  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.
