Magnetic Dipolar Broadening in Fluorine-Based Solid-State ²²⁹Th Nuclear Clocks

Recent experimental demonstrations of laser excitation of the ²²⁹Th nuclear isomer transition have established the feasibility of nuclear optical clocks. Because the transition lies in the vacuum ultraviolet, transparent host materials containing fluorine have been considered for solid-state implementations. However, such materials present a significant challenge due to broadening from the dense bath of ¹⁹F nuclear spins. We analyze the impact of dipolar magnetic fields from fluorine nuclei on the Th clock transition, including static inhomogeneous broadening as well as dynamic contributions arising from spin fluctuations and phonon-mediated processes. In addition, we examine the role of nuclear quadrupolar interactions, which define the quantization axis and introduce further broadening through electric field gradient distributions. Using realistic crystal structures, we estimate broadening parameters for several fluoride-based host materials proposed for Th clocks. We also discuss possible mitigation strategies, including the use of oriented single crystals to reduce static dipolar broadening and symmetric excitation schemes addressing opposite Zeeman components to suppress systematic shifts. These results clarify fundamental limitations of fluorine-containing hosts and provide guidance for material selection and clock architecture in future solid-state nuclear clock efforts.