Controlling phase transitions and magnetic order in a ruby artificial spin ice

Artificial spin ices are arrangements of dipolar-coupled nanomagnets with magnetic moments that behave like Ising spins due to shape anisotropy [1, 2]. The ruby lattice consists of a network of edge-sharing triangles, rectangles and hexagons. A unique feature of the ruby artificial spin ice is that the couplings between nanomagnets can be tuned using two lattice parameters, a and b, while maintaining the same ground state. We have controlled the energy hierarchy in this system and, consequently, how ordering proceeds by varying independently the two lattice parameters [3]. We directly observed the magnetic configurations on thermal annealing using X-PEEM.

When the two lattice constants are of similar size (a ≈ b), the interactions between nanomagnets in triangles and hexagons are approximately balanced, and the system orders in a single step. When one lattice constant is much greater than the other (a >> b or a << b), the system orders in two steps. These steps correspond to the formation of head-to-tail loops of nanomagnet moments associated with the individual hexagonal and triangular shapes. The formation of these moment loops can be successfully captured with an effective three-state spin model with nearest-neighbor interactions. This provides a basis for exploring exotic spin Hamiltonians in artificial spin ice lattices, opening the way to directly observe the resulting emergent phenomena.