Colloquium: Artificial spin ice: Designing and imaging magnetic frustration

Frustration, the presence of competing interactions, is ubiquitous in the physical sciences and is a source of degeneracy and disorder, which in turn gives rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than in correlated spin systems, where it has been studied in the most detail. In disordered magnetic materials, frustration leads to spinglass phenomena, with analogies to the behavior of structural glasses and neural networks. In structurally ordered magnetic materials, it has also been the topic of extensive theoretical and experimental studies over the past two decades. Such geometrical frustration has opened a window to a wide range of fundamentally new exotic behavior. This includes spin liquids in which the spins continue to fluctuate down to the lowest temperatures, and spin ice, which appears to retain macroscopic entropy even in the low-temperature limit where it enters a topological Coulomb phase. In the past seven years a new perspective has opened in the study of frustration through the creation of artificial frustrated magnetic systems. These materials consist of arrays of lithographically fabricated single-domain ferromagnetic nanostructures that behave like giant Ising spins. The nanostructures' interactions can be controlled through appropriate choices of their geometric properties and arrangement on a (frustrated) lattice. The degrees of freedom of the material can not only be directly tuned, but also individually observed. Experimental studies have unearthed intriguing connections to the out-of-equilibrium physics of disordered systems and nonthermal granular materials, while revealing strong analogies to spin ice materials and their fractionalized magnetic monopole excitations, lending the enterprise a distinctly interdisciplinary flavor. The experimental results have also been closely coupled to theoretical and computational analyses, facilitated by connections to classic models of frustrated magnetism, whose hitherto unobserved aspects have here found an experimental realization. Considerable experimental and theoretical progress in this field is reviewed here, including connections to other frustrated phenomena, and future vistas for progress in this rapidly expanding field are outlined.