Stability of skyrmions in perturbed ferromagnetic chiral magnets

Magnetic skyrmions, topological spin textures observed in chiral magnets, have attracted huge interest due to their applications in the field of spintronics. In this work we study the stability of circular isolated skyrmions in ferromagnetic chiral magnets under the influence of different perturbations and external fields. To this end we develop a general systematic procedure based in a harmonic expansion series of the skyrmion boundary which allows the identifycation of the breakdown of the skyrmion circular shape on each instability channel independently. We apply our approach to a few representative spin models with actual interest in order to obtain the zero temperature phase diagram, where isolated skyrmions emerge as metaestable states. The results presented in this paper are in agreement with properties of isolated skyrmions observed in recent experiments opening the possibility of extending the analysis to more complex situations.