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.     

Missing fractions in heavy gases: Xe and CCl4?

The spin polarization of positive muons thermalized in Xe has been measured as a function of pressure up to 4660 Torr (6.1 atm) by the muon spin rotation (MSR) technique. At 4660 Torr, triplet muonium (F=1, M=1) accounts for about 40% of the initial muon polarization and no significant signal from diamagnetic muons has been observed. The unexpectedly slow recovery of the polarization in Xe at high pressures is discussed in conjunction with similar results seen in CCl₄ and CHCl₃ vapors.     

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.     

Observation of “decoupled” diamagnetic muon states in Alkali halides by muon spin resonance

The states of positive muons in KCl, NaCl and KI were studied with the muon spin resonance method under a 3 kG decoupling longitudinal field, revealing a considerably larger fraction of diamagnetic muon state than observed by the conventional spin rotation method. The origin of this fraction, which increases with temperature, is attributed to a muonium to muon transition in solids.     

Dynamics of muons in the ferroelectric material KDP

Muon spin relaxation in zero field and longitudinal field was measured in single crystal samples of KH₂PO₄ (KDP) and KD₂PO₄ (DKDP) over a temperature range of 5 K to 300 K. At low temperatures, diamagnetic muons and muon substituted radicals with nuclear hyperfine coupling can be observed. For both KDP and DKDP, a minor change was observed in the dynamics of the muon below 140 K. Above 140 K, the mobility of the muon appears to increase and the diffusion rate becomes faster with increasing temperature. Only a small increase in the relaxation rate is observed in KDP due to the presence of theH ⁺, suggesting that the relaxation effects probably originate from the³¹P.     

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.     

Measurement of17O quadrupole interactions and identification of the diamagnetic fraction in ice by muon level crossing resonance

By means of Level Crossing Resonance in a sample of ice which is enriched in H₂ ¹⁷O, the final diamagnetic state of implanted positive muons is determined to be the muonium-substituted molecule HMuO, accommodated in the regular and fully relaxed Ih structure. The¹⁷O quadrupole coupling constant is measured to be 6.1 MHz at 200 K assuming an asymmetry parameter close to unity, a decrease of about 5% relative to that in normal ice Ih at 77 K. The isotope effect is attributed to a greater polarization in the vicinity of a muonium (as opposed to a normal hydrogen) bond. At 50 K, an additional resonance is observed which could correspond to a precursor state, so far not definitely identified. One possibility is a muon trapped at a Bjerrum L-defect, giving a {H₂O−Mu−OH₂}⁺ species with an,¹⁷O quadrupole coupling constant of 8.2 MHz and asymmetry parameter of 0.55. Above this temperature, the fall in the (Gaussian) line-width parameter is attributed to the increasing rate of proton or muon migration, the correlation time dropping from 4 μs at 80 K to 1 μs near the melting-point. The increase in the diamagnetic fraction with rise in temperature is attributed to the increasing proportion of trapping sites available for muon capture.     

Theμ + state under decoupling field observed by spin resonance method in CS2, water and benzene

The muon spin resonance method was applied to measure the ⁺ polarization corresponding to the muon state in diamagnetic compounds in CS₂, water and benzene under 3 kG decoupling field. We observed almost the same diamagnetic polarizations under decoupling field, compared to those at zero decoupling field observed under the transverse field, except in CS₂ The results indicate that most of the so called missing fraction is not associated with diamagnetic species produced as a final state of rapid chemical reactions of muonium in these samples.The authors acknowledge helpful discussions with Professor T. Yamazaki. This work is supported by the Grant-in-Aid of the Japanese Ministry of Education, Culture and Science.     

Positive muons in [Co(NH3)6]Cl3 and [Co(ND3)6]Cl3

We have carried out SR experiments on [Co(NH₃)₆]Cl₃ and [Co(ND₃)₆]Cl₃. At 293 K, all the muons implanted into the complexes were in the diamagnetic state. The observed Gaussian-type muon spin relaxation function proved that the internal magnetic field was caused by nuclear dipole moments of the atoms in the complexes. In addition, another exponential-type muon spin relaxation function was observed in [Co(ND₃)₆]Cl₃ below 50 K.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Radical reorientation dynamics studied by positive-muon avoided level crossing resonance

Spin polarised positive muons substituted for a hydrogen nucleus in organic radicals are used as spin labels to sense reorientational motion of the radicals in orienting environments. The effect of uniaxial motion on the spectrum of the muonated cyclohexadienyl radical in a benzene single crystal and of its hexamethyl derivative in polycrystalline hexamethylbenzene is demonstrated. Isotopic spectra for cyclohexadienyl radicals adsorbed on SiO₂ are explained by translational diffusion around the 7 nm grain. The potential of the technique to study transient radical intermediates of processes in heterogeneous catalysis is discussed.     

Charge exchange of muons in gases: Experimental implications from rate theory

The effects of the charge exchange process on muon spin dynamics have been investigated using a density operator formalism with special interest placed upon the diamagnetic muon and paramagnetic muonium signals observed after thermalization. In the charge exchange region the dynamics of the spin density operator is assumed to be determined by the muonium hyperfine interaction and by electron capture and loss processes for muons. Analytical expressions are obtained for the amplitudes and phases of the diamagnetic muon and paramagnetic muonium signals as a function of the duration of the charge exchange region,t _c, which is inversely proportional to the number density of the moderating gas. The theoretical signals exhibit three features which have, as yet, to be experimentally observed, namely: (i) that the amplitudes associated with the muonium Larmor frequency and with the hyperfine frequency are not, in general, equal, (ii) that all the amplitudes are, in general, damped oscillatory functions oft _c (temperature/pressure) and (iii) that phase jumps occur when an amplitude decreases to zero and then increases with falling pressure. Fits to the experimental argon data are discussed in light of the above points.     

Production of high-energy muons in gamma showers

We have calculated the number of high-energy muons in gamma showers generated by photoproduction and by muon pair creation. The prompt muons have flatter energy spectrum than the muons, which come from photoproduction and contribute significant fraction of the total muon rates for E_μ ? 1 TeV. The total rate of high-energy muons in gamma showers is, however, very low.     

Muonium adduct radicals from vinyl-aromatic compounds

During irradiation of liquid samples of 1-vinylimidazole, 2-vinylnaphthalene, 2-vinylpyridine, 4-vinylpyridine and 1,1-diphenylethene with positive muons, radicals of the type MuCH₂ĊHAr (Ar=the appropriate aromatic group), and the MuCH₂ĊPh₂ radical were observed by transverse field μSR; the muon hyperfine couplings are considered in the context of the effectiveness of the aryl groups in delocalising the unpaired electron.     

Muon spin relaxation studies of extremely concentrated paramagnetic electrolyte solutions

The diamagnetic signal in aqueous solutions of non-reacting salts arises from muons substituted for protons in water molecules. For concentrated solutions of paramagnetic salts, muon spin relaxation results from the strong dipolar and scalar interactions between the paramagnetic ion and the muon. Information on dynamic and structural aspects of such solutions is derived from measurements of the transverse relaxation rate as a function of applied field over a wide range. Data are presented for concentrated solutions of Mn(NO₃)₂ and solutions of composition Mn _x Ca_(1–x (NO₃)₂·6H₂O.     

Muon spin resonance — A variant of magnetic resonance

Spin polarized positive muons injected in matter serve as magnetic probes for the investigation of various properties. The evolution of muon spin polarization rests on the same basis as in conventional magnetic resonance techniques. The background of the technique, different variants of the experimental set-up, and potential and limitations of the muon as a probe are described.     

Muon level crossing resonance in niobium

A useful guide to detecting quadrupole level crossing resonance (QLCR) spectra is to search in the vicinity of B_E\cdot(\gamma_n/\gamma_μ), where B_E is the onset magnetic field for the decoupling of the quadrupole interaction, as seen in muon spin rotation linewidths. More detailed predictions of the positions and intensities of the resonances require numerical simulations taking account of the local geometry of the muon site. We present such simulations for muons adjacent to nuclei of spin 9/2 and demonstrate a pronounced dependence on the anisotropy of the quadrupole coupling tensor. Simulations for the specific cases of muons located at the octahedral and tetrahedral interstices in niobium metal are compared with the experimentally detected spectrum in a polycrystalline sample. This revised version was published online in August 2006 with corrections to the Cover Date.     

Frictional accumulation of negative muons and its application

A novel method is proposed for the efficient conversion of intermediate energy negative muons into a low-energy muon beam. It is based on using an electric field to eject muons from a moderator consisting of a large number of thin carbon foils placed perpendicularly to the axis of a high-field solenoid. High-energy muons are made to slow down within the moderator to an energy where further slowing down is inhibited by the electric field acceleration between the foils. The muons accumulate at low energy within the moderator hopping from one foil to the next until they come out as a low-energy muon beam. The resulting phase compression factor exceeds 1000. Efficient initial injection of the muons into the moderator is obtained either by letting the muons enter it in a direction opposite to the acceleration force or by producing the muons within a magnetic trap containing the moderator. A practical configuration based on the second scheme is presented. By implementing the method into the most intense muon production configurations a new pathway is opened that may ultimately compete with other schemes in the selection of the optimal source for high-energy muon colliders.     

Evidence for muonium emission from an SiO2 layer on n-type Si and the positive muon state in Si

Evidence for the emission of slow muonium atoms from a 3.0-nm-thick SiO₂ layer covered on an n-type Si is reported. Also, upon applying an rf-resonance technique at the muon frequency, a time-differential observation of a delayed state-change from muonium to diamagnetic muon at room temperature was observed. Combining results obtained by use of longitudinal field decoupling and transverse spin rotation methods, the conversion rate was estimated to be 5 to 10 μs⁻¹. Both of the above results, namely the observation of the emission and state-change of muonium, suggest a process in which μ⁺ initially captures an electron from Si, then quickly converts to μ⁺ again during thermal diffusion in the Si towards the SiO₂ layer. Within the oxide layer, muonium is again formed and subsequently is emitted from the SiO₂ surface.     

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.