Landau Theory Of Phase Transitions Research Articles

Two-leg-ladder Bose-Hubbard models with staggered fluxes

We investigate the ground state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex anti-vortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field theory approach.

Landau effective Hamiltonian and its application to magnetic systems

The Landau definition of the effective Hamiltonian (of the nonequilibrium free energy) is realized in a microscopic theory. According to Landau remark, the consideration is based on classical statistical mechanics. In his approach nonequilibrium states coinciding with equilibrium fluctuations are taken into account (the Onsager principle). The definition leads to the exact fulfillment of the Boltzmann principle written in the form with the complete free energy. The considered system is assumed to consist of two subsystems. The first subsystem is an equilibrium one. The second subsystem is a nonequilibrium one and its state is described by quantities that are considered as order parameters. The effective Hamiltonian is calculated near equilibrium in the form of a series in powers of deviations of the order parameters from their equilibrium values. The coefficients of the series are expressed through equilibrium correlation functions of the order parameters. In the final approximation correlations of six and more order parameters are neglected and correlations of four parameters are assumed to be small that leads to the corresponding perturbation theory. The developed theory is compared with the phenomenological Landau theory of phase transitions of the second kind. The obtained results are concretized for paramagnetic-ferromagnetic system. The consideration is restricted by paramagnetic phase.

Anisotropy of the Refractive Indices and Thermal Expansion Coefficients of Rb2ZnCl4 Crystals

The temperature dependences of the optical path difference ∆і(Т) and relative changes δlі/lі in the thickness of Rb2ZnCl4 crystals have been studied. The temperature dependences of the relative changes in the refractive indices δnі/(nі – 1) are calculated. The critical index of the temperature changes in the refractive indices is estimated to be β = 0.31 ± 0.02, a value that is well consistent with the Landau theory of phase transitions. The coefficients of anisotropy of refractive indices Аn – 1(Т) are calculated. A characteristic minimum near the phase transition temperature is found in these dependences.

Phase transitions in nanofilms of polar smectic liquid crystals with multilayer periodicity

Optical investigations and calculation of structures were performed on films of liquid crystal with the sequence of phase transitions in the bulk sample $\mathrm{Sm}{C}_{A}^{*}\ensuremath{-}\mathrm{Sm}{C}_{d3}^{*}\ensuremath{-}\mathrm{Sm}{C}_{d4}^{*}\ensuremath{-}\mathrm{Sm}{C}^{*}\ensuremath{-}\mathrm{Sm}{C}_{\ensuremath{\alpha}}^{*}\ensuremath{-}\mathrm{Sm}A\ensuremath{-}I$. We investigated freestanding nanofilms with number of smectic layers from 2 to 6 with thickness commensurate, smaller, or greater than the period of $\mathrm{Sm}{C}_{d3}^{*}$ and $\mathrm{Sm}{C}_{d4}^{*}$ phases of the bulk sample. The number of phase transitions increases as the film thickness increases. Under temperature change the transitions occur with conservation as well as with change of the direction of film polarization with respect to the molecular tilt plane. In thick films at high temperature the film can be switched by electric field from the state with longitudinal (parallel to the molecular tilt plane) into a state with transverse (perpendicular to the molecular tilt plane) electric polarization. In the framework of Landau theory of phase transitions, structures and phase transitions in the bulk sample and in nanofilms were calculated; values of interlayer interactions were estimated. The molecular structure was assumed to be planar with different sequences of synclinic and anticlinic orderings in nearest layers. The results of calculations are in good agreement with experiment.

Anomalies in the Magnetic Susceptibility in the Second-Order Phase Transitions beyond the Curie Point

Taking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field HC at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C4, the magnetic susceptibility becomes infinite at H → HC. It is shown that as the magnetic field direction deviates from the C4 axis, the magnetic susceptibility in the critical field HC proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C4 axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.

On Inhomogeneous Polarized States near the Phase Transition Point in a Thin Ferroelectric Film

It is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector k⊥ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4.

The spinel oxide AlV2O4 is a unique material, in which the formation of clusters is accompanied by atomic, charge and orbital ordering and a rhombohedral lattice distortion. In this work a theory of the structural phase transition in AlV2O4 is proposed. This theory is based on the study of the order-parameter symmetry, thermodynamics, electron density distribution, crystal chemistry and mechanisms of formation of the atomic and orbital structures of the rhombohedral phase. It is established that the critical order parameter is transformed according to irreducible representation k9(τ4) (in Kovalev notation) of the Fd \bar{3}m space group. Knowledge of the order-parameter symmetry allows us to show that the derived AlV2O4 rhombohedral structure is a result of displacements of all atom types and the ordering of Al atoms (1:1 order type in tetrahedral spinel sites), V atoms (1:1:6 order type in octahedral sites) and O atoms (1:1:3:3 order type), and the ordering of dxy, dxz and dyz orbitals. Application of the density functional theory showed that V atoms in the Kagomé sublattice formed separate trimers. Also, no sign of metallic bonding between separate vanadium trimers in the heptamer structure was found. The density functional theory study and the crystal chemical analysis of V-O bond lengths allowed us to assume the existence of dimers and trimers as main clusters in the structure of the AlV2O4 rhombohedral modification. The trimer model of the low-symmetry AlV2O4 structure is proposed. Within the Landau theory of phase transitions, typical diagrams of possible phase states are built. It is shown that phase states can be changed as a first-order phase transition close to the second order in the vicinity of tricritical points of the phase diagrams.

Electric-field-dependent mechanical and electrical properties of barium strontium titanate films for tunable device applications

Developing the novel electric field tunable, reconfigurable, adaptive and frequency-agile microwave devices with specific properties involves technological and scientific activities in the studying of material properties. Measurements of its properties could be a difficult and expensive issue, especially when it concerns thin-film ferroelectrics. Their electromechanical properties change significantly under applied DC bias field. The material coefficients of barium strontium titanate thin films are still unknown; therefore, it is expedient to carry out their calculations. In the present paper, the linear equations of piezoelectric effect have been written for thin barium strontium titanate films under DC bias electric field in paraelectric phase (induced piezoelectric effect) based on the grand potential of Landau theory of phase transitions. The dependence of material constants for thin films of Ba0.65Sr0.35TiO3 (BST65) on the applied planar field at different lattice misfit strains has been studied for this phase. All induced piezoelectric moduli show extreme behavior during field alteration. Elastic moduli show similar abnormal behavior. The alterations increase as misfit strain is approaching the critical value.

Devil's staircase of odd-number charge order modulations in divalent β -vanadium bronzes under pressure

A novel phase transition with a stepwise evolution of odd-number charge modulation is discovered in $\ensuremath{\beta}$-vanadium bronzes under pressures of about 1 GPa. All the charge modulation vectors of the many kinds of charge-ordered phases can be represented as a primitive lattice translation vector along the $b$ axis multiplied by several odd numbers. This discovery demonstrates interplay between the charge degree of freedom and the crystallographic symmetry. This phenomenon is rationally explained by self-charge transfer (carrier redistribution) between two kinds of subsystems in the structure and sequential symmetry reduction as outlined in Landau theory of phase transitions.

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems.

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.

Аномалии магнитной восприимчивости при фазовых переходах второго рода вне точки Кюри

AbstractTaking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field H _C at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C _4, the magnetic susceptibility becomes infinite at H → H _C. It is shown that as the magnetic field direction deviates from the C _4 axis, the magnetic susceptibility in the critical field H _C proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C _4 axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.

О неоднородных поляризованных состояниях вблизи точки фазового перехода в тонкой сегнетоэлектрической пленке

AbstractIt is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector k _⊥ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.

Simulation of proton radiation on electrocaloric effect in BaTiO3 ferroelectric thin film

A theoretical study of the influence of proton radiation on the electrocaloric effect (ECE) in BaTiO3 thin film has been present in this work. The radiation induced oxygen vacancy density has been obtained using a computer program Stopping and Range of Ions in Matter, and a phenomenological model based on Landau phase transition theory has been established to study the ECE. It shows that the radiation induced oxygen vacancy density is linear with the proton fluence. The ECE of the BaTiO3 thin film is roughly unaffected by the irradiation up to the proton fluence of 5 × 1016 cm−2, and then decreases with increase of proton fluence and energy of the incident proton.

Magnetic and magnetocaloric properties of the La0.9−xAgxMn1.1O3 compounds

The influence of Ag+ ions and Mn non-stoichiometry on the magnetic properties and magnetocaloric effect in the La0.9–xAgxMn1.1O3 compounds has been studied. The Ag+ ions content substituting for trivalent lanthanum ions was varied from x = 0.05 to 0.3. Magnetic measurements have been performed over a wide temperature (350–5 K) and magnetic field (up to 5 T) ranges. All the manganites studied show the ferromagnetic-like ordering with a first order magnetic phase transition. The magnetic entropy changes were evaluated from the isothermal curves of magnetization versus an applied magnetic field using both the thermodynamic Maxwell relation (MR) and calculation based on the Landau theory of phase transitions. The largest values of the magnetocaloric effect as well as the relative cooling power among the studied manganites are equal to 5.76 J/(kg K) and 185 J/kg, respectively, for La0.7Ag0.2Mn1.1O3 in the magnetic field change of 5 T near the Curie temperature of TC = 271 K. A good correlation between the magnetization, colossal magnetoresistance and magnetic entropy changes as a function of Ag concentration in the La0.9–xAgxMn1.1O3 manganites was established.

Large Anhysteretic Deformation of Shape Memory Alloys at Postcritical Temperatures and Stresses

Magnetic and nonmagnetic shape memory alloys (SMAs) exhibit thermoelastic martensitic transformations (MTs) which are hysteretic due to their first‐order nature. According to the thermodynamic Landau theory of phase transitions, which assumes ideal thermoelastic equilibrium at each point of the MT interval, the hysteresis is explained by the different limits of stability for austenite and martensite in the phase diagram. No interactions on the phase boundaries are taken into account. In the real alloys, the hysteresis of MT is related not only to the stability intervals of two phases but also to the processes of nucleation and growth of the resultant phase inside the parent phase. In turn, the features of these processes are related to the heights of energy barriers caused by the incompatibility of austenitic and martensitic lattices, crystal defects and some other physical factors. However, the defects, normally, play a minor role in the width of MT hysteresis if compared to the thermodynamic and crystallographic factors. A reduction of hysteresis of MT in SMAs, being crucial for technology, presents a challenging problem for science. A decrease of hysteresis width of MT was observed recently for the single crystals of ferromagnetic SMAs such Ni–Fe(Co)–Ga and Fe–Pd on approaching of their transformation paths to the critical point in stress–temperature phase diagram. Moreover, the superelastic and shape memory properties characterized by the nearly‐zero hysteresis width were observed in the postcritical transformational regime. Here we show that both the Landau‐type theory of ferroelastic phase transitions and neutron diffraction experiments carried out under axial compression describe the essential features of these properties. We also interpret the experimentally observed anhysteretic phenomena in Ni–Mn–Ga thin films and nanobeam actuators in terms of their postcritical state.

Mode selection of magneto-Rayleigh-Taylor instability from the point of view of Landau phase transition theory

A theoretical model referring to mode selection of Z-pinch-driven magneto-Rayleigh-Taylor (MRT) instability, which explains the generation of fundamental instability mode and evolution of fundamental wavelength in experiments, is proposed on the basis of the Landau theory of phase transition. The basic idea of this phase transition model lies in that the appearance of MRT instability pattern can be considered as a consequence of the spontaneous generation of interfacial structure like the spontaneous magnetization in a ferromagnetic system. It is demonstrated that the amplitude of instability is responsible for the order parameter in the Landau theory of phase transition and the fundamental wavelength appears to play a role analogous to inverse temperature in thermodynamics. Further analysis indicates that the MRT instability is characterized by first order phase transition and the fundamental wavelength is proportional to the square root of energy entering into the system from the driving source. The theory predicts that the fundamental wavelength grows rapidly and saturates reaching a limiting wavelength of the order of the liner's final outer radius. The results given by this theory show qualitative agreement with the available experimental data of MRT instability of liner implosions conducted on the Sandia Z machine as well as Primary Test Stand facility at the Institute of Fluid Physics.

Effect of annealing temperature on structural and magnetocaloric properties of nanocrystalline BaCo0.90Mn0.10O3-δ

Nanocrystalline BaCo0.90Mn0.10O3-δ (BCMO) was synthesised under normal atmospheric condition using sol-gel method. The X-ray diffraction patterns show the crystal structure changes from 2H- to 12H-type hexagonal phase depending on annealing temperature. The 2H-type hexagonal phase was observed for 900 °C annealed BCMO and 12H-type phase was formed for 1100 °C annealed BCMO sample. Temperature dependence of the zero-field-cooled and field cooled magnetization data shows the ferromagnetic to paramagnetic (FM-PM) ordering at ∼49 K in a 12H-type phase, whereas weak ferromagnetic ordering is observed in 2H-type phase. The saturation magnetization increases as phase changes from 2H to 12H type-hexagonal phase. The magnetocaloric effect (MCE) was studied near the magnetic ordering temperature for both type+s of phases (2H and 12H). The maximum magnetic entropy changes (|ΔSMmax|) were found to be 0.28 Jkg−1K−1 and 2.50 Jkg−1K−1 for a magnetic field change of 5 T for 2H- and 12H-type phases sample respectively. The critical exponent and theoretical analysis of the MCE using Landau theory of phase transition confirm that the contributions to the free energy in the presence of ferromagnetic clusters are strongly influencing the MCE by coupling with the order parameter around the ordering temperature for 12H-type hexagonal phase sample.

Unconventional Surface Critical Behavior Induced by a Quantum Phase Transition from the Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to a Néel-Ordered Phase.

A symmetry-protected topological phase has nontrivial surface states in the presence of certain symmetries, which can either be gapless or be degenerate. In this work, we study the physical consequence of such gapless surface states at the bulk quantum phase transition (QPT) that spontaneously breaks these symmetries. The two-dimensional Affleck-Kennedy-Lieb-Tasaki phase on a square lattice and its QPTs to Néel ordered phases are realized with the spin-1/2 Heisenberg model on a decorated square lattice. With large-scale quantum MonteCarlo simulations, we show that even though the bulk QPTs are governed by the conventional Landau phase transition theory, the gapless surface states induce unconventional universality classes of the surface critical behavior.

Effect of a generalized shape Peierls potential and an external stress field on kink mechanism in a continuum model

The a0/2〈111〉 screw dislocation glides through the nucleation and propagation of the kink-pair which dominates the plastic deformation of the BCC iron. A continuum model and the corresponding numerical methods are developed to investigate the kink mechanism on an arbitrary shape Peierls potential and subject to an external stress field. This model gives a link between the Landau theory of phase transitions and the line tension theory of string models. The order parameter is associated with the screw dislocation in BCC iron for describing the relative slip between adjacent Peierls valley. The kink configurations on the different Peierls potentials, such as the sinusoidal, Eshelby, anti-parabolic and camel-hump potential, are derived. By considering the motion of the screw dislocation on a 2-D Peierls potential surface, the 3-D saddle-point configuration of a non-planar kink-pair is obtained. The configuration is directly related to the details of the 2-D potential surface and it changes along with the applied stress tensor. A parameterized constitutive equation is derived for describing the temperature dependence of the flow stress which is compared with the experimental data from literature. The twinning/anti-twinning (T/AT) asymmetry and the tension-compression (T/C) asymmetry are reproduced in the model. The results rule out the possibility that the non-Schmid plasticity of the BCC iron is ascribed to split configuration.

Field dependence of magnetocaloric properties of 20% Cr-doped Pr0.7Ca0.3MnO3 perovskite

In this study, we have investigated the effect of 20% Cr doping at the Mn site on the magnetic and magnetocaloric properties of Pr0.7Ca0.3MnO3 polycrystalline manganites elaborated using the solid-state reaction. The X-ray powder diffraction shows that compounds crystallize in the orthorhombic system with Pnma space group. The parent compound Pr0.7Ca0.3MnO3 is a well-known charge-ordered (CO) compound. The selective substitution of Cr for Mn in the pristine compound destroys the CO ordering observed in Pr0.7Ca0.3MnO3, and a paramagnetic to ferromagnetic transition takes place. The field dependence of the magnetic entropy change ∆S and of the relative cooling power RCP is reported. The \(\left| {\Delta S^{\hbox{max} } } \right|\) are found to be 0.8 and 2.87 J kg−1 K in a magnetic field change of 5 T for x = 0 and 0.2, respectively. The RCP is found to be 253.2 J kg−1 in the Pr0.7Ca0.3Mn0.8Cr0.2O3 at 5 T. With the scaling laws, the experimental ∆S and n collapse onto a universal curve for Pr0.7Ca0.3Mn0.8Cr0.2O3 sample, where an average curve is obtained for ∆S. With the phenomenological universal curve, the magnetic entropy change ∆S curves are well predicted for Cr-substituted sample. Additionally, Banerjee’s criteria, the universal behavior and Landau theory of phase transitions were also studied to assess magnetic ordering in the Pr0.7Ca0.3Mn0.8Cr0.2O3 material.