Defect assignment of the clock site in $^{229}\text{Th:CaF}_2$

Abstract

The performance of solid-state $^{229}\text{Th}$ nuclear clocks depends sensitively on the microscopic environment of the thorium nucleus in the host crystal. Here we reassess the dominant quadrupole-split thorium site in $^{229}\text{Th:CaF}_2$, which has been assigned to a thorium dimer in recent spectroscopic work. Thermodynamic estimates, density functional theory calculations, and electric-field-gradient comparisons instead favor an isolated $\text{Th}^{4+}$ substitution on a $\text{Ca}^{2+}$ site charge-compensated by two nearby fluorine interstitials in a relaxed $90^\circ$ motif. The same calculation identifies a higher-energy mixed-shell interstitial motif as a plausible minor site. The clock-active quadrupole-split site is therefore controlled by local fluoride compensation rather than unavoidable thorium aggregation. This defect assignment also has implications for achievable linewidths and provides a microscopic basis for reducing broadening in solid-state nuclear clocks.