Resonant X-ray scattering and the $j_{\mathrm{eff}}=1/2$ electronic ground state in iridate perovskites

The resonant X-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir$^{4+}$ at the L$_{2,3}$ edges relevant to spin-orbit Mott insulators A$_{n+1}$Ir$_{n}$O$_{3n+1}$ (A=Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a non-trivial dependence on the direction of the magnetic moment, $\boldsymbol\mu$. Crucially, we show that for $\boldsymbol\mu$ in the \emph{ab}-plane, RXMS at the L$_2$ edge is zero \emph{irrespective} of the tetragonal crystal-field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally being zero at L$_2$ when $\boldsymbol\mu$ is perpendicular to the \emph{ab}-plane. Our results provide important insights into the interpretation of X-ray data from the iridates, including that a $j_{\mathrm{eff}}=1/2$ ground state cannot be assigned on the basis of L$_2$/L$_3$ intensity ratio alone.