Linear dichroic x-ray absorption response of Ti-Ti dimers along the $c$ axis in Ti${}_2$O${}_3$ upon Mg substitution

Corundum oxide Ti${}_2$O${}_3$ shows the metal-insulator transition around 400-600 K accompanying the nearest Ti${}^{3+}$-Ti${}^{3+}$ bond ($a_{1g}{a}_{1g}$ singlet state) formation along the $c$ axis. In order to clarify the hole-doping effect for the $a_{1g}{a}_{1g}$ singlet bond in Ti${}_2$O${}_3$, we investigated Ti $3d$ orbital anisotropy between corundum-type Ti${}_2$O${}_3$ and ilmenite-type MgTiO${}_3$ using linear dichroism of soft x-ray absorption spectroscopy of the Ti $L_{2,3}$ edge. From the linear dichroic spectral weight in Mg${}_y$Ti${}_{2-y}$O${}_3$, we confirmed that the $a_{1g}{a}_{1g}$ state is dominant not only in $y=0.01$ (almost Ti${}_2$O${}_3$), but also in $y=0.29$, indicating that the Ti-Ti bond survives against a certain level of hole doping. In $y=0.63$ corresponding to 46% hole doping per Ti, the $3d$ orbital symmetry changes from $a_{1g}$ to $e_g^{\pi }$.