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.
Pole piece
The traditional material for pole pieces was soft iron. While still often used with permanent magnets, soft iron suffers from eddy currents which make it less suitable for use with electromagnets, and particularly inefficient when the magnet is excited by alternating current.