Exchange Interactions within Nearest-Neighbor Cr3+ Pairs in Chromium-Doped Spinel ZnGa2O4

Abstract

Exchange interactions within nearest-neighbor ${\mathrm{Cr}}^{3+}$ pairs in Cr-doped spinel Zn${\mathrm{Ga}}_2$ ${\mathrm{O}}_4$ are studied by means of electron spin resonance. Apart from isotropic exchange, biquadratic and anisotropic terms are needed for an adequate description of the experimental results: ${\mathcal{H}}_{\mathrm{ex}}=-J{\overrightarrow{\mathrm{s}}}_1·{\overrightarrow{\mathrm{s}}}_2+j{\left({\overrightarrow{\mathrm{s}}}_1·{\overrightarrow{\mathrm{s}}}_2\right)}^2+A[{\overrightarrow{\mathrm{s}}}_1·{\overrightarrow{\mathrm{s}}}_2-3({\overrightarrow{\mathrm{s}}}_1·{\overrightarrow{\mathrm{r}}}_{12}\left)\frac{\left({\overrightarrow{\mathrm{s}}}_2·{\overrightarrow{\mathrm{r}}}_{12}\right)}{r_{12}^2}\right]$. The coefficients are found to be $\overrightarrow{\mathrm{s}} \frac{J}{k}=(-16.\mathrm{}5\pm 1.0)$ °K, $\frac{j}{k}=(-2.\mathrm{}5\pm 1.0)$ °K, and $A=+0.\mathrm{}016\pm 0.001$ ${\mathrm{cm}}^{-1\mathrm{}}$. Since dipole-dipole interactions would lead to $A_{\mathrm{dip}}=+0.\mathrm{}067$ ${\mathrm{cm}}^{-1\mathrm{}}$, it follows that a negative anisotropic exchange counteracts the $d-d$ interaction to an appreciable amount. The large negative biquadratic exchange is explained in terms of Kittel's exchange-striction mechanism.