Depinning Model Research Articles

Criticality in the fracture of silica glass: Insights from molecular mechanics.

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

Results and Conjectures on a Toy Model of Depinning

We review recent results and conjectures for a simplified version of the depinning problem in presence of disorder which was introduced by Derrida and Retaux in 2014. For this toy model, the depinning transition has been predicted to be of the Berezinskii--Kosterlitz--Thouless type. Here we discuss under which integrability conditions this prediction can be proved and how it is modified otherwise.

The Role of Substrate Roughness in Superfluid Film Flow Velocity

It is known that the apparent film flow rate $j_0$ of superfluid $^4$He increases significantly when the container wall is contaminated by a thin layer of solid air. However, its microscopic mechanism has not yet been clarified enough. We have measured $j_0$ under largely different conditions for the container wall in terms of surface area (0.77-6.15 m$^2$) and surface morphology using silver fine powders (particle size: $0.10$ \mu m) and porous glass (pore size: 0.5, 1 \mu m). We could increase $j_0$ by more than two orders of magnitude compared to non-treated smooth glass walls, where liquid helium flows down from the bottom of container as a continuous stream rather than discrete drips. By modeling the surface morphology, we estimated the effective perimeter of container $L_{\mathrm{eff}}$ and calculated the flow rate $j~(= j_0L_0/L_{\mathrm{eff}})$, where $L_0$ is the apparent perimeter without considering the microscopic surface structures. The resultant $j$ values for the various containers are constant each other within a factor of four, suggesting that the enhancement of $L_{\mathrm{eff}}$ plays a major role to change $j_0$ to such a huge extent and that the superfluid critical velocity, $v_{\mathrm{c}}$, does not change appreciably. The measured temperature dependence of $j$ revealed that $v_{\mathrm{c}}$ values in our experiments are determined by the vortex depinning model of Schwarz (Phys. Rev. B $\textbf{31}$, 5782 (1986)) with several nm size pinning sites.

Imaging in-plane 90° magnetization switching in a (Ga,Mn)As epitaxial layer

The dynamics associated with in-plane, 90° magnetization switching in a (Ga,Mn)As epitaxial layer is studied on the basis of images obtained using a home-made magneto-optical microscope. A small contrast between two different 90° domains caused by magnetic birefringence (MB) is enhanced by digital image processing. Two consecutive 90° switchings are captured clearly in temperature regimes below and above the half-value of the Curie temperature. The dynamics is not the same for the first and the second switching, presumably reflecting the influence of the ⟨110⟩ uniaxial anisotropy and spin-dependent pinning sites. In particular, in the low-temperature regime, the first switching that passes via the relatively easy uniaxial (REU) axis (the [1–10] axis) is dominated by smooth 90° domain wall (DW) motion, whereas the second switching that passes via the relatively hard uniaxial (RHU) axis (the [110] axis) occurs through nucleation and coalescence of 90° domains together with the DW motion. In the high-temperature regime, the first switching via the REU axis is initiated by nucleations and their rapid expansion, whereas the second switching via the RHU axis is dominated by relatively slow DW motion. DW velocity is extracted from MB images and analyzed on the basis of thermally activated depinning and flow models. The values of two key parameters, namely, the activation volume and DW mobility, are deduced and compared with values from the literature. They are (28 nm)3 and 0.35 nm s−1 Oe at 10 K, respectively.

Joule heating and temperature effects on current-induced magnetization switching in perpendicularly magnetized Pt/Co/C structures

We study the temperature (T) dependence of the anisotropy field (Hk), switching field (Hsw), saturation magnetization (Ms), spin–orbit torques (SOTs), and critical switching current density (Jc) as well as Joule heating effect in the current-induced magnetization switching using Pt/Co/C stacks with perpendicular magnetic anisotropy. The results show that Hk remains roughly constant and Jc gradually decreases as T increases. The increased damping-like-SOT-induced effective field per unit current density (ΔHDL/Je) with T increasing reveals the enhanced SOT efficiency at higher T. However, the calculated ΔHDL at Jc is still a relatively small magnitude and cannot overcome the large Hk. In contrast, a significantly reduced Hsw was observed with the current or T increasing. It indicates that the magnetization switching is dominated by a depinning model. Only when the out-of-plane component of the ΔHDL overcomes Hsw, the magnetization realizes a full reversal. Especially, both ΔHDL and Hsw codetermine Jc. Meanwhile, T or current-generated Joule heating plays an assisted role in the switching by increasing SOT efficiency and decreasing Hsw. Moreover, our results also show that the enhanced ΔHDL/Je at higher T is determined by the reduced Ms and the spin Hall angle keeps invariable at different T. These findings could provide a new perspective towards improving the switching efficiency in SOT-based spintronic devices.

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

We have proposed and developed a microscopic model of depinning (escape) of a multiquantum vortex in a superconductor with a cylindrical nonconducting cavity with the transverse size smaller than or on the order of the superconducting coherence length ξ0 at zero temperature. The spectrum of subgap quasiparticle excitations in two- and three-quantum vortices trapped by a cylindrical cavity has been calculated in the quasiclassical approximation. It is shown that the transformation of the spectrum is accompanied by break of anomalous spectral branches due to normal reflection of quasiparticles from the surface of a defect. A microscopic (spectral) criterion for multiquantum vortex pinning has been proposed; according to this criterion, the multiquantum vortex can be trapped in the cavity during the formation of a minigap in the elementary excitation spectrum near the Fermi level. Self-consistent calculations of density of states N(r, e) for two- and three-quantum vortices trapped by a cylindrical cavity of radius on the order of ξ0 have been performed using quasiclassical Eilenberger equations. In the pure limit and for low temperatures T ≪ T c , peculiarities observed in the N(r, e) distribution reflect the presence of M anomalous spectral branches in the M-quantum vortex and confirm the correctness of the spectral criterion of pinning (depinning) of a multiquantum vortex.

Universal features of amorphous plasticity

Plastic yielding of amorphous solids occurs by power-law distributed deformation avalanches whose universality is still debated. Experiments and molecular dynamics simulations are hampered by limited statistical samples, and although existing stochastic models give precise exponents, they require strong assumptions about fixed deformation directions, at odds with the statistical isotropy of amorphous materials. Here, we introduce a fully tensorial, stochastic mesoscale model for amorphous plasticity that links the statistical physics of plastic yielding to engineering mechanics. It captures the complex shear patterning observed for a wide variety of deformation modes, as well as the avalanche dynamics of plastic flow. Avalanches are described by universal size exponents and scaling functions, avalanche shapes, and local stability distributions, independent of system dimensionality, boundary and loading conditions, and stress state. Our predictions consistently differ from those of mean-field depinning models, providing evidence that plastic yielding is a distinct type of critical phenomenon.

Shearing a glass and the role of pinning delay in models of interface depinning.

When a disordered solid is sheared, yielding is followed by the onset of intermittent response that is characterized by slip in local regions usually labeled shear-transformation zones. Such intermittent response resembles the behavior of earthquakes or contact depinning, where a well-defined landscape of pinning disorder prohibits the deformation of an elastic medium. Nevertheless, a disordered solid is evidently different in that pinning barriers of particles are due to neighbors that are also subject to motion. Microscopic yielding leads to destruction of the local microstructure and local heating. It is natural to assume that locally a liquid emerges for a finite timescale before cooling down to a transformed configuration. For including this characteristic transient in glass depinning models, we propose a general mechanism that involves a "pinning delay" time T(pd), during which each region that slipped evolves as a fluid. The new timescale can be as small as a single avalanche time step. This is a local, effective, and dynamical in nature mechanism that may be thought as dynamical softening. We demonstrate that the inclusion of this mechanism causes a drift of the critical exponents toward higher values for the slip sizes τ, until a transition to permanent shear-banding behavior happens causing almost oscillatory, stick-slip response. Moreover, it leads to a proliferation of large events that are highly inhomogeneous and resemble sharp slip band formation.

Influence of magnetization on field quality in cosine-theta and block design dipole magnets wound with coated conductors

We carried out electromagnetic field analyses on the cross sections of two dipole magnets wound with coated conductors. One was a cosine-theta magnet, and the other was a block design magnet. The electric field–current density characteristics of the coated conductors were formulated using a percolation depinning model based on the measured voltage–current characteristics. We calculated the temporal evolutions of the current-density distributions in all the turns of each magnet and used these evolutions to calculate the multipole components of the magnetic field. We compared the two magnets, which differed in coated-conductor orientations, regarding the influence of coated-conductor magnetization on the field qualities.

Thickness dependence of voltage-driven magnetization switching in FeCo/PI/piezoelectric actuator heterostructures

Strain mediated magnetization switching of ferromagnetic/substrate/piezoelectric actuator heterostructures has become a hot issue due to the advantage of low-power consumption. In this work, Fe65Co35 thin films were deposited on a flexible polyamides (PI) substrate, which has quite low Young’s module (~4 GPa for PI as compared to ~180 GPa for Si) and benefits from complete transfer of the strain from the piezoelectric actuator to magnetic thin films. A complete 90° transition of the magnetic easy axis was realized in 50 nm thick FeCo films under the voltage of 70 V, while a less than 90° rotation angle of the magnetic easy axis direction was observed in other samples, which was ascribed to the distribution of the anisotropy field and/or the orthogonal misalignment between stress induced anisotropy and original uniaxial anisotropy. A model considering two uniaxial anisotropies with orthogonal arrangement was used to quantitatively understand the observed results and the linear-like voltage dependent anisotropy field, especially for 10 nm FeCo films, in which the switching mechanism along the easy axis direction can be explained by the domain wall depinning model. It indicates that the magnetic domain-wall movement velocity may be controlled by strain through tuning the energy barrier of the pinning in heterostructures. Moreover, voltage-driven 90° magnetization switching with low-power consumption was achieved in this work.

Mixed order transition and condensation in an exactly soluble one dimensional spin model

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [], an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to form a bridge between two classes of 1D models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper, we elaborate on the calculations performed in []. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins and also consider a broader class of interactions that decay with distance using a power law different from 2.

Cracks in random brittle solids:

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.

Experimental and numerical investigation of screening currents induced in a Bi-2223/Ag double pancake coil for space applications

We modelled the screening currents (Is) induced in high-temperature superconducting (HTS) coils to develop a method for the characterization and design of HTS magnets for space applications. The analysis made use of so-called percolation depinning and flux creep models to describe the current density versus the electric field in HTS tapes. We compared the model results with the experimental data obtained from a Bi-2223/Ag double pancake coil. The experimental residual magnetization due to the Is in the Bi-2223/Ag coil can be effectively modelled, assuming an equivalent loop length of approximately 9 mm for the Is in the coil. The values calculated from the method quantitatively agreed with the results for various experimental conditions. We also successfully modelled the hysteresis of the magnetization due to the Is. These results demonstrate the validity of our model for the Is, which considers the effects of flux creep and smaller Is loops in the multi-filamentary Bi-2223/Ag tape.

P-doping-free III-nitride high electron mobility light-emitting diodes and transistors

We report that a simple metal-AlGaN/GaN Schottky diode is capable of producing GaN band-edge ultraviolet emission at 3.4 eV at a small forward bias larger than ∼2 V at room temperature. Based on the surface states distribution of AlGaN, a mature impact-ionization-induced Fermi-level de-pinning model is proposed to explain the underlying mechanism of the electroluminescence (EL) process. By experimenting with different Schottky metals, Ni/Au and Pt/Au, we demonstrated that this EL phenomenon is a “universal” property of metal-AlGaN/GaN Schottky diodes. Since this light-emitting Schottky diode shares the same active structure and fabrication processes as the AlGaN/GaN high electron mobility transistors, straight-forward and seamless integration of photonic and electronic functional devices has been demonstrated on doping-free III-nitride heterostructures. Using a semitransparent Schottky drain electrode, an AlGaN/GaN high electron mobility light-emitting transistor is demonstrated.

Numerical Investigation on Thermal Stability of Conduction-Cooled Bi-2223/Ag Coil Under AC Ripple Current for Space Applications

This study investigated the transport ac loss in a high-temperature superconducting (HTS) coil under ac ripple currents with dc offsets for space applications of the HTS coil. We developed an analysis method to evaluate the effective ac loss in the HTS coil on the basis of the percolation depinning model. Our analysis clarified that larger dc offsets greatly increase the effective ac loss even under a smaller ac current. In addition, we investigated the effect of the ac loss with the ripple current on the thermal behavior of a conduction-cooled Bi-2223/Ag coil. As a result, the ac loss decreased the thermal stability of the conduction-cooled coil in case that HTS tapes in the coil are in the flux-flow state such as the load factor of 80%. However, at a lower load factor such as less than 60%, the ripple current did not have much effect on the thermal stability of the conduction-cooled coil because most of the ac power were consumed as a reactive power. These results suggested that, in order to apply the ac ripple current to HTS coils, the operational load factor must be properly selected. This study leads to a design of the light-weight HTS coil system for space missions.

Role of the sample thickness in planar crack propagation

We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.

Coupled-analysis of current transport performance and thermal behaviour of conduction-cooled Bi-2223/Ag double-pancake coil for magnetic sail spacecraft

This paper investigated the quantitative current transport performance and thermal behaviour of a high temperature superconducting (HTS) coil, and the effect of the critical current inhomogeneity along the longitudinal direction of HTS tapes on the coil performances. We fabricated a double-pancake coil using a Bi-2223/Ag tape with a length of 200m as a scale-down model for a magnetic sail spacecraft. We measured the current transport property and temperature rises during current applications of the HTS coil in a conduction-cooled system, and analytically reproduced the results on the basis of the percolation depinning model and three-dimensional heat balance equation. The percolation depinning model can describe the electric field versus current density of HTS tapes as a function of temperature and magnetic field vector, and we also introduced the longitudinal distribution of the local critical current of the HTS tape into this model. As a result, we can estimate the critical currents of the HTS coil within 10% error for a wide range of the operational temperatures from 45 to 80K, and temperature rises on the coil during current applications. These results showed that our analysis and conduction-cooled system were successfully realized. The analysis also suggested that the critical current inhomogeneity along the length of the HTS tape deteriorated the current transport performance and thermal stability of the HTS coil. The present study contributes to the characterization of HTS coils and design of a coil system for the magnetic sail spacecraft.

Quantum dynamics of vortices in mesoscopic magnetic disks

Model of quantum depinning of magnetic vortex cores from line defects in a disk geometry and under the application of an in-plane magnetic field has been developed within the framework of the Caldeira-Leggett theory. The corresponding instanton solutions are computed for several values of the magnetic field. Expressions for the crossover temperature Tc and for the depinning rate \Gamma(T) are obtained. Fitting of the theory parameters to experimental data is also presented.

Size effects in dislocation depinning models for plastic yield

Typically, the plastic yield stress of a sample is determined from a stress–strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale samples measured this way should display the correct finite size scaling. Here we study plastic yield as a depinning transition of a 1 + 1 dimensional interface, and consider how finite size effects depend on the choice of yield strain, as well as the presence of hardening and the strength of elastic coupling. Our results indicate the existence of a crossover length that depends on the yield strain. It is only above this length scale that standard finite size scaling is expected to hold. These results are also expected to be particularly relevant for simulations of single dislocations, such as those used to study strengthening due to included particles.

Determination of the universality class of crystal plasticity

Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to accurately measure scaling exponents and functions. Here we present comprehensive simulations of two-dimensional dislocation dynamics under shear, using finite-size scaling to extract scaling exponents and the avalanche profile scaling function from time-resolved measurements of slip avalanches. Our results provide compelling evidence that both the static and dynamic universality classes are consistent with the mean-field interface depinning model.