  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.
