Further, a second insulating cover layer 280 is formed over the first insulating cover layer 227. The second insulating cover layer 280 includes one or more layers of insulating material different from the first insulating cover layer 227. In some embodiments, an aluminum-based insulating material is used. In certain embodiments, the aluminum-based insulating material includes aluminum oxide, aluminum nitride, aluminum oxynitride, aluminum carbide and/or aluminum oxycarbide. In some embodiments, the concentrations of Al, O, C and/or N in the thickness direction are not uniform. In certain embodiments, the concentration of Al gradually decreases from the bottom to the top of the second insulating cover layer 280, while the concentrations of O, C and/or N gradually increase from the bottom to the top of the second insulating cover layer 280. The thickness T2 of the second insulating cover layer 270 is smaller than the thickness T1 of the first insulating cover layer in some embodiments. The thickness T2 is in a range from about 1 nm to about 10 nm in some embodiments, and is in a range from about 3 nm to about 5 nm in other embodiments.

Further a third ILD layer 230 is disposed in spaces between the MRAM cell structures. The third ILD layer 230 includes one or more dielectric layers, such as silicon oxide, silicon nitride, silicon oxynitride, fluorine-doped silicate glass (FSG), low-k dielectrics such as carbon doped oxides, extremely low-k dielectrics such as porous carbon doped silicon dioxide, a polymer such as polyimide, combinations of these, or the like. In some embodiments, the material for the first ILD layer 210, the material for the second ILD layer 225 and the material for the third ILD layer 230 are the same. In other embodiments, at least two of them are made of different dielectric materials.