Muon Relaxation Research Articles

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.

μSR on the novel heavy‐fermion system Nd 2-y Ce y CuO 4

The magnetic correlations in Nd2-yCeyCuO4 have been studied by zero and longitudinal field μSR. Nd1.8Ce0.2CuO4 reveals a saturation of the muon relaxation rate below 0.5 K. Even down to 70 mK LF spectra evidence spin fluctuations in the dynamic regime with a rate of \sim 109 s-1 excluding long range magnetic order or spin glass freezing. The average Nd moment is estimated to be \approx 0.2\muB, i.e., strongly reduced from the value determined for the ground state Kramers doublet of Nd2CuO4. Extending former μSR measurements on Nd2CuO4, a gradual enhancement of the internal field has been detected below 10 K which is accompanied by an increase of the relaxation rate. These results are attributed to the development of ordered Nd moments.

μSR study of intermediate heavy fermion system CeRuSi2

ZF, LF and TF μSR measurements have been carried out with a polycrystalline CeRuSi2 sample. ZF data show a sharp increase of the muon relaxation rate below the temperature T=12 K (0.42 μ s-1 at T=4.2 K) justifying the phase transition to the magnetically ordered state. The results of LF measurements at T=4.2 K show that the magnetic fields on the muon Bμ, produced by the cerium magnetic moments, are mainly static – external longitudinal field of 150 Oe practically recovers the muon spin polarization. In the paramagnetic phase the polarization decay has an exponential form at all measured temperatures 20 K < T < K, though LF experiment at T=20 K clearly shows a significant static contribution (\sim 75%). This situation is discussed in frames of double relaxation model. The ferromagnetic type of magnetic ordering was proved by hysteresis behavior of (B–H) observed in TF‐experiment.

μSR investigations of gadolinium in the paramagnetic regime near the ferromagnetic transition

We report on the measurements of the muon relaxation rate in gadolinium (Gd) in the critical regime down to T-TC=0.1 K. The results are compared to the predictions of mode‐coupling calculations for a uniaxial and dipolar ferromagnet. One observes that even if the uniaxiality in Gd is quite small, it should not be neglected in order to get a consistent description of our data. Most striking is the fact that these investigations support the assumption that above TC the muon resides on the tetrahedral interstitial sites and not on the octahedral sites which are chosen in the low temperature phase.

Spontaneous magnetic ordering in CeRh3B2 observed by zero-field muon-spin relaxation

Abstract Muon-spin relaxation measurements have been made on polycrystalline CeRh3B2 in zero magnetic field. Well above the Curie temperature (T c ≅ 120 K) muon relaxation is described by a Gaussian rate (∼ 0·1 μs−1) indicative of static and random nuclear 11B dipole moments. Near Tc the relaxation rate increases dramatically due to slowing down of fluctuating Ce magnetic moments. Oscillations are observed in the muon spin polarization below Tc , which is unambiguous evidence for the onset of local magnetic ordering. The magnitude of the ordered field initially increases with decreasing temperature and attains a maximum value of 13mT near 50 K. The general shape of the field versus temperature curve resembles the magnetization curve, as expected for an ordinary ferromagnet. However, further decrease in temperature reduces the field to 11 mT at 12K, which we attribute to magnetic ordering of Rh moments. Below 50 K these moments appear to order antiferromagnetically with Ce moments thus producing an effecti...

Probing the Spin-Spin Dynamical Autocorrelation Function in a Spin Glass above Tg via Muon Spin Relaxation.

We report zero and longitudinal field muon spin relaxation measurements in the metallic spin glass AgMn(0.5 at. %) at $Tg{T}_{g}$. We find that muon polarization obeys a time-field scaling relation which allows us to distinguish between three possible forms of the spin-spin dynamical autocorrelation function: a power law, a stretched exponential, and a cutoff power law. We also discuss the evolution of the muon relaxation line shape as the temperature approaches ${T}_{g}$.

Studies on spin dynamics in doped URu 2Si 2

We present muon relaxation studies on two doped URu 2Si 2-based compounds — (U 0.95La 0.05)Ru 2Si 2 and (U 0.5Y 0.5) Ru 2Si 2. In the 5% La doped sample, we found the time dependence of muon spin depolarisation rather similar to our previous observations on (U 0.95Y 0.05)Ru 2Si 2. Surprisingly, similar behaviour has also been shown in our work on (U 0.5Y 0.5)Ru 2Si 2. The onset temperatures of magnetic order from μSR agree well with our conclusions from previous transport and thermodynamic studies that a magnetic order parameter develops at 14 and 17 K for 5% La and 50% Y doped samples respectively and as in pure URu 2Si 2 never saturates down to 5 K. Comparisons will be made with previous studies on URu 2Si 2 and other doped URu 2Si 2.

Muon spin relaxation and hydrogen diffusion in the HfV2 Laves phase

Muon spin relaxation has been measured using the zero-magnetic-field technique in the HfV2 Laves compound containing interstitial hydrogen. At low temperatures the relaxation profiles have the characteristic form associated with fluctuating local fields. The correlation time is almost independent of temperature. As the temperature is raised above about 100 K, motional narrowing takes place in which the correlation time of the local field decreases rapidly. Comparison with the hopping rate of the hydrogen atoms, as measured by means of nuclear magnetic relaxation, shows that the change in the correlation time is consistent with an increasingly rapid motion of the hydrogen atoms. If the sample is then cooled, hysteresis occurs, in which the motional narrowing is retained to lower temperatures. The hysteresis in the muon relaxation rate together with parallel effects present in the nuclear magnetic relaxation are discussed in relation to the phase changes that are known to occur in this alloy.

Comment on "Generalization of the Abragam relaxation function to a longitudinal field"

The muon spin relaxation technique (\ensuremath{\mu}SR) has proven to be a powerful experimental tool for the investigation of light interstitial diffusion in metals and magnetic phenomena. In order to deduce, from the \ensuremath{\mu}SR data, information on the physical properties of the investigated system a model is needed for the measured depolarization function. Recently Keren [Phys. Rev. B 50, 10 039 (1994)] has proposed an analytic result (AR) for the muon relaxation function in a dynamical magnetic environment and an external longitudinal field. He argues that his result is valid in the motional-narrowing limit or at the early time. In this comment we point out that the applicability of the proposed AR to real systems is limited because it does not incorporate some basic physical facts.

Muon spin relaxation in antiferromagnets: a study of RbMnF3 based on the coupled mode theory of paramagnetic and critical spin fluctuations

The relaxation rate for the depolarization of a positive muon implanted in an antiferromagnetically coupled Heisenberg magnet is studied on the basis of a coupled mode theory of critical and paramagnetic spin fluctuations, which gives overall an unrivalled account of spin fluctuations. The paper includes the first comprehensive treatment of the dipole field that couples the muon and atomic (spin) magnetic moments. An analytical calculation of the relaxation rate is feasible in the vicinity of the critical temperature, because of the dominant role of the critical fluctuations, whereas in general numerical methods are required to calculate the spin response function and the dipole field. In the approach to the critical temperature, the muon relaxation rate increases as the square root of the correlation length. Results for the isotropic antiferromagnet RbMnF3 demonstrate that the relaxation rate is not a monotonic function of the temperature, and the magnitude and temperature variation of the relaxation rate depend to a significant degree on the site of the implanted muon. A theoretical framework for the interpretation of the muon relaxation rate is reviewed in a set of appendices.

Studies of hydrogen in semiconductors using the positive muon as a proton analogue

Implanted in a material, the positive muon mimics the proton in its chemical and elastic interactions. In non-metals it can pick up an electron to form muoniurn , Mu = [μ + e - ], which behaves as a light isotope of hydrogen. This may be observed with remarkable sensitivity by the μSR techniques (muon rotation, relaxation and resonance), whereas hydrogen, when present only as a trace impurity, may be difficult or impossible to detect by conventional spectroscopies. Much of the structural information on isolated hydrogen defect centres in semiconductors has in fact come from μSR studies of their muonium counterparts: particularly important has been the discovery of metastability and identification of the bond-centred state. Current studies are of both fundamental and technological interest and concern the interplay of site and charge state, the trapping and detrapping of carriers at these deep level centres, and the nature of interstitial diffusion. Extension to the modelling of hydrogen passivation in doped material, the development of optical and IR spectroscopy and of thin-film or surface studies, all appear timely and promising.

Spin dynamics in the commensurate antiferromagnet PrCo2Si2 probed by muon spin relaxation measurements

Muon relaxation measurements on the uniaxial commensurate antiferromagnet PrCo2Si2 show that whereas the relaxation rate probing the fluctuations along the c-axis has a strong maximum at TN, the rate probing the c-plane fluctuations presents only a weak maximum which occurs at ∼ 3 K below TN.

Transverse field dependence of muonium relaxation: Spin exchange and chemical reaction

It has been shown experimentally that the muonium relaxation due to spin exchange is 1.5 times faster in intermediate transverse fields (say, atB=50 G, where the so-called two-frequency muonium signal is observed) than in low fields (say, atB=5 G), in agreement with an earlier theoretical prediction. It has also been confirmed experimentally that this distinct field dependence is totally absent in the case of chemical reaction.

Muons and muonium in cryocrystals

We present a collection of measurements of the muon and muonium asymmetries and relaxation parameters in cryocrystals of N2, CO, Xe,136Xe and Ne as functions of temperature. Generally, the fractions of the two species can be attributed to a competition between the formation of muonium or a diamagnetic species, where processes involving transport of spur electrons are important.

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-14N2) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T1−1) and transverse (T2−1) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation timeτc; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate τc−1 gives clear evidence that Mu quantum diffusion ins-N2 is governed by the two-phonon interaction.

Muon spin-lattice relaxation and muonium diffusion in ice

Longitudinal muon spin relaxation is measured in ice, using samples with and without enrichment in H217O, with a view to studying the mobility of the muonium fraction. A conventional analysis of the data, on the assumption that relaxation of the diamagnetic fraction is negligible, suggests that more than one mechanism of muonium relaxation is at work. A Bayesian analysis warns that separation of the diamagnetic and paramagnetic signals may not be so straightforward.

Generalization of the Abragam relaxation function to a longitudinal field.

We obtain an analytical form for the muon relaxation function in a dynamical magnetic environment and an external logitudinal magnetic field using perturbation theory. The new relaxation function is compared with the semiclassical Kubo-Toyabe function and the result of Monte Carlo simulation. We also demonstrate the application of our result to the case of dilute spin glasses.

Magnetic muon relaxation in liquid helium-3

The transverse and longitudinal muon (μ +) spin relaxation in liquid 3He was studied in the temperature range 0.5 – 2.5 K. The obtained results manifest two different relaxation mechanisms: “recombinational” depolarization, i.e. slow muonium formation, and magnetic relaxation, which is due to the presence of 3He nuclear magnetic moments.

Muonium exchange as a Poisson process: magnetic field dependence transverse fields

The muonium spin exchange has been investigated as a function of transverse magnetic field strength, where the Poisson nature of collisions is exploited to simplify the calculation. In intermediate fields where the so-called two-frequency muonium signal is observed, the muonium relaxation due to spin exchange is 1.5 times faster than in low fields. In even higher fields, the observed relaxation rate drops back to the low field value. Since the relaxation rate due to a chemical reaction is field independent, such a distinct field dependence in spin exchange can be used in distinguishing experimentally spin exchange from chemical reactions. The time evolution of the muon spin polarization in the presence of muonium spin exchange has been expressed in a simple analytical closed form.

Weird muonium diffusion in solid xenon

Muon and muonium spin rotation and relaxation parameters were studied in liquid and solid xenon. The small diamagnetic fraction (∼10%) observed in condensed xenon is believed to be Xeμ +. The muonium hyperfine frequency was measured for the first time in liquid Xe and was found to be in agreement with the vacuum value. A nonmonotonic temperature dependence of the muonium relaxation rate probably indicates that muonium diffusion in solid Xe is of quantum nature.