Muonium dynamics in transparent conducting oxides

The motional and electrical properties of positively charged muonium (Mu⁺)$({\mathrm{Mu}}^{+})$ centers in single crystal β-Ga₂O₃$\mathrm{\beta }\mathrm{-}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are investigated via zero field muon spin relaxation (ZF-MuSR). Below room temperature we find two distinct shallow muonium centers with ionization energies of 7 and 16 meV. Above room temperature, at least three different Mu⁺ signals are resolved; two of these are metastable while the third shows characteristics of a stable ground state. As the temperature is elevated, metastable centers undergo several transitions. We obtain the relevant barrier energies associated with these site-change transitions. By 700 K, most muons occupy the mobile ground state, and an activation energy of about 1.65 eV is inferred for Mu⁺ diffusion from the hop rates obtained for this state.