Energetics and thermodynamics of bilayer rectangular artificial spin ices

Bilayer rectangular artificial spin ices (BRASIs) with distinct aspect ratios, $\gamma$, are considered. Namely, we investigate how the underlying geometry modifies the interaction between two rectangular artificial spin ice layers separated by a height offset, $h$, whenever compared to the square case. Actually, rectangular layers interact by means of a Buckingham-like potential, whereas in the square case, one has an algebraic (van der Walls-like) interaction. In addition, Moir\'e patterns for BRASIs are less definite than for the square bilayer. We also deal with their basic thermodynamics, showing the behavior of the specific heat as a function of temperature and $\gamma$ for a number of height offsets.