On the magnetostatic interactions between nanoparticles of arbitrary shape

The general expression for the magnetostatic energy of two magnetized nanoparticles with arbitrary shape and magnetization state is derived within the framework of a Fourier space approach. It is shown how the standard dipole–dipole interaction, valid for large interparticle distances, should be modified in order to take into account the shape anisotropy of each particle. Explicit computations are given for a simple system of two interacting cylinders. For magnetic nanowires, i.e., cylinders with a very large aspect ratio, a simple derivation shows that the interaction is of monopolar, rather than dipolar, nature.