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Topological defects from doping and quenched disorder in artificial ice systems

We examine the ice-rule obeying and ice-rule breaking vertices in an artificial spin ice system created using magnetic vortices in type-II superconductors with nanostructured pinning arrays. We show that this system can be doped by changing the external field to move the number of vortices away from commensurability and create sites that contain two or zero vortices. For a square ice, the doping leads to the formation of a grain boundary of vertices that do not obey the ice rules. In commensurate systems where the ice rules are obeyed, we can introduce random disorder at the individual pinning sites to create regions where vortices may not be able to flip from one side of the trap to another. For weak disorder, all of the vertices still obey the ice rules, while at intermediate levels of disorder we find grain boundaries of vertices which do not obey the ice rules. For strong disorder it is possible to create isolated paired vertices that do not obey the ice rules.