Scattering modes of skyrmions in a bilayer system with ferromagnetic coupling

Magnetic skyrmions are quasiparticle-like textures that are topologically different from a single domain magnetization state. Their topological protection, combined with the low current density needed to move them, make these objects relevant to be used as information storage structures. In such a context, the analysis of the interactions between skyrmions is interesting and relevant for future applications. In this work, through micromagnetic simulations and numerical calculations, we studied the interaction between two skyrmions living on different parallel ferromagnetic racetracks connected by an exchange-like interaction. The upper and lower racetracks are separated by a height offset and the interaction between the upper and the lower skyrmion is analyzed in terms of the magnetic and geometrical parameters. Three states are predicted, as a function of these parameters: scattered or free skyrmions, bound skymions, and annihilated skyrmions. Our results, presented in a phase diagram, demonstrate that even in the case here called free skyrmions, there is a small and brief interaction when both are close enough, but the skyrmion in the top layer does not drag the skyrmion in the bottom layer. For bound skyrmions, both keep linked during larger times. In the latter case, there are strong changes in the velocity of the skyrmions induced by the effect of a higher effective mass when both are coupled.