Determination of ${\mathrm{Eu}}^{3+}$-${\mathrm{Fe}}^{3+}$ and ${\mathrm{Eu}}^{3+}$-${\mathrm{Gd}}^{3+}$ Exchange Interactions from Electron Paramagnetic Resonance Shifts in Europium Gallium Garnet

The paramagnetic resonance from ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Gd}}^{3+}$ ions substituted into weakly paramagnetic europium gallium garnet has been investigated at 77°K and 26 Gc/sec. The spectra have been fitted to conventional spin Hamiltonians for ${\mathrm{Fe}}^{3+}$ occupying the [$a$] site and ${\mathrm{Gd}}^{3+}$ occupying the {$c$} site. No resonance was observed from ($d$)-site ${\mathrm{Fe}}^{3+}$, indicating a strong preferential population of the [$a$] site in these garnets. By comparing the spin-Hamiltonian parameters found with those for other diamagnetic garnets, shifts due to the interaction of the substituted ions with the ${\mathrm{Eu}}^{3+}$ host lattice have been determined. A general theory for shifts of $S$-state ion resonances in europium compounds is developed and used to give quantitative estimates of the interactions in the garnet. From the shift in the ${\mathrm{Fe}}^{3+}$ $g$ values, the isotropic part of ${\mathrm{Eu}}^{3+}\mathrm{}\left\{c\right\}\mathrm{}-{\mathrm{Fe}}^{3+}\mathrm{}\left[a\right]\mathrm{}$ interaction is found to be small and ferromagnetic in sign, $J_{\mathrm{is}}\sim -0.016\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ (where $\mathcal{H}=+J_{\mathrm{is}}{\mathbf{S}}^1·{\mathbf{S}}^2$), and comparable anisotropic interactions are indicated. Moreover, a large apparent shift observed in the parameter $D$ suggests a dominant antisymmetric (Moriya) interaction of at least ∼1 ${\mathrm{cm}}^{-1\mathrm{}}$ between these ions, which is unobservable in the ordered concentrated iron garnet. The shifts in the ${\mathrm{Gd}}^{3+}$ $g$ values are well explained by an isotropic exchange of the magnitude expected, $J_{\mathrm{is}}\sim +0.07\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, together with the calculated magnetic dipole interaction.