Spin-Orbit Excitons in a Correlated Metal: Raman Scattering Study of Sr_{2}RhO_{4}.

Using Raman spectroscopy to study the correlated 4d-electron metal Sr_{2}RhO_{4}, we observe pronounced excitations at 220 meV and 240 meV with A_{1g} and B_{1g} 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 α-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 Δ 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=1/2 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.