{"id":"b11b81f5-e033-4365-9c0c-4186ae06287b","arxiv_id":"2507.12587","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A model calculation attributes current-induced out-of-plane spin densities in TMD/ferromagnet heterostructures to itinerant orbital angular momentum, not atomic orbital moments.","lead":"This paper models how an electric current in a low-symmetry molybdenum telluride monolayer creates swirling orbital motion that is about a thousand times larger than the electron spin response. The authors argue this 'itinerant' orbital motion transfers into an adjacent ferromagnet and generates the out-of-plane spin polarization needed to switch tiny magnets.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The FM spin density attributed to itinerant OAM is never causally separated from direct leakage of the TMD's own current-induced spin polarization; the mechanism is inferred from magnitude comparisons only.","rationale":"The reader's conditional verdict is appropriate, but my load-bearing concern is the causal link in the heterostructure, not only the OAM operator or minimal model. The reader's weakest_assumption field names the operator/model issue; the causal gap appears in the reader's rationale but is not the selected weakest assumption. I agree that the paper needs additional support before the central claim can be accepted. The proposed leakage-baseline control is a decisive, implementable test: it separates OAM-mediated conversion from simple wavefunction leakage of the TMD's own spin response. If the leakage baseline already explains the FM spin density, the title claim is overreaching and the paper should be revised to present the heterostructure result as a proximity-induced spin response rather than an OAM-transfer mechanism. If it does not, the conditional acceptance should stand pending the operator/model checks. I therefore keep the reader's CONDITIONAL verdict unchanged.","tokens_in":9176,"tokens_out":15759,"duration_ms":192923,"concrete_test":"Compute a leakage baseline for the weak-hybridization case: take the isolated TMD spin susceptibility chi^{Sz}_x(E), weight it by the FM-layer projection of the corresponding TMD-derived eigenstates in the coupled system, and compare this baseline with the full heterostructure chi^{Sz}_x(E) shown in Fig. 2(b). If the baseline reproduces the full curve, the FM spin density is proximity leakage and the itinerant-OAM transfer claim is not supported. If the full response is substantially larger than the baseline, the OAM-conversion mechanism would be corroborated. Repeat the same comparison for the strong-hybridization case in Fig. 2(f).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central application claim—that itinerant OAM generated in the TMD transfers across the interface and produces the spin density in the FM—is not established by the calculation. In the heterostructure section, the FM is modeled with px/py/pz orbitals plus exchange splitting and no resolved SOC; its isolated spin susceptibility is zero by symmetry, so any spin density on FM sites must come from hybridization with the TMD. But the isolated TMD already has a nonzero current-induced spin susceptibility (Fig. 1(c), blue), only 10^3 times smaller than the itinerant OAM response. When TMD and FM hybridize, the TMD's spin-polarized Bloch states acquire weight on FM sites, so a nonzero Sz projected on the FM is expected from direct spin leakage alone, with no OAM transfer or orbital-to-spin conversion involved. The paper rules out the ACA orbital-torque channel by noting that the FM spin density is about 4 times larger than the ACA orbital density, but this comparison does not rule out the spin-leakage channel. Because the FM has no SOC, OAM cannot be converted to spin inside the FM; any conversion must occur in the TMD, which blurs the claimed transfer mechanism. Thus the title's causal statement is an inference from correlated nonzero responses, not a demonstrated mechanism.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript investigates current-induced orbital and spin densities in low-symmetry transition-metal dichalcogenide monolayers, specifically 1Td-MoTe2, using the Kubo-Bastin linear-response formalism combined with the kernel polynomial method and a real-space representation of the itinerant orbital angular momentum operator. The authors report that the itinerant OAM response exceeds the spin response by about three orders of magnitude in the isolated monolayer, and that in a TMD/ferromagnet heterostructure the itinerant OAM generated by the orbital Rashba-Edelstein effect transfers across the interface and produces out-of-plane spin density in the ferromagnet. The paper concludes that itinerant OAM is the dominant electrically generated angular momentum channel and proposes this as a mechanism for magnetization control.","tokens_in":9420,"tokens_out":4410,"duration_ms":54173,"significance":"If demonstrated, the work would be significant for orbitronics and for proposals to control magnetization without heavy metals. The strengths of the paper are its use of standard linear-response machinery, tight-binding parameters taken from prior DFT-based work, and the absence of any fitting of the calculated responses to the headline ratio. The energy-resolved spin and orbital susceptibilities are presented clearly, and the dependence on the inversion-breaking parameter is checked. However, the central claims are weakened by the minimal model's orbital content, which guarantees a vanishing ACA contribution, and by the lack of a causal separation in the heterostructure calculation between direct spin leakage from the TMD and the claimed OAM transfer mechanism. These issues are load-bearing for the title's claim that spin polarization is driven by itinerant OAM.","major_comments":[{"comment":"The minimal model of Eq. (3) contains only py and dyz orbitals, and the text states that the ACA matrix elements of Lz are zero for these orbitals. The conclusion that itinerant OAM dominates charge-to-orbital conversion is therefore partly guaranteed by the choice of basis and does not test the claim against the full orbital manifold of 1Td-MoTe2. To establish the 'three orders of magnitude' statement as a material property rather than a model artifact, the authors should include orbitals with nonzero atom-centered OAM, for example dxy/dx2-y2 or other d orbitals, or use a DFT-derived tight-binding model containing the full orbital manifold, and compare the ACA and itinerant susceptibilities in that setting.","section":"Orbital Rashba-Edelstein Effect in 1Td TMDs; Eq. (3)"},{"comment":"The real-space itinerant OAM operator in Eq. (2) is one of several definitions discussed in Refs. 56-58, and the decomposition into ACA and itinerant parts is operator-dependent. The manuscript does not justify why Eq. (2) is the physically correct representation of OAM for these systems, nor does it show that the predicted dominance of itinerant OAM is robust against the alternative definitions. A comparison of the itinerant susceptibility obtained from Eq. (2) with the approaches of Refs. 56-58 would quantify this uncertainty; as written, the headline ratio may reflect the choice of operator rather than a robust physical property.","section":"Methodology; Eq. (2)"},{"comment":"The heterostructure section claims that any spin density induced in the FM arises from hybridization with the TMD, and then attributes that spin density to itinerant OAM transfer. However, the isolated TMD already possesses a nonzero current-induced spin susceptibility (Fig. 1(c), blue), and the FM has no SOC and no intrinsic spin response. When the TMD and FM hybridize, the spin-polarized TMD Bloch states acquire weight on FM sites, so a nonzero Sz projected onto the FM is expected from direct spin leakage alone, with no OAM transfer or orbital-to-spin conversion involved. The argument that the spin density is about four times larger than the ACA orbital density does not rule out this direct spin-leakage channel. To support the causal claim, the authors should separate the direct spin-leakage contribution from the OAM-mediated contribution, for example by computing the FM spin density with the TMD spin response suppressed or by decomposing the FM spin density into contributions from the TMD spinor components.","section":"Orbital-driven spin polarization in van der Waals heterostructures; Fig. 2"}],"minor_comments":[{"comment":"The caption contains a typo: 'show s' should be 'shows'.","section":"Fig. 2(e)"},{"comment":"The abstract and conclusion state that the mechanism can induce magnetization dynamics, but the paper computes static linear-response susceptibilities and does not calculate torques or magnetization dynamics. Please qualify this statement or explicitly connect the computed susceptibilities to torque expressions.","section":"Abstract and Conclusion"},{"comment":"The strong-hybridization case uses η = 108 meV, which is twenty times larger than the weak-hybridization value of 5.4 meV. The physical correspondence of this value to a displacement field or structural distortion should be clarified, since it is far outside the range used for the isolated monolayer.","section":"Fig. 2(e), strong hybridization"},{"comment":"The main text does not state the KPM numerical parameters, such as system size, number of Chebyshev moments, and the broadening used in the Green's function expansion. These should be given explicitly or with a clear reference to the Supplemental Material so that convergence of the reported susceptibilities can be assessed.","section":"Methodology, Figs. 1-2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and addresses a timely topic in orbitronics. The proposed mechanism is plausible, but the current evidence does not distinguish it from direct spin leakage in the heterostructure, and the isolated-layer claim is weakened by the choice of orbitals. If the authors can provide the additional model calculations and control decompositions suggested in the major comments, I would support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline: this paper has a genuinely new numerical result—current-induced orbital and spin densities on a ferromagnet adjacent to a low-symmetry TMD—but the causal interpretation attached to it, that itinerant OAM is transferred and converted into spin, is not actually demonstrated. The calculation is internally consistent and the method is sound; the interpretation is a magnitude-based inference.\n\nWhat is new: the heterostructure calculation itself. The isolated-MoTe2 result, that the itinerant OAM response exceeds spin by about three orders of magnitude, is already in the cited literature; the coupled FM calculation is not. The setup is clean: a square-lattice FM with px/py/pz orbitals has zero intrinsic spin and orbital responses, so any signal on FM sites must come from hybridization with the TMD. The Kubo-Bastin/KPM machinery is standard, and the parameters come from prior DFT-based work, not from fitting the headline ratio. That is real evidence.\n\nThe soft spots are where the reader and the stress-test agree. First, the minimal model contains only py and dyz orbitals, whose atom-centered Lz matrix elements vanish by construction. So the dominance of itinerant OAM is partly baked into the model, not a fair comparison against the full orbital manifold. The authors acknowledge this in the text, but the abstract does not.\n\nSecond and more serious: the FM spin density could be direct leakage of the TMD's own current-induced spin polarization, which is nonzero only about 10^3 below the OAM response. The paper rules out the ACA orbital-torque channel by comparing spin density to ACA orbital density, but that comparison does not rule out spin leakage. Since the FM has no SOC, any OAM-to-spin conversion must happen in the TMD, which blurs the claimed transfer mechanism. This is a load-bearing gap in the title's causal claim.\n\nThird, the supplement is missing. Parameters, KPM details, and the separation of Fermi-sea and surface contributions are all deferred to an SM that does not exist in this version. That alone makes the paper hard to referee.\n\nSummarizing: this is useful as a model study of proximity-induced spin and orbital densities in TMD/FM stacks, and it deserves a serious referee. But the central mechanism—that itinerant OAM is what drives the spin polarization—needs a controlled test, such as switching off TMD SOC or explicitly separating spin leakage from OAM conversion. I would not cite it as evidence for OAM-driven torques yet.\n\nRecommendation: send it to peer review, expecting major revision. The referee time is warranted because the heterostructure setup is a good test bed and the missing separation of channels is fixable.","headline":"A clean model calculation of proximity-induced spin and orbital densities in TMD/FM stacks, but the claim that itinerant OAM drives the spin signal is not separated from direct spin leakage.","tokens_in":9989,"tokens_out":4031,"would_cite":false,"duration_ms":49467,"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":"This paper claims that in low-symmetry transition-metal dichalcogenides, current-induced itinerant orbital angular momentum exceeds the spin response by three orders of magnitude and, when coupled to a ferromagnet, transfers across the…","keywords":["itinerant orbital angular momentum","orbital Rashba-Edelstein effect","spin polarization","transition-metal dichalcogenides","van der Waals heterostructures","spin-orbit torque","Kubo-Bastin formalism","1Td-MoTe2"],"falsifier":"A first-principles calculation of the charge-to-orbital conversion in 1Td-MoTe2 using the full set of atomic orbitals and the modern theory of orbital magnetization: if the atom-centered or full-manifold orbital response comes within an order of magnitude of the itinerant response, or exceeds it, the paper's claim that itinerant OAM dominates would be falsified.","tokens_in":8934,"feed_emoji":"🧲","tokens_out":6114,"duration_ms":63814,"temperature":0.7,"pith_summary":"The paper attempts to establish that, in low-symmetry transition-metal dichalcogenide monolayers such as 1Td-MoTe2, the orbital angular momentum carried by moving electrons — its 'itinerant' part — is the dominant response to an applied current, exceeding the spin response by roughly three orders of magnitude. It then argues that this itinerant orbital angular momentum, created by the orbital Rashba-Edelstein effect, can cross a van der Waals interface into a ferromagnet that by itself has no orbital or spin response, producing out-of-plane spin densities in the ferromagnet. If correct, this would supply a microscopic mechanism for the out-of-plane anti-damping torques seen in recent TMD/ferromagnet experiments and point toward magnetization control without heavy metals.","feed_headline":"Orbital motion beats spin by 1000x in TMDs","feed_subtitle":"Electron orbital motion, not spin, carries the response, and this flow across a TMD-ferromagnet interface can steer magnetization.","key_machinery":"The load-bearing object is the real-space 'itinerant' OAM operator, which defines orbital angular momentum from position and velocity operators (and Green's functions) rather than from atomic-site matrix elements. This operator is inserted into the Kubo-Bastin formula for the susceptibility, and the Green's functions are expanded in Chebyshev polynomials via the kernel polynomial method. It is paired with a minimal tight-binding Hamiltonian containing py and dyz orbitals per site for the TMD and a Slater-Koster px/py/pz ferromagnet; the fact that py and dyz have zero atom-centered OAM means the calculated dominance of the itinerant part is built into the model.","core_discovery":"The central claim is that itinerant orbital angular momentum, not spin or atom-centered orbital moment, is the dominant source of electrically generated angular momentum in low-symmetry TMDs. Using a real-space formulation of the OAM operator combined with the Kubo-Bastin linear-response formula, the authors compute current-induced spin and orbital susceptibilities for the minimal two-orbital model of 1Td-MoTe2 and find the itinerant OAM response about a thousand times larger than the spin response. When this TMD is coupled to a ferromagnet modeled with px, py, pz orbitals on a square lattice, which has vanishing intrinsic spin and orbital responses, the itinerant OAM generated in the TMD transfers across the interface and imprints an out-of-plane spin density in the ferromagnet, with the spin density roughly four times larger than the atom-centered orbital density. The authors conclude that the itinerant OAM mechanism, particularly when the TMD and ferromagnet bands hybridize near the Q point, explains the observed out-of-plane spin torques and provides an engineering route for magnetization control.","pith_inferences":["An implication not tested in the paper: the three-orders-of-magnitude ratio depends on the chosen OAM operator and on restricting the model to py and dyz orbitals; a full-orbital DFT calculation with the modern theory of orbital magnetization could either confirm or shrink it.","A natural next experiment is gating a TMD/ferromagnet stack and measuring the sign of the out-of-plane torque: if the OREE picture is right, the torque sign should follow the displacement-field reversal of the Berry curvature dipole.","The same framework should apply to other low-symmetry 2D materials such as 1Td-WTe2 and TaIrTe4, where out-of-plane OAM and antidamping torques have been reported, and to orbital torque in light-element systems."],"forward_implications":["Charge-to-angular-momentum conversion in low-symmetry TMDs is dominated by itinerant OAM, so spin-orbit torques in such systems should be analyzed with the full OAM operator rather than atom-centered orbital moments.","A TMD with negligible intrinsic atomic OAM can still inject orbital angular momentum into an adjacent ferromagnet, producing out-of-plane spin densities that can act on magnetization; hybridization near the Q point maximizes the effect.","Reversing the displacement field, changing the sign of the symmetry-breaking parameter, reverses both spin and orbital susceptibilities, giving an electrostatic handle to switch the sign of the induced torque.","The mechanism offers a path to field-free magnetization switching in low-symmetry TMD/ferromagnet heterostructures without relying on heavy metals."],"supporting_citations":[{"why":"Supplies the real-space representation of the itinerant OAM operator used in Eq. (2).","marker":"[51]"},{"why":"Provides the minimal two-orbital tight-binding model for low-symmetry TMDs used in Eq. (3).","marker":"[60]"},{"why":"Gives the Kubo-Bastin linear-response formula that underlies the susceptibility calculations.","marker":"[53]"},{"why":"Describes the kernel polynomial method used to expand the Green's functions for real-space transport.","marker":"[52]"},{"why":"Supports the attribution of the response along y to Fermi-sea contributions accessible through exchange splitting in the ferromagnet.","marker":"[64]"},{"why":"Connects the reversal of the Berry curvature dipole to the reversal of charge-to-orbital conversion under displacement field changes.","marker":"[35]"},{"why":"Links experimentally observed antidamping torques to the orbital Rashba-Edelstein effect, which the paper explains mechanistically.","marker":"[50]"}],"fun_headline_variants":["Itinerant orbital momentum beats spin by 1000x","Orbital flow across interface sets spin direction","Orbital motion, not spin, steers magnetization","OAM transfer generates spin densities in ferromagnets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the assumption that the real-space 'itinerant' angular momentum formula is the correct definition of orbital angular momentum for these materials, and that the simplified model containing only py and dyz orbitals captures the low-energy physics of 1Td-MoTe2; because those orbitals carry no atomic-site angular momentum by construction, the model itself ensures the itinerant part dominates.","fun_headline_variants_meta":{"raw":{"variants":["Itinerant orbital momentum beats spin by 1000x","Orbital flow across interface sets spin direction","Orbital motion, not spin, steers magnetization","OAM transfer generates spin densities in ferromagnets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000258,"raw_usage":{"total_tokens":1584,"prompt_tokens":948,"completion_tokens":636,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":564,"completion_tokens_details":{"reasoning_tokens":570}},"tokens_in":564,"tokens_out":636,"duration_ms":7915,"temperature":1.0,"reasoning_tokens":570,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:44:06.788365+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A first-principles calculation of the charge-to-orbital conversion in 1Td-MoTe2 using the full set of atomic orbitals and the modern theory of orbital magnetization: if the atom-centered or full-manifold orbital response comes within an order of magnitude of the itinerant response, or exceeds it, the paper's claim that itinerant OAM dominates would be falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the real-space representation of the itinerant OAM operator used in Eq. (2)."},{"cited_title":"Vila , author C.-H","cited_arxiv_id":null,"evidence_quote":"Provides the minimal two-orbital tight-binding model for low-symmetry TMDs used in Eq. (3)."},{"cited_title":"Bastin , author C","cited_arxiv_id":null,"evidence_quote":"Gives the Kubo-Bastin linear-response formula that underlies the susceptibility calculations."},{"cited_title":"Fan , author J","cited_arxiv_id":null,"evidence_quote":"Describes the kernel polynomial method used to expand the Green's functions for real-space transport."},{"cited_title":"Medina Due \\ n as , author J","cited_arxiv_id":null,"evidence_quote":"Supports the attribution of the response along y to Fermi-sea contributions accessible through exchange splitting in the ferromagnet."},{"cited_title":"\\ Pan , author D","cited_arxiv_id":null,"evidence_quote":"Links experimentally observed antidamping torques to the orbital Rashba-Edelstein effect, which the paper explains mechanistically."}],"review_version":1}