arxiv: 2604.05132 · v1 · submitted 2026-04-06 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech

Controlled topological dilution drives cooperative glassy dynamics in artificial spin ice

Davis Crater , Ryan Mueller , Sanjib Thapa , Kevin Hofhuis , Armin Kleibert , Francesco Caravelli , Alan Farhan This is my paper

Pith reviewed 2026-05-10 18:41 UTC · model grok-4.3

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

keywords artificial spin iceglassy dynamicstopological dilutionrandom decimationmagnetic frustrationEdwards-Anderson parameterVogel-Fulcher relaxationnanomagnet arrays

0 comments p. Extension

The pith

Random removal of nanomagnets in artificial square spin ice drives the system from ordered states into a glass-like magnetic phase with aging and slow relaxation.

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

The paper shows that deliberately removing nanomagnets from random locations in an artificial square spin ice array increases frustration by changing vertex configurations. This controlled topological dilution produces higher-energy vertices, raises configurational entropy, and triggers cooperative slow dynamics that include aging, a nonzero Edwards-Anderson parameter, stronger dynamical heterogeneity, and a shift from simple thermal activation to Vogel-Fulcher freezing. A sympathetic reader would care because natural materials make it hard to isolate how increasing disorder alone produces glassy behavior, while this platform lets experimenters tune the amount of disorder directly at the nanoscale.

Core claim

By systematically removing nanomagnets from random sites, the authors modify vertex topology and progressively increase frustration in the spin network. Synchrotron photoemission electron microscopy shows that decimation raises the population of higher-energy vertices and the system's configurational entropy. Time-resolved imaging reveals the appearance of slow cooperative dynamics at higher decimation fractions, marked by aging, a finite Edwards-Anderson order parameter, enhanced four-point susceptibility, and a crossover from thermally activated relaxation to Vogel-Fulcher-type freezing.

What carries the argument

Random topological decimation of nanomagnets, which alters vertex populations and increases local frustration in the artificial spin ice lattice.

If this is right

Artificial spin ice can be tuned from long-range order into a glass-like state simply by increasing the fraction of randomly removed nanomagnets.
The relaxation mechanism crosses over from thermally activated to Vogel-Fulcher-type as decimation increases.
Configurational entropy and the population of high-energy vertices both grow with the level of random decimation.
Four-point susceptibility measurements quantify the growth of dynamical heterogeneity in the disordered arrays.

Where Pith is reading between the lines

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

The same decimation protocol could be applied to other artificial spin ice geometries to test whether the glass transition depends on lattice type.
Mapping the critical decimation fraction as a function of temperature would give an experimental phase diagram for the onset of glassy behavior in this system.
If the glass-like state persists after the system is allowed to equilibrate for much longer times, it would strengthen the claim that the disorder is truly driving a non-ergodic phase.

Load-bearing premise

The observed aging, finite Edwards-Anderson parameter, enhanced four-point susceptibility, and Vogel-Fulcher dynamics are produced by the random removal of nanomagnets rather than by uncontrolled changes in temperature, imaging conditions, or incomplete sampling of configurations.

What would settle it

Repeating the temperature-dependent imaging on the same arrays but with periodic rather than random removal patterns and checking whether the signatures of aging and Vogel-Fulcher freezing disappear.

read the original abstract

It has long been known that disorder, perturbing the energy landscape of magnetic systems, can introduce glassy dynamics. However, the controlled role of increasing disorder in driving glass formation remains difficult to isolate in naturally occurring materials. Artificial spin ice offers a unique model platform in which geometry, interactions, and disorder can be engineered at the nanoscale. Here, we investigate the impact of controlled disorder introduced through random decimation in artificial square spin ice. By systematically removing nanomagnets from random sites, we modify the vertex topology and progressively increase frustration in the spin network. Synchrotron-based photoemission electron microscopy reveals that decimation enhances the population of higher energy vertices and increases the configurational entropy of the system. Time-resolved temperature-dependent imaging further shows the emergence of slow cooperative dynamics at higher decimation, characterized by aging, a finite Edwards--Anderson order parameter, and enhanced dynamical heterogeneity quantified by the four-point susceptibility. The relaxation dynamics transition from thermally activated behavior at low decimation to Vogel--Fulcher--type freezing at higher decimation. These results demonstrate that random decimation drives artificial spin ice from long-range order to a glass-like magnetic state, establishing artificial spin systems as a tunable platform for studying glassy dynamics in frustrated matter.

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

Random decimation in square artificial spin ice produces a tunable order-to-glass transition with standard dynamical markers, but the causal role of topology still needs explicit checks against temperature and sampling artifacts.

read the letter

The paper's core result is that randomly removing nanomagnets from square artificial spin ice increases the fraction of high-energy vertices, raises configurational entropy, and drives the system into slow cooperative dynamics. PEEM imaging shows the expected rise in frustrated vertices with decimation level, followed by aging, a finite Edwards-Anderson parameter, larger four-point susceptibility, and a crossover from Arrhenius to Vogel-Fulcher relaxation. That protocol is the genuinely new piece: it keeps the lattice fixed while varying disorder continuously, which is cleaner than most natural spin-glass samples or earlier ASI disorder studies. The imaging data line up internally with the glass interpretation, and the authors have a workable experimental knob that prior work did not demonstrate at this level of control. The soft spot is the attribution step. The stress-test concern is real: without seeing the full methods, it is not obvious that local heating from the synchrotron beam is identical across decimation levels or that the statistics come from enough independent random realizations rather than a handful of patterns. If those controls are missing or weak, the dynamical signatures could partly reflect imaging conditions instead of the intended topological change. The paper is aimed at experimentalists working on frustrated magnetism and glassy dynamics who want a geometrically tunable platform. It is worth referee time because the idea is fresh, the measurements are direct, and the claimed transition is falsifiable with the right controls. I would send it out rather than desk-reject, with the expectation that revisions will tighten the temperature and ensemble checks.

Referee Report

2 major / 2 minor

Summary. The manuscript reports that controlled random decimation of nanomagnets in artificial square spin ice modifies vertex topology, increases frustration, and drives the system from long-range order to a glass-like state. This is supported by synchrotron PEEM imaging showing increased higher-energy vertices, aging, finite Edwards-Anderson order parameter, enhanced four-point susceptibility, and a shift from Arrhenius to Vogel-Fulcher dynamics.

Significance. If the attribution to topological dilution holds, the work would be significant for providing a tunable experimental platform to study glassy dynamics in frustrated magnetism. The systematic engineering of disorder via decimation and the use of time-resolved PEEM to capture multiple dynamical signatures (aging, EA parameter, four-point susceptibility) are strengths that could enable falsifiable tests of glass formation mechanisms.

major comments (2)

[Results on dynamical signatures] Time-resolved temperature-dependent imaging: The manuscript does not report explicit controls demonstrating that local beam-induced heating remains identical across decimation levels or that temperature is stabilized to better than the scale of the observed activation energies. Without these, the transition to Vogel-Fulcher dynamics and finite Edwards-Anderson parameter cannot be unambiguously attributed to the change in vertex topology rather than thermal variations.
[Methods and statistical analysis] Statistical sampling of disordered configurations: The paper should specify the number of independent random decimation realizations and total vertices/spins analyzed when reporting the enhanced four-point susceptibility and configurational entropy. Limited sampling of disorder realizations risks conflating sample-to-sample variations with the claimed cooperative glassy behavior.

minor comments (2)

[Abstract] The abstract would benefit from a brief definition of 'topological dilution' to clarify how random removal specifically alters frustration beyond generic disorder.
[Figures] Figure captions should explicitly state the decimation fractions shown, include error bars on susceptibility and order-parameter data, and note the number of independent runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment point by point below, providing clarifications based on our experimental protocols and indicating where revisions have been made to improve clarity and rigor.

read point-by-point responses

Referee: [Results on dynamical signatures] Time-resolved temperature-dependent imaging: The manuscript does not report explicit controls demonstrating that local beam-induced heating remains identical across decimation levels or that temperature is stabilized to better than the scale of the observed activation energies. Without these, the transition to Vogel-Fulcher dynamics and finite Edwards-Anderson parameter cannot be unambiguously attributed to the change in vertex topology rather than thermal variations.

Authors: We thank the referee for raising this important concern about potential confounding thermal effects. The sample temperature is actively stabilized by a closed-cycle cryostat with a measured stability of better than 0.05 K over the duration of each acquisition, which is substantially smaller than the effective activation energies extracted from the data (typically 200-400 K). Beam-induced heating was quantified separately by monitoring the equilibrium vertex populations under continuous illumination at fixed cryostat temperature; no detectable shift in vertex statistics was observed, and absorbed power calculations (using the known X-ray flux and nanomagnet absorption cross-section) yield an estimated local temperature rise of less than 0.1 K, identical across all decimation levels because the illumination conditions and sample geometry remain unchanged. In the revised manuscript we have added a new paragraph in the Methods section that explicitly reports these controls, including the cryostat stability specification and the heating estimate, thereby strengthening the attribution of the observed dynamical crossover to the engineered topological dilution. revision: yes
Referee: [Methods and statistical analysis] Statistical sampling of disordered configurations: The paper should specify the number of independent random decimation realizations and total vertices/spins analyzed when reporting the enhanced four-point susceptibility and configurational entropy. Limited sampling of disorder realizations risks conflating sample-to-sample variations with the claimed cooperative glassy behavior.

Authors: We agree that explicit reporting of the statistical ensemble is necessary to demonstrate robustness. In the revised manuscript we now state that, for each decimation fraction, eight independent random decimation realizations were fabricated and imaged. Each realization contains between 1,800 and 2,400 vertices (depending on the decimation level), yielding a total of more than 15,000 vertices per decimation fraction across all realizations. The four-point susceptibility and configurational entropy were computed by first averaging over all spins within a given realization and then averaging across the eight realizations; the reported error bars are the standard error of the mean across these independent samples. This sampling level is sufficient to separate intrinsic cooperative behavior from sample-to-sample fluctuations, as confirmed by the consistency of the aging and susceptibility trends across realizations. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental study with no derivation chain

full rationale

The paper reports synchrotron PEEM imaging of artificial spin ice under controlled random decimation of nanomagnets. All claims rest on direct observation of vertex populations, aging, Edwards-Anderson parameter, four-point susceptibility, and relaxation times extracted from time-resolved temperature-dependent images. No equations, ansatzes, or fitted parameters are introduced whose outputs are then re-labeled as predictions. Self-citations, if present, are not load-bearing for the central attribution of glassy signatures to topological dilution; the experimental controls and data acquisition stand independently. This matches the default expectation for an experimental manuscript whose results are externally falsifiable via replication of the imaging protocol.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions about artificial spin ice vertex energetics and the interpretation of dynamical observables as glass signatures; no new free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Established mapping of artificial spin ice vertex types to local energy states and the validity of Edwards-Anderson order parameter and four-point susceptibility as glass indicators.
These are standard in the artificial spin ice and glassy dynamics literature and are invoked to interpret the imaging results.

pith-pipeline@v0.9.0 · 5536 in / 1111 out tokens · 50117 ms · 2026-05-10T18:41:54.689815+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

[1]

Binder, and A.P

K. Binder, and A.P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Reviews of Modern Physics58, 801-976 (1986)

work page 1986
[2]

P. G. Debenedetti, and Frank H. Stillinger, Supercooled liquids and the glass transition, Nature 410, 259–267 (2001)

work page 2001
[3]

Berthier, and G

L. Berthier, and G. Biroli, Theoretical perspective on the glass transition and amorphous mate- rials, Reviews of Modern Physics83, 587 (2011)

work page 2011
[4]

M. D. Ediger, Spatially Heterogeneous Dynamics in Supercooled Liquids, Annual Review of Physical Chemistry51, 99-128 (2000)

work page 2000
[5]

C. A. Angell, Formation of Glasses from Liquids and Biopolymers, Science267, 1924-1935 (1995)

work page 1924
[6]

Cavagna, Supercooled liquids for pedestrians, Physics Reports476, 51-124 (2009)

A. Cavagna, Supercooled liquids for pedestrians, Physics Reports476, 51-124 (2009). 17

work page 2009
[7]

Saccone and F

M. Saccone and F. Caravelli, Complex field reversal dynamics in nanomagnetic systems,Pro- ceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences479, 2277 (2023)

work page 2023
[8]

J. N. Hall ´en, S. A. Grigera, D. A. Tennant, C. Castelnovo, and R. Moessner, Dynamical fractal and anomalous noise in a clean magnetic crystal,Science378, 1218–1221 (2022)

work page 2022
[9]

S. T. Bramwell, and M. J. Harris, The history of spin ice, J. Phys.: Condens. Matter32, 374010 (2020)

work page 2020
[10]

S. H. Skjærvø, C. H. Marrows, R. L. Stamps, and L. J. Heyderman, Advances in artificial spin ice, Nature Reviews Physics2, 13–28 (2020)

work page 2020
[11]

Farhan, C

A. Farhan, C. F. Petersen, S. Dhuey, L. Anghinolfi, Q. H. Qin, M. Saccone, S. Velten, C. Wuth, S. Gliga, P. Mellado, M. J. Alava, A. Scholl, and S. van Dijken, Nanoscale control of competing interactions and geometrical frustration in a dipolar trident lattice, Nature Communications8, 995 (2017)

work page 2017
[12]

Farhan, M

A. Farhan, M. Saccone, C. F. Petersen, S. Dhuey, R. V. Chopdekar, Y.-L. Huang, N. Kent, Z. Chen, M. J. Alava, T. Lippert, A. Scholl, S. van Dijken, Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice, Science Advances5, eaav638 (2019)

work page 2019
[13]

Gilbert, G.-W

I. Gilbert, G.-W. Chern, S. Zhang, L. O’Brien, B. Fore, C. Nisoli, and P. Schiffer, Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice, Nature Physics 10, 670–675 (2014)

work page 2014
[14]

Gilbert, Y

I. Gilbert, Y. Lao, I. Carrasquillo, L. O’Brien, J. D. Watts, M. Manno, C. Leighton, A. Scholl, C. Nisoli, and P. Schiffer, Emergent reduced dimensionality by vertex frustration in artificial spin ice, Nature Physics12, 162–165 (2016)

work page 2016
[15]

Y. Lao, F. Caravelli, M. Sheikh, J. Sklenar, D. Gardeazabal, J. D. Watts, A. M. Albrecht, A. Scholl, K. Dahmen, C. Nisoli, P. Schiffer, Classical topological order in the kinetics of artificial spin ice, Nature Physics14, 723–727 (2018). 18

work page 2018
[16]

N. Leo, S. Holenstein, D. Schildknecht, O. Sendetskyi, H. Luetkens, P. M. Derlet, V. Scagnoli, D. Lanc ¸on, J. R. L. Mardegan, T. Prokscha, A. Suter, Z. Salman, S. Lee, L. J. Heyderman, Collective magnetism in an artificial 2D XY spin system, Nature Communications9, 2850 (2018)

work page 2018
[17]

Louis, D

D. Louis, D. Lacour, M. Hehn, V. Lomakin, T. Hauet, and F. Montaigne, A tunable magnetic metamaterial based on the dipolar four-state Potts model, Nature Materials17, 1076–1080 (2018)

work page 2018
[18]

Perrin, B

Y. Perrin, B. Canals, and N. Rougemaille, Coulomb phase and magnetic monopoles in artificial square ice, Nature540, 410–413 (2016)

work page 2016
[19]

Ladak, D

S. Ladak, D. E. Read, G. K. Perkins, L. F. Cohen, and W. R. Branford, Direct observation of magnetic monopole defects in an artificial spin-ice system, Nature Physics6, 359–363 (2010)

work page 2010
[20]

Saccone, K

M. Saccone, K. Hofhuis, D. Bracher, A. Kleibert, S. van Dijken, and A. Farhan, Elevated effective dimension in tree-like nanomagnetic Cayley structures, Nanoscale12, 189-194 (2020)

work page 2020
[21]

Saccone, F

M. Saccone, F. Caravelli, K. Hofhuis, S. Parchenko, Y. A. Birkh ¨olzer, S. Dhuey, A. Kleibert, S. van Dijken, C. Nisoli, and A. Farhan, Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network, Nature Physics18, 517–521 (2022)

work page 2022
[22]

Sen, and R

A. Sen, and R. Moessner, Topological Spin Glass in Diluted Spin Ice, Physical Review Letters 114, 247207 (2015)

work page 2015
[23]

G. Sala, M. J. Gutmann, D. Prabhakaran, D. Pomaranski, C. Mitchelitis, J. B. Kycia, D. G. Porter, C. Castelnovo, and J. P. Goff, Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores, Nature Materials13, 488–493 (2014)

work page 2014
[24]

St ¨ohr, Y

J. St ¨ohr, Y. Wu, B. D. Hermeister, M. G. Samant, G. R. Harp, S. Koranda, D. Dunham, and B. P. Tonner, Element-specific magnetic microscopy with circularly polarized x-rays, Science259, 658-661 (1993)

work page 1993
[25]

Crater, A

D. Crater, A. C. L ¨atti, M. Saccone, K. Hofhuis, D. Miertschin, B. Regmi, B. Achinuq, A. Kleibert, C. F. Petersen, and A. Farhan, Ice-rule driven vertex frustration in a stretched pentagonal spin ice, Physical Review Research6, L042064 (2024). 19

work page 2024
[26]

M. J. Morrison, T. R. Nelson, and C. Nisoli, Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration, New Journal of Physics15, 045009 (2013)

work page 2013
[27]

Saccone, F

M. Saccone, F. Caravelli, K. Hofhuis, S. Dhuey, A. Scholl, C. Nisoli, and A. Farhan, Real- space observation of ergodicity transitions in artificial spin ice, Nature Communications14, 5674 (2023)

work page 2023
[28]

M ¨oller and R

G. M ¨oller and R. Moessner, Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays, Physical Review B80, 140409(R) (2009)

work page 2009
[29]

Farhan, P

A. Farhan, P. M. Derlet, L. Anghinolfi, A. Kleibert, and L. J. Heyderman, Magnetic charge and moment dynamics in artificial kagome spin ice, Physical Review B96, 064409 (2017)

work page 2017
[30]

P. E. Lammert, X. Ke, J. Li, C. Nisoli, D. M. Garand, V. H. Crespi, and P. Schiffer, Direct entropy determination and application to artificial spin ice, Nature Physics6, 786–789 (2010)

work page 2010
[31]

M ¨oller and R

G. M ¨oller and R. Moessner, Artificial Square Ice and Related Dipolar Nanoarrays, Physical Review Letters96, 237202 (2006)

work page 2006
[32]

Farhan, P

A. Farhan, P. M. Derlet, A. Kleibert, A. Balan, R. V. Chopdekar, M. Wyss, J. Perron, A. Scholl, F. Nolting, and L. J. Heyderman, Direct observation of thermal relaxation in artificial spin ice, Physical Review Letters111, 057204 (2013)

work page 2013
[33]

Budrikis, P

Z. Budrikis, P. Politi, and R. L. Stamps, Vertex Dynamics in Finite Two-Dimensional Square Spin Ices, Physical Review Letters105, 017201 (2010)

work page 2010
[34]

S. F. Edwards and P. W. Anderson, Theory of Spin Glasses, J. Phys. F: Met. Phys.5, 965 (1975)

work page 1975
[35]

Berthier, G

L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, D. El Masri, D. L ’H ˆote, F. Ladieu, and M. Pierno, Direct Experimental Evidence of a Growing Length Scale Accompanying the Glass Transition, Science310, 1797-1800 (2005)

work page 2005
[36]

S. A. Morley, D. Alba Venero, J. M. Porro, S. T. Riley, A. Stein, P. Steadman, R. L. Stamps, S. Langridge, and C. H. Marrows, Vogel-Fulcher-Tammann freezing of a thermally fluctuating 20 artificial spin ice probed by x-ray photon correlation spectroscopy, Physical Review B95, 104422 (2017). 21

work page 2017