Quantum diffusion of positive muon in pure tantalum

Quantum diffusion of positive muons has been studied in high purity Ta by zero and longitudinal field muon spin relaxation techniques. We found that the muon hopping rate in Ta is more or less the same as in pure Cu (i.e., \nu\simeq10⁵\sim10⁶\ s^™1), showing a characteristic temperature dependence proportional to T^™\alpha with \alpha ranging from 2 to 0.2 below 20 K. In addition, a step‐like change of the nuclear dipolar width was observed at 60 K associated with the sharp peak of hopping rate, suggesting a change of stable muon sites. This revised version was published online in August 2006 with corrections to the Cover Date.     

An improvement of the Griffiths-Hurst-Sherman inequality for the Ising ferromagnet

We prove the following inequality for the truncated correlation in the Ising model in zero external field: $$\begin{gathered} \langle \sigma _i \sigma _j \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _j \rangle \langle \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _k \rangle \langle \sigma _j \sigma _l \rangle - \langle \sigma _i \sigma _l \rangle \langle \sigma _j \sigma _k \rangle \hfill \\ \leqslant - 2\langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \langle \sigma _k \sigma _m \rangle \langle \sigma _l \sigma _m \rangle \hfill \\ - 2 \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right) \left( {\langle \sigma _j \sigma _k \rangle - \langle \sigma _j \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\langle \sigma _k \sigma _l \rangle \hfill \\ - 2 \langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\left( {\langle \sigma _i \sigma _l \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _l \rangle } \right) \hfill \\ \end{gathered} $$ This inequality is a strengthening of the Lebowitz inequality for the four-point function and implies the following improvement of the GHS inequality: $$\langle \sigma _i ;\sigma ;_j \sigma _k \rangle ^T \leqslant - 2\langle \sigma _i ;\sigma _k \rangle ^T \langle \sigma _j ;\sigma _k \rangle ^T \langle \sigma _k \rangle $$ This in turn implies the critical exponent inequality $$\Delta '_3 \geqslant \gamma ' - \beta $$      

High‐pressure μSR studies of ferro‐ and antiferromagnetic metals

High‐pressure μSR experiments on ferromagnetic nickel and \alpha‐iron and antiferromagnetic chromium are reported. In Ni above 260 K B_Fermi was found to be proportional to the saturation magnetization, whereas at lower temperatures it is temperature independent apart from a small anomaly below 30 K which is presumably caused by a magnetoelastic interaction. There was no evidence for an occupation of metastable sites by the μ⁺ below the Curie temperature. By contrast, in \alpha‐Fe the temperature dependence of \curpartialB_μ/\curpartialp shows a structure which might be attributed to the occupation of excited muon states at elevated temperatures. High‐pressure zero‐field experiments on Cr performed in the temperature regime between 4.5 K and 8 K revealed a pressure dependence of B_μ as large as \curpartialB_μ/\curpartialp=-(89.15\pm 0.06)\times 10^-12 T/Pa. In terms of volume dependence a very large negative Grüneisen parameter \gamma =-27 was obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Muon spin relaxation in diluted triangular‐lattice antiferromagnet

Zero and longitudinal field μSR measurements on diluted triangular‐lattice antiferromagnet LuFeMgO₄ have revealed gradual and highly anisotropic slowing‐down of spin fluctuation. Relaxation rate \lambda in the condition with initial muon spins perpendicular to the hexagonal c‐plane shows divergent behavior while that in the parallel configuration remains finite. At certain temperature range the fluctuation of spins is suppressed by a small external magnetic field. Monte Carlo calculation suggests that the correlation time for z(c)‐component of spins diverges first on cooling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Muonium desorption to vacuum from hot iridium surface

Slow muonium (Mu) emission from the surface of iridium (Ir) foil has been observed in vacuum above \sim1200\ K with a yield of 5(1)% Mu per incident muon stopped in the foil. The relative Mu signal was found to be thermally activated with E_a=1.86(1)\ eV. Analysis of the time‐differential evolution of Mu in vacuum at T_Ir=1580\ K showed that the trapping rate of positive muons during diffusion in the bulk Ir was nearly zero. In situ measurements of the surface of Ir with X‐ray photoelectron spectroscopy verified that the main source of impurities in the 99.9%‐Ir was molybdenum (Mo). This revised version was published online in August 2006 with corrections to the Cover Date.     

Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO3(001)

Exchange coupling across the interface between a ferromagnetic (FM) layer and an antiferromagnetic (AFM) or another FM layer may induce a unidirectional magnetic anisotropy and/or a uniaxial magnetic anisotropy, which has been extensively studied due to the important application in magnetic materials and devices. In this work, we observed a fourfold magnetic anisotropy in amorphous CoFeB layer when exchange coupling to an adjacent FeRh layer which is epitaxially grown on an SrTiO₃(001) substrate. As the temperature rises from 300 K to 400 K, FeRh film undergoes a phase transition from AFM to FM phase, the induced fourfold magnetic anisotropy in the CoFeB layer switches the orientation from the FeRh$\langle 110\rangle $ to FeRh$\langle 100\rangle $ directions and the strength is obviously reduced. In addition, the effective magnetic damping as well as the two-magnon scattering of the CoFeB/FeRh bilayer also remarkably increase with the occurrence of magnetic phase transition of FeRh. No exchange bias is observed in the bilayer even when FeRh is in the nominal AFM state, which is probably because the residual FM FeRh moments located at the interface can well separate the exchange coupling between the below pinned FeRh moments and the CoFeB moments.     

Spin fluctuations and magnetic order in the heavy fermion compound CePt2Sn2

We present zero and longitudinal field μ SR measurements of single crystal and polycrystalline specimens of the heavy fermion compound CePt₂Sn₂. Above 1 K the behaviour of the two samples is indistinguishable; the muon 1/T_1 increases with decreasing temperature until 25 K when it plateaus. The 1/T_1 relaxation rate differs strongly for the two cases below \sim\,0.8\ K. At 0.1 K a rate of about 20 μ s^-1 is seen in the polycrystal while in the single crystal it is only about 5 μ s^-1. Even more revealing is the fact that longitudinal field decoupling spectra at very low temperatures demonstrate an essentially static spin system to be present in the polycrystalline material while the single crystal shows definite dynamic spin properties. We conclude that, in the presence of the distortion, long range magnetic order occurs below 0.9 K while in tetragonal symmetry long range order is suppressed (probably due to frustration) and spin fluctuations remain for T\rightarrow0. This revised version was published online in July 2006 with corrections to the Cover Date.     

The giant muon Knight shift in antimony: Evidence for a Kondo impurity

A detailed study has been undertaken of the muon Knight shift in high purity antimony single crystals. No periodic variations with magnetic field (de Haas–van Alphen oscillations) are observed. The temperature dependence below 175 K is close to that expected for a Kondo‐like impurity with an anisotropic muon–electron hyperfine interaction. At higher temperatures the paramagnetic state becomes unstable and a transition occurs to a second state. The longitudinal relaxation rate rises from an apparently non‐zero value at T=0 to a maximum at 50 K, followed by a slow decline. This leads to a Korringa product which is strongly temperature dependent. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Time‐differential radio‐frequency muon spin resonance (TD‐RFμSR) technique at a pulsed muon beam

Longitudinal‐field μSR methods, e.g., radio‐frequency μ⁺ spin resonance (RFμSR), are well suited to investigate dynamic processes that destroy the phase coherence of the muon spin ensemble. Additional information on relaxation processes of the muon species under investigation is obtained from time‐differential (TD) data acquisition. In this paper we describe the set‐up of a TD‐RFμSR spectrometer installed at the ISIS pulsed muon facility at the Rutherford Appleton Laboratory (RAL, Chilton, UK). As an example, results of TD‐RFμSR measurements on muons in diamagnetic environment μ^d in a boron‐doped silicon sample under illumination at 55 K are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Influence of doping admixture and anisotropic tension on behaviour of muon spin polarization in insulators

Zero‐field μSR measurements have been carried out in the paramagnetic and magnetically ordered states of the heavy fermion alloys: Ce_1-xLa_xRu₂Si₂ (x=0.05,0.13,0.25). In Ce_1-xLa_xRu₂Si₂ system, T_K drastically decreases with x from 24 K for x=0 and becomes very close to the magnetic ordering temperature T_N. As functions of T_K and T_N, the magnetic instabilities were studied in this system. For x=0.05,\ 0.13\ \mboxand\ 0.25 samples, longitudinal muon spin relaxation was measured to study non‐magnetic to magnetic transition and the change from itinerant to localized electron state with increasing La impurities. We discuss the dynamics of muon spins in the paramagnetic and antiferromagnetic state. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ferromagnetic erbium studied by μSR

The ferromagnetic cone phase of erbium has been studied with μSR. Two precessing muon signals were observed with nearly equal intensities at T\approx15\ K. At lower temperatures, one of the signals is gradually reduced and disappeared below 5 K. The two observed muon frequencies and their depolarisation behaviour show that the magnetic structure deduced from neutron and X‐ray scattering must be modified and that a “squaring up” of the structure is likely to occur as the temperature is lowered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Anomalous field dependence of muon Knight shift and line width in the singlet ground state compound PrCu2

We report on ZF and TF‐studies of PrCu₂ above the induced Jahn–Teller transition at 7.3 K. Generally a two‐component signal is found, one showing inhomogeneous the other one homogeneous, temperature dependent line broadening. In ZF the former component is well represented by a Gaussian Kubo–Toyabe function with \varDelta \simeq 6.5\,μs^-1 at 7.5 K, corresponding to a field width of 76 G. This is about 30 times larger than what is calculated to arise from the ¹⁴¹Pr‐nuclear dipole moments alone, pointing to strong hyperfine enhanced features. TF‐field scans at 12 K revealed that the enhancement is suppressed in external fields exceeding 1 kG. In parallel the Knight shift drops from very large values well above 10% at 100 G to shifts of the order of 1% above 1 kG. A scaling of the Knight shifts with the corresponding relaxation rates seems to imply that the strange field dependence below 1 kG is associated with the magnetic susceptibility of the muons’s nearest neighbour Pr³⁺‐ions, a result for which we have no explanation yet to offer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Texture effect on vortex‐state TF‐μ+SR in Bi‐2223 high‐TC materials

The influence of texture in Bi‐2223 ingots on the temperature dependence of the μ⁺ spin relaxation rate has been investigated. Texture was induced during cold‐isostatic‐pressing by applying an additional uniaxial load which tends to align single grain c axes along the stress direction, \widehatz. Small plates were cut with faces either \Vert or \perp \widehatz and μSRwas measured in a 15 mT transverse field (TF) during cooling from room temperature to 6 K. While for highly‐textured material, low‐temperature limits are substantially smaller than expected, the large shift (55%) observed when switching from \widehatz\perp TF to \widehatz\,\Vert TF clearly indicates that anisotropy has developed. Relaxation rates for the weakly‐textured sample lie in between. To a lesser extent, sintering also enhanced the low‐temperature relaxation, but did not affect T_C significantly. All samples showed a weak onset of depolarization between 60 K and 90 K, most likely due to the presence of a Bi‐2212 impurity phase. This impurity phase might cause the transition‐temperature smearing in the 100–110 K range in the weakly textured (and less compacted) material. Thus the sharpness of the relaxation drop might be relevant for assessment of material quality and be used as a criterion in the improvement of the production process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electric field influence on spin polarization vector behaviour of the negative muon in silicon

When a negatively charged muon is captured by a silicon atom, the atom is transformed into a solitary acceptor center similar to an Al atom. An external electric field influences the formation process of the neutral acceptor center (A.C.). It is shown in this article that the behaviour of the muon polarization vector changes appreciably in electric fields with intensities E\,\gtrsim\,10 V/cm. We estimate the muon spin relaxation rate \varLambda_μ in the so‐called “dirty limit”; for example, interaction between an internal electric field from charged impurities and a nonzero dipole moment of the A.C. is taken into account. A phonon mechanism is proposed to explain the temperature dependence of \varLambda_μ. We also estimate the value of the paramagnetic shift of the muon spin precession frequency \delta\omega/\omega₀ which is also temperature dependent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Direct evidence for dia‐ and paramagnetic domains in beryllium

The first spectroscopic evidence for dia‐ and paramagnetic domains (Condon domains) in beryllium metal is presented. The domains, detected by the splitting of the μSR line, arise and disappear periodically in each de Haas–van Alphen cycle as the field \bf H, normal to the single crystal Be plate and parallel to its [0001] axis, is tuned near \bf H_0\approx 2.7\ T. The intensity of the lines in the doublet reflect the ratio of dia‐ to paramagnetic regions. For the difference in induction within the domains we obtain \Delta B\approx 30\mbox--40\ G in the investigated field range at T=0.8 K. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time \(\ensuremath \langle\tau\rangle\) , the average velocity of the center of mass \(\ensuremath \langle v_{{\rm CM}}\rangle\) , and the effective radius of gyration \(\ensuremath \langle {R}_g\rangle\) during the translocation process defined as \(\ensuremath \langle\tau\rangle \sim N^{\alpha}\) , \(\ensuremath \langle v_{{\rm CM}} \rangle \sim N^{-\delta}\) , and \(\ensuremath {R}_g \sim N^{\bar{\nu}}\) respectively, and the exponent of the translocation coordinate (s -coordinate) as a function of the translocation time \(\ensuremath \langle s^2(t)\rangle\sim t^{\beta}\) . We find \(\ensuremath \alpha=1.36 \pm 0.01\) , \(\ensuremath \beta=1.60 \pm 0.01\) for \(\ensuremath \langle s^2(t)\rangle\sim \tau^{\beta}\) and \(\ensuremath \bar{\beta}=1.44 \pm 0.02\) for \(\ensuremath \langle\Delta s^2(t)\rangle\sim\tau^{\bar{\beta}}\) , \(\ensuremath \delta=0.81 \pm 0.04\) , and \(\ensuremath \bar{\nu}\simeq\nu=0.59 \pm 0.01\) , where \( \nu\) is the equilibrium Flory exponent in 3D. Therefore, we find that \(\ensuremath \langle\tau\rangle\sim N^{1.36}\) is consistent with the estimate of \(\ensuremath \langle\tau\rangle\sim\langle R_g \rangle/\langle v_{{\rm CM}} \rangle\) . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent α = 1.36 ± 0.01 < 1 + ν. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the “cis” and “trans” parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For thek _⊥ jet finder withy _cut=0.02, we find as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

Temperature dependence of the muon and proton hyperfine constants of an \alpha‐muonium‐substituted methyl radical

Muon hyperfine constants A_μ have been measured by transverse field μSR for (CH₃)₃Si\mbox\.CHMu in hexane from 167 K to 332 K. In addition, avoided level‐crossing resonance was used to determine \alpha‐proton coupling constants A_p over a similar range of temperatures. The two hyperfine constants can be described by a common temperature dependence, d|A_i|/ dT=1.4\times 10^-3 MHz\,K^-1, where A_i represents A_p or the reduced muon constant A^\prime_μ=0.3141A_μ. There is a small isotope effect (A^\prime_μ is 2.2 % larger than A_p) consistent with zero‐point motion in the anharmonic C–H bond stretch. The common temperature dependence is tentatively attributed to a coupled deviation of the C–H and C–Mu bonds out of the nodal plane of the p orbital containing the unpaired electron. This revised version was published online in August 2006 with corrections to the Cover Date.