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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.

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High-speed optical communication requires ultrafast all-optical processing and switching capabilities. The Kerr nonlinearity, an ultrafast optical nonlinearity, is often used as the basic switching mechanism. A practical, small device that can be switched with ~1-pJ energies requires a large Kerr effect with minimal losses (both linear and nonlinear). We have investigated theoretically and experimentally a number of Se-based chalcogenide glasses. We have found a number of compounds with a Kerr nonlinearity hundreds of times larger than silica, making them excellent candidates for ultrafast all-optical devices.

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New developments involving nonlinear optical effects are conditioned by the improvement of pertinent figures of merit involving the characteristics of nonlinear optical materials within the ‘‘transparency’’ regime of their optic windows. This paper discusses, from a global standpoint, the maximum values of nonlinear refractive index n2, and of its ratio n2/α relative to intrinsic attenuation α, attainable for a multicomponent oxide glass. It also locates and analyses those classes of multicomponent oxide glass that, from the standpoint of these two measures, appear to be the most promising candidates for use as fast photonic switching elements in the 1–2.5-μm wavelength regime.