Investigation of Tunneling Magneto Resistance in Magnetic Multilayers with double barrier structures using keldish formalism

In this paper, we investigate the Tunneling Magneto Resistance (TMR) in magnetic multilayers. Keldish Non Equilibrium Greenʹs Functions (KNEGF) have been calculated via solving Schrodinger equation in WKB ap- proximation. Employing Keldish formalism electrical current density perpendicular to the plane of the layers are characterized, which ultimately leads to the tunneling magneto resistance versus the applied voltage on the lay- ers. The results for different layersʹ thicknesses are presented.