D. Ray

Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays

Conformal crystals are non-uniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of the sixfold ordering in the conformally transformed hexagonal lattice plays a crucial role. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

We study the dynamics and velocity-force curves of a skyrmion moving over a two-dimensional periodic substrate using simulations of a particle-based skyrmion model, focusing on the role of the non-dissipative Magnus term. In the overdamped limit, the skyrmion depins into a sliding state with a Hall angle of zero. When a Magnus term is included, the Hall angle is nonzero in the absence of a substrate. On a periodic substrate, the Hall angle varies with the drive amplitude. Due to the substrate symmetry the Hall angle does not change continuously with drive, but forms a series of discrete steps at rational ratios of the skyrmion velocity components perpendicular and parallel to the drive direction, when the skyrmion motion locks to symmetry directions of the substrate for fixed intervals of the drive amplitude. On each step, the Hall angle is constant and the skyrmion motion is orderly. Transitions between locked phases generate pronounced cusps in the velocity-force curves, as well as regions of negative differential mobility. The number of observable locking steps increases when the relative strength of the Magnus term increases. We find an overshoot phenomena where the Hall angle exceeds the clean limit value, as well as an acceleration effect where the skyrmion moves faster over a substrate than through a clean sample. These effects are robust for different types of periodic substrates. With a simple model for a skyrmion interacting with a single pin, we can capture the behavior of the Hall angle. The Magnus term induces a curvature in the skrymion orbit as it moves through the pin, resulting in a side step phenomenon that decreases with increasing drive. When the Magnus term is large, the range of impact parameters that permit the skyrmion to be trapped by the pin is small, which is a reasons that strong Magnus force effects reduce the pinning in skyrmion systems.

Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates

When a particle is driven with an ac force over an asymmetric potential, it can undergo a ratchet effect that produces a net dc motion of the particle. Ratchet effects have been observed in numerous systems such as superconducting vortices on asymmetric pinning substrates. Skyrmions, stable topological spin textures with particle-like properties, have many similarities to vortices but their behavior is strongly influenced by non-disspative effects arising from a Magnus term in their equation of motion. We show using numerical simulations that pronounced ratchet effects can occur for ac driven skyrmions moving over asymmetric quasi-one-dimensional substrates. We find a new type of ratchet effect called a Magnus-induced transverse ratchet that arises when the ac driving force is applied perpendicular rather than parallel to the asymmetry direction of the substrate. This transverse ratchet effect only occurs when the Magnus term is finite, and the threshold ac amplitude needed to induce it decreases as the Magnus term becomes more prominent. Ratcheting skyrmions follow ordered orbits in which the net displacement parallel to the substrate asymmetry direction is quantized. Skyrmion ratchets represent a new ac current-based method for controlling skyrmion positions and motion for spintronic applications.

Pinning, ordering, and dynamics of vortices in conformal crystal and gradient pinning arrays

We numerically investigate magnetization, pinning, ordering, and dynamics of vortices interacting with pinning arrangements which have a density gradient. We focus on conformal crystal structures obtained by conformally transforming a spatially uniform periodic array, as well as non-conformal gradient structures and structures with quasiperiodic order. The conformal structures feature a density gradient and local ordering. Using magnetization simulations we find that conformal pinning arrays exhibit enhanced pinning compared to non-conformal gradient arrays as well as compared to random, periodic, and quasiperiodic arrays, for a broad range of fields. The effectiveness of conformal arrays arises from the continuum of length scales introduced into the arrays by the conformal transformation, allowing for a broad range of local commensuration effects. At higher vortex fillings above the range of conformal effectiveness, we show that a non-conformal rectangular gradient array exhibits strong pinning due to a novel commensuration effect and vortex ordering. Using transport simulations where vortices are driven along the gradient and at an angle to the gradient, we confirm the effectiveness of conformal pinning at increasing the critical current. For a rotated drive, the gradient arrays produce a strong vortex guidance effect in the direction perpendicular to the gradient.

Pinning, flux diodes and ratchets for vortices interacting with conformal pinning arrays

Abstract A conformal pinning array can be created by conformally transforming a uniform triangular pinning lattice to produce a new structure in which the six-fold ordering of the original lattice is conserved but where there is a spatial gradient in the density of pinning sites. Here we examine several aspects of vortices interacting with conformal pinning arrays and how they can be used to create a flux flow diode effect for driving vortices in different directions across the arrays. Under the application of an ac drive, a pronounced vortex ratchet effect occurs where the vortices flow in the easy direction of the array asymmetry. When the ac drive is applied perpendicular to the asymmetry direction of the array, it is possible to realize a transverse vortex ratchet effect where there is a generation of a dc flow of vortices perpendicular to the ac drive due to the creation of a noise correlation ratchet by the plastic motion of the vortices. We also examine vortex transport in experiments and compare the pinning effectiveness of conformal arrays to uniform triangular pinning arrays. We find that a triangular array generally pins the vortices more effectively at the first matching field and below, while the conformal array is more effective at higher fields where interstitial vortex flow occurs.

Pattern formation for active particles on optically created ordered and disordered substrates (Presentation Recording)

There has been tremendous growth in the field of active matter, where the individual particles that comprise the system are self-driven. Examples of this class of system include biological systems such as swimming bacteria and crawling cells. More recently, non-biological swimmers have been created using colloidal Janus particles that undergo chemical reactions on one side to produce self-propulsion. These active matter systems exhibit a wide variety of behaviors that are absent in systems undergoing purely thermal fluctuations, such as transitions from uniform liquids to clusters or living crystals, pushing objects around, ratchet effects, and phase separation in mixtures of active and passive particles. Here we examine the collective effects of active matter disks in the presence of static or dynamic substrates. For colloids, such substrates could be created optically in the form of periodic, random, or quasiperiodic patterns. For thermal particles, increasing the temperature generally increases the diffusion or mobility of the particles when they move over a random or periodic substrates. We find that when the particles are active, increasing the activity can increase the mobility for smaller run lengths but decrease the mobility at large run lengths. Additionally we find that at large run lengths on a structured substrate, a variety of novel active crystalline states can form such as stripes, squares and triangular patterns.

Active matter transport on complex substrates

Colloids interacting with complex landscapes created by optical means exhibit a remarkable variety of novel orderings and equilibrium states. It is also possible to study nonequilibrium properties for colloids driven over optical traps when there is an additional external electric field or some other form of external driving. Recently a new type of colloidal system has been realized in which the colloids are self-driven or self-motile and undergo a persistent random walk. Self motile particle systems fall into the broader class of self-driven systems called active matter. For the case of externally driven colloidal particles moving over random or periodic arrangements of traps, various types of pinning or jamming effects can arise. Far less is known about the mobility of active matter particles in the presence or random or periodic substrates. For example, it is not known whether increasing the activity of the particles would reduce the jamming effects caused by effective friction between particles. Here we show by varying the activity and the density of active particles that various types of motion can arise. In some cases, increasing the self-driving leads to a reduction in the net flow of particles through the system.