Orbital Angular Momentum in the Theory of Paramagnetic Clusters

The statistical theory of paramagnetic clusters described in the literature to date is largely restricted to ``spin-only'' magnetism for which orbital angular momentum is quenched, or enters the calculations only as a trivially modified g factor. This paper discusses the extension of the theory to magnetic ions for which large unquenched orbital angular momentum is present, rendering the conventional approach completely inoperative. A theory is developed in detail for cobaltous cluster complexes, the cobaltous ion generally being one of the more difficult of the 3d transition metal ions to describe statistically. A preamble into relevant crystal-field theory is followed by the development of a statistical theory valid, to a good approximation, over the entire temperature range. Numerical results are presented to indicate the separate effects of spin—orbital reduction, and inter- as well as intracluster exchange. The full theory is also compared numerically with the results of simpler, but less adequate, approximations to demonstrate the penalty in accuracy paid for algebraically less onerous calculations. The theoretical principles involved are readily extendable for use with other magnetic ions (e.g., ferrous) for which unquenched orbital angular momentum plays an essential role.