Exciton Bands in AntiferromagneticCr2O3

We have calculated the energy dispersion of the lowest eight ${}_{}{}^2{}_{}{}^{}E$ Frenkel exciton branches in the four-sublattice antiferromagnet ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$. This is the first such calculation for a magnetic insulator. The symmetry properties and $\overrightarrow{\mathrm{k}}$ dependence of the interion exchange and Coulomb interactions which give rise to dispersion and Davydov splittings are presented in detail. Pairwise matrix elements of the interion Hamiltonian are treated as phenomenological parameters, and in most cases were determined from the $\overrightarrow{\mathrm{k}}=0\mathrm{}$ energies analyzed in an earlier paper. Dispersion curves for five directions in the rhombohedral Brillouin zone, and the exciton density of states, are given. Confirmation of the main features of the calculated exciton bands is provided by a measurement of the exciton-magnon absorption band shape. In the presence of a number of simplifying assumptions, this band shape is given by the joint exciton-magnon density of states. Good agreement between the calculated and observed band shape is obtained.