Two different approaches in the magnetic tunneling junctions

In this paper we use two different approaches to calculating the tunneling magnetoresistance (TMR) in magnetic tunnel junctions. It is found that the result for TMR calculated from the Slonczewski model is always greater than that of from the Julliere formula. In the Slonczewski model only a part of electrodes at the Fermi level participate in the tunneling process with the momentum parallel to the interface conservating if the magnetizations of two ferromagnetic electrodes are antiparallel to each other; while in the tunneling Hamiltonian approach all the electrodes at the Fermi level are assumed to participate in the tunneling process. Beside, there is only small difference between the magnitude of TMR calculated by using the delta-type barrier and the rec-tangular one in the Slonczewski model.