Field Evolution of Magnetization States With Different Combinations of Vortex Cores and Anti-Vortex Cores in Different Helicities

Field evolution of two types of mixed states made of four vortex cores and two anti-vortex cores are investigated numerically. The two types of mixed states both consist of one rhombic domain and one or two cross-tie walls. The two mixed states are found to exhibit different magnetization processes. As the field is applied along the long side direction, both mixed states exhibit two steps in magnetization curves; as the field is applied in parallel or antiparallel to the magnetization direction of the rhombic domain, however, it may exhibit two-step or three-step characteristic depending on its magnetization configuration.