Recently, a new class of 5d Mott insulator Sr₂IrO₄ has been discovered. In this system, the strong spin-orbit (SO) coupling as well as the Coulomb interaction is crucial for stabilizing the insulating state. Its 5d⁵ shell splits into half filled J_eff=1/2 and fully-occupied J_eff=3/2 state due to strong SO coupling. The narrow half filled J_eff=1/2 band tends to undergo a Mott transition under relatively small Coulomb repulsion. Thus, it is referred to as J_eff=1/2 Mott insulator.[1]

Because of strong SO coupling, Sr₂IrO₄ shows intriguing physical properties which do not appear in conventional 3d Mott insulators. The resonant inelastic scattering (RIXS) experiments have observed higher energy broad peak at ~0.5-0.8 eV, termed SO exciton[2]. The optical conductivity s(w) of Sr₂IrO₄ shows two peaks at ~0.5 eV and ~1.0 eV[1]. Simple interpretation based on picture of single-electron density of state insists that the first peak was assigned to the transition from occupied to unoccupied Jeff=1/2 band, while the second peak to that from occupied Jeff=3/2 to unoccupied Jeff=1/2 band. However, there has been no theoretical calculation of s(w) taking into account the many-electron multiplet structure of excited states.

We have calculated the magnetic coupling, optical conductivity, and RIXS spectra in by exact diagonalization of a microscopic model on small clusters, fully incorporating the multiplet structure of Ir ions. Magnetic couplings are consistent with the available data. Calculated RIXS spectra reproduce the SO exciton mode. We also found that two peak structure of s(w) arises from the unusual Fano-type overlap between the electron-hole continuum of the J_eff=1/2 band and the intrasite SO exciton[3].

[1] B. J. Kim et. al., Phys. Rev. Lett. 101, 076402 (2008)

[2] J. Kim et. al., Phys. Rev. Lett. 108, 177003 (2012)

[3] B. H. Kim, G. Khaliullin, and B. I. Min, Phys Rev Lett, 109, 167205 (2012)