Electron-Spin-Resonance Spectra of Nearest-Neighbor ${\mathrm{Cr}}^{3+}$ Pairs in the Spinel Zn${\mathrm{Ga}}_2$ ${\mathrm{O}}_4$

ESR spectra of nearest-neighbor ${\mathrm{Cr}}^{3+}$ pairs in Zn${\mathrm{Ga}}_2$ ${\mathrm{O}}_4$ are studied in detail at two frequency bands: $X$ band (9.9 GHz) and $Q$ band (32.5 GHz). Transitions within each of the spin multiplets $\Sigma =1,2, \mathrm{and} 3$ are observed. From the angular dependence of the spectra it is found that local lattice distortions due to Cr→Ga substitution are negligible. The Cr-Cr coupling is described by the spin Hamiltonian: ${\mathcal{H}}_{\mathrm{ex}}=-J{\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2+j{\left({\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2\right)}^2+A[{\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2-\frac{3\left({\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{r}}}_{12}\right)\left({\overrightarrow{\mathrm{S}}}_2·{\overrightarrow{\mathrm{r}}}_{12}\right)}{r_{12}^2}]$. The temperature dependence of the ESR intensities is used to determine the coefficients of the bilinear ($J$) and biquadratic ($j$) exchange as, $\frac{J}{k}=-(32\mathrm{}\pm 2)$ °K (antiferromagnetic coupling), $\frac{j}{k}=-(2\mathrm{}\pm 1)$ °K. The anisotropic part of the coupling can be fully accounted for by magnetic dipole-dipole interaction: $A=A_{\mathrm{dip}}=+0.0675\mathrm{}\pm 0.0005$ ${\mathrm{cm}}^{-1\mathrm{}}$. The value of $j$ can be explained on the basis of an exchange-striction model.