Magnetostatic interactions in planar ring-like nanoparticle structures

Numerical calculations of equilibrium state energies and local magnetic fields in planar ring-like nanoparticle structures were performed. The dipole–dipole, Zeeman and magnetic anisotropy interactions were included into the model. The result of their competition depends on the value of the external magnetic field, magnetic parameters of an individual nanoparticle, size and shape of the structures. Flux-closed vortexes, single domain, two- domain ‘‘onion’’-like, ‘‘hedgehog’’-like and more complex spin structures can be realized. The critical field, providing a sharp transition from the flux-closed vortex to the ‘‘onion’’-like state, can be regulated by a variation of the particle magnetization and anisotropy constant, their easy directions, and particle space arrangement.