Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

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.     

μ+ SR studies on pure MnF2 and site-diluted (Mn0.5Zn0.5)F2SR studies on pure MnF2 and site-diluted (Mn0.5Zn0.5)F2

Positive muon spin rotation and relaxation measurements have been carried out on the antiferromagnets, pure MnF₂ and site-diluted (Mn_0.5Zn_0.5)F₂, above and below the Néel temperature T_N using single-crystal specimens. Two different muon signals have been found in the pure MnF₂; with the precession frequency υ_A for the site A and υ_B for the site B measured in zero external magnetic field at T=5 K. We propose a picture that the signal from the A site represents the “muonium” state, and discuss the characteristic features of muonium in magnetic materials. The spin relaxation rate 1/T₁, measured in zero external field, decreases rapidly with decreasing temperature below T_N. The mechanism of the spin relaxation above T_N is explained by the exchange fluctuations of the Mn moments, while below T_N by the Raman scattering of spin waves. At the same normalized temperature T/T_N, 1/T₁ observed in the diluted (Mn_0.5Zn_0.5)F₂ is significantly larger than that in the pure MnF₂ below T_N. The difference between the pure and diluted systems is related to the large spectral weight of low-energy magnons in (Mn_0.5Zn_0.5)F₂ found by neutron scattering.     

Muonium quantum diffusion and spin dynamics in solid xenon

We present measurements of the transverse (T ₂ ^–1 ) and longitudinal (T ₁ ^–1 ) spin relaxation rates of muonium (Mu) atoms in solid natural xenon (n-Xe) as well as pure¹³⁶Xe (which has no nuclear moments). The temperature dependences ofT ₂ ^–1 andT ₁ ^–1 in natural Xe belowT 115 K demonstrate the quantum character of Mu diffusion governed by one-phonon interactions. Taking into account both the polaron effect (PE) and the effect of fluctuational preparation of the barrier (FPB) makes it possible to consistently describe Mu diffusion in Xe. Mu spin relaxation in¹³⁶Xe at high temperatures is not due to nuclear hyperfine (NHF) interactions.     

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 (T ₁ ^–1 ) and transverse (T ₂ ^–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 time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

Quantum diffusion of muonium in insulators

In this paper we review our recent experiments conducted at TRIUMF on muonium diffusion in alkali halides. First, the technique of longitudinal-field muonium spin relaxation (T ₁) due to nuclear hyperfine interaction, an indispensabletour de force for the present work. is described. It is demonstrated in KCl that the technique provides spectacular sensitivity for muonium diffusion as well as determining the average nuclear hyperfine coupling constant. The muonium hop rate shows a minimum (T ^*≃80 K) and steep increase with decreasing temperature. The result is compared with the current theory of quantum diffusion in non-metallic crystals. A few more sets of new data may be presented for other alkali halides. In addition, we show that muonium forms a delocalized state in NaCl as evidenced by a large change of the average nuclear hyperfine parameter. Related topics of local tunneling system may be briefly reviewed.     

Dynamical behavior of muonium on silica surfaces

The behavior of muonium on the surface of finely divided silica (amorphous SiO₂) powder (mean grain diameter 70 Å) has been studied as a function of the surface concentration of hydroxyl groups. The temperature dependence of the Mu relaxation rate in transverse field was measured for samples prepared with 0%, 50% and 70% of the surface hydroxyl groups removed over the temperature range 4 K <T < 300 K. The relaxation rate shows a distinct maximum at about 25 K and a minimum at about 16 K for all three samples, and shows a dramatic decrease below 16 K as the concentration of surface hydroxyls is reduced. A three-state nonequilibrium model describing the diffusion and trapping of muonium on the silica surface is used to interpret the data.On leave from Department of Physics, University of Saskatchewan, Saskatoon, Sask. S7N OWO, Canada.     

Muon spin relaxation studies in frustrated and/or low-dimensional spin systems

An overview is given on muon spin relaxation (SR) measurements in frustrated and/or low dimensional spin systems. In the frustrated Kagomé lattice system SrCr₈Ga₄O₁₉, we observed dynamic spin fluctuations of 30 GHz, without any static frozen component even atT=0.1 K, much below the susceptibility-cusp temperatureT _g=3.5 K. This is in clear contrast with the case in dilute-alloy spin glassesCuMn andAuFe, where static order develops belowT _g. We also present the dimensionality dependence of the sub-lattice magnetization curves in 2-d Heisenberg systems, the remarkable suppression of the ordering temperature in a 1-d system Sr₂CuO₃, the observation of activation type spin dynamics in a 1-d Ising ferromagnet (DMeFc)(TCNE) aboveT _c, slow spin fluctuations ( 60 MHz) in Haldane-gap systems at low temperatures, and some results from organic 1-d and 2-d magnetic systems.     

Muonium in ice

Muonium has been studied in single crystals of H₂O and D₂O. Two-frequency precession in low transverse fields and a single zero-field oscillation indicate a small anisotropy of axial symmetry in the muonium hyperfine interaction. The anisotropy is shown to be the cause of the hitherto unexplained temperature independent contribution to muonium spin relaxation in polycrystalline samples. Relaxation rates for 99 K–263 K are reported for muonium in a single crystal of H₂O. Relaxation is attributed to electron-nuclear dipolar coupling of muonium to lattice protons, modulated by translational diffusion of muonium alongc-axis channels of the ice lattice. A simple model for H and Mu diffusion in ice is investigated.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

Quantum diffusion of muonium in GaAs

The diffusion rate of muonium in the III–V compound semiconductor GaAs has been determined from measurements of muon spinT ₁ relaxation induced by motion in the presence of nuclear hyperfine interactions. It is shown for the first time in a semiconductor that (a) there is a crossover of the transport mechanism at about 90 K from stochastic to zero-phonon hopping, as evidenced by a steep rise in the hop rate at lower temperatures, and that (b) the muonium diffuses at the hop rate of 10¹⁰ s⁻¹ (corresponding diffusion constantD≈10⁻⁶ cm²s⁻¹) at lower temperatures as well as at room temperature.     

Temperature Dependence of Electron Spin Relaxation of 2,2-Diphenyl-1-Picrylhydrazyl in Polystyrene

The electron spin relaxation rates for the stable radical 2,2-diphenyl-1-picrylhydrazyl (DPPH) doped into polystyrene were studied by inversion recovery and electron spin echo at X-band and Q-band between 20 and 295 K. At low concentration (340 μM, 0.01 %), spin–lattice relaxation was dominated by the Raman process and a local mode. At high concentration (140 mM, 5 %), relaxation is orders of magnitude faster than at the lower concentration, and 1/T ₁ is approximately linearly dependent on the temperature. Spin lattice relaxation rates are similar at X-band and Q-band. The temperature dependence of spin echo dephasing was faster at about 140 K than at higher or lower temperatures, which is attributed to a wagging motion of the phenyl groups.     

Diffusion and trapping of muonium on silica surfaces

The spin relaxation rate λ_Mu of muonium atoms on fine silica powder surfaces was measured as a function of temperature and of the surface concentration of hydroxyl groups. Results indicate two-dimensional diffusion, trapping and detrapping of the muonium atoms on the silica surface. At low temperatures λ_Mu decreases dramatically as the concentration of surface hydroxyls is reduced. A three-state model is used to extract the muonium adsorption energy and other physical parameters.     

Temperature dependence of muonium spin exchange with O2 in the range 88 K to 478 K

Our group at TRIUMF reported earlier a study of the spin exchange reactions of Mu with O₂ and NO in the range 295 K to 478 K. We have extended the measurement with O₂ to a low temperature region down to 88 K. From 135 K to 296 K, the spin depolarization rate constantk _d(T) was found to vary according to the relative velocity of the colliding species,T ^1/2, which indicates that the spin exchange cross section of Mu-O₂ is temperature independent in this temperature range. The value ofk _d(T) at 296 K is in good agreement with our earlier study. However, it was found that below 105 K and above 400 K,k _d(T) tends to have stronger temperature dependences (T ⁿ , withn>1/2). This deviation fromT ^1/2-behavior can be attributed to the velocity (energy) dependence of the spin exchange cross section.     

Magnetic properties of Heisenberg triangular antiferromagnet V15 cluster studied by NMR

The magnetic properties of an s?=?1/2 Heisenberg triangular antiferromagnet V15 have been studied by proton nuclear magnetic resonance (NMR) at very low temperature down to 100 mK using a He³-He⁴ dilution refrigerator. In total spin S _T?=?3/2 ground state above 2.7 Tesla, proton spin-lattice relaxation rate (1/T₁) shows thermally activated behavior as a function of temperature. On the other hand, a temperature independent behavior of 1/T₁ at very low temperatures is observed in frustrated S _T?=?1/2 ground state below 2.7 Tesla. Possible origins for the peculiar behavior of 1/T₁ will be discussed in terms of magnetic fluctuations due to spin frustration.     

Correlation between the negative magnetoresistance effect and magnon excitations in single-crystalline CuCr1.6V0.4Se4

Structural, electrical and magnetic measurements, as well as electron spin resonance (ESR) spectra, were used to characterise the single-crystalline CuCr_1.6V_0.4Se₄ spinel and study the correlation between the negative magnetoresistance effect and magnon excitations. We established the ferromagnetic order below the Curie temperature T _C ≈ 193 K, a p-type semiconducting behaviour, the ESR change from paramagnetic to ferromagnetic resonance at T _C, a large ESR linewidth value and its temperature dependence in the paramagnetic region. Electrical studies revealed negative magnetoresistance, which can be enhanced with increasing magnetic field and decreasing temperature, while a detailed thermopower analysis showed magnon excitations at low temperatures. Spin–phonon coupling is explained within the framework of a complex model of paramagnetic relaxation processes as a several-stage relaxation process in which the V³⁺ ions, the exchange subsystem and conduction electron subsystem act as the intermediate reservoirs.     

H and Mu diffusion in ice

Detailed studies of muonium in ice carried out at TRIUMF in the mid eighties directly inspired EPR investigation of H and D atoms in ice at the Argonne National Laboratory, using a pulsed EPR spectrometer in conjunction with a Van de Graaff electron accelerator. T₂ measurements were made by the spin-echo method, Subsequent work resulted in a measurement of the longitudinal spin relaxation time T₁ at a single temperature. In combination with T₂ this permits an unambiguous determination of the strength of the magnetic interaction giving rise to relaxation, and hence permits conversion of all the existing T₂ data to diffusional correlation times, . We have recently initiated a further study of muonium in ice, this time concentrating on T₁ measurements. Preliminary work shows the feasibility of determining from the field dependence of T₁ at a given temperature. The result is in good agreement with our earlier, less direct determinations.     

Unusual magnetic hysteresis behavior of oxide spinel MnCo2O4

Magnetic hysteresis behavior of the oxide spinel MnCo₂O₄ has been studied at different temperatures below its T_c≈184 K. Normal hysteresis behavior is observed down to 130 K whereas below this temperature the initial magnetization curve, at higher magnetic fields, lies outside the main loop. No related anomaly is observed in the temperature variation of magnetization or coercivity. However, the anisotropy field overcomes the coercivity below 130 K. The unusual magnetic hysteresis behavior of MnCo₂O₄, at low temperatures, may be associated with irreversible domain wall movements due to the rearrangement of the valence electrons.     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

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.     

Effect of chirality on domain wall dynamics in molecular ferrimagnet [Mn<Superscript>II</Superscript>(HL-pn)(H<Subscript>2</Subscript>O)][Mn<Superscript>III</Superscript>(CN)<Subscript>6</Subscript>]·2H<Subscript>2</Subscript>O

In this paper we distinguish the contributions of switching, slide, creep and Debye relaxation modes of the domain wall dynamics to the low-frequency magnetic properties of chiral and racemic [Mn^II(HL-pn)(H₂O)][Mn^III(CN)₆]·2H₂O molecular ferrimagnets. We demonstrate that crystal and spin chirality affects the characteristic transition temperatures between different modes. In chiral crystals, transitions to the creep and Debye relaxation modes were observed at T = 7 K and 5 K, whereas in racemic crystals the same transitions occurred at higher temperatures T = 13 K and 9 K, respectively. Difference of the Peierls relief in chiral and racemic crystals is a possible reason of the chirality effect on the domain walls dynamics.