Spin-Orbit Coupling and Electronic Correlations in Sr_{2}RuO_{4}.

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr_{2}RuO_{4} using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC is found to change significantly the electronic structure at k points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate the effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an energy-dependent quasiparticle spin-orbit coupling λ^{*}(ω). This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.