Polymerization in magnetic metamaterials

We numerically study a mesoscopic system consisting of magnetic nanorings in the presence of thermal magnetization fluctuations. We find the formation of dipolar-field-mediated ``bonds" promoting the formation of annuli clusters, where the amount of bonds between two rings varies between zero and two. This system resembles the formation of polymers from artificial atoms, which in our case are the annuli and where the valency of the atom is set by the ring multipolarity. We investigate the thermodynamic properties of the resulting structures, and find a transition associated with the formation of the bonds. In addition, we find that the system has a tendency to form topological structures, with a distinct critical temperature in relation to the one for bond formation.