Muonium, a positive muon and an electron, is often used as an experimentally accessible substitute for hydrogen in materials research. In semiconductors and insulators, a large amount of information on the hydrogen behavior is deduced from this analogy; however, it is seldom demonstrated that this procedure is justified. We show here, via a comparison of the hyperfine interactions, that in ${\mathrm{TiO}}_2$ muonium and hydrogen form the same configuration with the same basic electronic structure. A detailed description of the bonding characteristics of the muon to the ${\mathrm{Ti}}^{3+}$ polaron is presented. The special role of muon motion within the so-called oxygen channel in the rutile structure, which occurs at a lower temperature than for hydrogen, is emphasized.

The incorporation of interstitial hydrogen in yttria was studied by means of ab initio calculations based on density-functional theory (DFT) and muonium spin polarization spectroscopy ($\mu$SR). The density-functional calculations, based on a semilocal functional within the GGA-PBE and a hybrid functional, uncovered multiple geometrical configurations for the neutral, H${}^0$, and the negatively charged, H${}^{-}$, states of hydrogen, thus demonstrating the existence of metastable minimum-energy sites. It was observed that the low-energy configurations for H${}^0$ and H${}^{-}$ are similar: they prefer to relax in deep, interstitial sites, whereas the equilibrium configurations for the positively charged state, H${}^{+}$, were bond-type configurations with the hydrogen forming a covalent O-H bond with an O anion. For all neutral and negative configurations, localized defect levels were found inside the gap. Overall, the results for the formation energies obtained by the two different functionals are qualitatively similar; an amphoteric behavior was found for hydrogen after considering the lowest-energy structures for each charge state. The calculated acceptor transition level, obtained by the hybrid functional and seen near midgap, is consistent with $\mu$SR data from literature. The results are consistent with the present $\mu$SR data, where the observed diamagnetic signal is attributed to a donor-like muonium at the oxygen-bonded configurations and the paramagnetic signal to an acceptor-like deep muonium at the interstitial sites.

In muon-spin-rotation experiments, positive muons are implanted in the material and come to rest in the unrelaxed host lattice. The formation of the final configuration requires a lattice relaxation which does not occur instantly. The present paper is concerned with the transition from the initial stopping state to the final muon configuration. We identify the often observed fast relaxing signal in muon experiments (e.g., in several oxides studied recently) with the transition state in this conversion process. This state is paramagnetic with a small hyperfine interaction (in the order of MHz) which fluctuates and averages to almost zero. Because of its apparent diamagnetic frequency behavior, the fast signal was in the past assigned to ${\mathrm{Mu}}^{+}$ or ${\mathrm{Mu}}^{-}$. We present evidence that this state is actually paramagnetic. The model presented in this paper is of importance for the interpretation of past and future $\mu \mathrm{SR}$ measurements.

The electronic structure of hydrogen impurity in ${\mathrm{Lu}}_2{\mathrm{O}}_3$ was studied by first-principles calculations and muonium spectroscopy. The computational scheme was based on two methods which are well suited to treat defect calculations in $f$-electron systems: first, a semilocal functional of conventional density-functional theory (DFT) and secondly a $\text{DFT}+U$ approach which accounts for the on-site correlation of the $4f$ electrons via an effective Hubbard-type interaction. Three different types of stable configurations were found for hydrogen depending upon its charge state. In its negatively charged and neutral states, hydrogen favors interstitial configurations residing either at the unoccupied sites of the oxygen sublattice or at the empty cube centers surrounded by the lanthanide ions. In contrast, the positively charged state stabilized only as a bond configuration, where hydrogen binds to oxygen ions. Overall, the results between the two methods agree in the ordering of the formation energies of the different impurity configurations, though within $\text{DFT}+U$ the charge-transition (electrical) levels are found at Fermi-level positions with higher energies. Both methods predict that hydrogen is an amphoteric defect in ${\mathrm{Lu}}_2{\mathrm{O}}_3$ if the lowest-energy configurations are used to obtain the charge-transition, thermodynamic levels. The calculations of hyperfine constants for the neutral interstitial configurations show a predominantly isotropic hyperfine interaction with two distinct values of 926 MHz and 1061 MHz for the Fermi-contact term originating from the two corresponding interstitial positions of hydrogen in the lattice. These high values are consistent with the muonium spectroscopy measurements which also reveal a strongly isotropic hyperfine signature for the neutral muonium fraction with a magnitude slightly larger (1130 MHz) from the ab initio results (after scaling with the magnetic moments of the respective nuclei).

We present a systematic study of isolated hydrogen in diverse forms of ${\mathrm{ZrO}}_2$ (zirconia), both undoped and stabilized in the cubic phase by additions of transition-metal oxides $({\mathrm{Y}}_2{\mathrm{O}}_3,{\mathrm{Sc}}_2{\mathrm{O}}_3$, MgO, CaO). Hydrogen is modeled by using muonium as a pseudoisotope in muon-spin spectroscopy experiments. The muon study is also supplemented with first-principles calculations of the hydrogen states in scandia-stabilized zirconia by conventional density-functional theory (DFT) as well as a hybrid-functional approach which admixes a portion of exact exchange to the semilocal DFT exchange. The experimentally observable metastable states accessible by means of the muon implantation allowed us to probe two distinct hydrogen configurations predicted theoretically: an oxygen-bound configuration and a quasiatomic interstitial one with a large isotropic hyperfine constant. The neutral-oxygen-bound configuration is characterized by an electron spreading over the neighboring zirconium cations, forming a polaronic state with a vanishingly small hyperfine interaction at the muon. The atom-like interstitial muonium is observed also in all samples but with different fractions. The hyperfine interaction is isotropic in calcia-doped zirconia $[A_{\mathrm{iso}}=3.02\left(8\right)$ GHz], but slightly anisotropic in the nanograin yttria-doped zirconia $[A_{\mathrm{iso}}=2.1\left(1\right)$ GHz, $D=0.13\left(2\right)$ GHz] probably due to muons stopping close to the interface regions between the nanograins in the latter case.

We present a systematic study of isolated hydrogen in $\alpha$-TeO${}_2$ (paratellurite) by means of muon-spin spectroscopy measurements complemented by ab initio calculations based on density-functional theory (DFT). The observable metastable states accessible by means of the muon implantation allowed us to probe both the donor and the acceptor configurations of hydrogen, as well as to follow their dynamics. A shallow donor state with an ionization energy of 6 meV as well as a deep acceptor state are proposed, together with their atomic-level configurations and associated formation energies obtained from the DFT calculations. The latter show a tendency of interstitial hydrogen to bind strongly to bridging oxygen ions but also to coexist at sites deeper in the interior of the Te–O–Te rings with a more atomiclike character and a defect level in the gap. Atomlike interstitial muonium was observed; it has a hyperfine interaction of about 3.5 GHz. Charge and site changes with temperature are discussed.