Skyrmion ground state and gyration of skyrmions in magnetic nanodisks without the Dzyaloshinsky-Moriya interaction

We show by micromagnetic simulations that spontaneous skyrmion ground state can exist in Co/Ru/Co nanodisks without the Dzyaloshinsky-Moriya interaction (DMI), which can remain stable in the applied magnetic field along +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 novel 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 vortex or bubble. One of the coupled skyrmions could move without an external magnetic field, but only induced by the motion of the other one due to strong inter-layer magnetostatic interactions. This work sheds light on how novel skyrmions can be discovered in various (not limited to magnetic) systems with competing energies and contributes to the understanding of the dynamical properties of skyrmion.