We investigate the dynamics of two skyrmions lying in distinct layers of an antiferromagnetic bilayer system, consisting of nanostripes with the shape of racetracks. The top and bottom nanostripes are separated by a height offset and they are coupled through a ferromagnetic exchange, allowing the interaction between the skyrmions from both layers. Depending on the distance between the skyrmions they attract each other sufficiently to achieve a bound state. We also analyze their dynamics when an electric current is applied in a unique layer and we determine how the bound-state nucleation depends on the current density and vertical distance between the skyrmions. Finally, we analyzed the robustness of the bound states by considering two situations: 1) a system constituted by clean or homogeneous antiferromagnetic racetracks; 2) a system in which randomly distributed magnetic impurities in both layers are included in the system.
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