Electron transmission across ferromagnetic layers

Abstract Movement of spin-polarized electrons through a finite periodic system formed by n pairs of alternating ferromagnetic and nonmagnetic layers is considered. General features of electron scattering in super layers and their dependence on a number of layers are described. An electron wave function is found in one-dimension rectangular potential with finite number of periods. It is written as superposition of eigenvectors of a translation matrix or Bloch-like functions for an infinite periodic system. We obtain an exact solution for scattering of monochromatic wave on a system with an arbitrary number of layers. Energy dependence of a reflection and transmission coefficients is presented in an explicit symbol form. Number of spectral windows, their energy positions and widths are found as well as regions of almost full reflection. The system can be used as spin filter due to high-energy dispersion and dependence of exchange energy on electron spin direction.