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

TL;DR

This study investigates the interplay of spin-orbit coupling and crystal-field splitting in Ti-doped Ca2RuO4 using ellipsometry, revealing the ratio of these effects and their temperature dependence.

Contribution

It provides a quantitative analysis of the crystal-field to spin-orbit coupling ratio in Ca2RuO4 through optical spectral weights, clarifying their roles in orbital occupation.

Findings

The ratio Δ_CF/ζ is between 2.4 and 4 at 15 K.

Spin-orbit coupling is crucial for accurate property description.

Δ_CF decreases with increasing temperature due to reduced octahedral distortions.

Abstract

In Ca2RuO4, the competition of spin-orbit coupling $\zeta$ and tetragonal crystal field splitting $\Delta_{CF}$ has been discussed controversially for many years. The orbital occupation depends on $\Delta_{CF}/\zeta$, 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 Ca$_2$Ru$_{0.99}$Ti$_{0.01}$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 $2.4 \leq \Delta_{CF}/\zeta \leq 4$ 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 $\Delta_{CF}$ with increasing temperature, as expected based on the reduction of octahedral distortions.