Optical conductivity, Fermi surface, and spin-orbit coupling effects in Sr 2 RhO 4

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties of Sr 2 RhO 4 in a realistic setting, and compare to Sr 2 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 Sr 2 RuO 4 , the zero-frequency effective crystal-field “enhancement” due to Coulomb repulsion, Δ ɛ CF ( ω = 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 Sr 2 RuO 4 , the t 2 g intraorbital contributions are small; thus, the single-band picture does not apply.