Hyperfine field and diffusion of μ+ in Fe single crystals

In recent positive-muon spin rotation experiment at TRIUMF on single crystal Fe, a clear temperature dependent change has been observed, for the first time, both in frequency and depolarization rates from 300 K down to 23 K. The μ⁺ depolarization was explained by the μ⁺ diffusion through inhomogeneous dipolar fields and the diffusion constant was found to obey an Arrhenius law (activation energy 17 meV) above 70 K but surprisingly deviated from this at lower temperatures, indicating quantum diffusion. We have also found that the μ⁺ hyperfine field has a temperature dependence slightly stronger than that of the magnetization.     

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).     

Anisotropic dielectric function in polar nanoregions of relaxor ferroelectrics

The Letter suggests treating the infrared reflectivity spectra of single crystal perovskite relaxors as fine-grained ferroelectric ceramics: locally frozen polarization makes the dielectric function strongly anisotropic in the phonon frequency range and the random orientation of the polarization at nanoscopic scale requires taking into account the inhomogeneous depolarization field. Employing a simple effective medium approximation (the Bruggeman symmetrical formula) turns out to be sufficient for reproducing all principal features of room temperature reflectivity of Pb(Mg(1/3)Nb(2/3))O3. One of the reflectivity bands is identified as a geometrical resonance entirely related to the nanoscale polarization inhomogeneity. The approach provides a general guide for systematic determination of the polar mode frequencies split by the inhomogeneous polarization at the nanometer scale.     

Magnetic dynamics of dilute iron nano-clusters in silver films from Mössbauer spectroscopy and muon spin rotation

A silver film containing nanometer size clusters of iron (nominal conc. 1 at%) has been studied by Mössbauer spectroscopy and Low-Energy Muon Spin Rotation. Below about 20 K spin glass freezing due to interparticle interactions is found from both methods. Whereas Mössbauer spectra are insensitive to the fast fluctuations of cluster moments above spin glass freezing temperature, muon spin rotation in magnetic fields applied perpendicular to the polarized muon spins allows tracing the fluctuations of superparamagnetic moments. The temperature dependence of the damping of the muon spin rotation signal shows Arrhenius behavior between 10 to 100 K. Depending on the assumed shape of damping the activation energy of superparamagnetic fluctuations of cluster moments ranges between about 20 K ·k _B and 40 K ·k _B . Above about 120 K muon spin depolarization indicates diffusion and trapping of muons.     

The localization and thermal diffusion of positive muons in niobium

The depolarization rate for spin polarized ⁺ particles implanted into a high purity niobium crystal was studied as a function of temperature. The results were analyzed in terms of nuclear dipolar field inhomogeneity due to the host⁹³Nb, and the local field averaging effect of the muon's motion. An analysis is presented in terms of the structure of the muon wavefunction and parameters characterizing the muon diffusion.Supported in part by the U. S. National Science FoundationSupported by the U. S. Energy Research and Development AdministrationSupported by the U. S. National Aeronautics and Space Administration     

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.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

The effect of uniaxial static pressure on the behavior of an aluminum acceptor impurity in silicon

The effect of uniaxial compression on the behavior of shallow aluminum acceptor centers in silicon has been studied. The _μAl impurity atoms were created by implanting negative muons into silicon single crystals doped with phosphorus to 1.6×10¹³ cm^?3 (sample 1) and 1.9×10¹³ cm^?3 (sample 2). The muon polarization was studied in the temperature range 10–300 K. Measurements were performed in a magnetic field of 2.5 kG oriented perpendicularly to the muon spin. The samples were oriented so that the selected crystal axis ([111] and [100] in samples 1 and 2, respectively), the magnetic field, and the initial muon-spin polarization were mutually perpendicular. External pressure applied to the sample along the indicated crystal axis changed both the absolute value of the acceptor magnetic-moment relaxation rate and the character of its temperature dependence.     

Anomalously strong relaxation of the polarization of muons in the magnetically ordered and paramagnetic states of the TbMnO<Subscript>3</Subscript> multiferroic

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO₃ multiferroic has been revealed by the method below the μSR Néel temperature (42 K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO₃. A true paramagnetic state has been observed only at T ≥ 150 K.     

Manifestation of a structural disorder in the polarization kinetics of a KD2PO4 ferroelectric

Crystalline potassium dideuterophosphate subjected to a slowly varying or a dc electric field has been found to exhibit polarization features which indicate the presence of a structural disorder characteristic of inhomogeneous systems. Continuous distribution spectra of the relaxation time are drawn from the experimental data and a phenomenological analysis of the depolarization of the crystal. It is shown that the spectra have an anomalous width and vary with temperature in a way suggesting the transformation of domain-wall potential barriers.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

μSR in antiferromagnetic α-Fe2O3

The first muon spin rotation (μSR) measurement of an internal magnetic field in an antiferromagnet is reported. Experiments on powder and single crystal α-Fe₂O₃ show a discontinuous change in the magnitude and direction of the local field at the Morin transition. The muon is localized at low temperatures, and thermally activated diffusion sets in at about 500 K.     

SR evidence of low frequency spin fluctuations in the AF phase of hole-doped NiO

μSR measurements in the antiferromagnetic (AF) phase of Ni_1-xLi_xO for are reported. While in pure NiO the muon longitudinal depolarization rate is found almost temperature independent, in the Li-doped compounds broad maxima around 130 K are observed. These maxima are associated with the progressive freezing of the spin fluctuations of S =1/2 defects induced by the localization of the extra-holes. From the temperature dependence of and the stretched exponential form of the depolarization, insights on the distribution of correlation times for the fluctuating field at the muon site are derived. Received: 27 April 1998 / Received in final form and Accepted: 21 August 1998     

Electrical conduction and polarization in PbWO<Subscript>4</Subscript> crystals

The regularities of ion-electron processes in an undoped PbWO₄ single crystal upon transition to a quasi-equilibrium state in an external dc electric field with a linear variation in the temperature in the range 290–600 K are investigated using different methods. The total conductivity, thermally stimulated polarization current, and thermally stimulated depolarization current are measured. It is assumed that the temperature dependence of the conductivity can be described within the theory of small-radius polarons. The thermally stimulated polarization (depolarization) currents are interpreted in terms of the space-charge (peaks of the current in the range 400–550 K) and dipole (peaks of the current in the range 290–370 K) mechanisms of generation of a polarization charge in the sample. The inference is drawn that the dominant contribution to the dipole polarization is made by dipolons, namely, doubly charged (cation-anion) vacancy pairs coupled through electrostatic interaction. The basic parameters of relaxation phenomena and charge transfer are calculated.     

Spin dynamics in Cd1−xMnx Te studied by muon spin rotation

Spin fluctuations in Cd_1−xMn_xTe (x=0.05, 0.10, 0.20, 0.30, 0.40, 0.54, 0.60, 0.68) were studied by the muon spin rotation (μSR) technique. Correlation times of the Mn-spins are deduced from the muon depolarization rates. A strong increase of the depolarization rate near the Mn-spin freezing temperature is observed. At 88 K, larger depolization rates are found forx=0.10 andx=0.20 than for higher Mn-concentrations, indicating that the exchange narrowing is considerably reduced (spin fluctuations slow down) for lower Mn-concentrations.     

Quantum diffusion of muon and muonium in solids

The quantum tunneling diffusion of muon and muonium in crystalline solids is discussed with emphasis on the effects of disorder and superconductivity. The complex effect of disorder on muonium diffusion in inhomogeneous crystals is scrutinized. The enhanced muon diffusion in the superconducting state of high-purity tantalum establishes the predominant influence of conduction electrons on the quantum diffusion in metals.     

μSR Investigation of magnetic phases in R1−xSrxCoO3 oxides (R=Pr, Nd)

We report results of our muon spin relaxation measurements in the series of polycrystalline compounds Pr_1−xSr_xCoO₃ (x=0.3, 0.4 and 0.5) and Nd_1−xSr_xCoO₃ (x=0.3 and 0.5). For the Pr-based samples our data clearly indicate the existence of two magnetic transitions, as also inferred from macroscopic measurements. While the high temperature transition is typical for cobaltites (∼200 K), the low temperature one is unusual. In our experiments it occurs below about 120 K and it manifests itself as a change in the slope of the temperature variation of the muon spin depolarization rate λ(T). For the Nd-based samples we found an increase of the muon spin depolarization rate below 45 K, temperature at which the sample is ferrimagnetic, when the Nd sublattice coupled antiparallel to the Co lattice. No phase separation could be evidenced in our samples by μSR experiments.     

Muon spin rotation in liquid noble gases

A new mechanism of slow muon depolarization in liquid noble gases is suggested. The muon spin polarization in [A-μ-A]⁺ complexes is calculated. The results allow one to observe [A-μ-A]⁺ experimentally and to measure hyperfine interaction constants.     

Rochelle salt in an inhomogeneous electric field

The parameters of the hysteresis loop in the ferroelectric Rochelle salt were investigated using a sample with two pairs of electrodes: measurement electrodes and the side ones. It has been shown that the difference between the potentials of the measurement and the side electrodes (generating an inhomogeneous electric field) leads to gradual decay in time t of the remanent polarization P_r. The time required for the hysteresis loop to disappear in the inhomogeneous electric field (not parallel to the ferroelectric axis) decreases with temperature increase from 44±3 h at – 9°C to 2.3±0.1 h at 21.9 °C. On the other hand, the crystal placed for a sufficiently long time simultaneously in the measuring electric field and in the constant inhomogeneous one may finally exhibit a stationary hysteresis loop with a reduced remanent polarization and the unchanged coercive field. It has been shown that the crystal as a whole does not have to be polarized perpendicularly to the ferroelectric axis in order for its hysteresis loop to be reduced.     

Study of magnetic ordering of the high Tc superconductor GdBa2Cu3O7−y by muon spin rotation

Muon spin rotation experiments were performed on the high T_c superconductor GdBa₂Cu₃O_7−y in the temperature range from 30 mK to 130 K. Below 2.3 K, we observe in zero external field well defined muon spin precession showing clearly the presence of magnetic ordering in the sample. Two different frequencies could be distinguished which correspond to internal magnetic fields of 33 and 52 mT, respectively. Above 2.3 K up to about 10 K a fast depolarization of the muon spin is observed indicating the persistance of correlations among the Gd moments well above the Néel temperature.