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 $\kappa$ 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.

中文翻译：

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磁场各向异性微调产生的Skyrmion的分形分析

磁性天体离子在拓扑上受到保护，并由其他铁磁态形核，形成了旋转旋转的自旋结构，这些纳米结构在纳米级器件中具有巨大的潜在应用前景。为了实现这一潜力，重要的是找到有用的方法以可控的方式生成天敌，并找到定量描述其形成的工具。在这里，我们在垂直磁化的情况下生成了天空粒子$镁\mathrm{Ø}/{锰}_2\mathrm{有限公司}铝/钯$超薄膜并通过分形分析研究其形成。使用面内场，我们修改了薄膜的有效磁各向异性，以控制薄膜中两个不同畴态的天蝎子形核：通常在垂直材料中发现的迷宫畴和无特征的单畴铁磁相。通过使用分形分析，我们获得了与磁畴的分形维数有关的磁相图，该磁相图可以描述磁态的演化，并且可以用于对天体离子的形成进行分类。此外，我们发现天敌离子的密度不仅取决于关键的材料参数$\kappa$而且还可以通过在高面内磁场中产生排斥性的Skyrmion-Skyrmion相互作用来实现。因此，我们建立了一种可靠而强大的生成天敌的方法，并分析了天敌的演变。