Optical conductivity, Fermi surface, and spin-orbit coupling effects in Sr2RhO4

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties of ${\mathrm{Sr}}_{2}{\mathrm{RhO}}_{4}$ in a realistic setting, and compare to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. We investigate the interplay of spin-orbit coupling, crystal field, and Coulomb interaction, including the tetragonal terms of the Coulomb tensor. We find that (i) differently than in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, the zero-frequency effective crystal-field ``enhancement'' due to Coulomb repulsion, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\varepsilon}}_{\mathrm{CF}}(\ensuremath{\omega}=0)$, is small and, depending on the parameters, even negative. (ii) In addition, the effects of (realistic) anisotropic Coulomb terms are weak. (iii) Instead, the effective zero-frequency enhancement of the spin-orbit interaction doubles the value of the corresponding local-density approximation couplings. This explains the experimental Fermi surface and supports a previous proposal based on static mean-field calculations. We find that the sign of the Coulomb-induced spin-orbit anisotropy is influenced by the octahedral rotation. Based on these conclusions, we examine recent optical conductivity experiments. (iv) We show that the spin-orbit interaction is key for understanding them; differently than in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, the ${t}_{2g}$ intraorbital contributions are small; thus, the single-band picture does not apply.