Anisotropic Exchange Effects in the Exciton Spectrum of GdCl3and Gd(OH)3

The first detailed application of a general anisotropic exchange operator to energy-transfer problems in magnetic insulators is described for exciton dispersion in Gd${\mathrm{Cl}}_3$ and Gd${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$. Relationships, which are independent of the two parameters in the theory and are consistent with experiment, are found between transfer-of-energy matrix elements for different excited states, providing strong evidence that anisotropic exchange is the dominant mechanism of energy transfer.