Magnetic Interactions between Rare-Earth Ions in Insulators. I. Accurate Electron-Paramagnetic-Resonance Determination of ${\mathrm{Gd}}^{3+}$ Pair-Interaction Constants in La${\mathrm{Cl}}_3$

A series of experiments is described which illustrate an accurate method of measuring both isotropic and anisotropic interactions between pairs of similar magnetic ions. The method is applicable whenever there are sufficient admixtures of the pair states by anisotropic interactions or crystal-field terms and the effective spin of each ion is greater than ½. These conditions are well illustrated by ${\mathrm{Gd}}^{3+}$ neighbors in La${\mathrm{Cl}}_3$. Paramagnetic-resonance measurements at 25 and 9 GHz have been made on crystals of La${\mathrm{Cl}}_3$ containing about 1% ${\mathrm{Gd}}^{3+}$ at temperatures between 1.6 and 360°K, and a large number of weak lines have been identified as due to transitions in isolated nearest-neighbor and next-nearest-neighbor pairs. Detailed analyses of both spectra show that the interactions for both types of pairs are well represented by isotropic (Heisenberg) terms $J{\mathrm{S}}_1·{\mathrm{S}}_2$, plus magnetic-dipole coupling appropriate to the separation between the neighbors. For the nearest neighbors we find $J_{\mathrm{nn}}=0.01330\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ (antiferromagnetic) at 20°K, decreasing to 0.01254 ${\mathrm{cm}}^{-1\mathrm{}}$ at 360°K; while for the next-nearest neighbors $J_{\mathrm{nnn}}=-0.0602\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ (ferromagnetic) at 20°K increasing to -0.0532 ${\mathrm{cm}}^{-1\mathrm{}}$ at 360°K. (Below 20°K somewhat increased linewidths precluded accurate measurements, but the parameters appeared to remain virtually unchanged.) Neither the magnitudes nor the signs of these values can be explained by present superexchange theories, but they are in generally good agreement with values deduced from the bulk properties of concentrated Gd${\mathrm{Cl}}_3$, and they resolve an ambiguity in the earlier analyses. The observed magnetic-dipole interaction parameters are also found to vary somewhat with temperature, and this may be used to estimate changes in the mean separation between neighbors due to thermal expansion. These estimates may then be combined with the observed temperature variations of the $J\text{'}\mathrm{s}$ to deduce approximate separation dependences for $J_{\mathrm{nn}}$ and $J_{\mathrm{nnn}}$. Both are found to be very marked ($\sim r^{13}$ and $r^{22}$, respectively) and appreciably more rapid than the recently proposed tenth-power law for superexchange.