Phase diagram of YBa2Cu3O7−y at T<T c according to transverse nuclear relaxation data for Cu(2)

Two peaks are observed at T=35 and 47 K in the transverse relaxation rate for Cu(2) nuclei in YBa₂Cu₃O_7?y . A comparison of the relaxation rates for isotopes ⁶³Cu(2) and ⁶⁵Cu(2) at T=47 K indicates the magnetic nature of relaxation. The enhancement of local magnetic field fluctuations perpendicular to CuO₂ planes at T=47 K is associated with critical fluctuations of orbital currents. The peak at T=35 K is attributed to the emergence of an inhomogeneous superconducting phase. The obtained experimental results and the available data from the literature made it possible to propose a qualitatively new phase diagram of the superconducting state.     

Critical nuclear relaxation in cobalt metal

Nuclear magnetic resonance of cobalt metal was investigated in the paramagnetic and ferromagnetic states and in the critical region below T_c. The Knight shift and spin lattice relaxation times were measured in the paramagnetic phase in the solid and liquid states from 1578 K to 1825 K. The resonant frequency, spin-lattice and spin-spin relaxation times were measured in the ferromagnetic phase from room temperature to 1385 K. The main part of (T₁T)^-1 results from fluctuating orbital moments in both phases except near T_c where this process forms the background for critical spin relaxation. The critical exponents for T^-1₁ and for the magnetization in the ferromagnetic state were found to be n' = 0.96 ± 0.07 and β = 0.308 ± 0.012, respectively.     

Exploiting the flexibility of a family of models for taxation and redistribution

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures T ₁?<?T _c ?<?T ₂, where T _c is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase (T?<?T _c ) and a disordered one (T?>?T _c ) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization m????0 corresponding to T?=???, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization m?=?m ₀, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T?=?0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements (t??????) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.     

Das kritische magnetische Verhalten von EuO

Mössbauer effect and magnetization measurements were employed in order to study the static and especially the dynamic magnetic properties of the nearly Heisenberg ferromagnet EuO near its Curie temperature,T _c=69.2 °K. The critical exponent β of the spontaneous magnetization was determined to be β=0.34±0.02. It was shown that critical slowing down of spin fluctuations takes place nearT _c with spin relaxation times between 7×10^?11 sec (T=1.01T _c) and 1.5×10^?1 sec (T=1.03T _c). The experimental values of the relaxation time were found to be in satisfactory agreement with theoretically computed ones. Just belowT _c the Mössbauer spectra exhibit relaxation effects, which are characteristic for the occurence of critical super-paramagnetism. Investigations of several samples indicated quantitatively, that critical superparamagnetism has its origin in the non ideal composition of the real crystal.     

Some peculiarities of spin-lattice relaxation of impurity rare-earth ions in crystals caused by the structure defects

The spin-lattice relaxation times for Nd³⁺ ions in yttrium-aluminum garnets (YAG) and for Yb³⁺ ions in CaF₂ in the low-temperature range have been measured. For the first system the temperature dependence of the relaxation rate is determined to a great extent by the method of sample preparation. For samples grow by the method of the horizontally oriented crystallization the dependence is described asT ₁ ^?1 =AT ⁿ ,n ? 4.7, which is an evidence of an influence of local structure disordering on the relaxation. The temperature dependence of the relaxation rate in CaF₂:Yb is also “anomalous”:T ₁ ^?1 =AT ^3.3. The results are compared with the previous data on the relaxation in similar systems, and with other cases of observation of “anomalous” temperature dependences. Different manifestations of the local crystal defects in spin-lattice relaxation are discussed.     

Optical solitons in dense resonant media

Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times (T _p ? T ₁, T ₂), and “incoherent,” where the pulse duration falls between the relaxation times (T ₂ ? T _p ? T ₁). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.     

Cluster glass magnetism in the phase-separated Nd2/3Ca1/3MnO3 perovskite

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd_2/3Ca_1/3MnO₃ perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T_g∼60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T_max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole–Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at “macroscopic” time scale. Slow relaxation in the zero-field-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T_g, associated with its antiferromagnetic–ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T_g and above it are strongly different. Magnetic field up to about μ₀H∼0.4 T suppresses the glassy magnetic state of the compound.     

Phase space analysis of interacting dark energy in f(T) cosmology

In this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = ????T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(T) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet u* = (c ? 1)v* in the phase space, spanned by coordinates (u, v, ??, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ?? (?2, 0).     

Vacuum stability conditions from copositivity criteria

In this paper, we introduce a non-minimally conformally coupled scalar field and dark matter in F(T) cosmology and study their dynamics. We investigate the stability and phase space behavior of the parameters of the scalar field by choosing an exponential potential and cosmologically viable form of F(T). We found that the dynamical system of equations admits two unstable critical points; thus no attractor solutions exist in this cosmology. Furthermore, taking into account the scalar field mimicking quintessence and phantom energy, we discuss the corresponding cosmic evolution for both small and large times. We investigate the cosmological implications of the model via the equation of state and deceleration parameters of our model and show that the late-time Universe will be dominated by phantom energy and, moreover, phantom crossing is possible. Our results do not lead to explicit predictions for inflation and the early Universe era.     

Nuclear spin relaxation in liquids due to interaction with paramagnetic ions having anisotropic g tensors

Analytical expressions are derived for spin-lattice and spin-spin relaxation times (T_1M and T_2M) of a nucleus arising from magnetic interactions (dipolar and contact) with a paramagnetic ion which has an anisotropic g tensor. The relaxation rates depend on the orientation of the ion-nucleus vector in the principal-axis system of the g tensor. The deviations caused by this angular dependence with reference to the corresponding relaxation rates for an isotropic g tensor are numerically illustrated by considering a case typical for Co (II) complexes.     

Slowing down of the relaxational dynamics at the ferroelectric phase transition in one-dimensional (TMTTF)2AsF6

We present measurements of the dielectric response of quasi one-dimensional system (TMTTF)₂AsF₆ in a wide temperature and frequency range. We provide a thorough characterization of the relaxational dynamics observed close to the ferroelectric-like transition at T_c=100 K. Our measurements, extending up to 100 MHz, reveal a continuous slowing down of the mean relaxation time when approaching T_c from high as well as from low temperatures. The simultaneous critical rise of the dielectric constant and relaxation time point to an explanation of the transition in terms of a classic ferroelectric scenario.     

Paramagnetic–ferrimagnetic transition in strong coupling paramagnetic systems: effect of cubic anisotropy interaction

The purpose of the present work is a quantitative investigation of the biquadratic exchange interaction effects on the paramagnetic–ferrimagnetic transition arising from two strongly coupled paramagnetic (1-spin) sublattices, of respective moments m and M. The free energy describing the physics of the system is of Landau type. In addition to the quadratic and quartic terms, in both m and M, this free energy involves two mixing interaction terms. The first is a lowest order coupling −CmM, where C<0 stands for the coupling constant measuring the interaction between the two sublattices. While the second, which is relevant for 1-spin systems and which traduces the dipole–dipole (or biquadratic) interaction, is of type wm²M², where w>0 is the new coupling constant. These two interactions enter in competition, and then, they induce drastic changes of the magnetic behavior of the material. The main change is that, the presence of this high order coupling tends to destroy the ferrimagnetic order of the system. We first show that the introduction of this biquadratic interaction does not affect the values of critical exponents. Also, we find that the compensation temperature (when it exists) and the compensation magnetic field are shifted to their lowest values, in comparison with the w=0 case. The Arrott-phase-diagram shape is also investigated quantitatively. We show the existence of three regimes depending on the values of w. When the latter is small, we find that the region of competition between the coupling C and the applied magnetic field H becomes more narrow under the effect of w (by competition, we mean the passage from the antiparallel state to the parallel one). While for higher values of w, this competition disappears completely, and then, the system loses its ferrimagnetic character. Kinetics of the phase transition is also examined, when the temperature is lowered from an initial value T_i to a final one T_f very close to the critical temperature T_c. As in the w=0 case, we find that kinetics is controlled by two kinds of relaxation times τ₁ and τ₂. The former is the relevant time, and is associated to long-wavelength fluctuations driving the system to undergo a phase transition. The second is a short time, which controls local dynamics. Near T_c, we show that, in particular, the longest relaxation time τ₁ becomes less important in comparison with that relative to the w=0 case. Finally, we note that the existence of two relaxation times is consistent with the predictions of a recent experiment, which was concerned with the 1/2-spin compounds Li_xNi_2−xO₂, where the composition x is close to 1.     

Spin-lattice relaxation in the rotating frame and extreme slowing-down at the antiferroelectric transition in copper formate tetrahydrate

The effect on the temperature behavior of the spin-lattice relaxation rates in laboratory and rotating frames in presence of extreme slowing-down of the critical fluctuations in an Ising-type system is discussed. Proton spin-lattice relaxation measurements of T₁ and T_1? in water-deuterated copper formate tetrahydrate are presented. The data shown that the anomalous behavior of the proton T_1? in the neighbourhood of the antiferroelectric phase transition recently observed by Zumer and Pir? in the ordinary crystal cannot be ascribed to the critical slowing-down of the water molecules. A possible interpretation on the basis of a mechanism of creation and annihilation of paramagnetic excitons is discussed.     

Density correlation function and dynamic transient exponents for liquid helium at and aboveT λ

The critical dynamics of liquid helium are studied by means of renormalized field theory on the basis of the symmetric planar-spin model of Halperin, Hohenberg, and Siggia. The stability problem of the dynamic fixed point is discussed in detail. Two-loop results suggest, but do not establish, the stability of the dynamic scaling fixed point. The previously found small fixed point valuew ^*~O(0.15) is tentatively confirmed which implies a small ratio of relaxation rates of the order parameter and the entropy. The ensuing dynamic transient exponents are calculated. The density correlation function is determined toO(ε=4?d) at and aboveT _λ. Its properties in the casew ^*?1 provide quantitative support for the recently proposed explanation of the discrepancy between theory and light scattering experiments. A small value ofw ^* implies pronounced peaks of the frequency spectrum at finite frequencies at and aboveT _λ. It also suppresses the temperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value ofw ^*>0 and observable properties of the frequency spectrum is computed.     

<Superscript>63,65</Superscript>Cu NMR study of low-frequency spin dynamics in the infinite-layer antiferromagnetic compound SrCuO<Subscript>2</Subscript>

The spin-lattice and spin-spin relaxation times have been measured for ^63,65Cu NMR in the infinite-layer anti-ferromagnet SrCuO₂ in the ordered state for temperatures from 4.2 to 361 K. In the region of low temperatures (T≤250 K), both relaxation processes are of the same nature and the main contribution to the relaxation rate is associated with the diffusion of a small number of holes with an activation energy of ～42 meV. In the high-temperature range (T > 250 K), contributions to the transverse relaxation rate exhibit redistribution and this relaxation process is determined predominantly by indirect interactions.     

Some specific features of the NMR study of fluid flows

Some specific features of studying fluid flows with a NMR spectrometer are considered. The consideration of these features in the NMR spectrometer design makes it possible to determine the relative concentrations of paramagnetic ions and measure the longitudinal and transverse relaxation times (T₁ and T₂, respectively) in fluid flows with an error no larger than 0.5%. This approach allows one to completely avoid errors in determining the state of a fluid from measured relaxation constants T₁ and T₂, which is especially urgent when working with medical suspensions and biological solutions. The results of an experimental study of fluid flows are presented.     

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 ? √T _c /T _h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.     

Optimization,Stability, and Entropy in Endoreversible Heat Engines

The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.     

Specific features in the behavior of the central peak in Raman spectra of lithium tantalate

Low-frequency Raman spectra of a LiTaO₃ ferroelectric crystal are studied in the temperature range 300–1273 K. The central peak associated with the relaxation susceptibility of the crystal lattice is recorded throughout the temperature range covered, including the temperatures both substantially lower and considerably higher than the Curie point (T _c = 900 K). The critical slowing down of the relaxation response time predicted by the Ginzburg-Landau-Devonshire theory is observed in the temperature range from 0.9T _c to 1.1T _c . In contrast to the critical slowing down, the width of the central peak γ_R increases below 0.9T _c and decreases above 1.1T _c with increasing temperature.