Zeeman Effect in TiO$_{2}$:Cr$^{3+}$

We will describe the results of Zeeman effect measurements for single crystals of rutile TiO$_{2}$ doped with Cr$^{3+}$. These measurements, performed at the National High Magnetic Field Laboratory in magnetic fields with strengths up to 45 T, utilized the near-infrared luminescence of Cr$^{3+}$ at a temperature of T = 1.4 K. The Cr$^{3+}$ luminescence spectra show the evolution with field strength of the splitting of the Cr$^{3+}$ zero-phonon line at 12,684 cm$^{-1}$ in magnetic fields applied parallel or perpendicular to the crystallographic $c$-axis. In the former case the zero-phonon line splits into four Zeeman components, while for the latter case three components appear. These results will be discussed and compared to earlier measurements made in weaker magnetic fields.