Can the interface between a non-ideal ferromagnet and a semiconductor quantum wire acts as an ideal spin filter?

The problem of spin injection across the interface between a non-ideal ferromagnet (less than 100% spin polarization) and a semiconductor (paramagnetic) quantum wire is examined in the presence of Rashba spin orbit coupling and an axial magnetic field along the wire axis. The field is caused by the ferromagnet magnetized along the wire axis. At low temperatures and for certain injection energies, the interface can act as an ideal spin filter allowing injection only from the majority spin band of the ferromagnet. Thus, 100% spin filtering can take place even if the ferromagnet itself is less than 100% spin polarized. Below a critical value of the magnetic field, there are two injection energies for which ideal (100%) spin filtering is possible; above this critical field, there is only one such injection energy.