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 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 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. Muonium (Mu) is a pseudoisotope of hydrogen in which the proton is replaced by a positive muon (μ + ), with a factor of 9 lighter mass. Muon spin spectroscopy (μSR) uses muons implanted with 100% spin polarization and offers a very sensitive method to study the properties of this isolated pseudohydrogen in solids [1,2]. It is usually assumed that information obtained from μSR can be transferred with appropriate modifications to H. However, overlapping experiments to support this assumption are scarce. A particularly relevant case is the doping character of H in semiconductors and oxides [3][4][5][6], where practically all calculations refer to the electronic structure of H whereas most experimental information comes from μSR [7][8][9][10][11][12][13]. Overlapping data exist only for ZnO where proton-ENDOR (electron-nuclear double resonance) data [14] can be compared directly with μSR results [15][16][17][18]. A number of properties (e.g., ionization energy) are indeed similar for the two species. However, the measured hyperfine interaction (hfi), scaled with the magnetic moments, differs by almost a factor of 10. This raised the question of whether the same configuration is measured, or if the H center may involve an additional defect [19,20].Here, we report a case where the same configuration can be established for H and Mu. We compare the hfi of the μSR experiment with the proton-ENDOR result, both for rutile TiO 2 . The H center in TiO 2 was extensively studied by Brant et al.[21] using electron paramagnetic resonance (EPR) and ENDOR, who found that the electron is located at the Ti ion reducing it from Ti 4+ to Ti 3+ . H is bound to one of the six O atoms surrounding Ti and the magnetic interaction between the proton and the electron is mainly dipolar. This specific hfi permits a sensitive comparison of the two experiments. We have observed a dramatic change of the μSR spectra with increasing temperature and a complete disappearance of the hyperfine splitting at 10 K. We show that this is due to rapid jumps of the muon between neighboring bonding positions to O atoms around Ti 3+ . The very strong angle dependence of the dipolar interaction and the averaging over values in different * ruivilao@fis.uc.pt positions lead to the reduction and final disappearance of the hfi...

We present a systematic study of isolated hydrogen in diverse forms of ZrO 2 (zirconia), both undoped and stabilized in the cubic phase by additions of transition-metal oxides (Y 2 O 3 , Sc 2 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 iso = 3.02(8) GHz], but slightly anisotropic in the nanograin yttria-doped zirconia [A iso = 2.1(1) GHz, D = 0.13(2) GHz] probably due to muons stopping close to the interface regions between the nanograins in the latter case.

The electronic structure of hydrogen impurity in Lu 2 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 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 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 Lu 2 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).

In implantation experiments, the implanted particle is shot with a certain energy into the material and comes to rest at a site which may not correspond to the final position. The rearrangements of the surrounding atoms to accommodate the particle, i.e., the reaction with the host atoms may require some time and lead to delayed formation of the final states. In the case of the implantation of positive muons, this rearrangement process can be followed on a timescale of nanoseconds to microseconds. A delay is expected if an energy barrier inhibits the prompt reaction. We note that the barrier height may change during the rearrangement of the lattice, thus giving rise to a two-dimensional potential profile for the conversion process. The barrier model describes the reaction path of the muon in analogy to the passage over a mountain with a saddle point. The passing over the saddle point corresponds to the lowest energy trajectory. As an example, we discuss the application of the barrier model to solid Lu 2 O 3 .

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