Improved airy function formalism for the study of anti-parallel double δ-magnetic-barrier nanostructure under the modulation of the applied bias

Abstract

The Goos–Hänchen (GH) shift and the spin polarization are theoretically investigated under the anti-parallel double [Formula: see text]-magnetic-barrier nanostructure model by applying a bias using Airy’s function formalism and transfer-matrix technique, which is an improvement on previous calculation. The results show the magnitude and sign of GH shift and spin polarization can be easily changed by modulating the applied bias. The closer the applied bias to the critical value is, the more intensive GH shift and spin polarization will be. Furthermore, two critical values come through modulating the strength of magnetic fields, and an intensive GH shift and a spin polarization also exist near each critical value. These findings can provide a practical approach to designing and fabricating spin beam filters or splitters modulated by applied bias.