Equilibrium magnetisation structures in ferromagnetic nanorings

The ground state of the ring-shape magnetic nanoparticle is studied. Depending on the geometrical and magnetic parameters of the nanoring, there exist different magnetisation configurations (magnetic phases): two phases with homogeneous magnetisation (easy-axis and easy-plane phases) and two inhomogeneous (planar vortex phase and out-of-plane one). The existence of a new intermediate out-of-plane vortex phase, where the inner magnetisation is not strongly parallel to the easy axis, is predicted. Possible transitions between different phases are analysed using the combination of analytical calculations and micromagnetic simulations.