Magnetic tunnel junctions are disclosed that include ferromagnetic (or ferrimagnetic) materials and a bilayer tunnel barrier structure that includes a layer of alkaline earth oxide. The bilayer also includes a layer of crystalline material, such as MgO or Mg--ZnO. If MgO is used, then it is preferably (100) oriented. The magnetic tunnel junctions so formed enjoy high tunneling magnetoresistance, e.g., much greater than 100% at room temperature.