Magnetic dipole-vortex interaction in a bilayer superconductor/soft-magnet heterostructure

We study the penetration of the nonuniform magnetic field, created by a magnetic dipole with out-of-plane magnetization, into a film heterostructure composed of a type-II superconductor layer and a soft-magnet layer. In the framework of the London approach, the energy of the magnetic dipole-vortex interaction is derived and the critical value of the dipole moment for the first appearance of a vortex in the superconducting constituent is found for two cases of the layer ordering, namely when the dipole is located near the superconducting or, respectively, the magnetic constituent.