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

The equilibrium 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 p . 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. For isotropic shapes, the critical size for this transition increases with p, ranging from 49 nm for spheres to 56 nm for cubes, in agreement with experimental trends. 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. • We investigate the critical size for quasi-uniform ordering in magnetite nanoparticles using superball geometries. • Micromagnetic simulations reveal how faceting modulates the single-domain to vortex transition. • Cubic magnetocrystalline anisotropy reduces the critical volume and modifies vortex core morphology. • Aspect ratio and subtle deviations from sphericity significantly impact equilibrium magnetic states.