String phase in an artificial spin ice

The appearance of one-dimensional strings of local excitations represents an interesting feature of the physical behavior of strongly correlated topological quantum matter. Here we demonstrate that strings of local excitations can also describe the physics of a classical thermal system of interacting nanomagnets, the Santa Fe Ice geometry of artificial spin ice. We measure the moment configuration of the nanomagnets, both after annealing near the ferromagnetic Curie point and in a thermally dynamic state. While the Santa Fe Ice lattice structure is complex, we demonstrate that its disordered magnetic state is naturally described within a framework of emergent strings. We show experimentally that the string length follows a simple Boltzmann distribution with an energy scale that is associated with the system’s magnetic interactions and that is consistent with theoretical predictions. The results demonstrate that string descriptions and associated topological characteristics are not unique to quantum models, but that they also provide a simplifying description of complex classical systems with non-trivial frustration.