Weak Power Law Research Articles

Kondo Effect in Two-Dimensional Disordered Electron Systems

We investigate the Kondo effect in two-dimensional disordered electron systems using a finite-temperature quantum Monte Carlo method. Depending on the position of a magnetic impurity, the local moment is screened or unscreened by the spin of the conduction electron. On the basis of the results, we show that the distribution of the Kondo temperature becomes wide and the weight at $T_K=0$ becomes large as randomness increases. The average susceptibility shows a weak power-law or logarithmic divergence at low temperature, indicating a non-Fermi-liquid behavior.

F-Electron materials: a reservoir of novel electronic states and phenomena

f-Electron materials exhibit a rich variety of strongly correlated electron states and phenomena. Two examples, non-Fermi liquid (NFL) behavior at low temperatures and superconductivity in the vicinity of quantum critical points, are discussed in this article. Non-Fermi liquids are characterized by weak power law or logarithmic temperature dependences of the electrical resistivity, specific heat, and magnetic susceptibility at low temperatures, as well as a dynamical susceptibility whose imaginary part scales with frequency ω divided by T. These NFL characteristics were first established in chemically substituted f-electron materials and later observed in stoichiometric f-electron compounds, suggesting that the NFL behavior is a general phenomenon whose underlying mechanism(s) is (are) not primarily associated with atomic disorder. In certain antiferromagnetic and ferromagnetic f-electron intermetallic compounds, superconductivity has been observed in the vicinity of the critical pressure P c where the Néel or Curie temperature vanishes. We discuss recent experiments on the ferromagnetic compound UGe 2 and suggest that superconductivity, which is found to occur within the ferromagnetic phase below P c in this compound, may have s-wave character and coexist in a spatially inhomogeneous manner with the ferromagnetism.

Measurement of cell microrheology by magnetic twisting cytometry with frequency domain demodulation.

Magnetic twisting cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science 260: 1124-1127, 1993) is a useful technique for probing cell micromechanics. The technique is based on twisting ligand-coated magnetic microbeads bound to membrane receptors and measuring the resulting bead rotation with a magnetometer. Owing to the low signal-to-noise ratio, however, the magnetic signal must be modulated, which is accomplished by spinning the sample at approximately 10 Hz. Present demodulation approaches limit the MTC range to frequencies <0.5 Hz. We propose a novel demodulation algorithm to expand the frequency range of MTC measurements to higher frequencies. The algorithm is based on coherent demodulation in the frequency domain, and its frequency range is limited only by the dynamic response of the magnetometer. Using the new algorithm, we measured the complex modulus of elasticity (G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and ferromagnetic beads (approximately 5 microm) coated with an RGD peptide were bound to the cell membrane. Both the storage (G', real part of G*) and loss (G", imaginary part of G*) moduli increased with frequency as omega(alpha) (2 pi x frequency) with alpha approximately equal to 1/4. The ratio G"/G' was approximately 0.5 and varied little with frequency. Thus the cells exhibited a predominantly elastic behavior with a weak power law of frequency and a nearly constant proportion of elastic vs. frictional stresses, implying that the mechanical behavior conformed to the so-called structural damping (or constant-phase) law (Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD, and Fredberg JJ, J Appl Physiol 89: 1619-1632, 2000). We conclude that frequency domain demodulation dramatically increases the frequency range that can be probed with MTC and reveals that the mechanics of these cells conforms to constant-phase behavior over a range of frequencies approaching three decades.

Neutron reflectivity studies of the structure of polymer/polymer and polymer/substrate interfaces at the nanometer level

We review the use of neutron reflectivity as a probe of organic thin films, concentrating on its application to study buried interfaces in thin polymer films. For an interface between immiscible polymers of relatively low molecular weight, we find a width greater than that observed for higher molecular weight species, and we find that the width grows with time either logarithmically or following a weak power law. The conformation of a layer of very high molecular weight polymer chains chemically grafted to a silicon interface and coated by a chemically different polymer matrix is studied as a function of temperature, which controls the thermodynamic interaction between the grafted chains and the chemically different matrix chains. At high temperatures the layer abruptly changes from an extended conformation to one with a sharp interface with the matrix layer.

Electron heat flow carried by Kappa Distributions in the solar corona

We generalize the Spitzer and Härm [1953] description of electron heat flow to model the effects of the electron velocity distribution power law tails which are frequently observed [Vasyliunas, 1968; Christon et al., 1988; Maksimovic et al., 1997] in astrophysical plasmas. We apply our generalized heat flow model to the problem of electron heat flow in the solar corona, demonstrating that a weak power law tail in the electron velocity distribution can allow heat to flow up a radially directed temperature gradient.

Magnetic hysteresis dynamics of thin Co films on Cu(001)

Hysteresis properties of ultrathin (2--4 monolayers) epitaxial Co films grown on Cu(001) surfaces are studied as a function of film thickness, temperature and the strength ${(H}_{0}),$ in-plane direction, and frequency (\ensuremath{\Omega}) of applied sinusoidal magnetic field. Scaling of the hysteresis loop area (power loss) of the form ${A=A}_{0}{+H}_{0}^{\ensuremath{\alpha}}{\ensuremath{\Omega}}^{\ensuremath{\beta}}\ensuremath{\zeta}(H,\ensuremath{\Omega})$ where \ensuremath{\zeta} is a scaling function is explored. All films exhibit a threshold field ${(H}_{t})$ where switching between equivalent magnetized states is initiated. Hysteresis loop areas measured over five decades in frequency exhibit very weak power-law dependence $(\ensuremath{\beta}\ensuremath{\sim}0.02).$ No evidence of a dynamic phase transition is observed and no indication of a low-frequency $({\ensuremath{\Omega}}_{0}\ensuremath{\sim}{10}^{2}\mathrm{Hz})$ characteristic resonance is apparent over the drive frequency range covered. The observed weak power-law scaling does not support results of prior experiments that have been interpreted as corroborating the mean-field Ising model $(\ensuremath{\alpha}=\ensuremath{\beta}=\frac{2}{3})$ and continuum spin models of thin-film hysteresis energy-loss scaling. The measured frequency and applied field-dependent scaling of the dynamic coercive force ${(H}_{c}^{*})$ also appears to be inconsistent with recent phenomenological models of hysteresis behavior based on domain-wall motion that predict that ${H}_{c}^{*}$ scales as $\mathrm{ln}\mathrm{H\ifmmode \dot{}\else \.{}\fi{}}.$ The results of this study of Co on Cu(001) and a corresponding study of Fe on W(110) suggest that the dynamics of magnetization reversal in real ultrathin film systems do not exhibit universal behavior in the low-field low-frequency limit. Recent theoretical results based on a more realistic model that accounts for thermal noise and spatial fluctuations in the dynamics yield logarithmic scaling at low \ensuremath{\Omega} and effective exponents \ensuremath{\beta} that are compatible with the experiments. A simple physical picture of low drive-frequency energy-loss scaling is described that accounts for the experimental observations.

Quadrupolar Kondo effect in U 3Ni 3Sb 4− xSn x alloys

In the pseudobinary series U 3Ni 3Sb 4− x Sn x there is a cross-over from a localised non-magnetic state to a many-body Kondo singlet state, accompanied by a transition from semiconducting to metallic behaviour. Our analysis of the crystal field spectra of U 3Ni 3Sb 4 has shown that its non-magnetic ground state is a doublet, so that the system meets the criteria for the quadrupolar Kondo effect. For intermediate compositions the susceptibility shows weak power law divergences at low temperature, consistent with non-Fermi liquid behaviour.

Single-ion scaling of the low-temperature properties of f-electron materials with non-Fermi-liquid groundstates

Certain chemically substituted Ce and U compounds have low-temperature physical properties that exhibit non-Fermi-liquid (NFL) characteristics and apparently constitute a new class of strongly correlated f-electron materials. The NFL behaviour takes the form of weak power law or logarithmic divergences in the temperature dependence of the physical properties that scale with a characteristic temperature , which, in some systems, can be identified with the Kondo temperature . These systems have complex temperature T - chemical substituent composition x phase diagrams, which contain regions displaying the Kondo effect, NFL behaviour, spin glass freezing, magnetic order, quadrupolar order, and, sometimes, even superconductivity. Possible origins of the NFL behaviour include a multichannel Kondo effect and fluctuations of an order parameter in the vicinity of a second-order phase transition at T = 0 K. Recent experiments on the systems and are reviewed. In the and systems, the low-temperature physical properties in the NFL regime scale with the U concentration and , suggesting that single-ion effects are responsible for the NFL behaviour.

Fluctuation-induced forces in stacked fluid membranes

We present a new entropic interaction between foreign inclusions (e.g. proteins) confined to fluid membranes in a layered phase. This interaction arises from the coupling of thermal shape fluctuations to the variation in rigidity associated with the presence of inclusions. The force between inclusions exhibits interesting nonmonotonic behaviour as a function of the separation distance. At large separation, we find a weak power law attraction between inclusions of similar composition

Evidence for nonequilibrium dynamics and an overlap length scale in a reentrant (Fe0.65Ni0.35)0.882Mn0.118 ferromagnet.

The relaxation of the low-field thermoremanent magnetization has been measured, as a function of temperature and system age, for a reentrant (${\mathrm{Fe}}_{0.65}$${\mathrm{Ni}}_{0.35}$${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ ferromagnet with x=0.118. A dynamic crossover is observed in the vicinity of the reentrant transition from a high-temperature (T\ensuremath{\ge}65 K) regime of equilibrium dynamics, where the relaxation isotherms are compatible with a weak power law, and exhibit no measurable dependence on system age, to a low-temperature (T\ensuremath{\le}60 K) regime, where the isotherms exhibit an age dependence symptomatic of nonequilibrium dynamics, and are describable analytically by a stretched exponential. Moreover, temperature-cycling experiments clearly confirm the instability of this low-temperature reentrant phase to variations in temperature, and thus support the existence of an overlap length scale, which is regarded by droplet scaling theories as a defining feature of the spin-glass state. The data are compared with the functional forms predicted by various phenomenological models of relaxation dynamics in systems with randomness.

Crossover from equilibrium to nonequilibrium dynamics in a reentrant AuFe ferromagnet

Measurements of the decay of the low field thermoremanent magnetization, over four decades of observation time, 6 s≤t≤10 4 s, as a function of temperature T and wait time t w , have been performed on two AuFe alloys located on either side of the multicritical point: a Au 90 Fe 10 spin glass and a strongly bond-disordered reentrant Au 83 Fe 17 ferromagnet. The spin glass relaxation isotherms exhibit the canonical symptoms of nonequilibrium ordering: below T SG , the isotherms are characterized by an inflection point, on a logarithmic time perspective, which is sensitive to the wait time t w , display a memory for a history of field reversals, and are all compatible with an analytical representation based on a streched exponential function, M R (t)=M 0 +M 1 exp[-(t/τ) 1-n ], with τ=t infl and a weakly temperature and wait time dependent exponent n≅0.7. The reentrant ferromagnet exhibits a temperature-driven crossover between two distinct relaxation regimes: a «high temperature» regime coincident with the ferromagnetic phase, characterized by an extremely rapid approach to equilibrium, negligible wait time effects, and a weak power law decay, M R (t)=M 0 +M 1 t -m , with a weakly temperature dependent exponent 0.04≤m≤0.08, consistent with the predictions of droplet fluctuation models of random Ising ferromagnets, and a «low temperature» regime coincident with the reentrant phase, with nonequilibrium, age-dependent dynamics which are virtually indistinguishable from those in the «pure» spin glass phase and describable by the same streched exponential relaxation function. This study represents the first systematic comparison of relaxatiion dynamics in the reentrant and ferromagnetic phases of a system with sequential transitions, and provides compelling evidence for the equivalence of the reentrant and spin glass phases

A wedge disclination along the vertex of the wedge-like inhomogeneity in an elastically anisotropic solid

Abstract The problem of a straight wedge disclination lying along the axis of a rotationally inhomogeneous elastic medium is considered. The existence criterion for the logarithmic singularities in the stress field is established. It is shown that the wedge disclination lying along the vertex of the wedge-like inhomogeneity in an elastically anisotropic composite body can be formed by the uniform deformation and the uniform rotation of the matrix and the inhomogeneity. Non-uniform elastic strains arise only as the image effects due to the boundary conditions at the external surface. The image stresses either are regular or have a weak power-law (in some particular cases logarithmic) singularity, depending on the relation between the elastic constants of the matrix and the inhomogeneity.

Thermoremanent relaxation in a reentrant [formula omitted] ferromagnet close to the tricritical point

Measurements of the low-field static magnetization, dynamic susceptibility, and thermoremanent decay of a Ni-23.4 at % Mn sample are presented. The dynamic susceptibility in a fixed static biasing field exhibits a triple-peaked structure characteristic of reentrant ferromagnetism. Within the reentrant phase, the decay of the thermoremanent magnetization exhibits a stretched exponential time dependence with parameters typical of spin glasses, and with significant waiting time effects. By contrast, the decay in the ferromagnetic phase is a weak powerlaw, with no observable waiting time dependence.

An explanation for the “weak” fluence broadening of spectral holes in glasses

It is shown that the weak power law observed thus far for the hole-broadening due to burning fluence of spectral holes in glasses could be the result of not taking the natural holewidth into account i.e. the holewidth due to guest-host interactions. If this width is compensated for, hole-broadening as a function of burning fluence, F, in glasses follows an approximate F 0.5 dependence expected for saturation broadening.

Anomalies of compatibility stresses in elastically anisotropic solids with wedge-like inhomogeneities

The problem of a wedge-like inclusion subjected to uniform intrinsic (stress free) strains is considered. The elastic constants of the inclusion differ from those of the matrix. The stresses are found to exhibit various anomalies accompanied by a change in the type of the stress singularity. It is shown that the stresses can have either a weak power law or a logarithmic singularity, and that they also can be regular, depending on the wedge angle and the relationship between the elastic constants of the matrix and the inclusion. The analogy between the mechanism underlying this phenomenon and the Carothers-Sternberg-Koiter paradox of a wedge loaded by a concentrated couple is discussed.

Monte-Carlo calculations of Ge detector escape-peak efficiencies

The authors present calculated first and second escape peak efficiencies for a variety of n-type coaxial Ge detectors using the Monte Carlo method. The results are given for right-circular cylindrical geometries of size ranging from 3-cm diameter * 3-cm thick to 8-cm diameter * 8-cm thick. For completeness, the intrinsic interaction and photopeak efficiencies for energies ranging from 20 keV to 20 MeV are listed. The calculations have been tested against experimental measurement and found to be in agreement to within the quoted errors (typically 10%). It is found that the ratio of the second escape peak efficiency to the first escape peak efficiency, R, is approximately independent of energy for small detector volumes but has a weak power law energy dependence for large volumes. It is shown that R also varies as an inverse power law of the active volume. >

Relaxation of entangled polymers at the classical gel point

We examine the relaxation behaviour of an entangled cross-linked polymer gel as it approaches the gel point in mean field (Flory-Stockmayer) percolation. The calculation is based on a tube model for the topological interactions in which stress is lost via hierarchical fluctuation of the primitive paths between cross-links. The decay time of a segment is calculated via a recursion relation which has an analytic solution near the gel point. The startling conclusion is that all clusters relax in a finite time T~ giving a relaxation modulus G (t ) = Go 03B3-2[03B1-1 ln (T~/t)]4, where 03B1 counts the number of entanglements between cross-links and 03B3 is a constant of order unity. For timescales much shorter than T~ this may resemble a weak power law. The unphysically rapid relaxation of the largest clusters is prevented by a transition to percolation statistics at long length scales. The timescale separating the two regimes is close to

Universal Conductance Fluctuations, Magnetofingerprints, and the Aharonov-Bohm Effect in Metals

The conductance of any metallic sample is shown to fluctuate as a function of chemical potential, magnetic field, or impurity configuration by an amount of order e2/h independent of sample size and degree of disorder at low temperature. Fluctuations of this size are present as long as kT and the inelastic scattering rate are less than the inverse time to diffuse across the sample; at higher T they are reduced as a weak power law of T. This fluctuation effect means that weak localization theory may fail to describe experimental systems in this regime of size and temperature. This provides a quantitative explanation for the observability of sample-specific h/e Aharonov-Bohm oscillations in normal metal rings. The conductance of a given sample is found to be extremely sensitive to very small changes in impurity configuration. This result may provide the basis for a quantitative microscopic theory of low-frequency noise in dirty metals. It also suggests that the sample-specific magnetoresistance patterns ("magnetofingerprints") may provide a useful tool for probing microscopic processes associated with defects in dirty metals. The theory is in good agreement with experiments on small wires, rings and FETs, and also has implications for experiments studying classical wave motion in random media.

A Simple Self-Consistent Method in the Theory of Spinodal Decomposition

A kinetic model of the spherical spin system is proposed and is applied to the problem of the spinodal decomposition in the quenched mixture. The time-dependence of the structure function can be exactly calculated in a self-consistent manner, which serves as a late stage approximation for the mode-couplings in the spin-conserved TDGL model. The well-known sharp peak appears at temperatures below the transition point and it shifts to the small wave-number region. The peak position obeys the weak power law in time. The classical spinodal line is not found so far as the transient behaviour of the structure function is concerned.

Shear viscosity of nitroethane-3-methylpentane in the critical region

The viscosities of nitroethane-3-methylpentane mixtures were measured in an Ostwald viscometer over the entire composition range, and over a temperature range of ΔT(= T - Tc) from 11.673 °C to 0.003 °C. The experimental data of this work show quantitatively that the best fit of the viscosity data is to the equation η = (A/φ) (ε−φ − 1) + Bε + C, where A/φ = 0.478 ± 0.04, B = − (1.09 ± 0.05), C = 0.335 ± 0.01, and φ = 0.03 ± 0.01. The value of φ is within experimental error positive and not zero. It clearly indicates that at a temperature very close to the critical temperature the anomalous viscosity shows a very weak power law divergence and is not a cusp nor a logarithmic divergence. The excess shear viscosity is approximately related to the composition by a Gaussian distribution in composition centered about the critical composition, X2c: Δη = f(T) exp {− (1/2)[10(X2 − X2c)]2}.