Showing papers on "Landau theory published in 2001"

Landau levels in the presence of topological defects

Abstract: In this paper we study the Landau levels in the presence of topological defects. We analyse the behaviour of electrons moving in a magnetic field in the presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topological defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric Katanaev-Volovich theory of defects in solids. The presence of the defect breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using Kaluza-Klein theory we solve the Landau level problem for a dispiration and compare the results with the ones obtained in the previous cases.

Landau theory of second-order phase transitions in ferroelectric films

Abstract: A detailed discussion is given of the predictions of the Landau-Devonshire theory for the behavior of thin ferroelectric films. It is assumed that the phase transition in the bulk is second order, and the theory is extended by the inclusion in the free-energy density of a term proportional to $|\ensuremath{ abla}P{|}^{2}$ together with a boundary condition involving an extrapolation length \ensuremath{\delta}. Expressions for the polarization profile $P(z)$ are given in terms of Jacobi elliptic functions; some of these are in a clearer and simpler form than has been available previously. Interesting analytic results for the entropy in terms of elliptic integrals and elliptic functions are also presented. Graphical illustrations of the main results are included. Careful consideration is given to the nature of the phase transition, and it is concluded that it is second order in all cases.

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

Abstract: The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

Spin Fluctuations in Itinerant Electron Systems

Abstract: Spin fluctuations are introduced to describe the finite temperature properties of itinerant electron ferromagnets To this end it is shown how Gaussian fiuctuations of the magnetic moment can be included in a Landau type free energy expansion From this model various properties are derived such as the temperature dependence of the magnetic moment and the susceptibility By including magneto - volume effects an application to Invar alloys is shown Finally the properties of the spin fluctuations are derived from a Landau - Ginzburg model A discussion of the Curie temperature in itinerant electron ferromagnets is given

Monte Carlo simulation of liquid-crystal alignment and chiral symmetry-breaking

Abstract: We carry out Monte Carlo simulations to investigate the effect of molecular shape on liquid-crystal order. In our approach, each model mesogen consists of several soft spheres bonded rigidly together. The arrangement of the spheres may be straight (to represent uniaxial molecules), Z-shaped (for biaxial molecules), or banana-shaped (for bent-core molecules). Using this approach, we investigate the alignment of the nematic phase by substrates decorated with parallel ridges. We compare results for wide and narrow ridge spacing and examine local order near the substrates, and show that our results are consistent with the predictions of Landau theory. We also investigate chiral symmetry-breaking in systems of bent-core molecules. We find a chiral crystalline phase as well as a nonchiral smectic-A phase, but not a chiral smectic-C phase.

Molecular dynamics study of the α–β transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure

Abstract: The α–β transition in quartz is investigated by molecular dynamics simulations in the constant stress ensemble. Based on a frequently used two-body interaction potential for silica, it is found that anomalies in the elastic constants are at least in semiquantitative agreement with experiment despite the fact that no anomaly in the c/a ratio is observed in the simulations. A finite-size scaling analysis shows that first-order Landau theory is applicable to the employed model potential surface. This statement also applies to the susceptibility below the transition temperature T tr, which has not yet been measured experimentally. Examination of the local order near T tr reveals that the deformation of SiO4 tetrahedral units is equally large in the β phase as in the α phase. However, large hysteresis effects can be observed in the local structure for distances r > 4 A. The results are in agreement with the picture of a first-order displacive phase transformation which is driven by the motion of deformed tetrahedral SiO4 units. Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz. The averaged configurations resemble the ideal structure only if averaged over at least a few nanoseconds.

Antiferroelectric phase transition in (Sr1-xCax)TiO3 (0.12<x⩽0.40): I. Dielectric studies

Abstract: Results of a detailed dielectric study of phase transition in Sr1-xCaxTiO3 in the composition range 0.18≤x≤0.40 are reported. It is shown that the temperatures T'm and T''m corresponding to the peaks in the real (e'(T)) and imaginary (e''(T)) parts of the dielectric constant, respectively, are not only coincident but also frequency independent, suggesting that these anomalies are due to a thermodynamic phase transition and not a dipole glass/relaxor ferroelectric transition. The Curie-Weiss temperature, as determined from the e'(T) data above the transition temperature, is found to be negative. Using Landau theory considerations, the negative Curie-Weiss temperature is interpreted in terms of an antiferroelectric phase transition. It is proposed that the smearing of the e'(T) data in the composition range 0.016≤x≤0.12 reported by Bednorz and Muller is due to the frustration introduced by the antiferroelectric interactions caused by Ca2+ substitution and the ferroelectric interactions of the SrTiO3 matrix.

Nanoquartz vs. macroquartz: a study of the α↔β phase transition

Abstract: The first-order character of the α↔β transition in micron-size quartz is shown to be strongly reduced in natural nano-size quartz with no significant variation of the transition temperature. Three different experimental techniques (differential scanning calorimetry, X-ray diffraction and second-harmonic generation) are applied on natural nano-size quartz to evaluate the variation of the character of the transition. The excess entropy of nano-size quartz is described in the framework of Landau theory. The renormalization of the fourth-order term is explained to arise from the elastic 3D-clamping imposed on each grain by the surrounding nanocrystallites. The presence of hydrous species and inhomogeneous internal stress due to the growth process are considered as well in the interpretation. The anomalous increase in the linewidth of diffraction maxima at the transition temperature is related to surface relaxation phenomena.

Monte Carlo Simulation of Liquid-Crystal Alignment and of Chiral Symmetry-Breaking

Abstract: We carry out Monte Carlo simulations to investigate the effect of molecular shape on liquid-crystal order. In our approach, each model mesogen consists of several soft spheres bonded rigidly together. The arrangement of the spheres may be straight (to represent uniaxial molecules), Z-shaped (for biaxial molecules), or banana-shaped (for bent-core molecules). Using this approach, we investigate the alignment of the nematic phase by substrates decorated with parallel ridges. We compare results for wide and narrow ridge spacing and examine local order near the substrates, and show that our results are consistent with the predictions of Landau theory. We also investigate chiral symmetry-breaking in systems of bent-core molecules. We find a chiral crystalline phase as well as a nonchiral smectic-A phase, but not a chiral smectic-C phase.

Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension

Abstract: We analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field [Phys. Rev. Lett. 85, 1803 (2000)]. We determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in $D=2,3,4,5$ dimensions. A comparison of our results and those obtained from a mean-field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four.

Phenomenological model for the antiferroelectric phase transition in thin films and small particles

Abstract: A phenomenological Landau model for the antiferroelectric phase transition in thin films and small cylindrical and spherical particles is developed The boundary value problem was solved numerically for polarizations of polar sublattices and components of the susceptibility tensor The spatial distribution of polarization and susceptibility and their temperature dependences were calculated The enhancement of diagonal components of the susceptibility tensor compared to bulk was found The size-dependent shift of the antiferroelectric phase transition temperature was obtained

Dielectric studies of phase transitions in the ferroelectric CdTiO3 and the Sr1−x CdxTiO3 solid solution

Abstract: Temperature dependences of the permittivity and of the dielectric hysteresis loops in ceramic samples of nominally pure CdTiO3 and a Sr1−xCdxTiO3 solid solution were studied. At 76.5±0.5 K, CdTiO3 was established to undergo a ferroelectric phase transition close to the tricritical point. The temperature dependence of spontaneous polarization of CdTiO3 is described within the Landau theory of phase transitions with the critical order parameter exponent ≈0.25. The phase diagram of the Sr1−xCdxTiO3 solid solution was drawn in (T, x) coordinates, and the critical concentration x c =0.002, above which an induced polar state sets in the solid solution, was determined.

Quadrupolar phase transition and field-dependent multipolar fluctuation in CeB6

Abstract: The effect of multipolar fluctuations on the quadrupolar phase transition in CeB 6 is investigated. The d -1 -correction to the mean-field solution of the multipolar Ruderman–Kittel–Kasuya–Yoshida (RKKY) model is analyzed in terms of a generalized Landau expansion of free energy, with d being the spatial dimension. It is shown that the multipolar fluctuations become strong and field-dependent when the model is close to the SU(4)-symmetric limit. As a result, various unusual phenomena around the transition are shown to be reasonably explained within the RKKY model. The realistic form of the interactions for CeB 6 is discussed on the basis of a quantitative comparison with experiments.

Light scattering from (K0.5Na0.5)0.2(Sr0.75Ba0.25)0.9Nb2O6 with the tungsten bronze structure: An analogy with relaxor ferroelectrics

Abstract: The Brillouin and Raman scattering from a complex single crystal from the tungsten–bronze family, (K0.5Na0.5)0.2(Sr0.75Ba0.25)0.9Nb2O6 doped with Cu2+ (KNSBN:Cu), have been comparatively studied in a wide temperature range around the ferroelectric transition. Step-like anomalies in hypersonic velocity and damping confirm the first-order structural transition. These anomalies look like some perturbations on the high-temperature slopes of both a broad dip in sound velocity and a broad maximum in damping that develop in a wide temperature range. The acoustic behavior of KNSBN:Cu does not simply follow the Landau theory prediction valid for many ferroelectrics. Instead it resembles that of relaxors, to which the KNSBN:Cu behavior is analogous intrinsically. The total intensity of the Raman spectra as well as the intensity of separate internal and external vibrations and their width correlate with acoustic anomalies, namely there are step-like drops at the same temperature as the first-order transition and a b...

Phase transitions and molecular dynamics in the cyclohexane'thiourea inclusion compound

Abstract: In thiourea inclusion compounds the host structure comprises a hydrogen bonded arrangement of thiourea molecules and contains unidirectional, nonintersecting channels within which guest molecules are located. Structural and dynamic properties of the cyclohexane/thiourea inclusion compound have been studied previously by a wide range of experimental techniques, providing contradictory interpretations. This organic composite crystal displays three thermotropic structural phases on cooling from room temperature, denoted phase I (rhombohedral), phase II (monoclinic), and phase III (monoclinic). However, until now, there has been no attempt to understand the relationship between the dynamics of the guest molecules and the structural and symmetry properties of the composite inclusion compound in the three phases. In the first part of this paper, we determine the space group of each phase from powder x-ray diffraction data. From this knowledge of the symmetry properties of each phase, the phase transitions are described in terms of order parameters defined on the basis of the symmetry principles of Landau theory. Theoretical analysis of the crystal strain occurring at the phase transitions allows a direct comparison between the experimental temperature dependence of the lattice parameters and predictions derived from Landau theory. In the second part of this paper, we report results from powder and single-crystal ${}^{2}\mathrm{H}$ NMR spectroscopy on samples of cyclohexane/thiourea containing perdeuterated cyclohexane guest molecules $({\mathrm{C}}_{6}{\mathrm{D}}_{12}).$ These ${}^{2}\mathrm{H}$ NMR experiments have shown that in phase I, the motionally averaged quadrupole coupling tensor is axially symmetric. On passing from phase I to phase II, the threefold symmetry axis of the $R=3\ifmmode\bar\else\textasciimacron\fi{}c$ space group of phase I is lost, such that the motionally averaged quadrupole interaction tensor is not axially symmetric in phase II. The single crystal ${}^{2}\mathrm{H}$ NMR spectra probe very precisely the relative orientations of the guest molecules, which are consistent with the site symmetry properties of the structure and proposed modes of crystal twinning, and demonstrate that there is only one type of dynamic species of guest molecule in phase II. In phase III, a greater degree of orientational ordering of the cyclohexane molecules is evident. From a detailed consideration of the symmetry properties of the inclusion compound, the dynamics of the guest molecules may be described using simple jump models (i.e., multidimensional pseudospin models) in all three phases. Using these models, the temperature dependence of the order parameter components has been established. These results, in conjunction with x-ray diffraction, provide important information needed to propose a microscopic model for the mechanisms of the phase transitions in the cyclohexane/thiourea inclusion compound.

A phenomenological model for dielectric relaxation processes in the B2 phase

Abstract: A simple model based on the Landau theory is used to describe the dielectric relaxation modes of the antiferroelectric B2 phase. The model allows us to explain the occurrence of two separated dielectric modes based on particle rotation about the molecular long axes.

Landau-de Gennes theory of surface-enhanced ordering in smectic films.

Abstract: A Landau theory for surface-enhanced ordering in smectic-A free-standing films is described, based on a generalization of de Gennes' model for a "presmectic" fluid confined between two walls. According to the theory, smectic ordering in free-standing films heated above the bulk smectic melting temperature is due to an intrinsic surface contribution rather than an external field. The theory yields a persistent finite-size effect, in that the film melting temperatures do not tend to the bulk transition temperature in the limit of infinite film thickness. It also predicts that a continuous transition from (N+1)- to N-layer films is impossible without an external field. The theory closely fits existing experimental data on layer-thinning transitions in compounds which exhibit a bulk smectic-A to nematic phase transition. Possible origins of the intrinsic surface contribution are discussed.

Role of tilt order in the asymmetric ripple phase of phospholipid bilayers.

Abstract: We present the electron density map of the asymmetric ripple phase of dilauroylphosphatidylcholine. We find that the primary feature characterizing the ``asymmetry'' of the rippled bilayers is the difference in the bilayer thickness in the two arms, and not the asymmetry of the bilayer height profile as is generally assumed. This difference in the bilayer thickness can be attributed to a mean tilt of the hydrocarbon chains of the lipid molecules along the direction of the ripple wave vector. We propose a Landau theory for this phase which takes into account the anisotropic elastic properties of a bilayer with tilt order.

Multi-resolution analysis and fractional quantum Hall effect: An equivalence result

Abstract: In this article we prove that any multi-resolution analysis of L2(R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translation, gives rise to an orthonormal set in the LLL. We also discuss the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.

Evidence for competing order parameters in the paramagnetic phase of layered manganites (invited)

Abstract: The magnetic field and temperature dependence of the magnetic susceptibility is studied for the ferromagnetic layered manganites SrO(La1−xSrxMnO3)2 in the composition range x=0.32–0.40. In the paramagnetic phase, the susceptibility exhibits an anomalous maximum at an intermediate magnetic field value. The size of this field-induced susceptibility enhancement increases dramatically with x from 10% for x=0.32 to 160% for x=0.40. The temperature dependence of the effect shows a maximum at T≈1.1 TC for all x. Quantitative analysis in terms of the Landau theory of phase transitions enables us to identify a distortion of the free energy F in the paramagnetic phase that is associated with the susceptibility anomaly. This free energy distortion corresponds to a magnetic system that approaches a first order magnetic phase transition as the temperature is lowered toward TC. Such a behavior is indicative of a second, competing order parameter, which is identified as the recently observed charge density wave. In the ...

Analysis of Switching in Perovskite Ferroelectrics on the Tetragonal Side of the Morphotropic Phase Boundary Using a Landau-Theory-Based Lattice Model with Polarization Vector Rotations

Abstract: The polarization reversal in perovskite ferroelectrics having a tetragonal phase is studied using the Landau-theory-based lattice model, extended to the three-dimensional polarization case. Switching at various electric field levels is analyzed for near and far distances from the theoretical morphotropic phase boundary (MPB), in the presence of the latent nuclei. The calculated time dependence of average polarization during switching is correlated with the changes of polarization profiles in the lattice. For low electric fields, switching can be achieved by polarization vector rotations triggered by infinitesimal tilting at the latent nuclei sites. Polarization vector rotations are most significant close to the MPB, where the free energy is isotropic in the space spanned by the polarization components. For electric fields beyond the longitudinal polarization instability, the transversal polarization components do not play a very significant role. Inferior retention properties near the MPB due to the polarization vector rotations are predicted, though higher reversal speed and lower switching threshold are expected.

Acoustic and dielectric anomalies in the temperature range of a ferroelectric phase transition in glycine phosphite crystals

Abstract: The acoustical and dielectric properties of glycine phosphite crystals are investigated in the temperature range of a ferroelectric phase transition. The acoustic anomalies for longitudinal waves along the X, Y, and Z crystallographic axes (where Y is the spontaneous polarization axis) are analyzed in the framework of the Landau theory. It is shown that pronounced acoustic anomalies of the velocity can be quantitatively described within the pseudoproper ferroelectric phase transition model with due regard for the long-range dipole-dipole interaction. For longitudinal acoustic waves propagating along the polar crystal axis, the striction anomaly of the velocity is only partly suppressed by the long-range dipole-dipole forces and an abrupt jump in the velocity is observed in the vicinity of the phase transition. The temperature coefficients of the velocity in the paraphase are determined. The striction contribution and the contributions biquadratic in the order parameter and in the strain to the velocity anomaly are separated.

Tetrasulphur Tetranitride: Phase Transition and Crystal Structure at Elevated Temperature

Abstract: Rietveld X-ray crystal structure investigations on S4N4 give evidence for a new orthorhombic high-temperature phase (Pbcn, a = 883.9(1) pm, b = 875.5(1) pm, c = 725.81(9) pm) very close to the explosion temperature of the solid-state material. The phase transition can be described using Landau's theory, yielding a critical temperature of 397 K and a critical exponent of 0.50. Tetraschwefeltetranitrid: Phasenubergang und Kristallstruktur bei erhohter Temperatur Rietveld-Kristallstrukturuntersuchungen mit Rontgenstrahlen an S4N4 geben eine neue orthorhombische Hochtemperaturphase (Pbcn, a = 883,9(1) pm, b = 875,5(1) pm, c = 725,81(9) pm) sehr nahe an der Explosionstemperatur des Feststoffs zu erkennen. Der Phasenubergang kann mit Hilfe der Landautheorie beschrieben werden; man erhalt eine Umwandlungstemperatur von 397 K und einen kritischen Exponenten von 0,50.