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

TL;DR

This study uses a single-ion model to analyze resonant X-ray scattering in iridate perovskites, revealing complex dependencies on magnetic moment orientation and challenging the use of L2/L3 intensity ratios to identify the $j_{eff}=1/2$ ground state.

Contribution

It provides a detailed theoretical analysis of RXMS and RIXS in iridates, showing their dependence on magnetic moment direction and questioning previous methods for identifying the $j_{eff}=1/2$ state.

Findings

RXMS at L2 edge is zero when magnetic moment is in the ab-plane.

Spin-flip RIXS is zero at L2 when magnetic moment is perpendicular to the ab-plane.

L2/L3 intensity ratio alone cannot confirm the $j_{eff}=1/2$ ground state.

Abstract

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.