A method of recovering a rare earth element. The method comprises dissolving a rare earth element magnetic material in a dissolution organic solvent and a β-diketone compound to form a dissolved rare earth element mixture. A rare earth element of the rare earth element magnetic material and the β-diketone compound are reacted to form a β-diketonate chelate complex and the dissolution organic solvent is removed. The β-diketonate chelate complex is removed using a separation organic solvent, and the β-diketonate chelate complex is recovered. Additional methods are also disclosed.