Magnetic interaction of submicron-sized ferromagnetic rings in one-dimensional array

Magnetization characteristics of submicron-sized ferromagnetic rings in a one-dimensional array with various inter-ring distances, $lx$⁠, were investigated by the magneto-optical Kerr effect and micromagnetic simulation. The onion (vortex)-to-vortex (onion) transition fields were found to be proportional to $1∕lxn$ with $n=1.36$ (0.79), instead of being a simple dipole interaction model $(n=3)$⁠. It was demonstrated that the transition mechanism and the inter-ring dependence are governed by the energy gain originating from the deformation of the local vortex. As a result, exchange energy as well as magnetostatic energy play important roles in the magnetization reversal of ring array.