A linear chain of S=½ molecules with alternating intermolecular exchange integrals is used as a model to investigate the properties of paramagnetic excitons in solid free radicals from a theoretical point of view. The spin exchange Hamiltonian for the problem is H=Σν(JS2ν·S2ν+1+J′S2ν·S2ν−1),when J>J′>0. In the limiting case that J≫J′, the exciton bandwidth is simply J′. For this case we have calculated (a) the fine-structure splitting of the paramagnetic resonance of isolated (noninteracting) excitons, (b) wave functions for a free exciton gas of arbitrary excitation density, (c) the magnetic susceptibility of the exciton gas, and (d) first-order exchange interactions between excitations. In the case that thermal energies are much larger than the exciton bandwidth, exchange interactions between excitations are simply proportional to the excitation concentration, but at temperatures corresponding to thermal energies less than the bandwidth, there is a ``Fermi hole'' type repulsion between the excitons that reduces the exchange interaction. In fact, the excitons behave somewhat like Fermi particles, except their number is not constant (depending on the temperature), and only one exciton may occupy a given momentum state, irrespective of spin. Also, when the exciton bandwidth is comparable to or larger than kT, it is predicted that the exciton fine-structure splitting will be temperature dependent. When J′ becomes comparable to J, then the elementary exciton takes on a complicated, distributed spin structure.
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