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.