Paramagnetic Muonium Research Articles

Sapphire α−Al2O3 puzzle: Joint μSR and density functional theory study

Sapphire $(\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3})$ has been investigated by the muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ method in several experiments in the past. The main $\ensuremath{\mu}\mathrm{SR}$ component is a diamagnetic-like signal with a fast relaxation. Because of this diamagnetic-like behavior, the signal was assigned to either positively charged muonium $({\mathrm{Mu}}^{+})$ or negatively charged muonium $({\mathrm{Mu}}^{\ensuremath{-}})$, but neither of the two assignments was satisfactory (the so-called ``sapphire puzzle''). We have proposed that the signal is due to a weakly paramagnetic muonium configuration (transition state) which is formed during the reaction of muonium with the host lattice. In the present paper, we report new experimental data on ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and discuss these and earlier data in the ${\mathrm{Mu}}^{\ensuremath{-}}$ and in the transition state model. Calculations based on density functional theory were also performed with detailed findings on the energetics of the different muonium configurations and their migration energies. We conclude that the transition state model is more plausible than the ${\mathrm{Mu}}^{\ensuremath{-}}$ model, but the ${\mathrm{Mu}}^{\ensuremath{-}}$ interpretation cannot be excluded completely. In addition, the evidence is presented that the bare muon performs local motion but no long-range diffusion below room temperature in the microsecond time range.

Muon Interaction with Negative- U and High-Spin-State Defects: Differentiating Between C and Si Vacancies in 4H - SiC

Low-energy muon-spin-rotation spectroscopy (LE-$\ensuremath{\mu}\mathrm{SR}$) is employed to study silicon and carbon vacancies in proton-irradiated $4H$-$\mathrm{Si}\mathrm{C}$. We show that the implanted muon is quickly attracted to the negative $\mathrm{Si}$ vacancy (${V}_{\mathrm{Si}}$), where it forms a paramagnetic muonium (${\mathrm{Mu}}^{0}$) state, resulting in a reduction of the diamagnetic fraction. In samples with predominantly $\mathrm{C}$ vacancies (${V}_{\mathrm{C}}$), on the other hand, the formation of ${\mathrm{Mu}}^{0}$ is very short lived and the muon quickly captures a second electron to form a diamagnetic ${\mathrm{Mu}}^{\ensuremath{-}}$ state. The results are corroborated by density-functional calculations, where significant differences in the relaxation mechanism of the nearest-neighbor dangling bonds of the vacancies are discussed. We propose that the LE-$\ensuremath{\mu}\mathrm{SR}$ technique is capable of differentiating between high-spin and negative-$U$ behavior in semiconducting materials. Finally, our findings emphasize the large potential of LE-$\ensuremath{\mu}\mathrm{SR}$ to probe near-surface semiconductor defects, a capability that is crucial for further development of many electronic and quantum technology applications.

Electron polarization and formation probability of bound muonium in CdS and Si

Positive muons implanted in CdS and Si create electrically active defect centers that mimic and model the contrasting donor states of interstitial hydrogen in these two materials---a shallow donor in CdS and a deep donor in Si. In the present experiment the polarization of the muonium electron and the formation probability of these states are investigated. We find that the polarization is rather weak and strongly deviates from the polarization expected for a paramagnetic center at low temperatures and high magnetic fields. We assume that the polarization is built up in a precursor stage and is not completed at the time of conversion to the observed final state. The polarization depends on the purity of the samples and is larger for samples with a higher concentration of defects. In addition, the branching ratio between paramagnetic muonium and diamagnetic muon depends on the purity of the samples and on the strength of the magnetic field. These different findings are interpreted in the following model: after implantation, the muon comes to rest at an interstitial site in the unrelaxed lattice. This site is unstable and relaxes to the final configuration. The total energy along the transition path and the strength of the single electron binding to the positive muon during the transformation determine the parameters of the experiment.

Mechanisms of electron polarization of shallow muonium in CdTe and CdS

The low temperature electron polarization of the shallow muonium state in CdTe and CdS has been measured. We find a strong deviation of the polarization from that expected for paramagnetic muonium in thermodynamical equilibrium. In addition, in CdTe the observed polarization changes with the age of the sample and even an inversion of the polarization is observed upon annealing. An explanation of these findings is given in terms of two different routes for the formation of shallow muonium, i.e., formation by capture of an electron from the conduction band and formation via conversion from deep to shallow muonium. We conclude that the electron polarization is not due to the paramagnetism of the final shallow state but to the polarization buildup in the preceding stage immediately following muon implantation.

Muon spin relaxation in synthetic type IIa diamond grown by high-pressure and high-temperature (HPHT) synthesis

Abstract The behaviour of hydrogen in the low strain pure diamond material synthesized by the high pressure high temperature (HPHT) route has been studied using the longitudinal field muon spin relaxation technique ( LF - μ SR ) . This study almost completes a survey of muonium in diamond with a range of defect compositions. The result may provide information on the so-called missing fraction (MF) observed in many previous studies of muons implanted into semiconductors. The experimental results showed the existence of a diamagnetic muon state ( μ + ) , two paramagnetic muonium states (tetrahedral interstitial ( Mu T 0 ) and bond-centred ( Mu BC 0 ) ), and MF formed by positive muons implanted into the sample. The absolute fractions of μ + , Mu T 0 , Mu BC 0 and MF in the sample were 4%, 54%, 30% and 12%, respectively.

Studies of grey and white tin, - and -Sn

The behaviour of monatomic hydrogen defect centres is modelled using implanted positive muons in both allotropes of elemental tin. A new search for paramagnetic muonium is made in α-Sn, the semiconducting allotrope with the diamond structure. No deep state is found, nor any enhanced Korringa relaxation that would suggest localized moment formation on interstitial protons in this intriguing material. In relation to muonium in the other Group-IV semiconductors, tantalizing indications of shallow state formation below 30 K suggest that a deep-to-shallow transition may be responsible. The diamagnetic state remains static to 200 K and may be tentatively identified as the bond-centred positive ion, by comparison with recent data for silicon. This behaviour contrasts with the abrupt onset of mobility at 50 K for muons in β-Sn, the normal metallic allotrope with tetragonal structure, for which a more conventional interstitial site has lately been determined. Mobility studies are admittedly difficult in the presence of such weak nuclear magnetism but a discrepancy arises between reported migration barriers in white tin.

Delayed electron capture and formation in ZnSe

Abstract We have investigated a single crystal of the wide bandgap II–VI semiconductor ZnSe. The sample was highly resistive due to heavy compensation of this n-type semiconductor. In low transverse fields, clear signs of conversion from a paramagnetic to a diamagnetic fraction are observed, at about 60 K. The data are interpreted as delayed electron capture by paramagnetic muonium, forming the negatively charged state Mu - . The implications with respect to the electrical activity of muonium, and by analogy hydrogen, in this semiconductor are analyzed.

Muonium in boron

Abstract A paramagnetic muonium centre is detected in elemental boron at cryogenic temperatures and characterized by hyperfine decoupling in longitudinal magnetic fields. The contact term is only 0.52 GHz or 12% of the free muonium value. An effective ionization energy of 0.1 eV is estimated from polarization transfer to the muon Larmor precession signal in transverse field, beginning around 100 K and complete by room temperature. AIMPRO density functional calculations identify candidate sites for monatomic hydrogen defect centres in the rather complex boron lattice and predict the local distribution of unpaired electron spin density. One of these, bridging between two boron atoms in the inter-icosahedral space, provides an adequate match to the muonium hyperfine parameters, as well as its relatively weak binding energy. Negative-U behaviour is predicted, implying that H 0 centres are not thermodynamically stable. Identification of the high diamagnetic muon fraction found at all temperatures is also discussed.

Dynamics and Supramolecular Organization of the 1D Spin Transition Polymeric Chain Compound [Fe(NH2trz)3](NO3)2. Muon Spin Relaxation

The thermal spin transition that occurs in the polymeric chain compound [Fe(NH(2)trz)3](NO3)2 above room temperature has been investigated by zero-field muon spin relaxation (microSR) over the temperature range approximately 8-402 K. The depolarization curves are best described by a Lorentzian and a Gaussian line that represent fast and slow components, respectively. The spin transition is associated with a hysteresis loop of width DeltaT = 34 K (T1/2 upward arrow = 346 K and T1/2 downward arrow = 312 K) that has been delineated by the temperature variation of the initial asymmetry parameter, in good agreement with previously published magnetic measurements. Zero-field and applied field (20-2000 Oe) microSR measurements show the presence of diamagnetic muon species and paramagnetic muonium radical species (A = 753 +/- 77 MHz) over the entire temperature range. Fast dynamics have been revealed in the high-spin state of [Fe(NH(2)trz)3](NO3)2 with the presence of a Gaussian relaxation mode that is mostly due to the dipolar interaction with static nuclear moments. This situation, where the muonium radicals are totally decoupled and not able to sense paramagnetic fluctuations, implies that the high-spin dynamics fall outside the muon time scale. Insights to the origin of the cooperative effects associated with the spin transition of [Fe(NH(2)trz)3](NO3)2 through muon implantation are presented.

Study of muonium precession signals in optically excited silicon

Many of the experiments on muonium interacting with photo-excited carriers are conducted at pulsed muon beam facilities and typically concentrate on studying the muon polarization in a longitudinal magnetic field. In this paper, we discuss some of the early progress we have recently made in carrying out optical excitation experiments on semiconductors at a continuous beam facility, i.e. TRIUMF. Here, additional information is potentially available because the muon precession signatures associated with the various paramagnetic and diamagnetic muonium signals can be monitored directly. Some results in high-resistivity Si are presented.

Oxide muonics: I. Modelling the electrical activity of hydrogen in semiconductingoxides

A shallow-to-deep instability of hydrogen defect centres in narrow-gap oxidesemiconductors is revealed by a study of the electronic structure and electrical activity oftheir muonium counterparts, a methodology that we term ‘muonics’. In CdO,Ag2O and Cu2O, paramagnetic muonium centres show varying degrees of delocalization of the singlyoccupied orbital, their hyperfine constants spanning 4 orders of magnitude. PbO andRuO2, on the other hand, show only electronically diamagnetic muon states, mimickingthose of interstitial protons. Muonium in CdO shows shallow-donor behaviour,dissociating between 50 and 150 K; the effective ionization energy of 0.1 eV is atsome variance with the effective-mass model but illustrates the possibility ofhydrogen doping, inducing n-type conductivity as in the wider-gap oxide, ZnO. ForAg2O, the principal donor level is deeper (0.25 eV) but ionization is nonetheless complete byroom temperature. Striking examples of level-crossing and RF resonance spectroscopyreveal a more complex interplay of several metastable states in this case. InCu2O, muonium has quasi-atomic character and is stable to 600 K, although the electron orbitalis substantially more delocalized than in the trapped-atom states known in certainwide-gap dielectric oxides. Its eventual disappearance towards 900 K, with an effectiveionization energy of 1 eV, defines an electrically active level near mid-gap in thismaterial.

Structures and hyperfine properties of ferrocene muonium adducts

The existence of multiple paramagnetic muonium adducts to ferrocene was first reported by Jayasooriya et al. in 1997, based on the presence of more than one component in the muon's spin relaxation (U.A. Jayasooriya, J.A. Stride, G.M. Aston, Appl. Magn. Reson. 13 (1997) 165.) Interpretation of the data was based on a model involving three paramagnetic species, assigned to two cyclopentadienyl ring adducts and a radical in which Mu binds directly to the metal. In this work, these species are studied by density functional methods. All three adducts are found to be stable in the staggered (antiprismatic) ring geometry, with the cyclopentadienyl adduct favored energetically by ∼ 80 kJ mol - 1 . No evidence is found for an agostic species of the type known for protonated ferrocenes. Computed values of A iso show strong method-dependence attributed to spin polarization and spin contamination effects.

Muonium as a shallow center in GaN.

A paramagnetic muonium (Mu) state with an extremely small hyperfine parameter was observed for the first time in single-crystalline GaN below 25 K. It has a highly anisotropic hyperfine structure with axial symmetry along the <0001> direction, suggesting that it is located either at a nitrogen-antibonding or a bond-centered site oriented parallel to the c axis. Its small ionization energy (<or=14 meV) and small hyperfine parameter (approximately 10(-4) times the vacuum value) indicate that muonium in one of its possible sites produces a shallow state, raising the possibility that the analogous hydrogen center could be a source of n-type conductivity in as-grown GaN.

Muon spin relaxation in CVD polycrystalline diamond film

The behavior of hydrogen in chemical vapor deposition (CVD) polycrystalline diamond film characterized by Raman spectroscopy, cathode luminescence and electron spin resonance measurements was studied using the longitudinal magnetic field muon spin relaxation technique. The experimental results showed the existence of a diamagnetic muon state (μ +) and two paramagnetic muonium (Mu: μ +e −) states (tetrahedral interstitial (Mu T) and bond-centered (Mu BC)) formed by positive muons implanted into the sample. Moreover, unknown states, generally called missing fraction (MF), were observed. This is the first time in this research that absolute fractions of Mu BC and MF in CVD polycrystalline diamond film have been determined. The absolute fractions of μ +, Mu T, Mu BC and MF in the present sample were 50, 7, 19 and 24%, respectively. The absolute fraction of Mu T for the present sample with crystallite size of 20–70 μm is comparable to that published for natural IIa single crystal diamond and CVD polycrystalline diamond film with average crystallite size of 100 μm. However, the MF of the present sample was much higher than that of IIa single crystal diamond.

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.

Muon Korringa relaxation

Significant muon spin-lattice relaxation is found in a number of non-magnetic semimetals and metals. Measured in longitudinal magnetic field, the relaxation rate is independent of field up to several kilogauss and generally increases monotonically with temperature. This suggests a form of Korringa relaxation, originating in the hyperfine interaction between the implanted muons and the conduction electrons. Bearing in mind that NMR data on Korringa relaxation refers chiefly to the host nuclei, the muon offers a probe of conduction–electron encounter at an interstitial site, linking the topic to the nature of defect screening in metals, to relaxation by spin-density fluctuations in magnetic materials and to spin- and charge-exchange on paramagnetic muonium centres in semiconductors. Data are presented for C (graphite), Bi, Pb and Cd and compared with the Korringa predictions using known values of the muon Knight shift. Control experiments are described on Zn and Cu, both pure and deliberately doped with magnetic impurity. For graphite, an interpretation is given in terms of charge-exchange on a molecular radical formed by the chemical reaction of interstitial muonium.

Radio-frequency μSR investigations on paramagnetic muonium centres in crystalline silicon

Radio frequency (RF) muon-spin resonance (RFμSR) experiments on the paramagnetic muonium centres Mu T (muonium located at tetrahedral sites) and Mu BC (bond-centred muonium), present in crystalline silicon, were carried out at applied magnetic fields B 0 up to 6 mT and a constant irradiated frequency ν RF of approximately 80 MHz. In the magnetic-field dependence of the RF asymmetry a RF, i.e. the RF induced change of the muon-decay asymmetry, two resonances were observed, one corresponding to Mu T, the other to Mu BC. Systematic RFμSR measurements were performed on intrinsic silicon single crystals grown by the Czochralski method (oxygen concentration 2×10 17 cm −3 ) and the float-zone method (oxygen concentration <10 15 cm −3 ). No Mu T signal has been observed in transverse field (TF) μSR, below T=50 K in the Czochralski-grown sample whereas a Mu T signal was found with RFμSR. This RFμSR result proves that the Mu T species in this sample undergo dynamic processes, in which presumably oxygen is involved.

Muon spin relaxation studies of interstitial and molecular motion

The unusual methods of preparation and analysis of spin polarization in μSR spectroscopy, which exploit the unique properties of the positive muon, are introduced in this article. Following a summary overview of applications, particular attention is paid to the problem of spin-lattice relaxation for a muon experiencing a hyperfine interaction with a single unpaired electron. The specific cases considered are the interstitial diffusion of muonium—the 1-electron atom which may be considered as a light isotope of hydrogen—and the molecular dynamics of organic radicals labelled by muonium. Rate equations for the evolution of population in the hyperfine-coupled spin states are solved numerically for various relaxation mechanisms. The formalism is equally valid for conventional ESR studies of paramagnetic states but is pursued specifically to simulate T 1-relaxation in μSR. The simulations are compared with literature data. Also treated is the case of intermittent hyperfine coupling, appropriate to electron capture and loss in semiconductors or soliton motion in polymers; for this, a Monte Carlo approach is used to simulate the muon response. (For low-dimensional motion, the relaxation function is not exponential, so that a unique value of T 1 cannot be defined.) Finally, a proposal is made to implement muon- T 1 ρ measurements in the rotating frame; this is designed for the selective study of electronically diamagnetic muonium states (i.e., those without hyperfine coupling) in the presence of a paramagnetic muonium or radical fraction.

Muon state dynamics in germanium and silicon

The dynamics of the various muon states (paramagnetic states muonium Mu and anomalous muonium Mu*, diamagnetic states μd) were studied by means of radio‐frequency μ+ spin resonance (RFμSR), longitudinal field‐quenching (LFQ), and transverse μ+ spin rotation (TFμSR) in an undoped high‐purity and a gallium‐doped germanium single crystal in the temperature range 3.5–320 K.

Level-crossing resonance spectra for bond-centred muonium in silicon

Abstract Previous avoided level-crossing experiments have revealed the microscopic structure of the paramagnetic anomalous muonium state in silicon: in addition to the axially symmetric hyperfine interaction along a (1, 1, 1) axis, distinct orientation-dependent superhyperfine interactions with first and second nearest neighbour 29Si nuclei have been observed. Here we report a theoretical study of the influence of further distant 29Si nuclei. Their contribution to the field dependence of the time-integrated longitudinal polarization function is investigated. The appearance of additional resonances is discussed and their locations as a function of field strength are calculated analytically by perturbation theory as well as numerically.