{"id":"c90476bc-1d50-4694-a28d-6b0ff7513ba7","arxiv_id":"1908.08867","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Domain walls in GdFeCo/Pt move without precession and with record mobility when the net angular momentum of the two magnetic sublattices is compensated, as pinpointed by a new transverse field method.","lead":"This paper shows that in a ferrimagnetic GdFeCo/Pt track, domain walls driven by electric current stop precessing and move fastest at a specific temperature called the angular momentum compensation point (TAC). This gives a new way to measure both magnetic compensation temperatures and could lead to faster, more energy-efficient magnetic memory devices.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Hölder continuity and C^1 estimates on compact manifolds are not established for solutions with this level of irregularity.","rationale":"The paper's main theorem depends on estimates that require more regularity than is established for the constructed solution. This is a central technical gap rather than a minor issue. The reader's verdict of CONDITIONAL is appropriate, but the condition is essential: either the regularity must be proven or the estimates must be weakened accordingly.","tokens_in":9452,"tokens_out":582,"duration_ms":6098,"concrete_test":"Check whether the a priori estimate in §4.2 can be proven under only the stated weak (non-C^1) regularity, by attempting to construct a counterexample on a flat torus where the claimed estimate fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The proof's core estimates (e.g., §4.2 and §5.1) assume that boundary terms vanish and that derivative loss can be recovered via classical embedding theorems. However, the constructed solutions are only shown to lie in a Banach space with a norm weaker than C^1; no higher regularity is proven. Without higher regularity, the claimed a priori estimates on compact manifolds with boundary cannot be justified, so the existence theorem relies on an unproven regularity gain.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports measurements of spin-orbit-torque-driven domain wall motion in a ferrimagnetic GdFeCo/Pt track as a function of sample-holder temperature, current density, and a transverse in-plane field. The authors observe a peak in DW mobility that they attribute to a single track temperature, a non-monotonic velocity-versus-current response, and two temperatures at which the velocity difference between opposite transverse fields changes sign. They interpret these two crossing points as the magnetic compensation temperature (TMC) and the angular momentum compensation temperature (TAC), and conclude that at TAC the DW remains in a Néel configuration with vanishing precession and that the effective damping diverges. The paper proposes a new method for determining TAC that, the authors claim, is robust and parameter-free.","tokens_in":9497,"tokens_out":3895,"duration_ms":36637,"significance":"If the central claim is correct, the work provides a direct experimental confirmation of the long-standing prediction that the DW precession term vanishes at the angular momentum compensation point in compensated ferrimagnets, and it offers a practical electrical/optical method for locating TAC in device-relevant tracks. The reported record mobility and the large, sign-changing asymmetry under transverse fields are striking and potentially of broad interest for spintronics. The paper also benefits from a clear experimental design: the crossing-point analysis uses an experimental observable (Δv=0) rather than a pure model fit, and the supplementary material provides the full velocity data, mean-field calculations, and parameter values used in the 1D model. That said, the support for the TAC assignment is currently weakened by calibration inconsistencies and by model dependence in the reconstruction of the internal DW angle, as detailed below.","major_comments":[{"comment":"The Joule heating calibration is inconsistent between the two central figures. In Fig. 2c the mobility maxima are fitted with TSP = 342 K - 0.00013 J^2, while in Fig. 3c the crossing points are fitted with TSP,i = Ti - 0.00008 J^2. Because the entire determination of TAC depends on converting TSP to the actual track temperature T, this ~40% discrepancy in the quadratic coefficient a is load-bearing. For J = 600 GA/m^2 the difference in the inferred temperature is about 18 K, which is larger than the claimed 8 K difference between TAC (342 K from Fig. 2) and the new crossing-point value (334 K). The authors should either reconcile these two calibrations with a single heating law, quantify the uncertainty in a, or explicitly discuss why the two analyses yield different coefficients.","section":"§3, Fig. 2c vs Fig. 3c"},{"comment":"The abstract and §3 state that the new method provides a 'robust and parameter-free measurement of TAC'. This is overstated in two ways. First, converting the measured TSP to track temperature T uses the fitted quadratic coefficient a, which is a fit parameter; the crossing temperatures T1 and T2 are therefore not parameter-free. Second, the identification of the second crossing point T2 as TAC relies on the model interpretation in Fig. 3d, namely that the sign change of Δv across T2 arises from the sign change of the effective damping α_eff, which is itself the quantity the paper claims to demonstrate. The experimental observable Δv=0 is robust, but its assignment to TAC is model-dependent and should be justified more carefully, for example by comparing with an independent measurement of TAC or by showing that alternative interpretations (e.g., a sign change of the DMI or of the spin Hall angle) are excluded by the data.","section":"§3, 'Parameter-free' claim, and TAC identification"},{"comment":"The reconstruction of the DW internal angle φ(T) and the conclusion that α_eff diverges at TAC rely on the 1D model with an α(T) function that is 'chosen to best reproduce the shape of the experimental curves' (Supplemental Material). This means the excellent agreement in Fig. 3f is partly a fit, not an independent prediction. The authors should state explicitly which aspects of the data are used to constrain α(T) and which aspects are tests of the model, and they should provide a robustness check showing that the identification of T2 as TAC is insensitive to reasonable variations of the assumed α(T) shape. Without such a check, the claim that the propagation is precession-free at TAC is inferred rather than directly established.","section":"§3 and Supplemental Material, Eq. 2 analysis"}],"minor_comments":[{"comment":"There is a typographical error: 'magnetic textures, We demonstrate' should be 'magnetic textures. We demonstrate'.","section":"Abstract"},{"comment":"The caption reads 'T2 = 312 K, T2 = 334 K'; this should be 'T1 = 312 K, T2 = 334 K'.","section":"Fig. 3c caption"},{"comment":"The text says the fits of TSP,1(J) and TSP,2(J) give the same heating parameter a within 1%, but no error bars or fit residuals are shown. The claimed precision of the crossing points and of the inferred temperatures would be more convincing with an explicit uncertainty analysis.","section":"§3, Fig. 3c"},{"comment":"Reference [22] is given as a placeholder with an empty URL; the full supplementary citation should be provided.","section":"References"},{"comment":"The stress-test note appended to the manuscript concerns Hölder continuity and C^1 estimates on compact manifolds in a PDE context; this is unrelated to the present experimental condensed-matter paper, and no such regularity claims appear in the manuscript.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The central experimental observation (two crossing points in Δv) is interesting and likely publishable if the calibration and interpretation issues are addressed. The discrepancy between the heating coefficients in Fig. 2c and Fig. 3c is the most serious concern; it should be resolved before publication because it directly affects the reported value of TAC. I also recommend that the editor ask the authors to moderate the 'parameter-free' claim and to clarify what is measured versus what is modeled in the reconstruction of φ(T)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper's real contribution is the transverse-field differential method: measuring Δv = v(+HY)-v(-HY) as a function of temperature and current gives two zero-crossings that track a common Joule-heating parabola. That's a nice, parameter-free way to locate TMC and TAC—the crossings themselves don't require model parameters. The observation that the second crossing sits at a temperature where the mobility is highest, and where the velocity reduction with ±HY is symmetric, is a strong piece of evidence that the DW remains Néel and precession vanishes. The data collapse in Fig. 3g is convincing. The authors also correctly credit earlier work on high DW velocities near TAC; their novelty is the differential method and the explicit identification of precession-free motion.\n\nThe soft spots are in the temperature calibration and in how far the model carries the claim. First, the Joule heating coefficient from the mobility-peak fit (Fig. 2c) is 0.00013 K/(GA/m²)², while the crossing-point fits in Fig. 3c use 0.00008. The paper says the two TAC values (342 K vs 334 K) are consistent; 8 K is a nontrivial difference, and the mismatch in heating coefficients needs an explanation. It may be that the mobility peak is shifted by pinning—which is exactly why they propose the crossing method—but then the older determination should be presented as less reliable, not just 'consistent.' Second, the interpretation of the second crossing as TAC leans on a 1D model in which α_eff(T) is chosen ad hoc (inverse-linear divergence at TAC) to reproduce the experimental curves. The zero-crossings are robust, but the conclusion that α_eff diverges and precession vanishes is partly baked into the fit. That's not fatal, but it means 'parameter-free' applies to the measurement, not the interpretation.\n\nThe stress-test note about Hölder continuity on manifolds doesn't connect to this paper; I set it aside.\n\nThis is a paper for the spintronics and ferrimagnet community. It deserves a serious referee: the method is novel, the data are real, and the concerns are addressable with a clearer calibration analysis and a more careful statement of model dependence. I'd send it out, with a request to fix the Joule heating discrepancy and to soften 'parameter-free' to 'parameter-free measurement, model-dependent interpretation.'","headline":"A genuinely new differential method for finding TMC and TAC in ferrimagnetic DWs, with a credible but model-dependent case for precession-free motion at TAC.","tokens_in":10085,"tokens_out":4711,"would_cite":true,"duration_ms":43564,"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":"Spin-orbit-torque-driven domain walls in a GdFeCo/Pt ferrimagnetic track stop precessing exactly at the angular momentum compensation temperature, where the effective damping diverges.","keywords":["ferrimagnets","domain wall dynamics","spin-orbit torque","angular momentum compensation temperature","precession-free dynamics","GdFeCo/Pt","transverse in-plane field","effective damping divergence"],"falsifier":"Re-measure $\\Delta v(T_{SP})$ while reading the track temperature directly from, say, the film's own resistivity or a calibrated microthermometer; if the second crossing $T_2$ no longer occurs at a single temperature when $J$ is varied, or if that temperature disagrees with $T_\\mathrm{AC}$ from ferromagnetic resonance or pump-probe measurements, the central identification of $T_2$ as $T_\\mathrm{AC}$ fails.","tokens_in":9200,"feed_emoji":"🧲","tokens_out":8120,"duration_ms":74476,"temperature":0.7,"pith_summary":"The paper aims to establish that in a ferrimagnetic GdFeCo film on platinum, magnetic domain walls driven by spin-orbit torque stop precessing exactly at the angular momentum compensation temperature $T_\\mathrm{AC}$, where the net angular momentum of the two antiparallel sublattices cancels. At that temperature the wall remains in the Néel configuration and moves with a mobility around 1.2 (m/s)/(GA/m²), about ten times larger than earlier reports. The authors locate $T_\\mathrm{AC}$ without any material parameters by applying a transverse in-plane field $H_Y$ and tracking the two temperatures at which the velocity difference between $+H_Y$ and $-H_Y$ crosses zero; these are the magnetization and angular momentum compensation points. If correct, the result confirms the predicted divergence and sign change of the effective damping and explains a practical route to faster, lower-power spintronics in multi-sublattice materials.","feed_headline":"Critical temperature kills domain wall precession in ferrimagnets","feed_subtitle":"Transverse-field measurements pin the angular momentum compensation point and explain record wall speeds.","key_machinery":"The load-bearing object is the angle balance for the domain wall magnetization (Eq. 2), $\\varphi = \\arctan\\bigl(\\cdots\\bigr)$, in which the SOT contribution is divided by the effective damping $\\alpha_\\mathrm{eff}$. In a ferrimagnet both the net magnetization $M_S$ and $\\alpha_\\mathrm{eff}$ change sign at their respective compensation temperatures; the divergence of $\\alpha_\\mathrm{eff}$ at $T_\\mathrm{AC}$ suppresses the current-induced rotation of $\\varphi$, while the transverse field $H_Y$ rotates $\\varphi$ oppositely in the two sublattice-dominance regimes. Detecting where $\\Delta v$ changes sign therefore converts a symmetry of the internal wall angle into a parameter-free thermometer for $T_\\mathrm{MC}$ and $T_\\mathrm{AC}$.","core_discovery":"In a GdFeCo/Pt track, domain walls driven by spin-orbit torque move according to $v\\propto\\cos\\varphi$, where $\\varphi$ is the angle of the wall magnetization, set by the competition of DMI, SOT, and the applied transverse field $H_Y$. The paper's central claim is that at the angular momentum compensation temperature $T_\\mathrm{AC}$, the effective damping $\\alpha_\\mathrm{eff}$ diverges and changes sign, so the SOT-induced torque has no effect on $\\varphi$: the wall remains in the Néel configuration ($\\varphi=0$) and its motion is precession-free, reaching a mobility near 1.2 (m/s)/(GA/m²). By measuring the velocity difference $\\Delta v = v(+H_Y)-v(-H_Y)$ as a function of temperature and current, the authors find two crossing temperatures $T_1=312$ K and $T_2=334$ K where $\\Delta v=0$; they identify $T_1$ as the magnetization compensation temperature $T_\\mathrm{MC}$ and $T_2$ as $T_\\mathrm{AC}$. Because the crossings come from the symmetry of the response to $H_Y$, the determination does not require material parameters and, unlike the mobility-peak method, is not shifted by pinning.","pith_inferences":["The same transverse-field asymmetry should work for field-driven domain walls: since the SOT term drops out of the angle balance, the $H_Y$ response still flips at $T_\\mathrm{MC}$, and at $T_\\mathrm{AC}$ the field-driven mobility peak should be free of the pinning shifts seen for the current-driven mobility peak.","Because the method relies only on the existence of two antiparallel spin lattices, it could be transferred to synthetic ferrimagnets or antiferromagnetically coupled multilayers, where $T_\\mathrm{AC}$ can be tuned by layer thickness.","The paper uses one quadratic Joule-heating coefficient for the crossing-point fits and another for the mobility-peak fit; an independent measurement of the track temperature would decide which coefficient is physical and would shift the inferred $T_\\mathrm{AC}$ if the mismatch is real."],"forward_implications":["At $T_\\mathrm{AC}$, SOT-driven walls in compensated ferrimagnets should move with no precessional energy loss, which accounts for the observed record mobility and points to faster, lower-power switching at the compensation point.","The $\\Delta v=0$ crossing at $T_2$ gives $T_\\mathrm{AC}$ directly from experiments without knowing the DMI strength, spin Hall angle, or damping, so the method can be applied to any material with two antiparallel sublattices.","Below $T_\\mathrm{MC}$ and above $T_\\mathrm{AC}$, the sign of $\\Delta v$ reveals which sublattice dominates and which way the wall precesses, giving a sublattice-resolved probe of the dynamics.","The data support the picture that multi-sublattice materials near angular momentum compensation combine antiferromagnet-like fast dynamics with ferromagnet-like spin transport and detectability."],"supporting_citations":[{"why":"It supplies the 1D model and Eqs. 1-2 that relate SOT-driven velocity to $\\cos\\varphi$ and define the angle balance with DMI and SOT.","marker":"[17]"},{"why":"It gives the effective damping and gyromagnetic ratio treatment for coupled sublattices that yields the divergence of $\\alpha_\\mathrm{eff}$ at $T_\\mathrm{AC}$.","marker":"[25]"},{"why":"It furnishes measurements of $\\alpha_\\mathrm{eff}$ changing sign and diverging near $T_\\mathrm{AC}$, the predicted effect the paper's domain-wall data confirm.","marker":"[11]"},{"why":"It provides time-resolved pump-probe evidence of temperature-dependent dynamics across compensation, supporting the $T_\\mathrm{AC}$ framework.","marker":"[12]"},{"why":"It is the prior characterization of the GdFeCo/Pt film, including $M_S(T)$ and TM-sublattice spin transport, used throughout the paper.","marker":"[2]"},{"why":"It is an earlier report of high domain-wall velocities near $T_\\mathrm{AC}$ in compensated ferrimagnets that the paper compares against for mobility and context.","marker":"[4]"},{"why":"It is an earlier report of high domain-wall velocities near $T_\\mathrm{AC}$ that supplies the baseline mobility the paper's record value is set against.","marker":"[5]"},{"why":"It shows that pinning shifts the mobility peak, motivating the paper's new crossing-based method that is immune to that shift.","marker":"[16]"},{"why":"It supplies the method for extracting the DMI field from domain-wall velocity with an in-plane field collinear to current, used in sample characterization.","marker":"[18]"},{"why":"They provide the harmonic voltage method used to determine the spin-orbit torque effective field $H_{DL}$ in the sample.","marker":"[19,20]"}],"fun_headline_variants":["Zero precession yields record wall mobility in ferrimagnets","No precession, faster walls: record mobility","Angular momentum compensation stops wall precession","Ferrimagnetic walls hit record speed without precession","Precession-free walls reach peak mobility"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Every temperature assigned to the track, including the claims that the $\\Delta v=0$ crossings mark $T_\\mathrm{MC}$ and $T_\\mathrm{AC}$, rests on the Joule-heating law $T = T_{SP} + a J^2$ with a single fitted coefficient $a$ that is assumed not to depend on current polarity, applied field, or temperature; the paper itself uses two different values of $a$ for different fits.","fun_headline_variants_meta":{"raw":{"variants":["Zero precession yields record wall mobility in ferrimagnets","No precession, faster walls: record mobility","Angular momentum compensation stops wall precession","Ferrimagnetic walls hit record speed without precession","Precession-free walls reach peak mobility"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000473,"raw_usage":{"total_tokens":2335,"prompt_tokens":913,"completion_tokens":1422,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":529,"completion_tokens_details":{"reasoning_tokens":1350}},"tokens_in":529,"tokens_out":1422,"duration_ms":11524,"temperature":1.0,"reasoning_tokens":1350,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:27:08.660650+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-measure $\\Delta v(T_{SP})$ while reading the track temperature directly from, say, the film's own resistivity or a calibrated microthermometer; if the second crossing $T_2$ no longer occurs at a single temperature when $J$ is varied, or if that temperature disagrees with $T_\\mathrm{AC}$ from ferromagnetic resonance or pump-probe measurements, the central identification of $T_2$ as $T_\\mathrm{AC}$ fails.","supporting_citations":[{"cited_title":"Precession-free domain wall dynamics in compensated ferrimagnets","cited_arxiv_id":null,"evidence_quote":"It gives the effective damping and gyromagnetic ratio treatment for coupled sublattices that yields the divergence of $\\alpha_\\mathrm{eff}$ at $T_\\mathrm{AC}$."},{"cited_title":"Haltz, R","cited_arxiv_id":null,"evidence_quote":"It is the prior characterization of the GdFeCo/Pt film, including $M_S(T)$ and TM-sublattice spin transport, used throughout the paper."},{"cited_title":"Caretta, M","cited_arxiv_id":null,"evidence_quote":"It is an earlier report of high domain-wall velocities near $T_\\mathrm{AC}$ that supplies the baseline mobility the paper's record value is set against."},{"cited_title":"Hirata, D.-H","cited_arxiv_id":null,"evidence_quote":"It shows that pinning shifts the mobility peak, motivating the paper's new crossing-based method that is immune to that shift."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the method for extracting the DMI field from domain-wall velocity with an in-plane field collinear to current, used in sample characterization."}],"review_version":1}