Effect of Barrier Width on Bias-Dependent Tunnelling in Ferromagnetic Junctions

We present a finite temperature theory for bias-dependent tunnelling in ferromagnetic tunnelling junctions. The effects of the barrier width d on the tunnelling magnetoresistance (TMR) and its sign change behaviour are discussed with this theory. Numerical results show that both the zero-bias TMR and the critical voltage Vc at which the TMR changes its sign decrease with the increasing barrier width for a considerably thick barrier junction. Furthermore, it is found that a minimum exists in the curve of Vc versus d if a composite junction is under oxidized.