Vortex-antivortex configurations in a superconducting film due to a ferromagnetic strip: Edge barrier versus annihilation barrier

Magnetic response of a hybrid structure containing a thin ferromagnetic (FM) strip, placed above a superconducting (SC) film of finite width, is studied. It is shown that depending on the system parameters the maximum value of the Meissner current may be reached either at the SC film edges or at its symmetry axis. Total energy of the symmetrical vortex-antivortex (VA) configuration (which is only possible due to the symmetry of a system) is calculated depending on the FM magnetization. It is found that the emergence of the VA pairs is controlled by two potential barriers: A Bean-Livingston-like edge barrier and the annihilation barrier. The former one controls the VA pair entry from the SC film edges, the latter determines the creation of the VA pair at the center of the SC film. The threshold magnetization is obtained at which the transition of the SC film from the Meissner state to the VA-pair-formed mixed state, takes place. The conditions are found at which the VA pair is not allowed to exist inside the SC film.