Random Pinning Research Articles

Static and dynamic phases for magnetic vortex matter with attractive and repulsive interactions

Exotic vortex states with long range attraction and short range repulsion have recently been proposed to arise in certain superconducting hybrid structures such as type-I/type-II layered systems as well as multi-band superconductors. In previous work it has been shown that such systems can form clump or phase separated states, but little is known about how they behave in the presence of pinning and under an applied drive. Using large scale simulations we examine the static and dynamic properties of such vortex states interacting with random and periodic pinning. In the absence of pinning this system does not form patterns but instead undergoes complete phase separation. When pinning is present there is a transition from inhomogeneous to homogeneous vortex configurations similar to a wetting phenomenon. Under an applied drive, a dynamical dewetting process can occur from a strongly pinned homogeneous state into pattern forming states, such as moving stripes that are aligned with the direction of drive or moving labyrinth or clump phases. We show that a signature of the exotic vortex interactions observable with transport measurements is a robust double peak feature in the differential resistance curves. Our results should be valuable for determining whether such vortex interactions are occurring in these systems and also for addressing the general problem of systems with competing interactions in the presence of random and periodic pinning.

Probing a liquid to glass transition in equilibrium.

We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles have been frozen. By probing the equilibrium statistics of the overlap between independent configurations of the liquid, we find strong evidence that this random pinning induces a glass transition. At low temperatures, our numerical findings are consistent with the existence of a random first-order phase transition rounded by finite size effects.

Domain wall creep in a 2D magnetic wire in the presence of antiferromagnetic coupling

We have studied the dynamics of propagation in one dimension of a magnetic domain wall (DW) in the presence of an exchange bias field in nanowires patterned in two-dimensional ultra-thin perpendicularly magnetized ferromagnetic–antiferromagnetic (F–AF) films. The DW velocity v(H) is strongly reduced when the DW propagates against the exchange bias field, and its field dependence is consistent with a creep process with a critical exponent μ = 1/4. The increase in energy barrier responsible for the reduction of v(H) cannot be explained by the introduction of a macroscopic exchange bias field. Instead it arises from the AF–F interface that provides an extra-source of random pinning.

Variational characterization of the critical curve for pinning of random polymers

In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process [Birkner, Greven and den Hollander, Probab. Theory Related Fields 148 (2010) 403-456], we derive variational formulas for the quenched, respectively, annealed critical curve separating the two phases. These variational formulas are used to obtain a necessary and sufficient criterion, stated in terms of relative entropies, for the two critical curves to be different at a given inverse temperature, a property referred to as relevance of the disorder. This criterion in turn is used to show that the regimes of relevant and irrelevant disorder are separated by a unique inverse critical temperature. Subsequently, upper and lower bounds are derived for the inverse critical temperature, from which sufficient conditions under which it is strictly positive, respectively, finite are obtained. The former condition is believed to be necessary as well, a problem that we will address in a forthcoming paper. Random pinning has been studied extensively in the literature. The present paper opens up a window with a variational view. Our variational formulas for the quenched and the annealed critical curve are new and provide valuable insight into the nature of the phase transition. Our results on the inverse critical temperature drawn from these variational formulas are not new, but they offer an alternative approach, that is, flexible enough to be extended to other models of random polymers with disorder.

Random pinning glass transition: Hallmarks, mean-field theory and renormalization group analysis

We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three-dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.

Smectic order, pinning, and phase transition in a smectic-liquid-crystal cell with a random substrate

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.

Random pinning glass model

Glass transition, in which viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics despite tremendous research efforts in past decades. On the other hand, disordered freezing of spins in magnetic materials with decreasing temperature, the so-called "spin glass transition," is understood relatively better. A previously found similarity between some spin glass models and the structural glasses inspired development of theories of structural glasses based on the scenario of spin glass transition. This scenario, although it looks very appealing, is still far from being well established. One of the main differences between standard spin systems and molecular systems is the absence of quenched disorder and the presence of translational invariance: it often is assumed that this difference is not relevant, but this conjecture still needs to be established. The quantities, which are well-defined and characterized for spin models, are not easily calculable for molecular glasses because of the lack of quenched disorder that breaks the translational invariance in the system. Thus the characterization of the similarity between spin and the structural glass transition remains an elusive subject. In this study, we introduced a model structural glass with built-in quenched disorder that alleviates this main difference between the spin and molecular glasses, thereby helping us compare these two systems: the possibility of producing a good thermalization at rather low temperatures is one of the advantages of this model.

Jamming transition of randomly pinned systems

We consider a system of hard spheres close to jamming, where the translation invariance is broken by pinning a randomly chosen set of particles. By using two different protocols, we generate two kinds of packing at the jamming point, isostatic and hyperstatic packing. In the case where the packing is isostatic, the jamming transition is not affected by random pinning: the jamming density is only slightly reduced, a generalized isostaticity condition holds, the system is marginally rigid over the entire glass phase, and the typical structural signatures of jamming are unchanged. Besides, random pinning does not have an effect on the vibrational modes of the amorphous system, at least on the time and length scale that we are able to probe. For packing that is hyperstatic at jamming, the microscopic properties of the system are strongly affected by the random pinning; the frozen degrees of freedom introduce an excess of constraints that drive the system far from the mechanical marginality conditions and stabilize the low frequency modes of the system, shifting them to higher frequencies. The distance from the isostatic point seems to be the only relevant parameter in the system in both cases. These two cases are in contrast with the behavior of the plane waves of a crystal; the whole spectrum in this case is shifted to higher frequencies as soon as some particles are pinned.

Random pinning model with finite range correlations: Disorder relevant regime

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.

Ideal glass transitions by random pinning

We study the effect of freezing the positions of a fraction c of particles from an equilibrium configuration of a supercooled liquid at a temperature T. We show that within the random first-order transition theory pinning particles leads to an ideal glass transition for a critical fraction c=c(K)(T) even for moderate supercooling; e.g., close to the Mode-Coupling transition temperature. First we derive the phase diagram in the T-c plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for |c-c(K)(T)|→0, in particular the divergence of length and time scales, which are dominated by two zero-temperature fixed points. We also show that for c=c(K)(T) the typical distance between frozen particles is related to the static point-to-set length scale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.

Disorder-induced Majorana metal in interacting non-Abelian anyon systems

We demonstrate that a thermal metal of Majorana fermions forms in a two-dimensional system of interacting non-Abelian (Ising) anyons in the presence of moderate disorder. This bulk metallic phase arises in the $\ensuremath{\nu}=5/2$ quantum Hall state when disorder pins the anyonic quasiparticles. More generally, it naturally occurs for various proposed systems supporting Majorana fermion zero modes when disorder induces the random pinning of a finite density of vortices. This includes all two-dimensional topological superconductors in so-called symmetry class D. A distinct experimental signature of the thermal metal phase is the presence of bulk heat transport down to zero temperature.

Temperature dependence of magnetic-field angle dependent critical current density and the flux pinning in YBa2Cu3O7 thin films

The magnetic-field angle dependence of the critical current density Jc(H, θ) was measured over a wide temperature range (20–85K) in high-Jc YBa2Cu3O7 (YBCO) and DyBa2Cu3O7 (DyBCO) epitaxial films belonging to two categories. The films in the first category were prepared by thermal co-evaporation and were characterized by a high density of nanometer-sized precipitates (mostly<7nm), which act as small random (point) pins. The films in the second category were prepared by fluorine-free metalorganic deposition (FF-MOD), whose primary pinning centers were recently revealed to be dislocations (linear pins) associated with stacking faults parallel to the ab-plane. Relatively broad Jc(θ) peaks around H//ab in the shape of a stratovolcano were observed at 77–80K in the co-evaporated YBCO and DyBCO films in the first category, and the Jc(H, θ) data were scaled to be a single curve when plotted against scaled fields using an effective anisotropy parameter. However, the Jc(θ) curves became more gradual at 60–70K and the scaling behavior was broken because the radius of nano-precipitates was not sufficiently smaller than the temperature dependent Ginzburg–Landau coherence length ξ(T) at these temperatures. In contrast, sharp Jc(θ) peaks around H//ab were observed in the FF-MOD YBCO films in the second category at all temperatures in the range 20–85K. Anisotropic scaling analysis showed that the pinning was apparently due to small random pins and pins correlated with the ab-plane, and the linear pins whose radius is sufficiently smaller than ξ(T) can cause the observed Jc(H, θ). The temperature dependence of Jc due mainly to the random pinning was approximately ∼(1−T/Tc)2(1+T/Tc)2 for the FF-MOD thin films (dislocation pins), which is consistent with a simple theoretical model based on core pinning interactions. The T dependence of Jc for the co-evaporated films (nano-precipitate pins) was ∼(1−T/Tc)m (1+T/Tc)2 (m=2.1–2.6), which deviates from m=2.5 expected from the simple theoretical model because nano-precipitates are not sufficiently smaller than ξ(T) at T⩽70K.

Random pinning in glassy spin models with plaquette interactions

We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localization in a single state. At low temperatures, both models exhibit scaling behavior. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group treatments.

Flux pinning properties of correlated pinning at low temperatures in ErBCO films with inclined columnar defects

The effect of c-axis correlated pinning on the critical current density at low temperatures under high magnetic fields was investigated on the basis of the transport critical current density and irreversibility field properties of an ErBa2Cu3Oy film with inclined columnar defects. We found that the contribution of correlated pinning on Jc decreased drastically with decreasing temperature under high magnetic fields above the matching field, but still retained more than a 60% enhancement at 13 K. These effects of correlated pinning can be described using a cooperative model based on a combination of correlated and random pinning. At low temperatures, the presence of a matching field limited the flux pinning force for correlated pinning in comparison with that of random pinning, while the ratio of the maximum pinning force of the correlated pinning to the random one was proportional to the inverse of the irreversibility field. This suggests that the low efficiency of correlated pinning at low temperatures under a strong magnetic field is a result of a high irreversibility field and a low matching field. In order to improve the critical current properties at low temperatures under high magnetic fields, an increase in the matching field and/or the introduction of strong random pinning are effective.

Scaling behaviors and novel creep motion of ac-driven flux lines in type II superconductor with random point pins

We performed Langevin dynamics simulations for the ac-driven flux lines in a type II superconductor with random point-like pinning centers. Scaling properties of flux-line velocity with respect to an instantaneous driving force of small frequency and around the critical dc depinning force are revealed successfully, which provides precise estimates on dynamic critical exponents. From the scaling function, we derive a creep law associated with activation by regular shaking. The effective energy barrier vanishes at the critical dc depinning point in a square-root way when the instantaneous driving force increases. The frequency plays a similar role to temperature in conventional creep motions, but in a nontrivial way governed by the critical exponents. We have also performed systematic finite-size scaling analysis for flux-line velocity in transient processes with dc driving, which provide estimates on critical exponents in good agreement with those derived with ac driving. The scaling law is checked successfully.

Sharp critical behavior for pinning models in a random correlated environment

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e., without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion (Harris, 1974) [21].

Glassy phases and driven response of the phase-field-crystal model with random pinning

We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations, even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then, finally, a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.

Suppression of the intrinsic stochastic pinning of domain walls in magnetic nanostripes

Nanofabrication has allowed the development of new concepts such as magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls on magnetic nanostripes. One of the issues that has to be solved before devices can meet the market demands is the stochastic behaviour of the domain wall movement in magnetic nanostripes. Here we show that the stochastic nature of the domain wall motion in permalloy nanostripes can be suppressed at very low fields (0.6–2.7 Oe). We also find different field regimes for this stochastic motion that match well with the domain wall propagation modes. The highest pinning probability is found around the precessional mode and, interestingly, it does not depend on the external field in this regime. These results constitute an experimental evidence of the intrinsic nature of the stochastic pinning of domain walls in soft magnetic nanostripes.

Magnetic-field angle dependent critical current densities and flux pinning in commercial YBCO tapes below liquid nitrogen temperatures

We investigated the magnetic-field angle dependence of critical current densities (Jc) for commercial YBCO and Zr-doped (GdY)BCO tapes fabricated by an MOCVD method at temperatures from 80K down to 20K in fields (μ0H) up to 5T. For the YBCO tape it was observed that the flux pinning contribution from random pins smaller than 2ξ(T) (ξ(T) is the Ginzburg–Landau coherence length at temperature T) diminished as T decreased, while they were still important even at 20K. As the temperature went down, the peaks at H||ab were found to be increasingly sharp, which agrees well with the Tachiki–Takahashi intrinsic pinning model. The Zr-doped (GdY)BCO tape showed peaks near H||c as well as H||ab and exhibited improved in-field Jc properties, compared with the YBCO tape.

Vortex lattice dynamics in Nb films with competing intrinsic random and artificial periodicpinning

We study vortex lattice (VL) dynamics in patterned Nb films containing denseperiodic arrays of sub 50 nm magnetic nanodots or holes, by means of acsusceptibility measurements. For both types of samples, we observe matchingeffects within a wide temperature range, determined by the periodicity of thestrong artificial pinning potential. Below a crossover reduced temperaturet* = 0.75, the ac vortex mobility and matching fields are different for increasing ordecreasing fields. Low temperature field cooling experiments indicate that thehysteretic behavior is not related to different intensities of magnetic inductionB in the ac penetrated region of the samples. The fact that hysteresis appears in both patternedsamples when the intrinsic random pinning becomes stronger, together with the absence ofhysteresis in a reference unpatterned Nb film, suggests that the interplay between randomand periodic pinning, independent of its origin, induces VL metastability belowt*, which leads to the observed irreversibility.