Magnet
Rare earth (lanthanoid) elements have a partially occupied "f" electron shell (which can accommodate up to 14 electrons). The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore, these elements are used in compact high-strength magnets where their higher price is not a concern. The most common types of rare-earth magnets are samarium-cobalt and neodymium-iron-boron (NIB) magnets.
Ferrimagnetism
Ferrimagnetism is exhibited by ferrites and magnetic garnets. The oldest known magnetic substance, magnetite (iron(II,III) oxide; FeO), is a ferrimagnet; it was originally classified as a ferromagnet before Néel's discovery of ferrimagnetism and antiferromagnetism in 1948.