ESR Investigations of Nearest-Neighbor ${\mathrm{Cr}}^{3+}$-${\mathrm{Cr}}^{3+}$ Interactions in Cr-Doped Spinel Mg${\mathrm{Al}}_2$${\mathrm{O}}_4$

The ESR spectrum of nearest-neighbor (nn) ${\mathrm{Cr}}^{3+}$ pairs in a synthetic single crystal of Mg${\mathrm{Al}}_2$ ${\mathrm{O}}_4$ has been studied at $\nu =9.85\mathrm{}$ GHz ($X$ band). Transitions within the spin multiplets $\Sigma =2\mathrm{}$ and $\Sigma =3\mathrm{}$ are observed. The coefficients of the bilinear ($J$) and biquadratic ($j$) exchange are determined from the temperature dependence of the intensities as: $\frac{J}{k}=-(41\mathrm{}\pm 3)$ °K, $\frac{j}{k}=-(3\mathrm{}\pm 1)$ °K. It is found that the accomodation of a nn ${\mathrm{Cr}}^{3+}$ pair in the lattice is accompanied with a local lattice distortion. This is borne out by the fact that the zero-field-splitting parameters of the pair $D_p=+1.042\mathrm{}\pm 0.005$ ${\mathrm{cm}}^{-1\mathrm{}}$, $E_p=-0.038\mathrm{}\pm 0.002$ ${\mathrm{cm}}^{-1\mathrm{}}$ differ appreciably from those of the single ion $D=+0.910\mathrm{}\pm 0.002$ ${\mathrm{cm}}^{-1\mathrm{}}$, $E=0\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Moreover, the anisotropic (traceless) part of the spin-spin coupling tensor is orthorhombic: ${\mathcal{J}}_{PP}=+0.1015\mathrm{}\pm 0.0025$ ${\mathrm{cm}}^{-1\mathrm{}}$, ${\mathcal{J}}_{QQ}=+0.0535\mathrm{}\pm 0.0025$ ${\mathrm{cm}}^{-1\mathrm{}}$, and ${\mathcal{J}}_{RR}=-0.1550\mathrm{}\pm 0.0010$ ${\mathrm{cm}}^{-1\mathrm{}}$, with principal axes along $P=\left[001\right]\mathrm{}$, $Q=\left[1\mathrm{}\overline{1}0\right]$, $R=\left[110\right]\mathrm{}$ for a Cr-Cr pair along the $R$ axis.