The site symmetry of ${\mathrm{Cr}}^{3+}$ in Ti${\mathrm{O}}_2$ is $D_{2h}$ which splits the cubic $\left(O_h\right){}_{}{}^4{}_{}{}^{}T_{2g}^{}{}_{}{}^{}$ state into ${}_{}{}^4{}_{}{}^{}B_{1g}^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}B_{2g}^{}{}_{}{}^{}$, and ${}_{}{}^4{}_{}{}^{}B_{3g}^{}{}_{}{}^{}$. Spin-orbit interaction further splits these states into six Kramers doublets all of symmetry ${\Gamma }_5^{+}$. Previous optical work on Ti${\mathrm{O}}_2$: ${\mathrm{Cr}}^{3+}$ established the lowest-lying sharp lines at 12 685 and 12 732 ${\mathrm{cm}}^{-1\mathrm{}}$ as no-phonon lines of magnetic dipole character. It proposed these lines as due to transitions between the ${}_{}{}^4{}_{}{}^{}A_{2g}^{}{}_{}{}^{}$ ground state and two of the above six states. The present report extends this work by a Zeeman study, in emission, at 4 K of the line at 12 685 ${\mathrm{cm}}^{-1\mathrm{}}$. The results are: The Zeeman splitting of this line identifies the excited state of this transition as the $M_s=\pm \frac{3}{2}$ spin-orbit component of an orbital state consisting of $77\%{}_{}{}^4{}_{}{}^{}B_{2g}^{}{}_{}{}^{}$, $17\%{}_{}{}^4{}_{}{}^{}B_{1g}^{}{}_{}{}^{}$, and $6\%{}_{}{}^4{}_{}{}^{}B_{3g}^{}{}_{}{}^{}$ with an effective $g=1.73\mathrm{}$. Furthermore, the line at 12 732 ${\mathrm{cm}}^{-1\mathrm{}}$ is identified as the $M_s=\pm \frac{1}{2}$ spin-orbit component by its effect in second order in the magnetic field on the Zeeman pattern of the line at 12 685 ${\mathrm{cm}}^{-1\mathrm{}}$. For the excited state the spin is quantized along the $x$ direction of the magnetic axes while for the ground state it is quantized along the $z$ direction. The reason for spin quantization along the $x$ axis is discussed.

• Received 2 April 1973

DOI:https://doi.org/10.1103/PhysRevB.8.1032