Landau Expansion Of Free Energy Research Articles

Structural mode coupling in perovskite oxides using hypothesis-driven active learning

Finding the ground-state structure with minimum energy is paramount to designing any material. In ABO3-type perovskite oxides with Pnma symmetry, the lowest energy phase is driven by an inherent trilinear coupling between the two primary order parameters such as rotation and tilt with antiferroelectric displacement of the A-site cations as established via hybrid improper ferroelectric mechanism. Conventionally, finding the relevant mode coupling driving phase transition requires performing first-principles calculations which is computationally time-consuming as well as expensive. It involves following an intuitive iterative hit and trial method of (a) adding two or multiple mode vectors, followed by (b) evaluating which combination would lead to the ground-state energy. In this study, we show how a hypothesis-driven active learning framework can identify suitable mode couplings within the Landau free energy expansion with minimal information on amplitudes of modes for a series of double perovskite oxides with A-site layered, columnar and rocksalt ordering. This scheme is expected to be applicable universally for understanding atomistic mechanisms derived from various structural mode couplings behind functionalities, for e.g. polarization, magnetization and metal–insulator transitions.

Pressure dependence of elastic constants using Landau free energy and a numerical modeling analysis of W-InN

ABSTRACT In this work, we study the pressure dependence of elastic constants of wurtzite indium nitride semiconductor based on Landau free energy expansion. Elastic constants are obtained as functions pressure up to second order. We have also evaluated the bulk modulus (B) and anisotropies of compressibility and shear for wurtzite indium nitride as functions of pressure. Agreement with previously obtained results based on first-principles calculations is found to be satisfactory.

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature TN≈400 K and a charge density wave (CDW) transition at TCDW≈110 K, followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around TN, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10−4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to TCDW, the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

Impact of Sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV3Sb5

Elucidating the microscopic mechanisms responsible for the charge density wave (CDW) instability of the AV$_3$Sb$_5$ (A=Cs, K, Rb) family of kagome metals is critical for understanding their unique properties, including superconductivity. In these compounds, distinct CDW phases with wave-vectors at the $M$ and $L$ points are energetically favorable, opening the possibility of tuning the type of CDW order by appropriate external parameters. Here, we shed light on the CDW landscape of CsV$_3$Sb$_5$ via a combination of first-principles calculations and phenomenology, which consists of extracting the coefficients of the CDW Landau free-energy expansion from density functional theory. We find that while the main structural distortions of the kagome lattice in the staggered tri-hexagonal CDW phase are along the nearest-neighbor V-V bonds, distortions associated with the Sb ions play a defining role in the energy gain in this and all other CDW states. Moreover, the coupling between ionic displacements from different unit cells is small, thus explaining the existence of multiple CDW instabilities with different modulations along the c-axis. We also investigate how pressure and temperature impact the CDW phase of CsV$_3$Sb$_5$. Increasing pressure does not change the staggered tri-hexagonal CDW ground state, even though the $M$-point CDW instability disappears before the $L$-point one, a behavior that we attribute to the large nonlinear coupling between the order parameters. Upon changing the temperature, we find a narrow regime in which another transition can take place, toward a tri-hexagonal Star-of-David CDW phase. We discuss the implications of our results by comparing them with experiments on this compound.

Effect of Disparity in Self Dispersion Interactions on Phase Behaviors of Molten A-b-B Diblock Copolymers.

Phase behaviors of molten A-b-B diblock copolymers with disparity in self dispersion interactions are revisited here. A free energy functional is obtained for the corresponding Gaussian copolymers under the influence of effective interactions originating in the localized excess equation of state. The Landau free energy expansion is then formulated as a series in powers of A and B density fluctuations up to 4th order. An alternative and equivalent Landau energy is also provided through the transformation of the order parameters to the fluctuations in block density difference and free volume fraction. The effective Flory χ is elicited from its quadratic term as the sum of the conventional enthalpic χH and the entropic χS that is related to energetic asymmetry mediated by copolymer bulk modulus. It is shown that the cubic term is balanced with Gaussian cubic vertex coefficients in corporation with energetics to yield a critical point at a composition rich in a component with stronger self interactions. The full phase diagrams with classical mesophases are given for the copolymers exhibiting ordering upon cooling and also for others revealing ordering reversely upon heating. These contrasting temperature responses, along with the skewness of phase boundaries, are discussed in relation to χH and χS. The pressure dependence of their ordering transitions is either barotropic or baroplastic; or anomalously exhibits anomalously both at different stages. These actions are all explained by the opposite responses of χH and χS to pressure.

Insights into Cation Ordering of Double Perovskite Oxides from Machine Learning and Causal Relations

This work investigates the origins of cation ordering of double perovskites using first-principles theory computations combined with machine learning (ML) and causal relations. We have considered various oxidation states of A, A', B, and B' from the family of transition metal ions to construct a diverse compositional space. A conventional framework employing traditional ML classification algorithms such as Random Forest (RF) coupled with appropriate features including geometry-driven and key structural modes leads to highly accurate prediction (~98%) of A-site cation ordering. We have evaluated the accuracy of ML models by entailing analyses of decision paths, assignments of probabilistic confidence bound, and finally introducing a direct non-Gaussian acyclic structural equation model to investigate causality. Our study suggests that the structural modes are the most important features for classifying layered, columnar and rock-salt ordering. For clear layered ordering, the charge difference between the A and A' is the most important feature which in turn depends on the B, B' charge separation. Based on the outputs from ML models, we have designed functional forms with these features to derive energy differences forming clear layered ordering. The trilinear coupling between tilt, rotation, and A-site antiferroelectric displacement in Landau free-energy expansion becomes the necessary condition behind the formation of A-site cation ordering.

Calculation of the T-X phase diagram for the first-order smectic–hexatic transitions in binary mixtures

This work gives the T-X phase diagram calculated from the Landau mean field model for the smectic–hexatic transitions in binary mixtures, particularly, in THI-13+THI-17. It is calculated near the SmC-SmF (Hex F)–Hex B triple point by considering transitions of SmC-SmF, SmF-HexB, and SmC-Hex B as the first order. The phase line equations are fitted to the experimental T-X phase diagram from the literature for this binary mixture by assuming the temperature and concentration dependence of the coefficients in the Landau free energy expansion. Calculations are given in some detail to describe the smectic–hexatic transitions in the THI-13+THI-17, which can also be considered for other binary mixtures under the Landau mean field model studied here.

Theory of the charge density wave in AV3Sb5 kagome metals

The family of metallic kagome compounds $A$V$_3$Sb$_5$ ($A$=K, Rb, Cs) was recently discovered to exhibit both superconductivity and charge order. The nature of the charge-density wave (CDW) phase is presently unsettled, which complicates the interpretation of the superconducting ground state. In this paper, we use group-theory and density-functional theory (DFT) to derive and solve a phenomenological Landau model for this CDW state. The DFT results reveal three unstable phonon modes with the same in-plane momentum but different out-of-plane momenta, whose frequencies depend strongly on the electronic temperature. This is indicative of an electronically-driven CDW, stabilized by features of the in-plane electronic dispersion. Motivated by the DFT analysis, we construct a Landau free-energy expansion for coupled CDW order parameters with wave-vectors at the $M$ and $L$ points of the hexagonal Brillouin zone. We find an unusual trilinear term coupling these different order parameters, which can promote the simultaneous condensation of both CDWs even if the two modes are not nearly-degenerate. We classify the different types of coupled multi-$\bf{Q}$ CDW orders, focusing on those that break the sixfold rotational symmetry and lead to a unit-cell doubling along all three crystallographic directions, as suggested by experiments. We determine a region in parameter space, characterized by large nonlinear Landau coefficients, where these phases - dubbed staggered tri-hexagonal and staggered Star-of-David - are the leading instabilities of the system. Finally, we discuss the implications of our results for the kagome metals.

Order parameter induced by an extremely short optical pulse in a medium with chiral carbon nanotubes

We study the effect of a three-dimensional extremely short optical pulse in a medium with chiral carbon nanotubes on the order parameter of this medium. The possibility of the appearance of a phase transition in such a medium is shown. We investigate the dependence of the pulse shape on the relaxation rate of the order parameter and on the parameter β in the Landau expansion of free energy.

Phase stability and Landau phenomenological model of relaxor ferroelectric single crystals 0.78Pb(Mg1/3Nb2/3)O3-0.22PbTiO3

Relaxor-based ferroelectric single crystal with lower PbTiO3 content has complex phase transitions and mixed ferroelectric and relaxor characteristics, making it very challenging for the construction of Landau free energy expansion crucially used for theoretical investigation of this system. In this work, relaxor behavior in 0.78Pb(Mg1/3Nb2/3)O3-0.22PbTiO3 (PMN-0.22PT) single crystals was well suppressed through careful experimental design, leaving preserved single domain state for the Landau parameter extraction in this rhombohedral-phase composition. Using these extracted Landau free energy expansion parameters, energy profile and phase coexistence were theoretically studied and compared with those of PMN-0.30PT and PMN-0.36PT single crystals. Results show that rhombohedral phase dominates in PMN-0.22PT, and tetragonal phase dominates in PMN-0.36PT around room temperature. While, rhombohedral phase and tetragonal phase coexist in MPB composition PMN-0.30PT with small discrepancy of both free energies and polarization vectors.

Density–driven superfluid transition of the constrained bosons on a lattice

We formulate the Landau theory and study its consequences for lattice bosons, which are stabilized by a three-body on-site constraint. This is relevant for experiments with cold atoms in optical lattices, where the presence of three-body dissipative loss processes renders the occupation number n for bosons on short timescales effectively constrained to n≤2. We elaborate on the Landau free energy expansion resulting from the Hamiltonian of bosons in the restricted Hilbert space, and present the phase diagram of the constrained Bose lattice gas.

Analysis of rotator phase transitions in the linear alkanes hexacosane to triacontane by adiabatic scanning calorimetry and by photopyroelectric calorimetry

The study of the nature of various phase transitions between rotator phases in several linear alkanes was performed by analyzing the hysteretic behavior of the specific heat between heating and cooling measurements. The investigations have been carried out by both adiabatic scanning calorimetry and photopyroelectric calorimetry techniques, whose combined use has provided complementary information concerning the changes occurring in the samples’ structure during their temperature change. The study enabled to establish that, unlike what previously reported, the Riii-Riv and the Rii-Riv transitions are of first order, despite them not showing any sharp peak profile in the temperature dependence of the specific heat. The first order of the Rv-Rii transition was confirmed also in the present study and, finally the Rv-Riii transition could be observed by calorimetric detection for the first time and shown to be of second order. The obtained results were discussed in terms of order parameters power terms in the Landau free energy expansion.

To Boil an Egg: Substrate Binding Affects Critical Stability in Thermal Unfolding of Proteins.

Thermal unfolding of proteins is used extensively in screening of drug candidates because molecular interactions with ligands and substrates affect strongly protein stability, transition temperature, and cooperativity. We use synchrotron radiation circular dichroism to monitor the thermal evolution of secondary structure in proteins as they approach the melting point and the impact of substrate on their thermal behavior. Using Landau free energy expansion, we quantify transition strength and proximity to a critical point through the relative separation τ+ between the transition temperature Tm and the spinodal T+, obtained from the equation of state. The weakest transition was observed in lysozyme with τ+ = -0.0167 followed by holo albumin with τ+ = -0.0208 with the strongest transition in monomeric apo albumin τ+ = -0.0242. A structural transition at 45 °C in apo albumin leads to a noncooperative melt with τ+ = -0.00532 and amyloidogenic increase in beta content.

Monte Carlo Simulations of Thermal Hysteresis in Ni‐Mn‐Based Heusler Alloys

We present a study of the thermal hysteresis that takes place across the magnetostructural phase transition of the Ni‐Mn‐based Heusler alloys. The results have been obtained by means of first‐principles calculations and Monte Carlo simulations based on the proposed Potts‐Blume‐Emery‐Griffiths Hamiltonian involving magnetic and elastic degrees of freedom. First, separating the structural and magnetic contributions, we calculate the phase diagram including the martensitic transformation as a function of ratio between exchange structural constants in martensite and austenite (K/J). It is shown that the width of the thermal hysteresis depends on K/J and it is found to increase at a ratio of K/J between 0.20 and 0.37. A similar trend is also observed for the Landau free energy expansion. The evolutions of the magnetization and deformation order parameter of alloys studied under various applied magnetic fields are simulated as functions of temperature upon heating and cooling cycles. Furthermore, under high applied fields the nonlinear shift of and change of hysteresis width according to the relation between magnetostructural interaction constants ( and ) are observed. The results obtained with the Monte Carlo routine are discussed and demonstrated a good agreement with experimental data.

First-principles calculations of the high-temperature phase transformation in yttrium tantalate

The high-temperature phase transition between the tetragonal (scheelite) and monoclinic (fergusonite) forms of yttrium tantalite (${\mathrm{YTaO}}_{4}$ ) has been studied using a combination of first-principles calculations and a Landau free-energy expansion. Calculations of the Gibbs free energies show that the monoclinic phase is stable at room temperature and transforms to the tetragonal phase at 1430 \ifmmode^\circ\else\textdegree\fi{}C, close to the experimental value of $1426\ifmmode\pm\else\textpm\fi{}7$ \ifmmode^\circ\else\textdegree\fi{}C. Analysis of the phonon modes as a function of temperature indicate that the transformation is driven by softening of transverse acoustic modes with symmetry ${E}_{u}$ in the Brillouin zone center rather than the Raman-active ${B}_{g}$ mode. Landau free-energy expansions demonstrate that the transition is second order and, based on the fitting to experimental and calculated lattice parameters, it is found that the transition is a proper rather than a pseudoproper type. Together these findings are consistent with the transition being ferroelastic.

Theory of biomolecular interactions at phospholipid-decorated surfaces of liquid crystals

To discuss the biomolecular interactions at phospholipid-decorated surfaces of liquid crystals, we propose a Ginzburg–Landau free energy, which is functional of three kinds of order parameters. The mean-field treatment of the Ginzburg–Landau free energy expansion shows the existence of assembly of phospholipid monolayer at planar interfaces between thermotropic liquid crystals and aqueous phases. Several structure functions characterizing the assembly of phospholipid at the interfaces are calculated. The model qualitatively explains some aspect of the experimental observations on the physical behavior of phospholipid monolayer formed at the above described interfaces.

A high-resolution powder neutron diffraction study of the crystal structure of neighborite (NaMgF3) between 9 and 440 K

The temperature dependence of the unit-cell dimensions and the crystal structures of the fluorperovskite neighborite, NaMgF 3 (analyzed in the Pbnm setting of the space group), have been determined at 88 temperatures between 9 and 440 K from high-resolution, time-of-flight, powder neutron diffraction data. Lattice parameters exhibit saturation at low temperatures, before developing linear thermal expansion coefficients at temperatures above ~ 350 K. The temperature dependence of each axis has been analyzed, and fitted, using a two-term expression related to an Einstein internal energy function. The unit-cell parameters a and c behave in a conventional manner, however, an unexpected, and previously unobserved, region of negative linear thermal expansion has been found for the b axis in the temperature interval 20 ≤ T ≤ 90 K. Estimated, high-temperature axial thermal expansion coefficients derived from the lattice parameter fitting are in good agreement with those experimentally determined from an earlier synchrotron study, and indicate that high-temperature saturation has been achieved in neighborite by 440 K. The unit-cell volume varies smoothly and monotonically over the whole temperature interval, and the two-term Debye model of Barron has been successfully used to fit these data with characteristic temperatures of 369(2) and 1055(14) K. For the temperature interval 313.15-443.15 K, the thermodynamic Grüneisen constant has been determined using the Debye parameterization of the unit-cell volume, coupled with literature values of the isobaric molar heat capacity. The evolution of the crystal structure as a function of temperature is presented, and explained, in terms of the temperature dependence of the amplitudes of the seven symmetry-adapted basis-vectors of the aristotype phase that are consistent with the orthorhombic space group. The calculated temperature variations of the bond lengths are in excellent agreement with those experimentally determined. The primary order parameters for centrosymmetric, zone-boundary phase transitions in perovskite-structured compounds, i.e., the amplitudes of the basis vectors that transform as the irreducible representations R + 4 (anti-phase tilt) and M + 3 (in-phase tilt), have been fitted to a Landau free energy expansion that incorporates low-temperature saturation. Within the temperature range studied, the temperature dependence of the displacement corresponding to the anti-phase tilt is consistent with tricritical behavior. Experimental evidence is presented for a quadratic coupling of the in-phase tilt to the anti-phase tilt for temperatures greater than ~ 135 K, suggesting critical behavior at the orthorhombic-cubic transition is purely related to an instability at the R point of the pseudocubic Brillouin zone.

Phase diagram of the mixed spin-2 and spin-[formula omitted] Ising system with two different single-ion anisotropies

We study the effect of two different single-ion anisotropies in the phase diagram and in the compensation temperature of mixed spin-2 and spin-5/2 Ising ferrimagnetic system. We employed the mean-field theory based on the Bogoliubov inequality for Gibbs free energy. We use the Landau expansion of free energy in the order parameter to describe the phase diagram. In the temperature versus single-ion anisotropy plane the phase diagram displays tricritical behavior. The critical and compensation temperatures increase with increasing values of the single-ion anisotropies.

Thin film bulk acoustic wave resonators tuning from first principles

Being important for the antiresonance frequency tuning of tunable thin Film Bulk Acoustic wave Resonators (FBARs), the non-linear electrostrictive coefficient was for the first time calculated for BaTiO3 and SrTiO3 using ab initio methods. Further, taking into account the small difference of obtained values for BaTiO3 and SrTiO3 these results were linearly interpolated to the BaxSr1−xTiO3 (BST) compositions. The obtained values are consistent with previously made order-of-magnitude estimates. Using parameters obtained with first principles calculations, we simulated the resonance parameters of BST based tunable FBARs. Resulting antiresonance tuning was smaller than expected due to the compensation of two competing terms conditioned by linear and non-linear electrostrictions. Our calculations confirm that, for tunable FBAR modeling, it is important to use a polarization-based Landau free energy expansion taking into account both non-linear electrostriction and background permittivity.

Ultrasonic Relaxation in Phase Transition Region in Ferroelectric Semiconductors of Sn<sub>2</sub>P<sub>2</sub>S<sub>6 </sub>Family

The paper presents recent results of ultrasonic investigation of Sn2P2S6 family ferroelectric crystals and their solid solutions in the temperature range 100-300 K. It was shown that in Sn2P2(S,Se)6 crystals the critical ultrasonic velocity slowing down for longitudinal waves propagating along main crystallographic directions is quite sharp and large. The relative change of longitudinal ultrasonic velocity along z-axis at the phase transition gradually increased from 10 % in pure Sn2P2S6 till 25 % for sample with 0.4 content of Se. Such large velocity change causes the large ultrasonic attenuation anomaly. The increase of relaxation time: τ=τ0/(TC-T) leads to the increase of attenuation. Prefactor τ0 was shown to be very small and the critical attenuation anomaly arises in the narrow temperature range close to phase transition. In the 0.4 Se sample the phase transition is of the first order because small thermal hysteresis exists. The ultrasonic velocity behaviour in the ferroelectric phase was described using Landau theory and free energy expansion including sixth order terms. For (Sn,Pb)2P2S6 system the critical ultrasonic anomalies were smaller and the phase transition temperature substantially decreased (for 0.45 Pb sample the phase transition point was at Tc =140 K). The ultrasonic anomalies at phase transition in (PbxSn1-x)2P2S6 have large hysteresis showing that transition is of the first order, far from the critical point.