  By imposing the constraints of structural compatibility, stability and a
large tunneling magneto-resistance, we have identified the
Fe$_3$Al/BiF$_3$/Fe$_3$Al stack as a possible alternative to the
well-established FeCoB/MgO/FeCoB in the search for a novel materials platform
for high-performance magnetic tunnel junctions. Various geometries of the
Fe$_3$Al/BiF$_3$/Fe$_3$Al structure have been analyzed, demonstrating that a
barrier of less than 2~nm yields a tunneling magneto-resistance in excess of
25,000~\% at low bias, without the need for the electrodes to be half-metallic.
Importantly, the presence of a significant spin gap in Fe$_3$Al for states with
$\Delta_1$ symmetry along the stack direction makes the TMR very resilient to
high voltages.
