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Density Functional Theory Study of Th-doped LiCAF and LiSAF for Nuclear Clock Applications

Thorium-doped LiCaAlF$_6$ and LiSrAlF$_6$ (Th:LiCAF and Th:LiSAF) are promising crystals for a solid-state nuclear clock based on the 8 eV transition in $^{229}$Th; however, their complex crystal structures complicate understanding the atomic arrangement of the thorium defects. In this work, density functional theory simulations are employed to systematically investigate these systems, including temperature-dependent effects and environmental conditions of fluorine saturation and deficiency. We investigated 20 distinct charge compensation schemes for each material, revealing lower defect formation energies in Th:LiSAF than in Th:LiCAF. This suggests that the former may attain a higher concentration of thorium nuclei. Furthermore, we calculated the electric field gradient for the lowest energy structure per compensation pathway. Our investigation shows that results previously reported in the literature apply only to a subset of experimental conditions.