Colloquium: Artificial spin ice: Designing and imaging magnetic frustration

Abstract

Frustration -the presence of competing interactions -is ubiquitous in the physical sciences and is a source of degeneracy and disorder, which in turn give 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 spin-glass 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 on 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 non-thermal '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. We review the considerable experimental and theoretical progress in this field, including connections to other frustrated phenomena, and we outline future vistas for progress in this rapidly expanding field.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

“…Arrays of interacting, single-domain nanomagnets known as artificial spin ice have proved to be useful model systems with which to experimentally explore the microscopic nature of geometrical frustration [6][7][8] . Simple square and kagome artificial spin ice lattices have been subject to intense study because they provide unique insight into the consequences of frustrated magnetism, such as residual entropy 9,10 and magnetic charge excitations [11][12][13][14] .…”

Emergent geometric frustration of artificial magnetic skyrmion crystals

“…The system reveals a rich phase behavior when skyrmion-current interactions compete with structural confinement strength. In contrast to lattices of interacting nanoscale particles/islands such as artificial spin ice [43,44], or colloids [71,72,105], the spin-torque reconfigurability of the proposed skyrmion ices makes them compatible with standard spintronic devices such as magnetic tunnel junctions and thus straightforwardly integrable to the existing semiconductor manufacturing processes.…”

“…The observed disordered states, composed of a mixture of ice-rule-obeying and ice-rule-breaking vertices [43], may arise due to the relatively weak magnetic interactions between the nanomagnets and the relatively high energy barrier between the two possible nanomagnet states, as well as from quenched disorder effects in the nanomagnet array [44]. Recently, it was demonstrated that the GS could be approached more closely by using certain dynamical annealing protocols [43,51,70].…”

“…The most studied artificial spin ice systems are created using arrays of nanomagnets with a bistable single-domain magnetization [43,44,[46][47][48][49][50][51][52][53][54][55][56][57][63][64][65][66][67]. Artificial nanomagnet spin ice systems have been realized experimentally for square [43,50,51,56,66], and honeycomb [49,52,68] lattices, each having different analogous features to the naturally occurring rare-earth pyrochlore lattice [37].…”

“…Although the naturally occurring spin ices exhibit interesting types of topological monopole defects and "ice-rule" states [39,40], the frustrated behaviors occur only at very low temperatures and the individual spin ordering or defects cannot be directly visualized on the atomic scale size. Recent advances in nanofabrication technology have permitted the creation of artificial ice systems [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] that mimic the behavior of geometrically frustrated atomic spin ices at much larger length scales and higher temperatures, where direct visualization of the microscopic effective spin configurations under controlled conditions is possible.…”