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 $J_{\mathrm{nnn}}(\mathrm{Gd}-\mathrm{Eu})=-0.061\mathrm{}\pm 0.030$ ${\mathrm{cm}}^{-1\mathrm{}}$. The similarity of these results to the corresponding ${\mathrm{Gd}}^{3+}$-${\mathrm{Gd}}^{3+}$ interactions suggests that the average electron-electron exchange interaction may be relatively insensitive to the particular configuration of the individual ions, as proposed theoretically by Van Vleck. On the other hand, comparisons between the results for different isostructural lattices shows that some of the interactions can be extremely sensitive to even small changes in the neighbor distances, and great care is therefore required in extrapolating from one lattice to another.

• Received 2 October 1968

DOI:https://doi.org/10.1103/PhysRev.179.275