Coupled spin-orbital fluctuations in a three orbital model for 4dand 5doxides with electron fillingsn=3, 4, 5-application to NaOsO3, Ca2RuO4and Sr2IrO4.

A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillingsn= 3, 4, 5 in thet2gsector ofdyz,dxz,dxyorbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds NaOsO3, Ca2RuO4, and Sr2IrO4.