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arxiv: 2412.04376 · v1 · submitted 2024-12-05 · ❄️ cond-mat.str-el · cond-mat.stat-mech

Power spectrum of magnetic relaxation in spin ice: anomalous diffusion in a Coulomb fluid

D. Billington , E. Riordan , C. Cafolla-Ward , J. Wilson , E. Lhotel , C. Paulsen , D. Prabhakaran , S. T. Bramwell
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F. Flicker S. R. Giblin
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Pith reviewed 2026-05-23 07:42 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.stat-mech
keywords spin iceDy2Ti2O7magnetic monopolespower spectrumanomalous diffusionCoulomb fluidAC susceptibilitycrystal defects
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The pith

AC susceptibility up to 1 MHz shows b(T) for spin ice noise deviates from 2 up to 20 K and is sample dependent.

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

The paper measures the high-frequency tail of the magnetization noise power spectrum in Dy2Ti2O7 using AC susceptibility measurements from 2 K to 20 K that reach 10^6 Hz. It finds that the exponent b(T) in S(f,T) ~ f^{-b} stays below the Brownian value of 2, indicating anomalous diffusion of magnetic monopoles in the dense Coulomb fluid. Previous lower-frequency noise data underestimated b(T), and the new results show that b(T) depends on the sample in ways that partly match the expected influence of crystal defects on monopole population and diffusion. The work characterizes how multiple dynamical processes combine in this correlated state without ruling out a fractal landscape at much lower temperatures where the monopole gas is dilute.

Core claim

Using a.c. susceptibility measurements extending to 10^6 Hz, the authors establish that b(T) deviates from 2 up to about 20 K in Dy2Ti2O7, with the deviation being sample dependent in a manner that partially agrees with studies of crystal defects affecting monopole diffusion. This form of b(T) describes the combined dynamical processes in the dense Coulomb fluid of magnetic monopoles.

What carries the argument

The anomalous exponent b(T) in the high-frequency tail of the noise power spectrum S(f,T), which quantifies deviations from normal diffusion of monopoles.

Load-bearing premise

AC susceptibility measurements up to 10^6 Hz directly yield the intrinsic high-frequency tail of the noise power spectrum without significant instrumental or extra relaxation contributions.

What would settle it

Simultaneous noise and AC susceptibility measurements on the same sample above 10^4 Hz that disagree on the value of b(T) would indicate that the susceptibility data do not capture the true intrinsic tail.

Figures

Figures reproduced from arXiv: 2412.04376 by C. Cafolla-Ward, C. Paulsen, D. Billington, D. Prabhakaran, E. Lhotel, E. Riordan, F. Flicker, J. Wilson, S. R. Giblin, S. T. Bramwell.

Figure 1
Figure 1. Figure 1: FIG. 1. Imaginary part of the intrinsic, differential magnetic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Normalized power spectrum of magnetic noise, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Magnetization noise measurements on the spin ice Dy${}_2$Ti${}_2$O${}_7$ have revealed a remarkable `pink noise' power spectrum $S(f,T)$ below 4 K, including evidence of magnetic monopole excitations diffusing in a fractal landscape. However, at higher temperatures, the reported values of the anomalous exponent $b(T)$ describing the high frequency tail of $S(f,T)$ are not easy to reconcile with other results in the literature, which generally suggest significantly smaller deviations from the Brownian motion value of $b=2$, that become negligible above $T=20$ K. We accurately estimate $b(T)$ at temperatures between 2~K and 20~K, using a.c. susceptibility measurements that, crucially, stretch up to the relatively high frequency of $f = 10^6$ Hz. We show that previous noise measurements underestimate $b(T)$ and we suggest reasons for this. Our results establish deviations in $b(T)$ from $b=2$ up to about 20 K. However studies on different samples confirms that $b(T)$ is sample dependent: the details of this dependence agree in part, though not completely, with previous studies of the effect of crystal defects on monopole population and diffusion. Our results establish the form of $b(T)$ which characterises the subtle, and evolving, nature of monopole diffusion in the dense Coulomb fluid, a highly correlated state, where several dynamical processes combine. They do not rule out the importance of a fractal landscape picture emerging at lower temperatures where the monopole gas is dilute.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript uses a.c. susceptibility measurements extending to 10^6 Hz on Dy2Ti2O7 to estimate the anomalous exponent b(T) in the high-frequency tail of the magnetization noise power spectrum S(f,T) for temperatures from 2 K to 20 K. The authors find that b(T) deviates from the value 2 expected for Brownian motion up to approximately 20 K, that b(T) is sample dependent, and that previous noise measurements underestimated b(T) due to their lower frequency range. They interpret this in the context of magnetic monopole diffusion in a dense Coulomb fluid, noting that several dynamical processes are at play.

Significance. This experimental study clarifies the temperature range over which anomalous diffusion persists in spin ice, addressing inconsistencies in the literature regarding b(T) at higher temperatures. The extension to higher frequencies and the comparison across samples provide stronger evidence for the reported trends. The work highlights the evolving nature of monopole dynamics in the correlated state. Strengths include the direct experimental approach and the suggestion of reasons for prior discrepancies. If the assumption that the AC data directly probes the intrinsic S(f) tail holds, the results advance the understanding of diffusion in this highly correlated system.

major comments (2)
  1. [Results] The extracted values of b(T) lack reported quantitative error bars or uncertainty estimates. This makes it difficult to rigorously assess the statistical significance of the deviations from b=2 and the degree of sample dependence claimed in the abstract.
  2. [Experimental methods / FDT discussion] The central mapping from the imaginary part of the AC susceptibility χ''(f) to the noise spectrum S(f) via the fluctuation-dissipation theorem is assumed to hold without contamination in the 10^5–10^6 Hz range. Explicit checks or arguments ruling out contributions from other relaxation channels in this window would be necessary to fully support the claim that previous noise measurements are underestimated due to frequency limitations.
minor comments (1)
  1. [Abstract] The abstract mentions agreement 'in part, though not completely' with previous studies on crystal defects; a brief reference to those studies would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their supportive summary and constructive major comments. We address each point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Results] The extracted values of b(T) lack reported quantitative error bars or uncertainty estimates. This makes it difficult to rigorously assess the statistical significance of the deviations from b=2 and the degree of sample dependence claimed in the abstract.

    Authors: We agree that the absence of quantitative uncertainties on the fitted b(T) values limits the ability to assess significance. In the revised manuscript we will include error bars on b(T) derived from the covariance matrix of the power-law fits to the high-frequency tail of χ''(f), together with a brief discussion of how these uncertainties affect the claimed deviations from b=2 and the observed sample-to-sample differences. revision: yes

  2. Referee: [Experimental methods / FDT discussion] The central mapping from the imaginary part of the AC susceptibility χ''(f) to the noise spectrum S(f) via the fluctuation-dissipation theorem is assumed to hold without contamination in the 10^5–10^6 Hz range. Explicit checks or arguments ruling out contributions from other relaxation channels in this window would be necessary to fully support the claim that previous noise measurements are underestimated due to frequency limitations.

    Authors: The measurements were performed well within the linear-response regime, and the temperature and frequency dependence of χ''(f) show no additional features that would indicate contamination by other processes. We will add a short paragraph in the methods section that uses the known hierarchy of relaxation timescales in Dy2Ti2O7 (from earlier dielectric and muon studies) to argue that no other channels contribute appreciably above 10^5 Hz in the 2–20 K window. This will strengthen the justification for applying the FDT mapping and for attributing the difference with prior noise data to frequency range. revision: partial

Circularity Check

0 steps flagged

No significant circularity; purely experimental extraction of b(T) from data

full rationale

The paper reports AC susceptibility measurements up to 10^6 Hz on Dy2Ti2O7 samples to extract the anomalous exponent b(T) in the high-frequency tail of the noise power spectrum S(f,T) via the fluctuation-dissipation theorem. No derivation chain, model fitting, or theoretical prediction is claimed; b(T) values are obtained directly from measured χ''(f) data across temperatures and samples. No self-citations are load-bearing for the central result, and no equations reduce reported quantities to prior parameters or ansatzes by construction. The sample dependence and comparison to prior work are observational, not self-referential.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of linear-response AC susceptibility and on the interpretation that the measured imaginary susceptibility component maps directly onto the noise power spectrum via the fluctuation-dissipation theorem. No new entities or ad-hoc parameters are introduced; the only fitted quantities are the per-temperature exponents b(T) extracted from the data.

free parameters (1)
  • b(T)
    Exponent fitted to the high-frequency tail of the measured susceptibility spectrum at each temperature; these are the reported results rather than inputs.
axioms (2)
  • standard math Fluctuation-dissipation theorem relates AC susceptibility to the equilibrium noise power spectrum.
    Invoked implicitly when the authors equate their susceptibility data to the noise spectrum S(f,T) studied in prior work.
  • domain assumption No significant non-monopole relaxation channels contribute above ~10^4 Hz in the measured temperature window.
    Required for the claim that the extracted b(T) purely reflects monopole diffusion.

pith-pipeline@v0.9.0 · 5872 in / 1600 out tokens · 29111 ms · 2026-05-23T07:42:58.173534+00:00 · methodology

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Reference graph

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