Superposition model analysis of spin-Hamiltonian parameters forGd3+in rare-earth metal trichloride hexahydrates

The second-order spin-Hamiltonian parameters for ${\mathrm{Gd}}^{3+}$-doped single crystals of $R{\mathrm{Cl}}_3·6{\mathrm{H}}_2\mathrm{O}$ ($R=\mathrm{N}\mathrm{d},\mathrm{S}\mathrm{m},\mathrm{E}\mathrm{u},\mathrm{T}\mathrm{d},\mathrm{D}\mathrm{y},\mathrm{H}\mathrm{o},\mathrm{E}\mathrm{r},\mathrm{T}\mathrm{m}$) are analyzed using the linear superposition model of Newman. It is found that, in order to explain satisfactorily the observed values of the parameters, the model requires different values of $t_2$ for different hosts; these values are linear in the host-ion radius. Further, the analysis enables one to decouple the metal-ligand distance effects from other factors which influence $t_2$. A similar result is found for ${\overline{b}}_2$.