Multiple Order Parameters Research Articles

Ultrastrong Coupling between Polar Distortion and Optical Properties in Ferroelectric MoBr2O2.

Tuning the properties of materials by using external stimuli is crucial for developing versatile smart materials. Strong coupling among the order parameters within a single-phase material constitutes a potent foundation for achieving precise property control. However, cross-coupling is fairly weak in most single materials. Leveraging first-principles calculations, we demonstrate a layered mixed anion compound MoBr2O2 that exhibits electric-field switchable spontaneous polarization and ultrastrong coupling between polar distortion and electronic structures as well as optical properties. It offers feasible avenues of achieving tunable Rashba spin-splitting, electrochromism, thermochromism, photochromism, and nonlinear optics by applying an external electric field to a single domain sample and heating, as well as intense light illumination. Additionally, it exhibits an exceptionally large photostrictive effect. These findings not only showcase the feasibility of achieving multiple order parameter coupling within a single material but also pave the way for comprehensive applications based on property control, such as energy harvesting, information processing, and ultrafast control.

Sensing multiferroic states non-invasively using optical second harmonic generation

The current boost in the search for energy-efficient device paradigms motivates the integration of materials with coexisting and coupled electric and magnetic order parameters into application-relevant architectures. In the so-called multiferroic magnetoelectrics, the understanding of switching events, however, is most of the time obstructed by the complex physics involved and in the non-trivial domain and domain wall configurations. This perspective offers an insightful overview of the most recent progress in the non-invasive optical probe of technology-significant ferroelectricity and antiferromagnetic order: the optical second harmonic generation (SHG). Over the last decade, its use in materials science has evolved, and SHG now enables the monitoring of the emergence of polarization in thin films, even during the epitaxial deposition process. Its long working distance further expedites the probe of multiple order parameters in various environments and under multi-stimuli excitations. The potential for the probe of complex electric dipole textures, such as ferroelectric skyrmions and time-resolved measurements, using SHG-based approaches in the most recent materials systems will be discussed.

Competitive driving effect on calorics by dual-fields in ferroic materials with strong magnetostructural coupling

Solid state refrigeration based on caloric effect of a solid has received extensive attention. From theoretical viewpoint, the caloric effect driven by multiple fields yields larger caloric response due to cross-interaction for ferroic materials with multiple order parameters. However, experimental evidence involving cross-responses is very limited. Here, we report the first experimental study on the modulation of the barocaloric effect (BCE) by magnetic field in Ni50Mn35In15 materials with strong magnetostructural coupling. The results demonstrate that the modulating behavior of BCE by magnetic field, which is dominated by cross-response, depends crucially on the magnitude of pressure. At low pressures, an abnormal minimum appears in the magnetic field dependent barocaloric entropy change |ΔSTBCE|, while it turns into a monotonic enhancement as the pressure reaches 4 kbar or larger. The enhanced ratio of |ΔSTBCE| is as much as ∼ 40 % when a magnetic field of 5 T is applied, accordingly the barocaloric refrigeration performance enhances. For the underlying mechanism, Ab initio calculations were performed, which provide a theoretical explanation about the driving effect by single pressure, single magnetic field, and dual-fields on the magnetostructural transition from the perspective of total energy and Mn-d/Ni-d electronic hybridization. The present work reveals that the modulation of BCE by magnetic field is not independent or additive but a synergistic effect of dual-fields, which lays a solid basis in guiding dual-fields driven solid-state refrigeration applications.

Study on Evaluation of Order Degree of Water Resources Coupling System Considering Time Series Characteristics—Take Jiangxi Province as an Example

In recent years, the order evaluation method of a coupled system based on synergetics has been successfully applied in the field of water resources evaluation and management. The evaluation of system order degree needs to comprehensively consider the simple giant system entropy of multiple order parameters. At this stage, the calculation of simple giant system entropy ignores the time series characteristics of order parameters, which makes the evaluation results of system order degree deviate from the actual changes of the system. Therefore, considering the time factor in the entropy calculation of a simple giant system, this paper proposes a synergetic order evaluation method considering the characteristics of time series. Then, taking Jiangxi Province as the research object, an example of a comprehensive evaluation of the order degree of the water resources coupling system is carried out. The relevant experimental results show that: The evaluation results of the synergetic order degree method considering the characteristics of time series presented in this paper are closer to the actual evolution situation of the system than the evaluation results without considering the characteristics of the time series, and maintaining high consistency with the actual evolution situation; the order degree of the water resources subsystem is greatly affected by the changes of water resources; and the entropy change of the water resources coupling system in Jiangxi Province is greatly affected by the entropy change of the water resources subsystem. The research result enhances the universality of the application of the synergetic order evaluation method in the related fields of a comprehensive evaluation of water resources systems and has a certain practical significance.

Thermodynamic calculations using reverse Monte Carlo: Simultaneously tuning multiple short-range order parameters for 2D lattice adsorption problem.

Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice thermodynamic calculations that is based on the use of the reverse Monte Carlo (RMC) technique and multiple short-range order (SRO) parameters. The approach is comparable in accuracy to the Metropolis Monte Carlo (MC) method. The equilibrium configuration is determined in 5-10 Newton-Raphson iterations by solving a system of coupled nonlinear algebraic SRO growth rate equations. This makes the RMC-based method computationally more efficient than MC, given that MC typically requires sampling of millions of configurations. The technique is applied to the interacting 2D adsorption problem. Unlike grand canonical MC, RMC is found to be adept at tackling geometric frustration, as it is able to quickly and correctly provide the ordered c(2 × 2) adlayer configuration for Cl adsorbed on a Cu (100) surface.

Kinetic reconstruction of free energies as a function of multiple order parameters.

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Achieving High-Temperature Multiferroism by Atomic Architecture

Materials with multiple order parameters, typically, in which ferroelectricity and magnetism are coupled, are illuminative for next-generation multifunctional electronics. However, searching for such single-phase multiferroics is challenging owing to antagonistic orbital occupancy and chemical bonding requirements for polarity and magnetism. Appropriate multiferroic candidates have been proposed, but their practical implementation is impeded by the low working temperature, weak coupling between ferroic orders, or antiparallel spin alignment in magnetic sublattices. Here, we report a family of single-phase multiferroic materials in which high-temperature magnetism and voltage-switchable ferroelectricity are coupled. Using pulsed laser deposition, we have fabricated single-crystalline thin films incorporating a uniformly percolated open-shell dn framework, which are composed of Fe cations with B-site occupancy and exhibit long-range spin ordering into the displacive ferroelectric PbTiO3 lattice, as demonstrated by atomically resolved chemical analysis. The tetragonal polar Pb(Ti1-x,Fex)O3 (PFT(x), x ≤ 0.10) family exhibits a switchable ferroelectric nature and magnetic interaction with a moderate coercive field of around 300 Oe at room temperature. Notably, the magnetic order even persists above 500 K, which is higher than already reported potential multiferroic candidates until now. Our strategy of merging a spin-ordered sublattice into inherent ferroelectrics via atomic occupancy engineering provides an available pathway for highly thermally stable multiferroic and spintronic applications.

The jumping dielectric breakdown behavior induced by crack propagation in ferroelectric materials: A phase field study

Ferroelectric materials often experience fracture and dielectric breakdown under large mechanical and/or electrical loads. These two failure behaviors can affect each other and may lead to new phenomena. This study predicts a new type of jumping dielectric breakdown during crack propagation in ferroelectric materials using a phase field model involving multiple order parameters. The driving forces for the evolution of polarization, fracture, and dielectric breakdown were analysed based on the concept of configurational forces. The jumping dielectric breakdown was attributed to the competition between crack propagation and breakdown initiation at the moving crack tip. The breakdown pattern is related to the polarization domain structure and is significantly influenced by the applied electric field and crack boundary conditions. Furthermore, the jumping breakdown associated with possible mechanical degradation of the material can change the driving and resistance forces for crack propagation. This study introduces a novel dielectric breakdown behavior during crack propagation and provides new insights into the coupling failure of ferroelectric materials.

Well-tempered metadynamics applied to field-theoretic simulations of diblock copolymer melts.

Well-tempered metadynamics (WTMD) is applied to field-theoretic simulations (FTS) to locate the order-disorder transition (ODT) in incompressible melts of diblock copolymer with an invariant polymerization index of N̄=104. The polymers are modeled as discrete Gaussian chains with N = 90 monomers, and the incompressibility is treated by a partial saddle-point approximation. Our implementation of WTMD proves effective at locating the ODT of the lamellar and cylindrical regions, but it has difficulty with that of the spherical and gyroid regions. In the latter two cases, our choice of order parameter cannot sufficiently distinguish the ordered and disordered states because of the similarity in microstructures. The gyroid phase has the added complication that it competes with a number of other morphologies, and thus, it might be beneficial to extend the WTMD to multiple order parameters. Nevertheless, when the method works, the ODT can be located with impressive accuracy (e.g., ΔχN ∼ 0.01).

Phase field modeling of coupling evolution of fracture and dielectric breakdown in ferroelectric materials

Ferroelectric materials have attracted increasing attention due to their distinguished electromechanical coupling properties. Fracture and dielectric breakdown are two main failure behaviours of ferroelectric materials, which may occur simultaneously under large mechanical and electrical loads. Understanding the coupling evolution of fracture and dielectric breakdown is crucial for the application of ferroelectric materials under complex electromechanical environments. In the present study, a phase field model with multiple order parameters is developed to investigate the coupling evolution behaviours of fracture and dielectric breakdown of ferroelectric materials subjected to the mechanical and electrical loadings. In the phase field model, coupled electromechanical degradation functions are proposed to model the interface boundary conditions of fracture and dielectric breakdown. Generalized configurational forces of fracture and dielectric breakdown are obtained from the phase field model to analyse the driving forces for the evolution of fracture and dielectric breakdown. The interaction between fracture and dielectric breakdown is predicted by using the phase field model with a set of interface boundary conditions. The simulation results show that dielectric breakdown occurs at impermeable crack tips due to the concentrated electric field, while the stress distribution around the crack tip and the driving force of crack propagation are influenced by dielectric breakdown. The attraction of crack to electrical treeing path and the deflection of electrical treeing to crack path are predicted during the coupling evolution of fracture and dielectric breakdown. The results of this work provide an in-depth insight into the electromechanical coupling failure of fracture and breakdown of ferroelectric materials. The developed model framework can be employed to investigate more complex electromechanical coupling failures of dielectric, piezoelectric and ferroelectric materials and structures.

Quantitative Diagnosis of TCM Syndrome Types Based on Adaptive Resonant Neural Network.

Artificial intelligence has become one of the most rapidly developing disciplines in the application field of pattern recognition. In target recognition, sometimes, there are multiple identical or similar copies of the target to be recognized in the image, and it is difficult to classify and estimate by traditional methods. In this case, it is necessary to use the SOM network to separate multiple targets and use the multiple order parameters in the improved SNN to pair the target. The change of its thickness can intuitively reflect the abnormality of its tissue. Therefore, the choroidal thickness of the central fovea can be measured to study the relationship between the choroidal structure and BRVO and arteriosclerosis. The purpose of this study is to further study the correlation between branch retinal vein occlusion and arteriosclerosis by quantitatively measuring retinal vessel diameter and choroidal thickness, to analyze the correlation between different TCM syndrome types of nonischemic BRVO and retinal arteriosclerosis, and to provide theoretical basis for clinical nonischemic BRVO TCM syndrome types and traditional Chinese medicine treatment, so as to reflect its clinical application value. In order to solve the single fixed structure of traditional SNN and poor scalability, combined with the Kohonen layer structure in the self-organizing mapping network, an improved collaborative neural network model is proposed. This paper studies the network training method and operation convergence and analyzes the converged network and the pattern classification results obtained by the network. In order to solve the single fixed structure of traditional SNN and poor scalability, combined with the Kohonen layer structure in the self-organizing mapping network, an improved collaborative neural network model is proposed. The results of our proposed improved model on the MNIST dataset can achieve the same level of current state-of-the-art machine learning classifiers in recognition accuracy with a smaller network size and network complexity.

Phase-field modeling of crack propagation in heterogeneous materials with multiple crack order parameters

The phase-field method is widely established for modeling crack propagation in material science. It shows good agreement with analytical solutions and is able to describe a complex fracture behavior. Nevertheless, the models are mostly introduced for homogeneous systems, and there are only a few approaches for heterogeneous systems. So models, that are able to describe the crack propagation in such systems, are highly desirable. Based on a classic crack propagation phase-field approach, existing models are discussed, and a new model is derived. The first model, which is based on an already existing approach, uses homogenized properties and a single-crack order parameter, while the second model, a new approach, introduces multiple crack order parameters, each of which only tracks the damage of a corresponding phase. Furthermore, the issues of the single-crack order parameter model are demonstrated, such as the ability to reproduce the quantitative surface energies for an interfacial crack and the non-physical behavior of a crack propagating along a sloped material interface. In contrast, the novel multi-crack order parameter model prevents distortions for an interfacial crack and propagates along the interface in a more physical manner. In comparison with an analytical solution, based on linear elastic fracture mechanics, the novel model shows a good agreement, even for strongly sloped interfaces, where the single-crack order parameter model fails to reproduce the analytical solution. In a subsequent application to fiber-reinforced polymers, the new model has proven to be able to predict fractures in complex systems, including crack nucleation, branching, and merging. Finally, the applicability to a 3D system is illustrated.

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data.

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

Selective tuning of order parameters of multiferroicBiFeO3in picoseconds using midinfrared terahertz laser pulses

Selectively tuning the properties of a material with multiple order parameters, such as polarization and magnetization, requires precise control of the crystal structure. Recently developed midinfrared THz laser techniques provide an efficient way to manipulate the structure of materials at an ultrafast rate. This paper presents a methodology to evaluate the possibility of picosecond multiple switching of order parameters in perovskite structure oxides using first-principles calculations. With multiferroic ${\mathrm{BiFeO}}_{3}$ as a model system, we demonstrate that the desired property can be tuned by an external laser pulse's perturbation with frequency 15.2 THz. The dynamics of phonon modes are illustrated, revealing that lasers enable switching of polarization and magnetization within 1 ps. The switching mechanisms can be attributed to the nonlinear coupling of the pumped infrared-active mode with the ferroelectric and antiferrodistortive modes. Our work provides an initiative for more detailed experimental investigations to explore light control orders and dynamic material design.

Ferroelectricity and Ferromagnetism Achieved via Adjusting Dimensionality in BiFeO3/BiMnO3 Superlattices.

Integrating characteristics of materials through constructing artificial superlattices (SLs) has raised extensive attention in multifunctional materials. Here, we report the synthesis of BiFeO3/BiMnO3 SLs with considerable ferroelectric polarizations and tunable magnetic moments. The polarization of BiFeO3/BiMnO3 SLs presents a decent value of 12 μC/cm2, even as the dimensionality of BiFeO3 layers per period is reduced to about five-unit cells when keeping the BiMnO3 layers same. Moreover, it is found that the tunable magnetic moments of SLs are linked intimately to the dimensionality of BiFeO3 layers. Our simulations demonstrate that the superexchange interaction of Fe-O-Mn tends to be antiferromagnetic (AFM) with a lower magnetic domain formation energy rather than ferromagnetic (FM). Therefore, as the dimensionality of BiFeO3 per period is reduced, the AFM superexchange interaction between BiFeO3 and BiMnO3 in the SLs becomes weak, promoting a robust magnetization. This interlayer modulation effect in SLs presents an alluring way to accurately control the multiple order parameters in a multiferroic oxide system.

Particulate multiferroic Ba0.99Tb0.02Ti0.99O3 – CoFe1.8Mn0.2O4 composites: Improved dielectric, ferroelectric and magneto-dielectric properties

In present era, the challenge to design materials which unify multiple order parameters has motived the scientific community to work for multiferroic materials. In this work, the multiferroic particulate composites were fabricated from terbium doped BaTiO3 and manganese doped CoFe2O4. Terbium and manganese dopants improved dielectric and magnetic properties in BaTiO3 and CoFe2O4 respectively. Structural study revealed that doped BaTiO3 and CoFe2O4 crystalized into tetragonal and cubic structures, respectively in composites. In multiferroic composites, a dramatic drop in the unit cell volume of magnetic phase resulted in enhanced strain. The improvement in dielectric constant in composites is explained on the basis of bond and hopping lengths. The Curie Weiss Law ascertained that the dielectric peaks are widened. The calculated activation energy from resistivity measurements revealed insulating behavior of composites. The amphoteric nature of terbium and high resistivity of magnetic phase resulted in ferroelectric hysteresis loops which are free from leakage currents. The magneto-crystalline anisotropy was calculated by the Law of Approach to saturation, and was found to be small in composites, due to quenching of orbital angular momenta of the Co2+ ions by the non-magnetic ferroelectric phase. Temperature dependent magnetic study revealed increase in magnetization during zero field cooling as compared to field cooling, confirming magnetization of one sub lattice decreases at slower rate as compared to another sub lattice. The terbium and manganese doping improved the magneto-capacitance of prepared composites, suggesting the use of these composites in magnetoelectric devices.

Modeling multiorbital effects in Sr2IrO4 under strain and a Zeeman field

We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean field approach with multiple order parameters to characterize the resulting phases. While in some parameter regimes the compound is well described by an effective J=1/2 model, in other regimes the full multiorbital description is needed. As a function of the compressive strain, we uncover two quantum phase transitions: first a continuous metal-insulator transition, and subsequently a first order magnetic melting of the antiferromagnetic order. Crucially, bands of both J=1/2 and J=3/2 nature play important roles in these transitions. Our results qualitatively agree with experiments of Sr2IrO4 under strain induced by a substrate, and motivate the study of higher strains.

Pepsin-like aspartic proteases (PAPs) as model systems for combining biomolecular simulation with biophysical experiments.

Pepsin-like aspartic proteases (PAPs) are a class of aspartic proteases which shares tremendous structural similarity with human pepsin. One of the key structural features of PAPs is the presence of a β-hairpin motif otherwise known as flap. The biological function of the PAPs is highly dependent on the conformational dynamics of the flap region. In apo PAPs, the conformational dynamics of the flap is dominated by the rotational degrees of freedom associated with χ1 and χ2 angles of conserved Tyr (or Phe in some cases). However it is plausible that dihedral order parameters associated with several other residues might play crucial roles in the conformational dynamics of apo PAPs. Due to their size, complexities associated with conformational dynamics and clinical significance (drug targets for malaria, Alzheimer's disease etc.), PAPs provide a challenging testing ground for computational and experimental methods focusing on understanding conformational dynamics and molecular recognition in biomolecules. The opening of the flap region is necessary to accommodate substrate/ligand in the active site of the PAPs. The BIG challenge is to gain atomistic details into how reversible ligand binding/unbinding (molecular recognition) affects the conformational dynamics. Recent reports of kinetics (Ki, Kd) and thermodynamic parameters (ΔH, TΔS, and ΔG) associated with macro-cyclic ligands bound to BACE1 (belongs to PAP family) provide a perfect challenge (how to deal with big ligands with multiple torsional angles and select optimum order parameters to study reversible ligand binding/unbinding) for computational methods to predict binding free energies and kinetics beyond typical test systems e.g. benzamide–trypsin. In this work, i reviewed several order parameters which were proposed to capture the conformational dynamics and molecular recognition in PAPs. I further highlighted how machine learning methods can be used as order parameters in the context of PAPs. I then proposed some open ideas and challenges in the context of molecular simulation and put forward my case on how biophysical experiments e.g. NMR, time-resolved FRET etc. can be used in conjunction with biomolecular simulation to gain complete atomistic insights into the conformational dynamics of PAPs.

Multiple magnetic order parameters coexisting in multiferroic hexaferrites resolved by soft x rays

We investigated, by using soft x rays, one of the most fundamental properties in multiferroics, that is, coupled or decoupled feature among coexisting multiple (anti)ferroic order parameters for two types of multiferroic hexaferrites. Circular dichroic signals observed at x-ray resonance for diffraction and absorption enable us to resolve several kinds of magnetic domains, which are spatial distributions of the respective order parameters. We examined magnetic field effects on the domains and unveiled the features of the order parameters. It is found that the coupled or decoupled features of the order parameters are explained by the symmetry analysis based on the Landau theory. These findings contribute to an understanding of magnetoelectric couplings in multiferroics and to exploiting a wide variety of their functionalities. In addition, we suggest a circular dichroic specular off-peak scattering at resonance as a powerful technique for studying a surface state of a magnetic order in an expansive range of quantum materials.

Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials

Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. In this Review, we discuss the exotic polarization profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today’s topological systems. Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level and emergent functional properties. This Review discusses the exotic polarization profiles that arise at domain walls and the fundamental mechanisms responsible for domain-wall conduction.