<i>Ab initio</i> X-ray near-edge spectroscopy of sodium-based multi-alkali antimonides

Multi-alkali antimonides (MAAs) are promising materials for vacuum electron sources. While sodium-based MAAs have demonstrated superior characteristics for ultrabright electron sources, their synthesis remains challenging, often resulting in mixed stoichiometries and polycrystalline domains. To address this complexity and guide the characterization of experimentally grown photocathodes, we present a comprehensive theoretical study of the X-ray near-edge spectroscopy (XANES) of four ternary MAAs: cubic Na₂KSb and hexagonal NaK₂Sb, representing the experimentally known phase of each stoichiometry, as well as hexagonal Na₂KSb and cubic NaK₂Sb, two computationally predicted polymorphs. Employing state-of-the-art <i>ab initio</i> methods based on all-electron density-functional theory and the solution of the Bethe-Salpeter equation (BSE), we compute and analyze the XANES spectra at the sodium and potassium K-edges, potassium L_2,3-edge, and antimony K- and L₂-edges. Our analysis reveals distinct spectral fingerprints for the experimentally known phases, cubic Na₂KSb and hexagonal NaK₂Sb, particularly at the sodium K-edge and potassium L_2,3-edge, providing useful indications for their identification in complex samples. By comparing BSE spectra against their counterparts obtained in the independent-particle approximation, we address the role of excitonic effects, highlighting their influence on the near-edge features, especially for excitations from the alkali metals. Our findings offer a useful theoretical benchmark for the characterization and diagnostics of sodium-based MAA photocathodes, complementing experiments on resolved polymorphs and providing the spectral fingerprints of computationally predicted phases that could emerge in polycrystalline samples.