Landau Coefficients Research Articles

Multiphase-field modeling of domain structure evolution in ferroelectric thin film

The computational determination of domain structures in ferroelectric films is achieved through the implementation of a multiphase-field methodology. In this framework, domain structures are calculated by minimizing the total energy functional with respect to the multiphase-field order parameter ϕ. This energy functional includes the general interfacial energy, which consists of a multi-obstacle potential and a gradient energy, as well as the phase-dependent bulk energy that incorporates contributions from mechanical forces and electric fields. Using PbTiO3 (PTO) as the chosen model material, we report on the results of investigating domain structures, including an examination of the influence of substrate deformation, variations in misfit strains, different thin film thicknesses, and temperature fluctuations. By implementing the mechanical jump condition approach, the inelastic strain is calculated independently for both the thin film and the substrate, under different conditions. Furthermore, this model demonstrates its ability to investigate domain structures without relying on the Landau potential to characterize the structural stability, providing a valuable reference for studing various ferroelectric thin films that lack higher-order Landau coefficients.

Band Structure Calculations, Magnetic Properties and Magnetocaloric Effect of GdCo1.8M0.2 Compounds with M = Fe, Mn, Cu, Al

The magnetic properties, band structure results, and magnetocaloric effect of GdCo1.8M0.2 with M = Fe, Mn, Cu, and Al are reported. The band structure calculations demonstrate that all the samples have a ferrimagnetically ordered ground state, in perfect agreement with the magnetic measurements. Calculated magnetic moments and variation with the alloy composition are strongly influenced by hybridisation mechanisms as sustained by an analysis of the orbital projected local density of states. The XPS measurements reveal no significant shift in the binding energy of the investigated Co core levels with a change in the dopant element. The Co 3s core-level spectra gave us direct evidence of the local magnetic moments on Co sites and an average magnetic moment of 1.3 µB /atom was found, being in good agreement with the theoretical estimation and magnetic measurements. From the Mn 3s core-level spectra, a value of 2.1 µB/Mn was obtained. The symmetric shapes of magnetic entropy changes, the Arrott plots, and the temperature dependence of Landau coefficients clearly indicate a second-order phase transition. The relative cooling power, RCP(S), normalized relative cooling power, RCP(∆S)/∆B, and temperature-averaged entropy change values indicate that these compounds could be promising candidates for applications in magnetic refrigeration devices.

Thermodynamic model for electro-optical properties of antiferroelectric phase in mesogen W-330-3 and W-331-3

ABSTRACT A thermodynamic model developed by our group has been employed to explore the electro-optical properties of the chiral antiferroelectric smectic C (Sm C A ∗ ) phase. In the present study, the temperature dependence of tilt angle and spontaneous polarization of binary ferroelectric mixtures represented as W-330-3 and W-331-3 exhibiting ferroelectric Sm C* and antiferroelectric Sm C A ∗ phase has been investigated. Within the framework of this model, the free-energy density characterizing the system featuring the Sm C A ∗ phase is expressed as a series expansion that incorporates all pertinent degrees of freedom: tensor orientational order Q ij , scalar smectic order ψ, polarization vector P, wave vector q of the helix and the resulting coupling terms between these order parameters. The values of Landau coefficients featured in the expansion series are derived from experimental data (tilt angle and spontaneous polarization) of W-330-3 and W-331-3. A substantial agreement between the theoretical predictions and experimental observations has been found.

Stability of viscoelastic film on a slippery inclined plane

The linear and weakly nonlinear stability of viscoelastic film flowing down a slippery inclined plane is investigated analytically. Under the assumption of the long wave approximation, the first-order Benny equation of Oldroyd-B fluid thin film with slip condition is obtained. Through the normal mode analysis, the neutral stability curve and the temporal growth rates are calculated to explore the linear stability of the film. Linear results show that the critical Reynolds number decreases with the increase in slip length and viscoelastic parameter and that the liquid film may exhibit pure elastic instability. For the nonlinear stability analysis, both hydrodynamic instability and elastic instability are discussed. The primary bifurcations in the phase plane are identified by calculating the Landau coefficient, i.e., the unconditional stable region, the supercritical region, the subcritical region, and the explosive region. The dependence of primary bifurcation regions upon the slip length and Deborah number are studied, and the results indicate that the slip boundary and viscoelasticity destabilizes the flow. According to the Ginzburg–Landau equation, the threshold amplitude of the nonlinear equilibrium solution is analyzed as well.

Griffiths-like behavior and magnetocaloric properties of rare-earth silicide Tb2Co0.8Si3.2

Novel rare-earth silicide, Tb2Co0.8Si3.2 compound, crystallizes in Lu2CoGa3 structure, a distorted substitution variant of the AlB2 structure. The compound exhibits a complex magnetic state, with a ferromagnetic transition at 58 K, followed by successive antiferromagnetic transitions at 24 K and 8 K, respectively. Isothermal and magnetic hysteresis studies indicate the prominence of competing antiferro and ferromagnetic interactions in the compound. However, this does not lead to the formation of spin glass behavior, as confirmed by AC magnetic susceptibility and heat capacity studies. In the paramagnetic state, the short-range ferromagnetic ordering of cobalt creates a Griffiths-like anomaly that is suppressed at higher magnetic fields. Investigation of magnetocaloric and magnetoresistance properties identifies the compound as a conventional second-order magnetocaloric material with negative magnetoresistance. Furthermore, the determination of Landau coefficients and subsequent analysis indicate that the isothermal entropy change of the compound can be calculated from these coefficients.

Landau's theorem for harmonic Bloch functions on simply connected domains

For α ∈ ( 0 , ∞ ) , let B H , Ω ( α ) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω ⊆ C . In this article, we study coefficient estimates for harmonic α-Bloch mappings on a proper simply connected domain containing the unit disk. Furthermore, we establish the Landau's theorem and coefficient estimates for the harmonic α-Bloch space B H , Ω γ ( α ) on the shifted disk Ω γ , where Ω γ := { z ∈ C : | z + γ 1 − γ | < 1 1 − γ } and 0 ≤ γ < 1 .

Ultrafast and accurate prediction of polycrystalline hafnium oxide phase-field ferroelectric hysteresis using graph neural networks.

Polycrystalline hafnium oxide emerges as a promising material for the future of nanoelectronic devices. While phase-field modeling stands as a primary choice tool for forecasting domain structure evolution and electromechanical properties of ferroelectric materials, it suffers from a high computational cost, which impedes its applicability to real-size systems. Here, we propose a Graph Neural Network (GNN) machine-learning framework to predict the ferroelectric hysteresis of polycrystalline hafnium oxide, with the goal of significantly accelerating computations in contrast to high-fidelity phase-field methods. By leveraging the inherent graph structure of the polycrystalline system and incorporating edge-level feature properties through graph attentional layers, our approach accurately predicts hysteresis behaviors across a broad range of polycrystalline structures, grain numbers, and Landau coefficients. The GNN framework exhibits high accuracy, with an average relative error of ∼4%, and demonstrates remarkable computational efficiency with respect to ground truth phase-field simulations, offering speed-ups exceeding a million-fold. Furthermore, we showcase the transferability of our model to efficiently scale predictions in polycrystals comprising up to a thousand grains, paving the way for effective simulations of real-sized systems. Our approach, by overcoming computational limitations in polycrystalline hafnium oxide, opens doors for accelerating discovery and design in ferroelectric materials.

Finite-amplitude instability of the convection in a porous vertical slab with horizontal heterogeneity in permeability

The finite-amplitude instability of the natural convection in a vertical porous slab filled with variable permeability porous medium is investigated analytically. The side walls of the slab are kept at different temperatures, and the permeability in the horizontal direction is assumed to be exponential heterogeneous models. Two-dimensional, finite-amplitude solutions for the thermal buoyant flow are obtained for Darcy–Rayleigh numbers close to the critical values by using the amplitude expansion method. The dependence of the fundamental mode, the distortion of the mean flow, and the second harmonic upon the variable permeability constant are discussed. By calculating the first Landau coefficient, the primary bifurcations in the vicinity of the neutral stability curves are identified. The results show that only supercritical bifurcations are found to occur, rather than subcritical instabilities. In terms of the well-known Landau equation, the threshold amplitude of the nonlinear equilibrium solution is analyzed as well.

Thermodynamic model to study the structural and electro-optical properties of chiral antiferroelectric smectic C phase exhibited by mesogenic homologous series 3FnHBM6(s) and W-316 mixture

ABSTRACT Using a thermodynamic model developed by us to study the structural and electro-optical properties of Sm C A ∗ phase, we investigate the temperature dependence of helical pitch, tilt angle and spontaneous polarization of a homologous series of fluorinated biphenyl benzoate esters (3FnHBM6, n = 2, 5, 7) and one of the series W-316-3 obtained from the mixture of two chiral liquid crystalline compounds 6F2OBi and 3F6HBM6. The free-energy density of the system exhibiting Sm C A ∗ phase is written as an expansion series in terms of all the relevant degrees of freedom: Q i j , ψ, P, q and the resulting coupling terms between these order parameters. The values of Landau coefficients are determined from the experimental data of antiferroelectric mesogens 3FnHBM6 (n = 2, 5, 7) and W-316-3 in the Sm C A ∗ phase. Using these coefficients, the electro-optical and structural properties have been studied. We have found good agreements between the theoretical and experimental results.

A phase-field model for ferroelectric materials—Based on the multiphase-field method

A novel phase-field model is developed to investigate the domain structure in ferroelectric materials subjected to an external field. Differing from the time-dependent Ginzburg–Landau (TDGL) theory that describes domain structures based on the spatial and temporal evolution of polarization, our model utilizes the multiphase-field approach to calculate domain structures by minimizing the total energy functional with respect to the multiphase-field order parameter ϕ. The energy functional in the proposed model comprises the general multiphase interfacial energy and the phase-dependent bulk energy, accounting for the contributions from domain walls, and mechanical as well as electric fields. By considering the interplay between the different energy components, the model provides insights into the complex domain structure of ferroelectric materials and their response to external stimuli. This comprehensive approach is validated through simulations of both single-crystal and polycrystalline structures. The approach presented in this study simplifies the computational coefficients required to analyze the domain structure in ferroelectric materials, compared to the TDGL approach, by disregarding the Landau potential. This makes it possible to analyze the domain structure of materials without Landau coefficients. Furthermore, the proposed model serves as a reference for applying the multiphase-field concept to ferroelectric materials.

Magnetism of 3d electrons in YCo12-xFexB6 compounds

The magnetic properties of the polycrystalline YCo12-xFexB6 alloys are thoroughly investigated through the scope of the Kuz’min model describing the thermal evolution of the spontaneous magnetization. The analysis of this behavior reveals a strong composition dependence of the magnetization as well as its thermal evolution. This is interpreted as an evolution from first neighbor ferromagnetic (FM) interactions with progressively reinforced antiferromagnetic (AFM) interactions. The magnetization in the ordered state decreases when increasing Fe content from 0.45 µB/f.u. down to 0.11 µB/f.u. for x = 0 and x = 4, respectively. The Inoue-Shimizu s-d model has also been used close to the ordering temperature to investigate the evolution of the Landau coefficients and study in detail the order of the magnetic transition and have some insights on the magnetovolume coupling in this series of compounds. It revealed that Fe for Co substitution causes the already weak magnetovolume exchange to become even weaker.

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4e , and d -wave charge- 4e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the $\text{U}(1)$-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-$4e$ condensate, which itself can have an underlying $s$-wave, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave, or ${d}_{xy}$-wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-$N$ and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-$N$ approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-$4e$ order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and $s$-wave charge-$4e$ vestigial states are degenerate. We discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-$4e$ states in material candidates.

Magnetocaloric effect and critical behavior of the Mn5Ge3−xZnx alloys

In this paper, the magnetocaloric properties, phase transition and critical behavior of Mn5Ge3−xZnx (x = 0.1, 0.2 and 0.3) compounds fabricated by the arc-melting method were investigated. The Curie temperature and the magnetic entropy change of Mn5Ge3−xZnx alloys decrease with doping of Zn. The normalized curves of universal behavior further demonstrate the feature of second-order transition in the Mn5Ge3−xZnx alloys, consistent with the results of the Landau coefficient and Banerjee criterion analysis. To explore the properties near the phase transition, we investigated the critical behavior of this series using modified Arrott plots, Kouvel-Fisher method and critical isotherm curves. The critical exponents β, γ and δ were calculated in accordance with the Widom scaling relation, and magnetic state equation, demonstrating the experimentally obtained exponents are accurate. The spontaneous magnetization derived from the isothermal entropy change calculated from Maxwell equation, is in agreement with the spontaneous magnetization calculated from the curves, proving the validity of calculating the spontaneous magnetization from the curves.

Nonlinear stability analysis for severe slugging in an air–water two-phase flow

This works presents a numerical study of the types of severe slugging through nonlinear stability analysis. The Landau equation, considered as an asymptotic solution of a two-phase flow model in a pipeline–riser system, is derived. From the Landau equation, the Landau coefficient μ is calculated and, consequently, the saturation amplitudes of the state variables at the limit cycle are determined. Based on the amplitude of the gas superficial velocity at the bottom of the riser, the condition where severe slugging type 3 (SS3) occurs can be determined. Also, based on the amplitude of the liquid superficial velocity at the top of the riser, the condition of severe slugging with liquid fallback can be determined. The results are presented in stability maps and are compared with experimental data reported in the literature, with a good agreement.

Effect of Ni Substitution on the Structural, Magnetic, and Electronic Structure Properties of Gd0.4Tb0.6(Co1-xNix)2 Compounds.

The comprehensive research of magnetic and electronic structure properties of the new class of Gd0.4Tb0.6(Co1-xNix)2 compounds, crystallizing in the cubic Laves phase (C15), is reported. The magnetic study was completed with electrical resistivity and electronic structure investigations. The analysis of Arrott plots supplemented by a study of temperature dependency of Landau coefficients revealed that all compounds undergo a magnetic phase transition of the second type. Based on magnetic isotherms, magnetic entropy change (ΔSM) was determined for many values of the magnetic field change (μ0H), which varied from 0.1 to 7 T. For each compound, the ΔSM had a maximum around the Curie temperature. Both values of the |ΔSMmax| and relative cooling power RCP parameters increased with increasing nickel content. It is shown that structural disorder upon Co/Ni substitution influences some magnetic parameters. The magnetic moment values of Co atoms determined from different methods are quantitatively consistent. From the M(T) dependency, the exchange integrals JRR, JRT, and JTT between rare-earths (R) and transition metal (T) moments were evaluated within the mean-field theory (MFT) approach. The experimental study of the electronic structure performed with the use of the X-ray photoelectron spectroscopy (XPS) was completed by calculations using the full-potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT). The calculations explained experimentally observed changes in the XPS valence band spectra upon the Ni/Co substitution.

Role of temperature on linearity and analog/RF performance merits of a negative capacitance FinFET

Temperature plays a decisive role in semiconductor device performance and reliability analysis. The effect is more severe in a negative capacitance (NC) transistor, as the temperature modulates the ferroelectric polarization, implicitly included by the Landau coefficients (α, β, γ) in Technology Computer Aided Design (TCAD) simulations. In this paper, through TCAD simulations, the role of varying ambient temperature is investigated in the linearity and analog/radio-frequency (RF) merits of NC-FinFET. The varying temperature modulates the carrier mobility, the semiconductor bandgap, and the Landau parameter (α). We analyzed the analog/RF and linearity metrics, such as total gate capacitance (C gg), transconductance (g m), unity gain cut-off frequency (f T), the transconductance-frequency product, gain-bandwidth product, higher-order transconductance (g m2 and g m3), voltage intercept points, third-order power intercept and intermodulation points, and 1 dB CP using well-calibrated TCAD models. Our analysis reveals that these parameters are strongly dependent on temperature and the NC span (defined by using S-curve) shrinks with the rise in temperature. Finally, a source follower and three-stage ring oscillator are designed to test the frequency compatibility of the AC simulation for varying temperatures.

Finite-amplitude instability of the buoyancy boundary layer in a thermally stratified medium

The finite-amplitude instability of the buoyancy-driven boundary layer is considered on a vertical plate immersed in a thermally stratified ambient medium, where the wall and surrounding fluid have different temperature gradients. Although the linear stability in this configuration has been investigated, the finite-amplitude solution arising from the critical instability has been studied only for specific parameter values. We extend this by using the amplitude expansion method. The primary bifurcations to the two-dimensional least unstable mode for different temperature gradient ratios ( $0 \leqslant \lambda \leqslant 10$ ) and Prandtl numbers ( $10^{-1} \leqslant Pr \leqslant 10^{4}$ ) are investigated. Only supercritical bifurcations are found to occur when $0 \leqslant \lambda &lt; 2$ and $Pr \leqslant 2800$ , while subcritical bifurcations are also found for larger values of temperature gradient ratio and Prandtl number. Analysis of the contribution of the nonlinear terms in the Landau coefficient reveals that the interaction of the modification of the mean flow and second harmonic for velocity with the fundamental mode for temperature plays an important role in subcritical bifurcation. Based on the Landau equation, the threshold amplitude of the nonlinear equilibrium solution is discussed as well. These encouraging results should be helpful for understanding such a buoyancy-driven flow system.

Thermodynamic model to study the ferroelectric behaviour of lactic acid derivatives with keto linkage group

ABSTRACT The electro-optical and structural properties of chiral lactic acid derivatives with keto linkage group ((S)-4-((1-alkoxy-1-oxopropan-2-yloxy) carbonyl)phenyl4’-alkyloylbiphenyl-4-carboxylates denoted as KL n/m) exhibiting Sm C* phase and Sm A*−Sm C* phase transition have been studied by using a thermodynamic model based on Landau-de-Gennes theory. The free-energy density of the system is expanded in terms of three degrees of freedom – tensor orientational order , the scalar smectic order , the polarisation vector P, the wave vector q, and the couplings between these order parameters. The values of the Landau coefficients involved in the free-energy density have been calculated by comparing the experimental data of tilt angle, spontaneous polarisation, and pitch of KL n/m. The theoretical and experimental data have been analysed, and a close agreement has been found between the two.

Thermodynamic Model to Study the Phase Transition Properties of Sm CA* Phase in Antiferroelectric Mesogen W-358 Series

Employing the thermodynamic model which is centred on Landau-de-Gennes theory, the electro-optical properties of the Sm CA* phase in antiferroelectric mesogen has been studied. The wave vector q, the polarisation vector P, and the couplings between these order parameters are used to express the system's free-energy density. The Landau coefficients involved in the free-energy density have been computed using experimental data of tilt angle and spontaneous polarisation in the Sm CA* phase of chiral compounds (6F2OBi and 3F5HBM6(S)). Theoretical and experimental data have been compared in investigations

Electronic structure, magnetic properties and magnetocaloric effect of GdCo2-xNix

The electronic structure, magnetic properties, and magnetocaloric effect of GdCo2-xNix with x = 0.2, 0.25, and 0.3 were investigated. X-ray diffraction measurements showed that all studied samples are single phase with the cubic MgCu2 - Laves type structure. In agreement with experiments, the band structure calculations explain the following issues: the antiferromagnetic ground state of the system, the coupling between Gd and the transition metals (TM) mediated by the 5d electrons of Gd hybridized with the 3d electrons of the TM (Co, Ni), the reduction of the spin magnetic moment of Co when substituting with Ni due to Co-Ni hybridization. XPS measurements showed no significant shift in the binding energy of the investigated Co core levels with the change of Ni concentration. For all investigated samples the exchange splitting estimated to about 3.2 eV between the high spin final state and the low spin final state of the Co 3 s core level gives direct evidence of the local magnetic moments on Co sites. The measured increase of the saturation magnetizations when substituting cobalt by nickel confirms the ferrimagnetic-type ordering. The decrease of the Co magnetic moments is related to Co-Ni hybridization and filling of bands with the extra-electrons provided by Ni with respect to Co. Moreover, the Arrott plots, the temperature dependence of Landau coefficients and the shapes of magnetic entropy changes confirm the presence of a second order magnetic phase transition. The RCP(∆S)/∆B values decreases slowly when the Ni concentration increases and could be attributed to the narrowing of the │ΔSm│peaks.