The Bean-Livingston barrier at the interface of type-II superconductor/soft-magnet heterostructures is studied on the basis of the classical London approach. This shows a characteristic dependence on the geometry of the particular structure and its interface as well as on the relative permeability of the involved magnetic constituent. The modification of the barrier by the presence of the magnet can be significant, as demonstrated for a cylindrical superconducting filament covered with a coaxial magnetic sheath. Using typical values of the relative permeability, the critical field of first penetration of magnetic flux is predicted to be strongly enhanced, whereas the variation of the average critical current density with the external field is strongly depressed, in accord with the observations of recent experiments.
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