Spin Asymmetry Calculations of the $TMR\hbox {-}V$ Curves in Single and Double-Barrier Magnetic Tunnel Junctions

Spin-polarization asymmetry is the key parameter in asymmetric voltage behavior (AVB) of the tunnel magnetoresistance (TMR) in magnetic tunnel junctions. In this paper, we study the value of the TMR as a function of the applied voltage Va in the single as well as double barrier magnetic tunnel junctions (SMTJ & DMTJ, which are constructed from CoFeB/MgO interfaces) and numerically estimate the possible difference of the TMR-Va curves for negative and positive voltages in the homojunctions. As a result, we found that AVB may help to determine the exact values of Fermi wave vectors for minority and majority conducting spin sub-bands. Moreover, significant asymmetry of the experimental TMR-Va curves, which arises due to different annealing regimes, is explained by different heights of the tunnel barriers and values of the spin asymmetry. The numerical TMR-Va data are in good agreement with experimental ones.