Using Raman spectroscopy to study the correlated $4d$-electron metal ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$, 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 ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and $\alpha \text{−}{\text{RuCl}}_3$. This observation provides direct evidence for the unquenched spin-orbit coupling in ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$. A quantitative analysis of the data reveals that the tetragonal crystal field $\mathrm{\Delta }$ in ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$ has a sign opposite to that in insulating ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, 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 ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$ may transform it into a quasi-two-dimensional antiferromagnetic insulator.

• Received 8 September 2023
• Revised 28 December 2023
• Accepted 22 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.116502

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Published by the American Physical Society