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.
@article{arxiv.1802.09257,
title = {Controlled creation and stability of k{\pi}-skyrmions on a discrete lattice},
author = {Julian Hagemeister and Ansgar Siemens and Levente Rózsa and Elena Y. Vedmedenko and Roland Wiesendanger},
journal= {arXiv preprint arXiv:1802.09257},
year = {2018}
}