Muon sites in PbF2 and YF3 : Decohering environments and the role of anion Frenkel defects

Muons implanted into ionic fluorides often lead to a so-called F--$\ensuremath{\mu}$--F state, in which the time evolution of the muon spin contains information about the geometry and nature of the muon site. Nuclei more distant from the muon than the two nearest-neighbor fluorine ions result in decoherence of the F--$\ensuremath{\mu}$--F system, and this can yield additional quantitative information about the state of the muon. We demonstrate how this idea can be applied to the determination of muon sites within the ionic fluorides $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{PbF}}₂$ and ${\mathrm{YF}}₃$, which contain fluoride ions in different crystallographic environments. Our results can be used to distinguish between different crystal phases and provide strong evidence for the existence of anion Frenkel defects in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{PbF}}₂$.