Positive electrode active material for lithium secondary battery, positive electrode for lithium secondary battery, and lithium secondary battery

A positive electrode active material for a lithium secondary battery, the positive electrode active material comprising

• a lithium transition metal complex oxide having a spinel crystalline structure, wherein
• the lithium transition metal complex oxide includes:
• manganese and nickel as main transition metal elements;
• titanium and iron as additive transition metal elements;
• and
• oxygen and fluorine,
• wherein the lithium transition metal complex oxide is represented by a following general formula (I):
• LixMn2-a-b-c-dNiaTibFecMdO4-yFy (I)
• wherein
• M is at least one element selected from the group consisting of Al, Si, Mg, Ca, Ba, Sr, Sc, V, Cr, Co, Cu, Zn, Ga, Y, Ru Rh, Pd, In, Sn, Sb, La, Ce, Sm, Zr, Nb, Ta, Mo, W, B, C, P, and S,
• 0.9≤x≤1.3,
• 0.0005≤y≤0.1,
• 0.4≤a≤0.5,
• 0<b≤0.2,
• 0<c≤0.05, and
• 0≤d≤0.2.