Self-assembled magnetic nanospheres with three-dimensional magnetic vortex

We report the electron holography images of spin configurations in peculiar assemblies of soft magnetic nanoparticles in single-, double-, triple-, or quadruple-sphere geometrical arrangements, in which each particle has a three-dimensional (3D) magnetic-vortex structure. Micromagnetic numerical calculations reveal that the uniqueness of the nanoparticles' 3D vortex structure plays a crucial role in their assembly, especially in terms of the contrasting contributions of the exchange and dipolar interactions to their binding energies. The results represent physical insights into the assembly of 3D-vortex-structure magnetic nanoparticles in different geometrical configurations and offer a practical means of controlling those assemblies.