  Based on the microscopic model including strong spin-orbit coupling, on-site
Coulomb and Hund's interactions, as well as crystal field effects, we have
investigated magnetic and optical properties of Sr2IrO4. Taking into account
all possible intermediate state multiplets generated by virtual hoppings of
electrons, we calculated the isotropic Heisenberg, pseudodipolar, and
Dzyaloshinsky-Moriya coupling constants, which describe the experiment quite
well. We have also evaluated the optical conductivity {\sigma}({\omega}) by
employing the exact diagonalization method on small clusters, and obtained two
peaks at \sim 0.5 and \sim 1.0 eV in agreement with experiment. The two peak
structure of {\sigma}({\omega}) arises from the unusual Fano-type overlap
between electron-hole continuum of the Jeff = 1/2 band and the intrasite
spin-orbit exciton observed recently in Sr2IrO4 by resonant x-ray scattering.
