Comment on “Role of the transition state in muon implantation” and “Thermal spike in muon implantation”

Abstract

Vil\~ao et al. (Phys. Rev. B 96, 195205 (2017) and Phys. Rev. B 99, 195206 (2019)) have reported positive muon spin rotation/relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) experiments on various insulating metal oxides, solar cell materials, and alloyed Ge. They note the presence of a separate early component in the ${\ensuremath{\mu}}^{+}$ polarization time dependence which relaxes more rapidly than the longer lived signal and also exhibits (in ${\mathrm{ZrO}}_{2}$:Mg) a slightly increased frequency at low temperature in transverse field. They interpret this early component as a weakly bound ``transition state'' of the neutral muonium ($\mathrm{Mu}={\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$) atom formed epithermally by the incoming 4-MeV muon, in which the hyperfine interaction between the muon and the electron is ``motionally narrowed'' by rapid spin exchange, resulting in a ``diamagneticlike'' Larmor precession signal. This ``diamagneticlike transition state'' supposedly takes microseconds to relax into its final ground state due to the reluctance of the surrounding lattice to deform around the Mu atom. However, numerous earlier experiments (including those in electric fields) on various liquids and solids ranging from wide-gap insulators to narrow-gap semiconductors have convincingly shown that Mu formation proceeds through capture of radiolysis electrons by thermalized muons---a process crucially dependent on the electron mobility rather than epithermal dynamics. Therefore, we question the validity of the interpretation by Vil\~ao et al. and raise some important issues that need clarification.