  A discussion on the interaction between skyrmions in a bi-layer system
connected by a non-magnetic metal is presented. From considering a free charge
carrier model, we have shown that the Ruderman-Kittel-Kasuya-Yosida (RKKY )
inter- action can induce attractive or repulsive interaction between the
skyrmions depending on the spacer thickness. We have also shown that due to an
increasing in RKKY energy when the skyrmions are far from each other, their
widths are diminished. Finally, we have obtained analytical solutions to the
skyrmion position when the in-plane distance between the skyrmions is small and
it is shown that an attractive RKKY interaction yields a skyrmion precessory
motion. This RKKY-induced coupling could be used as a skyrmion drag mechanism
to displace skyrmions in multilayers.
