Role of nanoparticle shape on the critical size for quasi-uniform ordering: from spheres to cubes through superballs

The equilibrium magnetic states of single-domain magnetite nanoparticles (NPs) result from a subtle interplay between size, geometry, and magnetocrystalline anisotropy. In this work, we present a micromagnetic study of shape-controlled magnetite NPs using the superball geometry, which provides a continuous interpolation between spheres and cubes. By isolating the influence of shape, we analyze the transition from quasi-uniform (single-domain) to vortex-like states as particle size increases, revealing critical sizes that depend on the superball exponent. Our simulations show that faceted geometries promote the stabilization of vortex states at larger sizes, with marked distortions in the vortex core structure. The inclusion of cubic magnetocrystalline anisotropy, representative of magnetite, further lowers the critical size and introduces preferential alignment along the [111] easy axes. In contrast, the presence of slight particle elongation increases the critical size and induces another preferential alignment direction. These results demonstrate that even small deviations from sphericity or aspect ratio significantly alter the magnetic ordering and stability of equilibrium magnetic states.