Spin-dependent electronic transmission coefficient of a nanostructure in the free-electron approximation by transfer matrix method

In this paper, based on the transfer matrix method and within the free electron approximation, we study spin-dependent electronic transport through an array of magnetic quantum barriers. For this purpose, we first write the Schrodinger equation for the electron in the presence of barrier potentials and the magnetic field originating from system magnetic moments. Then, by its discretization, we reach a system of linear equations. In the following, by using the transfer matrix method for this system of equations, we obtain the spin-dependent transmission coefficients of the electron. With the help of present formalism, one can calculate the spin-dependent transmission coefficient of a transmitted electron through a magnetic multi-layer as a function of electron energy, magnitude and orientation of the magnetic moment, and the potential shape. Finally, as an example, the numerical results are presented for two cases, the one including two similar alternative magnetic barriers and the other including two alternative barriers and well. The presented method is useful for the study of the spin-dependent electronic conductance behavior of magnetic layers and superlattices.