Landau Coefficients Research Articles

Transient Response of Negative Capacitance in P(VDF0.75-TrFE0.25) Organic Ferroelectric Capacitor

The transient response of negative capacitance (NC) in an organic ferroelectric capacitor is experimentally investigated. To observe the transient response of the NC, a simple series network, consisting of an external series resistor and an organic ferroelectric capacitor, is built. The Landau coefficients of the organic ferroelectric capacitor were extracted from the measured polarization versus applied electric field data. A circuit level simulation was provided with the extracted parameters based on the Landau–Khalatnikov equation. To explore the impact of the RC time constant on the NC time duration in the RC series circuit, the external series resistor is altered as a tuning parameter. Also, the effect of various temperatures of the ferroelectric capacitor on the NC time duration is experimented. This paper demonstrates that either the external resistor or the ambient temperature can change the NC time duration in an organic ferroelectric capacitor.

S-Wave holographic superconductor in different ensembles and its thermodynamic consistency

In this paper, we analytically study the consistency between the Ginzburg–Landau theory of the holographic superconductor in different ensembles and the fundamental thermodynamic relation, we derive the equation of motion of the scalar field which depicts the superconducting phase in canonical ensemble (CE) and a consistent formula to connect the holographic order-parameter to the Ginzburg–Landau coefficients in different thermodynamic ensembles, and we also study the spatially nonuniform Helmholtz free energy.

Nonlinear effective properties of heterogeneous materials with ellipsoidal microstructure

The analysis and the synthesis of the nonlinear effective response of particulate composite materials are of great importance for developing new systems such as nonlinear elastic and electromagnetic metamaterials, nonlinear waveguides, nonlinear magnetoelectric devices and photonic or phononic crystals. Typically, classical homogenization schemes take into account the shape of the inhomogenieties but neglect the spatial correlation among them, a crucial feature for the above applications. In this paper we develop a nonlinear homogenization technique for dispersions of nonlinear particles in a linear matrix, which is able to take account of spatial correlation by means of the so-called ellipsoidal microstructure. While the linear result corresponds to the well known Ponte Castañeda–Willis estimate, we propose new formulae for the second and third order nonlinear behavior. We finally show applications to the nonlinear elastic Landau coefficients and to the nonlinear hypersusceptibility of transport processes.

Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations’ amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.

A phase-field study of domain dynamics in ferroelectric BCT-BZT system

ABSTRACTWe present a thermodynamically consistent phase-field model describing the free energy of perovskite-based BCT-BZT solid solution containing an intermediate morphotropic phase boundaries. The Landau coefficients are derived as functions of composition of zirconium. The electrostrictive and elastic constants are appropriately chosen from experimental findings. The resulting Landau free energy is constructed to describe the stable polarization states as a function of composition. The evolution of the polarization order parameters at a particular composition is described by a set of time-dependent Ginzburg-Landau (TDGL) equations. Additionally, we solve Poisson’s equation and mechanical equilibrium equation to account for the ferroelectric/ferroelastic interactions. We have performed two dimensional and three-dimensional simulations with appropriate electrical boundary conditions to study the effect of external electric field on domain dynamics in BCT-BZT system at the equimolar composition.

Structure, magnetic and magnetocaloric properties of new nanocrystalline (Pr,Dy)Fe9 compounds

Structural, magnetic and magnetocaloric properties for low-cost iron-based new pseudo binary nanocrystalline compounds (Pr,Dy)Fe9 has been investigated in detail. Four alloys with nominal composition Pr1−xDyxFe9 (x = 0.0625, 0.125, 0.1875, 0.25) were prepared. X-ray diffraction (XRD) coupled to Rietveld analysis with FULLPROF computer code show that the samples crystallize in the hexagonal P6/mmm phase, derived from CaCu5, with the stoichiometry 1/9. The diffraction domain sizes derived from Rietveld analysis are confirmed by transmission electron microscopy.The effect of Dy substitution on the Curie temperature TC, the saturation magnetization Ms and the magnetocrystalline anisotropy K is studied. The Landau coefficients, the Arrott plots and the magnetic entropy change ΔSM around the second-order magnetic transition were determined by measuring the magnetic properties. The Magnetocaloric effect properties in these compounds are comparable to that of gadolinium, which is very expensive for domestic use.

Weakly nonlinear stability analysis of subcritical electrohydrodynamic flow subject to strong unipolar injection

We analyse in detail the weakly nonlinear stability of electrohydrodynamic (EHD) flow of insulating fluids subject to strong unipolar injection, with and without cross-flow. We first consider the hydrostatic electroconvetion induced by a Coulomb force confined between two infinite flat electrodes, taking into account the charge diffusion effect. The effects of various non-dimensionalized parameters are examined in order to depict in detail and to understand better the subcritical bifurcation of hydrostatic electroconvetion. In addition, electrohydrodynamics with low- or high-$Re$cross-flow is also considered for investigating the combined effect of inertia and the electric field. It is found that the base cross-flow is modified by the electric effect and that, even when the inertia is dominating, the electric field can still strengthen effectively the subcritical characteristics of canonical channel flow. In this process, however, the electric field does not contribute directly to the subcriticality of the resultant flow and the intensified subcritical feature of such flow is thus entirely due to the modified hydrodynamic field as a result of the imposed electric field. This finding might be important for flow control strategies involving an electric field. Theoretically, the above results are obtained from a multiple-scale expansion method, which gives rise to the Ginzburg–Landau equation governing the amplitude of the first-order perturbation. The conclusions are deduced by probing the changes of value of the coefficients in this equation. In particular, the sign of the first Landau coefficient indicates the type of bifurcation, being subcritical or supercritical. Moreover, as a quintic-order Ginzburg–Landau equation is derived, the effects of higher-order nonlinear terms in EHD flow are also discussed.

DMFT+Σ approach to disordered hubbard model

We briefly review the generalized dynamical mean-field theory DMFT+Sigma treatment of both repulsive and attractive disordered Hubbard models. We examine the general problem of metal-insulator transition and the phase diagram in repulsive case, as well as BCS-BEC crossover region of attractive model, demonstrating certain universality of single - electron properties under disordering in both models. We also discuss and compare the results for the density of states and dynamic conductivity in both repulsive and attractive case and the generalized Anderson theorem behavior for superconducting critical temperature in disordered attractive case. A brief discussion of Ginzburg - Landau coefficients behavior under disordering in BCS-BEC crossover region is also presented.

Attractive Hubbard Within the Generalized DMFT: Normal State Properties, Disorder Effects and Superconductivity

Using the generalized DMFT+ Σ approach, we have studied disorder influence on the density of states, optical conductivity of the normal phase, superconducting transition temperature, and Ginzburg–Landau coefficients in the attractive Hubbard model. The wide range of attractive potentials U was studied—from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong coupling region, where superconducting transition is due to the Bose–Einstein condensation (BEC) of preformed Cooper pairs. For semi-elliptic “bare” density of states of conduction band, the disorder influence on all single-particle properties (e.g., density of states) is universal for arbitrary strength of electronic correlations and is due only to the general disorder widening of conduction band. Using the combination of DMFT +Σ and Nozieres–Schmitt-Rink approximations, we have studied the disorder influence upon superconducting transition temperature Tc for the range of characteristic values of U and disorder including the BCS-BEC crossover region. Disorder can either suppress Tc (in the weak coupling region) or significantly increase Tc (in strong coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of superconducting critical temperature are essentially due only to the general disorder widening of the conduction band.

Noncentrosymmetric superconductivity in a clean crystal of type II superconductor Bi-Pd

In this work, we present the bulk superconductivity of a high-quality single crystal of monoclinic BiPd (α-BiPd, space group P21) below 3.8 K by studying its electrical resistivity, magnetic susceptibility, and heat capacity. This is the cleanest noncentrosymmetric superconductor (NCS) that display anisotropy due to spin-orbit scattering and also exhibits unusual superconducting properties due to s and p wave mixing as evidenced by the observation of Andreev bound state and multiple energy gaps via point contact measurements. In addition, Fermi surface studies suggest multiband superconductivity in this compound. Penetration depth studies and NQR investigations support mixing of s and p wave Copper paring in this crystal. Moroever, Muon spin rotation measurements indicate strong field dependence of the Ginzburg- Landau coefficient of this superconductor. Unusual pairing and multiband superconductivity are extremely sensitive to disorder and they can be observed only in cleanest (RRR > 170) single crystals.

Effect of electric field on reentrance transition in a binary mixture of liquid crystals

Employing a phenomenological mean field theory, we analyze the effect of an electric field on the N − SmA phase transition for pure liquid crystal and on the reentrant nematic phase in a binary mixture of liquid crystals exhibiting the phase sequence I − N − SmA − NR on cooling. The basic idea of the work is to explain the phase transition behavior of the system by assuming that certain Landau coefficients associated with the order parameters coupling terms of the free-energy density expansion are field dependent. These parameters play a crucial role and show a rapid variation at the SmA − NR transition as compared to the SmA − N transition.

Effects of Electric Field and Temperature on Spontaneous Polarization in the Vicinity of Isotropic to Antiferroelectric B2 Phase Transition in a Banana-Shaped Mesogen 12OSOR

Using a phenomenological free‐energy density expansion, in this work, we have studied the effects of temperature and electric field on the spontaneous polarization of antiferroelectric B2 phase in the vicinity of I–B2 phase transition in a bent-core mesogen 12OSOR. The free-energy density of the system is written in terms of tensor orientational order parameter , scalar smectic order parameters and , the vector polarization order parameter and the resulting couplings between these order parameters. Using the Landau coefficients, as determined from the experimental values of relevant quantities, we evaluate the temperature and electric field variations of spontaneous polarization and found that the theoretical results agree well with the experimental data of bent core achiral thioester mesogen 12OSOR.

Spatio-temporal structure of the ‘fully developed’ transitional flow in a symmetric wavy channel. Linear and weakly nonlinear stability analysis

AbstractThis work addresses the transition from 2D steady to 2D unsteady laminar flow for a fully developed regime in a symmetric wavy channel geometry. We investigate the existence and characteristics of the spatio-temporal structure of the fully developed unsteady laminar flow for those particular geometries for which the steady flow presents a periodic variation of the main stream velocity component. We perform a 2D global linear stability analysis of the fully developed steady laminar flow, and we show that, for all the geometries studied, the transition is triggered by a Hopf bifurcation associated with the breaking of the symmetries and the invariance of the steady flow. Critical Reynolds numbers, most unstable modes and their characteristics are presented for large ranges of the geometric parameters, namely wavenumber${\it\alpha}$from 0.3 to 5 and amplitude from 0 (straight channel) to 0.5. We show that it is possible to define geometries for which the wavenumber is proportional to the most unstable mode wavenumber for the critical Reynolds number. From this modal study we address a weakly nonlinear stability analysis with a view to obtaining the Landau coefficient$g$, and then the sub- or supercritical nature of the first bifurcation characterising the transition. We show that a critical geometric amplitude beyond which the first bifurcation is supercritical is associated with each geometric wavenumber.

Effect of elastic compliances and higher order Landau coefficients on the phase diagram of single domain epitaxial Pb(Zr,Ti)O3 (PZT) thin films

We report the qualitative study of the influence of both elastic compliances and higher order terms of Landau free energy potential on the phase diagram of Pb(Zr0.5Ti0.5)O3 thin films by using a single domain Landau theory. Although the impact of elastic compliances and higher order terms of the Landau free energy potential on the phase diagram of ferroelectric thin films are known, the sensitivity of the phase diagram of PZT thin film on these parameters have not been reported. It is demonstrated that, while values of elastic compliances affect the positions of the phase boundaries including phase transition temperature of the cubic phase; higher order terms can potentially introduce an a1a2-phase previously predicted in PbTiO3 phase diagram.

Nonlinear instability and convection in a vertically vibrated granular bed

AbstractThe nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shaking is incorporated by specifying a constant granular temperature at the vibrating plate. Under these mean-field assumptions, the base-state temperature decreases with increasing height away from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis (Shukla & Alam, J. Fluid Mech., vol. 672, 2011b, pp. 147–195), the nonlinearities up to cubic order in the perturbation amplitude are retained, leading to the Landau equation, and the related adjoint stability problem is formulated taking into account appropriate boundary conditions. The first Landau coefficient and the related modal eigenfunctions (the fundamental mode and its adjoint, the second harmonic and the base-flow distortion, and the third harmonic and the cubic-order distortion to the fundamental mode) are calculated using a spectral-based numerical method. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the density-inverted Leidenfrost state. Near the bifurcation point the equilibrium amplitude ($A_{e}$) is found to follow a square-root scaling law, $A_{e}\sim \sqrt{{\it\Delta}}$, with the distance ${\it\Delta}$ from the bifurcation point. We show that the strength of convection (measured in terms of velocity circulation) is maximal at some intermediate value of the shaking strength, with weaker convection at both weaker and stronger shaking. Our theory predicts that at very strong shaking the convective motion remains concentrated only near the top surface, with the bulk of the expanded granular bed resembling the conduction state of a granular gas, dubbed as a floating-convection state. The linear and nonlinear patterns of the density and velocity fields are analysed and compared with experiments qualitatively. Evidence of 2:1 resonance is shown for certain parameter combinations. The influences of bulk viscosity, effective Prandtl number, shear work and free-surface boundary conditions on nonlinear equilibrium states are critically assessed.

Freezing in relaxor ferroelectrics and dipolar glasses

A recently proposed semi-phenomenological model of freezing in relaxor ferroelectrics, based on the concept of polar nanoregions (PNRs) embedded in a polarizable medium, is reviewed. A generalized Landau-type free energy for the medium is discussed, where the medium polarization couples linearly to the PNR polarization. When the fourth-order Landau coefficient is negative (b < 0), the correlation radius rc, which measures the PNR size, depends on the temperature T and the applied field E. As T is lowered or E increased, rc increases and the volume of a cluster of PNRs grows until the percolation limit is reached. This leads to a generalized expression for the Vogel-Fulcher (VF) relaxation time with a field-dependent VF freezing temperature T0(E). The case b > 0, in which the percolation mechanism cannot be realized, is considered to be appropriate for dipolar glasses.

Effect of Al content on the order of phase transition and magnetic entropy change in LaFe11Co0.8(Si1−xAlx)1.2 alloys

The comparative studies of the effect of partial substitution of Al by Si on the structure and magnetic entropy change in LaFe11Co0.8(Si1−xAlx)1.2 alloys produced by arc-melting followed by long time annealing at 1323K were performed. The X-ray diffraction analysis revealed almost single phase composition of annealed samples. The high intensity synchrotron radiation was used for studying the thermal evolution of lattice constant of the La(Fe,Co,Si)13 phase. Furthermore, calculations of temperature dependences of Landau coefficients were used to reveal changes in the character of phase transformation at around the Curie temperature.

Multi-electron systems in strong magnetic fields I: The 2D Landau–Hartree–Fock–Roothaan method

We present a 2-dimensional Hartree–Fock–Roothaan code to calculate wave functions and energies of light to heavy atoms in strong external magnetic fields, as they occur in the vicinity of neutron stars. The code enhances the previously presented HFFERII method, resulting in a very high precision for the energies with typical deviations less than 1% compared to extremely precise fixed-phase diffusion quantum Monte Carlo calculations. Despite this high precision the code is highly optimized regarding speed and reliability, which allows calculating large amounts of states in short time, even with small-scale computing clusters. Program summaryProgram title: 2DLHFRCatalogue identifier: AETE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 121429No. of bytes in distributed program, including test data, etc.: 561163Distribution format: tar.gzProgramming language: Fortran 95.Computer: Cluster of 1-15 Fujitsu ESPRIMO P920.Operating system: Linux.Has the code been vectorized or parallelized?: Yes, parallelized using MPI. Tested on 2–60 processors.RAM: At least 1 GByte per coreClassification: 2.1.External routines: GFortran, LAPACK, BLAS, MPINature of problem:The modeling of highly magnetized atmospheres of neutron stars and magnetic white dwarfs is a difficult task and is further complicated by the lack of atomic data. The absorption features in the thermal emission spectra of neutron stars are still not fully understood, which leads to different interpretations and thus large uncertainties for the atmospheric parameters, such as the magnetic field strength, the gravitational redshift, or the predominant atomic composition. Therefore, a fast and reliable program to scan through the large parameter space is necessary.Solution method:The strong magnetic fields present on neutron stars favor a wave function expansion in terms of Landau channels. Contrary to previous attempts we use a full 2-dimensional basis and assign individual z-wave functions to each Landau channel. This allows for an accurate description of the single-particle orbitals. These are combined in a Slater determinant, resulting in Hartree–Fock–Roothaan equations, which are solved iteratively. As initial wave functions we rely on the solutions calculated by the HFFERII program and reuse the optimized B-spline basis sets and Landau coefficients to maximize the speed of the program presented here.Restrictions:Intense magnetic field strengths B/Z2≳5×104T are required to yield accurate results.Unusual features:2DLHFR is based upon the wave functions calculated with the HFFERII program package, presented in [C. Schimeczek, D. Engel, G. Wunner, Comp. Phys. Comm. 183 (2012) 1502]. In turn, the results of this program may be enhanced beyond the Hartree–Fock limit with quantum Monte Carlo methods, as is shown in the accompanying paper.Additional comments:The gfortran compiler is recommended for this program (http://gcc.gnu.org/onlinedocs/gfortran/).Running time:Seconds to minutes

Magnetic properties of LaCo12B6 compound as probed by neutron diffraction and by magnetization study under high pressures

The magnetic properties have been studied by magnetization measurements and the crystal and magnetic structure investigated by neutron diffraction. It is shown that LaCo12B6 compound exhibits an incommensurate conical type magnetic structure. Significantly different magnetic moments have been observed on the two Co crystal sites. The ambient pressure data are compared to that of YCo12B6 isotype and Landau coefficients have been derived from the magnetization curves for both compounds as well as their temperature dependence. The LaCo12B6 compound undergoes a transition from ordered to paramagnetic state at 160K. The volume dependence of intrinsic magnetic properties of the LaCo12B6 compound has been determined by studies under hydrostatic pressure up to 10kbar in temperature range 5–200K. Both the Curie temperature TC and the spontaneous magnetization MS decreases with increasing pressure. The observed decrease of MS with pressure (dMS/dp=−7.4×10−3μB/kbar at 5K) can be attributed to the pressure induced decrease of Co magnetic moments. The decrease of TC with pressure (dTC/dp=−0.49K/kbar) is comparable to the decrease observed on RCo12B6 compounds with non-magnetic R and can be attributed to the volume dependence of Co–Co exchange interactions. The remarkable role of the hybridization as a consequence of small distances between Co and B atoms could be a background of this rather unexpected volume stability of magnetic properties.

Influence of pressure on the B2I phase transition of a banana-shaped liquid crystal

Employing a phenomenological mean field theory, we analyse the effect of high pressure on the B2I phase transition properties of a bent-core liquid crystal. The basic idea of the work is to explain the phase transition behaviour of system by assuming that certain Landau coefficients associated with the order parameters coupling terms of the free-energy density expansion are pressure dependent. We observe excellent agreement between the theoretical and experimental results of mesogen PHDBB and that the B2I transition remains first order even at the elevated pressures.