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A discussion on the interaction between skyrmions in a bi-layer systemconnected by a non-magnetic metal is presented. From considering a free chargecarrier model, we have shown that the Ruderman-Kittel-Kasuya-Yosida (RKKY )inter- action can induce attractive or repulsive interaction between theskyrmions depending on the spacer thickness. We have also shown that due to anincreasing in RKKY energy when the skyrmions are far from each other, theirwidths are diminished. Finally, we have obtained analytical solutions to theskyrmion position when the in-plane distance between the skyrmions is small andit is shown that an attractive RKKY interaction yields a skyrmion precessorymotion. This RKKY-induced coupling could be used as a skyrmion drag mechanismto displace skyrmions in multilayers.

Coupling of skyrmions mediated by RKKY interaction