Spin filtering in parallel magnetic-barrier structures

Recent studies have indicated that the final wave vector kf of the electron is exactly the same as the initial wave vector ki for electrons tunnelling through a parallel magnetic-barrier structure, where double δ-function magnetic fields point in the same direction. In contrast to the anti-parallel magnetic-barrier configuration, we have found that the parallel magnetic-barrier configuration as well as identical initial and final wave vectors cannot concur. We have derived the correct formula of the transmission and have shown that the spectra of both the transmission and the conductance are quite different from published results. Numerical results further confirm that spin filtering in the magnetic-electric barrier is relatively weak because the intrinsic Zeeman term between the electronic spin and the inhomogeneous magnetic field is local and it strength is small for the GaAs system.