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

• Received 12 October 2020
• Revised 2 February 2021
• Accepted 16 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.094405