Th${}^{4+}$ ion cluster structures and electric field gradients in ${}^{229}$Th:CaF${}_2$

Abstract

The low-energy nuclear isomeric transition of ${}^{229}$Th is a promising frequency reference for a solid-state nuclear optical clock. Wide-band-gap fluoride crystals such as CaF${}_2$ offer transparent hosts for embedding Th nuclei at high density. Substitution of Th${}^{4+}$ for Ca${}^{2+}$ requires charge compensation, linking the local defect structure to nuclear quadrupole splitting. We use first-principles calculations to examine neutral Th dimers compensated by four interstitial F ions (${\mathrm{F}}_i^{-}$). Screening different compensation geometries by their relative formation energies identifies a family of low-energy configurations with closely similar local structures. These configurations share large electric field gradients and small asymmetry parameters, consistent with the experimental high-EFG site 3. Their calculated quadrupole splittings are further compared with the measured C13 spectra. Together, the energetic and spectroscopic results support ${\mathrm{F}}_i^{-}$-compensated Th dimers as candidate microscopic structures for site 3 in Th:CaF${}_2$.