Spin relaxation studies of the muonium substituted ethyl radical in the gas phase

This short communication draws attention to the power of μSR and related measurements in providing an unusually complete characterisation of muonium substituted organic radicals in the gas phase. Spectroscopic information is available from muon spin rotation and muon level crossing resonance, giving all the nuclear hyperfine coupling constants, just as in the liquid phase. In addition, measurements of the relaxation time of the muon Zeeman energy become possible; these are potentially informative on the molecular collision dynamics. Demonstration results are presented in summary for the muonium substituted ethyl radical, ĊH₂CH₂Mu, in ethene gas.     

Muon-spin-rotation study of muon polarization losses in plastic scintillators and quartz

Muon polarization losses in plastic scintillators of two types and in fused quartz have been studied by the μSR method. The muon and muonium spin precession spectra have been measured on the μSR setup placed at the output of the muon channel of the Gatchina synchrocyclotron. It has been shown that a significant fraction of stopped muons participate in the formation of the muonium. As a result, these muons lose their polarization completely. The magnitude of muon depolarization depends considerably on the type of plastic. It has been found that the muon spin precession frequency in fused quartz in an external magnetic field (F _{Q, μ} = 0.116 ± 0.002 MHz) is shifted with respect to that in plastic scintillators (F _{1, μ} = 0.101 ± 0.005 MHz and F _{2, μ} = 0.101 ± 0.002 MHz).     

Radio-frequency muon spin resonance (RFμSR) experiments on condensed matter

In this paper we present an overview of the radio-frequency muon spin resonance (RFμSR) technique, an analogue to continuous-wave NMR, and an introduction to time-integral (TI) and time-differential (TD) RFμSR on muons in diamagnetic or in paramagnetic environments. The general form of the resonance line for TI-RFμSR as well as the expression for the time-dependence of the longitudinal muon spin polarization at resonance are given. Since RFμSR does not require phase coherence of the muon spin ensemble, this technique allows us to investigate muon species that are generated by transitions from, or in the course of reactions of, a precursor muon species even if in transverse-field (TF) μSR measurements the signal is lost due to dephasing. This ability of RFμSR is clearly demonstrated by measurements on doped Si. In this example, at low temperatures, a very pronounced signal from a muon species in diamagnetic environment has been found in RFμSR measurements, whereas in TFμSR experiments only a very small signal from muons in diamagnetic environment could be detected and a large fraction of the implanted muons escaped detection. These findings could be interpreted in terms of the delayed formation of a diamagnetic muonium-dopant complex, and, due to the large diamagnetic RFμSR signal, the RFμSR technique is a unique tool to study how the variation of parameters and experimental conditions such as illumination affects formation and behavior of these complexes. First results obtained on illuminated boron doped Si are reported. However, as illustrated by the example of experiments on the muonated radical in solid C₆₀, results from conventional TI-RFμSR cannot always be interpreted unambiguously since different parameters, namely the fraction of muons forming the investigated muon species, the longitudinal and the transverse relaxation rates, have similar effects on height and shape of the RFμSR resonance line. These ambiguities, however, may be resolved by collecting time-differential data. With this extension RFμSR becomes a very powerful complementary method to TFμSR in the studies of dynamic effects.     

Location of muonium and hydrogen in C60 fullerene and associated electronic structure and hyperfine properties

The unrestricted Hartree-Fock (UHF) procedure is used to investigate the locations, associated electronic structures and hyperfine interactions for muonium and hydrogen in C₆₀ fullerene. Our results indicate that from total energy considerations, in keeping with earlier investigations, the exohedral model has the lowest energy. However, the energies of the endohedral model involving the muonium (hydrogen) inside the fullerene and bonded to one of the carbon atoms, and of the muon at the center are found to be almost equal, contrary to earlier results. The hyperfine interaction constant for the endohedral site is in good agreement with that required to explain the lower observed muon spin-rotation (SR) frequency in the C₆₀-muonium system. The same appears to be the case for the exohedral model. However, there seems to be some uncertainty about the theoretical result in the latter case due to significant admixtures of higher spin states in the UHF wave-function. Additionally, in solid fullerene, the calculated location of the muonium for the exohedral model is such that it could be bonded to two fullerene molecules and therefore a muonium attached to a simple fullerene may not be representative of the exohedral state. This feature as well as the difficulty for the exohedral model of explaining the observed equality of the correlation times for relaxation effects associated with both SR and¹³C relaxation times in nuclear magnetic resonance (NMR) experiments suggests that the endohedral model for muonium cannot at present be ruled out as a viable model in favor of the exohedral model. Possible avenues for future investigations to resolve some of the problems for both exohedral and endohedral models are discussed. Results obtained for muonium at the center of fullerene are presented and compared to the features of the observed high frequency SR signal, and possible improvements in theory are discussed.     

Structures and isotope effects of fullerene hydrides

A summary account is given of various aspects of the structure and spin density distribution for the different isotopomers of C₆₀X (X=H, Mu) and for the different isomers of C₇₀Mu. The rigidity of the C₆₀X structure is exploited in describing the origin of the zero point hyperfine isotope effect.Ab initio Hartree-Fock calculations suggest that the deformation to the C₆₀ cage is highly localised and emphasizes the alkene nature of C₆₀. Addition of muonium to C₇₀ results in 5 possible structures for C₇₀MU, 3 with alkene and 2 with arene character.     

Positive muon spectroscopy of R2Fe14B

Muon spin rotation (μSR) experiments were performed on polycrystalline samples of R₂Fe₁₄B in zero applied field. In all samples a single spin precession frequency was observed. In Nd₂Fe₁₄B and Ho₂Fe₁₄B pronounced anomalies showed up in the temperature dependence of the μSR frequencies at the spin reorientation temperatures of 150 K and 60 K, respectively. Our data can be explained with the assumption that only thec-axis component of the magnetization is sampled by the muon. We find a strong dependence of the local field on the magnetic moment of the rare earth ion. This is in accordance with calculations of the dipolar fields at the assumed muon stopping site.     

Electron transport in solids and liquids

We review our recent experimental studies of the excess electron states in insulating solids and liquids. We use a muon spin relaxation technique to explore the phenomenon of delayed muonium formation: excess electrons liberated in the μ⁺ ionization track converge upon the positive muons and form Mu (μ⁺e^?) atoms in which the μ⁺ polarization is partially lost. The spatial distribution of such electrons with respect to the muon is shown to be highly anisotropic: the μ⁺ thermalizes well “downstream” from the center of the electron distribution. Measurements in electric fields up to 30 kV/cm allow one to estimate the characteristic muon-electron distance in different insulators: the results range from 10^?6 to 10^?4 cm. Such a microscopic length scale enables the electron to sometimes spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. This circumstance illustrates the potential of μ⁺SR techniques in studies of electron transport in matter. The muonium formation process in condensed matter is shown to depend critically upon whether the excess electron forms a polaron or remains in a delocalized state. Different mechanisms of electron transport in insulators are discussed.     

Fullerenes with μSR

The current status ofSR results on muonium states in the pure fullerenes C₆₀ and C₇₀ is summarized. The hyperfine interaction between the unpaired electron and the muon provides unique information on the molecular dynamics and local electronic structure of the fullerenes. Recent results on the alkali doped C₆₀ series are also presented.     

Lattice relaxation for normal muonium in diamond

The effects of symmetric lattice relaxation around the tetrahedral (T) and the hexagonal (H) interstitial sites are calculated for normal muonium (Mu) in diamond using the non-semiempirical method of Partial Retention of Diatomic Differential Overlap (PRDDO). We use clusters containing 3 and 4 host atom shells around the T and the H sites (C₂₀H₃₂ and C₃₀H₄₀). The only significant relaxations are the outward displacement of the 6 nearest neighbors (NN) to the H site and, when the muon is at the T site, the simultaneous outward displacement of the first and second NN to the T site. In the case of diamond, the effects of these relaxations on the energy profiles and spin densities are small.     

Radio-frequency μSR experiments at the ISIS pulsed muon facility

This paper explores the use of pulsed radio-frequency (RF) techniques to remove the frequency limitations imposed on conventional transverse muon spin rotation (μSR) experiments at a pulsed muon source by the finite muon pulse width. The implementation of the 90° pulse technique is demonstrated by observing the free precession signal of diamagnetic muons implanted in polythene, the change in signal amplitude as a function of RF pulse length is plotted and the precise condition for a 90° pulse determined. The technique is evaluated by comparing measurements made using conventional spin rotation experiments to those employing pulsed RF methods. The potential for applying standard NMR multiple-pulse methods to the μSR experiment is considered and the use of two-pulse RF sequences (90° _x ?τ?90° _x and 90° _x ?τ?180° _x ) to form a muon spin echo demonstrated.     

μSR studies of the metallic alkali fullerides

We report ZF μSR measurements in Cs₁C₆₀ at low temperature and LF μSR in the superconductor Rb₃C₆₀. In Cs₁C₆₀, the internal magnetic field distribution is broad and static, and the relaxation at 1.9 K resembles that of a spin density wave. In Rb₃C₆₀, we observe a strong field dependence to the coherence peak in the LF relaxation rate of endohedral muonium ( Mu@C₆₀) at anomalously low field and a residual low temperature relaxation. This revised version was published online in August 2006 with corrections to the Cover Date.     

MuSR/μ+SR studies in KDP and DKDP

The temperature dependence of muon interactions has been studied in ferroelectric KDP ( H₂KPO₄) and DKDP ( D₂KPO₄) using conventional μSR and muon spin resonance spectroscopy. In longitudinal field measurements, a fast relaxing component and a slow relaxing component were observed. The slow relaxing component is attributed to diamagnetic muons. The muon spin resonance measurements indicate that the fast relaxing component results from some muonium like species: either normal or anomalous. In zero field and weak longitudinal field μSR (0–100 G), a remarkable peak in the fast relaxing component is observed around 220 K in both KDP and DKDP. An additional feature is also seen around 300 K. The amplitude of the resonance measurement has a broad minimum around 200 K which corresponds to the maximum in the relaxation rate in longitudinal field (100 G). The temperature dependence of the muonium relaxation rate in KDP is almost identical to that of DKDP. The diamagnetic fraction also shows almost no difference in relaxation rate or asymmetry for DKDP and KDP. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hyperfine coupling constants of muonium-substituted cyclohexadienyl radicals in the gas phase: C6H6Mu, C6D6Mu, C6F6Mu

Muon spin rotation (μSR) and avoided level crossing resonance (ALCR) have been used to determine the hyperfine coupling constants (hfcs) of the muonium-substituted cyclohexadienyl radicals C₆H₆Mu, C₆D₆Mu and C₆F₆Mu in the gas phase, at pressures ～1 and 15 atm and temperatures in the range 40–80°C. Equivalent studies of polyatomic free radicals in gases, by electron spin resonance (ESR) spectroscopy, are generally not possible in this pressure range. The present gas phase results support the findings of earlier studies of cyclohexadienyl radicals in the condensed phase, by both μSR and ESR. Minor but not insignificant (～1%) effects on the hfcs are observed, which can be qualitatively understood for such nonpolar media in terms of their differing polarizabilities. This is the first time that comparisons of this nature have been possible between different phases at the same temperatures. These μSR/ALCR gas-phase results provide a valuable benchmark for computational studies on radicals, free from possible effects of solvent or matrix environments.     

Muon bonding versus muonium formation: Muon-Spin-Relaxation in α-Al2O3

Results of Muon-Spin-Relaxation (μSR) experiments on well-defined single crystals of corundum (α-Al₂O₃) are reported. Major issue in this study is the controversy of muon bonding or muonium formation in insulators. Transverse, zero-field and longitudinal field measurements were performed as a function of temperature or applied field. The obtained results indicate that muon-oxygen bonding occurs in α-Al₂O₃, having (at least) two (μO) states as found earlier for α-Fe₂O₃. The occurrence of a 10% missing fraction suggests Mu states, although Mu was not observed in our measurements. These results and their implications are discussed in light of other experimental μSR studies on insulating oxides and the above-mentioned controversy.     

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.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

Comparative Theoretical Study of Hyperfine Interactions of Muonium in A- and B-Form DNA

Muon Spin Relaxation (μSR) experiments in A- and B-form DNA have shown evidence for an enhanced electron mobility in the more closely-packed A-form. Besides dynamic effects (electronic diffusion) that could cause the observed difference in muon spin relaxation, one should also carefully examine the difference in the strengths of the hyperfine interactions of the muon (μ ⁺) with the moving electron in the two forms of DNA, since this could contribute to the observed difference in the muon spin relaxation rates as well. We have therefore investigated the (static) trapping properties of muon and muonium (μ ⁺ e ⁻) in A-form and B-form DNA from first-principles with the aim to understand how the different structural geometries of A- and B-form DNA can influence the hyperfine interaction of trapped muonium.     

Magnetism on Mg1−xZnxCyNi3

The magnetic phase diagram for Mg_1−xZn_xC_yNi₃ has been tentatively constructed based on magnetization and muon spin relaxation (μSR) measurements. The superconducting phase was observed to fade as x (y) increases (decreases). The low y samples show early stages of long-range ferromagnetism, or complete long-range ferromagnetism. In the phase diagram, the ferromagnetic phase exists in addition to the superconducting phase, suggesting that there is some correlation between superconductivity and ferromagnetism, even though the coexistence of ferromagnetism and superconductivity is not observed from the μSR measurements down to 20 mK for the superconducting sample (T_c=2.5 K, (x, y)=(0, 0.9)).     

Determination of Easy Axis in a Chemical Ferromagnet, 4-(p-Chlorobenzylideneamino)–TEMPO (TEMPO=2,2,6,6-Tetramethylpiperidin-1-Oxyl)

The trapping sites for muon and muonium in ferromagnetic p-Cl–Ph–CH=N–TEMPO [(4-(p-chlorobenzylideneamino)–TEMPO (TEMPO = 2,6,6-tetramethyl-piperidin-1-yloxyl)] and the hyperfine interaction tensors for these sites are obtained using first-principles Unrestricted Hartree–Fock theory. The calculated hyperfine interactions are used to compare the calculated zero field muon spin rotation (μSR) frequencies for different choices for the easy axis and the observed frequency. It has been concluded that the two trapping centers that can best explain the observed μSR frequency are a trapped singlet muonium near the radical oxygen and a trapped muon site near the chlorine. The direction of the easy axis also is determined to be the b-axis of the monoclinic lattice. This direction for the easy axis is confirmed by determining the direction of the distributed magnetization in the molecular solid which leads to a minimum dipole–dipole interaction energy. The consequences of this agreement for the easy axis direction by two independent procedures are discussed. This revised version was published online in September 2006 with corrections to the Cover Date.