Skyrmion Spin Ice in Liquid Crystals

Ayhan Duzgun; Cristiano Nisoli

REVIEW 3 major objections 5 minor 55 references

Skyrmion Spin Ice in Liquid Crystals

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that liquid-crystal skyrmions confined in open-ended traps act as binary pseudo-spins whose mutual repulsion drives the system into ice-rule states on square and hexagonal lattices.

desk verdict A credible numerical proposal for liquid-crystal skyrmion spin ice with a real 2D-to-3D gap, worth refereeing despite missing statistics. read the letter →

arxiv 1908.03246 v2 pith:DDZIDC3S submitted 2019-08-08 cond-mat.soft

Ayhan Duzgun , Cristiano Nisoli This is my paper · ORCID

classification cond-mat.soft

keywords artificialspiniceliquidcrystalskyrmionsrulegeometricfrustrationtopologicalsolitonschiralnematicparticleQ-tensormodel

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

Liquid-crystal skyrmions are particle-like topological solitons in the director field of a chiral nematic. The paper proposes that, when confined in open-ended traps, they behave as binary pseudo-spins whose mutual elastic repulsion is frustrated at lattice vertices, producing artificial spin ice. Two large numerical relaxations--288 skyrmions on a square lattice and 192 on a hexagonal lattice--converge to ice-rule-obeying states: an ordered antiferromagnetic tessellation of type-IV vertices on the square lattice and a disordered manifold of 2-in/1-out and 1-in/2-out vertices on the hexagonal lattice. If the two-dimensional model captures real three-dimensional confinement, this would make liquid crystals a reconfigurable platform for studying frustration, with trap geometry and skyrmion size tunable in place.

What carries the argument

The central object is the liquid-crystal skyrmion, a particle-like soliton in which the director rotates by 180 degrees from core to periphery, carrying unit topological charge. The key construction is the open-ended binary trap: a channel whose ends confine a skyrmion to either of two positions, with the middle left open so that skyrmions on neighboring traps can interact through their elastic fields; the paper explains that closed dumbbell traps would suppress this interaction and defeat the spin ice. The simulations evolve a Landau-de Gennes $Q$-tensor free energy with cholesteric twist, surface anchoring, and an electric field, using the $z$-invariant $K=0$ limit to make large two-dimensional systems tractable, and implement the relaxation on GPUs.

What would settle it

Run a full three-dimensional simulation, or a chiral-nematic cell experiment, of the same square trap array with intermediate aspect ratio and measure the vertex statistics after relaxation: if the fraction of ice-rule (type-IV) vertices is not substantially higher than random, with defect ratios near 1 rather than the low values reported in the paper, the central claim fails.

Watch

Extended reading notes

Core claim

The central claim is that a chiral nematic liquid crystal can realize a skyrmion spin ice: arrays of open-ended traps, each holding at most one skyrmion, define binary variables, and the elastic repulsion between skyrmions imposes the ice rule at every vertex. In overdamped relaxations, square-lattice arrays settle into an ordered 'antiferromagnetic' state of type-IV vertices (two skyrmions in, two out), with defects concentrated in domain walls, while hexagonal arrays settle into a disordered mixture of type-II and type-III vertices (2-in/1-out and 1-in/2-out) with sparse monopole defects. The paper identifies a window of trap aspect ratios where ice behavior is best, shows that cyclically swelling and deswelling skyrmions lowers defect counts, and finds that quenched disorder hurts square ice more than hexagonal ice. The main-text evidence is two-dimensional, using the $K=0$ $z$-invariant limit; full three-dimensional simulations are presented in the supplementary material. On this basis the authors state that they have demonstrated numerically that liquid crystals are a new platform for spin-ice physics on the two most common geometries.

Load-bearing premise

The load-bearing premise is that the two-dimensional, $z$-invariant model (the special $K=0$ case) captures the same binary-trap confinement and mutual repulsion that real three-dimensional skyrmions would experience in a cell of finite thickness, so that ice-rule behavior predicted in 2D survives in experiments.

Editorial extensions

If this is right

Square-lattice skyrmion ice should relax to an ordered antiferromagnetic state of type-IV vertices, with ice-rule violations appearing mainly inside domain walls.
Hexagonal-lattice skyrmion ice should remain a disordered manifold of 2-in/1-out and 1-in/2-out vertices, with sparse monopole defects.
Ice-rule behavior is conditional on trap shape and skyrmion size: traps that are too narrow freeze the particles, traps that are too wide allow centered positions, and intermediate aspect ratios are required.
Cyclically swelling and deswelling the skyrmions anneals the system and extends the range of trap parameters over which the ice rule is reached.
Because skyrmions can be created, annihilated, resized, and steered optically or electrically, the same sample can be reconfigured between different ice geometries, enabling memory, doping, and decimation experiments.

Reading between the lines

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

If the 2D $z$-invariant model carries over to finite-thickness cells, the defect-ratio curves in the paper give a quantitative target for an experiment: measuring vertex statistics as a function of trap aspect ratio and field strength would test the platform directly.
The open-ended trap design suggests a general principle for particle-based ices: confinement must not screen the inter-particle interaction, so traps should localize a particle without isolating it from its neighbors.
The wide-trap regime that spoils the binary character could be a practical route to classical spin-1 ice (vertex occupations 0, 1, or 2), a model that is hard to reach with magnetic islands.
The stronger sensitivity of square ice to quenched disorder points to a design heuristic: choose hexagonal lattices when robustness to fabrication disorder matters, and square lattices when an ordered ground state is desired.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 paper does what it says: it shows numerically that confined LC skyrmions in open-ended traps relax to ice-rule states on square and hexagonal lattices. The open-end trap design is a smart fix to the closed-dumbbell geometry used in colloidal ice, and the parameter scans for aspect ratio, field strength, and disorder are genuinely informative. Square ice orders antiferromagnetically, hexagonal ice stays disordered—exactly what the ice rule predicts. That is a solid numerical demonstration of a known physics in a new platform, not a new theoretical framework, and I think the authors are appropriately measured in most of their claims.

The soft spots are real but not fatal. The main one is exactly what the stress test flags: the headline results come from 2D K=0 simulations, while the experimental cell is 3D with finite thickness and anchoring. The authors are transparent about this and point to 3D results in the SM, but the main text does not show that the K=0 limit preserves the binary trap potential and repulsion that drive the ice-rule behavior. A referee should push for that evidence in the main text or a more explicit argument for why the 3D corrections do not change the vertex energetics. This is a load-bearing gap but not a collapse: the K=0 structure is a known limit of the same Landau–de Gennes model, and the physics likely survives, but the claim 'realized via confined skyrmions' needs the 3D check to be presented rather than deferred.

The other weaknesses are minor in comparison. There are no repeated-run statistics; each parameter point appears to be a single relaxation, so defect ratios in Fig. 4 could be noisy. The 'first Skyrmion Spin Ice' claim is slightly overbroad given the cited magnetic skyrmion work [18], though the LC-specific realization is new. No code or data is provided, which limits reproducibility. The citation practice is fine: the self-citations are to the authors' own earlier work on LC skyrmion stability and confinement, and they are used appropriately.

Who is this for? Researchers in artificial spin ice and soft matter topology. It is a good example of exporting spin-ice physics to a reconfigurable platform, and it suggests concrete experimental directions. I would bring it to a reading group.

My recommendation: send it to peer review. It is a serious, well-posed proposal with honest limitations. A referee should request 3D simulation results in the main text or a rigorous justification of the K=0 mapping, and repeated runs for the defect statistics. With those, it would be a solid contribution.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a liquid-crystal realization of artificial spin ice in which chiral nematic skyrmions are confined in binary, open-ended traps and interact through mutual repulsion. The authors simulate ensembles of skyrmions on square and hexagonal lattices using a Landau–de Gennes free energy, Eq. (1), starting from random skyrmion placements and employing a swell-and-deswell relaxation protocol. They report that the relaxed states obey the ice rule: square ice organizes into an ordered array of Type IV vertices with domain walls, and hexagonal ice relaxes into a disordered manifold of Type II and Type III vertices. The paper also presents parameter studies of trap aspect ratio, obstacle strength, skyrmion size, and quenched disorder. The central claim is that this is the first skyrmion spin ice and a viable new platform for frustrated soft-matter systems.

Significance. If the central claim holds, this is a substantive contribution to artificial spin ice: liquid-crystal skyrmions offer reconfigurable traps, optical creation and annihilation, size tunability, and controllable interactions, which are not readily available in magnetic or colloidal platforms. The modeling has real strengths. The free energy in Eq. (1) is a standard cholesteric Landau–de Gennes energy with no parameters fitted to the ice-rule states; the simulated systems are large (288 and 192 skyrmions); the initial configurations are random; and the paper explicitly examines parameter dependence and disorder effects. The main limitation is that the central ice-rule results are computed in the 2D, K = 0 limit, while the proposed experimental platform is a finite-thickness 3D cell with homeotropic anchoring and, for K ≠ 0, barrel-like skyrmions. Establishing quantitative fidelity of the 2D mapping for the spin-ice observables is therefore load-bearing for the platform claim.

major comments (3)

[Fig. 3 and the statement 'Main text includes only 2D simulations and full 3D simulations are presented in SM'] The central demonstration of ice-rule states is performed for the K = 0, z-invariant limit of Eq. (1), modeled in 2D, whereas the proposed experimental cell has thickness Nz/p ≈ 0.36, homeotropic anchoring at both boundaries, and barrel-like three-dimensional skyrmions when K ≠ 0. The effective binary trap potential and the range or anisotropy of skyrmion-skyrmion repulsion could change in a 3D texture because of cholesteric twist, boundary layers, and obstacle anchoring; the ice-rule statistics in Fig. 3 emerge specifically from frustrated mutual repulsion and binary occupancy. The manuscript therefore needs to show in the main text, or explicitly cite with quantitative values from the SM, that 3D simulations reproduce the same vertex fractions and defect ratios as the 2D K = 0 model. As written, the platform claim rests on an unverified dimensional-reduction assumption.
[Fig. 3 and Fig. 4(a,b): defect statistics] The reported defect ratios appear to come from single realizations or a very small number of runs, with no error bars or ensemble averages. The text itself acknowledges that the system 'preserves memory of its preparation' and that cyclic swelling and deswelling changes the final state, which implies that relaxation is history-dependent. Without repeated independent initializations and a statement of run-to-run variability, the reader cannot assess whether the ice-rule behavior is robust or an artifact of a particular random starting configuration and swell-deswell schedule. Please provide at least several independent runs for the key parameter values and report mean and standard deviation of the defect fraction.
[Fig. 4 and the paragraph beginning 'One last note'] The quantitative comparability of the parameter scans is compromised by the admitted differences in system size and simulation time across panels: Fig. 4(c,d) use systems four times smaller than Fig. 4(a,b), and Fig. 4(e) uses a simulation time four times longer. This makes the apparent zero-defect regions and the disorder-dependence comparison difficult to interpret as a function of the control parameters alone. The authors should either repeat the relevant scans with consistent system size, simulation time, and relaxation protocol, or provide a scaling analysis showing that these differences do not affect the conclusions.

minor comments (5)

[Conclusion] The word 'gemoetries' should be 'geometries'.
[Fig. 4(c)] The caption and text describe the light-exposure curve as modeled by q0 → q0/1.2, which 'produces an effect similar to changing K → 1.2K'; please clarify in the caption whether the plotted curve uses the q0 reduction or the equivalent K change, and define the dimensionless units used on the horizontal axis.
[Page 4] The phrase 'previously studies in detail' should read 'previously studied in detail'.
[Eq. (1) and SM] The main text repeatedly refers to the SM for simulation parameters but does not list the numerical values of L, a, b, c, Γ, lattice size, and grid spacing needed to reproduce the figures. Including a parameter table in the main text would improve reproducibility.
[Fig. 2(b,c)] The description of Type IV vertices as '2 skyrmions in the vertex, and two out of the vertex' would be clearer if the spin convention for each lattice edge were stated explicitly, since the square and hexagonal vertex types are defined relative to the four or three incident traps respectively.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ice-rule outcome is not encoded in the inputs; it emerges from unconstrained Landau–de Gennes relaxation with random initial skyrmion placements.

full rationale

The paper's derivation chain is self-contained against the target result. The free energy in Eq. (1) is a standard Landau–de Gennes model with bulk, elastic, cholesteric, anchoring, and field terms; no parameter is fitted to the ice-rule vertex statistics. The simulations begin with 288 or 192 skyrmions 'placed randomly inside the traps' and relax via an over-damped dynamic equation, so the final Type IV square and Type II/III hexagonal vertex populations are emergent outputs rather than built-in constraints. Prior work by the same authors is used for physically motivated inputs—skyrmion stability ranges, attraction to weak easy-axis regions, and trap manipulation [26,28,41]—but these are not the argument that ice rules are obeyed; the numerical free-energy minimization independently produces the ice-rule states. The 'special case of K = 0' yielding a z-invariant structure is a stated modeling simplification, and the main text notes that full 3D simulations are in the Supplemental Material; this is a validation gap or completeness concern about the 2D-to-3D mapping, not a circular step, because the 2D simulation is not defined in terms of the ice-rule outcome. The expectation that particle ices obey the ice rule is attributed to prior colloid-ice theory [3,21], but the paper's contribution is demonstrating that LC skyrmions in open-ended traps realize that physics, which is shown by simulation rather than assumed. No equation is equivalent to another by construction, and no fitted parameter is renamed as a prediction. Therefore the correct finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central simulation claim relies on standard LC modeling, a 2D approximation, and control parameters selected to produce ice behavior; no new physical entities are postulated and no parameters are fitted to the ice-rule result itself.

free parameters (4)

Landau-de Gennes coefficients a, b, c = not stated in main text, see SM
Chosen 'to ensure a reasonable value for S'; they set the bulk free energy but are not fitted to ice-rule states.
Background field coupling alpha = Delta epsilon E^2 = chosen in the skyrmion stability range, e.g., free skyrmions require 3 < alpha < 5.5 [28], with confined skyrmions…
Controls skyrmion size and interaction; values are hand-picked in the green and blue regions of Fig. 4 to obtain ice behavior.
Trap aspect ratio omega/D = 0.52 for square and 0.41 for hexagonal lattices
Chosen in the intermediate range where the trap is binary and skyrmions can move; scanning in Fig. 4 shows the ice rule only in this green region.
Anchoring strength K and obstacle type = K = 1.6, 16, 160 tests; light modeled as q0 to q0/1.2
Obstacle properties affect defect ratios but not the existence of ice-rule behavior; values are varied to map robustness.

assumptions (4)

domain assumption Landau-de Gennes Q-tensor free energy (Eq. 1) accurately models chiral nematic skyrmions.
Standard phenomenological model; all simulation results depend on it.
domain assumption Overdamped relaxational dynamics with periodic boundary conditions reach representative low-energy states.
This gradient flow underestimates thermal fluctuations and may trap in metastable states; the paper notes memory of preparation.
domain assumption The K = 0 z-invariant 2D model captures the relevant confined skyrmion interactions.
Main-text simulations are 2D; the paper claims this is valid for K = 0 and delegates 3D results to the SM.
domain assumption Energy ordering of vertex types follows prior spin ice and colloidal ice expectations.
The paper states 'It is expected [3], as a result of non-local frustration [21], that collective lowest energy states obey the ice rule'; the vertex classification and defect counting assume this ordering.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Skyrmion Spin Ice in Liquid Crystals." pith.science (2026). https://pith.science/paper/DDZIDC3S

@misc{pith2026190803246,
  author       = {Pith},
  title        = {Pith review of: Skyrmion Spin Ice in Liquid Crystals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DDZIDC3S}},
  note         = {Machine review of arXiv:1908.03246}
}

read the original abstract

We propose the first Skyrmion Spin Ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasi-particles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasi-particles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of LC skyrmions as elementary degrees of freedom in the design of collective complex behaviors.

Figures

Figures reproduced from arXiv: 1908.03246 by the authors.

**Figure 2.** (a) shows how to go from dumbbells to our much simpler and general geometry with open ends. There, smaller black circles represent trap ends and bigger circles provide the narrower mid-section of the trap. The usual nomenclature [17] for skyrmions’ configurations at the vertices are shown in Fig. 2b-c along with their spin representation for a square and hexagonal lattice respectively. It is expected [3], as a re… view at source ↗

**Figure 3.** shows snapshots of the final states for the two geometries. Square ice converges to an ordered “antiferromagnetic” [3, 43, 44] tessellation of ice-rule-obeying type-IV vertices, with two skyrmions close to, and two away from, each vertex. Deviations from type IV correspond to ice-rule obeying Type III, but also to violations of the ice rule in the form of monopoles [45], or Type II and V. Together, these excitatio… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: (c), shows how curves of ice-rule violations vs. aspect ratio for square ice varies depending on obstacle properties. Obstacles generated by weaker anchoring (K = 1.6) are softer and allows increased mobility for the skyrmions thus helps the system reach the ice-state…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 54 canonical work pages

[18]

Emergent geomet- ric frustration of artiﬁcial magnetic skyrmion crystals,

Fusheng Ma, Charles Reichhardt, Weiliang Gan, CJ Ol- son Reichhardt, and Wen Siang Lew, “Emergent geomet- ric frustration of artiﬁcial magnetic skyrmion crystals,” Physical Review B 94, 144405 (2016)

work page 2016
[1]

Artiﬁcial ’spin ice’ in a geo- metrically frustrated lattice of nanoscale ferromagnetic islands,

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 geo- metrically frustrated lattice of nanoscale ferromagnetic islands,” Nature 439, 303–6 (2006)

work page 2006
[2]

Magnetic interactions in a ferromagnetic honeycomb nanoscale network,

Masaaki Tanaka, E Saitoh, H Miyajima, T Yamaoka, and Y Iye, “Magnetic interactions in a ferromagnetic honeycomb nanoscale network,” Physical Review B 73, 052411 (2006)

work page 2006
[3]

Realizing Colloidal Artiﬁcial Ice on Arrays of Optical Traps,

A. Lib´ al, C. Reichhardt, and C. J. Olson Reichhardt, “Realizing Colloidal Artiﬁcial Ice on Arrays of Optical Traps,” Phys. Rev. Lett. 97, 228302 (2006)

work page 2006
[4]

Engineering of frustration in colloidal artiﬁcial ices realized on mi- crofeatured grooved lattices,

Antonio Ortiz-Ambriz and Pietro Tierno, “Engineering of frustration in colloidal artiﬁcial ices realized on mi- crofeatured grooved lattices,” Nature communications 7 (2016)

work page 2016
[5]

Cre- ating artiﬁcial ice states using vortices in nanostructured superconductors,

A Lib´ al, CJ Olson Reichhardt, and C Reichhardt, “Cre- ating artiﬁcial ice states using vortices in nanostructured superconductors,” Physical review letters 102, 237004 (2009)

work page 2009
[6]

Realization of artiﬁcial ice systems for magnetic vortices in a superconducting moge thin ﬁlm with patterned nanostructures,

M. L. Latimer, G. R. Berdiyorov, Z. L. Xiao, F. M. Peeters, and W. K. Kwok, “Realization of artiﬁcial ice systems for magnetic vortices in a superconducting moge thin ﬁlm with patterned nanostructures,” Phys. Rev. Lett. 111, 067001 (2013)

work page 2013
[7]

Freezing and thawing of artiﬁcial ice by thermal switch- ing of geometric frustration in magnetic ﬂux lattices,

J Trastoy, M Malnou, C Ulysse, R Bernard, N Bergeal, G Faini, J Lesueur, J Briatico, and Javier E Villegas, “Freezing and thawing of artiﬁcial ice by thermal switch- ing of geometric frustration in magnetic ﬂux lattices,” Nature nanotechnology 9, 710 (2014)

work page 2014

Show all 55 references

[8]

Colloquium: Artiﬁcial spin ice: Designing and imaging magnetic frustration,

Cristiano Nisoli, Roderich Moessner, and Peter Schiﬀer, “Colloquium: Artiﬁcial spin ice: Designing and imaging magnetic frustration,” Reviews of Modern Physics 85, 1473 (2013)

2013
[9]

Artiﬁcial ferroic sys- tems: novel functionality from structure, interactions and dynamics,

LJ Heyderman and RL Stamps, “Artiﬁcial ferroic sys- tems: novel functionality from structure, interactions and dynamics,” Journal of Physics: Condensed Matter 25, 363201 (2013)

2013
[10]

Frustration(s) and the ice rule: From natural materials to the deliberate design of exotic be- haviors,

Cristiano Nisoli, “Frustration(s) and the ice rule: From natural materials to the deliberate design of exotic be- haviors,” in Frustrated Materials and Ferroic Glasses (Springer, 2018) pp. 57–99

2018
[11]

A theory of water and ionic solution, with particular reference to hydrogen and hy- droxyl ions,

JD Bernal and RH Fowler, “A theory of water and ionic solution, with particular reference to hydrogen and hy- droxyl ions,” The Journal of Chemical Physics1, 515–548 (1933)

1933
[12]

The structure and entropy of ice and of other crystals with some randomness of atomic arrange- ment,

Linus Pauling, “The structure and entropy of ice and of other crystals with some randomness of atomic arrange- ment,” Journal of the American Chemical Society 57, 2680–2684 (1935)

1935
[13]

Frus- tration by design,

Ian Gilbert, Cristiano Nisoli, and Peter Schiﬀer, “Frus- tration by design,” Physics Today 69, 54–59 (2016)

2016
[14]

Deliberate exotic magnetism via frustration and topol- ogy,

Cristiano Nisoli, Vassilios Kapaklis, and Peter Schiﬀer, “Deliberate exotic magnetism via frustration and topol- ogy,” Nature Physics 13, 200–203 (2017)

2017
[15]

Switchable geometric frustration in an artiﬁcial-spin- ice–superconductor heterosystem,

Yong-Lei Wang, Xiaoyu Ma, Jing Xu, Zhi-Li Xiao, Alexey Snezhko, Ralu Divan, Leonidas E Ocola, John E Pearson, Boldizsar Janko, and Wai-Kwong Kwok, “Switchable geometric frustration in an artiﬁcial-spin- ice–superconductor heterosystem,” Nature nanotechnol- ogy 13, 560 (2018)

2018
[16]

Ice rule fragility via topo- logical charge transfer in artiﬁcial colloidal ice,

Andr´ as Lib´ al, Dong Yun Lee, Antonio Ortiz-Ambriz, Charles Reichhardt, Cynthia JO Reichhardt, Pietro Tierno, and Cristiano Nisoli, “Ice rule fragility via topo- logical charge transfer in artiﬁcial colloidal ice,” Nature communications 9, 4146 (2018)

2018
[17]

Col- loquium: Ice rule and emergent frustration in particle ice and beyond,

Antonio Ortiz-Ambriz, Cristiano Nisoli, Charles Reich- hardt, Cynthia JO Reichhardt, and Pietro Tierno, “Col- loquium: Ice rule and emergent frustration in particle ice and beyond,” Reviews of Modern Physics 91, 041003 (2019)

2019
[19]

Topological defects produce exotic mechanics in complex metamaterials,

Anne S Meeussen, Erdal C Oguz, Yair Shokef, and Martin van Hecke, “Topological defects produce exotic mechanics in complex metamaterials,” arXiv preprint arXiv:1903.07919 (2019)

2019 arXiv
[20]

Artiﬁcial spin (and potts) ice of skyrmions in liquid crystals,

Ayhan Duzgun and Cristiano Nisoli, “Artiﬁcial spin (and potts) ice of skyrmions in liquid crystals,” in APS Meet- ing Abstracts (2019)

2019
[21]

Unexpected phenomenology in particle-based ice absent in magnetic spin ice,

Cristiano Nisoli, “Unexpected phenomenology in particle-based ice absent in magnetic spin ice,” Physical Review Letters 120, 167205 (2018)

2018
[22]

P. G. de Gennes and J. Prost, The physics of liquid crys- tals, 2nd ed. (Clarendon Press,Oxford, 1993)

1993
[23]

Lan- dau theory of cholesteric blue phases,

H. Grebel, R. M. Hornreich, and S. Shtrikman, “Lan- dau theory of cholesteric blue phases,” Phys. Rev. A 28, 1114–1138 (1983)

1983
[24]

Two- dimensional skyrmions and other solitonic structures in conﬁnement-frustrated chiral nematics,

Paul J Ackerman, Rahul P Trivedi, Bohdan Senyuk, Jao van de Lagemaat, and Ivan I Smalyukh, “Two- dimensional skyrmions and other solitonic structures in conﬁnement-frustrated chiral nematics,” Physical Re- 6 view E 90, 012505 (2014)

2014
[25]

Surface an- choring as a control parameter for stabilizing torons, skyrmions, twisted walls, ﬁngers, and their hybrids in chiral nematics,

Jung-Shen B. Tai and Ivan I. Smalyukh, “Surface an- choring as a control parameter for stabilizing torons, skyrmions, twisted walls, ﬁngers, and their hybrids in chiral nematics,” Phys. Rev. E 101, 042702 (2020)

2020
[26]

Alignment induced re-conﬁgurable walls for patterning and assembly of liquid crystal skyrmions,

Ayhan Duzgun, Avadh Saxena, and Jonathan V. Selinger, “Alignment induced re-conﬁgurable walls for patterning and assembly of liquid crystal skyrmions,” (2020), arXiv:2001.09615 [cond-mat.soft]

2020 arXiv
[27]

Skyrmion states in chiral liquid crystals,

G. De Matteis, L. Martina, and V. Turco, “Skyrmion states in chiral liquid crystals,” Theoretical and Mathe- matical Physics 196, 1150–1163 (2018)

2018
[28]

Comparing skyrmions and merons in chiral liquid crystals and magnets,

Ayhan Duzgun, Jonathan V. Selinger, and Avadh Sax- ena, “Comparing skyrmions and merons in chiral liquid crystals and magnets,” Phys. Rev. E 97, 062706 (2018)

2018
[29]

Quasi-two- dimensional skyrmion lattices in a chiral nematic liquid crystal,

Jun-ichi Fukuda and Slobodan Zumer, “Quasi-two- dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nature Communications 2, 246 EP – (2011), article

2011
[30]

Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal ﬁlm,

Andriy Nych, Jun-ichi Fukuda, Uliana Ognysta, Slobo- dan Zumer, and Igor Musevic, “Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal ﬁlm,” Nature Physics 13, 1215 EP – (2017), article

2017
[31]

Topological states in chiral active mat- ter: Dynamic blue phases and active half-skyrmions,

Luuk Metselaar, Amin Doostmohammadi, and Ju- lia M. Yeomans, “Topological states in chiral active mat- ter: Dynamic blue phases and active half-skyrmions,” The Journal of Chemical Physics 150, 064909 (2019), https://doi.org/10.1063/1.5085282

2019 doi
[32]

Two-dimensional skyrmion bags in liquid crystals and ferromagnets,

David Foster, Charles Kind, Paul J. Ackerman, Jung- Shen B. Tai, Mark R. Dennis, and Ivan I. Smalyukh, “Two-dimensional skyrmion bags in liquid crystals and ferromagnets,” Nature Physics (2019), 10.1038/s41567- 019-0476-x

2019 doi
[33]

Ring-shaped liquid crystal structures through patterned planar photo-alignment,

Brecht Berteloot, Inge Nys, Guilhem Poy, Jeroen Beeck- man, and Kristiaan Neyts, “Ring-shaped liquid crystal structures through patterned planar photo-alignment,” Soft Matter 16, 4999–5008 (2020)

2020
[34]

Design of nematic liquid crystals to control microscale dynamics,

Oleg D. Lavrentovich, “Design of nematic liquid crystals to control microscale dynamics,” (2020), arXiv:2007.02187 [cond-mat.soft]

2020 arXiv
[35]

Light-controlled skyrmions and torons as reconﬁgurable particles,

Hayley R. O. Sohn, Changda D. Liu, Yuhan Wang, and Ivan I. Smalyukh, “Light-controlled skyrmions and torons as reconﬁgurable particles,” Opt. Express 27, 29055–29068 (2019)

2019
[36]

Squirming motion of baby skyrmions in nematic ﬂuids,

Paul J Ackerman, Timothy Boyle, and Ivan I Smalyukh, “Squirming motion of baby skyrmions in nematic ﬂuids,” Nature communications 8, 673 (2017)

2017
[37]

Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,

Hayley R. O. Sohn, Paul J. Ackerman, Timothy J. Boyle, Ghadah H. Sheetah, Bengt Fornberg, and Ivan I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97, 052701 (2018)

2018
[38]

Cholesteric liquid crystals in rectangular microchan- nels: skyrmions and stripes,

Yubing Guo, Sajedeh Afghah, Jie Xiang, Oleg D. Lavrentovich, Robin L. B. Selinger, and Qi-Huo Wei, “Cholesteric liquid crystals in rectangular microchan- nels: skyrmions and stripes,” Soft Matter 12, 6312–6320 (2016)

2016
[39]

Periodic arrays of liquid crystalline torons in mi- crochannels,

Yun Ho Kim, Min-Jun Gim, Hee-Tae Jung, and Dong Ki Yoon, “Periodic arrays of liquid crystalline torons in mi- crochannels,” RSC Adv. 5, 19279–19283 (2015)

2015
[40]

Electric ﬁeld generation of skyrmion-like structures in a nematic liquid crystal,

Laura Cattaneo, ˇZiga Kos, Matteo Savoini, Paul Kouwer, Alan Rowan, Miha Ravnik, Igor Muˇ seviˇ c, and Theo Ras- ing, “Electric ﬁeld generation of skyrmion-like structures in a nematic liquid crystal,” Soft Matter 12, 853–858 (2016)

2016
[41]

Commensurate states and pat- tern switching via liquid crystal skyrmions trapped in a square lattice,

Ayhan Duzgun, Cristiano Nisoli, Cynthia Reichhardt, and Charles Reichhardt, “Commensurate states and pat- tern switching via liquid crystal skyrmions trapped in a square lattice,” Soft Matter , – (2020)

2020
[42]

Optical pat- terning and dynamics of torons and hopﬁons in a chiral nematic with photo-tunable equilibrium pitch,

H. Sohn, P. Ackerman, and I. Smalyukh, “Optical pat- terning and dynamics of torons and hopﬁons in a chiral nematic with photo-tunable equilibrium pitch,” in APS Meeting Abstracts (2017) p. A17.013

2017
[43]

Crystallites of magnetic charges in artiﬁcial spin ice,

Sheng Zhang, Ian Gilbert, Cristiano Nisoli, Gia-Wei Chern, Michael J Erickson, Liam O´Brien, Chris Leighton, Paul E Lammert, Vincent H Crespi, and Peter Schiﬀer, “Crystallites of magnetic charges in artiﬁcial spin ice,” Nature 500, 553–557 (2013)

2013
[44]

Exploring thermally induced states in square arti- ﬁcial spin-ice arrays,

JM Porro, A Bedoya-Pinto, A Berger, and P Vavas- sori, “Exploring thermally induced states in square arti- ﬁcial spin-ice arrays,” New Journal of Physics 15, 055012 (2013)

2013
[45]

Magnetic monopoles in spin ice,

C Castelnovo, R Moessner, and S L Sondhi, “Magnetic monopoles in spin ice,” Nature 451, 42–5 (2008)

2008
[46]

Topological order in the six-vertex antiferromagnet and its breakdown in spin ice,

Cristiano Nisoli, “Topological order in the six-vertex antiferromagnet and its breakdown in spin ice,” arXiv preprint arXiv:2004.02107 (2020)

2020 arXiv
[47]

Dis- order strength and ﬁeld-driven ground state domain for- mation in artiﬁcial spin ice: experiment, simulation, and theory,

Zoe Budrikis, JP Morgan, J Akerman, A Stein, Paolo Politi, S Langridge, CH Marrows, and RL Stamps, “Dis- order strength and ﬁeld-driven ground state domain for- mation in artiﬁcial spin ice: experiment, simulation, and theory,” Physical review letters 109, 037203 (2012)

2012
[48]

Diversity enabling equilibration: disorder and the ground state in artiﬁcial spin ice,

Zoe Budrikis, Paolo Politi, and RL Stamps, “Diversity enabling equilibration: disorder and the ground state in artiﬁcial spin ice,” Physical review letters 107, 217204 (2011)

2011
[49]

Disorder regimes and equivalence of disorder types in artiﬁcial spin ice,

Zoe Budrikis, Paolo Politi, and RL Stamps, “Disorder regimes and equivalence of disorder types in artiﬁcial spin ice,” Journal of Applied Physics 111, 07E109 (2012)

2012
[50]

Unhappy vertices in artiﬁcial spin ice: new degeneracies from vertex frustration,

Muir J Morrison, Tammie R Nelson, and Cristiano Nisoli, “Unhappy vertices in artiﬁcial spin ice: new degeneracies from vertex frustration,” New Journal of Physics 15, 045009 (2013)

2013
[51]

Classical topological order in the ki- netics of artiﬁcial spin ice,

Yuyang Lao, Francesco Caravelli, Mohammed Sheikh, Joseph Sklenar, Daniel Gardeazabal, Justin D Watts, Alan M Albrecht, Andreas Scholl, Karin Dahmen, Cris- tiano Nisoli, et al. , “Classical topological order in the ki- netics of artiﬁcial spin ice,” Nature Physics 14, 723–727 (2018)

2018
[52]

Nanoscale control of competing interactions and geo- metrical frustration in a dipolar trident lattice,

Alan Farhan, Charlotte F Petersen, Scott Dhuey, Luca Anghinolﬁ, Qi Hang Qin, Michael Saccone, Sven Velten, Clemens Wuth, Sebastian Gliga, Paula Mellado, et al. , “Nanoscale control of competing interactions and geo- metrical frustration in a dipolar trident lattice,” Nature co...

2017
[53]

Doped colloidal artiﬁcial spin ice,

Andras Lib´ al, CJ Olson Reichhardt, and Charles Reich- hardt, “Doped colloidal artiﬁcial spin ice,” New Journal of Physics 17, 103010 (2015)

2015
[54]

Interaction of liq- uid crystal skyrmions with curved boundaries,

Avadh Saxena and Ayhan Duzgun, “Interaction of liq- uid crystal skyrmions with curved boundaries,” in APS March Meeting Abstracts , APS Meeting Abstracts, Vol. 2019 (2019) p. B30.011

2019
[55]

Schools of skyrmions with electrically tunable elastic interactions,

Hayley R. O. Sohn, Changda D. Liu, and Ivan I. Sma- lyukh, “Schools of skyrmions with electrically tunable elastic interactions,” Nature Communications 10, 4744 (2019)

2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [18]

Emergent geomet- ric frustration of artiﬁcial magnetic skyrmion crystals,

Fusheng Ma, Charles Reichhardt, Weiliang Gan, CJ Ol- son Reichhardt, and Wen Siang Lew, “Emergent geomet- ric frustration of artiﬁcial magnetic skyrmion crystals,” Physical Review B 94, 144405 (2016)

work page 2016

[2] [1]

Artiﬁcial ’spin ice’ in a geo- metrically frustrated lattice of nanoscale ferromagnetic islands,

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 geo- metrically frustrated lattice of nanoscale ferromagnetic islands,” Nature 439, 303–6 (2006)

work page 2006

[3] [2]

Magnetic interactions in a ferromagnetic honeycomb nanoscale network,

Masaaki Tanaka, E Saitoh, H Miyajima, T Yamaoka, and Y Iye, “Magnetic interactions in a ferromagnetic honeycomb nanoscale network,” Physical Review B 73, 052411 (2006)

work page 2006

[4] [3]

Realizing Colloidal Artiﬁcial Ice on Arrays of Optical Traps,

A. Lib´ al, C. Reichhardt, and C. J. Olson Reichhardt, “Realizing Colloidal Artiﬁcial Ice on Arrays of Optical Traps,” Phys. Rev. Lett. 97, 228302 (2006)

work page 2006

[5] [4]

Engineering of frustration in colloidal artiﬁcial ices realized on mi- crofeatured grooved lattices,

Antonio Ortiz-Ambriz and Pietro Tierno, “Engineering of frustration in colloidal artiﬁcial ices realized on mi- crofeatured grooved lattices,” Nature communications 7 (2016)

work page 2016

[6] [5]

Cre- ating artiﬁcial ice states using vortices in nanostructured superconductors,

A Lib´ al, CJ Olson Reichhardt, and C Reichhardt, “Cre- ating artiﬁcial ice states using vortices in nanostructured superconductors,” Physical review letters 102, 237004 (2009)

work page 2009

[7] [6]

Realization of artiﬁcial ice systems for magnetic vortices in a superconducting moge thin ﬁlm with patterned nanostructures,

M. L. Latimer, G. R. Berdiyorov, Z. L. Xiao, F. M. Peeters, and W. K. Kwok, “Realization of artiﬁcial ice systems for magnetic vortices in a superconducting moge thin ﬁlm with patterned nanostructures,” Phys. Rev. Lett. 111, 067001 (2013)

work page 2013

[8] [7]

Freezing and thawing of artiﬁcial ice by thermal switch- ing of geometric frustration in magnetic ﬂux lattices,

J Trastoy, M Malnou, C Ulysse, R Bernard, N Bergeal, G Faini, J Lesueur, J Briatico, and Javier E Villegas, “Freezing and thawing of artiﬁcial ice by thermal switch- ing of geometric frustration in magnetic ﬂux lattices,” Nature nanotechnology 9, 710 (2014)

work page 2014