We study the elementary excitations in 5d transition metal oxide Sr2IrO4 by calculating the particle-hole Green's function within the random phase approximation on an antiferromagnetic ground state in the two-dimensional multi-orbital Hubbard model. The obtained magnetic excitations of bound states show a characteristic dispersion in consistent with the experiments. In addition, two new types of excitations are found due to the interplay between spin-orbit interaction and Hund's coupling: a magnetic excitation as a bound state, which has energy gap at the Γ point, and an exciton as a resonant mode in the continuum of electron-hole pair creation.Electron correlation effects on transition metals and their compounds have attracted much interest since the discovery of high-T C cuprate superconductors. In the 3d transition metal ions, the spin orbit interaction (SOI) plays a minor role on the electronic structures, since it is usually much smaller than the on-site Coulomb interaction and the crystal field splitting. In the 5d transition metal ions, however, the SOI is one order of magnitude larger than that of the 3d systems while the Coulomb interaction becomes weaker due to the extended nature of the 5d electrons. Accordingly, the interplay between the electron correlation and the SOI is expected to bring about new intriguing phenomena. For this reason, much attention has recently been paid to Ir oxides such as Sr 2 IrO 4 1-8 and Na 2 IrO 3 . [9][10][11][12] In particular, we focus on Sr 2 IrO 4 , which consists of two-dimensional IrO 2 layers showing structural similarity to the parent compound of high-T C cuprate La 2 CuO 4 , and exhibits a canted antiferromagnetic (AFM) order below 230 K. 1-3 The energy of the e g orbitals is estimated about 2 eV higher than that of the t 2g orbitals due to the large crystal field. Five 5d electrons are occupied per Ir atom, and one hole is sitting in the t 2g orbitals. Since the hole states have an effective orbital angular momentum ℓ equal to −1, the lowest-energy states on the localized electron picture are doubly degenerate with the effective total angular momentum j eff = 1 2 under the SOI: 13,14 |φ ± = 1 √ 3 (|yz, ∓σ ± i|zx, ∓σ ± |xy, ±σ ), where yz, zx, and xy designate t 2g orbitals, and spin component σ =↑. By introducing the isospin operators acting on these states, the system is mapped onto the Heisenberg model, from which an insulating AFM phase is derived, consistent with the experiments. 1-3 Furthermore, it has been pointed out that the small anisotropic terms emerge in addition to the isotropic term, when Hund's coupling is taken into account in the second-order process in the strong coupling expansion. 15,16 Recently, resonant inelastic x-ray scattering (RIXS) experiment at the Ir L edge has detected the excitation spectra, 17 whose low energy part follows the dispersion relation similar to the spin wave in the Heisenberg model on a square lattice. A notable point is that the excitation energy at the M point is nearly half of that at the X point, in contrast to t...