Signatures of farther neighbor couplings in artificial square ice

The analysis of the magnetic structure factor obtained after imaging a field-demagnetized artificial square ice reveals qualitative deviations from what would predict six-vertex model. More specifically, additional features appear for certain $q$ vectors in experimental that are absent theoretical one. Using Monte Carlo simulations, we demonstrate these originate dipolarlike, farther neighbor couplings. Our results thus show long-range magnetostatic interactions coupling nanomagnets not totally washed out and cannot be neglected as they impact correlations within or at vicinity manifold. Artificial systems then expected to ultimately order, provided ground state can approached.