Diffusion, trapping, and relaxation of Mu+ and Mu- in heavily‐doped GaAs

The diamagnetic muonium states in heavily doped GaAs are investigated with a combination of transverse‐field and longitudinal‐field μSR techniques. In metallic n‐type GaAs, formation of Mu^- occurs because of the high Fermi energy. This analog of the hydride ion (H^-) is located in a T_Ga interstice where it is essentially immobile up to about 500 K. At higher temperatures, Mu_T acts as an electron–hole recombination center. In p‐type GaAs, Mu⁺ traps at two different sites, one at low temperatures and a second at higher temperatures after detrapping from the first. This revised version was published online in August 2006 with corrections to the Cover Date.     

Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonium centers in heavily n‐doped Si under illumination: Evidence for Mu–hole interaction

A small fraction of implanted muons exists as a paramagnetic state (presumably Mu_BC ⁰, muonium at the Si—Si bond center) in heavily Sb‐doped Si (n-type, [Sb]\ \simeq 10¹⁸\ cm^–3). The paramagnetic state is susceptible to illumination both at 10–20 K and 290 K, providing evidence that holes (minority carriers) play an important role in determining the dynamical properties of muonium centers, where change may occur via a process Mu_BC ⁰+ h⁺\to Mu_BC ⁺ followed by charge exchange reaction (or transition Mu⁺ _BC+ e⁻→ Mu⁰ _T). This revised version was published online in August 2006 with corrections to the Cover Date.     

Mu centers in crystalline Ge under illumination

A slow conversion to a diamagnetic state has been observed for muonium centers at the tetrahedral interstitial site (Mu⁰ _T) in dark Ge at low temperatures. While the conversion process is affected by illumination, no effect of illumination upon the initial (Mu⁰ _T) centers themselves was observed at 10 K. This is in marked contrast with the case of (Mu⁰ _T) centers in Si where strong interaction with photo‐induced carriers is observed, suggesting that the electronic level associated with (Mu⁰ _T) state in Ge is not located in the energy gap. This revised version was published online in August 2006 with corrections to the Cover Date.     

Opportunity for magnetic field spatial‐time correlation research using a μSR^2‐method

It is theoretically shown that in rare gases at P < /100 atm the external electric fields of the order of 100 V/cm could significantly change the value of electron density in the region of μ^- or μ⁺ stopping point and affect the muonic atoms formation in plasma‐chemical reactions. The kinetic model of processes which might explain the results of μSR‐experiments for μ^- in Ne and Ar both with and without external electric field is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Final states in Si and GaAs via RF μSR spectroscopy

The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu^* states at any temperature. However, our results on the diamagnetic final state (μ _f ⁺ ) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu^* and Mu. We observe a full μ _f ⁺ fraction at 317 K when the Mu relaxation rate is above 10 μs⁻¹. GaAs differs from the situation in Si in that we observed only a partial conversion of Mu^* and Mu to a μ⁺ final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively.     

Probing interaction of paramagnetic electron with conduction electrons in high Tc superconductor LaSrCuO by (μ-O) spin relaxation

The paramagnetic (μ^-O) state formed at the oxygen site in high T_c LaSrCuO was used to probe an interaction between the localized moment of the paramagnetic electron and the conduction electrons via zero field μ^- spin relaxation. The enhanced relaxation rates consistently observed in the superconducting state of various Sr concentrations are explained as an effect of spin‐pairing in the high T_c supercurrent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

Electric field gradients probed by μ+SR in Sc and \alpha\mbox-ScH_x solid solutions

In Sc and \alpha\mbox-ScH_x below 40 K two μ⁺ states are formed: a tunnelling state extending over two adjacent tetrahedral (T) interstices sharing one face in the ab‐plane of the hcp host lattice and a static μ⁺–Sc–H configuration analog to the T‐pair state formed by two H atoms across a Sc site along the crystalline c‐axis. This explains perfectly the high transverse‐field (TF) μSR measurements at low temperature and allows a qualitative understanding of the temperature dependence. The modelling of the low TF measurements requires in addition the consideration of the electric field gradient (EFG) components acting on the Sc nuclei near the μ⁺, i.e., of the radial EFG due to the μ⁺ and of the axially symmetric crystal field. The magnetic field dependence of the anisotropic μ⁺SR relaxation rate is strongly influenced by the H‐concentration in the solid solution system. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hyperfine interactions of muonium and hydrogen in semiconductors: Cluster calculations

The electronic structure of muonium (Mu) located at different interstitial sites of the silicon crystal is calculated by the complete neglect of differential overlap (CNDO) and intermediate neglect of differential overlap (INDO) methods. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “normal” (Mu′) and “anomalous” (Mu^*) muonium centers. It is shown that the most likely dynamic model for Mu′ is that in which neutral Mu diffuses rapidly in the silicon lattice, whereas for Mu^* it is the model wherein interstitial Mu is located at the bond-center site. A correlation is made between the characteristics of the hydrogen-bearing Si-AA9 center, recently observed by EPR in a silicon crystal, and those of Mu^*. The Si-AA9 center is shown to be a hydrogen-bearing paramagnetic analogue of the Mu^* center.     

Muon/Muonium in an Isotopically Pure 13C Diamond

A preliminary study of the diamagnetic (μ_d) and the paramagnetic (Mu _T ) states in a synthetic ¹³C diamond has been performed using the Transverse Field Muon Spin Rotation method. This system could be used to verify the quantum diffusion behaviour observed before, however, with a more reliable extraction of the hopping rate. The results were obtained in an applied magnetic field of 7.5 mT and at sample temperatures of 10 K, 100 K and 200 K. The prompt fraction, f, of the μ_d state remains constant at 22(5)% in the range 10–200 K; that of the Mu _T state increases from 53(10)% at 10 K to 78(10)% at 200 K. The fractions of the two states add to 100% at 200 K, suggesting non-population of the bond-centred state, Mu_BC, which is often observed in other diamond samples. The μ_d state has a spin relaxation rate of 0.20(5) μs⁻¹, in contrast to the zero value obtained in type II diamond samples. This indicates appreciable interaction of the μ_d state with the ¹³C atoms. The Mu _T state has a large spin relaxation rate ranging from 3.0(5) μs⁻¹ at 10 K to 7.0(5) μs⁻¹ at 200 K, consistent with values obtained in diamond samples with defects. This work is part of ongoing studies of muon/muonium-defect interactions in diamonds. This revised version was published online in September 2006 with corrections to the Cover Date.     

Time‐differential radio‐frequency muon spin resonance (TD‐RFμSR) technique at a pulsed muon beam

Longitudinal‐field μSR methods, e.g., radio‐frequency μ⁺ spin resonance (RFμSR), are well suited to investigate dynamic processes that destroy the phase coherence of the muon spin ensemble. Additional information on relaxation processes of the muon species under investigation is obtained from time‐differential (TD) data acquisition. In this paper we describe the set‐up of a TD‐RFμSR spectrometer installed at the ISIS pulsed muon facility at the Rutherford Appleton Laboratory (RAL, Chilton, UK). As an example, results of TD‐RFμSR measurements on muons in diamagnetic environment μ^d in a boron‐doped silicon sample under illumination at 55 K are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anomalous field dependence of muon Knight shift and line width in the singlet ground state compound PrCu2

We report on ZF and TF‐studies of PrCu₂ above the induced Jahn–Teller transition at 7.3 K. Generally a two‐component signal is found, one showing inhomogeneous the other one homogeneous, temperature dependent line broadening. In ZF the former component is well represented by a Gaussian Kubo–Toyabe function with \varDelta \simeq 6.5\,μs^-1 at 7.5 K, corresponding to a field width of 76 G. This is about 30 times larger than what is calculated to arise from the ¹⁴¹Pr‐nuclear dipole moments alone, pointing to strong hyperfine enhanced features. TF‐field scans at 12 K revealed that the enhancement is suppressed in external fields exceeding 1 kG. In parallel the Knight shift drops from very large values well above 10% at 100 G to shifts of the order of 1% above 1 kG. A scaling of the Knight shifts with the corresponding relaxation rates seems to imply that the strange field dependence below 1 kG is associated with the magnetic susceptibility of the muons’s nearest neighbour Pr³⁺‐ions, a result for which we have no explanation yet to offer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies of the positive muon behavior in solid H2 and D2

Using a pulsed muon beam, we have investigated the microscopic μ⁺ behavior in solid H₂ and D₂ down to 0.6 K by the μ⁺SR method. From the studies of μ⁺ spin relaxation phenomena in solid para‐ H₂ and ortho‐ D₂, we have found that μ⁺ forms three distinct microscopic states; H₂μ⁺( D₂μ⁺)(20\sim25\%), muonium (15\sim20\%) and μ⁺(\sim60\%). In H₂μ⁺, the μ⁺ spin is depolarized in solid para‐ H₂ and a local magnetic field B_loc=1\sim2 G is deduced from LF‐μ⁺SR measurements. The magnitude of B_loc is inconsistent with the magnetic dipolar field (\sim25 G) expected from the magnetic moments of two protons in the H₂μ⁺ molecule and suggests that the H₂μ⁺ molecule might be in the rotationally excited state. From LF‐μ⁺SR measurements, muonium and μ⁺ have been found to diffuse in solid o‐ D_2. The diffusion rate of muonium is two order of magnitude larger than that of μ⁺. This revised version was published online in August 2006 with corrections to the Cover Date.     

High‐pressure μSR studies of ferro‐ and antiferromagnetic metals

High‐pressure μSR experiments on ferromagnetic nickel and \alpha‐iron and antiferromagnetic chromium are reported. In Ni above 260 K B_Fermi was found to be proportional to the saturation magnetization, whereas at lower temperatures it is temperature independent apart from a small anomaly below 30 K which is presumably caused by a magnetoelastic interaction. There was no evidence for an occupation of metastable sites by the μ⁺ below the Curie temperature. By contrast, in \alpha‐Fe the temperature dependence of \curpartialB_μ/\curpartialp shows a structure which might be attributed to the occupation of excited muon states at elevated temperatures. High‐pressure zero‐field experiments on Cr performed in the temperature regime between 4.5 K and 8 K revealed a pressure dependence of B_μ as large as \curpartialB_μ/\curpartialp=-(89.15\pm 0.06)\times 10^-12 T/Pa. In terms of volume dependence a very large negative Grüneisen parameter \gamma =-27 was obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Low-field anomalous muonium depolarization in isotopically enriched germanium

The depolarization rate of anomalous muonium, Mu^*, in germanium isotopically enriched in⁷⁴Ge (I=0) was measured as a function of field. The concentration of⁷³Ge (I=9/2) was about 9 times less than natural abundance. The depolarization rate at 10 K in this isotopically enriched crystal for both lines of those Mu^* centers whose symmetry axes make an angle of 90° to the field is less than 1sec^–1 at all fields down to the lowest one measured, 14.5 gauss. This is in sharp contrast to the wide lines reported at low field in germanium having natural isotopic abundance. The spectrum of Mu^* in the isotopically enriched Ge crystal was also seen at zero field. These results confirm that the increased depolarization rate for Mu^* at low fields arises from unresolved nuclear hyperfine structure. The depolarization rates observed were consistent with an average hyperfine interaction with a single⁷³Ge nucleus of 2.5 MHz, a value requiring nearly 1% of the spin density to be on a typical atom.     

Interaction of Muons with H2/H3-Centres in Diamond

We report on transverse field muon spin rotation measurements on a nitrogen-rich type Ia diamond, both before and after the conversion of some of the aggregated nitrogen centres to nitrogen-vacancy complexes known as H2/H3-centres. The prompt fractions f and the spin relaxation rates λ were determined for the diamagnetic (μ_d) and the paramagnetic (Mu_T) states in the temperature range 10–300 K. The production of the nitrogen-vacancy complexes had little effect on the parameters of the Mu_T state for which f and λ remained unchanged at approximately 30% and 4 μs⁻¹, respectively. For the μ_d state, on the other hand, the formation of the H2/H3-centres resulted in an increase of the prompt fraction from 10(2)% to 20(3)%, and (for the first time) the spin relaxation rate showed a non-zero value of 0.020(3) μs⁻¹. These results show evidence of strong μ_d interactions with the nitrogen-vacancy complexes in diamond, and suggest a more complex structure for this state than a bare μ⁺. This revised version was published online in September 2006 with corrections to the Cover Date.     

Muon/muonium surface interactions

The interactions of muonium (μ ⁺ e ⁻, Mu) with the surfaces of fine silica powders have been extensively studied using zero, longitudinal and transverse field μSR techniques. These studies indicate diffusion and trapping behavior of the Mu atoms on the silica surface, which is strongly influenced by the surface hydroxyl (OH) concentration. Specifically, the presence of the surface OH groups is observed to inhibit the surface mobility of the Mu atoms at low temperatures. Information provided by zero and longitudinal field data suggest a random anisotropic distortion of the Mu hyperfine interaction (RAHD) as the principal relaxation mechanism. A recently developed RAHD spin relaxation theory is used to interpret these data. Additional investigations, using platinum loaded silica, have yielded the first observed surface reaction of Mu. Studies of the interactions of positive muons with surfaces have been also extended to single crystals, where low energy (<10 eV)μ ⁺ andMu ⁻ ions are observed to be reemitted from some materials (e.g., the <100> surface of lithium fluoride). Future applications of these emission phenomena toward the development of a slow^847-3 (or Mu⁻) beam are considered.     

Influence of the temperature and the ionisation potential on the hyperfine interaction of 111Cd ions in gaseous radioactive indium‐halides

The hyperfine interaction (HFI) of ¹¹¹Cd in different indium‐halides was studied by perturbed angular correlation (PAC). The ¹¹¹Cd ion arises from a ¹¹¹In by electron capture decay (EC) and joined Auger cascade. Coulomb fragmentation of the indium‐halide molecule produces the free excited ¹¹¹Cd ion. The nucleus decays via a γ–γ‐cascade which is perturbed by the HFI. Collisions of the ¹¹¹Cd ion with indium‐halide molecules can strongly change the perturbation. The perturbation was measured by the attenuation coefficient G₂₂(∞) and G₂₂(t). The molecular densities varied between 10¹⁴ and 10²⁰ cm⁻³. The present article shows the temperature dependence of the indium(III)‐halides and a fit for an empirical basic approach. The investigation of the InBr shows the independence of the attenuation coefficient from the temperature by indium(I)‐halides in contrast to the dependence of the indium(III)‐halides. This revised version was published online in July 2006 with corrections to the Cover Date.