A STT-RAM MTJ is disclosed with a composite tunnel barrier comprised of a CoMgO layer that contacts a pinned layer and a MgO layer which contacts a free layer. A CoMg layer with a Co content between 20 and 40 atomic % is deposited on the pinned layer and is then oxidized to produce Co nanoconstrictions within a MgO insulator matrix. The nanoconstrictions control electromigration of Co into an adjoining MgO layer. The free layer may comprise a nanocurrent channel (NCC) layer such as FeSiO or a moment dilution layer such as Ta between two ferromagnetic layers. Furthermore, a second CoMgO layer or a CoMgO/MgO composite may serve as a perpendicular Hk enhancing layer formed between the free layer and a cap layer. One or both of the pinned layer and free layer may exhibit in-plane anisotropy or perpendicular magnetic anisotropy.