Strength of the symmetry spin filtering effect in magnetic tunnel junctions

Strength of the the symmetry spin filtering effect (as defined by the asymptotic behavior of the tunneling magnetoresistance (TMR) at large barrier thicknesses induced by this effect) is studied for the Fe/MgO/Fe magnetic tunnel junctions (MTJ). Based on the analysis of the band structure of bulk Fe and complex band structure of MgO we predict \emph{native} for the symmetry spin filtering effect linear increase of the TMR in Fe/MgO/Fe MTJ with increasing number of MgO layers, $N$. \emph{Ab initio} calculations of transmission functions performed for the Fe/MgO/Fe MTJ confirm our theoretical predictions for the strength of the symmetry spin filtering effect in broad range of energies and $N$. Our calculations also show that the \emph{combination} of the symmetry spin filtering effect and small surface transmission function in minority spin channel at the Fe/MgO interface is responsible for large $TMR>10,000\%$ predicted for Fe/MgO/Fe MTJ for $N \geqslant 8$. Proposed analysis of the strength of the symmetry filtering effect derived from the band structure of bulk electrode material could serve as a tool for quick material discovery search of suitable electrodes in context of emerging technologies that require high TMR.