{"id":"860400c8-e160-460d-8fcd-7c5a1fb637af","arxiv_id":"2607.12322","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In polar Weyl ferromagnet PrAlGe, AC-driven spin-orbit torques generate a time-dependent toroidal moment T=P\times M whose derivative produces a frequency-linear out-of-phase Hall voltage, demonstrating emergent toroidal induction in a uniform magnet.","lead":"Researchers observed emergent electromagnetic induction in a uniform polar ferromagnet PrAlGe, where current-driven magnetization dynamics create a time-varying toroidal moment that induces a Hall voltage. This could enable intrinsic spin-charge conversion without needing magnetic textures or interfaces.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"The frequency-linear Im Z_xy after 30 K subtraction is not yet shown to be free of residual circuit or heating artifacts at the level needed for the texture-free EEMI claim.","rationale":"The Reader correctly isolates the post-subtraction assignment of Im Z_xy as the weakest assumption. The experimental controls (Tc cutoff, field suppression, linear-f regime, higher-harmonic checks) are real and make a pure artifact explanation non-trivial, yet they do not close the loophole of a residual, magnetization-dependent circuit or heating contribution that tracks the same controls. Because the paper offers no independent microscopic estimate of the expected inductance magnitude, that loophole remains load-bearing for the texture-free EEMI interpretation. The proposed control measurement is a direct, feasible test that would settle the issue without requiring new theory. The Reader’s CONDITIONAL verdict and medium correctness risk are therefore unchanged; the concern is already the one they flagged, only sharpened to a concrete falsification protocol.","tokens_in":13351,"tokens_out":615,"duration_ms":7390,"concrete_test":"Repeat the full frequency- and field-dependent Im Z_xy measurement on an identically fabricated non-magnetic or paramagnetic isostructural Hall bar (e.g., LaAlGe or PrAlGe above Tc but with matched resistance and geometry) under the same current densities and cable configuration; any residual Im Z_xy that survives the same 30 K-style subtraction and scales with frequency would quantify the artifact floor. If that floor is ≤ 10 % of the reported ferromagnetic signal, the EEMI assignment is secure; if comparable, the claim weakens.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that the background-subtracted imaginary Hall impedance Im Z_xy is exclusively the emergent electric field e ∝ −∂T/∂t generated by collective, spatially uniform magnetization dynamics (Eq. 4 and surrounding text). The paper subtracts the entire 30 K (paramagnetic) complex response as a reference for extrinsic phase rotation (Methods; Supplementary Fig. S4) and rules out a pure Joule-heating model via higher-harmonic checks (Supplementary Fig. 5). However, residual frequency-dependent inductive or capacitive coupling that is temperature- or magnetization-dependent, or weak nonlinear heating that survives the higher-harmonic filter, would produce a signal that still vanishes above Tc, is suppressed by field (via reduced tilt), and is linear in frequency at low f—exactly the reported phenomenology. Because no absolute magnitude comparison to a microscopic calculation of L_xy is given, and the multi-step AHC-to-tilt conversion already shows that electronic-structure changes are large, the subtraction step remains the least secure link between the measured voltage and the claimed toroidal induction.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript reports that a spatially uniform polar ferromagnet, PrAlGe, can host emergent electromagnetic induction (EEMI) without real-space spin textures. An AC current drives spin-orbit torques that tilt the magnetization, generating a time-dependent toroidal moment T = P \times M that acts as an effective gauge potential; its time derivative produces an emergent electric field observed as a frequency-linear imaginary Hall impedance Im Z_xy. The signal is suppressed by magnetic field, vanishes above Tc, and is argued to be free of pure Joule-heating artifacts via higher-harmonic checks. Supporting DFT calculations show that magnetization tilt redistributes Berry curvature and displaces Weyl nodes, providing a microscopic picture of the toroidal vector as a collective shift of monopoles in momentum space. The work therefore claims a new, texture-free realization of EEMI rooted in SOC and polar symmetry.","tokens_in":13608,"tokens_out":1239,"duration_ms":12905,"significance":"If the identification of the background-subtracted Im Z_xy with e ∝ −∂T/∂t holds, the result substantially enlarges the scope of emergent electromagnetism: EEMI would no longer require domain walls, helices or skyrmions, but could appear in any non-centrosymmetric ferromagnet with strong SOC. The low current densities (~10^8 A m^{-2}) needed to drive the dynamics and the explicit link to Weyl-node motion are attractive for both fundamental topology and potential spintronic inductors. The experimental phenomenology (linear frequency dependence, Tc cutoff, field suppression) is coherent and the DFT maps of Berry-curvature reconstruction under tilt are a clear strength. The principal remaining uncertainty is whether residual circuit or magnetization-dependent artifacts have been fully excluded by the 30 K subtraction, which is load-bearing for the texture-free claim.","major_comments":[{"comment":"Methods and Supplementary Fig. S4: the entire 30 K (paramagnetic) complex impedance is subtracted to remove extrinsic phase rotation. Residual frequency-dependent inductive/capacitive coupling that is temperature- or magnetization-dependent, or weak nonlinear heating that survives the higher-harmonic filter (Supplementary Fig. 5), would still vanish above Tc, be suppressed by field (via reduced tilt), and remain linear in f at low frequency—exactly the reported phenomenology. No absolute-magnitude comparison of the measured L_xy to a microscopic estimate of e ∝ −∂T/∂t is provided. A control that quantifies residual circuit inductance under identical cabling but with a non-magnetic polar reference, or an explicit calculation of the expected inductance scale, is needed to secure the exclusive assignment of Im Z_xy to toroidal induction.","section":null},{"comment":"Extended Data Fig. 1 and Methods (Steps 1–6): the magnetization tilt angle \theta_M is extracted by equating the normalized AHC reduction under current to that under a deliberately tilted field. The AHC reduction under current already exceeds the geometric 1−cos \theta expectation by a large factor (Extended Data Fig. 1d), indicating strong electronic-structure reconstruction. Because the same reconstruction is later invoked as the microscopic origin of the toroidal gauge field, the multi-step conversion introduces a circularity risk: the \theta_M used to interpret the dynamics already encodes the Berry-curvature changes that the dynamics are claimed to produce. An independent probe of the in-plane magnetization component (e.g., anisotropic magnetoresistance or second-harmonic Hall) would strengthen the quantitative link.","section":null},{"comment":"Eq. (4) and surrounding text: the emergent field is written e ∝ −P \times ∂M/∂t ∝ iω e^{iωt}, predicting a purely imaginary, frequency-linear Hall impedance. While the low-frequency data (Fig. 4a) are linear, a Debye-type roll-off appears above ~2 kHz whose microscopic origin is left open. Without a model that relates the relaxation time to the SOT-driven dynamics or to the Weyl-node motion, it remains unclear whether the observed inductance is the adiabatic toroidal response or a more conventional magnetic-relaxation contribution. A minimal dynamical model connecting SOT, \theta_M(t) and L_xy would close this gap.","section":null}],"minor_comments":[{"comment":"Fig. 2d–g: the Brillouin-zone orientation and the precise k-path used for the band-structure cuts are defined only in Extended Data Fig. 2; a brief reminder in the main-text caption would improve readability.","section":null},{"comment":"Notation for the toroidal moment alternates between T and bold T; a consistent vector notation throughout would avoid ambiguity with temperature.","section":null},{"comment":"The anisotropy field HA = 14 T is obtained from a linear extrapolation of ΔM to zero (Extended Data Fig. 1a); the uncertainty on this extrapolation should be stated, as it propagates into the \theta_M error bars.","section":null},{"comment":"References 28 and 29 discuss the Joule-heating controversy for emergent inductance; a short explicit statement of how the higher-harmonic data (Supplementary Fig. 5) discriminate against that model would help non-specialist readers.","section":null}],"recommendation":"major_revision","confidential_remarks":"The central experimental claim is interesting and potentially high-impact, but rests heavily on a single background-subtraction step whose completeness is hard to verify from the present data. I would not reject on that ground alone, yet a major revision that either (i) supplies an absolute-magnitude estimate or (ii) adds a non-magnetic control is essential before the texture-free EEMI interpretation can be regarded as secure. The DFT and low-current-density aspects are genuine strengths and should be retained."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The new result is a frequency-linear imaginary Hall impedance Im Z_xy in bulk PrAlGe that tracks magnetization dynamics, vanishes above Tc, and is suppressed by field. Prior EEMI work needed real-space textures; this is the first clear experimental realization of the SOC-enabled uniform-magnet case predicted by Yamane et al. (PRL 2022). The toroidal framing T = P × M and the DFT link to Weyl-node motion under tilt are coherent and useful.\n\nWhat they do well: FIB Hall bars, careful Joule-heating compensation via Rxx thermometry, higher-harmonic checks against pure heating models, and a multi-control phenomenology (f-linear at low f, Debye roll-off, field and T dependence). The AHC suppression under DC current is large and they convert it to tilt angle via a control experiment with deliberately tilted B; the DFT shows clear Weyl-node shifts and antisymmetric Berry-curvature redistribution. Citations are appropriate and the theory section is clean.\n\nSoft spots, in proportion: the 30 K background subtraction is the weakest link. Residual T- or M-dependent circuit inductance/capacitance or weak nonlinear heating that survives the harmonic filter could still produce a signal that vanishes above Tc and is field-suppressed. They do not close this with an absolute magnitude comparison of L_xy to a microscopic calculation, so the identification of the voltage with e ∝ −∂T/∂t remains interpretive rather than quantitative. The multi-step AHC-to-tilt conversion also shows that electronic-structure changes are large, which is interesting but makes the simple geometric picture incomplete. Low Tc (15 K) and incomplete switching limit device claims; they acknowledge this.\n\nThis is for people working on EEMI, spin-orbit torques, and Weyl magnets. The central claim holds up under the controls they present; the stress-test concern is real but does not invalidate the observation. I would send it to peer review. Engage with it if you care about bulk spin-charge conversion or topological induction.","headline":"Clean experimental signature of frequency-linear imaginary Hall impedance in a uniform polar ferromagnet, framed as texture-free EEMI via toroidal moment; subtraction and magnitude remain the soft links.","tokens_in":14309,"tokens_out":517,"would_cite":true,"duration_ms":5283,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A uniform polar ferromagnet can host emergent electromagnetic induction through dynamics of its toroidal moment T = P × M.","keywords":["emergent electromagnetic induction","toroidal moment","polar Weyl ferromagnet","spin-orbit torque","Berry phase","PrAlGe","Weyl nodes","spin-charge conversion"],"falsifier":"If the imaginary Hall impedance continued to rise linearly with frequency and remain field-suppressible well above the Curie temperature, or if it failed to track the independently estimated magnetization tilt angle under controlled current densities, the toroidal-induction claim would be ruled out.","tokens_in":14222,"feed_emoji":"🧲","tokens_out":866,"duration_ms":16010,"temperature":0.7,"pith_summary":"The paper shows that emergent electromagnetic induction—the conversion of magnetization dynamics into an electromotive force via a spin-dependent Berry phase—does not require real-space magnetic textures such as domain walls, helices or skyrmions. In the polar Weyl ferromagnet PrAlGe, an alternating current generates spin-orbit torques that tilt the otherwise uniform magnetization, producing a time-varying toroidal moment T = P × M. This moment acts as an effective gauge potential whose time derivative induces a Hall voltage that appears exclusively in the out-of-phase component of the AC response and scales linearly with frequency. First-principles calculations further link the effect to collective motion of Weyl nodes in momentum space. If correct, the result supplies an intrinsic, bulk route to spin–charge interconversion that needs neither engineered nanostructures nor spatial spin gradients.","feed_headline":"Uniform ferromagnet yields induction via toroidal moment","feed_subtitle":"Current-driven spins in PrAlGe produce a frequency-linear Hall voltage without any magnetic textures","key_machinery":"The emergent toroidal moment T = P × M, which acts as a uniform effective vector potential a_eff ∝ T; the emergent electric field is then e ∝ −∂T/∂t and is detected as the frequency-linear imaginary Hall impedance Im Z_xy.","core_discovery":"Even a spatially uniform ferromagnet can host emergent electromagnetic induction when spin-orbit coupling and a polar crystal axis coexist. In PrAlGe, current-driven magnetization dynamics generate a time-dependent toroidal moment T = P × M that functions as a Berry-phase gauge potential; its time derivative produces a measurable Hall voltage that appears in the imaginary part of the AC impedance, scales linearly with frequency, vanishes above the Curie temperature and is suppressed by magnetic field.","pith_inferences":["Analogous toroidal induction should appear in other non-centrosymmetric Weyl or Rashba ferromagnets once their magnetization can be dynamically tilted by current.","Frequency-dependent Hall inductance could become a spectroscopic probe of collective Weyl-node dynamics under drive.","Optimizing the RAlX family for higher transition temperature and coercivity may yield all-metallic inductive elements that integrate directly into spintronic circuits without heterostructures."],"forward_implications":["Bulk polar magnets can exhibit emergent electromagnetic induction without real-space spin textures.","Magnetization dynamics sufficient for a detectable inductive Hall voltage can be driven at unusually low current densities (~10^8 A m^{-2}).","Polar magnetic systems with higher coercivity and higher transition temperatures could realize field-free switching accompanied by stronger topological electromotive forces.","The imaginary Hall inductance constitutes a condensed-matter analogue of a classical inductor whose ‘flux’ is the magnetization-driven vector potential.","Collective Weyl-node motion in momentum space can itself serve as an intrinsic electromotive source."],"fun_headline_variants":["Uniform ferromagnet hosts EEMI via toroidal moment","Polar Weyl magnet yields frequency-linear Hall from dT/dt","Texture-free PrAlGe shows emergent toroidal induction","Spin dynamics in uniform polar ferromagnet induce Hall voltage","Toroidal gauge potential drives AC Hall in PrAlGe"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The residual out-of-phase Hall voltage left after subtracting the 30 K paramagnetic background is purely the emergent electric field from toroidal-moment dynamics, not leftover circuit inductance, capacitive coupling or unaccounted nonlinear heating.","fun_headline_variants_meta":{"raw":{"variants":["Uniform ferromagnet hosts EEMI via toroidal moment","Polar Weyl magnet yields frequency-linear Hall from dT/dt","Texture-free PrAlGe shows emergent toroidal induction","Spin dynamics in uniform polar ferromagnet induce Hall voltage","Toroidal gauge potential drives AC Hall in PrAlGe"]},"model":"grok-4.5","effort":"low","cost_usd":0.00556,"raw_usage":{"total_tokens":1508,"prompt_tokens":824,"num_sources_used":0,"completion_tokens":83,"cost_in_usd_ticks":55600000,"prompt_tokens_details":{"text_tokens":824,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":601,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":824,"tokens_out":83,"duration_ms":5798,"temperature":1.0,"reasoning_tokens":601,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-15T07:00:45.585705+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"If the imaginary Hall impedance continued to rise linearly with frequency and remain field-suppressible well above the Curie temperature, or if it failed to track the independently estimated magnetization tilt angle under controlled current densities, the toroidal-induction claim would be ruled out.","supporting_citations":[],"review_version":1}