Orbital effects on exchange interactions

Many magnetic materials contain ions in which the orbital contribution to the magnetic moment is important. This is normally the case in the rare earths and the actinides, where there is strong spin-orbit coupling and weak crystal fields, and it also occurs in transition metal ions like Fe²⁺ and Co²⁺. This orbital contribution leads to asymmetric charge clouds and the corresponding asymmetry of the transfer and overlap integrals means that the exchange interaction between pairs of such ions is not of the Heisenberg form but contains more complicated functions of the angular momentum operators. The microscopic form of the exchange and coulomb interaction between pairs of electrons is considered in the single-electron representation and transformed to the (L, S) and J representations of many-electron atomic states, and finally to a pseudospin representation which spans the lowest-lying atomic states in the presence of crystal fields. The symmetry restrictions on this pseudospin Hamiltonian are considered. Detailed calculations are made of a model of UO ₂ using Anderson's kinetic exchange mechanism.