Showing papers on "Landau theory published in 2006"

Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi.

Abstract: MnSi is an itinerant magnet which at low temperatures develops a helical spin-density wave. Under pressure it undergoes a transition into an unusual partially ordered state whose nature is debated. Here we propose that the helical spin crystal (the magnetic analog of a solid) is a useful starting point to understand partial order in MnSi. We consider different helical spin crystals and determine conditions under which they may be energetically favored. The most promising candidate has bcc structure and is reminiscent of the blue phase of liquid crystals in that it has line nodes of magnetization protected by symmetry. We introduce a Landau theory to study the properties of these states, in particular, the effect of crystal anisotropy, magnetic field, and disorder. These results compare favorably with existing data on MnSi from neutron scattering and magnetic field studies. Future experiments to test this scenario are also proposed.

Shape phase transitions and critical-point phenomena in atomic nuclei

Abstract: Atomic nuclei exhibit phase transitions as a function of the number of their constituent protons and neutrons. These phase transitions are not of the usual thermodynamic type, but rather they are quantum phase transitions in the equilibrium shape and structure of the ground and low-lying states. This realization has sparked a new area of research, focusing on the concept of 'critical-point symmetries', which describe the structure of nuclei at phase-transitional points. Both macroscopic (geometric or algebraic) and microscopic (shell-model) aspects of these phase transitions and of changes in structure with proton and neutron number in nuclei are discussed, along with an interpretation in terms of simple Landau theory. Finally, some alternative scenarios and schematic models for different classes of nuclei based on other simple potentials are briefly summarized.

Zn13Sb10: A Structural and Landau Theoretical Analysis of Its Phase Transitions

Abstract: Composition, crystal structures, polymorphic transformations, and stability of the thermoelectric material known in the literature as "Zn 4 Sb 3 " have been studied on a polycrystalline sample and Bi-flux-grown single crystals using X-ray diffraction techniques, resistance, and Seebeck coefficient measurements at various temperatures ranging from 4 to 773 K. Microprobe analysis yields the composition of the flux-grown crystals to be close to Zn 13 Sb 10 , with minor Bi doping. High-temperature X-ray and Seebeck coefficient studies show that the phase is unstable at high temperatures in a vacuum because of Zn losses. Both X-ray diffraction and resistivity measurements indicate the presence of two consecutive symmetry-breaking transitions below room temperature, in agreement with_our previous results on polycrystalline samples. Application of Landau theory suggests that the first R3c - C2/c symmetry breaking may be second-order in nature. The second, low-temperature symmetry breaking may proceed along two routes. One of these pathways, a first-order C2/c - Cl symmetry reduction, may lead to an incommensurate structure and is consistent with our experimental observations.

Depolarizing field and “real” hysteresis loops in nanometer-scale ferroelectric films

Abstract: The authors give detailed analysis of the effect of depolarizing field in nanometer-size ferroelectric capacitors studied by Kim et al. [Phys. Rev. Lett. 95, 237602 (2005)]. They calculate a critical thickness of the homogeneous state and its stability with respect to domain formation for strained thin films of BaTiO3 on SrRuO3∕SrTiO3 substrate within the Landau theory. While the former (2.5nm) is the same as given by ab initio calculations, the actual critical thickness is set by the domains at 0.8nm. There is a large Merz’s activation field for polarization relaxation. Remarkably, the results show a negative slope of the “actual” hysteresis loops, a hallmark of the domain structures in ideal thin films with imperfect screening.

Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

Abstract: Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10^{-9}. Our study establishes the existence of two strain thresholds, the first, epsilon_L, below which the material is essentially linear, and the second, epsilon_M, below which the material is nonlinear but where quasiequilibrium thermodynamics still applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above epsilon_M the behavior becomes truly nonequilibrium -- as demonstrated by the existence of material conditioning -- and Landau theory no longer applies. The main focus of this paper is the study of the region below the second threshold, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

Elastic properties of minerals and the influence of phase transitions

Abstract: Elastic anomalies that accompany cation ordering and displacive phase transitions can be understood in terms of coupling between strain components and the driving order parameter in Landau free energy expansions. Non-convergent cation ordering in spinel, MgAl2O4, is accompanied by changes in individual elastic constants, shear modulus, and bulk modulus that vary linearly with the order parameter. Convergent cation ordering, such as Al/Si ordering in anorthite, is expected to give changes in elastic properties that scale with the square of the order parameter. The elastic anomalies that develop in association with displacive phase transitions show greater diversity, due to the additional influence of the order parameter susceptibility. These are illustrated for the cases of the proper ferroelastic transition at high pressure in stishovite and the improper ferroelastic transition in SrTiO3 perovskite. Low temperature transitions in lawsonite show a more complex pattern of softening and stiffening that depends on coupling with both cation ordering and displacive processes. Variations of the spontaneous strain and elastic constants are indicative of the underlying thermodynamic mechanism for a phase transition. If any such transitions occur in minerals of the Earth’s crust or mantle they should be identifiable from their distinctive influence on seismic velocities.

Theory of the high-pressure structural phase transitions in Si, Ge, Sn, and Pb

Abstract: Displacive mechanisms are proposed for the high-pressure structural transitions which take place in Si, Ge, Sn, and Pb The mechanisms are analyzed in the framework of the Landau theory of phase transitions It reveals a number of unifying features which are discussed in connection with the electronic structures of these elements, leading to a more precise understanding of the diversity of phase diagrams found for the elements of Group IVa

Scalar Order: Possible Candidate for Order Parameters in Skutterudites

Abstract: Phenomenological Landau analysis shows that the properties of ordered phases in some skutterudites are consistently accounted for by a scalar-order parameter which preserves the cubic symmetry, even in the ordered phase. A universal value is found for the anisotropy ratio of the transition temperature in a magnetic field, homogeneous magnetization, and induced staggered magnetization. The difference in magnetic behavior between PrFe 4 P 12 and PrRu 4 P 12 near their phase transitions is explained within a single framework. For the low-field phase of PrFe 4 P 12 , the scalar order with Γ 1 g symmetry can explain (i) the absence of field-induced dipoles perpendicular to the magnetic field, (ii) isotropic magnetic susceptibility in the ordered phase, (iii) the field-angle dependence of the transition temperature, and (iv) the splitting pattern of the 31 P nuclear magnetic resonance (NMR) spectra. It is proposed how the order parameter in SmRu 4 P 12 is identified by NMR analysis of a single crystal.

Temperature-dependent vortex motion in a square mesoscopic superconducting cylinder: Ginzburg-Landau calculations

Abstract: In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

Psi-series solution of fractional Ginzburg–Landau equation

Abstract: One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α with polynomial nonlinearity of order s have the noninteger power-like behaviour of order α/(1 − s) near the singularity.

Modelling hysteretic behaviour in magnetorheological fluids and dampers using phase-transition theory

Abstract: A dynamical mathematical model is proposed to model the hysteretic behaviour of magnetorheological fluids and dampers using phase-transition theory. To construct the model involving hysteresis, the magnetorheological fluids are assumed to be switchable between different phases upon the application of a shear strain rate, with one solid-like phase and two fluid-like phases. The Landau theory for phase transition is employed to model the dynamics of the phase transition in the fluids. The proposed model is able to capture hysteresis loops, and is rate dependent (frequency dependent). A comparison between predicted and experimental behaviour of the damper is presented, and perfect agreement is obtained.

Superconductors with topological order

Abstract: We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivity is concretely realized as global superconductivity in Josephson junction arrays.

Unconventional continuous phase transition in a three-dimensional dimer model.

Abstract: Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.

Measurement of pressure effects on the magnetic and the magnetocaloric properties of the intermetallic compounds R(Co1-xSix)2 [R=Dy and Er]

Abstract: The effect of external pressure on the magnetic properties and magnetocaloric effect of R(Co1-xSix)2 [R= Er, Dy and x=0, 0.025 and 0.05] compounds has been studied. The ordering temperatures of both the parent as well as the Si substituted compounds are found to decrease with pressure. In all the compounds, the critical field for metamagnetic transition increases with pressure. It is seen that the magnetocaloric effect in the parent compounds is almost insensitive to pressure, while there is considerable enhancement in the case of Si substituted compounds. Spin fluctuations arising due to the magnetovolume effect play a crucial role in determining the pressure dependence of magnetocaloric effect in these compounds. Analysis of the magnetization data using the Landau theory has shown that the magnitude of the Landau coefficient (C3) decreases with Si concentration whereas it is found to increase with pressure. The isothermal magnetic entropy change is found to behave in the same manner as C3, both with Si concentration (at ambient pressure) as well as with the applied pressure.

Landau theory of the orthorhombic Fddd phase.

Abstract: Numerical self-consistent-field theory calculations by Tyler and Morse [Phys. Rev. Lett. 94, 208302 (2005)] predict a stable orthorhombic network phase with space group $Fddd$ in very weakly segregated diblock copolymer melts. Here, we examine the predicted stability of this phase within a simple Landau theory of weakly ordered crystals, and within a straightforward extension of Leibler's theory of weakly segregated diblock copolymer melts. An $Fddd$ structure with a ratio of unit cell parameters $(a:b:c)=(1:2:2\sqrt{3})$ is found to compete very closely with the hexagonal $(H)$ and lamellar $(L)$ phases along the predicted $H\text{\ensuremath{-}}L$ phase boundary, and to be stable within a very narrow range of parameters around this metastable boundary.

Iron melting curve with a tricritical point

Abstract: Solidification as a first-order phase transition is described in the Landau theory by the same equation as tricritical phenomena. Here, the solidification or melting temperature against pressure curve is modelled to end at a tricritical point. The model gives the phase transition temperature's dependence on pressure up to the quadratic term with a definite expression for the coefficients. This formula is expected to be generally valid for pure materials having melting curves with dT/dP approaching zero at very high P. Excellent experimental agreement is obtained for iron, the material having the most high pressure data which rather accurately determines the value of the coefficient defining the curvature. The geophysically interesting iron solidification temperatures at the Earth's core pressures are obtained. In addition, the general formulae for entropy change, latent heat and volume contraction in solidification are found and calculated for iron as functions of pressure and temperature.

Squeezing superfluid from a stone: coupling superfluidity and elasticity in a supersolid.

Abstract: Starting from the assumption that the normal solid to supersolid (NS-SS) phase transition is continuous, we develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic moduli and thermal expansion coefficients near the transition and, conversely, that inhomogeneous lattice strains can induce local variations of the superfluid transition temperature, leading to a broadened transition.

Evidence of extended defects in pure zirconia irradiated by swift heavy ions

Abstract: X-ray diffraction, transmission electron microscopy, and optical spectroscopy were used to investigate the microstructure of polycrystalline samples of pure monoclinic zirconia irradiated by high energy ions. These techniques point out the existence of extended defects and they allow to monitor the tetragonal to monoclinic phase transition as a function of the temperature during isochronal annealings. The Landau theory approach explains the phase transition mechanism via the presence of an important strain field induced by dislocations. Though high and low energy ions can effectively stabilize the same tetragonal phase in the irradiated layer, only point defects are produced at low energy whereas extended defects are also observed at high energy, showing the strong influence of the energy deposition modes on the observed microstructures.

Phase transition of pure zirconia under irradiation: A textbook example

Abstract: One of the most important goals in ceramic and materials science is to be able to design materials with specific properties. Irradiation seems to be a powerful tool for the design of advanced ceramics because of its ability to modify over different scales the microstructure of solids. Nowadays, it is clearly proved that irradiation induces order–disorder phase transitions in metallic alloys and in some ceramics. In this paper, we show that a displacive phase transition can also be induced by irradiation. Based on many experimental facts, a microscopic model is proposed to explain the displacive phase transition observed in this material after irradiation. Defects, produced in the oxygen sublattice, induce important strain fields on a nanometric scale. This strain field can be handled as a secondary order parameter within the Landau theory approach, leading to a decrease of the phase transition temperature and thus quenching the high temperature tetragonal phase.

Finite Element Analysis of Phase Transformation Dynamics in Shape Memory Alloys with a Consistent Landau-Ginzburg Free Energy Model

Abstract: The Landau theory of phase transition has been successfully applied to solve a number of important problems in the dynamics of martensitic phase transformations in alloys. On the other hand, although a precise mathematical description of the microstructures is known within the framework of Cauchy-Born hypothesis, its discrete version is not well elucidated in the literature, especially for multivariant transformations in three-dimensional samples. A major reason for such a situation lies with computational difficulties connected with quasi-convexity of the associated minimization problem. In this paper we develop a Landau-Ginzburg free energy model for dynamic problems of phase transformations and show a possible link of the developed framework with the continuum description of phase transformations. We demonstrate how the precise description of compatible microstructures in the phase-field model can be used in computational finite element models. The developed framework is sufficiently general to be appl...

Theory of magnetic phases of hexagonal rare earth manganites

Abstract: The magnetic phases of hexagonal perovskites RMnO3 (R = Ho, Er, Tm, Yb, Sc, Y) are analysed using group theory and the Landau theory of phase transitions. The competition between various magnetic order parameters is discussed in the context of antiferromagnetic interactions. A phenomenological model based on four one-dimensional magnetic order parameters is developed and studied numerically. It is shown that coupling of the various order parameters leads to a complex magnetic field–temperature phase diagram, and the results are compared to other experiments.

First principles derivation of Ginzburg Landau free energy models for crystalline systems

Abstract: The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory The goal here is to extend and complete an earlier derivation by Lowen et al [Europhys Lett 9 (1989) 791] The limitations of the resulting expressions are also discussed including the boundary conditions needed for finite systems and the fact that the results cannot, at present, be used to take into account elastic relaxation

Optimal Uniform Elliptic Estimates for the Ginzburg-Landau System

Abstract: We reconsider the elliptic estimates for magnetic operators in two and three dimensions used in connection with Ginzburg-Landau theory. Fur- thermore we discuss the so-called blow-up technique in order to obtain optimal estimates in the limiting cases.

Landau damping: Instability mechanism of superfluid Bose gases moving in optical lattices

Abstract: We investigate Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at finite temperatures. Using a one-dimensional tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain condensate velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence of the critical velocities reveals the microscopic mechanism of the Landau instability. This instability mechanism shows that a thermal cloud plays a crucial role in the breakdown of superfluids, since the thermal cloud is a vital source of Landau damping. We also examine the possibility of simultaneous disappearance of all damping processes.

Discontinuous evolution of single‐crystal elastic constants as a function of pressure through the C2/c ↔ P21/c phase transition in spodumene (LiAlSi2O6)

Abstract: A Landau free energy expansion in one order parameter has been developed to describe the first-order C2/c ↔ P21/c phase transition at high pressures in spodumene (LiAlSi2O6). The complete set of elastic constants required for this model was determined at ambient conditions by resonant ultrasound spectroscopy. Other coefficients in the 246 expansion were calibrated using lattice parameter data from the literature, which had been collected by following the transition in a diamond anvil cell. The complete calibration leads to predictions of significant, abrupt changes in elastic constants at the transition point, 3.19 GPa, which have then been tested against ultrasonic data obtained in situ at high pressures in a uniaxial split cylinder apparatus. Velocities of compressional waves in three mutually perpendicular directions through single crystals of spodumene were measured and used to extract elastic constant data. The transition, indeed, causes large, abrupt changes of single-crystal elastic constants with increasing pressure. Steep increases in attenuation were also observed in the vicinity of the transition point for two directions and over a broader pressure interval in the third direction. The Landau expansion reproduces the general form of the elastic anomalies, even though it does not do as well for spontaneous strain variations. If this type of transition occurred in mantle pyroxenes (or in any other mantle phase), it would be expected to leave a distinctive signature in seismic velocity profiles of the Earth's interior.

Systematic ab initio study of the phase diagram of epitaxially strained SrTiO3

Abstract: We use density-functional theory with the local-density approximation to study the structural and ferroelectric properties of SrTiO3 under misfit strains. Both the antiferrodistortive (AFD) and ferroelectric (FE) instabilities are considered by calculating all the phases predicted by Pertsev et al. [Phys. Rev. B 61, R825 (2000)] based on the phenomenological Landau theory. The rotation of the oxygen octahedra and the movement of the atoms are fully relaxed within the constraint of a fixed in-plane lattice constant. We find a rich misfit strain induced phase transition sequence which is in overall agreement with the prediction by Pertsev et al. and is obtained only when the AFD distortion is taken into account. Nevertheless, the calculated locations of the phase boundaries are different from the prediction by Pertsev et al. We also find that compressive misfit strains induce ferroelectricity in the tetragonal low temperature phase only while tensile strains induce ferroelectricity in the orthorhombic phase...

Structural evolution, strain and elasticity of perovskites at high pressures and temperatures

Abstract: Octahedral tilting transitions in perovskites are usually identified by the significant lattice distortions which accompany them. The underlying mechanism of coupling between the tilts and the macroscopic strain also gives rise to large anomalies in single crystal and bulk elastic moduli. Landau theory provides an effective framework for describing these different changes in properties and relating them, quantitatively, to the evolution of the driving order parameter for the transition. This approach has been used to analyse the overall elastic behaviour of perovskites belonging to the CaTiO3-SrTiO3 (CST) solid solution, which is expected to be closely analogous to the behaviour of silicate perovskites at higher pressures and temperatures. Pm3m ↔ I4/mcm and I4/mcm ↔ Pnma transitions in CST perovskites are marked by changes in the shear modulus of ∼ 10-30%. The evolution of the order parameter and, hence, of the octahedral tilt angles through these can be followed through the variations of spontaneous strains extracted from high resolution lattice parameter data. Contributions to the elastic softening which are due to strain/octahedral tilt coupling have been calculated using a fully parameterised Landau model of the Pm3m ↔ I4/mcm transition as a function of temperature, pressure and composition. Differences between calculated elastic constants and experimental data from Dynamical Mechanical Analysis, pulse-echo ultrasonics and Resonant Ultrasound Spectroscopy suggest that a proportion of the total softening in tetragonal samples may be due to anelastic effects. The anelastic contributions are observed at frequencies of both a few Hz and 10's of MHz, and can be understood in terms of strain contributions arising from movements of transformation twin walls in response to an externally applied shear stress. Similar transitions in other perovskites are likely to display small anomalies in the bulk modulus, due to weak coupling between octahedral tilts and volume strain, but much larger anomalies in the shear modulus. The elastic properties of tetragonal and orthorhombic structures are likely to be quite different due to different anelastic contributions from twin wall displacements.

Ginzburg-landau theory of the liquid-solid interface and nucleation for hard spheres

Abstract: The Ginzburg-Landau free energy functional for hard spheres is constructed using the fundamental measure theory approach to density functional theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.

Ginzburg-Landau theory of superconducting surfaces under the influence of electric fields

Abstract: A boundary condition for the Ginzburg-Landau wave function at surfaces biased by a strong electric field is derived within the de Gennes approach. This condition provides a simple theory of the field effect on the critical temperature of superconducting layers.