Assembly of nanocube super-structures directed by surface and magnetic interactions†
We study the stabilisation of clusters and lattices of cuboidal particles with long-ranged magnetic dipolar and short-ranged surface interactions. Two realistic systems were considered: one with magnetisation oriented in the  crystallographic direction and the other with magnetisation along the  direction. We have studied magnetic nanocube clusters first in the limit of T = 0 K intending to elucidate the structural genesis of low energy configurations and then analysed finite-temperature behaviour of the same systems in simulations. Our results demonstrate that dipolar coupling can stabilise nanoparticle assemblies with cubic, planar, and linear arrangements seen previously in experiments. While attractive surface energy supports the formation of super-cubes, repulsion results in the elongated structures in the form of rods and chains. We observe the stabilisation of the ferromagnetic planar arrangements of the cubes standing on their corners and in contact over edges. We illustrate that minimal energy structures depend only on the size of the assembly and balance of surface repulsion and magnetic dipolar coupling. The presented results are scalable to different particle sizes and material parameters.