Controlled creation and stability of k pi skyrmions on a discrete lattice

We determine sizes and activation energies of k pi skyrmions on a discrete lattice using the Landau-Lifshitz-Gilbert equation and the geodesic nudged elastic band method. The employed atomic material parameters are based on the skyrmionic material system Pd/Fe/Ir(111). We find that the critical magnetic fields for collapse of the 2 pi skyrmion and 3 pi skyrmion are very close to each other and considerably lower than the critical field of the 1 pi skyrmion. The activation energy protecting the structures does not strictly decrease with increasing k as it can be larger for the 3 pi skyrmion than for the 2 pi skyrmion depending on the applied magnetic field. Furthermore, we propose a method of switching the skyrmion order k by a reversion of the magnetic field direction in samples of finite size.