Correlation between ferroelectricity and torsional motion of acetyl groups in tris(4-acetylphenyl)amine observed by muon spin relaxation

A. Koda; F. L. Pratt; H. Okabe; J. G. Nakamura; M. Hiraishi; R. Kadono; R. Kumai

REVIEW 3 major objections 4 minor 45 references

Correlation between ferroelectricity and torsional motion of acetyl groups in tris(4-acetylphenyl)amine observed by muon spin relaxation

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Muon spin relaxation shows that thermally activated random torsional motion of acetyl groups, setting in near 350 K, promotes the ferroelectric-to-paraelectric transition in tris(4-acetylphenyl)amine (TAPA), rather than resulting from it.

desk verdict A solid muSR study with a likely kcal/mol-to-eV unit error that, as written, makes the central torsional-activation mechanism physically impossible at 350 K. read the letter →

arxiv 2501.16685 v1 pith:TJMBPODE submitted 2025-01-28 cond-mat.mtrl-sci

J. G. Nakamura , M. Hiraishi , H. Okabe , A. Koda , R. Kumai , F. L. Pratt , R. Kadono This is my paper · ORCID

classification cond-mat.mtrl-sci PACS 76.75.+i77.80.-e

keywords muonspinrelaxationorganicferroelectricacetylgrouptorsionmoleculardynamicshyperfineinteractionstris(4-acetylphenyl)aminestructuralphasetransitioncoercivefield

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

This paper tries to establish that the organic ferroelectric tris(4-acetylphenyl)amine (TAPA) owes its switchable polarization, and its loss of that polarization, to the twisting of its acetyl groups. Implanted positive muons form radicals on the phenyl rings and on the acetyl oxygen, and the measured relaxation of their spins tracks the fluctuating magnetic fields produced by acetyl-group torsion. The torsion turns on around $T_0\approx 350$ K, well below the structural transition at $T_c\approx 408$ K, and its random character explains why the coercive field shrinks as temperature rises. The conclusion is that the local molecular motion drives the ferroelectric-to-paraelectric transition, not the other way around.

What carries the argument

The central probe is the muonated radical: a positive muon substituted as a light hydrogen isotope binds to carbon sites on the phenyl ring (C11–C18) and to the O2 oxygen of the acetyl group, forming paramagnetic states whose hyperfine and nuclear-hyperfine couplings are sensitive to local motion. The paper analyses the magnetic-field dependence of the longitudinal relaxation rate with a Havriliak-Negami spectral density $J(\omega)$, a generalized broadened Lorentzian, to extract the mean fluctuation frequency $\tilde{\nu}\approx 1\text{--}4\times 10^4$ MHz and linewidth $\Delta_{\mathrm{eff}}$, and introduces an Edwards-Anderson order parameter $Q$ in the field autocorrelation function to separate static from dynamic fluctuations. A small $Q$ indicates that the fields fluctuate because surrounding molecules (the acetyl groups) move, not because the muon itself hops, which is what anchors the interpretation of the spin relaxation as a measurement of acetyl torsion.

What would settle it

Measure muon spin relaxation in a TAPA analogue whose acetyl groups are locked so they cannot twist (or are replaced by non-rotating groups of similar size): if $1/T_{1\mu}$ still rises with temperature and the coercive field still collapses near 408 K, the torsional-motion mechanism is wrong. A complementary check is quasielastic neutron scattering, which should show the acetyl torsional mode growing in the same 1–4$\times10^4$ MHz range above $T_0$; its absence would contradict the assignment.

Watch

Extended reading notes

Core claim

Muons implanted into TAPA form paramagnetic muonated radicals at five phenyl-carbon sites and at the acetyl oxygen (O2), and the longitudinal spin relaxation of these radicals is governed by fluctuations of hyperfine and nuclear-hyperfine fields that the paper attributes to random torsional motion of the acetyl group around the bond to the phenyl ring. The relative yield of phenyl radicals rises stepwise at $T_0\approx 350$ K, the mean relaxation rate $1/T_{1\mu}$ grows with temperature, the oxygen atomic displacement parameter increases non-linearly, and the coercive field decreases until order disappears at $T_c\approx 408$ K. Because the muon-observed torsion sets in at lower temperatures than the structural change, the authors conclude that thermally activated random twisting of the acetyl groups promotes the structural transition rather than resulting from it, and that the same randomness hinders the coherent dipole rotation needed for ferroelectric switching.

Load-bearing premise

The whole causal story depends on attributing the temperature-dependent muon spin relaxation to random torsional motion of the acetyl groups; if muon diffusion, radical hopping, or some other molecular libration produces the fluctuating hyperfine fields instead, the link to ferroelectric switching and to the structural transition is not established.

Editorial extensions

If this is right

The coercive field of TAPA is set by the competition between coherent field-driven rotation and thermally random torsion, so $E_c$ will always fall as temperature rises toward $T_c$.
The structural phase transition at $T_c$ is driven by the local torsional motion, implying that suppressing that motion (e.g., by deuteration or chemical stiffening of the acetyl bond) should raise $T_c$ and improve switchable polarization.
Muon spin relaxation as implemented here can serve as a general microscopic probe for rotary molecular groups in organic and hybrid ferroelectrics.
The stepwise change in radical yield at $T_0\approx 350$ K marks thermal activation of torsion and can be used as a microscopic onset signal for molecular mobility.
Therefore, maximum ferroelectric performance for TAPA occurs at the low-temperature end of the switchable range.

Reading between the lines

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

If the causal order is right, one testable extension is to deuterate the acetyl methyl groups or replace them with bulkier groups: both the muon relaxation onset $T_0$ and $T_c$ should shift in proportion to the torsional barrier, analogous to the observed deuteration shift of the transition in MAPbI$_3$.
The same muon-radical approach could be applied to other molecular ferroelectrics with rotating dipolar substituents to determine whether their phase transitions are also motion-driven rather than lattice-driven.
The identification of the Ad1 component with the O2 radical and the low-temperature C9 contribution are assumptions; a direct test would be to measure the muon level-crossing spectrum above $T_0$ to see whether the O2/C9 signals change exactly as the torsion activates.
The oxygen displacement parameter $U_{\mathrm{iso}}$ contains no timescale, so the paper's link relies on the muon data; a complementary quasielastic neutron scattering measurement of the acetyl torsion in the same temperature range would validate the timescale independently.

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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

The muSR experiment is real, new, and well executed. The paper gives the first direct microscopic probe of acetyl-group dynamics in TAPA, and the ALC/DFT assignment of the muonated radicals is careful. The stepwise change in radical yield at T0, the rise of 1/T1, and the concurrent oxygen Uiso increase track the fall of the coercive field. That correlation is genuine and worth reporting. The authors also know the limits of their own evidence: they concede Uiso carries no time scale and that the HN fits have large errors with only 4–5 field points. This is not a sloppy paper.

But the stress-test concern is right, and it is not a minor footnote. In Section IV the text says torsional motion is restricted to the bottom of a potential well of ≃ 2.3 eV, citing ref. 33. At 350 K, kBT is about 30 meV. A 2.3 eV barrier suppresses activated jumps by exp(-77), so thermal activation above T0 is impossible. That directly contradicts the central claim that random torsional motion sets in around 350 K and drives the structural transition. The cited Heliyon paper almost certainly reports barriers in kcal/mol, making this a probable unit error—2.3 kcal/mol ≈ 0.1 eV is a plausible hindered-rotation barrier. But as written, the paper is internally inconsistent. A referee must check ref. 33 and the units.

Even with the barrier fixed, the causal claim is stronger than the data. The experiment shows correlation between muSR relaxation, oxygen displacement, and coercive field. It does not manipulate the acetyl torsion, and the muSR relaxation could, in principle, arise from other molecular librations or muon-related dynamics. The Edwards–Anderson argument against muon hopping is reasonable, but it is not a proof. The abstract's "drives the structural transition" should be softened to "is associated with" or similar.

The paper deserves a serious referee. The experiment is important for the molecular ferroelectrics community, the analysis is mostly transparent, and the unit error is likely fixable. If the 2.3 eV is not a unit error, the mechanism is not plausible and the paper should be rejected. But the referee should be asked to verify that one number, not to redo the whole experiment.

I would bring this to reading group—the unit error and the correlation-versus-causation discussion are worth talking through. I would not cite it in my own work until the barrier question is resolved.

Referee Report

3 major / 4 minor

Summary. The manuscript reports muon spin relaxation (μSR) and avoided level-crossing (ALC) measurements on the organic ferroelectric tris(4-acetylphenyl)amine (TAPA), combined with DFT calculations, and interprets the temperature and field dependence of the longitudinal relaxation rate and radical yields as evidence that thermally activated random torsional motion of the acetyl groups sets in above T0 ≈ 350 K, hinders coherent polarization switching (thereby reducing the coercive field), and promotes the structural transition at Tc ≈ 408 K. The paper also presents XRD atomic displacement parameters showing non-linear oxygen Uiso above T0 and uses a Havriliak-Negami spectral analysis with an Edwards–Anderson order parameter Q to separate static and dynamic contributions to the observed relaxation.

Significance. The paper offers a concrete microscopic mechanism for ferroelectric switching degradation in a molecular ferroelectric and connects it to a muon-based local probe, with supporting DFT site assignments and systematic LF and TF μSR data. The empirical correlation between 1/T1μ, oxygen Uiso, and Ec is valuable in itself. However, the causal chain from muon relaxation to acetyl torsion to ferroelectric switching is not uniquely established, and one numerical statement about the rotational barrier is internally inconsistent as written, so the significance hinges on resolution of these points.

major comments (3)

[Section IV, potential-well paragraph] The statement that the torsional motion is restricted to "near the bottom of the rotational motion potential well (≃ 2.3 eV)" [Ref. 33] is irreconcilable with the paper's central claim of thermally activated torsional motion above T0 ≈ 350 K. At this temperature kBT ≈ 30 meV, so a 2.3 eV barrier would give an activation factor exp(−Ea/kBT) ≈ 10^−33, making the proposed mechanism impossible. The cited reference likely reports a barrier of ~2.3 kcal/mol (≈0.1 eV), implying a unit error; the authors must correct this and reassess the quantitative argument, since the discussion of Q and the step at T0 rely on the accessibility of the torsional motion.
[Section III.B, interpretation of 1/T1μ (Eq. 6, Fig. 4c)] The interpretation that the increasing 1/T1μ is dominated by acetyl-group torsion is not uniquely determined by the data. The paper itself notes (Section III.B, after Fig. 4) that Uiso carries no time scale, and the Ad1 component is attributed to spin/charge exchange (Section III.B, Eq. (2) analysis). Muon diffusion, radical hopping, or other low-frequency librations of the molecular backbone could produce similar temperature and field dependences. The Edwards–Anderson argument in Section IV that small Q excludes radical hopping depends on the specific assignment of Δ_eff and the HN spectral form, so it does not close the alternative-dynamics loophole. A more direct test (e.g., comparison with dielectric loss data, deuteration, or a second experimental probe) or a clearly softened causal claim is needed.
[Section III.B, C9 radical assignment] The stepwise increase in APh at T0 ≈ 350 K is attributed to a shift of population between the C9 and phenyl radicals, but the C9 assignment is explicitly "tentative" (Section III.B) and based on its being the only radical with larger HF parameter in a single DFT model. Since the HN fits for 1/T1μ did not converge at some points below T0 (Section III, Fig. 5(a)), the step-like changes in radical yields around T0 are not independently corroborated by the relaxation analysis. The authors should present the fit quality and any constraints on the C9 fraction more directly, or discuss how robust the step is to alternative decompositions.

minor comments (4)

[Abstract and Introduction] The phrase "first-principle density functional theory" should be "first-principles density functional theory."
[Section III.B, Eq. (13) and Fig. 5(e)] The notation for the mean fluctuation frequency is inconsistent: the text and equations use both B̃ν and Bν; please define the symbol once and use it consistently in equations, figure axes, and captions.
[Section IV, Ref. 33] Reference [33] should be checked carefully: if the rotational barrier is indeed 2.3 kcal/mol, the unit must be stated explicitly in the text to avoid the internal inconsistency discussed in the major comments.
[Fig. 4(a) caption] The figure caption does not define Ad1 and Ad2; adding a one-line definition would help readers follow the diamagnetic component discussion.

Circularity Check

1 steps flagged · score 4.0 of 10

Central muSR data are measured and fitted, but the key exclusion of muon/radical hopping — needed to attribute relaxation to acetyl torsion — is carried by a load-bearing self-citation (Ref. 37, same-group arXiv preprint).

self citation load bearing [Section IV, Discussion, paragraph following Eq. (16) (Edwards–Anderson Q interpretation)]
"Q = 1 is expected when the ﬂuctuations are due to self-diﬀusion of the diamagnetic Mu, while Q < 1 when they are dominated by the dynamics of the surrounding ions 36. Since the similar situation can be presumed for the paramagnetic Mu 37, the small Q suggested in TAP A can be regarded as evidence that the cause of the ﬂuctuations is not the hopping motion of radical itself."

To attribute the muon spin relaxation to torsional motion of the acetyl groups, the paper must rule out the competing mechanism in which the implanted muon or radical itself hops. That exclusion is not demonstrated with new data or a derivation here; it is imported from Ref. 36 (Ito and Kadono) and especially Ref. 37 (Kadono and Ito, arXiv:2410.23575), an unpublished preprint by the present corresponding author. Ref. 37 extends the Q<1 (‘surrounding-ion dynamics’) interpretation to paramagnetic muons, which is exactly the premise used to conclude that the fluctuations in TAPA are not caused by radical hopping. The text offers no machine-checked or independently reproduced support for this extension.

full rationale

The paper’s primary observations — the LF/ZF/TF muSR spectra, the ALC resonances, the stepwise change of APh near T0 ≈ 350 K, the temperature dependence of 1/T1µ, and the non-linear oxygen Uiso — are experimental quantities obtained by least-squares fits to well-defined models (Eqs. 1–5, 13). Fitting the Havriliak–Negami form to 1/T1µ does not by itself make the torsional interpretation circular: those parameters are outputs, not the claimed conclusion, and the paper does not rename a fitted parameter as a prediction. The main causal claim is an inference from the coincidence of the muSR step, the Uiso anomaly, and the drop in coercive field (measured in Ref. 15). That inference is plausible but not forced by definition, and no equation in the paper reduces the conclusion to the input data. The one genuinely load-bearing self-citation is the use of Refs. 36 and 37 to exclude muon/radical hopping as the source of the fluctuations. Ref. 36 is by a coauthor, and Ref. 37 is an unpublished same-group arXiv preprint that supplies the paramagnetic-muon Q interpretation; the paper's own sentence explicitly relies on it to rule out hopping. This raises the circularity score to 4, but not beyond, because the rest of the evidence chain (DFT radical sites, ALC identification, temperature-dependent muSR and XRD) stands independently of that citation. A separate physical concern — the quoted 2.3 eV rotational barrier (Ref. 33) versus thermal activation near 350 K (kB T ≈ 30 meV) — is a quantitative plausibility problem, not a circularity: it does not make the argument equivalent to its inputs, but it is an unaddressed limitation that a referee should require the authors to resolve before the central mechanism is accepted.

Assumptions & free parameters 6 free parameters · 8 assumptions · 2 invented entities

The central claim rests on a chain of modeling choices: DFT site assignment, a two-radical fit model, a single NHF second moment, and a generalized spectral density with Edwards-Anderson parameter. The measured temperature trends are real, but the causal attribution to acetyl torsion is inferred rather than directly controlled.

free parameters (6)

Ad1 and Ad2 partial asymmetries = Ad1 ~ 0.01-0.02, Ad2 ~ 0.05-0.06
Fit parameters in Eq. 2 used to separate diamagnetic muon states; the assignment of Ad1 to the O2 radical supports the site interpretation.
Radical partial asymmetries APh and AC9 = temperature dependent; APh stepwise increase near T0 ~ 350 K
Fit variables in Eq. 3; the stepwise change in APh is a central observation connecting radical yield to torsional activation.
Longitudinal relaxation rates 1/T1mu = not given numerically; increases with temperature
Main measured quantity; temperature dependence is the evidence for enhanced acetyl torsional fluctuation.
Havriliak-Negami parameters gamma, delta, Bnu = gamma ~0.3 to 0.6, delta ~1, Bnu ~0.01-0.04 T
Fit to 1/T1mu(BLF) with 4-5 data points per temperature; used to characterize the spectral density of fluctuations.
Effective linewidth Delta_eff = Delta_eff/2pi ~20 to 40-50 MHz above T0
Fit from Eq. 13; interpreted via Edwards-Anderson order parameter Q, not independently measured.
DFT hyperfine calibration shift = not reported; calibrated to muoniated benzene radical
The quantum correction to isotropic hyperfine couplings is set by comparison with benzene; this affects the predicted ALC positions and site assignments.

assumptions (8)

domain assumption Positive muon behaves as a light isotope of hydrogen, so interstitial H DFT states represent muonated radicals.
Used throughout Sec. III A to assign ALC and LF spectra; standard in muSR but not directly verified in TAPA.
domain assumption B3LYP/cc-pVDZ with PM7 geometries gives adequate hyperfine parameters for these radicals.
Used to predict 14 muon sites and to fix HF/NHF parameters in the fits; calibration against benzene only partially compensates for method error.
ad hoc to paper Two radicals, phenyl (C11 representative) and C9, capture all paramagnetic states.
Introduced in Sec. III B because LF resolution cannot distinguish the five phenyl sites and an extra high-HF component was required.
ad hoc to paper A single mean NHF second moment Delta_n/2pi ~41 MHz represents the nuclear hyperfine fields.
Justified by coincidence of the Ph and C9 values; simplifies Eq. 3 but is a modeling choice.
domain assumption Havriliak-Negami spectral density with Edwards-Anderson Q describes muon spin relaxation from molecular fluctuations.
Borrowed from prior work by the same group on poly(3-hexylthiophene) and diamagnetic Mu; no independent benchmark in TAPA.
domain assumption The potential barrier for acetyl rotation is about 2.3 eV, as estimated for similar aromatic substituents.
Reference 33 is a general computational study of internal rotation barriers; used in Sec. IV to justify restricted torsional motion in the lattice.
domain assumption The non-linear increase of oxygen Uiso reflects the acetyl torsional motion, not other dynamic or static disorder.
The authors explicitly note Uiso contains no timescale; the assignment rests on correlation with muSR and the high-temperature disordered structure.
ad hoc to paper The damped diamagnetic component Ad1 corresponds to the O2 radical undergoing spin/charge exchange.
Sec. III B: inferred from the magnitude of lambda_perp and ALC/DFT, not directly proven.

invented entities (2)

C9 muonated radical
purpose: Extra muon radical state with hyperfine parameters larger than the phenyl group, introduced to reproduce the low-temperature LF dependence of initial asymmetry.
DFT predicts a C9 radical about 1 eV above the ground state, but there is no separate ALC resonance assigned to it; the assignment is tentative.
O2-bonded muon (OMu) diamagnetic state independent evidence
purpose: Assigned to the Ad1 component to explain the weak ALC resonance at 200-300 mT and the damped diamagnetic fraction.
Has a matching weak ALC resonance and DFT energy minimum, so it has some independent support outside the LF fits.

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Cite this review

Pith. "Pith review of Correlation between ferroelectricity and torsional motion of acetyl groups in tris(4-acetylphenyl)amine observed by muon spin relaxation." pith.science (2026). https://pith.science/paper/TJMBPODE

@misc{pith2026250116685,
  author       = {Pith},
  title        = {Pith review of: Correlation between ferroelectricity and torsional motion of acetyl groups in tris(4-acetylphenyl)amine observed by muon spin relaxation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TJMBPODE}},
  note         = {Machine review of arXiv:2501.16685}
}

abstract

It is demonstrated by muon spin relaxation and resonance experiments that the switchable spontaneous polarization of the organic ferroelectric compound tris(4-acetylphenyl)amine (TAPA) is governed by the local molecular dynamics of the acetyl group. The implanted muon forms paramagnetic states which exhibit longitudinal spin relaxation due to the fluctuation of hyperfine fields exerted from unpaired electrons. The first-principle density functional theory calculations indicate that these states are muonated radicals localized at the phenyl group and on the carbon/oxygen of the acetyl group, thereby suggesting that the spin relaxation is dominated by the random torsional motion of acetyl group around the CC bond to the phenyl group. The stepwise change in the relative yield of radicals at $T_0\approx 350$ K and the gradual increase in the spin relaxation rate with temperature ($T$) indicate that the torsional motion is significantly enhanced by thermal excitation above $T_0$. This occurs concomitantly with the strong enhancement in the atomic displacement parameter of oxygen in the acetyl group (which is non-linear in $T$), indicating that it is the local molecular motion of the acetyl groups that drives the structural transition.

Figures

Figures reproduced from arXiv: 2501.16685 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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

Figures from the paper (2 more)

**Figure 4.** Figure 4: (c) shows that 1/T1µ steadily increases with increasing temperature at all measured LFs. As shown in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: (e)), indicating that the spin relaxation is induced mainly via the ω23 levels. These figures indicate that the magnitude of ν˜ at respective temperature range is in good agreement with the time scale of fluctuation for the orientation polarization of molecules30 . IV.…

Discussion (0). Continue with ORCID to comment.

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Pith tools

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

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