Excited configurations of hydrogen in the ${\mathrm{BaTiO}}_{3-x}{\mathrm{H}}_x$ perovskite lattice associated with hydrogen exchange and transport

Excited configurations of hydrogen in the oxyhydride ${\mathrm{BaTiO}}_{3-x}{\mathrm{H}}_x$ ($x=0.1–0.5$), 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 ${\mathrm{BaTiO}}_{3-x}{\mathrm{H}}_x$ 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 ${\mathrm{H}}^{-}$ ion at the anion site. The structure of the (H,Mu) complex agrees well with that of a neutralized center containing two ${\mathrm{H}}^{-}$ ions at a doubly charged oxygen vacancy, which was predicted to form in the ${\mathrm{SrTiO}}_{3-\delta }$ 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 ${\mathrm{BaTiO}}_{3-x}{\mathrm{H}}_x$ lattice.

Figure 1

ZF-${\mu }^{+}\mathrm{SR}$ spectra of (a) $x=0.5$, (b) $x=0.3$, (c) $x=0.2$, and (d) $x=0.1$ samples at 15 K. The solid curves show the best fits to Eq. (3). Partial contribution from the 2S component is displayed by the dashed curves. A LF-${\mu }^{+}\mathrm{SR}$ spectrum of the $x=0.5$ sample in a LF of 50 Oe was also shown in (a) together with an exponential fitting curve.

Figure 2

$x$ dependences of (a) $f_d$ and $d$, (b) $p_{2\mathrm{S}}$, (c) $\lambda$, and (d) $\mathrm{\Delta }$ at 15 K in ZF, and the most probable atomic configurations associated with (e) the 2S component and (f) the Gaussian component.

Figure 3

ZF-${\mu }^{+}\mathrm{SR}$ spectra of ${\mathrm{BaTiO}}_{2.5}{\mathrm{H}}_{0.5}$ ($x=0.5$) at 30, 150, and 295 K. The solid curves show the best fits to Eq. (3).

Figure 4

Temperature dependences of (a) $f_d$ and $d$, (b) $p_{2\mathrm{S}}$, (c) $\lambda$, and (d) $\mathrm{\Delta }$ in ZF for ${\mathrm{BaTiO}}_{2.5}{\mathrm{H}}_{0.5}$. The solid curve in (d) is the best fit to the simplified two-state model (see text).