Lithium-manganese complex oxide, production method thereof and use thereof

A lithium-manganese complex oxide represented by a formula Li[MnLiM]O(wherein M is at least one element selected from the groups IIa, IIIb and VIII of the 3rd and 4th periods, and 0.02 ≤ X ≤ 0.10, 0.05 ≤ Y ≤ 0.30 and -0.2 ≤ δ ≤ 0.2), having a spinel crystalline structure of 0.22° or less of half value width of the (400) plane of powder X-ray diffraction by CuKα and an average diameter of crystal grains by SEM observation of 2 µm or less, and a spinel crystalline structure lithium-manganese complex oxide having a BET specific surface area of 1.0 m·gor less; production methods thereof; and a lithium secondary battery which uses the lithium-manganese complex oxide as the positive electrode active material are described.