Landau Theory Of Phase Transitions Research Articles

Phase transitions in HfO2 probed by first-principles computations

Ever since ferroelectricity was discovered in HfO2, the question of its origin remains controversial. Here, we probe this question using a combination of Landau theory of phase transitions and first-principles computations. In such an approach, the energy landscape associated with the phase transition between cubic and different experimentally demonstrated phases of HfO2 (tetragonal, monoclinic, orthorhombic Pbca, orthorhombic Pnma, and orthorhombic Pca21) is explored using density functional theory calculations. Computations revealed that stabilization of all but orthorhombic Pbca phase is driven by a single unstable zone-boundary antipolar mode X2−. When coupled with zone-center modes (Γ1+ and Γ3+), it stabilizes the tetragonal phase. Coupling with four additional modes (Γ5+, X3−, X5−, X5+) results in the monoclinic phase, which is the ground state of the material. If, however, Γ5+ mode is replaced with Γ4− mode, orthorhombic polar phase Pca21 is stabilized. The application of this framework to examine the effect of electric field on the ferroelectric phase of hafnia reveals that the field of 5 MV/cm is capable of stabilizing ferroelectric phase over the monoclinic one at 0 K.

Ultrafast and persistent photoinduced phase transition at room temperature monitored by streaming powder diffraction

Ultrafast photoinduced phase transitions at room temperature, driven by a single laser shot and persisting long after stimuli, represent emerging routes for ultrafast control over materials’ properties. Time-resolved studies provide fundamental mechanistic insight into far-from-equilibrium electronic and structural dynamics. Here we study the photoinduced phase transformation of the Rb0.94Mn0.94Co0.06[Fe(CN)6]0.98 material, designed to exhibit a 75 K wide thermal hysteresis around room temperature between MnIIIFeII tetragonal and MnIIFeIII cubic phases. We developed a specific powder sample streaming technique to monitor by ultrafast X-ray diffraction the structural and symmetry changes. We show that the photoinduced polarons expand the lattice, while the tetragonal-to-cubic photoinduced phase transition occurs within 100 ps above threshold fluence. These results are rationalized within the framework of the Landau theory of phase transition as an elastically-driven and cooperative process. We foresee broad applications of the streaming powder technique to study non-reversible and ultrafast dynamics.

Exploration of the Character Representation of DNA Chiral Conformations and Deformations via a Curved Surface Discrete Frenet Frame.

While undergoing structural deformation, DNA experiences changes in the interactions between its internal base pairs, presenting challenges to conventional elastic methods. To address this, we propose the Discrete Critical State (DCS) model in this paper. This model combines surface discrete frame theory with gauge theory and Landau phase transition theory to investigate DNA's structural deformation, phase transitions, and chirality. Notably, the DCS model considers both the internal interactions within DNA and formulates an overall equation using unified physical and geometric parameters. By employing the discrete frame, we derive the evolution of physical quantities along the helical axis of DNA, including geodesic curvature, geodesic torsion, and others. Our findings indicate that B-DNA has a significantly lower free energy density compared to Z-DNA, which is in agreement with experimental observations. This research reveals that the direction of base pairs is primarily governed by the geodesic curve within the helical plane, aligning closely with the orientation of the base pairs. Moreover, the geodesic curve has a profound influence on the arrangement of base pairs at the microscopic level and effectively regulates the configuration and geometry of DNA through macroscopic-level free energy considerations.

Space-Group Determination of Superlattice Structure Due to Electric Toroidal Ordering in Ca5Ir3O12

Synchrotron X-ray diffraction measurements on a single crystal of Ca5Ir3O12 were performed to clarify the details of the superlattice reflections characterized by \(\mathbf{q} = (1/3,1/3,1/3)\). A search for superlattice reflections in a wide reciprocal space was performed using an imaging plate, and it was confirmed that there were no superlattice reflections at other than \(\mathbf{q} = (1/3,1/3,1/3)\). From the extinction rule of the superlattice reflections, the space group of the crystal structure below 105 K was found to be R3. The details of the superlattice reflections at specific q were investigated using a four-circle diffractometer. The temperature dependence of the integrated intensity at several q confirms that the order parameter of the phase transition of Ca5Ir3O12 at 105 K belongs to an A2 irreducible representation in the point group C3v from the discussion based on the Landau theory of phase transitions. The basis function of the A2 irreducible representation, which is a rotation around the c-axis, corresponds to an electric toroidal dipole.

Effect of flexibility of arms on the nematic ordering of V-shaped molecules

The nematic ordering of a melt of V-shaped molecules composed of two semiflexible arms connected by one end at an external angle α is inspected within the Landau theory of phase transitions. The conformational statistics of arms is described by a discrete worm-like chain model. It is found that for a sufficiently high stiffness of the arms the phase diagram contains the regions of stability of isotropic (I), prolate (NU+) and oblate (NU−) uniaxial, and biaxial (NB) nematic phases. The isotropic–uniaxial nematic and uniaxial nematic – biaxial nematic phase transitions are of the first and second order, respectively. At lowering the stiffness of arms the stability area of NB phase decreases; the re-entrant NB phase becomes possible in the certain range of angles α and the sequence of phase transitions I−NU−−NB−NU+−NB occurs. At a sufficiently low stiffness, the stability region of the nematic biaxial phase disappears completely, and phase diagrams display only the first order transitions between I−NU+, I−NU−, and NU+−NU− phases. A further decrease in the stiffness of arms leaves only the first order I−NU+ transition in the phase diagrams. The tricritical points appear at the curves of NU−−NB transition in the phase diagrams in certain intervals of values of the stiffness parameter.

Piezomagnetic and electromagnetic effects in the paramagnetic phase of antiferromagnets

Using the Landau theory of phase transitions, it is explained how the piezomagnetic and electromagnetic effects can exist at temperatures higher than the ordering temperature in antiferromagnets.

Magnetic phase diagrams of the pyrochlore-based magnets: Landau theory

The family of crystals with a pyrochlore lattice, including pyrochlores, spinels, and Laves phases (C15) is a fertile playground for the discovery and scientific study of exotic magnetic properties as well as search for new technological applications. In this work a possible magnetically long-range ordered phases derived from the archetypical pyrochlore lattice were studied within the Landau phase transition theory. A group-theoretical analysis reveals the existence of 20 low symmetrical phases, generated by the magnetic order parameters associated with the center of the Brillouin zone. For each of these phases, the symmetry-related magnetic and structural parameters were determined and discussed in detail. We extend this analysis by means of the thermodynamic theory: on the ground of the sixth-degree thermodynamic potential phase diagrams of the spin-ordered pyrochlore-based magnets are constructed in the exchange approximation. It is shown that an essential feature of all studied phase diagrams is the existence of singular elements: multiphase points, multicritical points of different types, lines of phase transitions of both the first and second order.

Simulating the giant magnetocaloric effect-from mean-field theory to microscopic models

Magnetocaloric materials are recognized as one of the major classes of magnetic materials for energy applications, and can be either employed as refrigerants in heat-pumping devices, or in thermomagnetic generators for energy conversion/harvesting. For both applications, having a material that presents a first-order magnetic phase transition is advantageous, as this typically leads to enhanced values of magnetization change in temperature (relevant to energy conversion) and of the magnetocaloric effect (relevant to heat-pumping). We present a brief overview of selected models applied to the simulation of applied magnetic field and temperature-dependent magnetization and magnetic entropy change of first-order magnetic phase transition systems, covering mean-field models such as the Landau theory of phase transitions and the Bean-Rodbell model, up to more recent developments using a Ising-like microscopic model with magnetovolume coupling effects. We highlight the fundamental and practical limitations of employing these models and compare predicted thermodynamic properties.

Landau theory for the Mpemba effect through phase transitions

The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

A thermodynamical model for paleomagnetism in Earth’s crust

A thermodynamically consistent model for soft deformable viscoelastic magnets is formulated in actual space (Eulerian) coordinates. The possibility of a ferro-paramagnetic-type (or ferri-antiferromagnetic) transition exploiting the Landau phase-transition theory as well as mechanical melting or solidification is considered, being motivated and applicable to paleomagnetism (involving both thermo- and isothermal and viscous remanent magnetization) in rocks in Earth’s crust and to rock-magma transition. The temperature-dependent Jeffreys rheology in the deviatoric part combined with the Kelvin-Voigt rheology in the spherical (volumetric) part is used. The energy balance and the entropy imbalance behind the model are demonstrated, and its analysis is performed by time discretization, proving existence of weak solutions.

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C9H18N2CuBr4

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C9H18N2CuBr4. Single-crystal heat capacity and neutron diffraction measurements reveal that the Néel-ordered phase breaks down beyond a critical pressure of Pc ∼ 1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above Pc.

Dimensional Crossover in the Superfluid-Supersolid Quantum Phase Transition

We assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition recently discovered in trapped dipolar quantum gases. We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first- and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively. The smooth crossover between the two regimes is peculiar to supersolids and can be controlled via the transverse confinement and the atom number. We justify our observations on the general ground of the Landau theory of phase transitions. The quasi-adiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.

Symmetry aspects of chiral superconductors

Recent developments in theory, synthesis, and experimental probes of quantum systems have revealed many suitable candidate materials to host chiral superconductivity. Chiral superconductors are a subset of unconventional superconductors which break time-reversal symmetry. Time-reversal symmetry breaking is possible given the order parameter's two-component nature, allowing for a complex relative phase. In this article, we focus on discussing the underlying symmetry aspects that allow for the development of chiral superconductivity. We provide an introductory account of key concepts in group theory and apply these to the classification of order parameters and the generalization of the Landau theory of phase transitions in the context of superconductivity.

Universality class and exact phase boundary in the superradiant phase transition

The Dicke model and Rabi model can undergo phase transitions from the normal phase to the superradiant phase at the same boundary, which can be accurately determined using some approximated approaches. The underlying mechanism for this coincidence is still unclear and the universality class of these two models is elusive. Here we prove this phase transition exactly using the path-integral approach based on the faithful Schwinger fermion representation, and give a unified phase boundary condition for these models. We demonstrate that at the phase boundary, the fluctuation of the bosonic field is vanished, thus it can be treated as a classical field, based on which a much simplified method to determine the phase boundary is developed. This explains why the approximated theories by treating the operators as classical variables can yield the exact boundary. We use this method to study several similar spin and boson models, showing its much wider applicability than the previously used approaches. Our results demonstrate that these phase transitions belong to the same universality by the classical Landau theory of phase transitions, which can be confirmed using the platforms in the recent experiments.

Modeling of the Gate Tunneling Current in MFIS NCFETs

In this article, we present a model for the gate tunneling current (GTC) in metal-ferroelectric-insulator-semiconductor (MFIS) negative capacitance FETs (NCFETs), which, to the best of our knowledge, is the first such report. The model is numerical in nature, and is developed using the Tsu–Esaki formulation, employing the Wentzel–Kramer–Brillouin (WKB) approximation, in order to estimate the transmission coefficients of the carriers through the barriers. The ferroelectric (FE) material considered is HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and is modeled using the Landau phase transition theory. Simulation results reveal a remarkable nonmonotonic dependence of the GTC on the FE layer thickness, an effect that we explain through the Landau model. Furthermore, it is shown how this GTC can be reduced by orders of magnitude without changing the overall dielectric capacitance—a feature that may prove to be beneficial in low-power circuit designs. Additionally, it is seen that the GTC is a weak function of the remanent polarization and coercive field of the FE. All the model predictions are validated through a comparison with the results obtained from Sentaurus 2-D TCAD simulations. The novel results presented in this work should serve as a guide for detailed experimental studies on the gate current characteristics of MFIS NCFETs.

Thermoelastic Properties and Elastocaloric Effect in Rapidly Quenched Ribbons of Ti2NiCu Alloy in the Amorphous and Crystalline State

The thermoelastic properties and the elastocaloric effect (ECE) were studied in rapidly quenched ribbons of the Ti2NiCu alloy samples in amorphous and crystalline states under periodic mechanical tension with a frequency of up to 50 Hz. In the amorphous samples, elastic behavior is observed, described by Hooke’s law, with a high coefficient of thermal expansion α = 1.7 × 10−4 K−1. Polycrystalline ribbons of the Ti2NiCu alloy have the classical shape memory effect (SME), the temperatures of the forward and reverse thermoelastic martensitic transitions being Ms = 345 K, Mf = 325 K, As = 332 K, and Af = 347 K and the coefficient of the dependence of the transition temperature on mechanical stress being β = 0.12 K/MPa. The experimentally measured value of the adiabatic temperature change under the action of mechanical stress (ECE) in the amorphous state of the alloy at room temperature (Tr = 300 K) was ΔT = −2 K, with a relative elongation of ε = 1.5% and a mechanical stress of σ = 243 MPa. For crystalline samples of Ti2NiCu alloy ribbons, the ECE is maximum near the completion temperature of the reverse thermoelastic martensitic transformation Af, and its value was 21 K and 7 K under cyclic mechanical loads of 300 and 100 MPa, respectively. It is shown that the ECE value does not depend on the frequency of external action in the range from 0 to 50 Hz. The specific power of the rapidly quenched ribbon was evaluated as a converter of thermal energy at an external mechanical stress of 100 MPa; its value was 175 W/g at a frequency of 50 Hz. The thermodynamic model based on the Landau theory of phase transitions well explains the properties of both amorphous ribbons (reverse ECE) and alloy ribbons with EPF (direct ECE).

Nematic ordering of model racemic mixture of stiff trimer chains

The nematic ordering of (1) a racemic mixture and (2) an enantiopure melt of trimer chains is inspected within the Landau theory of phase transitions. Each chain contains three rigid segments; consecutive segments are connected at an external angle ν while the planes of the first two and the last two segments form the dihedral angle φ. It is assumed that the rigid segments comprise monomer units. The Landau–de Gennes expansion of the free energy of the melt has been obtained up to the sixth order in powers of the nematic order parameter, the coefficients of this expansion have been calculated from the microscopic model of trimer molecule. It is found that phase diagrams for a racemic mixture may contains the regions of stability of isotropic, prolate uniaxial, oblate uniaxial, and biaxial nematic phases depending on the values of angles ν,φ, and monomer unit fractions of rigid segments that characterize the architecture of a trimer chain. In turn, a chiral nematic states are found for an enantiopure melt, depending on the architecture of the chains.

Magnetocaloric properties and analysis of the critical point exponents of Pr0.55CaxSr0.45-xMnO3 (x = 0.00, 0.05, 0.1 and 0.2) at PM-FM phase transition

The polycrystalline manganite Pr0.55CaxSr0.45-xMnO3 (x = 0.00, 0.05, 0.1, and 0.2) has been prepared by the solid state reaction technique to investigate its crystal structure, magnetic, and magnetocaloric properties. Critical behaviour around PM-FM phase transition has also been analyzed through various methods including modified Arrott plots (MAP), and critical isotherm analysis of Pr0.55CaxSr0.45-xMnO3 (x = 0.00, 0.05, 0.1, and 0.2). XRD analysis reveals that all the samples are found to be crystallized in the orthorhombic system with Pnma space group and lattice parameters a, b and c as well as the cell volume are found to decrease with increasing Ca (x) content. Microstructure is observed with the field emission scanning electron microscopy (FESEM) photograph and elemental compositions are determined by energy dispersive X-ray diffractometer (EDX). Temperature and field dependent magnetization measurement disclose that all the samples undergo second-order FM to PM phase transition but the Curie temperature (TC) value decreases from 290 K to 245 K with the increase in Ca (x) content from 0.00 to 0.20. The magnetocaloric effect (MCE) in terms of maximum entropy change, (-ΔSm)max and relative cooling power (RCP) was calculated from isothermal magnetization measurements around TC, using Maxwell’s thermodynamic relations. Both (−ΔSm)max and RCP increases with increasing Ca content suggests the suitability of this compound as a potential solid state refrigerent. Contribution of itinerant electron in the entropy change is found from modulating MCE with Landau theory of phase transition.

A differential model for the hysteresis in magnetic shape memory alloys and its application of feedback linearization

Magnetic shape memory alloys (MSMAs) are materials with strong nonlinearity, which will show hysteresis when it works. In the current paper, a differential model is proposed to describe the hysteresis in MSMAs caused by magnetic field induced martensite reorientation based on Landau theory of phase transitions. First, the three-dimensional model is simplified into a one-dimensional case, and the hysteresis in MSMAs is described by three martensite variant orientations. Then, a traditional Landau free energy is introduced, and the traditional Landau model is obtained by using the Euler–Lagrange equation. However, it is found that the prediction accuracy of the model is not ideal compared with the experimental data. Thus, an improved model is proposed, and the traditional Landau free energy is replaced by a function that can be determined by the easily measured physical quantities in the experimental curve. Numerical experiments show that the prediction effect of the improved model is much better than the traditional Landau model, and the stress dependence is also demonstrated. Moreover, the proposed improved model has the advantages for dynamic analysis and control with its differential form. Therefore, the frequency dependence of the improved model is demonstrated and a feedback linearization control methodology is proposed to make the system develops in the desired trajectory.

General Landau theory of non-symmetry-breaking and symmetry-breaking spin transition materials

Spin-transition materials, including the families of spin-crossover and charge-transfer systems, and more generally molecular-based materials exhibiting electronic and/or structural bistability, may undergo various types of phase transitions. The change of electronic state is stabilized by molecular reorganizations and both phenomena, which are usually non-symmetry breaking, can be described through the evolution of an order parameter q. Due to symmetry, q linearly couples to volume change. It is known that such elastic interactions are responsible for cooperative phenomena in non-symmetry-breaking spin-transitions. However, spin-transition materials may also exhibit symmetry-breaking phenomena related to various types of orders such as structural order as well as spin-state concentration waves. The universal framework of the Landau theory of phase transition is relevant for describing such ordering processes through the evolution of a symmetry-breaking order parameter η. The simultaneous or sequential occurrence of spin-transition and symmetry-breaking phenomena are reported for numerous spin-transition materials, and the coupling between these two types of instabilities is responsible for the emergence of various types of functions. In this work, we use the Landau approach to describe both symmetry-breaking phenomena and non-symmetry-breaking spin transition. We discuss how their coupling can generate sequences of phase transitions, from simple spin-crossover to spin-transition, continuous or discontinuous symmetry breaking, including ferroelasticity or stepwise spin transitions.