Vortex and nonvortex nucleation of superconductivity in ferromagnetic-superconducting-ferromagnetic triple layers

Superconducting nucleation fields for ferromagnetic-superconducting-ferromagnetic (M/S/M) triple layers are calculated when the magnetic field is applied parallel to the S/M interfaces, the S layer is of arbitrary thickness d, and the M metals are identical and very thick. Both vortex and nonvortex nucleation are considered and the thickness ${\mathit{d}}_{\mathrm{cr}}$ at which the vortices start to nucleate is determined. Since the superconductivity is significantly suppressed near the S/M interfaces, the thickness ${\mathit{d}}_{\mathrm{cr}}$ substantially increases with respect to the case of a single S film.