Calculating branching ratio and spin-orbit coupling from first-principles: A formalism and its application to iridates

Abstract

We present a simple technique to calculate spin-orbit coupling, $⟨\mathbf{L}\cdot \mathbf{S}⟩$, and branching ratio measured in x-ray absorption spectroscopy. Our method is for first-principles electronic structure calculation and its implementation is straightforward for any of standard formulations and codes. We applied this technique to several different large spin-orbit coupling iridates. The calculated $⟨\mathbf{L}\cdot \mathbf{S}⟩$ and branching ratio of a prototype $j_{\mathrm{eff}}$=1/2 Mott insulator, Sr${}_2$IrO${}_4$, are in good agreement with recent experimental data over the wide range of Rh-doping. Three different double perovskite iridates (namely, Sr${}_2$MgIrO${}_6$, Sr${}_2$ScIrO${}_6$, and Sr${}_2$TiIrO${}_6$) are also well described. This technique can serve as a promising tool for studying large spin-orbit coupling materials from first-principles and for understanding experiments.

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