Spin filtering through multi-δ-magnetic-barrier structures
We theoretically analyse the spin-dependent tunnelling through an array of δ-magnetic barriers and give a set of general recursive relations. Using the recursive relations we analyse spin transmissions and polarizations under the constraint of counterbalancing the vector potentials with an electric potential controlled by gate voltages. After the theoretical and numerical analysis, we find that the polarization of the current vanishes when the magnetic barriers' orientations are in a particular pattern. Also we give a set of explicit expressions for the orientations. Then we demonstrate the physical properties of the orientations and their applications for the spin-filtering effect.