Showing papers on "Landau theory published in 2013"

Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals.

Abstract: We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second-order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase composed of twist-bend or splay-bend deformations. To test the predictions of Landau theory, we perform Monte Carlo simulations to find the director and polarization configurations as functions of temperature, applied electric field, and interaction parameters.

Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles

Abstract: We introduce a methodology for constructing anharmonic vibrational Hamiltonians that are parametrized from first-principles electronic-structure calculations and can be used to study high-temperature properties of crystalline materials. Our method provides an accurate description of the Born-Oppenheimer potential energy surface of a crystal that can be systematically refined and is invariant to space-group symmetries of the ideal reference crystal and finite rigid-body rotations and translations. These features make it ideally suited for Monte Carlo or molecular dynamics simulations to predict finite-temperature thermodynamic properties, structural phase transitions, and thermal conductivity. We use this method to construct an anharmonic Hamiltonian for ZrH${}_{2}$, which exhibits a high-temperature cubic phase that undergoes a symmetry-breaking second-order transition to one of three equivalent tetragonal phases upon cooling. Although density functional theory predicts a zero-Kelvin dynamical instability of cubic ZrH${}_{2}$, we find via Monte Carlo simulation that the cubic phase can be anharmonically stabilized at high temperature and predict a cubic-to-tetragonal transition temperature that is in good agreement with extrapolation from experiments. We also calculate finite-temperature free energies for the cubic and tetragonal phases, finding that they are consistent with the phenomenological Landau theory of second-order phase transitions.

High-resolution electrocaloric and heat capacity measurements in barium titanate

Abstract: The electrocaloric (EC) effect in a BaTiO3 single crystal oriented along the [001] direction has been studied by direct high-resolution EC measurements in the vicinity of the field-induced critical point. It is shown that the observed behavior of the EC temperature change , as well as the heat capacity anomalies are in good agreement with the predictions of the Landau theory. We also present the electric field-temperature phase diagram for the field-induced paraelectric-to-ferroelectric phase transition line, derived from the calculated latent heat.

High-dimensional topological insulators with quaternionic analytic Landau levels.

Abstract: We study the three-dimensional topological insulators in the continuum by coupling spin-$1/2$ fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The three-dimensional lowest Landau level wave functions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the two-dimensional case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the ${\mathbb{Z}}_{2}$ class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied.

Role of high-order electromechanical coupling terms in thermodynamics of ferroelectric thin films

Abstract: Currently used methods for the description of thermodynamics of ferroelectric thin films (Landau theory or ab initio based Monte Carlo simulations) are based on an energy expansion in terms of internal degrees of freedom. It was shown that these methods can suffer from a substantial inaccuracy unless higher order electromechanical interactions are taken into account. The high-order electromechanical couplings strongly renormalize the sixth-power polarization terms of the thermodynamic energy expansion. In this paper, apart from the general statement, we illustrate it with an example of a temperature-misfit strain phase diagram of a BaTiO3 thin film derived with high-order electromechanical interactions evaluated using first-principles calculations.

Analysis of the multiferroicity in the hexagonal manganite YMnO3

Abstract: We performed magnetic and ferroelectric measurements, associated with Landau theory and symmetry analysis, in order to clarify the situation of the YMnO3 system, a classical example of type I multiferroics. We found that the only magnetic group compatible with all experimental data (neutron scattering, magnetization, polarization, dielectric constant, second harmonic generation) is the group. In this group a small ferromagnetic component along c is induced by the Dzyaloshinskii–Moriya interaction, and observed here in magnetization measurements. We found that the ferromagnetic and antiferromagnetic components can only be switched simultaneously, while the magnetic orders are functions of the polarization square and therefore insensitive to its sign.

Magnetocaloric effect in inhomogeneous ferromagnets

Abstract: The article is devoted to the theoretical study of magnetocaloric effect in imhomogeneous ferromagnets in vicinity of magnetic phase transitions of first and second orders as well as in vicinity of tricritical and critical points. In the frame of Landau theory the formulae for the magnetic field induced entropy change are derived. The theory is compared with the experimental data obtained on single crystals of La0.7Ba0.3MnO3 (second order transition) and La0.7Ca0.3MnO3 (first order transition).

Multiferroic Behavior in Elemental Selenium below 40 K: Effect of Electronic Topology

Abstract: The quasi-one-dimensional, chiral crystal structure of Selenium has fascinating implications: we report simultaneous magnetic and ferroelectric order in single crystalline Se microtubes below ≈40 K. This is accompanied by a structural transition involving a partial fragmentation of the infinite chains without losing overall crystalline order. Raman spectral data indicate a coupling of magnons with phonons and electric field, while the dielectric constant shows a strong dependence on magnetic field. Our first-principles theoretical analysis reveals that this unexpected multiferroic behavior originates from Selenium being a weak topological insulator. It thus exhibits stable electronic states at its surface and magnetism emerges from their spin polarization. Consequently, the broken two-fold rotational symmetry permits switchable polarization along its helical axis. We explain the observed magnetoelectric couplings using a Landau theory based on the coupling of phonons with spin and electric field. Our work opens up a new class of topological surface-multiferroics with chiral bulk structure.

Interplay between magnetism and magnetocaloric effect in NdCuSi

Abstract: We report the magnetic, thermal, magnetocaloric and transport properties of polycrystalline NdCuSi. The compound shows a weak antiferromagnetic ordering, as confirmed by different measurements. Arrott plots indicate that the magnetic phase transition is found to be second order in nature. The isothermal magnetic entropy change calculated using the magnetization data gives a value of 11.1 J/kg K for a field change of 50 kOe. The follows h2/3 dependence (h is the reduced field) with a negative intercept, which is predicted by mean field theory for second order phase transitions. Landau theory of phase transition was applied to calculate change in entropy, which was found to be in good agreement with that calculated directly from the magnetization data. Temperature dependence of electrical resistivity shows a pronounced anomaly at the ordering temperature, which is attributed to the spin fluctuations.

Ginzburg-Landau Analysis of the Critical Temperature and the Upper Critical Field for Three-Band Superconductors

Abstract: Using the microscopic formalism of Eilenberger equations, a three-band Ginzburg-Landau theory for the intraband dirty limit and clean interband scattering case is derived. Within the framework of this three-band Ginzburg-Landau theory, expressions for the critical temperature T c and the temperature dependence of the upper critical field H c2 are obtained. Based on some special cases of the matrix of interaction constants, we demonstrate the influence of the sign of the interband interaction on the critical temperature and the upper critical field as compared with a two-band superconductor where it plays no role. We study also analytically and numerically the effect of its magnitude.

Generalized effective-potential Landau theory for bosonic quadratic superlattices

Abstract: We study the properties of the Bose-Hubbard model for square and cubic superlattices. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multiple components and not only find the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. A comparison of our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective-potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.

Landau theory of the magnetic phase diagram of monoclinic multiferroics: Application to MnWO 4 and CuO

Abstract: We present a detailed analysis of the magnetic states of monoclinic multiferroic systems as a function of temperature and magnetic field. The proposed nonlocal Landau free energy derived using symmetry arguments accounts well for the phase diagram of MnWO4 with the field applied along each of the three principal crystallographic directions. A description is proposed for the high field magnetic spin configurations, above 10 T, which have not yet been identified by neutron scattering. The nature of the induced electric polarization in each of the magnetic states is described. Corresponding results for CuO are also presented.

Biaxiality-induced magnetic field effects in bent-core nematics: molecular-field and Landau theory.

Abstract: Nematic liquid crystals composed of bent-core molecules exhibit unusual properties, including an enhanced Cotton-Mouton effect and an increasing isotropic (paranematic)-nematic phase transition temperature as a function of magnetic field. These systems are thought to be good candidate biaxial liquid crystals. Prompted by these e xperiments, we investigate theoretically the effect of molecular biaxiality on magnetic field-induced phenomena for nematic liquid crystals, using both molecular field and Landau theory. The geometric mean approximation is used in order to specify the degree of molecular biaxiality using a single parameter. We reproduce experimental field-induced phenomena, and predict also an experimentally accessible magnetic critical point. The Cotton-Mouton effect and temperature dependence of the paranematic-nematic phase transition are more pronounced with increased molecular biaxiality. We compare our theoretical approaches and make contact with recent relevant experimental results on bent-core molecular systems.

Second-Order Phase Transitions, L. Landau and His Successors

Abstract: There are only two ways for solid-state phase transitions to be compliant with thermodynamics: emerging of infinitesimal quantity of the new phase, or infinitesimal "qualitative" change occurring uniformly throughout the bulk at a time. The suggested theories of phase transitions are checked here for that compliance and in historical perspective. While introducing the theory of "continuous" second-order phase transitions, L. Landau claimed that they "may also exist" along with the majority of first order phase transitions, the latter being "discontinuous", displaying "jumps" of their physical properties; the fundamental d ifferences between the two types were specified. But h is theoretical successors disregarded these irreconcilable differences by presenting all phase transitions as a cooperative phenomenon treatable by statistical mechanics. In the meantime, evidence has been mounted that all phase transitions have a nucleation-and-growth mechanism, thus eliminating a need in the above classification.

Evidence for a tricritical point coinciding with the triple point in (Pb 0.94 Sr 0.06 )(Zr x Ti 1 − x )O 3 : A combined synchrotron x-ray diffraction, dielectric, and Landau theory study

Abstract: We present here results of high resolution synchrotron x-ray diffraction (SXRD) and dielectric studies in conjunction with Landau theory considerations on (Pb0.94Sr0.06)(ZrxTi1-x)O3 compositions in the vicinity of the morphotropic phase boundary (MPB) to find evidence for the flattening of the free energy surface at the MPB proposed in recent ab-initio studies on strongly piezoelectric ceramics. SXRD results reveal that the tetragonal and pseudorhombohedral monoclinic compositions with x=0.515 and 0.550 transform directly into the cubic paraelectric phase, whereas for 0.520

Application of Finite Strain Landau Theory To High Pressure Phase Transitions

Abstract: In this paper we explain how to set up what is in fact the only possible consistent construction scheme for a Landau theory of high pressure phase transitions that systematically allows to take into account elastic nonlinearities We also show how to incorporate available information on the pressure dependence of elastic constants taken from experiment or simulation We apply our new theory to the example of the high pressure cubic-tetragonal phase transition in Strontium Titanate, a model perovskite that has played a central role in the development of the theory of structural phase transitions Armed with pressure dependent elastic constants calculated by density functional theory, we give a both qualitatively as well as quantitatively satisfying description of recent high precision experimental data Our nonlinear theory also allows to predict a number of additional elastic transition anomalies that are accessible to experiment

Landau theory description of polar smectic structures

Abstract: In this paper we review various amazing features of polar smectic structures and phase transitions between them. In a series of experimental and theoretical studies over the last decades, a lot of new and unexpected structures have been observed and described theoretically in the realm of polar smectic liquid crystals. Not all of these structures were correctly identified experimentally and/or correctly interpreted theoretically. At least in part, the problem is in the uncertainty about which theoretical model can provide an adequate minimal description of all available experimental data. The approach we are advocating in this work is to rely on a systematic, well elaborated, and perfectly suitable to describe mean field behavior in the vicinity of phase transition lines, theoretical frame – Landau phase transitions theory. Structural and symmetry properties of the polar smectic liquid crystals require utilization of the Landau theory with the discretized over the smectic layers two-component order parame...

Gauge theory of topological phases of matter

Abstract: We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a ?gauge theory of states of matter? complementary to the well-known Landau theory of order parameters. We illustrate the power of our approach by deriving and interpreting the gauge-invariant effective actions of (topological) superconductors, 2D electron gases exhibiting the quantized Hall- and spin-Hall effect, 3D topological insulators, as well as axion electrodynamics. We also use the theory to elucidate the structure of surface modes in these systems.

Perturbative calculation of critical exponents for the Bose–Hubbard model

Abstract: We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose–Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a 6 into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose–Hubbard model, deviate by less than 1 % from the best known estimates computed so far for the three-dimensional XY universality class.

Multiband Calculations on the Magnetic Properties of Superconductor KFe2As2

Abstract: Based on two-band Ginzburg–Landau theory, we study the temperature dependence of upper critical fields for superconducting crystal KFe2As2. The results reproduce the experimental data in a broad temperature range and directly underlie the multigap superconductivity in this crystal. Our calculations also indicate that the specific heat jump at the superconducting critical temperature is about 0.77, in accordance with the experimental data.

Hysteresis Behavior in the Stick-Slip Mode at the Boundary Friction

Abstract: A tribological system is considered that consists of two atomically smooth solid surfaces separated by an ultrathin lubricant film. A thermodynamic model based on the Landau theory of phase transitions is built that describes the behavior of this system in the boundary friction mode. The free energy density for an ultrathin lubricant film is given in the form of expansion in series in terms of the powers of order parameter that is reduced to the shear modulus of the lubricant. The kinetics of the system is studied on the basis of a model describing first-order phase transitions between kinetic modes of friction. It is shown that in the presence of spring between the external drive and block the width of temperature hysteresis increases versus fixed coupling.

Vortices of polarization in BaTiO 3 core-shell nanoceramics: Calculations based on ab initio derived Hamiltonian versus Landau theory

Abstract: In this paper, we want to emphasize the fact that many experimental properties of ceramics can be explained by the existence of a core-shell structure of the grains, particularly at small sizes. In this framework, we have studied BaTiO3 (BT) ceramics constituted of core-shell nanoparticles, nanowires, or nanoplanes by using ab initio derived effective Hamiltonian calculations whose application range is for large values of shell thickness and low values of shell permittivity. Many differences and new features compared to the situation of nanodots are induced by the core-shell structure. For instance, phase sequences are different; there is also a coexistence of vortices found by Naumov, Bellaiche, and Fu in the case of isolated dots with a homogeneous polarization, a transition from cubic paraelectric phase towards nonpolar rhombohedral phase, anomalies in dielectric permittivity associated with the onset of toroidal moments, etc. Afterwards, we compare these results with those obtained by the Landau theory of core-shell ceramics we have recently published. However, the ab initio calculations fail to capture the physics at small shell thickness and/or high shell permittivity, whereas the Landau theory fails to predict the peculiar properties of the phases in which vortices exist. Therefore, in a tentative way to build a global theory, we have constructed a Landau potential using both the polarization and the toroidal moment as competing order parameters, which allows us to propose a phase diagram, whatever the thickness and permittivity of the shell are. © 2013 American Physical Society.

Theory of the formation of the ordered LiZn 0.5 Mn 1.5 O 4 phase

Abstract: A theory of the structural phase transition in LiZn0.5Mn1.5O4 cathode material is proposed. The symmetry of the order parameter, thermodynamics, and mechanisms of formation of the atomic structure of low-symmetry ordered cubic lithium-zinc-manganese oxide spinel have been studied. The critical order parameter inducing the phase transition has been found. It is shown that the calculated LiZn0.5Mn1.5O4 structure is formed due to displacements and orderings of lithium, zinc, manganese, and oxygen atoms. Within the Landau theory of phase transitions, it is shown that the phase states may change from high-symmetry cubic disordered Fd3m phase to the low-symmetry ordered cubic P213 phase as a result of first-order phase transitions.

Impact of the volume change on the ageing effects in Cu–Al–Ni martensite: experiment and theory

Abstract: The time evolution of the physical properties of martensite during martensite ageing is traditionally explained by the symmetry-conforming short-range order (SC-SRO) principle, which requires the spatial configuration of crystal defects to follow the symmetry change of the host lattice. In the present study, we show that the volume change of the host lattice also contributes to the ageing effects in Cu–Al–Ni shape memory alloy besides the symmetry change. To substantiate this statement the gradual increase of the storage modulus with time at constant temperature was measured by dynamic mechanical analysis (DMA) and the experimental results were quantitatively described in the framework of the symmetry-conforming Landau theory of martensitic transformations in a crystal with defects. The comparison of experimental and theoretical results confirmed that the time dependence of the storage modulus is caused by two different physical mechanisms. Evaluations showing that the first mechanism is driven by the spontaneous symmetry change and the second mechanism is caused by the volume change after the martensitic transformation was carried out.

Ab-initio Calculations of the Relaxor Ferroelectric Na1/2Bi1/2TiO3 and its Solid Solutions

Abstract: The necessity of substituting PbZrxTi(1−x)O3 by lead-free piezoelectric materials in numerous applications, such as sensors, actuators and ultrasonic transducers, has lead to a large number of research activities on perovskite solid solutions based on Na1/2Bi1/2TiO3 in recent years. The present dissertation deals with the characterization of the relaxor ferroelectric Na1/2Bi1/2TiO3 (NBT) in terms of structure and ferroelectric properties as a function of various parameters such as chemical order/disorder, hydrostatic pressure and alloying with other lead-free perovskites by computational methods. For this analysis it is necessary to combine ab-initio calculations with Landau theory and group theoretical tools. Part I begins in Ch. 1 with the motivation of this work. In Ch. 2, a brief overview of the regulatory framework, which triggered research activities in the field of lead-free piezoelectrics, is given and an example how lead can be substituted by other elements with similar properties. Afterwards the development concepts for these materials are introduced in Ch. 3. They are borrowed from the lead-containing perovskite solid solution PbZrxTi(1−x)O3, i.e. the presence of stereochemically active cations and solid solution formation with a morphotropic phase boundary. In Ch. 4, first relaxor ferroelectrics are introduced and the importance of chemical order/disorder discussed. Finally, the crystal structures of pure Na1/2Bi1/2TiO3 and four selected lead-free solid solutions are presented. The introduction closes in Ch. 5 with a listing of 13 specific questions this work aims to answer. In Part II the methods employed in this work are introduced. We start our investigations on the atomistic level using quantum mechanics. The atomistic simulations are performed in the Density Functional Theory (DFT) framework, which will be introduced on a very basic level, in Ch. 6. Some important remarks on the technique of structure optimization and mechanical boundary conditions will be given and a new nomenclature characterizing local structures of low symmetry will be presented, which is very similar to the well-known Glazer notation. Phase transitions are well described within the phenomenological Landau theory outlined in Ch 7. Landau theory allows to expand the free energy of a system in terms of its so-called order parameters. The application of Landau theory on the order parameters and displacive phase transitions relevant in Na1/2Bi1/2TiO3 requires also knowledge of some group theoretical tools, which will be introduced in Ch. 8. These tools are not only necessary for the Landau treatment, they are enormously useful in the analysis of calculated crystal structures in an ultimately systematic way in terms of symmetry-adapted distortion modes. The amplitudes of these (frozen-in) distortion modes can be directly used as order parameters in the Landau potentials. As Landau theory and group theory both are absolutely concrete but not demonstrative at all, both chapters contain numerous examples, which are all relevant for the understanding of this work. After introduction of the methods, the results will be discussed in Part III. The results are divided into five chapters. In Ch. 9 first the problem of chemical order will be treated in the cubic perovskite structure, accompanied by the question, whether it is possible to change the ordering tendency by application of hydrostatic pressure or chemical substitution. Afterwards the complexity of the structures is enhanced by including lattice distortions like polar displacements and octahedral tilts in Ch. 10. Here also the question of phase stabilities under hydrostatic pressure is addressed, together with the investigation of possible phase coexistence and formation of chemically ordered nanoregions. Afterwards the experimentally relevant phases R3c, Pbnm and P4bm will be compared in two representative chemical configurations, in order to investigate the effects of chemical order and hydrostatic pressure on the presence of different lattice distortions by using the group theoretical analysis in Ch. 11. This analysis helps us to identify the dominating distortion modes active in these phases. Landau theory then gives insights into the coupling interactions between these. In Ch. 12 Landau potentials are derived and energies obtained from DFT calculations, under systematic variation of atomic displacements induced by the separate distortion modes, allow the determination of the coefficients of the Landau potential. Ch. 13 finally treats the question of the possibility of morphotropic phase boundary predictions in NBT-based solid solutions. The method of determining pressure-induced phase transitions in pure NBT from Ch. 10 is extended to solid solutions in order to predict composition-induced phase transitions. Part IV starts by answering the initially posed 13 questions based on the findings of this work and finalises with a concluding discussion of the results and abilities of atomistic simulations and an outlook on possible future works.

Bistability of ferroelectric domain walls: Morphotropic boundary and strain effects

Abstract: The internal structure of neutral 180 degrees domain walls in perovskite-type ferroelectrics is studied in terms of Landau theory taking into account electromechanical coupling. The study is focused on the wall bistability, a factor of potential interest for information storage. A strong impact of elastic effects on the wall structure is demonstrated. It is shown that the conclusion derived earlier by Houchmandzadeh et al. [J. Phys.: Condens. Matter 3, 5163 (1991)], neglecting the electrostictive coupling, that all the domain walls near the boundary between two ordered phases become bistable may not hold due to the elastic effects. Criteria for domain-wall bistability are formulated in terms of the materials thermodynamic properties and the wall orientation. The obtained general results are applied to the analysis of bistability of 180 degrees domain walls in Pb(Zr-c, Ti1-c)O-3 near the tetragonal-rhombohedral morphotropic boundary. It is shown that, on the tetragonal side, the electrostrictive interaction suppresses the wall bistability that was predicted in terms of the theory neglecting the elastic effects. On the rhombohedral side, the domain walls are found bistable or not depending on the anisotropy of the correlation energy, the information on which is not presently available. It is also shown that, in the rhombohedral phase, the anisotropy of the correlation energy results in appearance of additional polarization component in the plane of the wall.