plane spins at zero field","Zero-field Hall signal flips with in-plane spin direction","SrRuO3 film shows spontaneous in-plane anomalous Hall effect","In-plane magnetization triggers spontaneous Hall response"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that after a 9 T in-plane field is removed, the film's remanent magnetization remains strictly in the plane, so the zero-field Hall voltage cannot be a conventional out-of-plane anomalous Hall effect from magnetization canting; the paper infers this from transport angle scans, notably the closed hysteresis around the in-plane $[11\\bar{2}]$ direction in Fig. 4A, without a direct magnetization measurement.","fun_headline_variants_meta":{"raw":{"variants":["Spontaneous Hall voltage from in-plane spins at zero field","Zero-field Hall signal flips with in-plane spin direction","SrRuO3 film shows spontaneous in-plane anomalous Hall effect","In-plane magnetization triggers spontaneous Hall response"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000561,"raw_usage":{"total_tokens":2649,"prompt_tokens":917,"completion_tokens":1732,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":533,"completion_tokens_details":{"reasoning_tokens":1668}},"tokens_in":533,"tokens_out":1732,"duration_ms":11640,"temperature":1.0,"reasoning_tokens":1668,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T19:40:10.176778+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform SQUID or polar-MOKE magnetometry at 2 K on the same films using the exact 9 T in-plane polarization protocol, and compare the measured out-of-plane remanent moment with the threshold needed to produce the observed zero-field $\\rho_{yx}$ through the out-of-plane anomalous Hall hysteresis of Fig. 2A. If the out-of-plane remanence exceeds that threshold, the spontaneous in-plane interpretation fails; if it is negligible, the claim is supported.","supporting_citations":[],"review_version":1}