Time-dependent Ginzburg Research Articles

Understanding the kinetic anisotropy of the soft-sphere bcc crystal–melt interfaces

By employing the non-equilibrium molecular dynamics (MD) simulations and the time-dependent Ginzburg–Landau (TDGL) theory for the solidification kinetics, we predict the kinetic coefficients for the bcc(100), (110), and (111) CMIs of the soft-spheres, which are modeled with the inverse-power repulsive potential, and compare with the previous reported data of the bcc Fe system. We confirm a universal-like behavior of the spatial integrations of the (density wave amplitudes) Ginzburg–Landau order parameter square-gradient for the bcc CMI systems. The TDGL predictions of the kinetic anisotropies for bcc soft-sphere and bcc Fe CMI systems are identical; both agree well with the MD measurement for the soft-sphere system but differ strongly with the MD measurement for the Fe system. This finding implies that the current TDGL theory reflects a preference of presenting the generic anisotropy relationship due to the interfacial particle packings but lacks the contribution parameter which addresses the specificities in the kinetic anisotropies owing to the particle–particle interactions. A hypothesis that the density relaxation times for the interface melt phases to be anisotropic and material-dependent is then proposed.

Vortex state in a superconducting mesoscopic irregular octagon

Our study sample is a superconducting bi-dimensional octagon with different boundary conditions immersed in a magnetic external field [Formula: see text]. The boundary conditions are simulated by considering different values of the de Gennes extrapolation length [Formula: see text] on different surfaces of the sample. Our investigation was carried out by solving the time-dependent Ginzburg–Landau equations. We analyzed the superconducting electron density and the magnetization curves as functions of [Formula: see text] and temperature [Formula: see text] in field-cooling and in zero-field-cooling processes for different values of [Formula: see text] and size of the sample. We found a strong dependence of the critical fields on [Formula: see text] and size of the sample.

Intrinsic 90° charged domain wall and its effects on ferroelectric properties

The domain is an important characteristic of ferroelectric materials, and the type of domain can have significant effects on the performance of ferroelectric materials. In particular, the unique wake-up and fatigue effects of Hf0.5Zr0.5O2 (HZO) films severely restrict improvements in terms of film performance. Recently, using integrated differential phase contrast (iDPC) scanning transmission electron microscopy (STEM) imaging, we observed the existence of intrinsic tail-to-tail 90° domain structures, charged domain walls (CDWs), and polarization relaxation on the TiN/HZO/TiN interfaces of HZO films. Based on this experimental investigation, we establish a phase-field model of the tail-to-tail 90°CDWs based on the time-dependent Ginzburg–Landau equation. In our model, the tail-to-tail 90°CDW affects the mesoscopic domain switching through a built-in electric field, which, in turn, affects the macroscopic ferroelectric properties of the thin film. The following conclusions are drawn: (a) the CDWs that are distributed horizontally or vertically along the thickness of the film cause a A-wake-up effect (antiferroelectric-like wake-up) with double hysteresis loops or a S-wake-up effect (spindle-like wake-up), with thick portions in the middle and both ends points of the hysteresis loop; (b) the S-wake-up caused by the CDWs distributed along the thickness of the film performs badly in fatigue tests and is easier to break down. The model proposed herein reveals the mechanism of the wake-up effect in hafnium oxide-based ferroelectric films. It provides a theoretical basis for the development of a new type of hafnium oxide-based ferroelectric memory system.

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver’s visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver’s behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.

Violation of magnetic flux conservation by superconducting nanorings

The behavior of magnetic flux in ring-shaped finite-gap superconductors is explored from the view-point of the flux-conservation theorem, which states that under the variation of an external magnetic field ‘the magnetic flux through the ring remains constant’ (see, e.g., Landau and Lifshitz 1960 Electrodynamics of Continuous Media (New York: Pergamon)). Our results, based on the time-dependent Ginzburg–Landau equations and COMSOL modeling, made it clear that in the general case this theorem is incorrect. While for macroscopic rings the corrections are small, for micro- and nanorings they become rather substantial. The physical reasons behind this effect are discussed. The dependence of flux deviation on ring size, bias temperature and the speed of external flux evolution is explored. The detailed structure of flux distribution inside the ring opening, as well as the electric field distribution inside the ring wire cross section, are revealed. Our results and the developed finite element modeling approach can assist in elucidating various fundamental topics in superconducting nanophysics and in the advancement of nanosize superconducting circuits prior to time-consuming and costly experiments.

Dynamic peculiarities of interphase boundaries and domain walls for non-spin domains

The analysis of magnetization oscillations (de Haas – van Alphen effect; dHvA effect) and features of the Fermi surface shape in three (3D)- and two-dimensional (2D) metals shows that the dynamic phenomena — the dynamics of domain walls and interphase boundaries during diamagnetic phase transitions — are described by a new nonlinear partial differential equation. The equation is a result of the inclusion of the case of multiple extremal cross sections of the Fermi surface in these metals. Our consideration indicates the possibility of the appearance of metastable non-spin domains (Condon domains) and first-order phase transitions to the ordered phase in the regime of dHvA oscillations for the two-frequency case. Sine–Gordon, Klein–Gordon, double sine–Gordon, time-dependent Ginzburg–Landau equations, and the telegraph equation are limiting cases of the derived equation. We show that particular moving kink-soliton solutions of the equation describe traveling wave fronts being moving domain walls and interphase boundaries in the Condon domain phase.

An Extended Car-Following Model Based on Visual Angle and Electronic Throttle Effect

With the continuous advancement of electronic technology, auto parts manufacturing institutions are gradually applying electronic throttles to automobiles for precise control. Based on the visual angle model (VAM), a car-following model considering the electronic throttle angle of the preceding vehicle is proposed. The stability conditions are obtained through linear stability analysis. By means of nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation is derived first, and then the modified Korteweg-de-Vries (mKdV) equation is derived. The relationship between the two is thus obtained. Finally, in the process of numerical simulations and exploration, it is shown how the visual angle and electronic throttle affect the stability of traffic flow. The simulation results in MATLAB software verify the validity of the model, indicating that the visual angle and electronic throttle can improve traffic stability.

Dynamics of fractional vortices in two-band superconductors

The entry of fractional vortices and their subsequent dynamics inside a two-band superconductor is explored based on the numerical solutions of time-dependent Ginzburg–Landau (TDGL) equations. We consider the case when superfluid electron condensates from two zones are characterized by quite different parameters, such as coherence lengths ξi, and London penetration depths λi, which in turn leads to the different critical magnetic fields Hc,iand fractional flux quanta ϕivalues for the superconducting state in these two zones. Numerical solutions of TDGL equations in increasing external magnetic field followed by mathematical modeling of magnetic flux penetration were performed for this case by finite element method. We have explored the time evolution for the fractional vortices penetration process and their subsequent dynamics inside the specimens for two geometries: the circular disk, and the circular disk with a triangular cutout. Obtained results indicate that magnetic flux penetrates inside the specimen in the form of fractional vortices when they can overcome the edge barrier, which may be different for these two vortex types. Therefore, in increasing external magnetic field first penetrate vortices with a lower barrier height (i.e., lower Hc,i) while the other type of fractional vortices start their penetration at higher external field value. Another mechanism for the formation of fractional vortices during their entrance in a two-band superconductor is related to the difference in their flux values and viscosity coefficients which determine the rate of vortex proliferation inside the sample. Within the specimen, fractional vortices move in order to arrange. Vortices of different types attract to each other and try to stick together thus forming composite vortices with the whole flux quantum value ϕ0 = h/2e.

Simulation of nanoscale domain growth for ferroelectric recording

The growth process of nm-scale polarization domains is of great interest from a physical point of view and is also important in the design of ferroelectric recording, which is expected to be a high-density information recording method. To clarify the growth of nanoscale domains in probe-based ferroelectric recording, a simulation method based on the time-dependent Ginzburg–Landau equation has been developed. In this method, wall pinning is included in the phenomenological free energy by using a coercive field. The simulation results agreed with the experimental results for nanoscale domain writing using a probe. The developed method was used to determine the relationship between the smallest writable domain size and the material properties: smaller wall energy density and larger saturation polarization and coercive field enable writing smaller domains. The developed method is thus effective in designing ferroelectric recording systems for high-density information storage.

Superconductor in static gravitational, electric and magnetic fields with vortex lattice

We estimate the conjectured interaction between the Earth’s gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence of a vortex lattice. The proposed interaction could lead to multiple, measurable effects. First of all, a local affection of the gravitational field inside the superconductor could take place. Second, a new component of a generalized electric field parallel to the superconductor surface is generated inside the sample.The analysis is performed by using the time-dependent Ginzburg–Landau theory combined with the gravito-Maxwell formalism. This approach leads us to analytic solutions of the problem, also providing the average values of the generated fields and corrections inside the sample. We will also study which are the physical parameters to optimize and, in turn, the most suitable materials to maximize the effect.

Effect of defects density on the vortex penetration of a superconducting thin film and deep-learning enabled characterization of defects

In this paper, the effect of defects density on vortex penetration of thin superconducting film is investigated using the time-dependent Ginzburg–Landau (TDGL) equations. Thermal effects from superconductor energy dissipation are included by coupling the TDGL equations with heat equations. We studied a thin square-shaped superconducting film under a ramping magnetic field and considered the effects of geometry variations by edge dent. It is shown that the density of defects has a strong influence on the penetration and trajectories of vortices and we correlate them with traces of magnetization and Gibbs free energy density. We further demonstrate that these traces can be used in an artificial neural network (ANN) model to enable efficient and accurate characterization of defects density and achieved a reduced characterization error of 6.96% and 7.6% for superconducting films without and with edge dent. This work will provide new insights into the understanding of superconducting vortex dynamics, and into the implementation of deep learning to accelerate superconducting material characterization and development.

Weak-very weak uniqueness to the time-dependent Ginzburg–Landau model for superconductivity in [formula omitted

In this paper, we consider the n(n≥3) dimensional time-dependent Ginzburg–Landau model for superconductivity. First, we obtain a global existence of very weak solutions. Finally we prove a result of weak-very weak uniqueness.

Designing high-performance superconductors with nanoparticle inclusions: Comparisons to strong pinning theory

One of the most promising routes for achieving high critical currents in superconductors is to incorporate dispersed, non-superconducting nanoparticles to control the dissipative motion of vortices. However, these inclusions reduce the overall superconducting volume and can strain the interlaying superconducting matrix, which can detrimentally reduce Tc. Consequently, an optimal balance must be achieved between the nanoparticle density np and size d. Determining this balance requires garnering a better understanding of vortex–nanoparticle interactions, described by strong pinning theory. Here, we map the dependence of the critical current on nanoparticle size and density in (Y0.77, Gd0.23)Ba2Cu3O7−δ films in magnetic fields of up to 35 T and compare the trends to recent results from time-dependent Ginzburg–Landau simulations. We identify consistency between the field-dependent critical current Jc(B) and expectations from strong pinning theory. Specifically, we find that Jc ∝ B−α, where α decreases from 0.66 to 0.2 with increasing density of nanoparticles and increases roughly linearly with nanoparticle size d/ξ (normalized to the coherence length). At high fields, the critical current decays faster (∼B−1), suggesting that each nanoparticle has captured a vortex. When nanoparticles capture more than one vortex, a small, high-field peak is expected in Jc(B). Due to a spread in defect sizes, this novel peak effect remains unresolved here. Finally, we reveal that the dependence of the vortex creep rate S on nanoparticle size and density roughly mirrors that of α, and we compare our results to low-T nonlinearities in S(T) that are predicted by strong pinning theory.

Vortex domain configuration for energy-storage ferroelectric ceramics design: A phase-field simulation

The utilization of ferroelectrics in forms of ceramics, films, and composites toward energy-storage applications is of great interest recent years. However, the simultaneous achievement of high polarization, high breakdown strength, low energy loss, and weakly nonlinear polarization–electric field (P–E) correlation has been a huge challenge, which impedes progress in energy storage performance. In this work, a vortex domain engineering constructed via the core–shell structure in ferroelectric ceramics is proposed. The formation and the switching characteristics of vortex domains (VDs) were validated through a phase-field simulation based on the time-dependent Ginzburg–Landau kinetic equation. Benefiting from the smaller depth of a potential well in the energy profiles, the switching of VDs was much easier than that of conventional large-sized domains, which was found to be the origin of the lower coercive field, lower remanent polarization, and weaker nonlinear P–E correlation. Choosing BaTiO3 (BT) as a representative of ferroelectric ceramics, the shell fractions and permittivity values were varied in our phase-field simulation to optimize the energy storage performance. As a result, a large discharge energy of 6.5 J/cm3 was obtained in BT ferroelectric ceramics with a shell fraction of 5% and a shell permittivity of 20 under the applied electric field of 100 kV/mm, which is almost 140% higher than that with no shell structure. In general, the vortex domain engineering proposed in this work can serve as a universal method in designing high-performance ferroelectrics with simultaneous high breakdown strength, high discharge energy density, and high energy efficiency.

Stress effect on the electrocaloric properties of PbTiO3 nanocylinders with the consideration of surface polarization

The refrigeration technology of electronic devices has faced severe challenges with the increasing demand for miniaturization and high frequency, and the research on the electrocaloric effect (ECE) of ferroelectric nanomaterials has made it possible to solve such problems. Due to the symmetry breaking on surfaces of a ferroelectric crystal, the polarizations on surfaces are different from those inside the crystal, which can significantly affect the electrocaloric properties of the materials. In addition, considering the electromechanical coupling between the spontaneous polarization and stress field, the applied stress has a drastic influence on the ECE of the material. In this paper, the extrapolation length is incorporated in the phase-field method based on the time-dependent Ginzburg–Landau equation to investigate the effects of different stress and surface polarization on the ECE of PbTiO3 (PTO) nanocylinders. The stress–adiabatic temperature change (ATC) curves with different extrapolation lengths are obtained through the simulations, which reveal the effect of extrapolation length and stress on the PTO nanocylinders. The results of this paper can provide theoretical guidance for the design of next-generation solid-state cooling devices.

Manipulation of vortex arrays with thermal gradients by applying dynamic heat sources

In this paper, we investigate the manipulation of vortex arrays of magnetic flux by using dynamic heat sources in the superconducting strip. The time-dependent Ginzburg–Landau (TDGL) equations and the heat diffusion equation are numerically solved to study the effect of the dynamic heat sources and the vortex dynamics of the sample. Three distinct velocity ranges were shown to occur, depending on the vortex motion and the corresponding characteristics of the induced voltage. Due to the relationship among the driving force, viscous force, and vortex–vortex interaction, the vortex motion changes from direct motion to a roughly harmonic motion with the velocity of the heat source. Meanwhile, the electromagnetic performance of the sample is also related to the heat source parameters, the applied magnetic fields and the pinning centers. In addition, the thermal effect leads to a more complex non-linear relationship between the induced voltage and the heat source velocity.

Possible Alterations of Local Gravitational Field Inside a Superconductor.

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high– and classical low– superconductors with respect to the gravity/superfluid interplay.

Dynamics of Composite Domain Walls in Multiferroics in Magnetic Field and Their Instability

We study theoretically the dynamics of composite domain walls (DW) in multiferroic material GdFeO3 driven by magnetic field H. Two antiferromagnetic orders of Fe and Gd spins and Gd-ion displacement interact with each other in this system with coupling c at low temperatures. We have numerically simulated the corresponding time-dependent Ginzburg–Landau equations in which magnetic field H couples to Fe-spin order parameter. We vary H and c systematically and calculate velocity v and the internal structure in a stationary state for magnetic DW and magneto-electric DW. DW mobility v/H increases with H and decreases with c for both DWs, but their characteristics differ between the two. We have also analytically studied the smooth characteristics of magneto-electric DW by a perturbation theory. Another finding is a splitting instability at a large H. A magneto-electric DW splits into a pair of magnetic DW and electric DW when c is large, while a magnetic DW splits when c is small. The internal structure of composite DW deforms with increasing c and H, and modulations in different order parameters separate in space. Their relative distances show a noticeable enhancement with approaching the splitting instability.

Obtaining Underlying Parameters from Magnetic Domain Patterns with Machine Learning

The question of how to understand the underlying mechanisms of complicated spatiotemporal patterns formed in various physical, chemical, and biological systems is still and open issue. Here, we give a successful example using the machine learning methods of a convolutional neural network (CNN) and a kernel ridge regression (KRR). By using these methods, we could quantitively identify an underlying parameter, the anisotropy coefficient α, from images of magnetic domain patterns formed in ferromagnetic thin films. We demonstrated that models based on both machine learning methods successfully identify α, with a mean absolute error of less than 0.077, from data synthesized with the time-dependent Ginzburg–Landau (TDGL) equation. Further, we showed that the CNN model outperformed the KRR model, but the KRR model provided significant pattern features for representing α more interpretably than the CNN could. Our results provide new insights into pattern analysis of magnetic materials from a machine learning viewpoint.

Supercurrent Induced by Chiral Coupling in Multiferroic/Superconductor Nanostructures.

We study the transport and the superconducting dynamics in a layer of type II superconductor (SC) with a normal top layer that hosts a helical magnetic ordering that gives rise to spin-current-driven ferroelectric polarization. Proximity effects akin to this heterostructure result in an anisotropic supercurrent transport and modify the dynamic properties of vortices in the SC. The vortices can be acted upon and controlled by electric gating or other means that couple to the spin ordering in the top layer, which, in turn, alter the superconducting/helical magnet coupling characteristics. We demonstrate, using the time dependent Ginzburg–Landau approach, how the spin helicity of the top layer can be utilized for pinning and guiding the vortices in the superconducting layer.