Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii-Moriya interaction~(DMI). In this study, we propose a generalized semi-implicit backward differentiation formula projection method, enabling the simulations of the Landau-Lifshitz~(LL) equation in chiral magnets in a typical time step-size of $1$ ps, markedly exceeding the limit subjected by existing numerical methods of typically $0.1$ ps. Using micromagnetics simulations, we show that the LL equation with DMI reveals an intriguing dynamic instability in magnetization configurations as the damping varies. Both the isolated skyrmionium and skyrmionium clusters can be consequently produced using a simple initialization strategy and a specific damping parameter. Assisted by the string method, the transition path between skyrmion and skyrmionium, along with the escape of a skyrmion from the skyrmion clusters, are then thoroughly examined. The numerical methods developed in this work not only provide a reliable paradigm to investigate the skyrmion-based textures and their transition paths, but also facilitate the understandings for magnetization dynamics in complex magnetic systems.
翻译:磁性天线在各种磁性系统中广泛存在,包括以Dzyaloshinkii-Moriya(DMI)相互作用为特征的具有非中心对称结构的手性磁性体中。本研究提出了广义半隐式向后差分公式投影方法,使得在典型时间步大小为1ps的情况下,可以模拟具有DMI的手性磁体中的Landau-Lifshitz(LL)方程,明显超过现有数值方法所受限制的0.1ps。通过微磁学模拟,我们发现LL方程中的DMI表现出一种有趣的动态不稳定性,当阻尼变化时,磁化构型会发生变化。使用简单的初始化策略和特定的阻尼参数,可以产生孤立的天线状物和天线状物聚集体。在串方法的帮助下,随着过渡路径的变化,研究了天线和天线状物之间的转换路径,以及天线从天线聚集体中的逃逸。本研究开发的数值方法不仅为研究基于天线的纹理及其转换路径提供了可靠的范例,也促进了对复杂磁性系统中磁化动力学的理解。