{"id":"4361858d-7165-4e56-9061-e332fb45852c","arxiv_id":"2505.03891","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"The paper reports transport hysteresis in 9-layer rhombohedral graphene interpreted as a new transdimensional anomalous Hall effect with both out-of-plane and in-plane orbital magnetization.","lead":"Experiments on nine-layer rhombohedral graphene show magnetic hysteresis in both out-of-plane and in-plane magnetic field sweeps, interpreted as a new kind of anomalous Hall effect called transdimensional AHE. If correct, this would be the first material where both out-of-plane and in-plane orbital magnetism contribute to the Hall response.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The B-parallel hysteresis that anchors the TDAHE claim is not controlled against a ~1 degree tilt artifact: at 160 mT, 1 degree tilt yields ~2.8 mT perpendicular field, matching the 3 mT perpendicular coercive field.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the B-parallel hysteresis can be mimicked by an out-of-plane magnetization if the sample plane is tilted by about 1 degree, and the paper provides no alignment calibration to exclude this. My independent reading of the transport data and Methods confirms that no angular control or residual-field measurement is reported. The numbers are quantitatively damning: the ratio of in-plane to out-of-plane coercive fields is about 160 mT / 3 mT, which implies an apparent tilt of about 1.1 degrees. Because the symmetrization procedure preserves a tilt-induced perpendicular-field hysteresis, the standard data processing does not protect the claim. The Hartree-Fock calculations are a useful theoretical proposal, but they do not independently establish the experimental observation. The device B data in Extended Data Fig. 9 strengthen reproducibility but do not address the artifact. I therefore agree with the reader's REJECT verdict as submitted: the central claim, first observation of transdimensional AHE with in-plane orbital magnetization, is not yet established. A revision with explicit field-alignment calibration, angle-dependent control measurements, and ideally a public data release could change this assessment. I would keep the reader's verdict unchanged rather than moving it, because my concern reinforces the stated weakness rather than introducing a new one.","tokens_in":21044,"tokens_out":4069,"duration_ms":49274,"concrete_test":"Perform a controlled tilting experiment in a vector magnet at the same n and D used in Fig. 3b: measure Rxy hysteresis loops for nominal in-plane field at several sample tilt angles, e.g. theta = 0, +-0.5, +-1, +-2 degrees relative to the sample plane, using an in-situ rotation stage with calibrated angular accuracy better than 0.1 degree. If the hysteresis is caused by a residual perpendicular field, the coercive field measured in nominal B_parallel should scale as B_c^perp / sin(theta) and vanish as theta approaches zero. If the state is genuinely transdimensional with in-plane orbital magnetization, the coercive field should remain finite and roughly theta-independent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central experimental evidence for in-plane orbital magnetization is the B-parallel (B_parallel) hysteresis in the antisymmetrized Hall resistance Rxy shown in Fig. 3b and reproduced for device B in Extended Data Fig. 9b. The interpretation requires that the applied field is essentially in the sample plane, but the paper reports no alignment calibration, no in-situ angular control, and no measurement of the residual perpendicular component. At the quoted in-plane coercive field of about 160 mT, a tilt of only about 1 degree produces B_perp = B_parallel * sin(theta) ~ 2.8 mT, which is essentially the same as the out-of-plane coercive field of about 3 mT seen in Fig. 3d. A misalignment of this size is routine for mechanically exfoliated flakes unless a vector magnet with a calibrated in-plane sample mount is used. Moreover, the symmetrization/antisymmetrization procedure cannot remove this artifact: when the nominal B_parallel sweep reverses sign, a tilt-induced B_perp component also reverses, so the resulting out-of-plane Stoner-type hysteresis survives antisymmetrization and looks like an in-plane hysteresis. The paper's Methods do not state whether the magnets are vector magnets or whether the sample angle was calibrated, so this alternative explanation is not excluded. The Hartree-Fock calculation in Fig. 4d provides a plausible mechanism, but it assumes the symmetry-broken state it is trying to establish; it cannot by itself rule out a misalignment artifact in the transport data. The vertical mean free path premise (l_z > 3 nm) is also unmeasured, but the tilt artifact is the more direct threat to the headline claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the observation of a 'transdimensional anomalous Hall effect' (TDAHE) in electrostatically gated rhombohedral ennealayer graphene. The authors identify a correlated metallic phase (phase V) at low carrier density and large displacement field that shows no Shubnikov-de Haas oscillations up to 13 T. In this phase, Hall resistance hysteresis loops are observed for both out-of-plane and in-plane magnetic field sweeps (Fig. 3b, d). The in-plane hysteresis, with a coercive field of about 160 mT, is attributed to an in-plane orbital magnetization My arising from coherent out-of-plane electron motion in the 'transdimensional' regime where the sample thickness (~3 nm) is within the vertical mean free path. Unrestricted Hartree-Fock calculations predict a symmetry-broken metallic state with a crescent-shaped Fermi surface, spontaneous breaking of time-reversal, C3, and mirror symmetries, and an in-plane orbital magnetization of about 2.2 mu_B per electron. The authors argue that this constitutes a fundamentally new class of anomalous Hall effect that violates the conventional orthogonality rule E_H ∝ J x M.","tokens_in":21346,"tokens_out":7857,"duration_ms":76015,"significance":"If the claims are correct, the work is significant: it would introduce a new type of anomalous Hall effect driven by in-plane orbital magnetization, expanding the classification of Hall effects and opening a new direction in correlated-electron physics in rhombohedral graphene multilayers. The paper includes two devices, comprehensive density-displacement-field phase diagrams, quantum oscillation analysis, and a concrete theoretical mechanism. The experimental data are reproducible across devices (Extended Data Fig. 9). However, the central experimental evidence—the B-parallel hysteresis—is not convincingly separated from a likely artifact of field misalignment, and the 'transdimensional' interpretation lacks direct support for the assumed vertical mean free path. The Hartree-Fock theory provides a plausible but post-hoc and parameter-dependent scenario.","major_comments":[{"comment":"The claim that the B-parallel hysteresis evidences in-plane orbital magnetization rests on the assumption that the applied field is essentially in the sample plane. The paper does not report any calibration of the sample angle relative to the magnetic field, nor does it state whether the magnets are vector magnets or have in-situ rotation capability. At the quoted in-plane coercive field of about 160 mT, a misalignment of only about 1 degree produces a perpendicular component of about 2.8 mT, which is essentially the same as the out-of-plane coercive field of about 3 mT shown in Fig. 3d. Since phase V also exhibits out-of-plane Stoner-type hysteresis, a tilt-induced perpendicular component would generate a hysteresis loop in the B-parallel sweep that mimics the claimed in-plane magnetization. The antisymmetrization procedure described in the Methods does not remove this artifact, because the tilt-induced perpendicular component reverses sign when the nominally in-plane field reverses, and the hysteresis is odd under that reversal. The authors should provide a control measurement (e.g., a phase with out-of-plane magnetization but no in-plane magnetization, or a measurement with active compensation of the perpendicular component) and a quantitative angular calibration. Without this, the central observation is not established.","section":"Transdimensional anomalous Hall state (Fig. 3b, 3d) and Methods"},{"comment":"The term 'transdimensional' and the interpretation of the in-plane orbital magnetization require that the vertical mean free path lz be comparable to or larger than the sample thickness d ~ 3 nm. The paper asserts that d falls in the transdimensional range ('providentially within the transdimensional range') but no measurement or estimate of lz is given. Without evidence that coherent out-of-plane orbital motion survives across the thickness, the connection between the observed hysteresis and out-of-plane orbital currents is unjustified. The authors should provide an estimate of lz from the quantum oscillation lifetime or from a thickness-dependence study, or clearly state that the 'transdimensional' interpretation is one of several possibilities.","section":"Discussion and Extended Data Fig. 1d"},{"comment":"The theoretical prediction of the crescent-shaped Fermi surface and the in-plane orbital magnetization relies on parameter renormalization that involves several free inputs (epsilon_BN ~ 4, ds = 40 nm, E*_C ~ 0.3 eV, Lc = 2.25 nm). The paper does not discuss the sensitivity of the predicted orbital magnetization and the stability of the symmetry-broken state to these parameters. Additionally, the theory is presented as a post-hoc explanation (with a separate manuscript in preparation, ref. 37), so it cannot by itself disambiguate the experimental artifact discussed above. I recommend that the authors report the parameter region in which the crescent state is stable and compare the predicted anomalous Hall conductivity with the measured Rxy.","section":"Supplementary Section III (Hartree-Fock treatment) and Fig. 4d"}],"minor_comments":[{"comment":"The sentence 'using a anodic-oxidation-assisted atomic force microscope cutting' contains an article error; it should read 'using anodic-oxidation-assisted atomic force microscope cutting'.","section":"Methods"},{"comment":"The caption lists labels 'c' and 'd' twice; the figure appears to show B-parallel hysteresis (b), B-perpendicular hysteresis (c), and maps (d, e), so the labels should be corrected.","section":"Extended Data Fig. 9 caption"},{"comment":"The list of densities 'n = 0.8, 1.1, 1.4, 17, 1.9' likely contains a typo: '17' should probably be '1.7'.","section":"Fig. 3g"},{"comment":"The compound formula 'EuCd 2Sd2' appears to be a typo; it should be 'EuCd2As2' or another correct chemical formula.","section":"Introduction"},{"comment":"Abbreviations such as SdH, PIP, and LPI are used without definitions at first appearance; please define them in the main text.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The central concern is the uncontrolled field alignment: the B-parallel hysteresis could be a misalignment artifact given that phase V also shows out-of-plane hysteresis at a matching coercive field. If the authors can supply a control experiment with calibrated in-plane geometry or nulled perpendicular field, the paper would be very strong. Otherwise, the observation does not support the claimed in-plane orbital magnetization. The Hartree-Fock theory is plausible but post-hoc and parameter-sensitive, so it should not be used as a substitute for experimental control."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—\n\nYou should know two things about arXiv:2505.03891. First, it is a serious candidate for a genuinely new transport effect: coexisting out-of-plane and in-plane Hall hysteresis in a correlated metallic phase of rhombohedral ennealayer graphene, which the authors attribute to a “transdimensional” orbital ferromagnet. Second, the central experimental evidence is not yet protected against a mundane misalignment artifact, and the paper does not provide the control that would settle it.\n\nWhat is genuinely new: the transdimensional framing is thought-provoking, and the observation that phase V shows no quantum oscillations up to 13 T while sitting in a metallic region is interesting. The phase diagram work is careful—SdH frequency extraction, isospin flavor assignment, and extended data on two devices are all solid. The Hartree-Fock calculation gives a plausible mechanism: a crescent Fermi surface breaking T, C3, and My symmetries, with an in-plane orbital moment. This is worth engaging with.\n\nThe problem is in figure 3. The B-parallel hysteresis is the load-bearing evidence, but the paper never reports how well the field was aligned with the sample plane. The magnets are described as superconducting, not vector magnets, and no calibration of the in-plane angle is given. At the reported in-plane coercive field of ~160 mT, a tilt of just over one degree produces a perpendicular component of ~3 mT—the same as the out-of-plane coercive field shown in the same figure. The antisymmetrization procedure does not remove this, because reversing the nominal B-parallel sweep also reverses the tilt-induced B-perp component. The numbers are exactly consistent with the in-plane hysteresis being the out-of-plane hysteresis projected onto a slightly tilted field axis. A second, smaller issue: the interpretation assumes vertical mean free path lz larger than the 3 nm thickness, and that is not measured.\n\nThe theory side also has soft spots: the magnitude of the in-plane orbital moment is quoted as 2.2 μB per electron, but the quantitative details are deferred to an unpublished companion paper, and the RG renormalization uses formulas from a self-cited reference. That is not fatal, but it caps how much independent confirmation the theory can provide without the companion.\n\nBottom line: this is a well-made paper with a striking claim, but the central new element is vulnerable to an artifact that the work does not control for. It deserves a serious referee, but the manuscript as submitted should be revised. I would not cite it until the tilt control is done. Good reading-group topic for exactly this reason.","headline":"A bold in-plane magnetization claim in rhombohedral graphene that lacks the field-alignment calibration needed to rule out a tilt-induced artifact.","tokens_in":21977,"tokens_out":3209,"would_cite":false,"duration_ms":32386,"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":"Nine-layer rhombohedral graphene shows a Hall effect driven by in-plane orbital magnetization, breaking the rule that Hall fields require magnetization perpendicular to current.","keywords":["transdimensional anomalous Hall effect","rhombohedral graphene","in-plane orbital magnetization","orbital ferromagnetism","spontaneous symmetry breaking","Hartree-Fock calculation","van Hove singularity","correlated metal"],"falsifier":"Run the same hysteresis sweeps with the field direction calibrated in situ (for example, rotating the sample in a vector magnet to better than 0.1 degrees): if the parallel hysteresis weakens or vanishes as residual perpendicular field is removed, or tracks the perpendicular component at all tilt angles, the transdimensional claim is falsified. A second check is to measure the vertical mean free path directly, through a thickness series or magnetotransport analysis, to verify the premise that $\\ell_z$ exceeds the 3 nm thickness.","tokens_in":20820,"feed_emoji":"🧲","tokens_out":8520,"duration_ms":82303,"temperature":0.7,"pith_summary":"This paper reports the first observation of a transdimensional anomalous Hall effect in electrostatically gated rhombohedral ennealayer graphene, a nine-layer stack about three nanometres thick. The central claim is that a correlated metallic phase near the van Hove singularity breaks time-reversal, mirror, and rotational symmetries on its own, allowing electrons to sustain coherent orbital motion both in the plane and across the thickness. The result is a coexistence of out-of-plane and in-plane orbital magnetizations, seen as magnetic hysteresis in the Hall resistance for magnetic fields along both directions. If the interpretation holds, the standard rule that the Hall field must be perpendicular to both current and magnetization, $\\mathbf{E}_H \\propto \\mathbf{J} \\times \\mathbf{M}$, is violated by a genuinely new class of anomalous Hall effect that needs no spin-orbit coupling.","feed_headline":"Electrons looping out of plane create a new kind of Hall effect","feed_subtitle":"Nine-layer graphene shows Hall hysteresis for in-plane fields, opening a new route to orbital magnetism.","key_machinery":"The load-bearing object is the transdimensional orbital loop: the sample is thick enough ($d\\approx 3$ nm) to host out-of-plane electron motion, yet thin enough that the vertical mean free path $\\ell_z$ is not interrupted by scattering, so current loops can close both in the plane and through the thickness. In the correlated phase, the machinery that produces the effect is spontaneous symmetry breaking driven by long-range electron-electron interactions, treated by unrestricted Hartree-Fock theory. The calculation finds that the system breaks time-reversal, threefold rotation $C_3$, and vertical mirror $M_y$ symmetries, turning a ring-shaped Fermi surface into a crescent-shaped one whose Bloch states carry orbital magnetization parallel to the current. That in-plane orbital magnetization couples directly to an in-plane magnetic field and yields the parallel Hall hysteresis, while the coexisting out-of-plane orbital magnetization gives the perpendicular hysteresis.","core_discovery":"On the paper's own terms, the discovery is that in a narrow region of density and displacement field -- the phase labelled V, flanked by quarter-metal and partial-isospin-polarized phases -- the device shows robust magnetic hysteresis in both the perpendicular and the parallel field directions. The perpendicular hysteresis has a coercive field near 3 mT and is assigned to Stoner-type isospin ferromagnetism; the parallel hysteresis, with coercive fields between 160 and 500 mT, is assigned to the switching of an in-plane orbital magnetization arising from coherent out-of-plane electron loops. Because the measurement current lies in the plane, an in-plane orbital magnetization parallel to the current makes the observed Hall field incompatible with the conventional orthogonality relation. Unrestricted Hartree-Fock calculations support this assignment: interactions spontaneously break the threefold rotation and vertical mirror symmetries, producing a crescent-shaped, fully spin- and valley-polarized Fermi surface with an in-plane orbital magnetization of order $2.2\\,\\mu_B$ per electron, and no spin-orbit coupling in the model.","pith_inferences":["Editorial extension: if the alignment issue is resolved and the in-plane hysteresis is real, the same transdimensional mechanism should appear in other rhombohedral multilayer stacks whose thickness lies between one monolayer and the vertical mean free path, with the phase boundary set by the displacement field.","Editorial extension: the spontaneous symmetry breaking is purely orbital and needs no spin-orbit coupling, so placing a moiré superlattice on such a transdimensional state is a plausible route to quantized transdimensional anomalous Hall phases; the paper only mentions this as a future direction.","Editorial extension: the sharp collapse above 1.6 K could be dominated by the vertical mean free path shortening rather than thermal domain-wall dynamics; a thickness series of devices would separate the two mechanisms."],"forward_implications":["The anomalous Hall effect can no longer be classified only by out-of-plane orbital magnetization: a material with in-plane orbital magnetization can produce a Hall voltage even when the magnetization is parallel to the current.","The TDAHE phase resists Landau quantization up to at least 13 T, so it represents a strongly correlated metallic ground state rather than a quantum Hall or Chern insulator.","The effect survives to temperatures near 1.5 K and vanishes sharply by 1.6 K, implying an interaction energy scale that is substantial for a purely orbital, SOC-free state.","Magnetization reversal with doping at the quarter-metal boundary offers a route to electrically switch the sign of the in-plane orbital magnetization within a metallic phase, without an insulating topological gap."],"supporting_citations":[{"why":"Defines the standard anomalous Hall effect and the orthogonality rule that this paper claims to break.","marker":"[4]"},{"why":"Supplies the recent context of SOC-free, Coulomb-interaction-driven orbital magnetic states in graphene moiré systems.","marker":"[12]"},{"why":"Theoretical proposal of quantum anomalous Hall effect from in-plane magnetization; the baseline that used spin magnetization and designed spin-orbit coupling.","marker":"[18]"},{"why":"Extends the in-plane-magnetization QAHE idea to atomic crystal layers; a previous scenario this paper distinguishes from its orbital mechanism.","marker":"[19]"},{"why":"Gives the searching rule and material prediction for in-plane-magnetization QAHE; another contrast for the purely orbital state.","marker":"[20]"},{"why":"Reports orbital multiferroicity in pentalayer rhombohedral graphene, the thinner-stack context for out-of-plane orbital magnetization.","marker":"[23]"},{"why":"Demonstrates fractional quantum anomalous Hall effect in multilayer graphene, proving correlated orbital states in rhombohedral stacks.","marker":"[24]"},{"why":"Establishes the half-metal and quarter-metal phases used here to map the phase diagram around phase V.","marker":"[26]"},{"why":"Provides the electrical-switching comparison in an orbital Chern insulator used to interpret doping-induced magnetization reversal.","marker":"[28]"},{"why":"The accompanying separate theoretical work on transdimensional orbital magnetism that supplies the detailed mechanism.","marker":"[37]"}],"fun_headline_variants":["New Hall effect from electrons looping out of plane","In-plane Hall effect from orbital loops in nine-layer graphene","Transdimensional Hall effect: orbital loops both ways","Hall effect with magnetic memory in two directions","Nine-layer graphene shows novel Hall hysteresis"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim collapses if the parallel-field hysteresis is a misalignment artifact -- the paper gives no in-situ alignment calibration, and a one-degree tilt at 160 mT produces a perpendicular component equal to the measured out-of-plane coercive field -- and it also depends on the vertical mean free path exceeding the three-nanometre sample thickness, a quantity the paper does not measure.","fun_headline_variants_meta":{"raw":{"variants":["New Hall effect from electrons looping out of plane","In-plane Hall effect from orbital loops in nine-layer graphene","Transdimensional Hall effect: orbital loops both ways","Hall effect with magnetic memory in two directions","Nine-layer graphene shows novel Hall hysteresis"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1584,"prompt_tokens":1058,"completion_tokens":526,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":674,"completion_tokens_details":{"reasoning_tokens":456}},"tokens_in":674,"tokens_out":526,"duration_ms":5228,"temperature":1.0,"reasoning_tokens":456,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:43:46.305123+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same hysteresis sweeps with the field direction calibrated in situ (for example, rotating the sample in a vector magnet to better than 0.1 degrees): if the parallel hysteresis weakens or vanishes as residual perpendicular field is removed, or tracks the perpendicular component at all tilt angles, the transdimensional claim is falsified. A second check is to measure the vertical mean free path directly, through a thickness series or magnetotransport analysis, to verify the premise that $\\ell_z$ exceeds the 3 nm thickness.","supporting_citations":[{"cited_title":"Liu and X","cited_arxiv_id":null,"evidence_quote":"Supplies the recent context of SOC-free, Coulomb-interaction-driven orbital magnetic states in graphene moiré systems."},{"cited_title":"Liu, H.-C","cited_arxiv_id":null,"evidence_quote":"Theoretical proposal of quantum anomalous Hall effect from in-plane magnetization; the baseline that used spin magnetization and designed spin-orbit coupling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Extends the in-plane-magnetization QAHE idea to atomic crystal layers; a previous scenario this paper distinguishes from its orbital mechanism."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the searching rule and material prediction for in-plane-magnetization QAHE; another contrast for the purely orbital state."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports orbital multiferroicity in pentalayer rhombohedral graphene, the thinner-stack context for out-of-plane orbital magnetization."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the half-metal and quarter-metal phases used here to map the phase diagram around phase V."},{"cited_title":"Polshyn, J","cited_arxiv_id":null,"evidence_quote":"Provides the electrical-switching comparison in an orbital Chern insulator used to interpret doping-induced magnetization reversal."},{"cited_title":"Li et al","cited_arxiv_id":null,"evidence_quote":"The accompanying separate theoretical work on transdimensional orbital magnetism that supplies the detailed mechanism."}],"review_version":1}