The Orbital Origins of Magnetism: From Atoms to Molecules to Ferromagnetic Alloys

A chemical view of spin magnetic phenomena in finite (atoms and molecules) and infinite (transition metals and their alloys) systems using the concepts of bonding and electronic shielding is presented. The concept is intended to serve as a semiquantitative signpost for the synthesis of new ferromagnets. After a concise overview of the historic development of related theories developed within the physics community, the consequences of spin-spin coupling (made manifest in the exchange or Fermi hole) in atoms and molecules are explored. Upon moving to a paramagnetic state, the majority/minority spin species become more/less tightly bound to the nucleus, resulting in differences in the energies and spatial extents of the two sets of spin orbitals. By extrapolating well-known arguments from ligand-field theory, the paucity of ferromagnetic transition metals arises from quenching the paramagnetism of the free atoms due to strong interatomic interactions in the solid state. Critical valence electron concentrations in Fe, Co, and Ni, however, result in local electronic instabilities due to the population of antibonding states at the Fermi level varepsilon(F). Removal of these antibonding states from the vicinity of varepsilon(F) is the origin of ferromagnetism; in the pure metals this results in strengthening the chemical bonds. In the 4d and 5d transition metals, the valence d orbitals are too well shielded from the nucleus, so a transition to a ferromagnetic state does not result in sufficiently large changes to occur. Thus, the exceptional occurence of ferromagnetism only in the first transition series appears to parallel the special main-group chemistry of the first long period. A connection between ferromagnetism in the transition metals and Pearson's absolute hardness eta is easily established and shows that ferromagnetism appears only when eta<0.2 eV in the nonmagnetic calculation. As expected from the principle of maximum hardness, Fe, Co, and Ni all become harder upon moving to the more stable ferromagnetic state. Magnetism in intermetallic alloys follows the same path. Whether or not an alloy contains ferromagnetic elements, the presence of antibonding states at varepsilon(F) serves as a "fingerprint" to indicate a ferromagnetic instability. The differences in the sizes of the local magnetic moments on the constituent atoms of a ferromagnetic alloy can be understood in terms of the relative contributions to the density of states at varepsilon(F) in the nonmagnetic calculations. Appropriately parameterized, nonmagnetic, semi-empirical calculations can also be used to expose the ferromagnetic instability in elements and alloys. These techniques, which have become relatively commonplace, can be used to guide the synthetic chemist in search of new ferromagnetic materials.