  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.
