Field-induced spin dynamics in i-MAX Tb compound

Ariel Maniv; Asaf Pesach; Daniel Potashnikov; Dror Yahav; El'ad N. Caspi; Eran Maniv; Johanna Ros'en; Moshe Schechter; Quanzheng Tao

REVIEW 3 major objections 6 minor 24 references

Field-induced spin dynamics in i-MAX Tb compound

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that the Tb-based i-MAX compound (Mo2/3Tb1/3)2AlC develops field-controlled spin dynamics in the kHz range, probably a superparamagnetic state, in the magnetic-field window 0.2 T to 6 T.

desk verdict Useful new ac susceptibility data on Tb-i-MAX, but the superparamagnetic label is not yet earned—the fitted attempt times alone argue against canonical blocking. read the letter →

arxiv 2501.01520 v1 pith:W3D2L5DF submitted 2025-01-02 cond-mat.str-el

Dror Yahav , Daniel Potashnikov , Asaf Pesach , El'ad N. Caspi , Quanzheng Tao , Johanna Ros'en , Moshe Schechter , Ariel Maniv

show 1 more author

Eran Maniv

This is my paper · ORCID

classification cond-mat.str-el

keywords i-MAXcompoundsrare-earthmagnetismacsusceptibilityspindynamicssuperparamagnetismMydoshparameterdensitywavemagneticphasediagram

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using ac susceptibility at frequencies from 0.75 to 10 kHz and fields up to 9 T, this paper claims that (Mo2/3Tb1/3)2AlC develops a field-induced dynamical regime: between µ0H ≈ 0.2 T and 6 T the magnetic transition splits and the loss signal shifts with frequency. The shift, measured by the Mydosh parameter ⟨ϕ⟩ = 0.168(5), is large enough to indicate superparamagnetism—slowly flipping magnetic clusters—rather than a collective spin-glass freeze. The authors conclude that Tb-i is a transitional member of the i-MAX family, bridging rare-earth compounds with stable spin dynamics and those dominated by fluctuations, and that its known spin-density-wave order coexists with superparamagnetic domains in this field window. A sympathetic reader would care because the result gives a concrete, field-tunable magnetic phase diagram for a layered magnetic laminate and shows that ac susceptibility can expose dynamics invisible to static magnetization and neutron diffraction.

What carries the argument

The analytical engine is the frequency dependence of the complex ac susceptibility. The Mydosh parameter, ϕ = ΔTf/[Tf Δ(log ν)], quantifies how much the freezing/loss peak shifts with measurement frequency; a value near 0.168 is read as superparamagnetic blocking, while spin glasses typically give smaller values. The relaxation time τ is then extracted by fitting the imaginary part χ′′(ω) to the generalized Debye model, and its temperature dependence is converted to energy barriers and attempt times through Arrhenius fits. This machinery turns raw loss-peak shifts into the phase assignments, relaxation times, and energy barriers that support the claimed dynamic phase.

What would settle it

Measure the ac susceptibility of a Tb-i-MAX sample that is free of the Mo2C and Mo3Al2C impurity phases, or else measure separately synthesized impurity powders over 3-40 K and 0-7 T. If the frequency-dependent split and the ⟨ϕ⟩ ≈ 0.168 shift disappear or are reproduced entirely by the impurity phases, then the superparamagnetic assignment for the intrinsic compound is falsified; if they survive, the claimed intrinsic dynamic phase is confirmed.

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Extended reading notes

Core claim

The central claim is that Tb-i-MAX, the compound (Mo2/3Tb1/3)2AlC, exhibits slow, field-controlled spin dynamics in the kHz range throughout 0.2 T < µ0H < 6 T, and that these dynamics are best described as a probable superparamagnetic state rather than a spin glass. The evidence is the frequency shift of the ac-loss peak: computing the Mydosh parameter at several fields gives an essentially field-constant ⟨ϕ⟩ = 0.168(5), a value that the literature associates with superparamagnetic blocking. Within this field window the high-temperature phase (phase I) splits into two transitions at high frequency, the low-temperature phase (phase II) becomes frequency independent, and a proposed combined texture of spin-density-wave order plus superparamagnetic domains accounts for the data. Temperature-frequency scans fitted with the generalized Debye model give relaxation times that follow an Arrhenius law (with a double Arrhenius behavior at 0.2 T and a plateau suggestive of quantum tunneling of magnetization at 0.5 T) and hopping times and energy barriers that grow with field. Above about 6 T the frequency dependence disappears, the Mydosh parameter vanishes, and phases I and II merge, matching the field at which hysteresis loops in earlier work terminate. The paper reads these observations, together with earlier muon-spin-rotation results, as evidence that Tb-i sits at the boundary between stable and fluctuation-dominated rare-earth i-MAX compounds.

Load-bearing premise

The load-bearing premise is that the kHz frequency-dependent signal measured between 0.2 T and 6 T comes from the Tb-i-MAX matrix itself and not from the superconducting impurity phases (Mo2C, Mo3Al2C) known to be present in the sample, since the paper dismisses impurities mainly on the grounds that their transition temperatures lie below 10 K.

Editorial extensions

If this is right

The Tb-i-MAX phase diagram acquires a field-controlled dynamical region (0.2 T to 6 T) in which single-frequency ac-susceptibility scans misplace or merge transitions, so multiple frequencies become necessary to resolve the phases.
The Mydosh parameter ⟨ϕ⟩ = 0.168(5) provides a quantitative fingerprint that distinguishes this material from spin-glass behavior and aligns it with superparamagnetic blocking.
If the superparamagnetic interpretation holds, the known spin-density-wave order in Tb-i is not a static texture alone; a frequency-dependent, slowly relaxing component coexists with it in the same field-temperature window.
The disappearance of frequency dependence above about 6 T, together with the merging of phases I and II, ties the dynamic regime to the field scale where magnetization hysteresis terminates, suggesting a field-induced crossover from blocking to a more rigid magnetic state.
The double Arrhenius behavior and the plateau near 0.5 T imply at least two distinct relaxation channels and call for finer-field temperature-frequency scans to map their boundary.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, the cleanest test of the superparamagnetic assignment is a control experiment on impurity-free material or a direct ac-susceptibility measurement of the Mo2C and Mo3Al2C impurity phases in the same field-temperature window; if the kHz loss peak survives, the intrinsic interpretation is strongly supported.
If the zero-field frequency dependence extends, as the authors hypothesize, to MHz rates, then the 'zero-field transition' measured by static probes may be a superposition of two dynamic transitions; combining ac data with muon-spin-rotation spectra at the same fields could map the full relaxation spectrum.
A neighboring system to watch is the lighter rare-earth i-MAX compounds: the same frequency-resolved protocol should show a much weaker or absent Mydosh shift if Tb really is the transitional member, turning this single-compound claim into a family trend.
The field-dependent growth of the fitted attempt frequency and energy barrier hints at an external-field-tuned energy-level splitting; a theoretical single-domain or cluster model with RKKY and anisotropy terms could predict whether the barrier should increase or saturate with field.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

New data first: this is the first frequency-resolved ac susceptibility study of Tb-i-MAX in applied fields, covering roughly 0.2–6 T and 10 Hz–10 kHz. The core observation is solid: a frequency-dependent splitting of the high-temperature transition, a Mydosh parameter of 0.168(5), and a phase diagram that extends earlier work. The data look credible, the paper is clearly written, and the raw data are deposited, which helps.

Where I part company is the interpretive label. The claim that this is a "probable superparamagnetic state" rests almost entirely on the Mydosh parameter being above the spin-glass range. That is a weak discriminator. The paper's own Arrhenius fits give attempt times τh1 ≈ 0.4 μs at 0.2 T, about four to six orders of magnitude slower than canonical superparamagnetic blocking. That alone should have raised a flag. It could be strong inter-cluster interactions (Vogel-Fulcher), cluster-glass dynamics, or an artifact of fitting a single Debye peak over a broad multiple-process response. The paper reports no error bars on these fits, so we cannot tell. The phrase "probable" is honest, but the abstract and conclusions push the superparamagnetic state harder than the data support.

The impurity concern is real but minor. The dynamic peaks sit at 16–28 K, far above the superconducting transitions of Mo2C and Mo3Al2C listed in Table I, so impurities are unlikely to generate that signal. The extrapolation to MHz dynamics at zero field is speculative and should be labeled as such.

Bottom line: this is a useful, citable experimental contribution—a solid phase diagram and a frequency-dependent fingerprint for one compound. As a claim to a new dynamic phase, it needs more work: alternative relaxation models, error propagation on the Arrhenius parameters, and ideally a test that distinguishes blocking from cluster glass. That is refereeable. I would send it to review, and I would probably recommend publication after the interpretation is reined in or the fits are made quantitative.

Referee Report

3 major / 6 minor

Summary. The paper reports ac susceptibility measurements on the i-MAX compound (Mo2/3Tb1/3)2AlC as a function of temperature (3–300 K), magnetic field (0–9 T), and frequency (0.75–10 kHz). The main claim, stated in the Conclusions, is that the compound shows spin dynamics in the kHz range in the field interval 0.2 T < μ0H < 6 T, interpreted as a 'probable superparamagnetic state.' The supporting evidence is a frequency-dependent splitting of the high-temperature transition, a Mydosh parameter ⟨φ⟩ = 0.168(5), and generalized-Debye fits that yield relaxation times τ(T). These are analyzed with Arrhenius fits to extract energy barriers and attempt times. A field–temperature phase diagram is constructed, and the compound is positioned as a transitional member of the i-MAX family between spin-stable and fluctuation-dominated systems. Raw data are deposited on Zenodo.

Significance. If the superparamagnetic interpretation holds, the paper establishes a field-controlled dynamic state coexisting with the known spin-density-wave order in a rare-earth i-MAX compound, which would be a useful addition to the magnetic phase diagram of this materials family. The work is also valuable as a systematic ac susceptibility study of an i-MAX system, with data spanning a wide field range and multiple frequencies. Credit is due for making raw data available and for using standard models (Mydosh parameter, generalized Debye, Arrhenius) in a transparent way. However, the central interpretive claim rests mainly on a single Mydosh parameter and fits whose uncertainties and physical consistency are not fully addressed; the reported Arrhenius prefactor is orders of magnitude slower than canonical superparamagnetic attempt times, which weakens the conclusion.

major comments (3)

[Relaxation Measurements, Eq. (3)] The Arrhenius fit at μ0H = 0.2 T yields τh1 ≈ 0.4 μs for the high-temperature process, which is four to six orders of magnitude larger than typical superparamagnetic attempt times (10^-9 to 10^-13 s). No confidence intervals or goodness-of-fit measures are reported for this or any other fit. Such a large prefactor is equally compatible with cluster-glass dynamics, domain-wall motion, or an artifact of fitting multiple overlapping processes with a single generalized-Debye expression. Because the superparamagnetic label is the paper's central conclusion, this issue is load-bearing and needs to be addressed either by providing physically motivated constraints on τ0, by reporting uncertainties and fit quality, or by softening the interpretation to a broader 'slow dynamics' claim.
[Results, Fig. 3] The Mydosh parameter ⟨φ⟩ = 0.168(5) is the primary evidence for superparamagnetism, but this value is also found in interacting cluster-glass and superspin-glass systems. The paper does not provide independent blocking evidence such as FC/ZFC magnetization bifurcation, memory or aging effects, or non-linear susceptibility measurements. Without such corroboration, the qualitative distinction between superparamagnetic blocking and other glassy dynamics is not established. The use of 'probable' in the Conclusions is appropriate, but the Discussion goes further and asserts 'the existence of superparamagnetism' based on the same data; the manuscript should either supply additional evidence or consistently present the superparamagnetic state as one plausible scenario.
[Table I and phase IV in Discussion] The paper dismisses the listed impurities (Mo2C and Mo3Al2C, superconducting below 10 K) on the grounds that their transition temperatures are lower than the Tb-i magnetic transitions, yet it attributes the low-field, low-temperature phase IV to a superconducting impurity. This shows that impurity signals do appear in the ac susceptibility data. No control measurement, impurity subtraction, or quantitative estimate of the impurity contribution in the 0.2–6 T, 16–28 K region is provided. While the temperature separation makes a direct impurity explanation of the high-temperature dynamics unlikely, a quantitative statement is needed to fully secure the intrinsic nature of the observed frequency-dependent response.

minor comments (6)

[Title and header] The title contains a typo: 'spin dynamics ini -MAX' should read 'spin dynamics in i-MAX'.
[Discussion] The word 'superparamgnetism' is misspelled; it should be 'superparamagnetism'.
[References] Reference [5] has an incomplete author list ('M. , J. Lu'); the first author's name is missing.
[Results, Fig. 3(b)] The Mydosh parameter is calculated using only the highest and lowest measured frequencies; for most fields only two frequencies are available. The authors should state whether the multi-frequency data at μ0H = 1.4 T give a consistent φ when computed from intermediate frequency pairs.
[Phase diagram, Fig. 5] The caption states that the color gradient is a guide to the eye based on the derivative dχ'/dT. This is difficult to interpret without a scale; consider adding a brief explanation in the text of how the gradient regions were assigned.
[Discussion] The extrapolation of the dynamic phase to zero field, with spin dynamics in the MHz range, is explicitly labeled as a hypothesis, which is good. However, the physical justification for this extrapolation (based on μSR data) should be expanded, since the ac data do not extend below 0.2 T.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the superparamagnetic claim is an interpretation of new frequency-dependent ac-susceptibility data using external Mydosh and Debye criteria.

full rationale

The paper performs no derivation that reduces to its inputs. It reports ac susceptibility measurements and uses the generalized Debye model to extract relaxation times τ(T), then fits τ(T) to the Arrhenius law and computes the Mydosh parameter from measured peak shifts. The superparamagnetic interpretation is based on an external literature threshold (⟨ϕ⟩ = 0.168(5), cited to refs. [19,20] and [22]) and on the observed frequency-dependent peaks, not on a parameter fitted to the target conclusion. Self-citations to refs. [6,11,12,13] are used to label previously characterized SDW phases and to note that the sample comes from the same batch, but the claimed new spin dynamics in the 0.2–6 T field range is established by the present frequency-dependent χ′ and χ″ measurements. The load-bearing external inputs—the Debye relaxation model, Arrhenius law, and the Mydosh classification—are generic literature tools, not outputs of this paper. The questionable Arrhenius prefactors (e.g., τh ≈ 0.4 μs at 0.2 T) raise a physical-reasonableness concern about the superparamagnetic label, but they are not a circularity: they are fitted parameters that are then interpreted, not predictions forced by construction. No equation in the paper is equivalent to its own input by definition.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central claim depends on standard model assumptions (Debye and Arrhenius) and on one key domain assumption about impurity contribution. The paper introduces one interpretive entity, superparamagnetic domains, with no independent evidence beyond the ac susceptibility data itself. The fitted Arrhenius parameters are honest fits, not predictions, so they do not inflate the free-parameter count beyond what is normal for this kind of analysis.

free parameters (3)

Arrhenius energy barrier U0 and hopping time tau_h0 (per field) = e.g., at 0.2T: U1=97 K, tau_h1=0.4 microseconds (high-T); U2=6 K, tau_h2=60 microseconds (low-T); other fields in…
Fit of tau(T) to Eq. 3 (Arrhenius) for each field; used to characterize relaxation dynamics and support the superparamagnetic interpretation.
Debye model distribution parameter alpha = not reported in main text
Fit of chi''(f) to Eq. 2 at each temperature; controls the spread of relaxation times and enters the extraction of tau.
Freezing temperature T_f = peak positions of chi'' at each field and frequency
Measured peak positions used to compute the Mydosh parameter; not a free parameter in a model fit but a chosen observable.

assumptions (5)

domain assumption Peaks in the real and imaginary parts of ac susceptibility mark magnetic transitions.
In the Results section, peaks are associated with possible magnetic transitions; this is standard for ac susceptibility but is an interpretive step, not proven for this compound.
domain assumption Impurities (Mo2C, Mo3Al2C) do not significantly affect the measured ac susceptibility because their transition temperatures are below 10 K.
Sample characterization section; no quantitative subtraction or control measurement is shown, yet the central field/frequency-dependent signal is attributed to the Tb-i-MAX matrix.
domain assumption The Mydosh parameter criterion and generalized Debye model (Eq. 2) are valid for identifying superparamagnetism in this compound.
Relaxation model from refs 14 and 20 is applied to the measured chi''(f); applicability to a compound with coexisting spin-density-wave order is assumed.
domain assumption The sample is of the same batch and phase purity as that reported in ref 13.
Experimental section states the sample was prepared from the same batch reported in [13], so prior structural and magnetic characterization transfers to this work.
ad hoc to paper Extrapolation of the frequency-dependent phase boundary to zero field relies on the assumption that the mechanism persists below 0.2 T.
Discussion hypothesizes that frequency dependence stretches to zero field and MHz frequencies despite no data below 0.2 T; this is introduced to support the 'border compound' narrative.

invented entities (1)

Superparamagnetic domains in phase I
purpose: Explain the frequency-dependent peak splitting and the Mydosh parameter value in the field range 0.2-6 T.
No direct microscopic or local-probe imaging is provided; the interpretation is inferred from ac susceptibility frequency dependence and comparison to (Eu,Sr)S in ref 22. It is a proposed state rather than a measured object.

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Cite this review

Pith. "Pith review of Field-induced spin dynamics in i-MAX Tb compound." pith.science (2026). https://pith.science/paper/W3D2L5DF

@misc{pith2026250101520,
  author       = {Pith},
  title        = {Pith review of: Field-induced spin dynamics in i-MAX Tb compound},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W3D2L5DF}},
  note         = {Machine review of arXiv:2501.01520}
}

read the original abstract

We report a comprehensive study of spin dynamics in the (Mo2/3Tb1/3)2AlC i-MAX compound using ac susceptibility measurements across a range of magnetic fields. Unique behaviors were observed, including spin dynamics in the kHz range between mu_0 H~0.2T-6T, indicating a non-trivial superparamagnetic state, suggesting that the compound acts as a transitional system within the i-MAX family, bridging stable spin-dynamic materials and fluctuation-dominated ones. Field- and frequency-dependent magnetic phase transitions, coupled with relaxation behaviors, reveal complex interactions between spin density waves and superparamagnetic components. These findings, corroborated by uSR studies, deepen our understanding of magnetic phase diagrams and field-induced phenomena in i-MAX systems, laying the groundwork for further exploration of their unique properties and applications.

Figures

Figures reproduced from arXiv: 2501.01520 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

M. W. Barsoum, The M N +1AXN phases: A new class of solids, Progress in Solid State Chemistry 28, 201 (2000)

work page 2000

[2] [2]

Dahlqvist, J

M. Dahlqvist, J. Lu, R. Meshkian, Q. Tao, L. Hultman, and J. Ros´ en, Prediction and synthesis of a family of atomic laminate phases with Kagom´ e-like and in-plane chemical ordering, Science Advances 3, e1700642 (2017)

work page 2017

[3] [3]

Dahlqvist, M

M. Dahlqvist, M. W. Barsoum, and J. Rosen, MAX phases - Past, present, and future, Materials Today (2023)

work page 2023

[4] [4]

Naguib, M

M. Naguib, M. W. Barsoum, and Y. Gogotsi, Ten Years of Progress in the synthesis and Development of MXenes, Advanced Materials 33, e2103393 (2021)

work page 2021

[5] [5]

Q. Tao, M. , J. Lu, S. Kota, R. Meshkian, J. Halim, J. Palisaitis, L. Hultman, M. W. Barsoum, P. O. Persson, and J. Rosen, Two-dimensional Mo1.33C MXene with di- vacancy ordering prepared from parent 3D laminate with in-plane chemical ordering, Nature Communications 8, 14949 (2017)

work page 2017

[6] [6]

Q. Tao, J. Lu, M. Dahlqvist, A. Mockute, S. Calder, A. Petruhins, R. Meshkian, O. Rivin, D. Potashnikov, E. N. Caspi, et al., Atomically layered and ordered rare- earth i-MAX phases: a new class of magnetic quaternary compounds, Chemistry of Materials 31, 2476 (2019)

work page 2019

[7] [7]

J. Yang, G. Yao, S. Sun, Z. Chen, S. Yuan, K. Wu, X. Fu, Q. Wang, and W. Cui, Structural, magnetic properties of in-plane chemically ordered (Mo 2/3R1/3)2AlC (R= Gd, Tb, Dy, Ho, Er and Y) MAX phase and enhanced capac- itance of Mo 1.33C MXene derivatives, Carbon 179, 104 (2021)

work page 2021

[8] [8]

J. Yang, R. Liu, N. Jia, K. Wu, X. Fu, Q. Wang, and W. Cui, Novel W-based in-plane chemically ordered (W2/3R1/3)2AlC (R= Gd, Tb, Dy, Ho, Er, Tm and Lu) MAX phases and their 2D W 1.33C MXene derivatives, Carbon 183, 76 (2021)

work page 2021