  We have studied superconducting properties of the spin-valve thin layer
heterostructures CoO$_x$/F1/Cu/F2/Cu/Pb where the ferromagnetic F1 layer was
standardly made of Permalloy whereas for the F2 layer we have taken a specially
prepared film of the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al with a small degree
of spin polarization of the conduction band. The heterostructures demonstrate a
significant superconducting spin-valve effect, i.e. a complete switching on and
off of the superconducting current flowing through the system by manipulating
the mutual orientations of the magnetization of the F1 and F2 layers. The
magnitude of the effect is doubled in comparison with the previously studied
analogous multilayers with the F2 layer made of the strong ferromagnet Fe.
Theoretical analysis shows that a drastic enhancement of the switching effect
is due to a smaller exchange field in the heterostructure coming from the
Heusler film as compared to Fe. This enables to approach almost ideal
theoretical magnitude of the switching in the Heusler-based multilayer with the
F2 layer thickness of $\sim 1$\,nm.
