从第一性原理计算分支比和自旋-轨道耦合：一种形式及其在铱酸盐中的应用
Calculating branching ratio and spin-orbit coupling from first-principles: A formalism and its application to iridates
摘要：
我们提出了一个简单的技术来计算自旋轨道耦合，$\langle {\bf L}\cdot{\bf S} \rangle$，和分支比在X射线吸收光谱测量。我们的方法是第一性原理电子结构计算和它的实施是直接的任何标准配方和代码。我们将这种技术应用于几种不同的大自旋轨道耦合的虹彩。计算的原型$j_{\rm eff}$ =1/2莫特绝缘体Sr $_2$ IrO $_4$的$\langle{ {\bf L}\cdot{\bf S}} \rangle$和分支比在很宽的Rh掺杂范围内与最近的实验数据吻合得很好。三种不同的双钙钛矿铱酸盐（即Sr $_2$ MgIrO $_6$、Sr $_2$ ScIrO $_6$和Sr $_2$ TiIrO $_6$）也被很好地描述。这种技术可以作为一个有前途的工具，研究大自旋轨道耦合材料的第一性原理和理解实验。
英文摘要：
We present a simple technique to calculate spin-orbit coupling, $\langle {\bf L}\cdot{\bf S} \rangle$, 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 $\langle{ {\bf L}\cdot{\bf S}} \rangle$ and branching ratio of a prototype $j_{\rm eff}$=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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