Magnetic van der Waals-like framework in bilayer artificial spin ice

We study an artificial spin ice system consisting by two identical layers separated by a height offset $h$. For short separation, the layers are shown to attract each other, provided the whole system is in the ground state. Such an attraction comes about by means of a power-law force compared to van der Waals forces. Whenever magnetic monopoles show up in one (or both) layers, the scenario becomes even more interesting and these layers may also repel each other. By tuning parameters like $h$ and monopole distance, switching between attraction and repulsion may be accomplished in a feasible way. Regarding its thermodynamics, the specific heat peak shifts to lower temperature as $h$ increases.