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

Abstract

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.

The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds

“…An inspection of the non-spin-polarized COHP curves for 3d transition-metals (T; Figure 8) indicates that the Fermi levels in the ferromagnetic metals cross antibonding regions of the T−T COHP curves [131,132]; however, in the case of the spin-polarized COHP curves for the ferromagnetic metals, the states occupied by the majority α spins lower in energy, while the states comprising the minority β spins shift upward in energy. As a result, the formerly antibonding states at the Fermi levels have disappeared and the T−T bonding has been strengthened (e.g., by 5% in bcc-Fe).…”

Scaffolding, Ladders, Chains, and Rare Ferrimagnetism in Intermetallic Borides: Electronic Structure Calculations and Magnetic Ordering

“…At a given VE count, the occupation of antibonding states between magnetically active atoms has been previously described to indicate ferromagnetic ordering, whereas when nonbonding or bonding states between magnetic atoms are occupied, antiferromagnetic coupling is preferred. 6,7,23 Therefore, from the ÀCOHP curves presented in Figure 6c, along the [001] direction the magnetic moments at the M2 and M3 sites should order, respectively, ferromagnetically and antiferromagnetically. Furthermore, the Fe1ÀM2 interaction along {110} should be ferromagnetic.…”

Study of Vacancies and Pd Atom Decoration on the Electronic Properties of Bilayer Graphene

“…Another simpler way to explain COOP is as follows: COOP could be understood as the orbitals (from each atom that form the solid) working together to make bonds in the crystal. Figure 4 provides a COOP figure for sample C. In the figure, energy in eV (vertical axis) vs. antibonding/bonding contribution (in %) (horizontal axis) is depicted, where the [20] demonstrated that a driven force for the creation of ferromagnetism was the removal of M-M antibonding states from the vicinity of E F as a result of the exchange splitting. The exchange splitting as well as the differential spatial extent of the two spin sublattices arises because of differential shielding of α and β electrons.…”

“…A technique has been developed by Landrum et al [20]. They showed that the presence of M-M (M = metal) antibonding states at the Fermi level serves as a finger print to indicate the possibility for the existence of ferromagnetic instabilities.…”

“…Landrum et al [20] showed that using the concept of Crystal Orbital Hamiltonian Population (COHP) is equivalent to the use of the Crystal Orbital Overlap Population (COOP) technique used when extended Hückel theory is performed. COOP provides the total overlap population, which is not identical to the bond order, but scales like it [22].…”