{"id":"966bd2ba-35b1-4233-b9bb-31df7b2dd325","arxiv_id":"2504.19803","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"The paper claims ac susceptibility of Co8Zn7Mn5 and Co8Zn8Mn4 requires an inertial relaxation term and reports 10^-5 s relaxation times, but the model comparison that would support the claim is not shown.","lead":"Ac susceptibility data on two beta-manganese-type cobalt-zinc-manganese chiral magnets are said to require an extra 'inertial' relaxation term beyond the standard Debye and Cole-Cole models. If true, inertial magnetization dynamics would extend beyond spin ices; the evidence shown, however, is a narrow-window fit whose basis is not demonstrated.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The inertial-term necessity claim is underdetermined: at the reported window (ω/ω0)^2 ≤ ~0.01 if ω0=0.101 MHz is cyclic, and no failed Debye/Cole-Cole fits or model-selection statistics are shown.","rationale":"The reader identified the resolution of the experimental window as the weakest assumption, and this is precisely the load-bearing point. For the paper's central claim to hold, the measured 1.7–9.7 kHz window must be able to distinguish Eq. 3 from Eq. 2. The reported ω0=0.101 MHz is close enough to the window that the inertial term might matter only under a favorable unit interpretation, but the paper never states which convention is used and never demonstrates that Debye or Cole-Cole fits fail. The absence of any fit comparison is decisive against the necessity claim: Eq. 3 has one extra parameter and will generally fit better regardless of physical relevance. The admitted low-frequency mismatch of χ'' further weakens the claim that Eq. 3 is a proper description. I therefore agree with the reader's REJECT verdict; the surviving evidence supports frequency-dependent non-Debye dissipation and a newly characterized phase diagram, not inertial effects as an intrinsic property. The proposed concrete test—a formal BIC/AIC comparison on the actual data with a stated unit convention—would settle whether this concern lands.","tokens_in":14869,"tokens_out":6565,"duration_ms":67364,"concrete_test":"Using the raw χ'(f) and χ''(f) data behind Figures 6 and 8, refit each curve with Debye (Eq. 1), Cole-Cole (Eq. 2), and inertial (Eq. 3) models, reporting ΔBIC/AIC, residual RMS, and bootstrap confidence intervals for ω0, and explicitly stating whether 0.101 MHz is angular or cyclic. If ΔBIC(Eq. 3 vs Eq. 2) is less than about 10, or the confidence interval for ω0 includes values for which max(ω/ω0)^2 over the window is below about 0.05, the inertial necessity claim is not established. A decisive extension would be to measure susceptibility up to at least 50 kHz to cross the reported resonance.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, that Debye/Cole-Cole models fail and an inertial term is required, rests on the fitted value ω0=0.101 MHz in Section B and on the unshown comparison between Eq. 2 and Eq. 3. The experimental window is 1.747–9.747 kHz. If 0.101 MHz is an ordinary frequency, then max(ω/ω0)^2 ≈ 0.0093 over the window, so Eq. 3 is numerically Debye/Cole-Cole to within about 1% and the inertial term is essentially invisible. If 0.101 MHz is instead an angular frequency, f0 ≈ 16.1 kHz, the correction reaches about 0.37 only at the top edge and is below about 0.05 for most of the window; the inertial resonance region is still never crossed. In neither reading does the experiment directly resolve the inertial response. The paper also never presents failed Debye/Cole-Cole fits, residuals, goodness-of-fit statistics, or parameter uncertainties, and it admits that Eq. 5 deviates from χ''(f) below 3 kHz. Since Eq. 3 reduces to Eq. 2 in the limit ω0→∞, adding the inertial parameter can only improve the fit; without model-selection evidence, the claim that conventional models 'cannot explain' the data is not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports ac susceptibility measurements on Co8Zn7Mn5 and Co8Zn8Mn4 in the frequency range 1747-9747 Hz at constant temperatures (240 K and 265 K) under dc fields spanning helical, conical, skyrmion, and ferromagnetic phases. The authors claim that the standard Debye and Cole-Cole relaxation models cannot describe the frequency dependence of chi' and chi'', and that an 'inertial' extension (Eq. 3, after Armitage) is required, yielding relaxation times of order 10^-5 s, zero relaxation-time distribution (alpha = 0), and a constant inertial frequency omega0 (0.101 MHz from chi' fits). They further report field-dependent A = chi_T - chi_inf and tau with double peaks at the skyrmion phase boundaries and attribute the proposed inertia to intrinsic spin fluctuations. They also present the first magnetic phase diagram of Co8Zn7Mn5.","tokens_in":15089,"tokens_out":8240,"duration_ms":76791,"significance":"If established, the claim that Debye/Cole-Cole relaxation fails for this material family and that an inertial term is necessary would be of genuine interest, extending inertial relaxation phenomena beyond spin ice and suggesting that standard ac-susceptibility analysis misses a dynamical degree of freedom in chiral magnets. The phase diagram of Co8Zn7Mn5 and the observation of nonzero dissipation in all phases are potentially useful. However, the central claim is not supported by the evidence presented. The manuscript contains no direct comparison to Debye or Cole-Cole fits, no goodness-of-fit statistics, no parameter uncertainties, and it admits a low-frequency discrepancy in the chi'' fits. Combined with the ambiguous meaning of the fitted omega0, the data do not demonstrate that an inertial term is required.","major_comments":[{"comment":"The paper asserts that 'neither model was able to adequately represent' the data, but it never shows a Debye (Eq. 1) or Cole-Cole (Eq. 2) fit, residual plot, or any goodness-of-fit statistic. Because Eq. (3) reduces to Eq. (2) in the limit omega_0 -> infinity, adding the inertial parameter can only improve the fit; without a model-selection criterion (e.g., reduced chi-square, AIC/BIC, or F-test), the claim that conventional models 'fail' and that inertia is 'needed' is not established. This is the load-bearing step for the abstract's main conclusion.","section":"Section B, paragraph introducing Eqs. (3)-(5)"},{"comment":"The value omega_0 = 0.101 MHz is ambiguous. Since omega is defined as angular frequency in Eq. (1), if 0.101 MHz is a cyclic frequency, then over the experimental window 1.747-9.747 kHz the inertial correction (omega/omega_0)^2 is at most about 0.0093, making Eq. (3) numerically nearly identical to Eq. (2); if 0.101 MHz is an angular frequency, then f_0 ≈ 16.1 kHz and the correction reaches roughly 0.37 only at the top edge. The paper does not specify the convention, and in neither reading does the measurement resolve an inertial resonance. The alleged superiority of Eq. (3) therefore cannot be assessed from the reported value.","section":"Section B, paragraph reporting omega_0"},{"comment":"The text states that Eq. (5) 'accurately reflects the overall trend' of chi''(f) but that 'there is some discrepancy observed in the low-frequency region below 3 kHz.' Since the measured window begins at 1.747 kHz, this admitted discrepancy affects a sizable part of the data used for fitting. The authors do not quantify the discrepancy or explain it; this weakens the internal-consistency argument that the same model describes both chi' and chi''.","section":"Section B, paragraph after Eq. (5)"},{"comment":"No error bars or confidence intervals are given for any fitted parameter (A, tau, alpha, omega_0). The statements that tau values from chi' and chi'' fits are 'of the same order' and that parameters for Co8Zn7Mn5 and Co8Zn8Mn4 'lie within the same range' are qualitative. Without uncertainties, the double-peak structure in A and tau at the skyrmion boundaries—one of the paper's principal results—cannot be distinguished from noise in the fitting procedure. Moreover, this structure is a property of the fitted parameters of the model being validated, not an independent observable; the agreement between chi' and chi'' fits is internal consistency of that same model.","section":"Section B, Figures 6-9"},{"comment":"The paper claims to rule out monopoles, domain-wall inertia, and skyrmion-mass effects, but the exclusions are indirect. For example, the argument that domain-wall motion 'might play a role... but not be the main cause' is not supported by any quantitative test, and the conclusion that the inertial effect is 'an intrinsic property' of the material family is claimed essentially from the constancy of omega_0 across fields. This is too strong a conclusion from a model that has not been established against the standard alternatives.","section":"Section B, Discussion of physical mechanisms"}],"minor_comments":[{"comment":"Reference [34] is cited as the source of the Co8Zn8Mn4 sample, but [34] is Pan et al., Nature Physics 2016, on the spin ice Yb2Ti2O7; the authors presumably intended their own previous study, possibly ref. [35]. Please correct this citation.","section":"Experimental Techniques"},{"comment":"The notation for the susceptibility amplitudes is inconsistent: Eq. (1) uses chi_0, while Eq. (4) uses A = chi_T - chi_inf. Unify the notation for readability.","section":"Equations (1)-(4)"},{"comment":"The abstract states a frequency range of 1 kHz to 10 kHz, while the experimental section reports 1747 Hz to 9747 Hz; make these consistent.","section":"Abstract and Experimental Techniques"},{"comment":"The phrase 'reentrant spin glass phase' is mentioned without a definition or dedicated citation; a brief explanation or a reference to the prior Co-Zn-Mn literature would help.","section":"Results and Discussions, dc susceptibility"},{"comment":"The phrase 'our analysis reveal' should read 'our analysis reveals'.","section":"Abstract"}],"recommendation":"reject","confidential_remarks":"The paper contains a potentially useful first magnetic phase diagram for Co8Zn7Mn5, but the central claim of inertial effects is not supported by the present analysis. The absence of any direct comparison with Debye/Cole-Cole fits, the lack of parameter uncertainties, the admitted low-frequency discrepancy in chi'', and the ambiguous convention for omega_0 collectively prevent the conclusion. If the authors were to resubmit with a thorough model-selection analysis and a much more cautious interpretation (e.g., 'the data are not inconsistent with an inertial term'), the manuscript might be considered; as it stands, the abstract and conclusions overclaim. There is also a citation error for the provenance of the Co8Zn8Mn4 sample."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First of all, this paper is not a waste of time. The new phase diagram and ac susceptibility data for Co8Zn7Mn5 are genuinely new, and the observation that chi'' is nonzero across all magnetic phases, not just at the skyrmion boundaries, is an interesting empirical result. The sample work looks careful: PXRD, EDX, and the phase boundaries derived from chi'(H) are consistent with the broader CoxZnyMnz family. The authors also engage honestly with the literature on spin ice and B20 compounds, and the decision to test the Armitage inertial model is reasonable.\n\nBut the central claim—that Debye and Cole-Cole models fail and an inertial term is required—is not demonstrated. The paper says the conventional models failed but never shows a single failed fit, a residual, or a goodness-of-fit statistic. Instead, we only see fits of equations 4 and 5. Since equation 3 reduces to equation 2 as omega0 tends to infinity, an extra parameter can always improve the fit. Without model selection (AIC, BIC, or at least a comparison of residuals), the necessity claim doesn't follow.\n\nThere is also a units ambiguity. The text reports omega0 = 0.101 MHz without saying whether this is an angular frequency or an ordinary frequency. If it is ordinary, the inertial term (omega/omega0)^2 is at most about 0.01 over the 1747–9747 Hz window, so equation 3 is numerically almost identical to the Cole-Cole form. If it is angular, the equivalent f0 is about 16 kHz, and only the top of the window feels the inertial term. In neither case does the experiment actually resolve an inertial resonance. The authors also admit that equation 5 deviates below 3 kHz, and they give no error bars on any fitted parameter. The fact that tau from chi' and chi'' are of the same order is nice internal consistency, but it is not a proof of the model.\n\nThe weaker claims do survive: chi'' is nonzero in all phases, the relaxation time is about 10^-5 s, and there is a double-peak structure near the skyrmion transitions. These suggest non-Debye dissipation, not necessarily inertia. The paper is probably worth refereeing—the data are real and the phase diagram is new—but a referee should demand that the failed Debye/Cole-Cole fits be displayed, error bars and model-selection statistics be provided, and the omega0 convention be clarified. I'd also encourage the authors to extend the frequency window toward omega0 if possible. As it stands, the inertial claim is not yet supported.","headline":"Useful new phase diagram and ac data for Co8Zn7Mn5, but the inertial-effect case is under-built: no failed standard fits, no error bars, and the omega0 unit ambiguity makes the inertial term almost invisible on one reading.","tokens_in":15776,"tokens_out":3163,"would_cite":false,"duration_ms":28310,"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":"The paper claims that ac susceptibility relaxation in Co8Zn7Mn5 and Co8Zn8Mn4 cannot be described by standard Debye or Cole-Cole models and requires an inertial term.","keywords":["ac susceptibility","magnetic relaxation","inertial effect","skyrmion","beta-Mn type chiral magnet","Co-Zn-Mn compound","Cole-Cole model","spin fluctuations"],"falsifier":"A decisive check would be to refit the same $\\chi'(f)$ and $\\chi''(f)$ scans with Eq. 2 and Eq. 3 under an explicit convention for $\\omega_0$ (cyclic or angular) and compare residuals across the full 1.7–9.7 kHz range; if the improvement disappears or is confined to the highest-frequency points, the inertial claim is not established. A cleaner experiment would extend ac susceptibility to 0.1–1 MHz on the same crystals and look for the $\\chi'$ turnover predicted near the fitted $\\omega_0$.","tokens_in":2040,"feed_emoji":"🧲","tokens_out":2168,"duration_ms":77285,"temperature":0.7,"pith_summary":"This paper argues that the frequency-dependent magnetic response of two $\\beta$-manganese-type chiral magnets, Co8Zn7Mn5 and Co8Zn8Mn4, cannot be captured by the usual Debye or Cole-Cole relaxation formulas. The authors fit the data only after adding an inertial term proportional to $\\omega^2/\\omega_0^2$ to the response function. Across all magnetic phases the fitted relaxation time is about $10^{-5}$ s, with zero spread in relaxation times, and the inertial frequency $\\omega_0$ stays near 0.1 MHz. If true, this means the relaxation physics of this material family is qualitatively different from other skyrmion hosts, and that strong intrinsic spin fluctuations, rather than monopoles, domain walls, or skyrmions themselves, may govern the dynamics.","feed_headline":"Magnetic relaxation in Co-Zn-Mn needs an inertial term","feed_subtitle":"Standard Debye and Cole-Cole fits fail in two beta-Mn chiral magnets; an inertial correction fits all phases.","key_machinery":"The central object is the modified complex ac susceptibility of Eq. 3: $\\chi(\\omega) = \\chi_{\\mathrm{inf}} + (\\chi_T - \\chi_{\\mathrm{inf}})/(1 + (i\\omega\\tau_0)^{1-\\alpha} - \\omega^2/\\omega_0^2)$. It adds a second-order-in-frequency inertial term to the denominator of the Cole-Cole response, making the response fall faster at high frequency. The characteristic frequency $\\omega_0$ is the parameter whose field independence signals an intrinsic inertial effect, and the Casimir–du Pré interpretation of $\\chi_T$ and $\\chi_{\\mathrm{inf}}$ as isothermal and adiabatic susceptibilities supplies the dissipation measure $A = \\chi_T - \\chi_{\\mathrm{inf}}$ used to track slowing dynamics at phase boundaries.","core_discovery":"The central claim is that the Debye relaxation model (Eq. 1) and its generalized Cole-Cole form (Eq. 2) fail to describe $\\chi'(f)$ and $\\chi''(f)$ in Co8Zn7Mn5 and Co8Zn8Mn4 over 1747–9747 Hz, while the modified response $\\chi(\\omega) = \\chi_{\\mathrm{inf}} + (\\chi_T - \\chi_{\\mathrm{inf}})/(1 + (i\\omega\\tau_0)^{1-\\alpha} - \\omega^2/\\omega_0^2)$ (Eq. 3), which contains the inertial term $-\\omega^2/\\omega_0^2$, succeeds. Fitting both components independently gives relaxation times of the same order, about $10^{-5}$ s, with $\\alpha = 0$, and an inertial frequency $\\omega_0$ that is constant across the helical, conical, skyrmion, and ferromagnetic phases. The paper interprets this constancy as evidence that the inertial effect is intrinsic to $\\beta$-Mn-type Co-Zn-Mn compounds, and proposes that persistent spin fluctuations, rather than monopole propagation or domain-wall motion, generate the inertial response.","pith_inferences":["The paper leaves implicit a direct spectral test: if $\\omega_0 \\approx 0.1$ MHz is a genuine inertial frequency rather than a fitting artifact, $\\chi'(f)$ should show a turnover or sign change as the drive frequency approaches $\\omega_0$, which extending measurements toward 0.1–1 MHz on the same crystals would reveal.","The manuscript does not state whether $\\omega_0 = 0.101$ MHz is a cyclic or angular frequency; under the cyclic reading the inertial correction is below about one percent in the measured window, so the claimed failure of the conventional model may rest on only a few high-frequency points.","If spin fluctuations are the root cause, the same inertial term should appear in other beta-Mn-type compounds with strong Mn fluctuations, and its size should correlate with Mn content; this is a compositional trend that goes beyond the two samples studied here.","The agreement of relaxation times extracted independently from $\\chi'(f)$ and $\\chi''(f)$ could be used as a general model-selection metric: any competing relaxation formula that makes the two independent fits agree within the noise would also need to be considered before accepting inertia."],"forward_implications":["If the central claim is correct, standard Cole-Cole analyses of ac susceptibility in beta-Mn-type Co-Zn-Mn compounds will misestimate relaxation times, because fitting $\\chi'$ and $\\chi''$ separately with Eq. 2 gives inconsistent values while Eq. 3 reconciles them.","The zero relaxation-time distribution ($\\alpha = 0$) across all phases means a single relaxation process with $\\tau \\sim 10^{-5}$ s governs helical, conical, skyrmion, and ferromagnetic regimes, a testable single-process picture for future experiments.","Nonzero $\\chi''$ and nonzero isothermal–adiabatic susceptibility difference in pure phases imply energy dissipation is not confined to skyrmion phase boundaries, which should matter for estimates of switching losses in skyrmion devices made from these materials.","Because $\\omega_0$ is phase-independent, the inertial term can serve as a material-specific fingerprint, allowing comparison of the same parameter across different Co-Zn-Mn compositions and related chiral magnets.","The proposed origin in spin fluctuations suggests that tuning Mn content or applying pressure should shift the inertial frequency $\\omega_0$ in a predictable way, providing a route to test the mechanism."],"supporting_citations":[{"why":"Supplies the inertial relaxation model (Eq. 3) by adding a second-derivative, inertia-like term to the standard response function.","marker":"[33]"},{"why":"Demonstrates the same inertial term in the quantum spin ice Yb2Ti2O7, the precedent the paper extends to chiral magnets.","marker":"[34]"},{"why":"Provides the Casimir–du Pré derivation of the ac susceptibility relaxation equation (Eq. 1) that the paper starts from.","marker":"[48]"},{"why":"Introduces the Cole-Cole generalized Debye form (Eq. 2) that the paper shows fails for these compounds.","marker":"[49]"},{"why":"Reports ac susceptibility relaxation in Fe1-xCoxSi, a skyrmion host against which the observed frequency range and model failure are compared.","marker":"[30]"},{"why":"Provides the phase diagram and relaxation analysis in Cu2OSeO3, the baseline for nonzero A and relaxation behavior at skyrmion boundaries.","marker":"[31]"},{"why":"Establishes the beta-Mn-type structure, site disorder, and Mn-spin fluctuations that the paper invokes as the origin of the inertial effect.","marker":"[18]"}],"fun_headline_variants":["Standard relaxation models fail in Co-Zn-Mn magnets","Inertial term required for Co-Zn-Mn relaxation dynamics","Co-Zn-Mn magnets defy Debye: inertial effect at play","Universal inertial response in chiral Co-Zn-Mn compounds","Why Co-Zn-Mn relaxation breaks conventional fits"],"cache_read_input_tokens":17664,"weakest_assumption_plain":"The load-bearing premise is that the 1747–9747 Hz window actually lets the fitted inertial term show up: if the reported $\\omega_0 \\approx 0.101$ MHz is a cyclic frequency, the term $(\\omega/\\omega_0)^2$ is below one percent in that window and the model's advantage over the conventional one may be a fitting artifact.","fun_headline_variants_meta":{"raw":{"variants":["Standard relaxation models fail in Co-Zn-Mn magnets","Inertial term required for Co-Zn-Mn relaxation dynamics","Co-Zn-Mn magnets defy Debye: inertial effect at play","Universal inertial response in chiral Co-Zn-Mn compounds","Why Co-Zn-Mn relaxation breaks conventional fits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000217,"raw_usage":{"total_tokens":1509,"prompt_tokens":1094,"completion_tokens":415,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":710,"completion_tokens_details":{"reasoning_tokens":330}},"tokens_in":710,"tokens_out":415,"duration_ms":4674,"temperature":1.0,"reasoning_tokens":330,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:44:11.412647+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to refit the same $\\chi'(f)$ and $\\chi''(f)$ scans with Eq. 2 and Eq. 3 under an explicit convention for $\\omega_0$ (cyclic or angular) and compare residuals across the full 1.7–9.7 kHz range; if the improvement disappears or is confined to the highest-frequency points, the inertial claim is not established. A cleaner experiment would extend ac susceptibility to 0.1–1 MHz on the same crystals and look for the $\\chi'$ turnover predicted near the fitted $\\omega_0$.","supporting_citations":[{"cited_title":"Inertial effects in systems with magnetic charge","cited_arxiv_id":null,"evidence_quote":"Supplies the inertial relaxation model (Eq. 3) by adding a second-derivative, inertia-like term to the standard response function."},{"cited_title":"A measure of monopole inertia in the quantum spin ice Yb 2 Ti 2 O 7","cited_arxiv_id":null,"evidence_quote":"Demonstrates the same inertial term in the quantum spin ice Yb2Ti2O7, the precedent the paper extends to chiral magnets."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Casimir–du Pré derivation of the ac susceptibility relaxation equation (Eq. 1) that the paper starts from."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the Cole-Cole generalized Debye form (Eq. 2) that the paper shows fails for these compounds."},{"cited_title":"Magnetic relaxation phenomena in the chiral magnet Fe 1− x Co x Si: An ac susceptibility study","cited_arxiv_id":null,"evidence_quote":"Reports ac susceptibility relaxation in Fe1-xCoxSi, a skyrmion host against which the observed frequency range and model failure are compared."},{"cited_title":"Phase diagram and magnetic relaxation phenomena in Cu 2 OSeO 3","cited_arxiv_id":null,"evidence_quote":"Provides the phase diagram and relaxation analysis in Cu2OSeO3, the baseline for nonzero A and relaxation behavior at skyrmion boundaries."},{"cited_title":"Deciphering structural and magnetic disorder in the chiral skyrmion host materials Co x Zn y Mn z (x+ y+ z= 20)","cited_arxiv_id":null,"evidence_quote":"Establishes the beta-Mn-type structure, site disorder, and Mn-spin fluctuations that the paper invokes as the origin of the inertial effect."}],"review_version":1}