Relation between chemical bonding and exchange coupling approaches to the description of ordering in itinerant magnets

Two different approaches to explain and predict the types of magnetic ordering in the 3d metal series and their compounds are reviewed. According to the crossing theorem of Heine and Samson, the effective exchange coupling changes sign from negative (antiferromagnetic ordering) in the middle of 3d band to positive (ferromagnetic ordering) for the nearly empty or nearly filled d band cases. On the other hand, the analytical properties of the Crystal Orbital Hamilton Population, which is a measure of chemical bonding, predict only one crossing at the center of the band in the region of nonbonding states. Thus intermetallic compounds with Fermi energies falling within metal-metal nonbonding states are ordered antiferromagnetically whereas they order ferromagnetically when the Fermi levels fall within antibonding states. The general character of these dependencies is demonstrated for various examples containing the magnetically active 3d metals, examples that include the bcc metals, Heusler alloys, and a series of novel quaternary intermetallic borides.