Hyperfine, Superhyperfine, and Quadrupole Interactions forV4+in Tetragonal GeO2

Single crystals of vanadium-doped tetragonal Ge${\mathrm{O}}_2$ have been studied at 300 and 92 K by electron-spin resonance. The observed spectra are attributed to tetravalent vanadium ions ($3d^1$) substitutional at the two inequivalent cation sites. With the choice of axes $\overrightarrow{\mathrm{x}}\parallel \left[\overline{1}10\right]$, $\overrightarrow{\mathrm{y}}\parallel \mathrm{}\left[001\right]\mathrm{}$, and $\overrightarrow{\mathrm{z}}\parallel \mathrm{}\left[110\right]\mathrm{}$, the spin-Hamiltonian parameters obtained at 300 K from the hyperfine, super-hyperfine, and forbidden-transition spectra are $g_x=1.9467\mathrm{}$, $g_y=1.9211\mathrm{}$, $g_z=1.9638\mathrm{}$; $A_x=18.48\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_y=37.27\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_z=134.63\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $P_x=-0.44\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $P_y=-0.35\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $P_z=+0.79\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $A_{\mathrm{ax}}=8.4\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_{\mathrm{ay}}=8.8\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_{\mathrm{az}}=8.3\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, where the last tensor corresponds to a shf interaction with a ${\mathrm{Ge}}^{73}$ nucleus at one of the nearest cation sites along the $c$ axis. Weaker interactions with other neighboring cations were also observed. On the basis of a molecular-orbital treatment of the unpaired spin, ligand-orbital-admixture coefficients were determined from these experimental results and from previously reported results ${\mathrm{V}}^{4+}$ in tetragonal Ti${\mathrm{O}}_2$ and Sn${\mathrm{O}}_2$. It is determined that the probability of finding the unpaired electron on the vanadium ion is about 0.71, while the probabilities for delocalization onto the anions and cations are about 0.27 and 0.02, respectively.