Periodic Pinning Arrays Research Articles

Nonequilibrium phases and segregation for skyrmions on periodic pinning arrays

Using particle-based simulations, we examine the collective dynamics of skyrmions interacting with periodic pinning arrays, focusing on the impact of the Magnus force on the sliding phases. As a function of increasing pinning strength, we find a series of distinct dynamical phases, including an interstitial flow phase, a moving disordered state, a moving crystal, and a segregated cluster state. The transitions between these states produce signatures in the skyrmion lattice structure, the skyrmion Hall angle, the velocity fluctuation distributions, and the velocity-force curves. The moving clustered state is similar to the segregated state recently observed in continuum-based simulations with strong quenched disorder. The segregation arises from the drive dependence of the skyrmion Hall angle, and appears in the strong pinning limit when the skyrmions have nonuniform velocities, causing different portions of the sample to have different effective skyrmion Hall angles. We map the evolution of the dynamic phases as a function of the system density, the ratio of the Magnus force to the dissipative term, and the ratio of the number of skyrmions to the number of pinning sites.

Transverse vortex commensurability effect and sign change of the Hall voltage in superconducting YBa2Cu3O7−δ thin films with a nanoscale periodic pinning landscape

The transverse (Hall) voltage in thin films of the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ with an artificial periodic pinning array is investigated. Columnar defect regions along the crystallographic $c$ axis, in which superconductivity is suppressed, are created by irradiation with He$^+$ ions through a silicon stencil mask. The commensurate arrangement of magnetic flux quanta with the artificial defect lattice is confirmed by maxima of the critical current and minima of the resistance, respectively. The magnetic field dependence of the transverse voltage reveals a commensurability effect characterized by a narrow peak of the Hall coefficient with reversed polarity compared to the background signal. This signature of vortex matching disappears at larger vortex velocities substantiating its close connection with enhanced pinning of vortices at the periodic pinning landscape.

Manipulation of individual superconducting vortices and stick-slip motion in periodic pinning arrays

We numerically examine the manipulation of vortices interacting with a moving trap representing a magnetic force tip translating across a superconducting sample containing a periodic array of pinning sites. As a function of the tip velocity and coupling strength, we find five distinct dynamic phases, including a decoupled regime where the vortices are dragged a short distance within a pinning site, an intermediate coupling regime where vortices in neighboring pinning sites exchange places, an intermediate trapping regime where individual vortices are dragged longer distances and exchange modes of vortices occur in the surrounding pins, an intermittent multiple trapping regime where the trap switches between capturing one or two vortices, and a strong couping regime in which the trap permanently captures and drags two vortices. In some regimes we observe the counterintuitive behavior that slow moving traps couple less strongly to vortices than faster moving traps; however, the fastest moving traps are generally decoupled. The different phases can be characterized by the distances the vortices are displaced and the force fluctuations exerted on the trap. We find different types of stick-slip motion depending on whether vortices are moving into and out of pinning sites, undergoing exchange, or performing correlated motion induced by vortices outside of the trap. Our results are general to the manipulation of other types of particle-based systems interacting with periodic trap arrays, such as colloidal particles or certain types of frictional systems.

Onset, evolution, and magnetic braking of vortex lattice instabilities in nanostructured superconducting films

In 1976 Larkin and Ovchinnikov [Sov. Phys. JETP 41, 960 (1976)] predicted that vortex matter in superconductors driven by an electrical current can undergo an abrupt dynamic transition from a flux-flow regime to a more dissipative state at sufficiently high vortex velocities. Typically this transition manifests itself as a large voltage jump at a particular current density, so-called instability current density $J^*$, which is smaller than the depairing current. By tuning the effective pinning strength in Al films, using an artificial periodic pinning array of triangular holes, we show that a unique and well defined instability current density exists if the pinning is strong, whereas a series of multiple voltage transitions appear in the relatively weaker pinning regime. This behavior is consistent with time-dependent Ginzburg-Landau simulations, where the multiple-step transition can be unambiguously attributed to the progressive development of vortex chains and subsequently phase-slip lines. In addition, we explore experimentally the magnetic braking effects, caused by a thick Cu layer deposited on top of the superconductor, on the instabilities and the vortex ratchet effect

Interference mode-locking of 2D magnetized colloids driven by dc and ac forces in periodic pinning arrays

Using the Langevin simulation, we investigate the interference mode-locking of two-dimensional (2D) magnetized colloids on a substrate with periodic pinning centers. The colloidal particles are prepared initially in a 2D crystalline state and then driven simultaneously by direct-current (dc) and alternating-current (ac) forces. In the presence of a superimposed ac force, we find pronounced mode-locking steps in the characteristics of the averaged velocity versus dc force within a certain range of amplitude and frequency of the ac force. The mode-locking steps are attributed to an interference effect between the ac force and the modulation generated by the coherent motion of colloidal particles in a weak pinning potential. The step width Δfdc is found to oscillate in a Bessel function-like form with the amplitude of the ac force, in good agreement with previous results of vortex lattices. But, we find that Δfdc changes in an inverted parabola form with the frequency of the ac force and the substrate pinning strength as well as the interaction strength between colloidal particles. The averaged velocity at the step vstep is shown to increase linearly with the frequency of the ac force and the interaction strength between colloidal particles. The obtained results are helpful for fractionation of mesoscopic particles.

WITHDRAWN: Strong fractional field-matching effects in YBa2Cu3O7−δ films with nanoscale periodic pinning arrays

WITHDRAWN: Strong fractional field-matching effects in YBa2Cu3O7−δ films with nanoscale periodic pinning arrays

Statics and Dynamics of Vortex Matter with Competing Repulsive and Attractive Interactions

We numerically examine vortex matter with repulsive interactions at short range and attractive interactions at long range in the presence of periodic pinning arrays. Such competing vortex interactions are predicted to occur in multiband superconductors or type-I and type-II hybrid materials. For weak pinning, the vortices form cluster states, while for strong pinning, the vortices form uniform states in which flux is evenly distributed among the pinning sites. As a function of external drive, the weak pinning system exhibits clump depinning with no structure changes, while the strong pinning system depins into a disordered fluctuating state followed by a transition to a partially aligned stripe state. For weak pinning, there is a single peak in the differential conductivity, while for strong pinning there are two peaks, indicating that transport curves could be used to distinguish between vortex systems with purely repulsive interactions and those with additional long range attractive interactions.

Vortex dynamics and matching effect in superconductors with planar pinning arrays

We have studied the dynamics of vortices interacting with periodic planar pinning arrays using molecular dynamics simulation. We consider three types of periodic pinning arrays consisting of long (L) and short (S) pinning intervals. Current–voltage curves and critical currents have been calculated as a function of vortex density for each pinning array model. Compared to the model with equally spaced pinning array, the models in which L/S is 2 show higher critical currents in certain vortex density range. This behavior comes from the appearance of broad matching peaks in the presence of planar pinning arrays. Meanwhile, in the models in which L/S is 1.618, the appearances of some of the matching peaks are suppressed because of the mismatch between the pinning interval and the vortex lattice constant. Thus, compared to the equally spaced model, the critical currents in this model are low in wide ranges of vortex density. On the basis of these results, we have discussed the matching effect in the presence of periodic arrays of planar pinning.

Artificial vortex pinning arrays in superconducting films deposited on highly ordered anodic alumina templates

A simple procedure is described for creating periodic vortex pinning centers in thin superconducting NbN films. We report on three different strategies which involve the use of highly ordered alumina templates. In this approach, NbN thin films are deposited either on the porous face of the template made of a triangular array of nanoholes or on the triangular array of bumps formed by the barrier layer or even on the top of perpendicularly oriented ferromagnetic nanowire arrays obtained by electrochemical deposition, thus forming superconductor–ferromagnet hybrids. In all cases, the ordered template allows NbN films to form a periodic pinning array during its growth. The interpore (or inter-bump) distance ranged between 50 and 100 nm and adjustable pore (or wire) diameter was varied between 30 and 60 nm. Numerous matching effects have been observed up to 2.5 T and are maintained at low temperature. These fields are considerably higher than those typical for periodic pinning arrays made by lithographic techniques, which reflects the benefits of nanostructuring superconductors by using self-organized growth to enhance vortex pinning in a large field and temperature range.

The Effects of Pinning on Critical Currents of Superconducting Films

Using molecular dynamics simulations, we analyze the effects of artificial periodic arrays of pinning sites on the critical current of superconducting thin films as a function of vortex density. We analyze two types of periodic pinning array: hexagonal and Kagomé. For the Kagome pinning network we make calculations using two directions of transport current: along and perpendicular to the main axis of the lattice. Our results show that the hexagonal pinning array presents higher critical currents than the Kagomé and random pinning configuration for all vortex densities. In addition, the Kagomé networks show anisotropy in their transport properties.

Vortex dynamics and symmetry locking on quasiperiodic and periodic substrates

We examine the dynamics of vortices driven over quasicrystalline and periodic pinning arrays where the direction of the external drive is varied with respect to the substrate orientation. For periodic arrays there is a strong directional locking and the vortex motion can lock to symmetry directions of the pinning lattice even when the drive is not applied along the same symmetry direction. This locking can be detected as a series of steps in the velocity vs driving angle curves and is also associated with dynamical ordering of the vortices along these steps into anisotropic square and triangular lattices. Even though quasicrystalline arrays lack translational order, we show that quasicrystalline substrates also exhibit symmetry locking due to their orientational ordering. The vortex configurations in the nonlocking regimes are much more disordered for the quasiperiodic substrates than for the periodic substrates.

Transport current carrying superconducting film with periodic pinning array under strong magnetic fields

The transport current carrying dissipative (flux flow) and dissipationless (pinned) vortex configurations and their dynamics are investigated numerically in the framework of the time-dependent Ginzburg-Landau approach. Assuming that magnetic induction is nearly uniform, the model is generalized to include strong inhomogeneous electric fields. Hexagonal array nanoholes of the size of coherence length and density ${n}_{\text{pin}}$ was considered for various filling factors [defined as $f=B/({\ensuremath{\Phi}}_{0}{n}_{\text{pin}})$]. The vortex depinning is closely associated with the appearance of a strongly varying electric field. For the matching field, $f=1$, the critical current is maximal and the transition to the resistive state occurs as a coherent depinning of the entire vortex lattice. For a system with interstitial vortices, $fg1$, the mechanism of depinning depends on the current direction with respect to the pinning array. There are two qualitatively distinct geometries: the obstacle and channel geometries. In the obstacle geometry lines of interstitial vortices are blocked by strongly pinned vortices, while in the channel geometry the lines move unimpeded confined in channels. It was found that slightly above the critical current the trajectories of the moving vortices are not straight, but rather acquire a snakelike shape enveloping the system of pins. In contrast to $ f=1$, the transition to a resistive state is not coherent and is going through formation of ``snakelike'' vortex trajectories. The critical current in the obstacle geometry is significantly larger than in the channel one.

Suppression of dissipation in Nb thin films with triangular antidot arrays by random removal of pinning sites

The depinning current ${I}_{c}$ versus applied magnetic field $B$ close to the transition temperature ${T}_{c}$ of Nb thin films with randomly diluted triangular arrays of antidots is investigated. Our experiments confirm essential features in ${I}_{c}(B)$ as predicted by Reichhardt and Olson Reichhardt [Phys. Rev. B 76, 094512 (2007)]. We show that, by introducing disorder into periodic pinning arrays, ${I}_{c}$ can be enhanced. In particular, for arrays with fixed density ${n}_{p}$ of antidots, an increase in dilution ${P}_{d}$ induces an increase in ${I}_{c}$ and decrease of the flux-flow voltage for $B>{B}_{p}={n}_{p}{\ensuremath{\Phi}}_{0}$.

Transport anisotropy as a probe of the interstitial vortex state in superconductors with artificial pinning arrays

We show using simulations that when interstitial vortices are present in superconductors with periodic pinning arrays, the transport in two perpendicular directions can be anisotropic. The degree of the anisotropy varies as a function of field due to the fact that the interstitial vortex lattice has distinct orderings at different matching fields. The anisotropy is most pronounced at the matching fields but persists at incommensurate fields, and it is most prominent for triangular, honeycomb, and kagome pinning arrays. Square pinning arrays can also show anisotropic transport at certain fields in spite of the fact that the perpendicular directions of the square pinning array are identical. We show that the anisotropy results from distinct vortex dynamical states and that although the critical depinning force may be lower in one direction, the vortex velocity above depinning may also be lower in the same direction for ranges of external drives where both directions are depinned. For honeycomb and kagome pinning arrays, the anisotropy can show multiple reversals as a function of field. We argue that when the pinning sites can be multiply occupied such that no interstitial vortices are present, the anisotropy is strongly reduced or absent.

Transverse commensurability effect for vortices in periodic pinning arrays

Using computer simulations, we demonstrate a type of commensurability that occurs for vortices moving longitudinally through periodic pinning arrays in the presence of an additional transverse driving force. As a function of vortex density, there is a series of broad maxima in the transverse critical depinning force that do not fall at the matching fields where the number of vortices equals an integer multiple of the number of pinning sites. The commensurability effects are associated with dynamical states in which evenly spaced structures consisting of one or more moving rows of vortices form between rows of pinning sites. Remarkably, the critical transverse depinning force can be more than an order of magnitude larger than the longitudinal depinning force.

Vortex pinning in superconductors laterally modulated by nanoscale self-assembled arrays

Being the exponent of the so-called “bottom-up” approach, self-assembled structures are now-a-days attracting a lot of attention in the fields of science and technology. In this work, we show that nanoscale self-assembled arrays used as templates can provide periodic modulation in superconducting thin films by studying their vortex pinning properties. In this work advantage was made of the fact that self-organized assemblies of identical units such as colloidal crystals and anodic aluminum oxide provide extended periodic topographic surfaces. By directly growing Nb on top of these self-assembled arrays, the templating effect was exploited in order to achieve triangular and honeycomb arrays of pinning centers in thin superconducting films. We show experimentally that periodic matching is achieved in both systems at magnetic fields, well above those present in lithographically prepared pinning arrays (up to 1T!). Furthermore, we demonstrate in the case of anodic aluminum oxide that the presence of porous antidots in Nb not only provides strongly increased critical currents but also conserves matching at temperatures well below the critical temperature. The studies conducted on these systems indicate that the method of template growth might be considered as a viable alternative for the incorporation of periodic pinning arrays in superconducting applications of today and the future.

Commensurability effects at nonmatching fields for vortices in diluted periodic pinning arrays

Using numerical simulations, we demonstrate that superconductors containing periodic pinning arrays, which have been diluted through random removal of a fraction of the pins, have pronounced commensurability effects at the same magnetic field strength as undiluted pinning arrays. The commensuration can occur at fields significantly higher than the matching field, produces much greater critical current enhancement than a random pinning arrangement due to suppression of vortex channeling, and persists for arrays with up to 90% dilution. These results suggest that diluted periodic pinning arrays may be a promising geometry to increase the critical current in superconductors over a wide magnetic field range.

Vortex pinning in superconducting Nb thin films deposited on nanoporous alumina templates

We present a study of magnetization and transport properties of superconducting Nb thin films deposited on nanoporous aluminium oxide templates. Periodic oscillations in the critical temperature vs. field, matching effects in fields up to 700 mT and strongly enhanced critical currents were observed. These fields are considerably higher than those typical for periodic pinning arrays made by lithographic techniques, which reflects the benefits of nanostructuring superconductors by using self-organized growth. This method provides a periodic pinning potential with sub-100 nm spacing between the pinning centers, which enhances vortex pinning in broad field and temperature ranges.

Nonuniform Self-Organized Dynamical States in Superconductors with Periodic Pinning

We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized (both stationary and nonstationary) two-dimensional dynamical structures.

Vortex lattices in different configurations of periodic pinning line-arrays

The vortex lattice (VL) ground-state configurations are found using Monte Carlo (MC) simulated annealing with a local molecular dynamics (MD) in the London limit. We study the field dependence of the melting temperature for commensurate and incommensurate vortex lattices interacting with different periodic arrays of pinning. We also investigated the proliferation of topological defects and its dependence on the periodic pinning array symmetry and temperature.