Breaking the ice: Scientists use attracting particles to form an anti-spin ice

November 1, 2026 feature Breaking the ice: Scientists use attracting particles to form an anti-spin ice Tejasri Gururaj Author Gaby Clark Scientific Editor Robert Egan Senior Editor In a recent Nature Communications study, researchers have reported the realization of an anti-spin ice, a system that does the opposite of conventional spin ices by breaking the ice rule that governs them. Spin ices are magnetic systems that mimic a rule found in water ice. In water ice, each oxygen atom keeps two hydrogen atoms close and two farther away. This is known as the ice rule. Because many arrangements satisfy this rule equally well, the hydrogen atoms in ice end up being disordered, meaning that there's no repeating pattern. This is a sign of geometric frustration, which occurs when competing interactions in a system can't all be satisfied at once, leaving many equally good compromises. Scientists have recreated this behavior in engineered systems called artificial spin ices, built from arrays of tiny magnets or microscopic particles called colloids. In colloidal ices, particles sit in tiny grooves, or wells, arranged along a lattice, each resting near one end or the other. Because the particles repel each other, they spread out evenly, keeping the imbalance of particles at each junction (its topological charge) as small as possible. For the most part, researchers have studied colloidal ices using repulsive particles. In the new study, researchers examined what happens when the particles attract each other instead, creating what they call an anti-spin ice. Phys.org spoke with co-author of the study Pietro Tierno from the University of Barcelona. Tierno said that the work "was motivated by the idea that changing something as fundamental as the sign of the pair interaction between the particles—from repulsive to attractive—might completely change the way geometric frustration emerges in a physical system." Charges, attraction and repulsion In colloidal ice, each groove holds a single particle and links two vertices of the lattice. The particle can sit near either vertex, acting like a tiny arrow, or spin, that points toward one vertex and away from the other. Researchers use these arrows to give each vertex a topological charge. They count how many particles sit close to the vertex and how many sit far away, and the difference gives the charge. On a square lattice, each vertex is surrounded by four grooves. A vertex with two particles near and two far has zero charge. Because each particle is shared between two vertices, moving it closer to one vertex moves it away from the other. With repulsive particles, the lowest-energy arrangement keeps every vertex as balanced as possible. The result is colloidal ice's version of the ice rule. "The rule is central because it governs the low-energy states of many frustrated systems. Indeed, for decades it has been the organizing principle behind most artificial spin-ice research," Tierno said. When the particles are attracted to each other instead, they crowd toward some vertices and away from others. "In an anti-spin ice, the system seeks to maximize rather than minimize the local topological charges," he said. On a square lattice, a vertex having all four particles nearby would have a high positive charge of +4, whereas a vertex with all four particles far away would have a high negative charge of −4. These configurations are forbidden by the ice rule. A rotating magnetic field The researchers used colloidal particles 2.8 micrometers wide, made of polystyrene embedded with iron oxide grains. The particles become magnetic when an external magnetic field is applied. In previous magnetic colloidal ices, the field, when pointed straight up from the surface, turned every colloidal particle into an upward-pointing, identical magnet. When side by side, they repelled each other. Making the particles attract is less straightforward. If the field is applied along the surface, every particle's magnetic moment points in the same direction. Pairs lined up head-to-tail along the field attract each other, while those sitting side by side repel. At low field strengths, random thermal motion can shift the particles' relative positions, potentially flipping whether a pair attracts or repels. To circumvent this problem, the team applied a magnetic field that rotates rapidly in the plane of the surface. As it spins, each pair of particles alternates between attracting and repelling. The head-to-tail attraction is about twice as strong as the side-by-side repulsion, resulting in a net attraction that is the same in every direction. The researchers then placed the particles in a pentaheptite lattice (a pattern of five- and seven-sided loops) made of tiny elliptical grooves, one particle per groove. In repulsive colloidal ices, a small hill or bump in the middle of each groove stopped repelling particles from settling at the center. With attraction, the center is unstable. Once random thermal motion nudges a particle slightly toward one end of its groove, the attraction from the particles at that end pulls it the rest of the way, so no hill was needed. The team slowly increased the strength of the rotating field, gradually strengthening the attraction between particles. The field rotated once per second. At higher speeds, the particles began spinning and moving around inside their grooves, disrupting the system. Alongside the experiments, the researchers used computer simulations to study square, honeycomb and pentaheptite lattices, with the field rotating 50 times per second. They also examined triangular and direct-kagome (a pattern of triangles and hexagons) lattices. Odd, even and frustrated loops In simulations of the square lattice, the vertices balanced by the ice rule disappeared as the researchers strengthened the attraction. In their place, vertices ended up with either all four particles near or all four far away, alternating across the lattice like a checkerboard. The same happened on the honeycomb lattice, where three grooves meet at each vertex: vertices with all three particles near alternated with vertices with all three far away. "Charge crystallization is a state of the system where high charges do not disappear, but rather arrange themselves in a staggered way, alternating between positive and negative values," explained Tierno. In both lattices, the system settled into a single ordered arrangement. For the honeycomb lattice, this contrasts with the repulsive case, where many arrangements satisfy the ice rule equally well. The researchers also identified single ordered arrangements for the triangular and direct-kagome lattices. Simulations and experiments both showed that the pentaheptite lattice did not behave like the others. As the attraction increased, most vertices became highly charged, but a share of low-charge vertices always remained. Even at the strongest attraction, roughly one in four vertices stayed low-charge. "In this geometry, it is impossible to arrange the charges in a staggered way so that every local charge-maximization requirement is satisfied simultaneously. As a result, the system becomes frustrated," said Tierno. On the pentaheptite lattice, the charges cannot alternate perfectly around the odd-sided loops. Two neighboring vertices always end up with the same sign. The leftover low-charge vertices can sit in different places, so the system has many nearly equivalent arrangements rather than one ordered pattern. "In our anti-spin ice, frustration comes from the opposite problem: the impossibility of globally maximizing charge on a lattice whose topology prevents perfect charge ordering," he added. The experimental results closely matched the simulations after the researchers rescaled the magnetic-field strengths to account for differences in particle spacing and magnetic response. Next steps The findings show that frustration in colloidal ices can emerge not only when a system tries to minimize local charges, but also when it tries to maximize them. This happens when the lattice prevents the charges from alternating in a consistent pattern. The researchers describe frustration as a question of compatibility between local rules and the overall layout of the lattice. How the layout creates the conflict depends on the interaction. With repulsion, vertices favor the smallest possible charge. With attraction, they favor the largest. On the pentaheptite lattice, the mix of odd-sided five- and seven-sided loops prevents these highly charged vertices from alternating everywhere. Since the interaction between the particles is set by the magnetic field, it could, in principle, be switched. Adding a vertical component to the rotating field would make it sweep out a cone. Depending on the cone's angle, the particles would attract or repel on average, with the changeover at about 54.7 degrees, known as the magic angle. Among the possible directions for future work, Tierno said the most exciting "is the fact that tuning the pair interactions from repulsive to attractive via the orientation of the applied magnetic field may be used to program a system to behave as either a conventional colloidal ice or a colloidal anti-spin ice." "This could not only help us understand how frustration emerges or disappears but could even be used to program frustration. These concepts could then be extended to other artificial-ice platforms, including nanomagnetic, superconducting or metamaterial systems," he said. Written for you by our author Tejasri Gururaj, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. Publication details Renaud Baillou et al., Emergent charge crystallization and frustration in a particle anti-spin ice, Nature Communications (2026). DOI: 10.1038/s41467-026-77905-2. Journal information: Nature Communications © 2026 Science X Network