Exchange Interactions within Nearest-NeighborCr3+Pairs in Chromium-Doped Spinel ZnGa2O4

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: ${\mathcal{H}}_{\mathrm{ex}}=\ensuremath{-}J{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{2}+j{({\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{2})}^{2}+A[{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{2}\ensuremath{-}3({\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}_{12})\frac{({\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}_{12})}{{r}_{12}^{2}}]$. The coefficients are found to be $\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}} \frac{J}{k}=(\ensuremath{-}16.5\ifmmode\pm\else\textpm\fi{}1.0)$ \ifmmode^\circ\else\textdegree\fi{}K, $\frac{j}{k}=(\ensuremath{-}2.5\ifmmode\pm\else\textpm\fi{}1.0)$ \ifmmode^\circ\else\textdegree\fi{}K, and $A=+0.016\ifmmode\pm\else\textpm\fi{}0.001$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Since dipole-dipole interactions would lead to ${A}_{\mathrm{dip}}=+0.067$ ${\mathrm{cm}}^{\ensuremath{-}1}$, it follows that a negative anisotropic exchange counteracts the $d\ensuremath{-}d$ interaction to an appreciable amount. The large negative biquadratic exchange is explained in terms of Kittel's exchange-striction mechanism.