Tunneling Magnetoresistance in Ferromagnetic Junctions: Bias Dependence

Abstract

By tunneling magnetoresistance (TMR) we mean in this paper a drop ΔR in the junction resistance when the magnetizations of two ferromagnetic electrodes rotate from antiparallel to parallel alignment. The effect was observed first by Julliere [1] in Co/Ge/Fe junctions. Similar observations were reported later also in other systems [2, 3]. Recent experimental data show additionally that TMR significantly decreases with increasing voltage V [4]. Two microscopic approaches have been developed to account for TMR in ferromagnetic junctions. One of them takes into account many-body features of the corresponding electronic wave functions in ferromagnetic electrodes [5]. In the second approach, on the other hand, one-electron wave functions are used to calculate the tunneling current [6]. In both models a complex electronic band structure of a ferromagnet was approximated by the one-band model with free-electron-like spin-polarized parabolic bands. However, there are some additional features of the electronic structure, which can contribute to TMR, and which have not been taken into account in the above models. The most important seems to be the s-d hybridization in the ferromagnetic electrodes [7] as well as at the electrode/barrier interfaces. Apart from this, the barrier height for d electrons can differ remarkably from the barrier height for s electrons [8]. Thus, the tunneling probability for a particular electronic state depends on the rate of s—d hybridization. This, on