An exemplary embodiment of a synthesis method includes the following acts or steps: providing LiMn2O4 material as a precursor; leaching Mn from the LiMn2O4 material using an acid to form a synthesized solution; adding carbonaceous material to the synthesized solution; adding phosphoric acid to the synthesized solution with carbonaceous material to form MnPO4 composite material; and adding Li containing compound to the MnPO4 composite material to form LiMnPO4 composite material.