Thermal ground-state ordering and elementary excitations in artificial magnetic square ice

Recent advances in nanotechnology allow model systems to be constructed, in which frustrated interactions can be tuned at will, such as artificial spin ice. The symmetry of the square ice lattice leads to the emergence of a long-range-ordered ground state from the manifold of frustrated states. However, it is experimentally very difficult to access using the effective thermodynamics of rotating-field demagnetization protocols, because the energy barriers to thermal equilibrium are extremely large. Here we study an as-fabricated sample that approaches the ground state very closely. We identify the small localized departures from the ground state as elementary excitations of the system, at frequencies that follow a Boltzmann law. We therefore identify the state we observe as the frozen-in residue of true thermodynamics that occurred during the fabrication of the sample. The relative proportions of different excitations are suggestive of monopole interactions during thermalization. Simply cooling down an artificial spin-ice does not necessarily lead to ground-state magnetic order. But as-grown artificial square ice reaches a thermodynamic ground state, with monopole dynamics possibly involved in the thermalization.