Tag: Artificial spin ices

Scientists Flip the Ice Rule to Create the First Anti- Spin Ice

Scientists have created the first “anti- spin ice” using colloidal particles that attract each other, inverting the usual ice rule so the system maximizes (rather than minimizes) local topological charges.

An illustration depicting a crystalline structure representing anti-spin ice, featuring blue and red spheres labeled +1 and -1, with dynamic energy lines radiating throughout the background.
AI generated by Grok

Scientists have created the first “anti- spin ice” using colloidal particles that attract each other, inverting the usual ice rule so the system maximizes (rather than minimizes) local topological charges.

This comes from a Nature Communications paper (published September 2026) by Renaud Baillou, Matthew Terkel, Cristiano Nisoli, and Pietro Tierno (University of Barcelona and Los Alamos National Laboratory).

A Phys.org feature summarizing it appeared on November 1, 2026, under the exact headline: Breaking the ice: Scientists use attracting particles to form an anti-spin ice.

Background: ordinary spin ices and the ice rule

Artificial spin ices (and colloidal particle ices) mimic the geometric frustration of water ice.

In water ice, each oxygen has two hydrogens close and two farther away (the “ice rule”). Analogous systems, arrays of nanomagnets or colloidal particles in lattice traps, follow a similar local rule that minimizes topological charge at each vertex (junction).

Because many arrangements satisfy the rule equally well, the systems often remain disordered or show residual entropy. Colloidal versions typically use repulsive paramagnetic particles confined in double- well grooves; repulsion keeps charges as balanced and small as possible.⁠

The anti- spin ice approach

The team inverted the interactions to attractive and isotropic. They used ~2.8 µm paramagnetic polystyrene colloids (with iron-oxide grains) in lithographic elliptical wells, one particle per well.

A fast in- plane rotating magnetic field (typically 1- 50 Hz) induces dipoles that average to net attraction in every direction: head- to- tail attraction is stronger than side- by- side repulsion, yielding isotropic attraction whose strength is tuned by field amplitude.⁠

Under attraction the particles crowd toward some vertices and away from others, so the system maximizes topological charge (e.g., all particles near a vertex or all far away) instead of minimizing it. This breaks the conventional ice rule.

Key results

  • Bipartite lattices (square, honeycomb): Simulations and experiments show spontaneous symmetry breaking into a staggered “charge crystal”. High positive and high negative charges alternate in a checkerboard-like pattern (a single ordered ground state). This differs from the repulsive case, where the honeycomb lattice is highly degenerate.⁠
  • Non- bipartite pentaheptite lattice (network of five- and seven- sided polygons): Charge crystallization is frustrated. Even at the strongest attraction, roughly one in four vertices remains low- charge. Odd- sided loops prevent perfect alternation of maximal charges, producing a new form of topological-charge frustration and a degenerate manifold of near- ground states. Experiments on a pentaheptite lattice of ~205 particles matched the simulations.⁠

The work shows that frustration can arise from the inability to maximize charges globally when lattice topology forbids it, not only from the inability to minimize them. Because the interaction sign is controlled by the magnetic-field orientation (a conical field can switch between attraction and repulsion around the “magic angle” ~54.7°), the same platform can be programmed to act as either conventional colloidal ice or anti- spin ice. The authors suggest this concept could extend to nanomagnetic, superconducting, or metamaterial artificial-ice systems.⁠

In short, by flipping repulsion to attraction the researchers reversed the organizing principle of spin ice and uncovered both ordered charge crystallization and a novel kind of frustration.

Microscopic view of numerous elongated, oval-shaped cells arranged in a repetitive pattern on a yellow background.
A pentaheptite lattice of lithographic double wells each filled with one paramagnetic colloid. The particles are subjected to an in-plane rotating magnetic field and attract each other at any vertex of the lattice. Credit: Renaud Baillou and Matt Terkel.

Emergent charge crystallization and frustration in a particle anti-spin ice

Abstract (key points)

Artificial spin ices are versatile platforms for engineering exotic states of matter. They are typically governed by the ice rule, which enforces minimization of local topological charge and often produces degeneracy and constrained disorder.

This work reports the first realization of an “anti- spin ice”: a system in which the ice rule is inverted. The system seeks to maximize (rather than minimize) spin- ice charges.

  • Method: Fast- rotating in- plane magnetic fields generate isotropic attraction between colloidal particles, reversing the usual repulsive interactions used in colloidal spin ices.
  • Lattices studied: Bipartite square and honeycomb lattices and non- bipartite pentaheptite geometries (experiments and simulations).
  • Main findings: Rules for order and disorder in the anti- spin ice are established. On the pentaheptite lattice, a new form of frustration appears, topological charge frustration, arising from networks of unequal, odd- sided polygons that suppress charge crystallization even at high interaction strengths.

Core idea and results

In conventional colloidal particle ice, repulsive paramagnetic colloids in double- well traps follow the ice rule (balanced topological charge at vertices).

Here, a rapidly rotating in- plane magnetic field averages the dipolar interactions into net isotropic attraction. Particles therefore crowd toward some vertices and away from others, maximizing local charges.

  • Bipartite lattices (square, honeycomb): Spontaneous symmetry breaking produces a staggered “charge crystal” in which high positive and high negative charges alternate. A single ordered ground state emerges in both geometries (in contrast to the highly degenerate honeycomb case under repulsion).
  • Pentaheptite lattice (5- and 7- sided polygons): Perfect staggered crystallization is topologically impossible. Roughly one- quarter of the vertices remain low- charge even at the strongest attractions tested, producing a degenerate manifold of near-ground states. This is a distinct form of frustration driven by the inability to maximize charge globally.

The interaction sign can be tuned continuously (e.g., via a conical field around the “magic angle” ≈ 54.7°), so the same platform can switch between conventional ice and anti-spin ice behavior.

The authors note that the concept could extend to other artificial- ice platforms (nanomagnetic, superconducting, metamaterial, etc.).

The full paper (including figures, methods, and supplementary videos of particle collapse and lattice dynamics) is freely available at the link you provided. An earlier arXiv version is also available (arXiv:2603.29389).

Paper: Emergent charge crystallization and frustration in a particle anti-spin ice

Journal: Nature Communications

DOI: 10.1038/s41467-026-77905-2

Published: 26 September 2026 (open access)

Authors: Renaud Baillou,
Matthew Terkel,
Cristiano Nisoli &
Pietro Tierno

Illustration of a particle lattice with brown spheres arranged on a gray surface, depicting interactions with an applied magnetic field (B).
Fig. 1: Repulsive and attractive interactions in the particle ice. | Nature Communications | Nature Communications

Scientists Flip the Ice Rule to Create the First Anti- Spin Ice

Scientists have created the first “anti- spin ice” using colloidal particles that attract each other, inverting the usual ice rule so the system maximizes (rather than minimizes) local topological charges.

The team inverted the interactions to attractive and isotropic. They used ~2.8 µm paramagnetic polystyrene colloids (with iron-oxide grains) in lithographic elliptical wells, one particle per well.

An illustration depicting a crystalline structure representing anti-spin ice, featuring blue and red spheres labeled +1 and -1, with dynamic energy lines radiating throughout the background.
AI generated by Grok

Scientists have created the first “anti- spin ice” using colloidal particles that attract each other, inverting the usual ice rule so the system maximizes (rather than minimizes) local topological charges.

This comes from a Nature Communications paper (published September 2026) by Renaud Baillou, Matthew Terkel, Cristiano Nisoli, and Pietro Tierno (University of Barcelona and Los Alamos National Laboratory).

A Phys.org feature summarizing it appeared on November 1, 2026, under the exact headline: Breaking the ice: Scientists use attracting particles to form an anti-spin ice.

Background: ordinary spin ices and the ice rule

Artificial spin ices (and colloidal particle ices) mimic the geometric frustration of water ice.

In water ice, each oxygen has two hydrogens close and two farther away (the “ice rule”). Analogous systems, arrays of nanomagnets or colloidal particles in lattice traps, follow a similar local rule that minimizes topological charge at each vertex (junction).

Because many arrangements satisfy the rule equally well, the systems often remain disordered or show residual entropy. Colloidal versions typically use repulsive paramagnetic particles confined in double- well grooves; repulsion keeps charges as balanced and small as possible.⁠

The anti- spin ice approach

The team inverted the interactions to attractive and isotropic. They used ~2.8 µm paramagnetic polystyrene colloids (with iron-oxide grains) in lithographic elliptical wells, one particle per well.

A fast in- plane rotating magnetic field (typically 1- 50 Hz) induces dipoles that average to net attraction in every direction: head- to- tail attraction is stronger than side- by- side repulsion, yielding isotropic attraction whose strength is tuned by field amplitude.⁠

Under attraction the particles crowd toward some vertices and away from others, so the system maximizes topological charge (e.g., all particles near a vertex or all far away) instead of minimizing it. This breaks the conventional ice rule.

Key results

  • Bipartite lattices (square, honeycomb): Simulations and experiments show spontaneous symmetry breaking into a staggered “charge crystal”. High positive and high negative charges alternate in a checkerboard-like pattern (a single ordered ground state). This differs from the repulsive case, where the honeycomb lattice is highly degenerate.⁠
  • Non- bipartite pentaheptite lattice (network of five- and seven- sided polygons): Charge crystallization is frustrated. Even at the strongest attraction, roughly one in four vertices remains low- charge. Odd- sided loops prevent perfect alternation of maximal charges, producing a new form of topological-charge frustration and a degenerate manifold of near- ground states. Experiments on a pentaheptite lattice of ~205 particles matched the simulations.⁠

The work shows that frustration can arise from the inability to maximize charges globally when lattice topology forbids it, not only from the inability to minimize them. Because the interaction sign is controlled by the magnetic-field orientation (a conical field can switch between attraction and repulsion around the “magic angle” ~54.7°), the same platform can be programmed to act as either conventional colloidal ice or anti- spin ice. The authors suggest this concept could extend to nanomagnetic, superconducting, or metamaterial artificial-ice systems.⁠

In short, by flipping repulsion to attraction the researchers reversed the organizing principle of spin ice and uncovered both ordered charge crystallization and a novel kind of frustration.

Microscopic view of numerous elongated, oval-shaped cells arranged in a repetitive pattern on a yellow background.
A pentaheptite lattice of lithographic double wells each filled with one paramagnetic colloid. The particles are subjected to an in-plane rotating magnetic field and attract each other at any vertex of the lattice. Credit: Renaud Baillou and Matt Terkel.

Emergent charge crystallization and frustration in a particle anti-spin ice

Abstract (key points)

Artificial spin ices are versatile platforms for engineering exotic states of matter. They are typically governed by the ice rule, which enforces minimization of local topological charge and often produces degeneracy and constrained disorder.

This work reports the first realization of an “anti- spin ice”: a system in which the ice rule is inverted. The system seeks to maximize (rather than minimize) spin- ice charges.

  • Method: Fast- rotating in- plane magnetic fields generate isotropic attraction between colloidal particles, reversing the usual repulsive interactions used in colloidal spin ices.
  • Lattices studied: Bipartite square and honeycomb lattices and non- bipartite pentaheptite geometries (experiments and simulations).
  • Main findings: Rules for order and disorder in the anti- spin ice are established. On the pentaheptite lattice, a new form of frustration appears, topological charge frustration, arising from networks of unequal, odd- sided polygons that suppress charge crystallization even at high interaction strengths.

Core idea and results

In conventional colloidal particle ice, repulsive paramagnetic colloids in double- well traps follow the ice rule (balanced topological charge at vertices).

Here, a rapidly rotating in- plane magnetic field averages the dipolar interactions into net isotropic attraction. Particles therefore crowd toward some vertices and away from others, maximizing local charges.

  • Bipartite lattices (square, honeycomb): Spontaneous symmetry breaking produces a staggered “charge crystal” in which high positive and high negative charges alternate. A single ordered ground state emerges in both geometries (in contrast to the highly degenerate honeycomb case under repulsion).
  • Pentaheptite lattice (5- and 7- sided polygons): Perfect staggered crystallization is topologically impossible. Roughly one- quarter of the vertices remain low- charge even at the strongest attractions tested, producing a degenerate manifold of near-ground states. This is a distinct form of frustration driven by the inability to maximize charge globally.

The interaction sign can be tuned continuously (e.g., via a conical field around the “magic angle” ≈ 54.7°), so the same platform can switch between conventional ice and anti-spin ice behavior.

The authors note that the concept could extend to other artificial- ice platforms (nanomagnetic, superconducting, metamaterial, etc.).

The full paper (including figures, methods, and supplementary videos of particle collapse and lattice dynamics) is freely available at the link you provided. An earlier arXiv version is also available (arXiv:2603.29389).

Paper: Emergent charge crystallization and frustration in a particle anti-spin ice

Journal: Nature Communications

DOI: 10.1038/s41467-026-77905-2

Published: 26 September 2026 (open access)

Authors: Renaud Baillou,
Matthew Terkel,
Cristiano Nisoli &
Pietro Tierno

Illustration of a particle lattice with brown spheres arranged on a gray surface, depicting interactions with an applied magnetic field (B).
Fig. 1: Repulsive and attractive interactions in the particle ice. | Nature Communications | Nature Communications