Fractal Analysis of Skyrmions Generated by Field-Assisted Fine-tuning of Magnetic Anisotropy

Abstract

Magnetic skyrmions are topologically protected whirling spin textures nucleated from other ferromagnetic states that have great potential applications for nanoscale devices. To realize this potential, it is important to find useful methods to generate skyrmions in a controlled fashion and to identify tools to quantitatively describe their formation. Here we generate skyrmions in perpendicularly magnetized $\mathrm{Mg}\mathrm{O}/{\mathrm{Mn}}_{2}\mathrm{Co}\mathrm{Al}/\mathrm{Pd}$ ultrathin films and investigate their formation by fractal analysis. Using an in-plane field, we modify the effective magnetic anisotropy of the films to control the nucleation of skyrmions from two distinct domain states in the films: labyrinth domains typically found in perpendicular materials and a featureless monodomain ferromagnetic phase. By using fractal analysis, we obtain a magnetic phase diagram related to the fractal dimension of the domains that can describe the evolution of the magnetic states and can be used to categorize the formation of skyrmions. Moreover, we find that the skyrmion density is determined not only by the critical material parameter $\ensuremath{\kappa}$ but also by a repulsive skyrmion-skyrmion interaction at high in-plane magnetic fields. We thus establish a reliable and powerful method to generate skyrmions and a way to analyze the evolution of skyrmions.