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.
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