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

Abstract

Spin-polarization asymmetry is the key parameter in asymmetric voltage behavior (AVB) of the tunnel magnetoresistance ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TMR</i> ) in magnetic tunnel junctions. In this paper, we study the value of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TMR</i> as a function of the applied voltage <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Va</i> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TMR</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Va</i> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TMR</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Va</i> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TMR</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Va</i> data are in good agreement with experimental ones.