Influence of multiplet structure on photoemission spectra of spin-orbit driven Mott insulators: application to \(\bf{Sr_2IrO_4}\)

Most of the low-energy effective descriptions of spin-orbit driven Mott insulators consider spin orbit coupling (SOC) as a second order perturbation to electron-electron interactions. However, when SOC is comparable to anisotropic Hund's coupling, such as in Ir, validity of this formally weak-SOC approach is not a priori known. Depending on the relative strength of SOC and anisotropic Hund's coupling, different descriptions of the multiplet structure should be employed in the weak and strong SOC limits, \textit{viz.} \textit{LS} and \textit{jj} coupling schemes, respectively. We investigate the implications of both the coupling schemes on the low-energy effective \(t-J\) model and calculate the angle resolved photoemission (ARPES) spectra using self-consistent Born approximation. In particular, we obtain the ARPES spectra of quasi-two-dimensional square-lattice iridate \({\rm Sr_2IrO_4}\) in both weak and strong SOC limits. The differences in the limiting cases are understood in terms of the composition and relative energy splittings of the multiplet structure. Our results indicate that the LS coupling scheme yields better agreement with the experiment, thus providing an indirect evidence for the validity of LS coupling scheme for iridates. We also discuss the implications for other metal ions with strong SOC.