  We show that spin-orbit coupling at the interface between a superconducting
film of the finite lateral size and the underlying ferromagnetic insulator with
in-plane exchange field gives rise to a series of non-reciprocal effects
provided the superconducting pairing is enhanced near the boundaries of the
superconductor due to, e.g., variation of the film thickness or of the
interlayer electron transparency. Specifically, the critical temperature and
the critical depairing current are shown to depend on the relative orientation
between the exchange field in the ferromagnet and the superconducting film
boundaries. The discovered anisotropy of the superconducting properties is
promising for the design of diode-type elements in superconducting spintronics.
