Physicists Build 'Anti-Spin Ice' by Making Magnetic Particles Attract Instead of Repel

Physicists have built a system that does the opposite of a spin ice, one that deliberately breaks the 'ice rule' that has governed the field for decades. Their paper in Nature Communications reports the realization of what they call an anti-spin ice.

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. Many arrangements satisfy the rule equally well, so the hydrogen atoms end up disordered, with no repeating pattern. That is a sign of geometric frustration, which occurs when competing interactions cannot all be satisfied at once and leave many equally good compromises. Scientists have recreated the behavior in engineered 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. Each particle acts like a small arrow pointing toward one vertex of the lattice and away from the other. Researchers give every vertex a topological charge by counting how many particles sit near it and how many sit far away. On a square lattice, a vertex with two near and two far has zero charge. Because the particles normally repel each other, they spread out evenly and keep those charges as small as possible, which is the ice rule.

The new study asks what happens if the particles attract instead. "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," co-author Pietro Tierno of the University of Barcelona told Phys.org. With attraction, particles 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," Tierno said, producing vertices with charges as extreme as +4 or -4 that the ice rule forbids.

Making particles attract is harder than it sounds. The team used colloids 2.8 micrometers wide, made of polystyrene embedded with iron oxide grains, which become magnetic in an applied field. A field pointing straight up makes all particles identical magnets that repel side by side. A field along the surface makes pairs lined up head to tail attract while side-by-side pairs repel, and at low strengths thermal motion can flip which is which.

To get around that, the researchers 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, so the net effect is an attraction that is the same in every direction. The particles sat in a pentaheptite lattice of lithographic double wells, with one colloid per well. The result gives physicists a new, tunable platform for studying frustration where the usual organizing rule no longer applies.