Magnetic Interactions between Rare-Earth Ions in Insulators. II. Electron-Paramagnetic-Resonance Measurements of ${\mathrm{Gd}}^{3+}$ Pair and ${\mathrm{Gd}}^{3+}$-${\mathrm{Eu}}^{3+}$ Interaction Constants in Eu${\mathrm{Cl}}_3$

Paramagnetic resonance has been observed from both single ions and isolated pairs of ${\mathrm{Gd}}^{3+}$ in Eu${\mathrm{Cl}}_3$ at 77°K and 25.6 GHz. The pair spectra were analyzed in the same way as those observed previously from ${\mathrm{Gd}}^{3+}$ in La${\mathrm{Cl}}_3$. The results give accurate values for the interaction parameters between both nearest (nn) and next-nearest neighbors (nnn). The dominant terms are of the form of isotropic exchange ($J{\mathrm{S}}_1·{\mathrm{S}}_2$), with $J_{\mathrm{nn}}\left(\mathrm{pair}\right)=0.0488\mathrm{}\pm 0.0010$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $J_{\mathrm{nnn}}\left(\mathrm{pair}\right)=-0.0637\mathrm{}\pm 0.0020$ ${\mathrm{cm}}^{-1\mathrm{}}$. The anisotropic parts of the interactions could be accounted for completely by the calculated magnetic dipole-dipole coupling. Combining these results with earlier measurements in La${\mathrm{Cl}}_3$, good estimates can be made of the exchange interactions in pure Gd${\mathrm{Cl}}_3$: $J_{\mathrm{nn}}\left(\mathrm{Gd}{\mathrm{Cl}}_3\right)=0.056\mathrm{}\pm 0.006$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $J_{\mathrm{nnn}}\left(\mathrm{Gd}{\mathrm{Cl}}_3\right)=-0.064\mathrm{}\pm 0.003$ ${\mathrm{cm}}^{-1\mathrm{}}$. These values are in excellent agreement with those inferred from analyses of susceptibility and specific-heat measurements, and they resolve unambiguously earlier uncertainties in the choice of possible parameters. The magnitudes and even the signs of the interactions remain unexplained. From measured $g$-value shifts relative to ${\mathrm{Gd}}^{3+}$ in La${\mathrm{Cl}}_3$ it was also possible to estimate the isotropic part of the ${\mathrm{Gd}}^{3+}$-${\mathrm{Eu}}^{3+}$ exchange interaction: $J_{\mathrm{nn}}(\mathrm{Gd}-\mathrm{Eu})=0.052\mathrm{}\pm 0.030$ ${\mathrm{cm}}^{-1\mathrm{}}$ and