Abstract
We consider pure square spin ice, that is, square ice, where only nearest neighbors are coupled. The gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes the height formalism of the disordered ground state to non-zero temperature. The framework can be applied to the zoology of recent experimental results, especially realizations on quantum annealers, and can be expanded to include longer range interactions.
Highlights
Degenerate artificial square ice is perhaps the simplest twodimensional system in which the disorder constrained by the ice rule[1] and its violations as monopole excitations are studied.[2,3]
While spin ice pyrochlores[4,5,6,7] had opened new vistas in the study of geometric frustration and constrained disorder, more recently, artificial spin ice—systems of interacting, magnetic nanoislands8–13—have provided controllable platforms that can be characterized at the constituent level
The field has developed to include new forms of frustration and geometries, allowing for the realization of magnets often not found in nature[14–21] and revealing the novel phenomena absent in its crystal analog,[12,22] recent fabrication and characterization advances[23–25] have brought back the austere simplicity of celebrated early models to the fore, such as kagome and square ice
Summary
Degenerate artificial square ice is perhaps the simplest twodimensional system in which the disorder constrained by the ice rule[1] and its violations as monopole excitations are studied.[2,3] While spin ice pyrochlores[4,5,6,7] had opened new vistas in the study of geometric frustration and constrained disorder, more recently, artificial spin ice—systems of interacting, magnetic nanoislands8–13—have provided controllable platforms that can be characterized at the constituent level. The scope of this work is to provide a unifying and expandable framework that can cover many different square ice systems around the ice rule degeneracy point[35,45] by considering topological charges and currents as the relevant degrees of freedom and subsuming the spin structure into effective, entropic interactions among them. This approach flows naturally from the gauge-free duality of the system, which is absent in three dimension (3D). These had included phenomenological approaches via coarse grained field, height models, or analogies with chemical physics approaches.[2,50–60] We particularized some results that we had already found on generic graphs.[61]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
