Spin-orbit coupling and crystal-field splitting in Ti-doped Ca2RuO4 studied by ellipsometry

In ${\mathrm{Ca}}₂{\mathrm{RuO}}₄$, the competition of spin-orbit coupling $\ensuremath{\zeta}$ and tetragonal crystal-field splitting ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{CF}}$ has been discussed controversially for many years. The orbital occupation depends on ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{CF}}/\ensuremath{\zeta}$, which allows us to address this ratio via the optical spectral weights of the lowest intersite Mott-Hubbard excitations. We study the optical conductivity of ${\mathrm{Ca}}₂{\mathrm{Ru}}_0.99{\mathrm{Ti}}_0.01{\mathrm{O}}₄$ in the range of 0.75--5 eV by ellipsometry, using the large single crystals that can be grown for small Ti concentrations. Based on a local multiplet calculation, our analysis results in $2.4\ensuremath{\le}{\mathrm{\ensuremath{\Delta}}}_{\mathrm{CF}}/\ensuremath{\zeta}\ensuremath{\lesssim}4$ at 15 K. The dominant crystal field yields a ground state close to $xy$ orbital order but spin-orbit coupling is essential for a quantitative description of the properties. Furthermore, we observe a pronounced decrease of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{CF}}$ with increasing temperature, as expected based on the reduction of octahedral distortions.