Micromagnetic simulations for magnetic multipoles

Cluster magnetic multipoles are order parameters that characterize the symmetry of spin arrangements in magnetic materials. In particular, high-order multipoles play a pivotal role in altermagnets and non-collinear antiferromagnets, where they govern electrical and optical phenomena. While spatially non-uniform multipole textures have been observed on the micrometer scale, their behavior at mesoscopic lengths remains largely unexplored. Here, we introduce a comprehensive micromagnetic framework for vector-like cluster magnetic multipoles, enabling quantitative, spatially resolved analysis of non-uniform multipole systems. As a demonstration, we apply the framework to magnetic-octupole domain-wall motion in the non-collinear antiferromagnet Mn3Sn. Our simulations capture key features of domain-wall dynamics, including profile deformation and the emergence of an effective inertial mass. This work provides a unified approach for investigating the mesoscopic dynamics of high-order cluster multipoles and opens new avenues for understanding and engineering the physical properties of functional magnetic materials, such as altermagnets and non-collinear antiferromagnets, for advanced spintronic technologies.