Density functional theory study of Th-doped LiCAF and LiSAF for nuclear clock applications

Thorium-doped <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>LiCaAlF</a:mi> <a:mn>6</a:mn> </a:msub> </a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>LiSrAlF</b:mi> <b:mn>6</b:mn> </b:msub> </b:math> (Th:LiCAF and Th:LiSAF) are promising crystals for a solid-state nuclear clock based on the 8 eV transition in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mmultiscripts> <c:mi>Th</c:mi> <c:mprescripts/> <c:none/> <c:mn>229</c:mn> </c:mmultiscripts> </c:math> ; 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. By examining 20 distinct charge compensation schemes for each material, we found that experimental conditions have a significant impact on the energies of charge compensation pathways. This has important implications for selectively favoring defect geometries with desirable properties, such as enhanced quenching rates, to improve the nuclear clock performance. In addition, we found lower defect formation energies in Th:LiSAF than in Th:LiCAF, suggesting that the former may attain a higher concentration of thorium nuclei. Furthermore, we calculated the electric field gradient for the lowest-energy structure associated with each compensation scheme, enabling the experimental identification of some crystal defect structures through nuclear quadrupole splittings.