Single crystals of Ti${\mathrm{O}}_2$:${\mathrm{Cu}}^{2+}$ have been investigated at 20 K using the technique of electron paramagnetic resonance. The major features of the EPR spectra can be attributed to divalent copper ($3d^9$) in substitutional (${\mathrm{Ti}}^{4+}$) sites. Information has been gained about both isotopes of copper and about the interactions which concern this ion. For the substitutional site, the spin-Hamiltonian parameters in the $S=\frac{1}{2}$, $I=\frac{3}{2}$ manifold are: $g_x=2.109\mathrm{}$, $g_y=2.094\mathrm{}$, $g_z=2.346\mathrm{}$, $A_x^{}{}_{}{}^{63}=+18.7\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_y^{}{}_{}{}^{63}=+27.2\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_z^{}{}_{}{}^{63}=-87.5\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_x^{}{}_{}{}^{65}=+18.8\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_y^{}{}_{}{}^{65}=+28.7\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $A_z^{}{}_{}{}^{65}=-93.7\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $P_x=-2.56\mathrm{}\times {10}^{-4\mathrm{}}$, $P_y=-2.37\mathrm{}\times {10}^{-4\mathrm{}}$, and $P_z=+4.93\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The magnitudes and relative signs of these parameters have been determined experimentally, while the absolute signs have been predicted theoretically from a model which gives a consistent picture of the ordering of the $d^9$ electronic states. In addition, the theoretical treatment gives a satisfactory estimate of $P$. Departure from tetragonality was taken into account. The covalency parameter ${\alpha }^2$ which measures the fraction of the hole wave function on the ${\mathrm{Cu}}^{2+}$ ion is found to be 0.71, and the factor $\kappa$ giving rise to isotropic hyperfine structure is found to be 0.31.

• Received 7 July 1969

DOI:https://doi.org/10.1103/PhysRev.188.703