Within the Landauer framework of ballistic transport, we theoretically
investigate spin-dependent resonant transmission and magnetoresistance in
symmetric cascade junctions of ferromagnetic metal (FM) and semiconductor
(SC). It is shown that spin-up and spin-down electrons possess different
bandgap structures against the Rashba spin-orbit wave vector. Due to the
mirror symmetry, multiple spin-dependent perfect transmissions of electrons
can be obtained within the bandgap, thereafter, spin polarization has
multiple reversals. Around each resonant wave vector, high spin polarization
is achieved and the electrical conductance comes from one kind of spin
electrons. The resonant transmissions originate from the spin-dependent
quasi-bound states at energies above the potential barriers, which are
demonstrated by the electronic charge distributions in the system.
Furthermore, if we change the magnetization of FM in the centre of the
junctions, inverse magnetoresistance can be observed. The investigations may
have potential applications in spin filters and spin switches.