Radio-Frequency Manipulation of State Populations in an Entangled Fluorine-Muon-Fluorine System.

Entangled spin states are created by implanting muons into single-crystal LiY_{0.95}Ho_{0.05}F_{4} to form a cluster of correlated, dipole-coupled local magnetic moments. The resulting states have well-defined energy levels allowing experimental manipulation of the state populations by electromagnetic excitation. Experimental control of the evolution of the muon spin polarization is demonstrated through application of continuous, radio-frequency electromagnetic excitation fields. A semiclassical model of quantum, dipole-coupled spins interacting with a classical, oscillating magnetic field accounts for the muon spin evolution. On application of the excitation field, this model shows how changes in the state populations lead to the experimentally observed effects, thus enabling a spectroscopic probe of entangled spin states with muons.

Muon-Nitrogen Quadrupolar Level Crossing Resonance in a Charge Transfer Salt.

Although muons are primarily regarded as a local spin probe, they can also access the charge state of an atom or molecule via quadrupolar level crossing resonance (QLCR) spectroscopy. We use Li+TCNQ- (TCNQ = 7,7,8,8-tetracyanoquinodimethane), a simple charge transfer salt, to test the potential of this technique in molecular systems by studying the interaction of a positive muon with the TCNQ nitrogen atoms. We show that both a positive muon and muonium are able to add to the nitrogen, leading to a singlet spin state for the addition molecule. This produces a characteristic three line QLCR spectrum, with the observed line positions and intensities determined by the principal values and orientation of the electric field gradient tensor at the nitrogen. Ab initio calculation of this field gradient and the resulting QLCR spectrum give good agreement with the experiment. A nonresonant background contribution to the relaxation rate also provides evidence for spin excitations rapidly diffusing along the TCNQ chains. These reflect mobile unpaired electrons introduced by muonium addition. It is thus shown that a single set of muon measurements can be sensitive to both spin and charge degrees of freedom in the same molecular material.

Dynamics of polystyrene probed by muon spin spectroscopy.

Muon spin spectroscopic measurements were made on atactic low-molecular-weight (LMW) (1.3 kg mol-1) and high-molecular-weight (HMW) (202 kg mol-1) polystyrene. Muoniated cyclohexadienyl radicals, which are formed by muonium addition to the phenyl side groups, are used as local probes of bulk dynamics. Muon spin relaxation is caused by the secondary γ-relaxation process, which involves motion of the phenyl rings, and is sensitive to the glass transition. The activation energy of the γ-relaxation process in the rubbery state is 0.60(2) eV in the HMW sample and 0.37(3) eV in the LMW sample.

Magnetism and ion diffusion in honeycomb layered oxide [Formula: see text].

In the quest for developing novel and efficient batteries, a great interest has been raised for sustainable K-based honeycomb layer oxide materials, both for their application in energy devices as well as for their fundamental material properties. A key issue in the realization of efficient batteries based on such compounds, is to understand the K-ion diffusion mechanism. However, investigation of potassium-ion (K[Formula: see text]) dynamics in materials using e.g. NMR and related techniques has so far been very challenging, due to its inherently weak nuclear magnetic moment, in contrast to other alkali ions such as lithium and sodium. Spin-polarised muons, having a high gyromagnetic ratio, make the muon spin rotation and relaxation ([Formula: see text]SR) technique ideal for probing ions dynamics in these types of energy materials. Here we present a study of the low-temperature magnetic properties as well as K[Formula: see text] dynamics in honeycomb layered oxide material [Formula: see text] using mainly the [Formula: see text]SR technique. Our low-temperature [Formula: see text]SR results together with complementary magnetic susceptibility measurements find an antiferromagnetic transition at [Formula: see text] K. Further [Formula: see text]SR studies performed at higher temperatures reveal that potassium ions (K[Formula: see text]) become mobile above 200 K and the activation energy for the diffusion process is obtained as [Formula: see text] meV. This is the first time that K[Formula: see text] dynamics in potassium-based battery materials has been measured using [Formula: see text]SR. Assisted by high-resolution neutron diffraction, the temperature dependence of the K-ion self diffusion constant is also extracted. Finally our results also reveal that K-ion diffusion occurs predominantly at the surface of the powder particles. This opens future possibilities for potentially improving ion diffusion as well as K-ion battery device performance using nano-structuring and surface coatings of the particles.

Rate constants and kinetic isotope effects for H-atom abstraction reactions by muonium in the Mu + propane and Mu + n-butane reactions from 300 K to 435 K: challenges for theory.

This paper reports measurements of the temperature dependence of the rate constants for H-atom abstraction reactions from propane and n-butane by the light isotopic H-atom muonium (Mu), kMu(T), over temperatures in the range 300 K to 435 K. Simple Arrhenius fits to these data yield activation energies, E, that are some 2-4 times lower than E found from corresponding fits for the H + propane and H + n-butane reactions studied elsewhere, both experimentally and theoretically, and fit over a similar temperature range. These activation energies E are also much lower than estimated from zero-point-energy corrected vibrationally adiabatic potential barriers, both results suggesting that quantum tunneling plays an important role in determining kMu(T) and for the Mu + propane reaction in particular. The results are expected to pose a considerable challenge to reaction rate theory for isotopic H-atom reactions in alkane systems.

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa2Cu3O y.

The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (µSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa2Cu3O y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures Tmag ≈ T*. The absence of any static field (to which µSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at Tmag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.

Li-ion diffusion in Li intercalated graphite C6Li and C12Li probed by µ+SR.

In order to study a diffusive behavior of Li+ in Li intercalated graphites, we have measured muon spin relaxation (µ+SR) spectra for C6Li and C12Li synthesized with an electrochemical reaction between Li and graphite in a Li-ion battery. For both compounds, it was found that Li+ ions start to diffuse above 230 K and the diffusive behavior obeys a thermal activation process. The activation energy (Ea) for C6Li is obtained as 270(5) meV, while Ea = 170(20) meV for C12Li. Assuming a jump diffusion of Li+ in the Li layer of C6Li and C12Li, a self-diffusion coefficient DLi at 310 K was estimated as 7.6(3) × 10-11 (cm2 s-1) in C6Li and 14.6(4) × 10-11 (cm2 s-1) in C12Li.

Microscopic muon dynamics in the polymer electrolyte poly(ethylene oxide).

The microscopic dynamics of protons (H^{+}) in poly(ethylene oxide) (PEO) have been investigated through a study of implanted positive muons (Mu^{+}), which can be considered a light proton analog. The exponential decay of the muon spin polarization in zero magnetic field indicated that Mu^{+} hopping is in the fast fluctuation limit between 140 and 310 K and the relaxation rate was found to be sensitive to the glass transition. Mu^{+} dynamics in PEO was monitored via the relaxation of the muon spin polarization in a transverse field of 10 mT. Activated hopping of Mu^{+} was observed above the glass transition temperature with an activation barrier of 122±1 meV. The temperature dependence of the diamagnetic muon polarization in PEO can be explained by diffusion of radiolytic electrons.

Muonium Chemistry at Diiron Subsite Analogues of [FeFe]-Hydrogenase.

The chemistry of metal hydrides is implicated in a range of catalytic processes at metal centers. Gaining insight into the formation of such sites by protonation and/or electronation is therefore of significant value in fully exploiting the potential of such systems. Here, we show that the muonium radical (Mu. ), used as a low isotopic mass analogue of hydrogen, can be exploited to probe the early stages of hydride formation at metal centers. Mu. undergoes the same chemical reactions as H. and can be directly observed due to its short lifetime (in the microseconds) and unique breakdown signature. By implanting Mu. into three models of the [FeFe]-hydrogenase active site we have been able to detect key muoniated intermediates of direct relevance to the hydride chemistry of these systems.

Rate constants for the slow Mu + propane abstraction reaction at 300 K by diamagnetic RF resonance.

The study of kinetic isotope effects for H-atom abstraction rates by incident H-atoms from the homologous series of lower mass alkanes (CH4, C2H6 and, here, C3H8) provides important tests of reaction rate theory on polyatomic systems. With a mass of only 0.114 amu, the most sensitive test is provided by the rates of the Mu atom. Abstraction of H by Mu can be highly endoergic, due to the large zero-point energy shift in the MuH bond formed, which also gives rise to high activation energies from similar zero-point energy corrections at the transition state. Rates are then far too slow near 300 K to be measured by conventional TF-µSR techniques that follow the disappearance of the spin-polarised Mu atom with time. Reported here is the first measurement of a slow Mu reaction rate in the gas phase by the technique of diamagnetic radio frequency (RF) resonance, where the amplitude of the MuH product formed in the Mu + C3H8 reaction is followed with time. The measured rate constant, kMu = (6.8 ± 0.5) × 10(-16) cm(3) s(-1) at 300 K, is surprisingly only about a factor of three slower than that expected for H + C3H8, indicating a dominant contribution from quantum tunneling in the Mu reaction, consistent with elementary transition state theory calculations of the kMu/kH kinetic isotope effect.

Questioning Antiferromagnetic Ordering in the Expanded Metal, Li(NH3)4: A Lack of Evidence from µSR.

We present the results of a muon spin relaxation study of the solid phases of the expanded metal, Li(NH3)4. No discernible change in muon depolarization dynamics is witnessed in the lowest temperature phase (≤25 K) of Li(NH3)4, thus suggesting that the prevailing view of antiferromagnetic ordering is incorrect. This is consistent with the most recent neutron diffraction data. Discernible differences in muon behavior are reported for the highest temperature phase of Li(NH3)4 (82-89 K), attributed to the onset of structural dynamics prior to melting.

Hyperfine coupling constants of the cyclohexadienyl radical in benzene and dilute aqueous solution.

The muon hyperfine coupling constant (Aµ) of the muoniated cyclohexadienyl radical (C6H6Mu) has been directly measured in a 5 mM solution of benzene in water by the radio-frequency muon spin resonance (RF-µSR) technique. The relative shift of Aµ in aqueous solution compared with the value in neat benzene (ΔAµ/Aµ = +0.98(5)% at 293 K) can now be compared directly with theoretical predictions. Application of the RF-µSR method to other dilute systems will provide extremely important information on understanding solvent effects.

New results for the formation of a muoniated radical in the Mu + Br2 system: a van der Waals complex or evidence for vibrational bonding in Br-Mu-Br?

New evidence is presented for the observation of a muoniated radical in the Mu + Br(2) system, from µSR longitudinal field (LF) repolarisation studies in the gas phase, at Br(2) concentrations of 0.1 bar in a Br(2)/N(2) mixture at 300 K and at 10 bar total pressure. The LF repolarisation curve, up to a field of 4.5 kG, reveals two paramagnetic components, one for the Mu atom, formed promptly during the slowing-down process of the positive muon, with a known Mu hyperfine coupling constant (hfcc) of 4463 MHz, and one for a muoniated radical formed by fast Mu addition. From model fits to the Br(2)/N(2) data, the radical component is found to have an unusually high muon hfcc, assessed to be ∼3300 MHz with an overall error due to systematics expected to exceed 10%. This high muon hfcc is taken as evidence for the observation of either the Br-Mu-Br radical, and hence of vibrational bonding in this H[combining low line]-L[combining low line]-H[combining low line] system, or of a MuBr(2) van der Waals complex formed in the entrance channel. Preliminary ab initio electronic structure calculations suggest the latter is more likely but fully rigorous calculations of the effect of dynamics on the hfcc for either system have yet to be carried out.

Spin evolution in a radio frequency field studied through muon spin resonance.

The application of composite inversion pulses to a novel area of magnetic resonance, namely muon spin resonance, is demonstrated. Results confirm that efficient spin inversion can readily be achieved using this technique, despite the challenging experimental setup required for beamline measurements and the short lifetime (≈2.2µs) associated with the positive muon probe. Intriguingly, because the muon spin polarisation is detected by positron emission, the muon magnetisation can be monitored during the radio-frequency (RF) pulse to provide a unique insight into the effect of the RF field on the spin polarisation. This technique is used to explore the application of RF inversion sequences under the non-ideal conditions typically encountered when setting up pulsed muon resonance experiments.

Local magnetism in palladium bionanomaterials probed by muon spectroscopy.

Palladium bionanomaterial was manufactured using the sulfate-reducing bacterium, Desulfovibrio desulfuricansm, to reduce soluble Pd(II) ions to cell-bound Pd(0) in the presence of hydrogen. The biomaterial was examined using a Superconducting Quantum Interference Device (SQUID) to measure bulk magnetisation and by Muon Spin Rotation Spectroscopy (µSR) which is uniquely able to probe the local magnetic environment inside the sample. Results showed behaviour attributable to interaction of muons both with palladium electrons and the nuclei of hydrogen trapped in the particles during manufacture. Electronic magnetism, also suggested by SQUID, is not characteristic of bulk palladium and is consistent with the presence of nanoparticles previously seen in electron micrographs. We show the first use of µSR as a tool to probe the internal magnetic environment of a biologically-derived nanocatalyst material.

Laser-muon spin spectroscopy in liquids - a technique to study the excited state chemistry of transients.

This study introduces laser-muon spin spectroscopy in the liquid phase, which extends muonium chemistry in liquids to the realm of excited states and enables the detection of muoniated molecules by their spin evolution after laser excitation. This leads to new opportunities to study the Kinetic Isotope Effects (KIEs) of muonium/atomic hydrogen reactions and to probe transient chemistry in radiolysis processes involved in muonium formation, as well as muoniated intermediates in excited states.

Muon implantation of metallocenes: ferrocene.

Muon Spin Relaxation and Avoided Level Crossing (ALC) measurements of ferrocene are reported. The main features observed are five high field resonances in the ALC spectrum at about 3.26, 2.44, 2.04, 1.19 and 1.17 T, for the low-temperature phase at 18 K. The high-temperature phase at 295 K shows that only the last feature shifted down to about 0.49 T and a muon spin relaxation peak at about 0.106 T which approaches zero field when reaching the phase transition temperature of 164 K. A model involving three muoniated radicals, two with muonium addition to the cyclopentadienyl ring and the other to the metal atom, is postulated to rationalise these observations. A theoretical treatment involving spin-orbit coupling is found to be required to understand the Fe-Mu adduct, where an interesting interplay between the ferrocene ring dynamics and the spin-orbit coupling of the unpaired electron is shown to be important. The limiting temperature above which the full effect of spin-orbit interaction is observable in the muSR spectra of ferrocene was estimated to be 584 K. Correlation time for the ring rotation dynamics of the Fe-Mu radical at this temperature is 3.2 ps. Estimated electron g values and the changes in zero-field splittings for this temperature range are also reported.

Muon spin relaxation study of Zr(H2PO4)(PO4).2H2O.

Muon spin relaxation has been used to study the muon dynamics in the layered zirconium phosphate Zr(H(2)PO(4))(PO(4)).2H(2)O as a function of temperature. Radiofrequency decoupling was used to establish the origin of the local dipolar field as coupling with (1)H spins. Muons were trapped at two sites, one identified as HMuO and the other consistent with PO-Mu on the basis of their zero-field second moments. Although a small decrease in the local nuclear dipolar field was seen with temperature, the muons remained essentially static over the temperature range 20-300 K.