Anomalous frequency shift of negative muon spin precession in n‐type silicon

The dependence of the residual polarization of negative muons in n‐type Si with impurity concentration (1.6\pm 0.2)\times 10¹³\ cm^-3 on temperature in the 10–300 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. Muon spin relaxation and frequency shift were observed at temperatures below 30 K. The relaxation rate at 30 K is equal to 0.25\pm 0.08\,μ s^-1. The frequency shift at 20 K is equal to 7\times 10^-3. Both the relaxation rate and the frequency shift grow with decrease of temperature. Below 30 K the relaxation rate is well described by the dependence \varLambda=bT^-q, where q=2.8. An analysis of present and earlier published data on behavior of negative muon polarization in silicon is given. A possible mechanism of relaxation and frequency shift of muon spin precession in silicon is considered. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ − SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×10¹³ cm⁻³) and antimony (Sb: 2×10¹⁸ cm⁻³) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center _μ A1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 61–66 (10 July 1998)     

μ+SR study of vacancies in thermal equilibrium in ferromagnets

Muon spin precession frequencies and transverse relaxation rates have been measured on demagnetized iron, cobalt, and FeCo alloys (3 at%–50 at% Co) between room temperature and the Curie temperatureT _c. The increase of the relaxation rate in iron between 930 K and 1010 K could be quantitatively attributed to the trapping of positive muons by vacancies in thermal equilibrium, resulting in an enthalpy of monovacancy formation ofH _1V ^F =(1.7±0.1) eV. the smallest vacancy concentrations detected are = 10⁻⁸.     

Zero-field muon spin rotation in monocrystalline chromium

Spin precession of positive muons in chromium in zero applied magnetic field is reported for the first time. The observations cover the temperature range from about 2.5 K to 10 K and thus pertain to the so-called longitudinal spin-density wave (LSDW) state of antiferromagnetic Cr. The conclusions that may be drawn from the existence of one rather sharp spin precession line are discussed, among them the estimateD _μ=2.4·10⁻¹⁴ m² s⁻¹ for the muon diffusivity at 4 K. Considerable evidence exists for a strong interactions of μ⁺ with the charge-density waves that are likely to accompany the LSDWs in Cr.     

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.     

μ+SR Study of Ordering Phenomena in the Heavy-Fermion State of Ce3Pd20Ge6

Magnetic and quadrupolar ordering phenomena in a Ce₃Pd₂₀Ge₆ single crystal have been investigated by muon spin rotation/relaxation (μ⁺SR) spectroscopy. We have observed spontaneous precession of muons in zero-field below T _N =0.7 K in the antiferromagnetic state. The precession frequency follows the power law: ν(T)=ν(0)(1−T/T _N ) ⁿ . The exponent n=0.43(2) is close to the mean-field value of 0.5. The muon longitudinal spin relaxation rate 1/T ₁ is found to be nearly independent of temperature in the range of 0.3 to 2 K, i.e., across either T _N or T _Q =1.2 K, the quadrupolar ordering temperature. Two likely mechanisms for the temperature independent behavior of 1/T ₁ are suggested. This revised version was published online in September 2006 with corrections to the Cover Date.     

Muon spin relaxation for Ar+NO2 systems in transverse and longitudinal magnetic fields

Surface muons produced in UT-MSL were introduced into argon gas of 4.0±0.2 atm with NO₂ (0–30 ppm), and muonium signals were detected in the presence of a transverse (1.7–3.4 G) and a longitudinal magnetic field (0–3.5 kG) at 295±1 K. The cross section for the transverse relaxation was (11.0±1.0)×10⁻¹⁶ cm². The relaxation rates in different longitudinal magnetic fields show that the rate does not follow the conventional equation which assumes that the relaxation occurs mainly by spin-exchange interaction. Similar measurements were performed for the Mu+O₂ system. These findings indicate that chemical reactions contribute to these relaxation rates.     

Investigation of the behaviour of the impurity atoms in Si by μ− SR-method

The dependence of the residual polarization of negative muons in p-type Si on temperature in the 4.2–270 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. The impurity concentration in the sample was 2 · 10¹³ cm^–3. Muon spin relaxation was observed at temperatures below 30 K. The relaxation rate atT=30 K is equal to 0.18±0.08s^–1. The relaxation rate grows with the decrease of temperature and at 4.2 K exceeds 30s^–1. The value of the residual polarization at zero timeP(t=0) is constant within the investigated temperature range.In the rangeT<30 K data on the relaxation rate are well described by the dependence =B·T^–q, whereq=2.75. Power dependence of may evidence the essential role of the phonon mechanism in the relaxation of the electron momentum of the acceptor center.The authors express their gratitude to V.B. Brudanin and I.A. Yutlandov for providing the sample, and to Yu.B. Gurov for advices.     

μ− SR in semiconductorsSR in semiconductors

μ⁻ SR experiments have been performed on Si between room temperature and 6 K. The amplitude of the muon spin precession signal in an applied magnetic field of 0.04 T decreased below 30 K. A zero-field measurement at 6 K revealed a μ⁻ spin precession frequency of 650 MHz. The muonic atom represents an aluminium acceptor in the silicon matrix, its electronic state is responsible for the μSR signal. A possible influence of the γ recoil produced by the X-ray cascade is discussed.     

Cosmic ray muons at a depth of 754 hg/cm2 in the Kolar gold Mines

A telescope of area 4 m², consisting of horizontal layers of plastic scintillators, neon flash tubes and absorbers was operated at a depth of 754 hg/cm² in the Kolar Gold Mines. New values for the vertical intensities of muons have been obtained from observations of the angular distribution over the slant depths ∼ 750–2300 hg/cm² and are compared with the existing measurements. From the angular distribution observed, we conclude that muons are produced wholly through the decay of pions and kaons up to energies of the order of 1 TeV. A value of 0.3±0.2 is estimated for theK/π ratio at production, for muon energies around 500 GeV. A decoherence distribution has been obtained for parallel muon events up to distances of the order of 10 m. From this we conclude that the averageP _t of the parents of muons of energy ∼ 250 GeV is of the order of 0.3 GeV/c. From an analysis of rock showers, we obtain the cross section for inelastic interaction of muons of mean energy 100 GeV as (3.8±1.5)×10⁻³⁰ cm²/nucleon.     

Experimental determination of the rate constant for spin exchange in collisions of polarized metastable helium atoms with ground-state cesium atoms

The rate constant for spin exchange in a system consisting of a metastable helium atom and an alkali-metal atom is determined. An experiment on optical orientation of atoms established that the rate constant for spin exchange in a collision of a metastable 2³ S ₁ helium atom with a cesium atom in the 6² S _1/2 ground state equals (2.8±0.8)×10⁻⁹ cm³ s⁻¹. The rate constant for chemoionization of cesium atoms by metastable helium atoms was determined at the same time to be (1.0±0.3)×10⁹ cm³s⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 145–148 (10 August 1997)     

Muons in type-II superconductors: μ+ diffusion in ultra-pure niobiumdiffusion in ultra-pure niobium

The diffusivityD _μ of positive muons (μ⁺) in the mixed state of superconducting high-purity, high-perfection niobium single crystals is investigated by measurements of the relaxation of the transverse muon spin polarization (μ⁺SR). The method makes use of the strong magnetic field gradients existing in the mixed state of Type-II superconductors and monitorsD _μ through the variation of the magnetic field felt by the μ⁺ during their diffusion through the crystals. For μ⁺ near the centres of the flux lines inNb it givesD _μ(4.6 K)=(8±2)·10⁻¹¹m²S⁻¹. The positive temperature coefficient ofD _μ indicates that at liquid-helium temperatures the diffusivity of μ⁺ inNb is mainly due to phonon-assisted tunnelling processes.     

Spin susceptibility of neutron-irradiation-disordered YBa2Cu3O6.9 in the normal and superconducting states

The spin-spin relaxation rate ⁶³ T ₂ ⁻¹ of ⁶³Cu nuclei in CuO₂ layers is measured in the normal and superconducting states of the compound YBa₂Cu₃O_6.9 (T _c ^onset =94 K) subjected to radiation-induced disordering by a fast-neutron flux Φ to T _c ^onset =68 K (Φ=7×10¹⁸ cm⁻²) and T _c ^onset <4 K (Φ=12×10¹⁸ cm⁻²). It is found that as the structural disorder increases, the contribution of the indirect spin-spin interaction ⁶³ T _2G ⁻¹ , which is related to the value of the spin susceptibility at the boundary of the Brillouin zone of the copper planes χ_s(q={π/a; π/a}), decreases slightly at the transition to the superconducting state for the initial sample and remains unchanged for the weakly disordered sample. This behavior of the short-wavelength contribution to the spin susceptibility attests to the stability of the x ²−y ² symmetry of the energy gap against structural disorder, in accordance with proposed theoretical models of Cooper pairing for high-T _c cuprates. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 172–177 (10 February 1998)     

Interaction of muonium with oxygen on silica powder surfaces

Results of the first μSR studies using Merck FO Optipur silica powder, which contains paramagnetic impurities at the ppb level and has a surface area of 610±20 m²/g. are reported. Above 20 K, the transverse field muonium relaxation rate is roughly constant at 0.5 μs⁻¹. Upon the addition of oxygen at ppm levels, the relaxation rate increases linearly with O₂ concentration in the temperature range from 40–100 K yielding two-dimensional depolarization rate constants on the order of 10⁻⁴ cm² molecule⁻¹ s⁻¹. As the temperature is increased further, both oxygen and muonium desorb from the surface yielding a three-dimensional rate constants at 300 K of 3.1(3)×10–10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, in agreement with the gas phase value. Longitudinal field measurements suggest that MuO₂ is formed and is able to spin exchange with other oxygen molecules.     

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ ⁺ e⁻). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu^* state in diamond and silicon.     

Study of single muons with the Large Volume Detector at the Gran Sasso Laboratory

The present study is based on the sample of 2.9×10⁶ single muons observed by the Large Volume Detector (LVD) at the underground Gran Sasso Laboratory during 36 500 live hours from June 1992 to February 1998. We have measured the muon intensity at slant depths from 3 to 20 km w.e. Most events are high-energy downward muons produced by meson decay in the atmosphere. The analysis of these muons has revealed the power index γ of the π and K spectrum: γ=2.76±0.05. The remainders are horizontal muons produced by the neutrino interactions in the rock surrounding the LVD. The value of this flux near 90° is (6.1±2.7)×10⁻¹³ cm⁻² s⁻¹ sr⁻¹. The results are compared with the Monte Carlo simulations and the world data. From Yadernaya Fizika, Vol. 66, No. 1, 2003, pp. 125–132. Original English Text Copyright ? 2003 by Aglietta, Alyea, Antonioli, Badino, Bari, Basile, Berezinsky, Bersani, Bertaina, Bertoni, Bruni, Cara Romeo, Castagnoli, Castellina, Chiavassa, Chinellato, Cifarelli, Cindolo, Contin, Dadykin, Dos Santos, Enikeev, Fulgione, Galeotti, Ghia, Giusti, Gomez, Granella, Grianti, Gurentsov, Iacobucci, Inoue, Kemp, Khalchukov, Korolkova, P. Korchaguin, V. Korchaguin, Kudryavtsev, Luvisetto, Malguin, Massam, Mengotti Silva, Morello, Nania, Navarra, Periale, Pesci, Picchi, Pless, Ryazhskaya, Saavedra, Saitoh, Sartorelli, Selvi, Taborgna, Talochkin, Trinchero, Tsuji, Turtelli, Vallania, Vernetto, Vigorito, Votano, Wada, Weinstein,Widgoff, Yakushev, Yamamoto, Zatsepin, Zichichi. The authors represent the LVD Collaboration This article was submitted by the authors in English.     

Interactions of μAl acceptor impurity in weakly and heavily doped silicon

The interactions of the aluminum acceptor impurity in silicon are investigated using polarized negative muons. The polarization of negative muons is studied as a function of temperature on crystalline silicon samples with phosphorus (1.6×10¹³ cm^?3) and boron (4.1×10¹⁸ cm^?3) impurities. The measurements are performed in a magnetic field of 4.1 kG perpendicular to the muon spin, in the temperature range from 4 to 300 K. The experimental results show that, in phosphorus-doped n-type silicon, an _μAl acceptor center is ionized in the temperature range T>50 K. For boron-doped silicon, the temperature dependence of the shift of the muon spin precession frequency is found to deviate from the 1/T Curie law in the temperature range T ? 50 K. The interactions of a _μAl acceptor that may be responsible for the effects observed in the experiment are analyzed.     

Frequency shift and relaxation of muon-spin-precession in Cd1−xMnxTe

Transverse-field muon spin roation (μSR) is studied in Cd_1−xMn_xTe, x=0.4 and 0.6 mixed crystals. A large temperature dependent frequency shift and a strong relaxation of the μSR-signal are observed. In the vicinity of the spinglass transition, the relaxation rate becomes so large that the signal disappears. The rate of Mn spin fluctuations causing the μ⁺-line narrowing at high temperatures is estimated to be of the order of 10⁹ S⁻¹.     

μ− SR studies of oxide-superconductorsSR studies of oxide-superconductors

The negative muon spin rotation method (μ⁻ SR) has been applied to studies of electronic states at oxygen sites of oxide superconductors YBa₂Cu₃O₇, Nd_2−x Ce _x CuO_4−δ (x=0.15, oxygen reduced), LiTi₂O₄ and related oxide-insulators La₂CuO_4−δ, CuO, Cu₂O. The paramagnetic shifts of μ⁻ trapped at oxygen nuclei in these polycrystalline powder samples have been measured at 300 K. All the measured shifts are positive. In copper-oxides the paramagnetic shifts are of the order 10⁻³, while in LiTi₂O₄ is very small (8.4±3.34×10⁻⁵). In YBa₂Cu₃O₇, a fast μ⁻ spin relaxation timeT ₂ ^* (∼ 200 ns) has been observed; the reason for this is unknown and further studies are now in progress.     

Theg-factor of the 659 keV level in117In

We have measured theg-factor of the 659 keV, 3/2⁺, state in¹¹⁷In, using time differential perturbed angular correlation technique. The spin precession of this state was measured in an external field of 20·2 kG. The values of the Larmor precession frequencyω and theg-factor are obtained to be (60·1±0·3)10⁶ rads/sec and 0·625±0·007 respectively.