Neutral Muonium Research Articles

Charge Asymmetry of Muons Generated in a Muon Generator from Ultra-Dense Hydrogen D(0) and p(0)

Laser-induced nuclear reactions in ultra-dense hydrogen H(0) (review in Physica Scripta 2019) create mesons (kaons and pions). These mesons decay mainly to muons. The muons created are useful (patented source) for the muon-induced fusion process. The sign of the muons from the source depends on the initial baryons used. With D(0) (ultra-dense deuterium) the source produces mainly positive muons and with p(0) (ultra-dense protium) the source produces mainly negative muons. Negative muons are required for muon-induced fusion. This charge asymmetry was reported earlier, and has now been confirmed by experiments with a coil current transformer as the beam detector. The current coil detector would give no signal from the muons if charge symmetry existed. The charge asymmetry could indicate unknown processes, for example, caused by the different annihilation processes in D(0) and p(0). The conclusions of a new analysis of the results are presented here. Using D(0) in the muon source, the asymmetry is likely due to the capture of µ- in D atoms and D2 molecules. This leads to emission of excess µ+ from D(0). With p(0) in the muon source, the capture rate of µ- is lower than in D(0). The emitted number of µ+ will be decreased by the reaction between µ+ and the surrounding abundant electrons, forming neutral muonium particles. This effect decreases the amount of emitted µ+ for both p(0) and D(0), and it is proposed to be the main reason for a larger fraction of emitted µ- in the case of p(0). Thus, there is no dominant emission of negative muons which would violate charge conservation.

Comment on “Role of the transition state in muon implantation” and “Thermal spike in muon implantation”

Vil\~ao et al. (Phys. Rev. B 96, 195205 (2017) and Phys. Rev. B 99, 195206 (2019)) have reported positive muon spin rotation/relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) experiments on various insulating metal oxides, solar cell materials, and alloyed Ge. They note the presence of a separate early component in the ${\ensuremath{\mu}}^{+}$ polarization time dependence which relaxes more rapidly than the longer lived signal and also exhibits (in ${\mathrm{ZrO}}_{2}$:Mg) a slightly increased frequency at low temperature in transverse field. They interpret this early component as a weakly bound ``transition state'' of the neutral muonium ($\mathrm{Mu}={\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$) atom formed epithermally by the incoming 4-MeV muon, in which the hyperfine interaction between the muon and the electron is ``motionally narrowed'' by rapid spin exchange, resulting in a ``diamagneticlike'' Larmor precession signal. This ``diamagneticlike transition state'' supposedly takes microseconds to relax into its final ground state due to the reluctance of the surrounding lattice to deform around the Mu atom. However, numerous earlier experiments (including those in electric fields) on various liquids and solids ranging from wide-gap insulators to narrow-gap semiconductors have convincingly shown that Mu formation proceeds through capture of radiolysis electrons by thermalized muons---a process crucially dependent on the electron mobility rather than epithermal dynamics. Therefore, we question the validity of the interpretation by Vil\~ao et al. and raise some important issues that need clarification.

Electronic structure of interstitial hydrogen in lutetium oxide fromDFT+Ucalculations and comparison study withμSRspectroscopy

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).

Muonium transitions in Ge-rich SiGe alloys

We discuss charge-state and site-change transitions of muonium (Mu) in bulk Czochralski-grown Si1−xGex alloys studied via longitudinal field muon spin relaxation (LF-μSR). A useful application of the muon spin research technique utilizes the similarities of neutral muonium (Mu0=μ+e−) to the hydrogen atom to provide an experimentally accessible analog to hydrogen. This contribution focuses primarily on three Ge-rich samples (x=0.94, 0.91 and 0.81) as well as a general discussion of the compositional trends of Mu chemical states and associated transition dynamics. These LF-μSR results, in conjunction with prior muon spin research studies, allow an extensive description of Mu defect chemistry in Si1−xGex as part of a larger project that has focused on the compositional trends in Mu hyperfine frequencies as well as the acceptor and donor energies.

Hyperfine spectroscopy and characterization of muonium in ZnGeP2

In this contribution, we report the initial observation of neutral muonium defect centers in ZnGeP2. The spin-precession frequencies in a 4.0 T field yield a zero-temperature hyperfine constant of ~1965 MHz for the promptly formed Mu0 state. Subsequently, we performed T1−1 longitudinal depolarization measurements in low magnetic fields. Decoupling curves show a different anisotropic Mu0 with A2=3185 MHz and D=374 MHz, where D is the dipolar contribution. The relaxation rates suggest rapid diffusion of Mu0, most likely via quantum tunneling below 80 K and by thermally activated hops above 100 K. We have determined the ionization energy to be roughly 200 meV. We present our preliminary evaluation of the motion or site transition dynamics in addition to hyperfine characterization of the neutral muonium centers observed in ZnGeP2.

RF- in electric fields studies of GaP

Abstract We report on combined RF- μ SR and electric fields (EF) μ SR measurements in semi-insulating GaP. At low temperature the capture of excess carriers by a neutral muonium ( Mu = μ + + e - ) center is suggested to be a dominant process in muonium charge dynamics. The charged muonium fraction ( Mu - or Mu + ) formed on the microsecond time-scale is increased with lowering the temperature. Contrary to the usually observed scenario, at T 40 K an EF prevents formation of the final charged state.

Muonium transitions in 4H silicon carbide

Preliminary low-field data on the diamagnetic muon spin rotation signal in 4H-SiC are presented. The initial results on all three electrical types of 4H-SiC are compared with those for the 6H polytype. Analysis of amplitude transitions at low temperatures in n- and p-type samples indicates carrier capture. At temperatures above 600 K, an increase in diamagnetic amplitude and an associated dip in the phase indicate a slowly formed state in the p-type material. We discuss possible identification of transitions evident from temperature dependent diamagnetic amplitudes and correlations with neutral muonium centers.

Diffusion and conversion dynamics for neutral muonium in aluminum nitride

Muon spin depolarization rates and hyperfine decoupling curves imply the existence of a neutral muonium center to high temperatures in AlN, providing an experimental model for interstitial atomic hydrogen. This center has a hyperfine interaction close to that of the free atom, but with a small temperature-dependent dipolar contribution indicating weak anisotropy. We discuss the site assignment and present results on the diffusion of these centers in AlN and associated conversion rates obtained from the depolarization data. Low-temperature motion is due to tunneling while thermally activated processes dominate at high temperatures. Diffusion-limited conversion out of the mobile atomic state is observed in both regimes.

Muonium diffusion dynamics in mercury oxide

The diffusion dynamics of the neutral muonium state found in HgO is addressed in this work. We propose a hopping model for the diffusion, and use it to analyse time-domain μSR data. It is found that the diffusion is an incoherent quantum process, with an activation energy of 5.2(2) meV. The analysis also points to the anti-bonding site as the best-suited candidate for the muon's localisation.

Anisotropic muonium centers in aluminum nitride

An atomic-like neutral muonium center with a small anisotropy is inferred from hyperfine decoupling curves and longitudinal relaxation data on AlN. The isotropic contribution of A = 4422 MHz , 99% of the full vacuum value, is accompanied by a weak dipolar term with D = 144 MHz as average values extracted from complete decoupling curves at a few temperatures. Simulations assuming the four nitrogen antibonding sites well reproduce the decoupling data. The hyperfine constants are consistent with those previously obtained from fitting temperature-dependent longitudinal relaxation rates to a simple model for Mu 0 motion.

Muonium states in II–VI zinc chalcogenide semiconductors

A systematic experimental study of muonium states in the binary compounds ZnSe, ZnS and ZnTe is presented. Deep muonium states are observed in ZnSe and ZnS but not in ZnTe. In ZnTe, only the diamagnetic signal is seen. The temperature dependence of the muonium and muon fractions is measured in the three materials by muon spin rotation and, for ZnTe, also by RF-μSR. In none of the three compounds any indication of the neutral donor state, known from ZnO, CdS and others, is found. We conclude that in the Zn chalcogenides the neutral (interstitial) muonium configuration is more stable than the neutral (anion bonded) shallow donor configuration. The significance of the results is discussed with respect to the behaviour of hydrogen.

Hyperfine spectroscopy of muonium in 4H and 6H silicon carbide

The hyperfine spectroscopy of neutral muonium impurity centers has been investigated for the two common hexagonal structures of SiC. Paramagnetic spin-precession frequencies obtained in a field of $6\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ applied parallel to the $c$-axis identify two atomiclike ${\mathrm{Mu}}^{0}$ centers in 4H-SiC and a total of $4\phantom{\rule{0.3em}{0ex}}{\mathrm{Mu}}^{0}$ centers in 6H-SiC. Hyperfine constants fall between those for the ``normal'' isotropic ${\mathrm{Mu}}^{0}$ centers in Si and diamond, and temperature dependences are well characterized by interaction with long-wavelength phonons having an effective Debye temperature near $800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. When suitably scaled by the ratio of nuclear moments, these results should apply to the analogous hydrogen impurities.

Frequency shifts and local spin susceptibility of muonium in heavily-doped Si and GaAs

We report high transverse field μSR measurements in heavily doped p-type Si as well as p-type and n-type GaAs. In all these samples, the precession frequencies due to diamagnetic Mu + and Mu − are within ≈10 ppm of the Larmor frequency of the bare muon. In contrast to heavily doped n-type Si, no metastable neutral muonium centers are observed.

Fastelectron spin exchange of anisotropic muonium

Muon spin dynamics of anisotropic Mu undergoing fast electronspin flip collisions with paramagnetic species has beeninvestigated theoretically, where the tensor nature ofanisotropic hyperfine interaction is fully taken into account.In the presence of fast electron spin exchange, the muon spin inMu behaves as if the muon were a free positive muon. It iscrucial to understand the true nature of the muon environment tointerpret experimental data correctly. It is shown that the muonspin relaxation rate and the precession frequency in such amuonium system mimicking diamagnetic species can be expressedentirely in terms of the quantities which appear in theHamiltonian. The orientation and field dependence of therelaxation rate and of the precession frequency can be used todistinguish a neutral muonium species undergoing rapid electronspin flip from a free positive muon. It has been shown that evenat zero field one can observe a finite single precessionfrequency which depends sensitively on Mu orientation.

The neutralfraction of muonium in silicon at high temperatures

Muon spin-rotation measurements on silicon above room temperatureshow the onset of a substantial paramagnetic shift from the muonLarmor frequency. The inferred fraction of the time spent asneutral paramagnetic muonium is close to unity above 600 K, sothe capture rate of conduction electrons greatly exceeds theeffective ionization rate. These findings are consistent with theconfiguration-coordinate model for the interplay between site andcharge state, in which a site change is the bottleneck impeding electronloss. Difficulty is found, however, in obtaining parameters whichalso account for the available data on muon spin relaxation.Extensions of the model are suggested with the aim of determiningthe site-change energy for neutral muonium between the bond-centredand cage-centred sites - an elusive parameter necessary fordetermining whether or not interstitial muonium or hydrogen atomsconstitute negative-U centres in silicon.

Electron transport to positive centers in GaAs

The origin of neutral muonium defect centers in semi-insulating GaAs has been studied using muon spin rotation/relaxation techniques employing alternating electric fields. This technique prevents the accumulation of near-surface charges which may screen the external field. Suppression of the bond-centered muonium signal with electric field suggests that muonium formation proceeds via transport of excess electrons from the ionization track to the muon. The characteristic field of about 5 kV/cm may correspond to an electric field induced ionization of the muon donor impurity center.

Thermionic emission of hydrogen isotopes (Mu, H, D and T) from W and interpretation of a role of the hot W as an atomic hydrogen source

Resonant ionization was applied to learn about the production mechanism of thermal neutral hydrogen isotopes including muonium (Mu; μ +e − ) from a hot tungsten surface as reaction products with pulsed 500 MeV protons. The activation energy E a obtained in the temperature dependence of production of neutral muonium (1.72 (5) eV) as well as that of T atom (1.89 (1) eV), is consistent with the emission of the atoms directly from bulk sites in the solid rather than from the surface for which one should expect E a≈3 eV. Since hydrogen molecules are easily dissociated into hydrogen atoms interacting with a surface of the hot tungsten, even residual H 2 in the ultra high vacuum chamber of 3×10 −10 mbar at 1200 K was found to be easily detected and extracted by this method. From the results obtained through the temperature and pressure dependence measurements for D 2 and H 2, we propose a view of the role of hot W as a catalyzer to dissociate H 2 molecules and producing hydrogen atoms. After dissociation on the surface, the hydrogen atoms are dissolved into the bulk solid, and are thermionically emitted from the bulk to the vacuum at high temperatures.

Muon sites and diffusion in lithium oxide

Muon spin relaxation measurements have been performed on the alkali metal oxides and in order to model the behaviour of hydrogen impurities in these materials. Lithium oxide has been suggested as a suitable blanket material for fusion reactions, hence the need to understand the location and dynamics of ions in the crystalline lattice. This oxide becomes a fast ion conductor at high temperatures and our experiments also provide information on the ion dynamics. Muon implantation into these oxides at low temperatures creates mainly neutral muonium (the analogue of the hydrogen atom) with a smaller fraction (%) of positive muons at interstitial sites closely associated with ions. At higher temperatures (T > 100 K) the proportion of formed increases, and there is an increased tendency for trapping at substitutional lattice sites. A sharp decrease in relaxation rate was observed in at temperatures above 250 K and from this temperature dependence we calculate the activation energy for muon hopping relative to the ions, which are also mobile, to be approximately 90 meV.

Muonium Formation via Electron Transport in Silicon

We report muon spin rotation measurements in $n$-type silicon from 10 to 310 K in electric fields up to 5 kV/cm. These experiments reveal the nature of the partition of neutral muonium centers into normal muonium $({\mathrm{Mu}}_{T}^{0})$ and anomalous muonium $({\mathrm{Mu}}_{\mathrm{BC}}^{0})$: Formation of ${\mathrm{Mu}}_{T}^{0}$ is consistent with epithermal processes prior to thermalization, while ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ is formed via electron transport to a thermalized positive muon. The spatial distribution of the excess electrons created in the ${\ensuremath{\mu}}^{+}$ ionization track is shown to be anisotropic with respect to the muon.

Muonium dynamics in doped Si above room temperature studied by longitudinal field — μSR

We report longitudinal fieldμSR 1/T1 measurements in Si from room temperature to 850 K. The data in pure Si and Si∶B (p-type) can be explained in a two-state model where muonium cycles between its positive and neutral charge states. Within this model, the average muon-electron hyperfine parameter in the neutral state is consistent with muonium at the tetrahedral interstitial site, indicating that at the highest temperatures measured, neutral muonium spends a significant amount of time away from the bond centered site, the calculated potential minimum. Although this is also true for Si∶P (n-type) at high temperatures, the data in the region between 300–450 K indicates that at least one other state is involved in the dynamics.