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