Electron-Spin-Resonance Studies of ${\mathrm{Mo}}^{6+}$, ${\mathrm{Mo}}^{5+}$, ${\mathrm{Mo}}^{4+}$, and ${\mathrm{Mo}}^{3+}$ in Rutile

Hydrogen treatment was used to vary the Fermi level in Mo-doped rutile. The stable valence states ${\mathrm{Mo}}^{5+}$ and ${\mathrm{Mo}}^{3+}$ were detected by ESR measurements. The existence of the states ${\mathrm{Mo}}^{6+}$ and ${\mathrm{Mo}}^{4+}$ was inferred from the data. The previously unreported ${\mathrm{Mo}}^{3+}$ resonances can be fit by a spin Hamiltonian $\mathcal{H}=\overrightarrow{\mathrm{H}}·\overleftrightarrow{\mathrm{g}}·\overrightarrow{\mathrm{S}}+D{S}_z^2+E(S_x^2-S_y^2)\overrightarrow{\mathrm{I}}·\overleftrightarrow{\mathrm{A}}·\overrightarrow{\mathrm{S}}$, with $S=\frac{3}{2}$, $g_c=1.94\mathrm{}$, $g_{\overline{1}10}=1.97\mathrm{}$, $g_{110}=1.95\mathrm{}$, $D=5.58\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $E=0.99\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_c=3.83\mathrm{}\times {10}^{-3}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_{\overline{1}10}=3.50\mathrm{}\times {10}^{-3}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $A_{110}=3.56\mathrm{}\times {10}^{-3}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The $z$ axis coincides with the crystalline $c$ axis.