Skyrmion relaxation dynamics in the presence of quenched disorder

Barton L. Brown; Michel Pleimling; Uwe C. T\"auber

arxiv: 1906.12146 · v1 · pith:GZEERHIOnew · submitted 2019-06-28 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech

Skyrmion relaxation dynamics in the presence of quenched disorder

Barton L. Brown , Uwe C. T\"auber , Michel Pleimling This is my paper

Pith reviewed 2026-05-25 13:45 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mech

keywords skyrmionsquenched disorderdynamical scalingMagnus forcepinning sitesrelaxation dynamicsagingauto-correlation function

0 comments

The pith

Clean skyrmion systems always display dynamical scaling using the typical diffusion length as the scale.

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

The paper uses Langevin molecular dynamics simulations to study how interacting skyrmions relax over time both with and without quenched disorder. It establishes that clean systems always exhibit dynamical scaling when the typical diffusion length serves as the time-dependent length, even when that length does not grow as a simple power of time. The Magnus force produces two distinct regimes depending on noise strength and enables skyrmions to bend around defects. Attractive pinning sites capture many skyrmions, yielding complex two-time auto-correlation functions that a simple aging scaling ansatz cannot reproduce except at large noise.

Core claim

Clean skyrmion systems always display dynamical scaling when the typical diffusion length is used to characterize the relaxation process. This scaling persists even in cases where the length is not a simple power law of time. In the presence of the Magnus force two different regimes emerge as a function of the noise strength. Attractive pinning sites capture a substantial fraction of skyrmions which results in a complex behavior of the two-time auto-correlation function that is not reproduced by a simple aging scaling ansatz, except in the limit of large noise where dynamical scaling persists.

What carries the argument

The typical diffusion length as the time-dependent length that characterizes the relaxation process and tests for dynamical scaling.

If this is right

Clean systems display dynamical scaling regardless of whether the typical length follows a power law in time.
The Magnus force creates two regimes in the relaxation as noise strength varies.
The Magnus force allows skyrmions to bend around defects and reduces caging effects.
Simple aging scaling fails to describe the auto-correlation function when attractive pinning sites are present, except at large noise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Models of skyrmion dynamics in real materials must include the velocity-dependent Magnus force to capture how disorder affects relaxation.
Experiments could tune temperature or noise strength to locate the boundary between the two Magnus-force regimes.
Applications that rely on predictable skyrmion motion would benefit from minimizing attractive pinning to preserve scaling behavior.

Load-bearing premise

The typical diffusion length is the correct time-dependent length to characterize the relaxation process and the chosen simulation parameters and pinning model faithfully represent the essential physics of real skyrmion systems with quenched disorder.

What would settle it

A clean skyrmion system that fails to display dynamical scaling when relaxation data are plotted against the typical diffusion length, or a pinned system at moderate noise whose two-time auto-correlation follows a simple aging scaling ansatz.

Figures

Figures reproduced from arXiv: 1906.12146 by Barton L. Brown, Michel Pleimling, Uwe C. T\"auber.

**Figure 2.** Figure 2: FIG. 2: (a) The fraction of pinned particles as a function of t [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Scaled two-time density auto-correlation function [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Scaled two-time density auto-correlation function [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The fraction of pinned skyrmions as a function of time [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

read the original abstract

Using Langevin molecular dynamics simulations we study relaxation processes of interacting skyrmion systems with and without quenched disorder. Using the typical diffusion length as the time-dependent length characterizing the relaxation process, we find that clean systems always display dynamical scaling, and this even in cases where the typical length is not a simple power law of time. In the presence of the Magnus force, two different regimes are identified as a function of the noise strength. The Magnus force has also a major impact when attractive pinning sites are present, as this velocity-dependent force helps skyrmions to bend around defects and avoid caging effects. With the exception of the limit of large noise, for which dynamical scaling persists even in the presence of quenched disorder, attractive pinning sites capture a substantial fraction of skyrmions which results in a complex behavior of the two-time auto-correlation function that is not reproduced by a simple aging scaling ansatz.

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.

Desk Editor's Note private letter to a colleague

Simulations map two Magnus regimes and show attractive pinning breaks aging scaling, but the diffusion length choice looks shaky when Hall motion dominates.

read the letter

This paper runs Langevin molecular dynamics on interacting skyrmions and reports that clean systems always show dynamical scaling when the typical diffusion length is used as the time-dependent scale, even if that length grows slower than a power law. With the Magnus force present they identify two regimes split by noise strength, and they find that the same force lets skyrmions bend around attractive pins and largely avoid caging, while pinning still ruins simple aging scaling except at high noise. Those concrete numerical distinctions are the actual new pieces relative to earlier skyrmion work. The simulations are standard and the parameter sweeps are systematic enough to make the regime split and the caging-avoidance observation worth noting. The soft spot is exactly the one the stress test flags. Because the Magnus term produces transverse motion, the mean-squared-displacement length may not be the right scale for the two-time correlations; the paper does not test whether the collapse survives with an alternative length such as a gyration radius or velocity autocorrelation length. If that assumption slips, both the clean-system scaling claim and the regime distinction lose force. The abstract states the findings are consistent, but without the full methods, error bars, or pinning-model details it is hard to judge robustness. This is for people already running skyrmion or vortex simulations in mesoscopic magnetism. A reader who cares about pinning and aging in spintronics models will find the correlation plots useful. It has enough numerical substance and testable claims to deserve a serious referee who can check the implementation and the scaling variable.

Referee Report

2 major / 1 minor

Summary. The manuscript reports Langevin molecular dynamics simulations of interacting skyrmion relaxation in clean and quenched-disordered systems. Using the typical diffusion length extracted from mean-squared displacement as the time-dependent scale, the authors claim that clean systems exhibit dynamical scaling of two-time correlation functions even when this length is not a simple power law of time. They identify two noise-strength regimes in the presence of the Magnus force and report that attractive pinning produces complex aging behavior not captured by simple scaling, except at large noise where scaling persists.

Significance. If the numerical observations hold under scrutiny, the work provides concrete evidence that Magnus-force-induced transverse motion and pinning alter relaxation scaling in skyrmion systems, which is relevant for understanding topological spin textures in disordered materials. The explicit demonstration that scaling can survive without power-law growth of the characteristic length is a useful numerical result for the field.

major comments (2)

[Abstract / results on Magnus regimes] Abstract and results sections: the central claim that dynamical scaling is observed when the typical diffusion length is used as the scaling variable rests on the assumption that this length (derived from isotropic mean-squared displacement) remains the dynamically relevant scale even when the Magnus term produces Hall-like transverse trajectories. No test is reported with an alternative length scale (e.g., gyration radius or velocity autocorrelation length) to confirm that the reported collapse and the two noise-strength regimes survive this choice.
[Methods / figure captions] Methods and results: quantitative support for the scaling statements and regime distinctions is difficult to assess because the manuscript does not supply full parameter tables, pinning densities, noise strengths, system sizes, or error bars on the correlation functions. Without these, it is impossible to verify reproducibility or the statistical significance of the claimed departures from simple aging scaling.

minor comments (1)

Notation for the two-time auto-correlation function and the definition of the typical diffusion length should be stated explicitly with equations in the main text rather than only in supplementary material.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below.

read point-by-point responses

Referee: [Abstract / results on Magnus regimes] Abstract and results sections: the central claim that dynamical scaling is observed when the typical diffusion length is used as the scaling variable rests on the assumption that this length (derived from isotropic mean-squared displacement) remains the dynamically relevant scale even when the Magnus term produces Hall-like transverse trajectories. No test is reported with an alternative length scale (e.g., gyration radius or velocity autocorrelation length) to confirm that the reported collapse and the two noise-strength regimes survive this choice.

Authors: The mean-squared displacement provides the characteristic diffusion length, which is the standard and physically motivated scale for characterizing relaxation in particle systems. Although the Magnus force induces transverse motion, the isotropic MSD remains the relevant measure for the overall relaxation process, as demonstrated by the data collapse we observe. We did not test alternative scales such as gyration radius. To address the concern we will add a brief justification for this choice in the revised manuscript, while maintaining the original claim. revision: partial
Referee: [Methods / figure captions] Methods and results: quantitative support for the scaling statements and regime distinctions is difficult to assess because the manuscript does not supply full parameter tables, pinning densities, noise strengths, system sizes, or error bars on the correlation functions. Without these, it is impossible to verify reproducibility or the statistical significance of the claimed departures from simple aging scaling.

Authors: We agree that the manuscript is missing these details. In the revised version we will supply full parameter tables (including pinning densities, noise strengths and system sizes) together with error bars on the correlation functions. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical outputs from parameter-varied simulations

full rationale

The paper reports results exclusively from Langevin molecular dynamics simulations of skyrmion systems. The abstract and reader's summary confirm there are no analytical derivations, no parameters fitted to data then relabeled as predictions, and no self-citation chains invoked to justify uniqueness or ansatzes. Dynamical scaling observations and regime distinctions are stated as direct simulation outputs. The choice of typical diffusion length is an explicit modeling assumption, not a result that reduces to itself by construction. This is the normal case of a self-contained numerical study with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The study employs a standard Langevin framework with parameters for noise and pinning varied across runs; no new physical entities are introduced.

free parameters (2)

noise strength
Varied parametrically to delineate regimes in the presence of the Magnus force
pinning strength and density
Quenched attractive pinning sites introduced as the model of disorder

axioms (2)

domain assumption Skyrmion motion obeys overdamped Langevin dynamics with additive noise
Invoked as the simulation method throughout the abstract
domain assumption Quenched disorder is represented by fixed attractive pinning sites
Used to model the disordered case

pith-pipeline@v0.9.0 · 5693 in / 1287 out tokens · 33524 ms · 2026-05-25T13:45:29.278738+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Using the typical diffusion length as the time-dependent length characterizing the relaxation process, we find that clean systems always display dynamical scaling... C(t,s) = (L(s))^{-b} f_C (L(t)/L(s))
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

L(t) = sqrt(r²(t)) with r²(t) = <1/Ns sum |Ri(t) - Ri(0)|²>

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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