  We have investigated the electronic structure of Sr2IrO4 within the
density-functional theory using the generalized gradient approximation while
taking into account strong Coulomb correlations in the framework of the fully
relativistic spin-polarized Dirac linear MT orbital band structure method. We
have investigated the x-ray absorption spectra, x-ray magnetic circular
dichroism, and resonant inelastic x-ray scattering spectra at the Ir L3 and O K
edges. The calculated results are in good agreement with the experimental data.
The RIXS spectrum of Sr2IrO4 at the Ir L3 edge in addition to the elastic
scattering peak at 0 eV possesses a sharp feature below 1.5 eV corresponding to
transitions within the Ir t2g levels. The excitation located from 2 eV to 5 eV
is due to t2g-eg transitions. The third wide structure situated at 5-12 eV
appears due to transitions between the Ir 5d_O states derived from the tails of
oxygen 2p states and eg and t2g states. The RIXS spectrum of Sr2IrO4 at the O K
edge consists of three major inelastic excitations at 0.7 eV, 3.5 eV, and
around 6.2 eV. We have found that the first low energy feature is due to
interband transitions between occupied and empty O t2g transitions, which
appear due to the strong hybridization between oxygen 2p and Ir t2g states in
the close vicinity of the Fermi level. The next two peaks at around 3.5 and 6.2
eV reflect the interband transitions from the occupied O 2p states and the
empty oxygen states which arise from the hybridization with Ir t2g and eg
states, respectively. We have found that the theory reproduces well the shape
and energy position of the low energy feature, but the second and the third
peaks are shifted towards smaller energy in comparison with the experimental
measurements.
