The role of magnetic dipolar interactions in skyrmion lattices

Magnetic skyrmions are promising candidates for information and storage technologies. In the last years, magnetic multilayer systems have been tuned to enable room-temperature skyrmions, stable even in the absence of external magnetic field. There are several models describing the properties of an isolated skyrmion in a homogeneous background for single repetition multilayer stack, however, the description on how the equilibrium skyrmion size in lattices scales with increasing the number of repetitions of the stack remains unaddressed. This question is essential for fundamental and practical perspectives, as the behaviour of an ensemble of skyrmions differs from the isolated case. Based on a multilayer stack hosting a skyrmion lattice, we have carried out a series of imaging experiments scaling up the dipolar interaction by repeating $n$ times the multilayer unit, from $n =1$ up to $n=30$. We have developed an analytical description for the skyrmion radius in the whole multilayer regime, $i.e.$, from thin to thick film limits. Furthermore, we provide insight on how nucleation by an externally applied field can give rise to a lattice with more skyrmions (thus, overfilled) than the predicted by the calculations.