Excited configurations of hydrogen in the BaTiO3−xHx perovskite lattice associated with hydrogen exchange and transport

Excited configurations of hydrogen in the oxyhydride ${\mathrm{BaTiO}}_{3\ensuremath{-}x}{\mathrm{H}}_{x}$ ($x=0.1\char21{}0.5$), which are considered to be involved in its hydrogen transport and exchange processes, were investigated by positive muon spin relaxation spectroscopy using muonium (Mu) as a pseudoisotope of hydrogen. Muons implanted into the ${\mathrm{BaTiO}}_{3\ensuremath{-}x}{\mathrm{H}}_{x}$ perovskite lattice were mainly found in two qualitatively different metastable states. One was assigned to a highly mobile interstitial protonic state, which is commonly observed in perovskite oxides. The other was found to form an entangled two spin-$\frac{1}{2}$ system with the nuclear spin of an ${\mathrm{H}}^{\ensuremath{-}}$ ion at the anion site. The structure of the (H,Mu) complex agrees well with that of a neutralized center containing two ${\mathrm{H}}^{\ensuremath{-}}$ ions at a doubly charged oxygen vacancy, which was predicted to form in the ${\mathrm{SrTiO}}_{3\ensuremath{-}\ensuremath{\delta}}$ perovskite lattice by a computational study [Y. Iwazaki et al., APL Mater. 2, 012103 (2014)]. Above 100 K, interstitial ${\mathrm{Mu}}^{+}$ diffusion and retrapping to a deep defect were observed, which could be a rate-limiting step of macroscopic Mu/H transport in the ${\mathrm{BaTiO}}_{3\ensuremath{-}x}{\mathrm{H}}_{x}$ lattice.