Spin-orbit coupling in first-principles optical and X-ray spectroscopy spectra under WDM conditions

The prediction and analysis of optical and X-Ray spectra of materials under WDM conditions is of great scientific interest. The Kubo-Greenwood (KG) formula associated with the Projector Augmented-Wave (PAW) approach [1] has proven its efficiency to compute these spectra and has been implemented in a few DFT codes, including the ABINIT code [2]. One important aspect when treating optical and X-Ray spectroscopy, especially for heavier elements, is the spin-orbit coupling (SOC).

We present some improvements in the implementation of the calculation of optical and X-Ray spectra. Spinors are now treated explicitly; SOC is added in the velocity operator and is taken into account in the dipole matrix elements in the KG formula. We are now able to predict the spin-orbit splitting and the ratio of the X-ray absorption edges correctly.
We present two applications in the WDM regime. We show that the inclusion of SOC allows for the correct description of the splitting and branching ratio of the L2/L3 edge in copper. We also show that SOC has a small and visible -- but still not sufficient -- effect on the optical properties of gold. We explore other options to improve the optical spectra of gold.

[1] Mazevet, Torrent, Recoules, Jollet. High Energy Density Physics, 6, 84 (2010)
[2] www.abinit.org