  Experiments have shown that the tunneling current in a Co/Al$_2$O$_3$
magnetic tunneling junction (MTJ) is positively spin polarized, opposite to
what is intuitively expected from standard tunneling theory which gives the
spin polarization as exclusively dependent on the density of states (DOS) at
$E_F$ of the Co layers. Here we report theoretical results that give a positive
tunneling spin polarization and tunneling magnetoresistance (TMR) that is in
good agreement with experiments. From density functional theory (DFT)
calculations, an Al-rich interface MTJ with atomic-level disorder is shown to
have a positively polarized DOS near the interface. We also provide an atomic
model calculation which gives insights into the source of the positive
polarization. A layer and spin dependent effective mass model, using values
extracted from the DFT results, is then used to calculate the tunneling
current, which shows positive spin polarization. Finally, we calculate the TMR
from the tunneling spin polarization which shows good agreement with
experiments.
