Magnetic tunnel junctions are disclosed that include ferromagnetic (or ferrimagnetic) materials and a bilayer tunnel barrier structure. The bilayer includes a crystalline material, such as MgO or Mg--ZnO, and Al.sub.2O.sub.3, which may be amorphous. If MgO is used, then it is preferably (100) oriented. The magnetic tunnel junctions so formed enjoy high tunneling magnetoresistance, e.g., greater than 100% at room temperature.