TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Battery: In the battery (B1), the spinel crystal structure includes regular tetrahedron structure composed of 4 oxygen ions; octahedron structure composed of 6 oxygen ions; and the magnesium ions that are disposed in the inner center of the regular tetrahedron structure and the octahedron structure. The magnesium secondary battery (B1) meets the following charge/discharge reaction equation: Mg+Fe2O4MgFe2O4 (II) (the forward reaction of the reaction equation is a discharge reaction and the inverse reaction of it is charge reaction). The cathode active material meets the formula (I). The carbon layer is formed on the surface of the cathode. The anode includes anode active material having metal oxide composed of the magnesium ions and the metal ions; and includes the spinel crystal structure. In the battery (B2), the spinel crystal structure is composed of the magnesium ions, the metal ions, and the oxygen ions, where the magnesium ions is positioned in the center of the regular tetrahedron structure composed of the oxygen ions and the metal ions is positioned in the center of the octahedron structure composed of the oxygen ions. The carrier ions include the magnesium ions. The magnesium secondary battery (B2) meets the charge/discharge reaction equation (II).    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Material: In the material (M1), the magnesium ions are positioned in the center of regular tetrahedron composed of the several oxygen ions. The metal ions are positioned in the center of octahedron composed of the several oxygen ions. The cathode active material (M1) meets the following formula: Mg(1+x)M(2-x)O4 (I).x=0-0.33;M=metal ion (preferably any one of titanium (Ti), vanadium (V), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), rubidium (Rd), germanium (Ge), molybdenum (Mo), silicon (Si), aluminum (Al), zinc (Zr), and boron (B));andO=oxygen ion. EXAMPLE - No suitable example given.