Far-infrared optical properties and the metal-insulator transition in Ti-doped Ca$_3$(Ru$_{\mathrm{1-x}}$Ti$_{\mathrm{x}})_2$O$_7$ (x$=$0.03)

The discovery of the intriguing phase diagram of Ca$_3$(Ru$_{\mathrm{1-x}}$Ti$_{\mathrm{x}})_2$O$_7$ is the new and exciting development in correlated electron ruthenates, as Ti doping drastically changes the material's ground state properties. The undoped Ca$_3$Ru$_2$O$_7$ is metallic at high temperature and undergoes an antiferromagnetic transition at 56 K that is followed by a metal-insulator transition at 48 K driven by the opening of a charge density wave gap. A quasi-2D metallic state develops below 30 K. At 5{\%} Ti doping, the metal-insulator transition temperature is T$_{\mathrm{MI}}=$80 K, below which the material is a Mott insulator. By contrast, a weakly localized electronic state is observed at intermediate dopings (2-4{\%} Ti) together with antiferromagnetic long range order. In the undoped Ca$_3$Ru$_2$O$_{\mathrm{7}}$, the metal-insulator transition at 48 K is accompanied by the development of a charge gap below 200 cm$^{-1}$. At low temperatures, a small Drude peak develops below 50 cm-1, resulting from small non-nested metallic pockets of the Fermi surface. We report a far-infrared spectroscopic ellipsometry study of Ca$_3$(Ru$_{\mathrm{1-x}}$Ti$_{\mathrm{x}})_2$O$_{\mathrm{7}}$ (x$=$0.03) at U4IR beamline of NSLS-BNL. Our data indicate that the low-temperature gap in optical conductivity opens at 1000 cm$^{-1}$, a dramatically different value from the one in the undoped compound. We relate our observations to the effects of Ti doping - the induced changes in carrier itinerancy and the modified double-exchange and superexchange interactions in the material.