Magnetic-dipole induced appearance of vortices in a bilayered superconductor/soft-magnet heterostructure

The penetration of the magnetic field of an infinitesimal magnetic dipole into a bilayered type-II superconductor/soft-magnet heterostructure is studied on the basis of the classical London approach. The critical values of the dipole moment for the first appearance of a single magnetic vortex and, respectively, a magnetic vortex-antivortex pair in the superconductor constituent are obtained, when the magnetic dipole faces the superconductor or the soft-magnet constituent. This reveals that the soft-magnet constituent inhibits penetration of vortices into the superconductor constituent, when the dipole faces the soft-magnet constituent