Spin relaxation of muonated radicals in the gas phase

We report on recent results obtained for longitudinal field (T ₁) spin relaxation of the muonium-substituted (muonated) free radicals MuCO, MuC₂F₄, MuC₂H₃F, and MuC₄H₈ (t-butyl), comparing with results reported earlier for MuC₂H₄ (and MuC₂D₄). Some comparison with transverse field (T ₂) data is also given. These data are fit to a phenomenological model based on NMR theory of spin relaxation in gases. The parameters of these fits are presented and discussed.     

Precise measurement of hfs constant of the muonium substituted radical in cis-polyacetylene

The state of the muon in cis-polyacetylene was studied by muon spin rotation method under high transverse magnetic field. The most of the muons are found to be in muonium substituted radical state. The hyperfine coupling constant was determined to be 91 MHz with a line width of 10 MHz.     

Transverse field dependence of muonium relaxation: Spin exchange and chemical reaction

It has been shown experimentally that the muonium relaxation due to spin exchange is 1.5 times faster in intermediate transverse fields (say, atB=50 G, where the so-called two-frequency muonium signal is observed) than in low fields (say, atB=5 G), in agreement with an earlier theoretical prediction. It has also been confirmed experimentally that this distinct field dependence is totally absent in the case of chemical reaction.     

Finite-temperature properties of the muonium substituted ethyl radical CH2MuCH2: nuclear degrees of freedom and hyperfine splitting constants

The finite-temperature (T) properties of the muonium substituted ethyl radical CH₂MuCH₂ have been theoretically studied by Feynman path integral quantum Monte Carlo (PIMC) simulations. To derive the ensemble averaged expectation values we have combined the PIMC formalism with an efficient tight-binding (TB) Hamiltonian and a density functional operator of the B3LYP type in the EPRIII basis. The TB operator has been used to calculate the potential energy surface (PES) of the ethyl radical in the doublet ground state, the harmonic and anharmonic vibrational wave numbers as well as several probability density functions of the nuclei. The harmonic linear response approximation, which makes use of the Feynman centroid density, has been adopted to evaluate the anharmonic wave numbers. The large anharmonicities in the nuclear potential lead to bond lengths in thermal equilibrium which exceed the vibrationless parameters at the PES minimum. This enhancement is particularly strong for the C–Mu bond. It is responsible for the suppression of the intramolecular rotation for temperatures below room temperature. In C₂ H₅ the rotation is allowed down to 10?K. The dissimilar rotational dynamics for H₂MuCH₂ and C₂ H₅ has been studied with the help of TB-based probability density functions. The nuclear configurations of CH₂MuCH₂ and C₂ H₅, which are populated in thermal equilibrium, have been used to evaluate the isotropic and anisotropic hyperfine splitting (hfs) constants under explicit consideration of the nuclear vibrations and the internal rotation. The hfs constants have been determined with the help of the B3LYP-EPRIII Hamiltonian. The hindered low-temperature rotation in the Mu isomer is responsible for roto-vibrational corrections to the isotropic hfs constants which are smaller than the corrections in C₂ H₅. The shortcomings of single-configuration approaches for the evaluation of isotropic hfs constants have been demonstrated for both radicals. The ensemble corrections to the isotropic hfs parameters are correlated with fluctuations in the atomic spin densities. Differences in the absolute values of the isotropic hfs parameters in CH₂MuCH₂ and C₂ H₅ can be traced back to differences in the nuclear degrees of freedom. The ensemble shift for each isotropic hfs parameter can be explained by characteristic nuclear motions. For this discussion we make use of the distribution functions of the isotropic hfs constants. Roto-vibrational corrections to the anisotropic hfs constants are rather small. PIMC simulations have been performed between 25 and 1000?K, i.e. in a T interval that is large enough to consider nuclear effects beyond zero-point motions. The TB and B3LYP-EPRIII based physical quantities of CH₂MuCH₂ and C₂ H₅ have been compared with experimental findings whenever possible.     

Reaction of the muonium substituted cyclohexadienyl radical with 2,3-dimethyl-1,3,-butadiene

The rate constant for the title reaction is represented by log (k _M/M^–1s^–1)=6.9(4)–700(350)K/T between 279 and 343K, whereas the H analogous radical, C₆H₇, reacts at room temperature withk _H 12 M^–1s^–1 with dimethylbutadiene. The title reaction is proposed to be transfer of the light hydrogen isotope, Mu, and the large kinetic isotope effect is discussed.Support by the Swiss National Foundation for Scientific Research and by the Swiss Institute for Nuclear Research (SIN) are gratefully acknowledged.     

Formation of muonium substituted free radicals

SR experiments with mixtures of benzene with cyclohexane, 2,3-dimethyl-1,3-butadiene and carbontetrachloride allow the conclusion that the direct muonic precursor of the muonic cyclohexadienyl radical is thermal muonium. In neat benzene it has a life time of 10 ps and disappears by the addition reaction. Muonium is formed within about 1 ps by combination of the positive muon with an electron near the end of the track of the thermalizing muon.Support by the Swiss National Foundation for Scientific Research and by the Swiss Institute for Nuclear Research (SIN) are gratefully acknowledged.     

Spin dynamics of the muon in muonium in normal metals

The question of the charge state of the proton (the positive muon) in metals is of fundamental importance for the theory of metal hydrides. The theory developed here permits determination of the charge state of μ ⁺ in normal metals. The experimental possibilities of the observation of Mu atoms in metals at various strengths of the external magnetic field and various temperatures are analyzed. Zh. éksp. Teor. Fiz. 111, 730–736 (February 1997)     

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.     

Spin relaxation and magnetic properties of benzo-1,2,3-trithiolium radical cations

Magnetic and dynamics properties of paramagnetic centers in various trithiolium cations were characterized by static magnetic susceptibility measurements and EPR spectroscopy. Magnetically correlated units consisting of at least pairs of spins with ferromagnetic exchange coupling were found in some trithioles. The rates of intramolecular spin diffusion and intermolecular spin hopping were estimated separately. The rates and the anisotropy (v/v=20–300) of spin dynamics were shown to depend on the molecular structure.     

Longitudinal relaxation of muonium in Ge and GaAs

Longitudinal-field muon-spin depolarization rates in high-purityGe and semiinsulatingGaAs are reported and compared to similar data for intrinsicSi. Depolarization onset temperatures provide a comparison of charge carrier concentrations leading to rapid charge exchange and a shift in the onset, for n-typeGaAs verifies anelectron process. The temperature dependence of the low-field rate constants imply more complicated dynamics inGe than observed earlier inSi. Features near 750K inGaAsTe appear consistent with dissociation of aMu-Te pair.This work was supported by the US National Science Foundation (DMR-8917639 [TLE, BH]), the Science and Engineering Research Council of the UK (EAD, AS, SFJC), the Robert A. Welch Foundation (D-1053 [RLL], and C-1048 [TLE]), and a NATO Collaborative Research Grant (RLL, SFJC, RCD, CS). We wish to thank D.A. Vanderwater of Hewlett Packard for providing theGaAsTe sample.     

Muon spin-lattice relaxation and muonium diffusion in ice

Longitudinal muon spin relaxation is measured in ice, using samples with and without enrichment in H₂ ¹⁷O, with a view to studying the mobility of the muonium fraction. A conventional analysis of the data, on the assumption that relaxation of the diamagnetic fraction is negligible, suggests that more than one mechanism of muonium relaxation is at work. A Bayesian analysis warns that separation of the diamagnetic and paramagnetic signals may not be so straightforward.     

Spin relaxation studies on conducting poly(tetrathiafulvalene)

Magnetic parameters and the relaxation behavior of paramagnetic centers in an iodine-doped poly(tetrathiafulvalene) semiconductor with a d.c. conductivity of 10^?5 S·cm^?1 have been studied using mainly the 2 mm waveband EPR technique in the temperature range of 110–270 K. The EPR line shape analysis confirms the existence of immobile radicals pinne on short polymer chains and mobile polarons with different relaxation parameters in slightly doped poly(tetrathiafulvalene). The temperature dependences of electron spin-lattice and spin-spin relaxation times of paramagnetic centers of both types have been determined independently using the saturation method at the operation frequency ν _e = 140 GHz. An anisotropic slow libration of immobile polarons with an activation energy of 0.02 eV have been registered for the first time using the saturation transfer EPR method. The temperature dependences of intrachain diffusion and interchain hopping rates in poly(tetrathiafulvalene) are determined from theT ₁ andT ₂ EPR data. The interchain spin dynamics is shown to correlate with libration of polarons trapped on polymer chains and is in good agreement with a hopping charge transport mechanism.     

Temperature dependence of the muon and proton hyperfine constants of an \alpha‐muonium‐substituted methyl radical

Muon hyperfine constants A_μ have been measured by transverse field μSR for (CH₃)₃Si\mbox\.CHMu in hexane from 167 K to 332 K. In addition, avoided level‐crossing resonance was used to determine \alpha‐proton coupling constants A_p over a similar range of temperatures. The two hyperfine constants can be described by a common temperature dependence, d|A_i|/ dT=1.4\times 10^-3 MHz\,K^-1, where A_i represents A_p or the reduced muon constant A^\prime_μ=0.3141A_μ. There is a small isotope effect (A^\prime_μ is 2.2 % larger than A_p) consistent with zero‐point motion in the anharmonic C–H bond stretch. The common temperature dependence is tentatively attributed to a coupled deviation of the C–H and C–Mu bonds out of the nodal plane of the p orbital containing the unpaired electron. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spin relaxation in fluids

The effect of spin relaxation in fluids on perturbed angular distributions is discussed. The first example, deals with dynamical perturbations resulting from collision-induced charge-transfer process in gases. A brief discussion of relaxation effects caused by molecular motion in non-metallic liquids is followed by a presentation of a new approach to the theory of quadrupole relaxation in liquid metals.     

Anomalous muonium relaxation rates in quartz at high temperatures

Muonium spin relaxation measurements of the \alpha‐, \beta‐, and \gamma‐tridymite phases of quartz have been carried out over a temperature range from 300 to 1250 K. Anomalous relaxation rate increases are observed which may result either from resonance coupling between the other impurity ions and defects in the lattice and the diffusing muonium, or may result from phonon interactions with the muonium quadrupole moment. This revised version was published online in August 2006 with corrections to the Cover Date.     

Formation of muonium and a muonic radical in fullerene

Three distinct electronic states were detected for positive muons (⁺) after implantation into a C₆₀ powder sample. About 40% of the ⁺ remained in the bare (diamagnetic) state, essentially an interstitial charged point particle. The rest of the muons were found to thermalize predominantly in two muonium (Mu=⁺ e^–) atomic species. A vacuum Mu state, with hyperfine coupling close to that of free Mu, most likely at the molecular center, and a muonic substituted radical, i.e. a hydrogen-like Mu addition to double bonds on the carbon rings. This opens up a rich subfield of fullerene spectroscopy using muons.     

Spin relaxation in the presence of electron-electron interactions

The D'yakonov-Perel' spin relaxation induced by the spin-orbit interaction is examined in disordered two-dimensional electron gas. It is shown that, because of the electron-electron interactions, substantially different spin relaxation rates may be observed depending on the technique used to extract them. It is demonstrated that the relaxation rate of a spin population is proportional to the spin-diffusion constant D(s), while the spin-orbit scattering rate controlling the weak-localization corrections is proportional to the diffusion constant D, i.e., the conductivity. The two diffusion constants get strongly renormalized by the electron-electron interactions, but in different ways. As a result, the corresponding relaxation rates are different, with the difference between the two being especially strong near a magnetic instability or near the metal-insulator transition.