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.     

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).     

Electronic structure, dynamics, and metastability of muonium in semiconductors

Muonium centers are light hydrogen-like centers formed when positive muons are stopped in crystalline semiconductors. Detailed information on the hyperfine structure, dynamics and metastability of muonium are obtained using a combination of muon spin rotation or relaxation, muon level-crossing resonance and related methods. The expected close similarity to hydrogen, especially with regard to electronic structure, is important since the equivalent information on isolated hydrogen is either less detailed or completely absent. There are also interesting differences between muonium and hydrogen. In particular muonium dynamics are expected to exhibit enhanced quantum mechanical effects since the muon has only 1/9th the proton mass. In this paper we review the current status of experiments.     

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).     

Local structure of isolated positively charged muonium as an analog for the hydrogen ion in p-type GaAs

We determine the local structure of isolated positively charged muonium (Mu+) in heavily doped p-type GaAs based on muon level crossing resonance and zero applied field muon spin depolarization data. These measurements provide the first direct experimental confirmation that Mu+, and by analogy H+, is located within a stretched Ga-As bond. The distances between Mu+ and the nearest neighbor Ga and As atoms are estimated to be 1.83 +/- 0.10 A; and 1.76 +/- 0.10 A, respectively. These results are compared to existing theoretical calculations on the structure of hydrogen in GaAs and additionally provide data on the induced electric field gradients.     

Muon spin rotation studies at SIN

Recently the accelerator and the muon channel at SIN became operational. We report here on some of the first positive muon spin rotation experiments at SIN. The first experiment we discuss concerns the chemistry of muonium. We have observed for the first time a muonium or radical signal in pure water. Next, we discuss the application of the positive muon for the study of ferromagnetic metals and alloys. First measurements on a single crystal of iron around liquid helium temperature seem to indicate that at low temperature the muon does not diffuse. We further report on the first stroboscopic observation of the muon spin rotation which will allow one to take full advantage of the high stopping density at SIN.     

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 depolarization in liquid3He

We report the first measurements of the positive-muon spin depolarization in liquid³He. The relaxation of the muon and muonium precession has been studied in transverse, longitudinal, and zero magnetic fields in the temperature range 0.5–2.5 K. The results are discussed in terms of two different depolarization mechanisms: recombinational depolarization (i.e. slow muonium formation) and magnetic relaxation due to the³He nuclear magnetic moments.     

Inhomogeneous quantum diffusion of muons in solids

This article deals with the problems raised when a muon(muonium) quantum diffusion in a crystal is highly inhomogeneous. It is shown how static disorder arising from the crystal doping influence the diffusion process and drastically changes both the time decay of the polarization function and the temperature dependence of the depolarization rate. The spin depolarization of muons moving in a spatially inhomogeneous defect potential and trapping of particles by the long-ranged traps is studied in detail. Most attention is given to the particle localization and delocalization phenomena resulting in the two-component behavior of muon polarization at low temperature. Finally, the experimental data on muon depolarization in insulators KCl, GaAs, N₂ and superconducting metals Al, V are analyzed.     

MuSR method and tomographic-probability representation of spin states

The muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. The time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. The entanglement phenomenon of a bipartite muon–electron system is investigated, in view of the tomographic analogs of the Bell number and the positive partial transpose (PPT) criterion. Reconstruction of the muon–electron spin state as well as the total spin tomography of the composed system is discussed.     

Muonium acoustic resonance

Theoretical consideration is given to the effect of ultrasonic oscillations on the spin polarization of the positive muon of muonium present in matter. The resonant action of the periodic acoustic perturbation on the muonium hyperfine structure levels is shown to result in characteristic oscillations and to modify the muon spin precession pattern considerably. The possibilities for experimental detection of the muonium acoustic resonance are discussed     

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.     

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.     

Muon spin relaxation in spin gap state of BaVS3

Positive muon spin relaxation measurements were performed on a spin-1/2 system BaVS₃, which shows a metal-insulator transition at T_MI= 70 K. We found a marked muon-spin depolarization below T_X= 30 K without appreciable critical divergence. The possibility of muonium formation in the insulating state rather than electron spin freezing is discussed taking into account the quenching of V spins evidenced by ⁵¹V NMR and NQR measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Level crossing resonance in muonium-like systems

This paper describes the phenomenon of level crossing resonance (or avoided level crossing) encountered in paramagnetic systems involving a muon. Recent experiments on muonated radicals and muonium defect centers in semiconductors are reviewed which demonstrate how the technique provides detailed information on nuclear hyperfine structure, which is unresolvable with more standard techniques. The science implications are discussed.     

Muon spin rotation studies of spin dynamics at avoided level crossings in LiY0.998Ho0.002F4

We have studied the Ho3+ spin dynamics for LiY0.998Ho0.002F4 via the positive muon (mu+) transverse field depolarization rate lambdaTF as a function of temperature and magnetic field. We find sharp minima in lambdaTF(H) at fields for which the Ho3+ ion system has field-induced (avoided) level crossings. The reduction scales with calculated level repulsions, suggesting that mu+ depolarization by slow fluctuations of nonresonant Ho3+ spin states is partly suppressed when resonant tunneling opens new fluctuation channels at frequencies much greater than the muon precession frequency.     

Spin-lattice relaxation in hyperfine-coupled systems: Applications to interstitial diffusion and molecular dynamics

The solid state diffusion of hydrogen, or of its pseudo-isotope muonium, provides an interesting example of spin-lattice relaxation in a 2-spin, 4-level system. The local field experienced by the interstitial atom fluctuates as it moves, inducing transitions between the coupled electron and nuclear spin states. Rate equations governing the populations of these states may be solved numerically to simulate the different relaxation functions which would be displayed by ESR, ENDOR and μSR spectroscopies and to assist in extracting motional correlation times from the experimental data. Spin relaxation in molecular radicals may be treated similarly, with different selection rules for different mechanisms: this paper treats the spin rotation mechanism and perturbation to anisotropic or isotropic components of the hyperfine interaction, caused by inter or intra-molecular motion. Conventional magnetic resonance monitors the population differences appropriate to particular transitions; only in sufficiently high fields do these distinguish the electronic and nuclear response. Muon spin relaxation is remarkable in separating out the nuclear spin projection whatever the degree of mixing of the spin states,via the asymmetry in the muon radioactive decay. Experimentally it has the advantage that measurements can be made over a wide range of field, from null external field up to thelevel crossing where the relaxation rate exhibits a striking peak.     

Muonium to diamagnetic muon conversion in KCl and NaCl revealed by time-differential muon spin resonance

The conversion of muonium into a diamagnetic muon state in KCl and NaCl was directly observed by detecting a time-delayed appearance of diamagnetic muon states with muon spin resonance. The conversion rate, determined from the time-differential resonance signals, shows a thermal activation characteristic in temperature variation.