Investigating magnetostatics of Fe-Ni nanosphere assemblies by electron holography and micromagnetic simulations

The alignment of vortex cores in magnetic nanospheres governs the collective response of nanoparticle assemblies, but the transition from collinear to non-collinear configurations remains unclear. We combine off-axis electron holography with micromagnetic simulations to investigate Fe-Ni nanosphere dimers, chains, and 2D or 3D arrays. Vortex-core alignment follows a size-dependent competition between exchange and demagnetization energies. For small particles, exchange dominates, keeping cores collinear. As size increases, demagnetization energy, which scales approximately with D³, increasingly influences the total energy, surpassing the exchange contribution, which scales approximately with D, and the system spontaneously breaks symmetry. The critical diameter decreases as saturation magnetization rises, enabling composition-based tuning. In chains and 2D and 3D arrays, the system achieves flux closure through multiple routes. Local ordering varies, but all assemblies keep the normalized net moment low and minimize demagnetization energy. Different vorticity sequences in chains are nearly degenerate, giving random chiral arrangements. Minimizing demagnetization energy, rather than preserving vortex-core alignment, is the main organizing principle. Given their robust flux closure across a range of sizes and geometries, vortex-state nanosphere arrays may prove valuable for applications in low-remanence nanomagnetic devices.