Static Correlation Length Research Articles

Neutron-scattering study of static antiferromagnetic correlations inLa2−xSrxCu1−yZnyO4

Neutron-scattering measurements have been performed to search for possible elastic incommensurate magnetic peaks in superconducting ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ with $x=0.10,$ 0.12, and 0.15. The most dramatic effects are found for $x=0.12;$ in this case, the peak intensity first appears at the onset of superconductivity ${T}_{c}(=31 \mathrm{K}).$ The resolution-limited peak width indicates that the static magnetic correlation length exceeds 200 \AA{} isotropically in the ${\mathrm{CuO}}_{2}$ planes. Weak elastic peaks are also observed at low temperatures for $x=0.10$ while for $x=0.15$ any incommensurate elastic scattering is below the limit of detectability. Elastic peaks are observed in Zn-substituted nonsuperconducting ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{Cu}}_{0.97}{\mathrm{Zn}}_{0.03}{0}_{4}.$ However, in this case, the Zn substitution degrades the magnetic order; the peak appears at lower temperature (17 K) and the correlation length is shorter (80 \AA{}) than that in the Zn-free $x=0.12$ sample.

Fine Structure of Polymer Networks As Revealed by Solvent Swelling

Measurements are reported of small-angle neutron scattering (SANS) from lightly cross-linked poly(vinyl acetate) gels swollen in good and ϑ solvents. In all the solvent conditions investigated the scattering response can be described satisfactorily by two characteristic length scales: a thermodynamic correlation length ξ that is related to the osmotic swelling pressure and a larger distance Ξ that is governed by the range of the random elastic forces exerted by the cross-links. ξ decreases significantly as the overall polymer concentration increases; the static correlation length Ξ, however, decreases only weakly as the gels shrink. For samples in a good solvent undergoing uniaxial stretching, a butterfly pattern is observed which is also well described in terms of two length scales. In ϑ conditions, however, this effect is masked by incipient phase separation in the gel in which the precipitated regions are elongated along the stretching direction.

Noise probes of underlying static correlation lengths in the superconducting peak effect

The sensitivity of low-frequency noise to ac magnetic-field perturbations is explored in the plastic flow regime near the ``peak effect'' in the clean type-II superconductor ${\mathrm{NbSe}}_{2}.$ Very small ac magnetic fields (on the order of 1 Oe in a dc field of about 20 000 Oe) substantially reduce the low-frequency spectral density by inducing rapid switching among metastable configurations present in the pinned state. This sensitivity to ac fields shrinks rapidly as $H$ increases in the peak-effect regime, indicating reduced static correlation lengths as the peak is approached.

Thermodynamics of two-dimensional XXZ easy-plane quantum Heisenberg magnets

We consider the quantum easy-plane (XXZ) magnet on the square lattice. In the classical case the system exhibits the Berezinskii–Kosterlitz–Thouless transition. Simulations, both for ferro- and antiferromagnets, using the method of the effective classical Hamiltonian, are made for different spin values and refer to the specific heat, the static spin correlation functions and correlation lengths in a broad range of temperatures, below and above the transition. The effects of quantum fluctuations are quantitatively evaluated and discussed.

Enormous Concentration-Induced Growth of Polymer-like Micelles

We report a detailed analysis of the effect of concentration on the micellar size, the static structure factor at q → 0, S(0), and the static correlation length ξs measured with static light scattering in aqueous solutions of the nonionic surfactant hexaethylene glycol n-hexadecyl monoether (C16E6) which forms giant polymer-like micelles in water. Measurements were performed at two different temperatures in order to test for possible contributions from critical scattering which could become important in the vicinity of the critical point. We find no measurable temperature dependence for the apparent molecular weight and the correlation length of the micelles for the given range of concentrations and temperatures. We demonstrate that the concentration dependence of the micellar size distribution and intermicellar interaction effects can be combined in a self-consistent way using results from conformation space renormalization group theory originally developed for semidilute polymer solutions. Our results indicate a much stronger micellar growth than that previously predicted by the theoretical models for micelle formation.

The static and dynamic critical behaviour of the two-dimensional Heisenberg antiferromagnet KFeF4

KFeF4 is a well characterized planar antiferromagnet with S=5/2 and is an excellent example of a two-dimensional Heisenberg antiferromagnet. Using neutron-scattering techniques, a study of both the static and dynamic critical behaviour above the Neel temperature, TN=136.75+or-0.35 K, has been undertaken. It is found that in the region above 1.04TN, the static correlation length, the structure-factor peak intensity and the width of the dynamic scattering are all qualitatively described by the theories developed for Heisenberg antiferromagnets. The data have been compared with both the theory for a quantum Heisenberg antiferromagnet. As developed for La2CuO4, and also the model for a classical Heisenberg antiferromagnet. Both these theories describe the data equally well. Below 1.04TN the system is expected to behave like a two-dimensional Ising system.

Thermodynamics and correlations of the easy-plane ferromagnet CsNiF3

The ferromagnetic compound CsNiF3 has been the object of plenty of experimental and theoretical research, due to its apparent 1D behavior (above the 3D ordering temperature TN=2.7 K). Indeed it can be modeled as a ferromagnetic chain with single-site easy-plane anisotropy. Its quantum Hamiltonian can also be expressed in terms of canonically conjugate operators by means of the Villain transformation, allowing us to apply a recently devised method, called the pure-quantum self-consistent harmonic approximation (PQSCHA), in order to obtain a classical effective Hamiltonian, by means of which the quantum thermal averages can be approximated by phase-space integrals. Comparing with the available quantum techniques, it is apparent that this is an enormous simplification. These classical-like formulas are able to describe the quantum behavior of the system, provided that the quantum coupling is not too strong. This is indeed the case for CsNiF3, whose effective Hamiltonian bears the form of the classical counterpart of the original one, but with suitably renormalized values of applied field, anisotropy, and exchange constant. An interesting feature is the appearance of an exchange anisotropy in competition with the easy-plane one, reflecting the effect of the quantum out-of-plane fluctuations. The classical transfer-matrix method is finally used in calculating various thermodynamic quantities, static structure factors and correlation lengths. Comparison with the available experimental data for CsNiF3, as well as with existing numerical simulation results, generally shows very good quantitative agreement.

Critical behavior in a binary polymer blend as studied by static and dynamic light scattering

We report static and dynamic light scattering experiments of an almost symmetric polymer mixture made up from poly(dimethylsiloxane) (PDMS), N=260, and poly(ethylmethylsiloxane) (PEMS), N=340, with N being the degree of polymerization, both below the entanglement molecular weights. The mixture exhibits an upper critical solution temperature Tc≂57 °C. The measurements were performed at the critical composition φc,PEMS = 0.465 in a broad temperature range in the one phase region above the spinodal point. The main results for the static case are: the temperature dependence of the static structure factor S(q=0) can be described by a mean field behavior. For T close to Tc, a crossover to an Ising behavior is observed according to a modified Ginzburg criterion. From the angular dependence of S(q), the static correlation length ξ is determined via an Ornstein–Zernike plot. Our experimentally determined values for limT→∞S(0) and limT→∞ ξ, respectively, are in agreement with theoretical predictions. For the dynamic case, the main results are summarized as follows: as expected, the mutual diffusion coefficient D̃, accessible by quasielastic light scattering, shows a critical slowing down for T→Tc. For qξ≥1, we observe that the q scaling of the Rayleigh linewidth Γ changes from a q2 to a q3 behavior, which is in agreement with mode coupled expressions. This occurs in a relatively broad temperature range, due mainly to the fact that polymer mixtures exhibit a larger ξ0 ∝√N, on the contrary to any other systems known, which allows us therefore to reach the region qξ≥1 even with light scattering easily. From the separation of the measured Rayleigh linewidth into a critical part and a background part, we have estimated the crossover between mode coupled to nonmode coupled dynamics. It is governed by the coil size. The scaling predictions for the critical part and the background part of the linewidth are in agreement with the predictions of the mode coupled theory by Kawasaki and subsequently by Fredrickson. We find that the mode coupled dynamics reaches far into the mean field regime which is not yet understood by theory. Furthermore, we can show that the critical part of the linewidth data is well represented by the Kawasaki shape function including the viscosity correction. Finally, we have estimated a segmental mobility W0∝D̃⋅S(q=0) which can be interpreted being a segmental quantity only down to characteristic lengths ξ(T)≂Rg. For ξ larger than the coil dimensions, W0∝ξ as predicted by mode coupled dynamics.

Deviation from mean-field behavior in a low molecular weight critical polymer blend

A deviation from mean-field behavior is observed in the static susceptibility and correlation length measured with small angle neutron scattering as a function of temperature near the phase boundary of a relatively low molecular weight critical polymer mixture. The possibility of a fluctuation influenced crossover from mean-field to nonmean-field behavior is considered.

Concentration fluctuation effects for dynamics of polymer solutions

Dynamics of concentration fluctuation in a semidilute polymer theta-solution in the regime of entanglements is studied theoretically. A number of relaxation modes is predicted, the largest amplitude corresponding to a reptation mode with the time , where q is the wave vector, the static correlation length, R the size of a polymer coil. A mode with a “superlong” time N2q−2 is predicted for . It is shown also that fluctuations of molecular field result in a substantial decrease of macromolecular curvilinear diffusion constant. The same effect gives rise to an increase of zero-shear viscosity of the solution; the dependence of viscosity on number of links per chain, N, is much stronger than N3 in the regime of high N.

A strongly fluctuating quasi-two-dimensional insulator (invited)

We describe neutron-scattering data for SrCr8−xGa4+xO19, a layered compound containing planes of S=3/2 Cr3+ ions which form Kagomé lattices. Despite strong antiferromagnetic interactions (θCW ≊ −500 K), fluctuations account for more than 75% of the free ion moment at 1.5 K. The spectrum (averaged over reciprocal space) is gapless and resembles that of a 2D long-range-ordered antiferromagnet, as does the low-temperature specific heat of the compound. Even so, the static correlation length does not exceed 7±2 Å. Monte-Carlo simulations of the antiferromagnetic three-state Potts model on the Kagomé lattice show that this model does not have a finite temperature phase-transition. Even at T=0, there does not seem to be true long-range antiferromagnetic-order. However, the magnetic correlations decay algebraically rather than exponentially. The implications of this result for the ground-state of SrCr8−xGa4+xO19 is discussed.

Critical behavior of an inverse micelle system.

We report measurements of the critical behavior of an inverted micelle system. The two-component system consists of a nonionic surfactant n-decyl octaoxyethylene glycol monoether (${\mathrm{C}}_{10}$${\mathrm{E}}_{8}$) in a hydrocarbon, dodecane. The system has an upper critical consolute point at 30\ifmmode\pm\else\textpm\fi{}2 wt. % ${\mathrm{C}}_{10}$${\mathrm{E}}_{8}$ at a temperature of T=28.05\ifmmode\pm\else\textpm\fi{}0.03 \ifmmode^\circ\else\textdegree\fi{}C. We demonstrate that both static and dynamic scaling are obeyed with universal three-dimensional Ising exponents describing the divergence of the osmotic compressibility and the static correlation length.

Static and dynamic behavior of semidilute polymer solutions

Reported results of dynamic light scattering experiments on semidilute solutions of linear non-charged polymers are reviewed. It is shown that, while for many systems the nature of the so-called slow modes may have a wide range of different causes, for a linear polymer in poor and moderately good solvents, the slow modes are mainly due to the effect of topological constraints. Values of static and dynamic correlation length reported by different research groups are compared with each other and with theory

Effect of topological excitations in the two-dimensional quantum Heisenberg antiferromagnet.

Using a continuum large-N U(1) gauge theory (${\mathrm{CP}}^{\mathit{N}\mathrm{\ensuremath{-}}1}$) for the low-temperature antiferromagnet in 2+1 dimensions, we recover previously obtained results for the static correlation length at the mean-field level. Phase fluctuations about mean field result in soundlike collective modes among a topological domain-wall loop liquid. To order ${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$, the sound modes are gapless in the quantum disordered phase. In the N\'eel phase they have small gaps, which results in an anomalous contribution to the spin-wave damping near the antiferromagnetic Bragg point.

The effects of random fields on the critical and bicritical behavior of Mn x Zn1?x F2

We have carried out a comprehensive study of the static and dynamic spin-spin correlations of Mn x Zn1−xF2 in a magnetic field. Samples withx=0.75 andx=0.5 have been studied. This system exhibits behavior closely related, if not identical, to that of the Random Field Ising Model (RFIM). An additional feature of Mn x Zn1−xF2 is that it exhibits an easily accessible bicritical point; thus one can study the changeover from the RFIM to the uniformXY model with a transverse random field. Quite generally, the instantaneous spin-spin correlations in a field are described by a combination of Lorentzian, Lorentzian-squared and delta function terms the latter corresponds to the long range order (LRO) component. In the Ising phase one finds history dependent behavior as discussed previously. In theXY phase, except very near the spin-flop boundary, one finds ergodic behavior withXY LRO and Lorentzian squared Ising fluctuations. Rather complicated instability effects are found all along the spin-flop boundary. Further, when one establishes LRO in theXY phase and lowers the field through the spin-flop value, one obtains a LRO Ising state in thex=0.75 sample whereas one obtains the field-cooled domain state in thex=0.50 sample. This dramatic difference in behavior is not understood. Our results on the RFIM aspects of the problem are consistent with our previous studies. The transition is dominated by the metastability effects with an underlying equilibrium transition which is either first order or weakly second order (β≈0). The underlying transition manifests itself directly in measurements of the dynamic response nearT N (H). From the data above the metastability boundary we deduce for the static correlation length exponentv=1.4±0.3 in good agreement with theory. We find for the RFIM crossover exponent φRF=1.5±0.2 where the errors represent the spread in values obtained from different techniques. Finally, we have determined in detail the field-temperature phase diagram of thex=0.5 sample including the critical behavior along the spin-flop line; the latter transition appears to be second order for an extended region.

Critical dynamics of random-field Ising systems with conserved order parameter.

Motivated by recent experiments on critical binary fluid mixtures in porous media, the dynamics of random-field Ising systems with conserved order parameter are considered. In the one-phase regime a new dynamic crossover length ${l}_{x}$ is found: for q\ensuremath{\ll}${q}_{x}$=2\ensuremath{\pi}/${l}_{x}$ the temporal decay of S(q,t) is well approximated by a single exponential whose decay rate is determined by diffusive dynamics, while for q\ensuremath{\gtrsim}${q}_{x}$ the temporal decay has a strongly nonexponential component, reflecting the activated dynamics of this system. As the ordering transition is approached, this dynamic length ${l}_{x}$ diverges as ${l}_{x}$\ensuremath{\sim}exp(c${\ensuremath{\xi}}^{\ensuremath{\psi}}$), where \ensuremath{\xi} is the static correlation length, and the activation free-energy barriers are of order cT${\ensuremath{\xi}}^{\ensuremath{\psi}}$ (T being the temperature and c a nonuniversal constant).

Statics and dynamics of concentration fluctuations in nonionic micellar solutions

Measurements of the angular distribution of light scattered from a nonionic surfactant, C12E6, are used to obtain the divergence of the static correlation length and isothermal compressibility near the critical point. The dependence of the apparent diffusion coefficient on momentum transfer yields a dynamic correlation length which agrees closely with the static values for the temperature regime (Tc−4 °C)<T<Tc. Outside this regime the scattering measurements are consistent with micelle growth. Dynamic scaling holds for this system near Tc but a significant background contribution to the diffusion coefficient is present due to the large micelle size.

Pressure-induced critical phenomena of a microemulsion system.

The critical phenomena of a microemulsion system were studied by applied external pressure for the first time. The divergence of the scattering intensity and the static correlation length as functions of $\ensuremath{\Delta}P\ensuremath{\equiv}|P\ensuremath{-}{P}_{c}|$ are described by the critical exponents $\ensuremath{\gamma}$ and $\ensuremath{\nu}$, respectively. The critical exponents $\ensuremath{\nu}$ and $\ensuremath{\gamma}$ associated with $\ensuremath{\Delta}P$ are the same as those obtained with other thermodynamic variables such as temperature and oil alkane carbon number.

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase ( h− h c h c ), χ ∼ (h−h c) 1 3 In -4 3 h c/h−h c and R c ∼ (h − h c) 2 3 . In 1 3 h c/h − h c . Far from commensurability (h⪢h c) χ∼ (a+h 2 c/h 2) -2 3 , R c ∼ (a + h 2 c/h 2) -2 3 , where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.

Critical-Like Behavior Observed for a Five-Component Microemulsion

The light-scattering techniques of intensity angular dissymmetry and photon correlation spectroscopy are used to determine the static correlation length, osmotic compressibility, and diffusivity of an oil-in-water microemulsion. The observed temperature dependence of these quantities near a phase separation point qualitatively resembles the critical behavior found for simple fluids and binary mixtures, but with substantially larger values of the critical exponents $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}$.