Interaction between a superconducting vortex and an out-of-plane magnetized ferromagnetic disk: Influence of the magnet geometry

The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness, and different geometries of the magnetic structures: disk, annulus (ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex position are possible, enabling the system to be suitable to act as a qubit. For FM's with sharp edges, like e.g., for squares and triangles, the vortex prefers to enter its equilibrium position along the corners of the magnet.