{"id":"82a2faf2-c9c9-419d-a1b7-7e47f2bd5815","arxiv_id":"2505.18029","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The skyrmion lattice in MnSi shows both Hall and longitudinal emergent reactance only during current-driven creep motion, attributed to skyrmion mass and internal deformation modes.","lead":"Researchers measured the complex electrical response of a current-driven skyrmion lattice in the magnet MnSi and found a phase-shifted (reactive) signal that appears only when the skyrmion lattice is creeping under current. The result is a new example of emergent electromagnetism, where moving electron spins act like an inductor or capacitor, and could open a way to tune the phase of AC currents in spintronic devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The longitudinal reactance attribution is not established: the paper's own spin-tilting calculation gives the wrong sign and the phason contribution is explicitly deferred to future work.","rationale":"The reader's phase-rotation concern is legitimate, but the data provide some indirect protection: the signals are confined to the SkL phase, appear only above the creep threshold, and Im[ρyx] changes sign with frequency while Im[ρxx] does not. A simple fixed phase error would not naturally produce this structure, so I do not regard the extrinsic-correction issue as the most decisive. The decisive gap is internal to the paper's claimed mechanism. In SI §V, the only calculated deformation contribution to the longitudinal emergent field is positive, whereas the measured Im[ρxx] is negative, and the authors explicitly defer the needed phason calculation to future work. Since the abstract and title assert that the longitudinal reactance is generated by phason and spin-tilting modes, this is a load-bearing part of the central claim, not a minor interpretive detail. The proposed calculation would settle it directly. Credit is due for the clean phase-constrained observation, the DC-bias consistency check, the Joule-heating controls, and the explicit admission of the missing theory. The paper is not fatally flawed, but it should remain conditional until the phason contribution is actually computed or constrained by measurements where the mode content is controlled.","tokens_in":18759,"tokens_out":9679,"duration_ms":89569,"concrete_test":"Perform the phason analog of the SI §V spin-tilting calculation: insert time-dependent φi(r,t) and βi(r,t) modes into the three-Q ansatz (main-text Eqs. 3-5), evaluate the spatially averaged emergent field (ħ/2e)⟨n·(∂x n × ∂t n)⟩ at frequency ω under an AC current, and compare the sign, frequency dependence, and order of magnitude of Im[ρxx] with Figs. 3e/4c and SI Fig. S4c. If the phason term is zero, positive, or orders of magnitude too small, the attribution to phason/spin-tilting modes is falsified. A complementary check is a time-dependent micromagnetic simulation of a pinned skyrmion lattice driven by AC current in the creep regime, with the same observable computed from the spin configuration.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim includes the attribution of the longitudinal reactance to emergent electric fields generated by the phason and spin-tilting modes excited by skyrmion deformation. The only quantitative support for this attribution is the calculation in SI §V, where a spin-tilting mode βx along the current direction in the three-Q skyrmion lattice gives ⟨ex⟩ = (3ℏQ/4e) ∂tβx and ⟨ey⟩ = 0. For a harmonic drive, this contribution has the positive, inductive-like sign also found for a spin helix. The observed longitudinal reactance Im[ρxx] is negative in the creep region (Figs. 3e and 4c). The paper then states that the phason mode is expected to play an important role because the sign is negative, and that further theoretical investigation remains a subject for future research. This is an explicit admission that neither the sign nor the magnitude of the longitudinal reactance has been derived for the three-Q skyrmion lattice. The Hall-reactance attribution is also qualitative, since Imρyx = P bem v''/jAC is introduced without a model for the sign or magnitude of v'', but the longitudinal case is more damaging because even the leading sign is not reproduced. If the negative longitudinal reactance cannot be obtained from the phason and spin-tilting modes, the central mechanistic claim fails even though the experimental observation may be genuine.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports AC transport measurements on a microfabricated MnSi thin plate and observes imaginary components of the longitudinal and Hall resistivities that appear only in the skyrmion-lattice phase and peak in the creep-motion regime. The authors use the current-density and frequency dependence of the topological Hall resistivity to identify pinned, creep, and flow regimes, and they attribute the Hall reactance to a phase-shifted translational skyrmion velocity arising from an effective mass, and the longitudinal reactance to emergent electric fields from phason and spin-tilting modes. The Supplementary Information includes phase-rotation corrections, DC-bias checks, Joule-heating estimates, and a phenomenological calculation for one spin-tilting mode.","tokens_in":19038,"tokens_out":7051,"duration_ms":70957,"significance":"The experimental observation of a reactance confined to the moving/deforming skyrmion lattice would be a notable extension of emergent electromagnetism and could be technologically interesting because of the low threshold currents. The data set is carefully built: the reactance is phase-constrained, tied to the creep regime through independent THE measurements, reproduced under DC bias, and checked against Joule heating. However, the paper's central mechanistic attribution is not yet quantitatively established; in particular, the sign of the longitudinal reactance is not reproduced by the provided calculation, and the phason contribution that would fix the sign is explicitly deferred.","major_comments":[{"comment":"The attribution of the longitudinal reactance to phason and spin-tilting modes is not supported by the calculation presented. SI §V derives ⟨ex⟩ = (3ℏQ/4e) ∂tβx for a spin-tilting mode, which for a harmonic drive gives a positive inductive-like Im[ρxx], whereas the observed longitudinal reactance in the creep region is negative (Figs. 3e and 4c). The paper then states that the phason mode is expected to be important because of the negative sign, and that further theoretical investigation remains future work. This leaves the sign and magnitude of the central longitudinal signal unexplained. The abstract's claim that the longitudinal reactance 'results from' these modes is therefore an overstatement; it should be presented as a conjecture unless a calculation reproducing the negative sign is provided.","section":"Main text, paragraph after Eq. (5); SI §V, Eqs. (7)-(8)"},{"comment":"The Hall-reactance explanation is qualitative. The relation Imρyx = P_bem v''_sk/jAC defines the out-of-phase velocity rather than predicting it, and the sign change is attributed to 'the damping parameters, the shape of the potential, and the frequency' without a concrete model. A solution of the Thiele equation with an anharmonic pinning potential showing that v''_sk can have either sign and tracking the observed frequency and field dependence is needed to substantiate the claim that inertial translational motion is the mechanism. Without it, the statement that Im[ρyx] arises from the skyrmion effective mass is not falsifiable at the quantitative level claimed.","section":"SI §V, after Eq. (1); main text around Imρyx = P_bem v''_sk/jAC"},{"comment":"The entire intrinsic-signal conclusion rests on the assumption that the field-polarized phase has zero imaginary resistivity and that a single global phase rotation per field sweep removes all extrinsic reactance. The manuscript should quantify the uncertainty in the fitted rotation angle across the SkL field/temperature window and demonstrate that the extracted Im[ρxx] and Im[ρyx] are insensitive to the choice of the field-polarized fitting region. If the parasitic phase or extrinsic reactance varies with field or temperature, the apparent phase confinement of the reactance to the SkL could be generated by the correction procedure rather than by the sample.","section":"SI §I"}],"minor_comments":[{"comment":"The phrase 'as a important factor' should be 'as an important factor'.","section":"Abstract"},{"comment":"The fitting function uses the symbol a both as a prefactor and inside the error-function integrand; this is likely a typo and should be clarified.","section":"Methods, Eq. (7)"},{"comment":"The sentence 'Whereas, for Im[ρyx], we simply subtract this component' should read 'for Im[ρxx]', since the preceding sentence states that the symmetric extrinsic reactance is automatically removed for Im[ρyx].","section":"SI §I"},{"comment":"The sentence 'insert Eq. (3) into Eqs. (6) and (7)' should refer to Eqs. (5) and (6), since those are the equations defining ex and ey.","section":"SI §V"},{"comment":"The value JAC = 9.21 A m^-2 appears to be missing an exponent; all other current densities in the paper are of order 10^7-10^8 A m^-2.","section":"Fig. S1 caption"},{"comment":"No error bars or noise-floor estimates are shown; please add them or state the noise level quantitatively so that the magnitude of the reactance signals can be assessed.","section":"Figs. 3d-e and 4b-c"},{"comment":"The argument that the skyrmion-Hall mechanism would give Im[ρxx] and Im[ρyx] the same sign assumes a real, frequency-independent skyrmion Hall angle; this assumption should be stated explicitly or justified.","section":"Main text, paragraph after Eq. (5)"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the experimental part is solid and likely publishable, but the theoretical attribution in the abstract and conclusions goes beyond what is derived. I would ask for a revised version that either supplies the missing calculation or explicitly reframes the longitudinal mechanism as a hypothesis, and that strengthens the phase-correction controls. I do not see a need to reject the dataset."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: the experiment is probably right, and the interpretation is not. The paper reports longitudinal and Hall reactance confined to the skyrmion-lattice phase in MnSi, appearing in the creep regime and vanishing in the pinned and flow regimes. That is a new observation—prior emergent reactance was seen in helices, domain walls, and pinned skyrmion textures, not in the deformational creep regime of a moving lattice. The measurements look careful: Joule-heating checks, phase-rotation corrections, and independent extraction of the creep/flow thresholds from the topological Hall effect. The scaling comparison with bulk MnSi is a nice touch. I would trust the data. The soft spot is the mechanism, especially for the longitudinal channel. The only quantitative calculation in the SI—spin-tilting mode along the current direction—gives a positive longitudinal reactance, but the measured Im[rho_xx] is negative. The paper then says the phason mode is expected to be important because the sign is negative, and defers further theory to future work. That is honest, but it means the central attribution in the abstract is not backed by any calculation that reproduces the observed sign. The Hall reactance is also qualitative: Im[rho_yx] = P_bem v''/j_AC with no predictive model for the sign or magnitude of v'', and the sign change is attributed to unspecified damping, potential shape, and frequency. None of this makes the data wrong, but it does mean the paper is stronger as an experimental report than as a mechanistic explanation. The reader's worry about the phase-rotation correction is minor in my view. The field-polarized baseline assumption is standard, and the paper does the correction and subtraction explicitly. A residual field-dependent phase rotation would be an artifact source, but they show the signals are SkL-phase-constrained, which is hard to fake with a global rotation. Who should read this: anyone working on emergent electromagnetism in spin textures, and experimentalists studying skyrmion dynamics. It deserves a serious referee—the observation is novel and the transport controls are solid. But the referee should push for either a quantitative model that reproduces the longitudinal sign, or a softened claim that acknowledges the mechanism is not yet established. I would accept it with major revision, not desk-reject.","headline":"Solid transport data on a new creep-regime reactance in a skyrmion lattice, but the longitudinal mechanism is not established—the paper's own spin-tilting calculation gives the wrong sign.","tokens_in":743,"tokens_out":958,"would_cite":true,"duration_ms":27468,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper reports that a current-driven skyrmion lattice in MnSi shows longitudinal and Hall reactance during creep motion, and attributes the two signals to inertial translation and internal deformation respectively.","keywords":["emergent reactance","skyrmion lattice","MnSi","Berry phase","emergent electric field","skyrmion effective mass","phason modes","creep motion"],"falsifier":"A decisive check would be to measure Im[ρyx] and Im[ρxx] through the full B-T plane with the same phase-correction procedure but with the sample in a field-polarized or conical state, and to repeat the correction at several temperatures and frequencies; if the corrected imaginary resistivity in non-skyrmion phases is not identically zero, or if the inferred skyrmion-phase reactance changes when the correction is recomputed with field-dependent phase rotation, the central claim fails. A second check is whether the sign change of Im[ρyx] near 500 Hz shifts with the creep and flow boundaries as expected from the Thiele mass term.","tokens_in":18586,"feed_emoji":"🌀","tokens_out":6683,"duration_ms":57526,"temperature":0.7,"pith_summary":"The paper reports the first experimental evidence of emergent reactance in a skyrmion lattice, using MnSi as the material. It measures the imaginary (out-of-phase) parts of both the longitudinal and Hall resistivities while an AC current drives the skyrmion lattice through creep motion, in which skyrmions hop between pinning sites and deform as they move. Both signals appear only in the skyrmion-lattice phase and only above the creep threshold, and they peak in the creep region and fall in the flow region. The authors attribute the Hall reactance to the phase-shifted emergent electric field from inertial translational motion (an effective skyrmion mass), and the longitudinal reactance to emergent fields from phason and spin-tilting deformation modes. If correct, deformation of skyrmions becomes a controllable source of phase-modifying emergent electromagnetism that operates at low critical current densities.","feed_headline":"Skyrmion creep motion creates emergent AC reactance","feed_subtitle":"Hall and longitudinal out-of-phase signals trace to inertial motion and lattice deformation in MnSi.","key_machinery":"The machinery is the emergent electromagnetic field formalism, in which the Berry phase acquired by conduction electrons traversing a non-collinear spin texture acts as fictitious fields: the emergent magnetic field bem deflects electrons (topological Hall effect), while motion of the texture produces an emergent electric field eem = (ħ/2πe) n · (∂i n × ∂t n). For translational motion this reduces to eem = -vSk × bem; the velocity obeys a Thiele equation with a deformation-renormalized skyrmion mass msk, anharmonic pinning potential, gyro-coupling, and damping, which shifts the phase of vSk relative to the AC current. For deformation, the skyrmion lattice is decomposed into three helices with phason φi and spin-tilting βi modes, and the spatial average of the emergent electric field from a longitudinal spin-tilting mode is ⟨ex⟩ = (3ħQ/4e) ∂t βa, with zero transverse average. The reactance signals Im[ρyx] and Im[ρxx] are the out-of-phase parts of these emergent fields relative to the applied AC current.","core_discovery":"The central discovery claim is that a moving and deforming skyrmion lattice produces measurable out-of-phase emergent electric fields, i.e., reactance, whose two components have distinct physical origins. The transverse reactance Im[ρyx] is attributed to the inertial term msk ˙vSk in the Thiele equation: since the skyrmion mass arises from deformation that stores energy, the creep-region velocity acquires a phase shift relative to the AC current, so the emergent field eem = -vSk × bem develops an imaginary Hall component that can change sign with frequency and field. The longitudinal reactance Im[ρxx] is attributed instead to the excitation of phason and spin-tilting modes of the three-helix decomposition of the skyrmion lattice, whose time derivatives generate an emergent electric field along the current direction. The paper argues that the sign behavior distinguishes these mechanisms: only Im[ρyx] changes sign in the B-T and JAC-frequency planes, ruling out a common origin through the skyrmion Hall angle.","pith_inferences":["Editorial inference: the same two-channel decomposition could be tested in other skyrmion hosts by checking whether Im[ρyx] changes sign at a frequency set by the ratio of the effective mass to the damping, as predicted by the Thiele equation.","Editorial inference: a device exploiting creep-region reactance would need to operate near the creep threshold; since thresholds rise with frequency, the useful frequency window may be limited by the freezing of skyrmion motion.","Editorial inference: if the sign of longitudinal reactance is dominated by phason modes, thermal tuning across the skyrmion phase could provide a way to switch emergent inductance between positive and negative values.","Editorial inference: the results imply that deformation, previously treated mainly as a dissipative correction, is itself a source of reactive power in topological spin-texture circuits."],"forward_implications":["The measured reactance provides a direct electrical readout of skyrmion deformation during creep, since both signals vanish in the pinned state and are reduced in the flow state.","The sign change of Im[ρyx] around 500 Hz distinguishes inertial translational dynamics from deformation-induced longitudinal effects, offering a frequency-domain test of skyrmion effective mass.","Because the skyrmion-lattice creep threshold is lower than those of helices and domain walls, skyrmion lattices may generate emergent reactance at lower current densities than other spin textures.","The longitudinal reactance from phason and spin-tilting modes appears only when the Q-vectors are not perpendicular to the current, explaining why the conical phase (Q parallel to B) shows no signal.","The reactance is absent in the helical phase under the currents used, consistent with its higher critical current density for motion."],"supporting_citations":[{"why":"Supplies the dynamic transition and Galilean relativity framework, the skyrmion velocity expression, and the precedence for creep and flow thresholds in microfabricated devices.","marker":"[12]"},{"why":"Establishes emergent electrodynamics of skyrmions in MnSi, including the reduction of topological Hall resistivity and the relation vSk = J Δρyx/(P bem).","marker":"[16]"},{"why":"Provides the theory that phason and spin-tilting modes of a spiral magnet generate an out-of-phase emergent electric field, i.e., emergent reactance.","marker":"[20]"},{"why":"Demonstrates emergent electromagnetic induction in a helical-spin magnet, the experimental baseline that the skyrmion result extends.","marker":"[21]"},{"why":"Gives the Thiele equation used to model translational skyrmion motion with mass, gyro-coupling, and pinning.","marker":"[39]"},{"why":"Provides the deformation-renormalized skyrmion mass (inertia) that underlies the inertial translational reactance mechanism.","marker":"[40]"},{"why":"Defines phason and spin-tilting modes of the skyrmion lattice used to decompose the deformation and compute the longitudinal emergent field.","marker":"[42]"},{"why":"Recent report of emergent induction in pinned skyrmion textures, used as comparison for the creep-regime longitudinal signal.","marker":"[32]"}],"fun_headline_variants":["Deformed skyrmions yield emergent AC reactance","Skyrmion deformation drives out-of-phase electric fields","Emergent reactance from moving, deforming skyrmions","Hall and longitudinal reactance from skyrmion deformation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The identification of the measured imaginary resistivities as intrinsic skyrmion-lattice reactance assumes that the field-polarized state has exactly zero imaginary response and that a single global phase-rotation correction plus subtraction fully removes cable and instrument artifacts; if the extrinsic phase rotation or reactance varies with magnetic field or temperature, the apparent skyrmion-phase signal could be spurious.","fun_headline_variants_meta":{"raw":{"variants":["Deformed skyrmions yield emergent AC reactance","Skyrmion deformation drives out-of-phase electric fields","Emergent reactance from moving, deforming skyrmions","Hall and longitudinal reactance from skyrmion deformation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000452,"raw_usage":{"total_tokens":2295,"prompt_tokens":985,"completion_tokens":1310,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":1245}},"tokens_in":601,"tokens_out":1310,"duration_ms":10485,"temperature":1.0,"reasoning_tokens":1245,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:36:02.567508+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to measure Im[ρyx] and Im[ρxx] through the full B-T plane with the same phase-correction procedure but with the sample in a field-polarized or conical state, and to repeat the correction at several temperatures and frequencies; if the corrected imaginary resistivity in non-skyrmion phases is not identically zero, or if the inferred skyrmion-phase reactance changes when the correction is recomputed with field-dependent phase rotation, the central claim fails. A second check is whether the sign change of Im[ρyx] near 500 Hz shifts with the creep and flow boundaries as expected from the Thiele mass term.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the dynamic transition and Galilean relativity framework, the skyrmion velocity expression, and the precedence for creep and flow thresholds in microfabricated devices."},{"cited_title":"Luo, S.-Z","cited_arxiv_id":null,"evidence_quote":"Establishes emergent electrodynamics of skyrmions in MnSi, including the reduction of topological Hall resistivity and the relation vSk = J Δρyx/(P bem)."},{"cited_title":"Yokouchi, N","cited_arxiv_id":null,"evidence_quote":"Provides the theory that phason and spin-tilting modes of a spiral magnet generate an out-of-phase emergent electric field, i.e., emergent reactance."},{"cited_title":"Kimoto, H","cited_arxiv_id":null,"evidence_quote":"Gives the Thiele equation used to model translational skyrmion motion with mass, gyro-coupling, and pinning."},{"cited_title":"Neubauer, C","cited_arxiv_id":null,"evidence_quote":"Provides the deformation-renormalized skyrmion mass (inertia) that underlies the inertial translational reactance mechanism."},{"cited_title":"Iwasaki, M","cited_arxiv_id":null,"evidence_quote":"Defines phason and spin-tilting modes of the skyrmion lattice used to decompose the deformation and compute the longitudinal emergent field."},{"cited_title":"Yamane, S","cited_arxiv_id":null,"evidence_quote":"Recent report of emergent induction in pinned skyrmion textures, used as comparison for the creep-regime longitudinal signal."}],"review_version":1}