Spin-orbit excitons in a correlated metal: Raman scattering study of Sr2RhO4

Using Raman spectroscopy to study the correlated 4$d$-electron metal Sr${}_2$RhO${}_4$, we observe pronounced excitations at 220 meV and 240 meV with $A_{1\mathrm{g}}$ and $B_{1\mathrm{g}}$ symmetries, respectively. We identify them as transitions between the spin-orbit multiplets of the Rh ions, in close analogy to the spin-orbit excitons in the Mott insulators Sr${}_2$IrO${}_4$ and $\alpha$-RuCl${}_3$. This observation provides direct evidence for the unquenched spin-orbit coupling in Sr${}_2$RhO${}_4$. A quantitative analysis of the data reveals that the tetragonal crystal field $\mathrm{\Delta }$ in Sr${}_2$RhO${}_4$ has a sign opposite to that in insulating Sr${}_2$IrO${}_4$, which enhances the planar $xy$ orbital character of the effective $J=1\mathrm{/}2$ wave function. This supports a metallic ground state, and suggests that $c$-axis compression of Sr${}_2$RhO${}_4$ may transform it into a quasi-two-dimensional antiferromagnetic insulator.