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：磁性斯格明子广泛存在于包括具有非中心对称结构的Dzyaloshinskii-Moriya相互作用（DMI）手性磁体在内的多种磁系统中。本研究提出一种广义半隐式后向微分公式投影方法，能够以典型时间步长$1$ ps对手性磁体中的Landau-Lifshitz（LL）方程进行模拟，显著超越现有数值方法通常受限于$0.1$ ps的极限。通过微磁模拟表明，含DMI的LL方程在阻尼变化时揭示了磁化构型中引人注目的动态不稳定性。采用简单的初始化策略和特定阻尼参数，可分别生成孤立斯格明子泡和斯格明子泡簇。借助弦方法，进一步深入研究了斯格明子与斯格明子泡之间的转变路径，以及斯格明子从斯格明子簇中的逃逸过程。本文发展的数值方法不仅为研究基于斯格明子的拓扑织构及其转变路径提供了可靠范式，也有助于理解复杂磁系统中的磁化动力学。