A study on new phase transitions in Cs2CaCl4·2H2O single crystals by observation of Cs NMR

The ¹³³Cs 1/2→−1/2 spin-lattice relaxation rate, , and the spin-spin relaxation rate, , for a Cs₂CaCl₄·2H₂O single crystal have been measured in function of temperature. The dominant relaxation mechanism of this crystal over the whole temperature range investigated here proceeds via quadrupole interaction. The changes in the ¹³³Cs spin-lattice relaxation rate near 325 K (=T_c1) and 360 K (=T_c2) correspond to phase transitions in the crystal. The change in the spin-lattice relaxation rate at T_c1 is small because the crystal lattice does not change very much during this phase transition. The change in near T_c2 is due to the critical slowing down of the soft mode that typically occurs in structural phase transitions. The temperature dependence of the spin-lattice relaxation rate for this crystal has maximum values at about 240 K, which is attributable to the effect of molecular motion as described by Bloembergen-Purcell-Pound theory. The phase transition temperatures T_c1 and T_c2 obtained from the temperature dependence of the relaxation rate is also clear from data obtained using differential scanning calorimetry. Therefore, we know that previously unreported phase transitions occur at 325 and 360 K.     

Spin physics in solid helium: Experimental results and applications

We have observed optical pumping signals from Cs atoms trapped in solid⁴He. While the longitudinal electronic spin relaxation timeT ₁ is found to be in the range of 1–2 s, the transverse relaxation timeT ₂, as inferred from magnetic resonance linewidths has a lower bound of 150 s, and is determined by magnetic field inhomogeneities. We present a quantitative discussion of how paramagnetic species trapped in solid He might be used in a highly sensitive search for permanent atomic electric dipole moments.     

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.     

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.     

Spin relaxation. The renormalized operator cumulant approach

Two-level systems under the influence of external noise are generic models of quantum relaxation processes. The spin 1/2 particle in a stochastic magnetic field is one of the best known examples. Interesting effects are observed if the noise is colored as is the case in most applications. The time-ordered operator cumulant expansion forms a convenient approach to this problem. Recently, a renormalization procedure has been proposed which corresponds to a partial summation of the naive expansion and hence constitutes an essential improvement over the second cumulant considered usually. For colored noise of intermediate strength and correlation time this approach is used to derive renormalized expressions for the transverse (T ₂) and longitudinal (T ₁) relaxation time and the frequency shift. In this parameter region, the ratioT ₁/T ₂= is found to deviate substantially from its value =2 valid for white noise exactly and for colored noise in the second cumulant approximation. This corroborates and extends results of Budimir and Skinner obtained by including the second and fourth cumulant only. However, their truncated expansion is shown to lead to unphysical results in the intermediate parameter region treated still correctly by the renormalized expansion.     

μ+SR study of two-dimensional antiferromagnets,delafossite-type compounds

⁺SR experiments were performed on delafossite-type compounds, CuCrO₂, AgCrO₂, CuFeO₂, which are model compounds of triangular lattice antiferromagnets. The initial asymmetries are much smaller than the expected value, implying muonium formation. The time spectra are composed of slow andfast relaxation components. We attributed the components to signals from ⁺ stopped at the center of O^2– ions andmuonium far from nuclear dipole moments, respectively. The asymmetries decrease belowT _N but no precession spectra were observed. Relaxation rates of slow andfast relaxation components show maxima atT _N.     

Spin relaxation of muonated radicals in the gas phase

We report on recent results obtained for longitudinal field (T ₁) spin relaxation of the muonium-substituted (muonated) free radicals MuCO, MuC₂F₄, MuC₂H₃F, and MuC₄H₈ (t-butyl), comparing with results reported earlier for MuC₂H₄ (and MuC₂D₄). Some comparison with transverse field (T ₂) data is also given. These data are fit to a phenomenological model based on NMR theory of spin relaxation in gases. The parameters of these fits are presented and discussed.     

NMR relaxation times and proton motion in HxWO3

The relaxation timesT ₁,T _1q,T _1D, andT ₂ for¹H in the tetragonal-A phase of H_xWO₃ have been measured over the temperature range 190 to 490 K. The¹H relaxation behaviour appears to be governed by diffusion over inequivalent jump distances, approximating to a short range planar diffusion and a long range isotropic diffusion. Parameters for the latter motion are estimated asE _a = 68 kJ/mol and ₀=2.5×10^–13 s. The powder X-ray diffraction pattern for this phase of H_xWO₃ has been studied over the temperature range 300–470 K. The tetragonal distortion diminishes with temperature and H_0.43 WO₃ becomes cubic at about 435 K. Volumetric studies of hydrogen evolution show that decomposition accelerates at approximately this temperature.     

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.     

Kondo effect in spin glasses: Electrical resistivity

We investigate the influence of the Kondo effect on the electrical resistivity of spin glasses. Our approximation reduces in the limit of vanishing impurity concentrations to the Suhl-Nagaoka theory for the Kondo effect. The magnetic impurity interactions are taken into account in the form of time dependent two-spin correlation functions which can be measured by neutron scattering. The dynamics of the impurity spins leads to a partial destruction of the Kondo effect. For the resistivity this can be described by a temperature dependent effective spinS _eff ² (T) withS _eff ² 0 forT0 andS _eff ² S(S+1) forT, and by a reduction of the Kondo temperatureT _K. Sufficiently strong interactions lead toT _K=0. We obtain a resistivity maximum at a temperatureT _m due to the interplay of the Kondo effect and the spin dynamics;T _m depends onT _K and on the excitation spectrum, and therefore on parameters such as impurity concentration or pressure. The ratioT _m/T_f (T _f is the freezing temperature) is calculated for a single relaxation time and for a square density of relaxation modes and is compared with experimental data forAuCr,AuMn,AgMn, andCuMn. The influence of other possible modes on various spin glass properties is discussed.SFB 125 Aachen-Jülich-Köln     

Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators

We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice , and subjected to stochastic forcing mimicking heat baths of temperatures T ₁ and T ₂ on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Partially supported by the Academy of Finland.     

Explaining μ+ spin-lattice relaxation in MnF2, belowT N,by scattering function

A relation between the spin-lattice relaxation rate (1/T ₁) of positive muons and the scattering functionS ^T (q,) is derived for the antiferromagnet MnF₂. We find good agreement between previousSR measurements of 1/T ₁ and our calculation using neutron scattering measurements ofS ^T (q,).     

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 Anomalies in Quasi-2D Organic Superconductors: Effects of Spin Fluctuations in a Fermi Liquid Approach

The -(BEDT-TTF)₂X organic superconductors are described by a two parameter 2D Fermi surface model, in which bandwidth and departure from perfect nesting can be varied. We have studied the spin fluctuations effect on the normal state properties in a Fermi liquid approach using the RPA approximation. The calculated NMR relaxation rate exhibits a peak in 1/(T ₁ T), which strongly decreases when the departure from perfect nesting of the Fermi surface and the bandwidth increase. These results are in good agreement with NMR experiments done in -(ET)₂X at least qualitatively. In conclusion, we have shown that, in the normal state and with a Fermi liquid approach, the spin fluctuations, which are present in the system due to an imperfect nesting property of the Fermi surface, can induce anomalies of the magnetic properties. Besides, we can restore the usual behaviour like the Korringa law by increasing the bandwidth or by considering a more imperfect nesting. Our calculation reproduces qualitatively the applied pressure relaxation rate experiment done in -(ET)₂X salt.     

MD simulation of concentrated polymer solutions: Structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T _g or critical temperature T _c of mode-coupling theory (MCT). Both T _g and T _c (> T _g decrease with increasing solvent concentration . The decrease is linear for the concentrations studied (up to = 25%. Above T _c we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T _c. Near T _c we investigate dynamic correlation functions, such as the incoherent intermediate scattering function (t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r;t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that (t) obeys the time-temperature superposition principle and has relaxation times which are compatible with a power law increase close (but not too close) to T _c. In divergence to MCT, however, the increase of depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the relaxation an analysis of P(ln r;t) reveals a double-peak structure close to T _c. The first peak correponds to “slow” particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These “fast” particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T _c.     

Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.     

μSR magnetic response in frustrated antiferromagnets of type RMn2 (R = rare earth)

Zero longitudinal and transverse fieldSR was carried out in the antiferromagnets YMn₂, Y_0.95 Tb_0.15 Mn₂, Y_0.9Tb_0.1Mn₂, Y_0.99 Sc_0.01 Mn₂, Y_0.98Sc_0.02Mn₂ and TbMn₂. The dynamics of Mn magnetic moments above T _N is typical for an itinerant antiferromagnet. Within a certain temperature range above T _N part of the material enters a randomly ordered (spin glass like) magnetic state as an outcome of frustration. At temperatures above 150 K the muon spin relaxation rate indicates that the muon has become mobile.This work was supported by the German Federal Minister for Research and Technology under Contract Nr. 03KA2-TUM-4.     

Diffusion and reaction among traps: some theoretical and simulation results

Diffusion and reaction in heterogeneous media arise in a host of phenomena in the physical and biological sciences. The determination of the mean survival time (i.e., inverse trapping rate) and relaxation timesT _n, n=1,2,3,... (i.e., inverse eigenvalues), associated with diffusion among partially absorbing, static traps with surface rate constantk are problems of long-standing interest. The limitsk= andk=0 correspond to the diffusion-controlled case (i.e., perfect absorbers) and reaction-controlled case (i.e., perfect reflectors), respectively. This paper reviews progress we have made on several basic aspects of this problem: (i) the formulation of rigorous bonding techniques and computational methodologies that enable one to estimate the mean survival time and principal relaxation timeT ₁ (ii) the quantitative characterization of the microstructure of nontrivial continuum (i.e., off-lattice) models of heterogeneous media; and (iii) evaluation of and T₁ for the same models. We also describe a rigorous link between the mean survival time t and a different effective parameter of the system, namely the fluid permeability tensork associated with Stokes flow through the same porous medium.     

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.