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REVIEW 2 major objections 4 minor 97 references

A flat domain wall in fragmented spin ice acts as a diode for magnetic monopoles: one charge passes, the opposite is reflected, and stacked walls form capacitors and batteries for monopole current.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-08-04 18:56 UTC pith:UZTUC4PQ

load-bearing objection A clever, largely self-contained proof of concept for monopole devices in fragmented spin ice; the core diode mechanism is real and clean, but the hard part—pinning a flat wall—is openly deferred. the 2 major comments →

arxiv 2608.01883 v1 pith:UZTUC4PQ submitted 2026-08-03 cond-mat.str-el

Diodes and capacitors for the transport of monopoles in fragmented spin ice

Anoop Raj , Sumiran Pujari , Ludovic D.C. Jaubert This is my paper
classification cond-mat.str-el
keywords spin icemagnetic monopolesmagnetricitymagnetic fragmentationdomain wallsmonopole diodemonopole capacitorMonte Carlo simulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper attempts to establish that a flat, immobile domain wall in fragmented spin ice is an asymmetric filter for magnetic monopoles: depending on its facet, a W+ wall transmits positive charges and reflects negative ones, while a W- wall does the opposite. Because the wall is one tetrahedron thick and preserves its shape, the asymmetry survives the random hopping of carriers, so the wall functions as a diode for monopole current. The paper then shows that a stack of such walls separates positive and negative charges into different reservoirs that cannot annihilate, realizing a capacitor, and that the separated charges can be used as a battery of same-sign monopoles. The claims are backed by a geometric counting argument and Monte Carlo simulations of millions of spins.

Core claim

In fragmented spin ice, where spin-ice monopole physics coexists with all-in/all-out antiferromagnetic order, a domain wall between the two time-reversed domains acts as a one-way gate for magnetic monopoles. The microscopic mechanism is geometric: at a W+ wall, tetrahedra in the wall layer that belong to the lower domain have their only inward spin at the top, so a negative charge coming from below can enter but cannot exit upward and is reflected, while a positive charge can enter through an outward spin and exit through the top inward spin into the upper domain. The opposite holds for a W- wall. A carrier that crosses the wall sees the opposite facet on the other side and is then reflecte

What carries the argument

The central object is the immobile domain wall in fragmented spin ice, defined by flipping all spins above a plane at height z=n d_w; it is one tetrahedron layer thick and comes in two facets, W+ (wall layer originally 3out-1in) and W- (originally 3in-1out). The wall's specific spin orientations enforce the rule that negative charges enter a tetrahedron through an inward spin and exit through an outward spin, while positive charges do the reverse. Combined with the fixed internal geometry of the wall layer, this rule determines whether a given charge can traverse the layer or is forced back, producing the diode effect. The same geometry, repeated in a stack of p walls, yields the capacitor a

Load-bearing premise

The entire design assumes the domain wall stays flat and immobile, one tetrahedron layer thick, while monopoles hop; the paper itself observes that if the wall fluctuates, the diode effect breaks and is replaced by charge conjugation, and that making an iridium-pyrochlore wall flat within one tetrahedron layer is the main technological challenge.

What would settle it

Simulate or measure a monopole approaching a domain wall that is allowed to fluctuate thermally: if the carrier crosses the wall without being reflected and emerges with opposite charge (rather than the predicted reflection for an immobile wall), the diode and capacitor claims fail. Concretely, in a Monte Carlo simulation with rule (ii) of the paper's Appendix A removed, a W+ wall should show negative charges on the D side crossing into D-bar after a wall fluctuation; the diode would then not survive at finite temperature.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A single immobile domain wall in a fragmented spin-ice sample acts as a diode for magnetricity: with a current of monopoles, the wall either blocks all carriers or lets them all cross, depending on its facet orientation, without any external magnetic field.
  • Stacking p domain walls (each with its W+ facet facing down) forces negative charges downward and positive charges upward; a pair created in the middle separates to opposite ends, with an average drift velocity proportional to the density of walls.
  • After a heat pulse creates monopoles in the central region, the surviving charges accumulate at the boundaries as a persistent charge separation, realizing a capacitor for magnetic monopoles; more walls suppress annihilation.
  • The separated reservoirs of same-sign topological charges can serve as a battery: because annihilation requires opposite charges, the monopoles persist even at very low temperatures.
  • If the capacitor's reservoirs are connected to external circuits made of a single domain, an AC magnetic field can drive an AC monopole current without the Lenz-type saturation that stops DC monopole currents.

Where Pith is reading between the lines

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

  • A fluctuating domain wall, which the paper shows converts a crossing carrier's charge via charge conjugation, could be engineered as a controllable charge inverter: tuning wall stiffness could toggle between diode and sign-reversing transmission.
  • The same geometric diode mechanism should operate in two-dimensional fragmented square ice, where the paper argues the arguments carry over; an artificial spin-ice experiment with a lithographically pinned wall could directly image monopole reflection and transmission with magnetic force microscopy.
  • The capacitor design suggests a memory application: the number and sign of monopoles stored in each reservoir could encode information, readable as a net magnetic moment, provided leakage paths are suppressed by keeping carrier density low relative to wall cross-section.
  • In other spin liquids with broken Z2 symmetry, such as chiral or nematic spin liquids, the analogous domain walls could act as charge/flavour filters for their quasi-particles; extending the geometric counting to those lattices would test whether the diode effect is a general feature of symmetry-breaking domain walls.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript proposes a theoretical proof of concept for monopole diodes, capacitors, and batteries in fragmented spin ice. It claims that a domain wall between two time-reversed fragmented domains acts as an asymmetric filter: for one facet, negative charges are reflected and positive charges transmitted, with the opposite behavior for the other facet. The mechanism is derived from the local in/out spin geometry of tetrahedra at a chosen (001) layer (Sec. III B 2) and tested by Monte Carlo simulations with up to ~1.5 million spins (L=72) for single charges and L=256 for multi-wall stacks. A stack of p walls separates positive and negative charges, giving a capacitor with a quasi-ballistic velocity v∝ρ_dw (Eq. 1); repeated heat pulses can populate reservoirs, which may be used as a battery in an AC circuit. The paper also discusses domain-wall fluctuations, which induce charge conjugation and destroy the diode effect, and reviews experimental platforms (iridium pyrochlores, artificial spin ice).

Significance. The central geometric counting argument is elegant and, in its core, parameter-free: the asymmetry follows from the in/out spin topology at the wall, not from tuned rates. The simulations are large, the protocol is clearly documented, and the paper is unusually explicit about its central assumption (immobile wall) and its consequences (Sec. IV B). If the wall can be pinned flat on the relevant timescale, this would be a genuinely new route to controlling magnetricity, with concrete experimental targets in pyrochlore oxides and artificial spin ice. The 'frontier between time-reversed worlds' interpretation is an appealing conceptual bonus. However, the significance is conditional: the device function is not yet established for a free fluctuating wall, which is the physical regime most likely in bulk materials.

major comments (2)
  1. [Sec. III B 2 / Appendix A] The diode mechanism is derived and simulated under the kinematic constraint that the domain wall is immobile (Appendix A, rule (ii)). Sec. IV B shows that once wall fluctuations are allowed, the reflection becomes transmission with charge conjugation, and Sec. IV A 1 states that preparing a flat single-layer wall is 'the main technological challenge.' Since the diode, capacitor, and battery designs all rely on an immobile wall, this is a central assumption rather than a peripheral idealization. Please provide a concrete pinning mechanism or an energy/time-scale estimate (e.g., AIAO-domain-wall roughening barrier relative to T and to the monopole hopping rate), or explicitly restrict the central device claims to 'conditional on an externally stabilized wall.' Without this, the operational basis of the proposal is not established.
  2. [Fig. 4(d), Eq. (1)] As described, the collapse plot uses R/ρ_dw vs tρ_dw and is claimed to confirm v∝ρ_dw. For the stated law R(t)=v t with v∝ρ_dw, one expects R/ρ_dw = const×t = const×(tρ_dw)/ρ_dw, so the curves should separate with ρ_dw rather than collapse. If the collapse is real, the early-time slope would instead imply R≈Cρ_dw^2 t, i.e. v∝ρ_dw^2, contradicting Eq. (1). The correct collapse for Eq. (1) would be R vs tρ_dw (or R/ρ_dw vs t). Please verify the axes and the data; if the axes are mislabeled, correct the figure/caption.
minor comments (4)
  1. [Sec. IV B] The text says the reflection mechanism is 'illustrated in section IV C and Figure 3(d,e)', but the relevant mechanism is in Sec. III B 2; section IV C is about the 'frontier between two worlds'. The cross-reference should be corrected.
  2. [Sec. IV C] The statement that under wall fluctuations the sign of matter on each side 'will stay the same' is ambiguous. If a positive charge crosses a fluctuating wall and becomes negative, the receiving side acquires an opposite-sign charge, so matter/antimatter separation is not preserved in the naive sense. This does not affect the main diode result, but the discussion should be clarified.
  3. [Introduction] Minor wording: 'an ap-n junction' should read 'a p-n junction' (also in the introduction).
  4. [Sec. III C 2] The capacitor charging protocol would benefit from a quantitative discussion of the maximum stored charge before leakage paths dominate; the current argument is qualitative ('as long as the density of carriers remains small compared to the domain-wall cross section').

Circularity Check

0 steps flagged

No significant circularity: central diode/capacitor mechanism is a parameter-free geometric argument; the only self-citation is a non-load-bearing protocol adoption.

full rationale

The claimed derivation is a conditional lattice-geometry argument, not a fit or self-citation chain. The diode effect (Sec. III B 2) is derived from the local spin texture: for a W+ wall, tetrahedra at the wall layer that stayed 3out-1in have their inward spin at the top, so a negative charge—which must enter through an inward spin—cannot enter from below, whereas a positive charge, entering through an outward spin, can cross. This is parameter-free. The simulations use the constrained dynamics of Appendix A, rule (ii): 'any given tetrahedron always remains in the same domain... throughout the monopole dynamics.' The paper explicitly treats this as an assumption, not as a prediction: 'we consider an immobile domain wall; the effects of fluctuations will be discussed in Sec. IV.' Sec. IV B then shows that a fluctuating wall induces charge conjugation and breaks the diode. This is an honest conditional, not circularity. The capacitor/battery results are outputs of the same constrained simulation; survival probabilities in Fig. 5 are measured, not fitted. Eq. (1), v ∝ p/Lz, is derived from Brownian crossing-time scaling and then confirmed by the data collapse of Fig. 4(d); no parameter is tuned. The only self-citation is the adoption of the monopole-hopping protocol of Refs. [10,11,21] (with co-author Jaubert), which is a method choice and does not assert the new results. No uniqueness theorem or ansatz is imported from those references. The admitted limitation—'The last ingredient is to make this AIAO iridium domain wall flat, within one tetrahedron layer. This is the main technological challenge'—affects experimental realizability, not the logical independence of the derivation. Verdict: no significant circularity; minor non-load-bearing self-citation only.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The central mechanism carries no fitted parameters: it is a geometric counting argument on the fragmented-phase texture. The ledger items are modeling constraints and protocol choices (equal chemical potentials, no-backtracking, immobile wall, low-temperature dynamics) whose qualitative impact the authors mostly disclose. The quantitative survival statistics (Fig. 5a) explicitly depend on protocol details. No new physical entities are introduced; the 'two worlds' discussion in Sec. IV C is presented as a classical analogy.

free parameters (2)
  • chemical potential offsets of 4in/4out vs 2in-2out excitations = 0 (equal chemical potentials)
    Sec. II states 4in, 4out and 2in-2out excitations are assigned the same chemical potential, 'as it can in practice vary one way or the other in materials'; the authors argue the choice does not affect the topology of the diode effect.
  • backtracking prohibition = forbidden
    Appendix A rule (iii) forbids immediate backtracking to prevent early annihilation; the paper explicitly says survival probabilities 'can be expected to vary noticeably' with this choice, so it is a hand-set protocol parameter affecting quantitative claims.
axioms (5)
  • domain assumption Fragmented spin ice phase exists with all up tetrahedra 3in-1out and all down tetrahedra 3out-1in (domain D), mapping onto a hard-core dimer model
    Invoked from Ref. 19 (Brooks-Bartlett et al., Phys. Rev. X 4, 011007 (2014)) and Ref. 20 (Nagle); central to defining the minority-spin texture that produces the diode geometry.
  • standard math A monopole conserves its topological charge and its local identity alternates with each hop (negative: 4out, 2in-2out, 4out, ...)
    Used in Sec. III B 2 to fix how charges enter and exit tetrahedra; follows from the dimer mapping but is stated, not derived, in Sec. II.
  • ad hoc to paper Domain wall is immobile while interface spins may fluctuate; any tetrahedron stays in its seed domain
    Appendix A rule (ii), the key modeling constraint; Sec. IV B shows fluctuating walls destroy the diode and induce charge conjugation.
  • domain assumption Very-low-temperature dynamics: no monopole creation, annihilation allowed, all allowed hops equiprobable (no energy barriers)
    Appendix A; the paper describes this as 'very-low-temperature dynamics' and assumes equal chemical potentials make energy costs irrelevant over two hops.
  • domain assumption Monopole Coulomb interactions are non-confining and treated only via scaling estimates
    From spin ice literature (Refs. 1, 21); used implicitly for the tau_c/tau_d estimate of Eq. (2).

pith-pipeline@v1.3.0-daily-deepseek · 25052 in / 18542 out tokens · 209769 ms · 2026-08-04T18:56:32.389191+00:00 · methodology

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read the original abstract

Spin-ice materials are famous for their quasi-particle excitations that behave like magnetic monopoles. Magnetricity is the concept that these monopoles can conduct an AC magnetic current, in analogy with conduction electrons. While monopole dynamics has been intensively studied and is reasonably well understood, very little has been done to design devices in order to control magnetricity. Here we develop a theoretical proof of concept for the design of diodes and capacitors for the transport of monopoles. We use the property of systems with magnetic fragmentation, where spin-ice physics co-exists with long-range antiferromagnetic order. The key point is that magnetic order allows for the existence of domain walls. Under certain conditions of preparation, this domain wall is equivalent to an asymmetric filter for monopoles. In a given direction, positive charges can go through while negative ones are repelled; the opposite applies in the opposite direction. This asymmetry effectively functions like a diode for monopole current. Successive domain walls separate positive from negative charges with a vacuum of charge in between, producing a capacitor for monopoles. Once the capacitor is charged, it can in principle be used as a battery for monopoles. All microscopic mechanisms are explained and our proof of concept is validated by simulations of more than a million spins. Application to experiments are discussed for rare-earth pyrochlore oxides and artificial spin ice. Finally, we discuss in general terms how a domain wall in fragmented spin ice can also be seen as an emergent boundary separating two mirror "worlds" separated by time-reversal symmetry. Beyond spin ice, our work opens a promising direction of investigation for the dynamics of emergent quasi-particles crossing domain walls in chiral and nematic spin liquids, which also possess a broken symmetry.

Figures

Figures reproduced from arXiv: 2608.01883 by Anoop Raj, Ludovic D.C. Jaubert, Sumiran Pujari.

Figure 1
Figure 1. Figure 1: Fragmentation in spin ice and domain walls: The pyrochlore lattice is made of corner-sharing tetrahedra with four spin sublattices, one at each tetrahedron corner. The centres of all tetrahedra form a bipartite diamond lattice. (a) In a fragmented Coulomb phase, all tetrahedra are for example in a 3in-1out state on up tetrahedra (blue) and a 3out-1in state on down tetrahedra (red), defined as domain D. Fli… view at source ↗
Figure 2
Figure 2. Figure 2: Domain walls in fragmented spin ice: (a) Starting from a fragmented spin configuration in domain D, we define a (green) plane at layer z = ndw, orthogonal to the [001] direction. (b) Flipping all spins above this plane transforms the upper part of the system from domain D to D¯. The domain wall is one-tetrahedron layer thick, where 3out-1in and 3in-1out states co-exist; the former (red) belong to the lower… view at source ↗
Figure 3
Figure 3. Figure 3: Diode effect: (a) Schematic representation of the system divided into domains D (bottom) and D¯ (top) via a domain wall at z = ndw = L/2. (b,c) Probability distribution function of the position of monopole carriers, as a function of z, during their diffusion in presence of a domain wall, for negative (b) and positive (c) charges. Simulation details are given in appendix A. (d,e) Microscopic mechanism of th… view at source ↗
Figure 4
Figure 4. Figure 4: Capacitor: (a) Schematic representation of the system with p domain walls, ensuring that positive charges can only go up while negative ones can only go down. A single pair of charges is created in the central region, and its evolution is tracked under Monte Carlo dynamics. (b) Distribution of the position of positive (blue) and negative (red) charges along the z−axis, as a function of simulation time for … view at source ↗
Figure 5
Figure 5. Figure 5: Capacitor with multiple charges: Initially, 10 pairs of charges (20 charges) are created in the central (zeroth) region. Annihilation between opposite charges is permitted but domain walls remain immobile. (a) Histogram of the number of surviving charges (Ns) at the end of simulations, for different densities of domain walls ρdw = 1 6 , 1 9 , 1 12 , 1 18 and L = 256. (b) Space and time evolution of those 2… view at source ↗
Figure 6
Figure 6. Figure 6: (a) thus transforms heat energy into magnetricity. However, as mentioned in the introduction, a constant DC current of magnetic monopoles is not possible [2, 6]. The dy￾namics of a monopole comes with an attached Dirac string that flips spins along the way. Once all possible Dirac strings have been flipped, magnetisation has become saturated and there is no more monopole dynamics. After enough time, the se… view at source ↗
Figure 7
Figure 7. Figure 7: Domain wall fluctuations (a) After a pair of charge excitations is created in domain D, the negative charge reaches the domain wall. (b) Here we allow the domain wall to fluctuate. This fluctuation enables the negative charge to cross. (c) The fluctuation is equivalent to creating a double charge inside the wall. In order to preserve charge neutrality, the hopping charge has to change sign. For more detail… view at source ↗

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Reference graph

Works this paper leans on

97 extracted references · 1 canonical work pages

  1. [1]

    [10, 11, 21] when confirming the Debye-Hückel theory and Coulomb potential between magnetic monopoles in spin ice

    Simulations In order to build our analysis on an unbiased method, we used the numerical protocol that has been validated in Refs. [10, 11, 21] when confirming the Debye-Hückel theory and Coulomb potential between magnetic monopoles in spin ice. Here we adapted this protocol to the presence of domain walls in the fragmented phase. To initiate the simulatio...

  2. [2]

    This will be the layer of our do- main wallz=n dw, and the two layers atz=n dw ±1are thus initially 3in-1out [Figure 2(a)]

    Mechanism Before creating the domain wall, when the entire system is in domainD, let us arbitrarily choose a layer where all tetra- hedra are in a 3out-1in state. This will be the layer of our do- main wallz=n dw, and the two layers atz=n dw ±1are thus initially 3in-1out [Figure 2(a)]. Once theW + domain wall is formed at layerz=n dw, tetrahedra atz=n dw ...

  3. [3]

    In this section, we will now build on this to design a capacitor for magnetic carriers

    Multiple domain walls and simulations The next step is to use this asymmetric filter made possible because of fragmentation physics to design more complex de- vices. In this section, we will now build on this to design a capacitor for magnetic carriers. To do so, let us consider not one, butpsuccessive domain walls, separatingp+ 1domains labeled by an ind...

  4. [4]

    If we heat up the central region, thermal fluctua- tions will induce a local monopole bath

    Protocol to charge the capacitor Let us consider the previous design of Figure 4(a) and as- sume a very low base temperature with a vanishing density of monopoles. If we heat up the central region, thermal fluctua- tions will induce a local monopole bath. In absence of domain walls, the physics is trivial. Once the heating stops, the sys- tem cools down t...

  5. [5]

    The crystal field on Dy3+ and Ho3+ in pyrochlore oxides is re- sponsible for a strong Ising anisotropy [27, 38, 59]

    Rare-earth iridium pyrochlore oxides Dy2Ir2O7 and Ho 2Ir2O7 are constituted of two interpene- trated pyrochlore lattices made of rare-earth ions on one hand (Dy or Ho), and transition-metal ions on the other hand (Ir). The crystal field on Dy3+ and Ho3+ in pyrochlore oxides is re- sponsible for a strong Ising anisotropy [27, 38, 59]. Alone on the pyrochlo...

  6. [6]

    qubit spin ice

    Artificial networks Stepping away from solid-state physics, magnetic fragmen- tation has also been sought after in artificial spin ice [6, 70]. Artificial lattices are realised by nano-lithography, typically as an array of micrometer-size islands of permalloy, deposited on a non-magnetic substrate of silicium. While initially inspired by spin ice, the fie...

    2022

  7. [7]

    Dusad, F

    R. Dusad, F. K. K. Kirschner, J. C. Hoke, B. R. Roberts, A. Eyal, F. Flicker, G. M. Luke, S. J. Blundell, and J. C. S. Davis, Magnetic monopole noise, Nature571, 234 (2019), num- ber: 7764

    2019

  8. [8]

    Castelnovo, R

    C. Castelnovo, R. Moessner, and S. L. Sondhi, Magnetic monopoles in spin ice, Nature451, 42 (2008)

    2008

  9. [9]

    L. D. C. Jaubert and P. C. W. Holdsworth, Signature of magnetic monopole and dirac string dynamics in spin ice, Nature Physics 5, 258 (2009)

    2009

  10. [10]

    D. J. P. Morris, D. A. Tennant, S. A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, K. C. Rule, J. U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, and R. S. Perry, Dirac strings and magnetic monopoles in the spin ice dy2ti2o7, Science326, 411 (2009)

    2009

  11. [11]

    S. R. Giblin, S. T. Bramwell, P. C. W. Holdsworth, D. Prab- hakaran, and I. Terry, Creation and measurement of long-lived magnetic monopole currents in spin ice, Nature Physics7, 252 (2011)

    2011

  12. [12]

    Kaiser, J

    V . Kaiser, J. Bloxsom, L. Bovo, S. T. Bramwell, P. C. W. Holdsworth, and R. Moessner, Emergent electrochemistry in spin ice: Debye-hückel theory and beyond, Phys. Rev. B98, 144413 (2018)

    2018

  13. [13]

    Jaubert and M

    L. Jaubert and M. Udagawa, eds.,Spin Ice, Springer Series in Solid-State Sciences, V ol. 197 (Springer, 2021)

    2021

  14. [14]

    Nisoli, R

    C. Nisoli, R. Moessner, and P. Schiffer, Artificial spin ice: De- signing and imaging magnetic frustration, Rev. Mod. Phys.85, 1473 (2013)

    2013

  15. [15]

    A. M. Samarakoon, S. A. Grigera, D. A. Tennant, A. Kirste, B. Klemke, P. Strehlow, M. Meissner, J. N. Hallén, L. Jaubert, C. Castelnovo, and R. Moessner, Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7, Proceedings of the National Academy of Sciences 119, e2117453119 (2022)

    2022

  16. [16]

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

    2022

  17. [17]

    Castelnovo, R

    C. Castelnovo, R. Moessner, and S. L. Sondhi, Debye-hückel theory for spin ice at low temperature, Phys. Rev. B84, 144435 (2011)

    2011

  18. [18]

    L. D. C. Jaubert and P. C. W. Holdsworth, Magnetic monopole dynamics in spin ice, Journal of Physics-Condensed Matter23, 164222 (2011)

    2011

  19. [19]

    S. T. Bramwell, S. R. Giblin, S. Calder, R. Aldus, D. Prab- hakaran, and T. Fennell, Measurement of the charge and current of magnetic monopoles in spin ice, Nature461, 956 (2009)

    2009

  20. [20]

    Mengotti, L

    E. Mengotti, L. J. Heyderman, A. F. Rodríguez, F. Nolting, R. V . Hügli, and H.-B. Braun, Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice, Nature Physics7, 68 (2011), number: 1

    2011

  21. [21]

    L. D. C. Jaubert, Monopole holes in a partially ordered spin liquid, Spin05, 1540005 (2015), http://www.worldscientific.com/doi/pdf/10.1142/S2010324715400056

    work page doi:10.1142/s2010324715400056 2015

  22. [22]

    Kapaklis, U

    V . Kapaklis, U. B. Arnalds, A. Farhan, R. V . Chopdekar, A. Balan, A. Scholl, L. J. Heyderman, and B. Hjorvarsson, Thermal fluctuations in artificial spin ice, Nature Nanotechnol- ogy9, 514 (2014)

    2014

  23. [23]

    Perrin, B

    Y . Perrin, B. Canals, and N. Rougemaille, Extensive degener- acy, coulomb phase and magnetic monopoles in artificial square ice, Nature540, 410–413 (2016)

    2016

  24. [24]

    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. Lip- pert, A. Scholl, and S. v. Dijken, Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice, Sci- ence Advances5, eaav6380 (2019), number: 2

    2019

  25. [25]

    L. Miao, Y . Lee, A. B. Mei, M. J. Lawler, and K. M. Shen, Two- dimensional magnetic monopole gas in an oxide heterostruc- ture, Nature Communications11, 1 (2020), number: 1 Pub- lisher: Nature Publishing Group

    2020

  26. [26]

    M. E. Brooks-Bartlett, S. T. Banks, L. D. C. Jaubert, A. Harman-Clarke, and P. C. W. Holdsworth, Magnetic- moment fragmentation and monopole crystallization, Phys. Rev. X4, 011007 (2014)

    2014

  27. [27]

    J. F. Nagle, New series-expansion method for the dimer prob- lem, Phys. Rev.152, 190 (1966)

    1966

  28. [28]

    Raban, C

    V . Raban, C. T. Suen, L. Berthier, and P. C. W. Holdsworth, Multiple symmetry sustaining phase transitions in spin ice, Phys. Rev. B99, 224425 (2019)

    2019

  29. [29]

    coulomb phase

    C. L. Henley, The "coulomb phase" in frustrated systems, Annu. Rev. Condens. Matter Phys.1, 179 (2010)

    2010

  30. [30]

    M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, and K. W. Godfrey, Geometrical frustration in the ferromagnetic py- rochlore ho2ti2o7, Phys. Rev. Lett.79, 2554 (1997)

    1997

  31. [31]

    Möller and R

    G. Möller and R. Moessner, Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays, Phys. Rev. B80, 140409 (2009)

    2009

  32. [32]

    Chern, P

    G.-W. Chern, P. Mellado, and O. Tchernyshyov, Two-stage or- dering of spins in dipolar spin ice on the kagome lattice, Phys. Rev. Lett.106, 207202 (2011)

    2011

  33. [33]

    R. A. Borzi, D. Slobinsky, and S. A. Grigera, Charge ordering in a pure spin model: Dipolar spin ice, Phys. Rev. Lett.111, 147204 (2013)

    2013

  34. [34]

    Lefrançois, V

    E. Lefrançois, V . Cathelin, E. Lhotel, J. Robert, P. Lejay, C. V . Colin, B. Canals, F. Damay, J. Ollivier, B. Fåk, L. C. Chapon, R. Ballou, and V . Simonet, Fragmentation in spin ice from mag- netic charge injection, Nature Communications8, 209 (2017)

    2017

  35. [35]

    K. B. Yogendra, S. Karmakar, and T. Das, Symmetry, super- position, and fragmentation in classical spin liquids: A general framework and applications to square kagome magnets, Phys. Rev. B110, L060401 (2024)

    2024

  36. [36]

    Slobinsky, L

    D. Slobinsky, L. Pili, G. Baglietto, S. A. Grigera, and R. A. Borzi, Monopole matter from magnetoelastic coupling in the Ising pyrochlore, Communications Physics4, 1 (2021)

    2021

  37. [37]

    Palle and O

    G. Palle and O. Benton, Exactly solvable spin- 1 2 xyz models with highly degenerate partially ordered ground states, Phys. Rev. B103, 214428 (2021)

    2021

  38. [38]

    Szabó, F

    A. Szabó, F. Orlandi, and P. Manuel, Fragmented spin ice and multi-kordering in rare-earth antiperovskites, Phys. Rev. Lett. 129, 247201 (2022)

    2022

  39. [39]

    Museur, E

    F. Museur, E. Lhotel, and P. C. W. Holdsworth, Neutron scat- tering from fragmented frustrated magnets, Phys. Rev. B107, 214425 (2023)

    2023

  40. [40]

    Saccone, A

    M. Saccone, A. Van den Berg, E. Harding, S. Singh, S. R. Gib- lin, F. Flicker, and S. Ladak, Exploring the phase diagram of 3D artificial spin-ice, Communications Physics6, 1 (2023)

    2023

  41. [41]

    Vijayvargia, E

    A. Vijayvargia, E. M. Nica, R. Moessner, Y .-M. Lu, and O. Erten, Magnetic fragmentation and fractionalized goldstone modes in a bilayer quantum spin liquid, Phys. Rev. Res.5, L022062 (2023)

    2023

  42. [42]

    Canals, I.-A

    B. Canals, I.-A. Chioar, V .-D. Nguyen, M. Hehn, D. La- cour, F. Montaigne, A. Locatelli, T. O. Mentes, B. S. Bur- gos, and N. Rougemaille, Fragmentation of magnetism in artifi- cial kagome dipolar spin ice, Nature Communications7, 11446 (2016)

    2016

  43. [43]

    Rougemaille, J

    N. Rougemaille, J. Coraux, and B. Canals, Ampère phase in frustrated magnets, Phys. Rev. B111, 064402 (2025)

    2025

  44. [44]

    Lhotel, L

    E. Lhotel, L. D. C. Jaubert, and P. C. W. Holdsworth, Frag- mentation in Frustrated Magnets: A Review, Journal of Low 15 Temperature Physics201, 710 (2020), number: 5

    2020

  45. [45]

    Cathelin, E

    V . Cathelin, E. Lefrançois, J. Robert, P. C. Guruciaga, C. Paulsen, D. Prabhakaran, P. Lejay, F. Damay, J. Ollivier, B. Fåk, L. C. Chapon, R. Ballou, V . Simonet, P. C. W. Holdsworth, and E. Lhotel, Fragmented monopole crystal, dimer entropy, and coulomb interactions indy 2ir2o7, Phys. Rev. Res.2, 032073 (2020)

    2020

  46. [46]

    Vlášková, M

    K. Vlášková, M. Diviš, and M. Klicpera, The magnetic be- haviour of Dy2Ir2O7 – Beyond the mean field approximation, Journal of Magnetism and Magnetic Materials538, 168220 (2021)

    2021

  47. [47]

    M. J. Pearce, K. Götze, A. Szabó, T. S. Sikkenk, M. R. Lees, A. T. Boothroyd, D. Prabhakaran, C. Castelnovo, and P. A. God- dard, Magnetic monopole density and antiferromagnetic do- main control in spin-ice iridates, Nature Communications13, 444 (2022)

    2022

  48. [48]

    Museur, J

    F. Museur, J. Robert, F. Morineau, N. Bujault, V . Simonet, E. Pachoud, A. Hadj-Azzem, C. V . Colin, L. Mangin-Thro, P. Manuel, J. R. Stewart, P. C. W. Holdsworth, and E. Lhotel, Ferromagnetic fragmented state in the pyrochloreho 2ru2o7, Phys. Rev. B113, L060406 (2026)

    2026

  49. [49]

    J. Xu, O. Benton, A. T. M. N. Islam, T. Guidi, G. Ehlers, and B. Lake, Order out of a coulomb phase and higgs transition: Frustrated transverse interactions ofnd 2zr2o7, Phys. Rev. Lett. 124, 097203 (2020)

    2020

  50. [50]

    Sendetskyi, L

    O. Sendetskyi, L. Anghinolfi, V . Scagnoli, G. Möller, N. Leo, A. Alberca, J. Kohlbrecher, J. Lüning, U. Staub, and L. J. Hey- derman, Magnetic diffuse scattering in artificial kagome spin ice, Phys. Rev. B93, 224413 (2016)

    2016

  51. [51]

    W.-C. Yue, Z. Yuan, Y .-Y . Lyu, S. Dong, J. Zhou, Z.-L. Xiao, L. He, X. Tu, Y . Dong, H. Wang, W. Xu, L. Kang, P. Wu, C. Nisoli, W.-K. Kwok, and Y .-L. Wang, Crystallizing kagome artificial spin ice, Phys. Rev. Lett.129, 057202 (2022)

    2022

  52. [52]

    Rougemaille and B

    N. Rougemaille and B. Canals, Cooperative magnetic phenom- ena in artificial spin systems: spin liquids, Coulomb phase and fragmentation of magnetism - a colloquium, The European Physical Journal B92, 62 (2019)

    2019

  53. [53]

    V . M. Parakkat, K. Xie, and K. M. Krishnan, Tunable ground state in heterostructured artificial spin ice with exchange bias, Phys. Rev. B99, 054429 (2019)

    2019

  54. [54]

    Petit, E

    S. Petit, E. Lhotel, B. Canals, M. Ciomaga Hatnean, J. Ollivier, H. Mutka, E. Ressouche, A. R. Wildes, M. R. Lees, and G. Bal- akrishnan, Observation of magnetic fragmentation in spin ice, Nature Physics12, 746 (2016)

    2016

  55. [55]

    Benton, Quantum origins of moment fragmentation in nd2zr2o7, Phys

    O. Benton, Quantum origins of moment fragmentation in nd2zr2o7, Phys. Rev. B94, 104430 (2016)

    2016

  56. [56]

    In addition, the numerical prefactor αc αd would also favour hit- ting the domain wall, sinceα c concerns the random walk of two point-like charges, whileα d is integrated over a plane of dimensionL 2

  57. [57]

    J. A. M. Paddison, H. S. Ong, J. O. Hamp, P. Mukherjee, X. Bai, M. G. Tucker, N. P. Butch, C. Castelnovo, M. Mourigal, and S. E. Dutton, Emergent order in the kagome Ising mag- net Dy3Mg2Sb3O14, Nature Communications7, ncomms13842 (2016)

    2016

  58. [58]

    Z. Dun, X. Bai, J. A. M. Paddison, E. Hollingworth, N. P. Butch, C. D. Cruz, M. B. Stone, T. Hong, F. Demmel, M. Mourigal, and H. Zhou, Quantum versus classical spin fragmentation in dipolar kagome iceho 3mg2sb3o14, Phys. Rev. X10, 031069 (2020)

    2020

  59. [59]

    Cruddas and B

    J. Cruddas and B. J. Powell, Multiple coulomb phases with temperature-tunable ice rules in pyrochlore spin-crossover ma- terials, Phys. Rev. B104, 024433 (2021)

    2021

  60. [60]

    D. I. Khomskii, Electric activity at magnetic moment fragmen- tation in spin ice, Nature Communications12, 3047 (2021)

    2021

  61. [61]

    C. O. Reichhardt and C. Reichhardt, Ratchet Effects in Active Matter Systems, Annual Review of Condensed Matter Physics 8, 51 (2017), type: Journal Article

    2017

  62. [62]

    L. D. C. Jaubert, M. Haque, and R. Moessner, Analysis of a fully packed loop model arising in a magnetic coulomb phase, Phys. Rev. Lett.107, 177202 (2011)

    2011

  63. [63]

    T. C. Fujita, Y . Kozuka, M. Uchida, A. Tsukazaki, T. Arima, and M. Kawasaki, Odd-parity magnetoresistance in pyrochlore iridate thin films with broken time-reversal symmetry, Scientific Reports5, 9711 (2015)

    2015

  64. [64]

    J. D. Jackson,Classical Electrodynamics(Wiley, New-York, 1999)

    1999

  65. [65]

    R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman lectures on physics, V ol. 1 (Basic Books, New York, NY , 2010) Chap. 46: Ratchet and pawl, originally published 1963-1965

    2010

  66. [66]

    J. S. Gardner, M. J. P. Gingras, and J. E. Greedan, Magnetic pyrochlore oxides, Reviews of Modern Physics82, 53 (2010)

    2010

  67. [67]

    Bansal, H

    C. Bansal, H. Kawanaka, H. Bando, and Y . Nishihara, Structure and magnetic properties of the pyrochlore ho2ru2o7: A possible dipolar spin ice system, Phys. Rev. B66, 052406 (2002)

    2002

  68. [68]

    Matsuhira, M

    K. Matsuhira, M. Wakeshima, Y . Hinatsu, and S. Takagi, Metal–Insulator Transitions in Pyrochlore Oxides Ln2Ir2O7, Journal of the Physical Society of Japan80, 094701 (2011), number: 9

    2011

  69. [69]

    Tardif, S

    S. Tardif, S. Takeshita, H. Ohsumi, J.-i. Yamaura, D. Okuyama, Z. Hiroi, M. Takata, and T.-h. Arima, All-in–all-out magnetic domains: X-ray diffraction imaging and magnetic field control, Phys. Rev. Lett.114, 147205 (2015)

    2015

  70. [70]

    R. F. Wang, C. Nisoli, R. S. Freitas, J. Li, W. McConville, B. J. Cooley, M. S. Lund, N. Samarth, C. Leighton, V . H. Crespi, and P. Schiffer, Artificial ’spin ice’ in a geometrically frus- trated lattice of nanoscale ferromagnetic islands, Nature439, 303 (2006)

    2006

  71. [71]

    Opherden, J

    L. Opherden, J. Hornung, T. Herrmannsdörfer, J. Xu, A. T. M. N. Islam, B. Lake, and J. Wosnitza, Evolution of anti- ferromagnetic domains in the all-in-all-out ordered pyrochlore nd2zr2o7, Phys. Rev. B95, 184418 (2017)

    2017

  72. [72]

    L. Bovo, X. Moya, D. Prabhakaran, Y .-A. Soh, A. Boothroyd, N. Mathur, G. Aeppli, and S. Bramwell, Restoration of the third law in spin ice thin films, Nature Communications5, 3439 (2014)

    2014

  73. [73]

    D. P. Leusink, F. Coneri, M. Hoek, S. Turner, H. Idrissi, G. Van Tendeloo, and H. Hilgenkamp, Thin films of the spin ice compound Ho2Ti2O7, Applied Physics Letter Materials2, 032101 (2014)

    2014

  74. [74]

    T. C. Fujita, M. Uchida, Y . Kozuka, S. Ogawa, A. Tsukazaki, T. Arima, and M. Kawasaki, All-in-all-out magnetic domain size in pyrochlore iridate thin films as probed by local magne- totransport, Applied Physics Letters108, 022402 (2016), pub- lisher: American Institute of Physics

    2016

  75. [75]

    L. Bovo, C. M. Rouleau, D. Prabhakaran, and S. T. Bramwell, Layer-by-layer epitaxial thin films of the pyrochlore tb 2 ti 2 o 7, Nanotechnology28, 055708 (2017)

    2017

  76. [76]

    Timsina, A

    P. Timsina, A. Chappa, D. Alyones, B. Kiefer, and L. Miao, Monopole traps for position-based information coding (2025), arXiv:2507.22315 [cond-mat.str-el]

    arXiv 2025

  77. [77]

    S. D. Pace, C. Castelnovo, and C. R. Laumann, Dynamical ax- ions inu(1)quantum spin liquids, Phys. Rev. Lett.130, 076701 (2023)

    2023

  78. [78]

    S. H. Skjærvø, C. H. Marrows, R. L. Stamps, and L. J. Heyder- 16 man, Advances in artificial spin ice, Nature Reviews Physics , 1 (2019)

    2019

  79. [79]

    A. May, M. Hunt, A. Van Den Berg, A. Hejazi, and S. Ladak, Realisation of a frustrated 3D magnetic nanowire lattice, Com- munications Physics2, 1 (2019), number: 1

    2019

  80. [80]

    A. May, M. Saccone, A. van den Berg, J. Askey, M. Hunt, and S. Ladak, Magnetic charge propagation upon a 3D artificial spin-ice, Nature Communications12, 3217 (2021), number: 1

    2021

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.