Topologically nontrivial magnetic nanostructures have attracted long-standing attention due to their peculiar spin configurations and dynamic behaviors for promising technological applications and, in particular, to the rich physics involved. The topological structure of skyrmions distinguishes from magnetic vortex and bubble. Skyrmions exist in helical magnets with the Dzyaloshinsky-Moriya interaction (DMI). We show by micromagnetic simulations that a spontaneous skyrmion ground state can exist in Co/Ru/Co nanodisks without the DMI, which can remain stable in the applied magnetic field along the +z direction even up to 0.44 T. The guiding center ((R_x, R_y) of skyrmion defined by the moments of the topological density presents a gyration with a star-like trajectory in a pulsed magnetic field and a hexagonal trajectory after the field is switched off, which is different from that of a vortex or bubble. One of the coupled skyrmions could move without an external magnetic field, just induced by the motion of the other one due to strong interlayer magnetostatic interactions. This work sheds light on how skyrmions can be discovered in various (not limited to magnetic) systems with competing energies and contributes to the understanding of the dynamical properties of skyrmions.

(a) Sketch of a Co/Ru/Co nanodisk. (b)Micromagnetic simulation result for a Co (20 nm)/Ru (2 nm)/Co (20 nm) nanodisk. Arrows and colors correspond to the directions of the local magnetization and the magnitude of the out-of-plane magnetization component (Mz) at every point, respectively. Spin textures in both the top and the bottom nanolayers are skyrmions.

Phase diagram of spin textures derived from micromagnetic simulations. The spin textures as functions of the thickness of Co and of Ru illustrate four regions: the vortex-like state, skyrmion-like state, multidomain state, and mixed state. Phase boundaries are marked by white lines.