Coulomb correlations in 4d and 5d oxides from first principles—or how spin–orbit materials choose their effective orbital degeneracies

The interplay of spin–orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin–orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr2IrO4) and its 4d metallic counterpart, strontium rhodate (Sr2RhO4). While a Mott-insulating state is obtained for Sr2IrO4 in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr2RhO4 show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin–orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin–orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d1 perovskites.