Nuclear magnetic relaxation of <Superscript>3</Superscript>He in contact with an aerogel above the Fermi temperature

The spin kinetics of ³He in an aerogel has been studied above the Fermi temperature. The magnetic relaxation times T ₁ and T ₂ of adsorbed, gaseous, and liquid ³He in a 95% silica aerogel at a temperature of 1.5 K have been determined as functions of frequency by means of pulse nuclear magnetic resonance. It has been found that the time T ₁ is linear in frequency in all three cases, whereas T ₂ is independent of frequency. To explain the observed behavior of the longitudinal relaxation rate, a theoretical model of relaxation in the adsorbed layer of ³He taking into account the filamentary structure of the aerogel is proposed.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

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.     

On the possibility of studying crystal field levels and excitations by μ+SR spectroscopy

We point out that ⁺SR relaxation timesT ₁ andT ₂ measured in metallic magnetic materials can sometimes be expressed in terms of the spin-spin correlation functions of the magnetic ions. We calculate these functions in a random phase approximation and notice they can strongly depend on the crystal field levels and excitations of the magnetic ions. The shortcomings of this approximation are discussed.Part of this work was done at the French Atomic Commission at Grenoble.     

Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Nuclear spin-lattice relaxation in54Mn-MnCl2.4H2O and lower dimensional magnetic systems

We report on nuclear spin-lattice relaxation studies on⁵⁴Mn-MnCl₂.4H₂O and 2-dimensional⁵⁴Mn-Mn(COOCH₃)₂.4H₂O. In the former crystal, we find that at the lowest temperatures a direct process, normally thought of as forbidden, becomes the mechanism for relaxation. In lower dimensional systems the relaxation might be expected to be relatively fast and indeed in the acetate the relaxation timeT ₁ is ≈1000 s in an applied field of 0.2 T for the Mn2 site and is much shorter at lower fields. In 1-dimensional⁵⁴Mn-(CH₃)₄NMnCl₃(TMMC) a significant γ-ray anisotropy is observed on cooling indicating thatT ₁ is also short in this system. The shortness ofT ₁ in the lower dimensional systems suggests that they may be suitable hosts for on-line experiments.     

Molecular motions in chloramphenicol studied by35Cl nuclear quadrupole and1H nuclear magnetic resonance spectroscopy

The³⁵Cl nuclear quadrupole resonance (NQR) frequency (v_Q), nuclear quadrupole spinlattice relaxation time (T_1Q),¹H nuclear magnetic resonance second moment (M₂) and nuclear magnetic spin-lattice relaxation timeT ₁) were measured for polycrystalline chloramphenicol (drug) as a function of temperature. Hindered rotation of the CHC1₂ group and the phenyl ring was detected, the relevant activation energies were determined. The rotations are discussed in detail.     

Generation of picosecond and subpicosecond light pulses with saturable absorbers

Single light pulses, generated by a mode-locked Nd-glass laser, were shortened with saturable absorbers of low initial transmissionT ₀. The pulse duration was reduced from 8 to 2.6 ps after a single pass through a dye cell ofT ₀=10^–7. Light pulses as short as 0.5 ps were observed after five transits through an absorberamplifier system. Detailed calculations of the stationary and the transient situation (with respect to the dye relaxation time) are presented to demonstrate optimum conditions for the pulse shortening.     

μSR studies of YFeMnO4

Muon spin relaxation (SR) studies were carried out on YFeMnO₄. Two interesting phenomena were found in measurements of longitudinal relaxation time spectra atT>T _cusp for a single crystal: (1) difference of the relaxation rates between the directions parallel with and perpendicular to thec-axis, and (2) suppression of local field fluctuations in a longitudinal external field. The spectra atT >T _cusp were reproduced with the function exp[-(₀ t)]. The results are discussed under a picture of the magnetic spin fluctuations of triangular antiferromagnets.     

Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-β- -glucopyranoside

Conventional relaxation parameters (T₁⁻¹, T₂⁻¹, and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-β- -glucopyranoside in a D₂O/DMSO cryosolvent. These data are interpreted with the Lipari–Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon–proton dipole–dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new “hybrid” approach, in which the Lipari–Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

Magnetic-relaxation study in melt-textured ErBa2Cu3O7−δ ceramic material

We have studied the zero-field-cooled magnetic relaxation in the melt-textured ErBa₂Cu₃O_7– ceramic material. The magnetic relaxation rate dM/d (ln t) exhibits strong temperature and field dependence in the temperature range up to 80 K and the field range up to 5.5 T. The magnetic relaxation behavior observed in the melt-textured ErBa₂Cu₃O_7– ceramic sample is similar to that in single crystals. The magnetization to noise ratio is much improved, in particular, for temperatures approaching the superconducting transition temperature and for low magnetic fields. Several theoretical models were explored to fit the experimental data.     

Measurements of magnetic moments of Tc isotopes and the hyperfine field of Tc in Fe and Ni

We report measurements of nuclear magnetic resonance on oriented nuclei (NMR-ON) on⁹⁴Tc (I=7⁺,T _1/2=4.9 h),⁹⁵Tc (I =9/2⁺,T _1/2=20 h) and⁹⁶Tc (I =7⁺,T _1/2=4.3 d) in Fe and on⁹⁵Tc and⁹⁶Tc in Ni. In order to elucidate the discrepancies on the hyperfine field of TcFe in the literature, the resonances were measured with high precision as a function of the external magnetic field B_ext up to 2.0 T. In addition, TDPAC measurements were performed on⁹⁹TcFe at T=300 K and 13 K. TheT=0 K hyperfine fields of Tc in Fe and Ni were determined to be –314(3) kG and –51.8(5) kG, respectively. The g-factors of⁹³Tc,⁹⁴Tc,⁹⁵Tc,⁹⁶Tc and⁹⁹Tc(E=181 keV;I =5/2⁺) are redetermined as g(⁹³Tc)=1.405(14), g(⁹⁴Tc)=0.731(7),g(⁹⁵Tc)=1.321(13), g(⁹⁶Tc)=0.727(7), g(⁹⁹Tc)=1.390(17).We wish to thank E. Smolic and G. Seewald for experimental help. This work was funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 06TM353/TP 4, by the Deutsche Forschungsgemeinschaft (DFG) under the contract numbers Ha 1282/3-1,2, and, partly, by the Kernforschungszentrum, Karlsruhe.     

Magnetic relaxation in a three-dimensional ferromagnet with weak quenched random-exchange disorder

Isothermal remanent magnetization decay,M _r(t), and ‘in-field’ growth of zero-field-cooled magnetization,M _ZFC(t), with time have been measured over four decades in time at temperatures ranging from 0.25T _c to 1.25T _c (whereT _c is the Curie temperature, determined previously for the same sample from static critical phenomena measurements) for a nearly ordered intermetallic compound Ni₃Al, which is an experimental realization of a three-dimensional (d = 3) ferromagnet with weak quenched random-exchange disorder. None of the functional forms ofM _r(t) predicted by the existing phenomenological models of relaxation dynamics in spin systems with quenched randomness, but only the expressions and closely reproduce such data in the present case. The most striking features of magnetic relaxation in the system in question are as follows: Aging effects are absent in bothM _r t andM _ZFC(t) at all temperatures in the temperature range covered in the present experiments. A cross-over in equilibrium dynamics from the one, characteristic of a pured = 3 ferromagnet with complete atomic ordering and prevalent at temperatures away from T_c, to that, typical of ad = 3 random-exchange ferromagnet, occurs asT → T_c. The relaxation times τ₁(T)(τ₁ ^′(T)) and τ₂(T)(τ₂ ^′(T)) exhibit logarithmic divergence at critical temperatures and ; and both increase with the external magnetic field strength,H, such that at any given field value, . The exponent characterizing the logarithmic divergence in τ ₁ ^′ (T) and τ ₂ ^′ T possesses a field-independent value of ≃16 for both relaxation times. Of all the available theoretical models, the droplet fluctuation model alone provides a qualitative explanation for some aspects of the present magnetic relaxation data     

NMR and NQR studies on superconducting Sr2RuO4

We review our nuclear-magnetic resonance (NMR) and nuclear-quadrupole-resonance (NQR) studies in superconducting Sr₂RuO₄, which have been performed in order to investigate the gap structure and the pairing symmetry in the superconducting state and magnetic fluctuations in the normal state. The spin-lattice relaxation rate (1/T₁) of a high-quality sample with shows a sharp decrease without a coherence peak just below T_c, followed by a T³ behavior down to 0.15 K. This result indicates that the superconducting gap in pure Sr₂RuO₄ is a highly anisotropic character with a line-node gap. The Knight shift, which is related to the spin susceptibility, is unchanged in the superconducting state irrespective of the direction of the applied fields and various magnitude of the field. This result strongly suggests that the superconducting pairs are in the spin-triplet state, and the spin direction of the triplet pairs is considered to be changed by small fields of several hundred Oe.     

Charge Carrier Dynamics in Zn-Doped Cuprates

We have measured the static magnetic susceptibility, the resistivity and muon spin relaxation (⁺SR) spectra of Zn and Sr doped La₂CuO₂. Our data show that non-magnetic Zn impurities lead to an increase of the Néel temperature T _N in weakly hole doped compounds. This increase of T _N correlates with an increase of the resistivity. The analysis of our data strongly suggests that the hole mobility is the most important source for the strong suppression of long range antiferromagnetic order in La_2–x Sr _x CuO₄.     

μ +SR study of some magnetic superconductors

The relaxation of the ⁺SR signal has been investigated for the three compounds YRh₄B₄, ErRh₄B₄ and SmRh₄B₄. In the non-magnetic superconducting (T _c 11 K) YRh₄B₄, the data display a Kubo-Toyabe (gaussian) shape for zero (transverse) magnetic fields. ErRh₄B₄ (superconducting below 8.7 K and ferromagnetic below 1 K) shows a dominant signal with very slow relaxation. In contrast SmRh₄B₄ (superconducting below 2.7 K and antiferromagnetic-superconducting below 0.87 K) shows a change in relaxation from gaussian above 60 K to exponential between 1 K and 4 K to two exponential signals (fast and slow) belowT _N=0.9 K. In the region 0.9 K <T < 4.5 K, the relaxation time and the asymmetry both increase withT.supported by the U.S. Department of Energy.Supported by NSERC of Canada.supported by the U.S. Department of Energy.We are grateful to Drs. H. Umezawa and H. Matsumoto for interesting discussions regarding the persistent current screening and the results of self-consistent calculations.     

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.     

Charge compensation and the luminescence of Cr3+ in KMgF3

Studies of the photoluminescence spectra of Cr³⁺ ions in KMgF₃ crystals co-doped with Cr³⁺ and Ni²⁺ ions are reported. Several crystal field sites are identified by the different R-line spectra due to the ² E⁴ A ₂ transition and broadband luminescences associated with the ⁴ T ₂⁴ A ₂ transitions. Cr³⁺ ions substituting without local charge compensation on the octahedral Mg²⁺ site give rise to a low temperature R line in photoluminescence at =702.3 nm with a radiative decaytime of 3 ms at T=14 K. At T=300 K this isotropic centre gives rise to an unpolarized broadband ⁴ T ₂⁴ A ₂ emission, which results from the thermal occupancy of an excited ⁴ T ₂ state just above the ² E level which, at lower temperature, gives rise to emission in the R-line. Other crystal field sites are due to some Cr³⁺ ions having Mg²⁺ or K⁺ vacancies in nearest-neighbour positions, these vacancies being required to maintain charge neutrality in doped fluoride perovskites. The Cr³⁺–K⁺ vacancy complex results in the centre having trigonal symmetry, and low temperature, photoluminescence via R ₁ and R ₂ lines at 716.8 nm and 716.0 nm, respectively. Finally, Cr³⁺ ions having a nearest neighbour Mg²⁺ vacancy have tetragonal symmetry, experiencing weak crystal fields. In consequence, the ⁴ T ₂ level lies below ² E and the photoluminescence spectrum at low temperature takes the form of a polarized broad ⁴ T ₂⁴ A ₂ band with peak at 760 nm and radiative decaytime of 54 s.