Magnetic Skyrmions are one of the fascinating and promising objects because of their small size and stability to perturbations such as electric currents and magnetic fields [1-4]. The major mechanism to stabilize small Skyrmions in ferromagnet/heavy-metal bilayers is the presence of Dzyaloshinskii-Moriya interaction (DMI). In thin films, the DMI arises at the interface between ferromagnet and heavy metal due to the presence of spin-orbit interaction and broken inversion symmetry [4, 5]. In this work we investigate the stability and internal structure of an isolated Skyrmion in bilayer (ferromagnet/heavy metal) and trilayer (heavy metal 1/ferromagnet/heavy metal 2) nanodisks. We study the static properties of the Skyrmions and obtain the phase diagrams of the Skyrmion existence depending on the thickness of the ferromagnetic layer and the DMI strength. We demonstrate the importance of fully taking into account the dipolar interaction even for a few atomic layers thin nanodisk and that together with DMI it has the stabilizing effect and defines the Skyrmion configuration. For the trilayer structures with two heavymetal interfaces (corresponding to two interfacial DMIs), we show that the type and configuration of the Skyrmion can be controlled by the thickness of ferromagnet. Furthermore, the interplay of two interfacial DMIs can lead to the formation of magnetic structures with higher winding number.
 N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899-911 (2013),
 A. Hoffmann, S. Bader, Opportunities at the Frontiers of Spintronics, Phys. Rev. Appl. 4, 047001 (2015).
 A. Fert, V. Cros, J. Sampaio, Skyrmions on the track, Nat. Nanotechnol. 3, 152-156 (2013).
 J. Sampaio, V. Cros, S. Rohart, A. Thiaville, and A. Fert, Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures, Nat. Nanotechnol. 8, 839-844 (2013).
 S. Heinze, et al., Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7, 713–718 (2011).
K. Chihay1,2*, J. Barker3 , V. Rodionova1,2 , O. Tretiakov3,4
1 STP Fabrica Immanuel Kant Baltic Federal University, Kaliningrad, Russia
2 Center for Functionalized Magnetic Materials, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
3 Institute for Materials Research, Tohoku University, Sendai, Japan
4 School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russia
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Immanuel Kant Baltic Federal University,
Gaidara 6, Kaliningrad, 236022, Russia