Optically enriched and guided dynamics of active skyrmions

Light provides a powerful means of controlling physical behavior of materials but is rarely used to power and guide active matter systems. We demonstrate optical control of liquid crystalline topological solitons dubbed “skyrmions”, which recently emerged as highly reconfigurable inanimate active particles capable of exhibiting emergent collective behaviors like schooling. Because of a chiral nematic liquid crystal’s natural tendency to twist and its facile response to electric fields and light, it serves as a testbed for dynamic control of skyrmions and other active particles. Using ambient-intensity unstructured light, we demonstrate large-scale multifaceted reconfigurations and unjamming of collective skyrmion motions powered by oscillating electric fields and guided by optically-induced obstacles and patterned illumination. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Active matter systems attract a great deal of recent interest because they provide the means of understanding many out-of-equilibrium phenomena in nature, enable new breeds of dynamic materials and promise to revolutionize technologies ranging from optofluidic to information displays [1][2][3][4][5]. The inanimate active matter systems range from colloids [2] to robots [3], lyotropic liquid crystals (LCs) [4,5], granular systems [6,7] and particle-like topological structures in physical fields with either singular [8] or solitonic continuous [9] configurations. While powered through conversion of chemical, mechanical or electrical energy into motions at the single particle level, these systems exhibit emergent collective behaviors that arise from many-body out-of-equilibrium interactions. By harnessing complex interactions of such systems with light, new means of light-matter interaction could be potentially envisaged. However, differently from conventional photo-responsive material systems, the means of guiding out of equilibrium phenomena in active matter remain limited, even though a few elegant demonstrations of such optical guiding of active matter already exist [10][11][12][13][14]. Optical guiding of active behavior in LCs could be of particular interest as it could allow for the ensuing control of light by these anisotropic materials, as is done in displays and spatial light modulators [15,16], while also invoking emergent many-body effects, such as schooling of skyrmions [9]. However, so far only equilibrium free energy landscapes for controlling behavior of these topological solitons have been tuned with light [17].
Topological solitons are localized field configurations that arise in nonlinear field theories, such as those found in particle physics and cosmology. Until recently, their realization and stabilization in experiments remained elusive [18,19]. Condensed matter systems have emerged as a favorable testbed for stabilization of topological solitons because of the facile ability to control the energetic landscape within materials such as solid-state magnets and LCs [20][21][22][23][24][25][26][27][28][29][30][31][32]. Chiral nematic LCs provide a favorable host for stabilization of twisted solitons, such as so-called skyrmions [28] and hopfions [20,21], because of the material's natural tendency to twist and the ensuing nonlinear nature of the free energy functional. [33][34][35] The simplest two-dimensional elementary skyrmion is an axi-symmetric translationally-invariant structure in which the field vectors exhibit π-twist radially outward from the center to the periphery [28]. Like their higher-dimensional counterparts, the two-dimensional elementary skyrmion cannot be eliminated or destroyed by smooth perturbations of the field and is therefore stable under a variety of conditions and external field manipulations [34]. One can drive skyrmion motion by electric currents in magnetic materials [26,27]. Skyrmion motion can also be realized in chiral LCs by means of rotational dynamics of the LC director field n(r) prompted by modulation of electric fields, in which the electric power is applied via electrodes on confining substrates, similar to those used in display technologies [9,15,16,36,37]. However, this electricallyinduced active motion has only limited types of collective emergent behavior. Previous developments only allow for one "setting" of motion where all skyrmions tend to synchronize to move together at a constant velocity and in the same direction [9]. Inspired by complex dynamics that one observes in crowds of people and other active systems interacting with various obstacles and environments, we present an experimental approach for selective control of skyrmion motion using diverse optical manipulation techniques. Optical tweezers are used to create obstacles and to set directions in the field of motion whereas patterned blue light illumination, coupled with photo-tunable cholesteric pitch behavior [17], provides hands-off manipulation of the energetic landscape within the sample. The combination of these optical manipulation tools is used to guide, deflect, and reconfigure skyrmion motion. The electricallypowered skyrmion motion [36], optical manipulation using laser tweezers [34], and photomanipulation using patterned light illumination [17,38] are combined to enhance collective motion controllability. We demonstrate reconfigurations of the dynamic skyrmion crowds into single-file lines, steer and inhibit skyrmion motion by changing polarization of patterned light illumination, optically induce skyrmion jamming and unjamming transitions, and other means of controlling complex motion with emergent active behavior. Since the system is based on materials and preparation techniques that are commonly used in the LC display industry [15,16], this work may lead to re-defining human-computer communications through LCbased touch-screen displays and expand the scope of augmented or virtual reality devices.

Materials and methods
We employ experimental implementation of samples reminiscent of LC displays, as is shown in the experimental schematic (Fig. 1a). These inch-square samples are created by infiltrating a chiral nematic LC mixture into a glass cell constructed by gluing two conductive substrates together and setting the cell gap with 10 µm glass spacers. The inner surfaces of the glass substrates have transparent conducting layers of indium-tin oxide and were pre-treated for finite-strength vertical surface boundary conditions via spin-coating with SE-1211 (purchased from Nissan) at 2700 rpm for 30 s. To induce crosslinking of the alignment layer, the substrates were then baked for 5 min at 90 C and for 1 h at 190 C. The LC mixture is composed of a nematic host with negative dielectric anisotropy, either MLC-6609 (Merck) or ZLI-2806 (EM Chemicals), that has been heated to the isotropic phase for thorough mixing with a chiral additive (Table 1). For experiments done in samples without photo-sensitivity to low-intensity blue light, the additive CB-15 from EM Chemicals was used. Alternatively, mixing the nematic hosts with the QL-76 additive (obtained from the Air Force Research Lab [39]) enabled phototuning of the chiral pitch, p0, via blue light exposure. The ground state helicoidal pitch of these mixtures can be calculated using the relation 0 = 1/ℎ • [40] (Table 1), where hHTP is the helical twisting power of the chiral additive in the host medium and c is its concentration by weight. In order to stabilize skyrmions spontaneously, we set the pitch to be approximately equal to the cell gap of 10 µm. For the photo-responsive materials, the pitch can be increased from p0 to excited-state value pe by blue-light illumination via a trans-cis isomerization that decreases the helical twisting power of the QL-76 dopant [41] which, in our samples, enables tunability from p0 = 10 µm to pe ≈ 22 µm [17]. Because we use low intensity ~ 1nW per square micron [13] blue patterning light in the 450-480 nm range and thin ~ 10 µm LC films with chiral additive concentrations near 0.2-0.3 wt%, absorbance within the sample is negligible [41,42]. Therefore, we assume that the illumination has consistent non-diminishing intensity throughout the sample thickness.
We take advantage of the high stability of skyrmion structures in samples with cell thickness d ≈ p0, and use a number of techniques for spontaneous or systematic generation of these topological structures. For spontaneous generation, the samples were heated past each material's clearing temperature (TNI, Table 1) to the isotropic phase and cooled rapidly using compressed air. Alternatively, skyrmions were generated by means of optical reorientation induced by a 1064 nm Ytterbium-doped fiber laser that comprises our "optical laser tweezer" setup (YLR-10-1064, IPG Photonics) [34][35][36][37]43]. This optical reorientation, known as the optical Fredericks transition [35], results in controlled generation of twisted structures when the laser beam is focused on the midplane of the sample and the power is tuned to > 50 mW, inducing local LC director realignment away from the homeotropic far-field background induced by the vertical surface boundary conditions. The same optical setup was also used to "pin" skyrmions to the cell substrates via altering the alignment layer when the focal plane of the laser focus is adjusted to be closer to one of the confining substrates, which in turn creates stationary solitonic obstacles within the sample. Using these techniques, skyrmions were selectively generated at ~50mW power and pinned at powers between 70 and 150 mW. We use the pinned obstacles as a means of experimentally-recreating real-world examples of crowd dynamics, such as those observed funneling through gates with some organized, persistent motion following the obstacles ( Fig. 1b-d, Visualization 1).
Because our LC skyrmions represent minima in the elastic free energy of our chiral nematic experimental systems, we minimize the Frank-Oseen free energy to computer simulate the n(r) of a single skyrmion at electric fields E corresponding to different applied voltages U: [9,20,35,36] In the expression above, the elastic constants K11, K22, and K33 represent the elastic energy costs for splay, twist, and bend deformations of n(r), respectively. Δε is the dielectric anisotropy and ε0 is the permittivity of free space. In this study we use materials with negative dielectric anisotropy such that, upon voltage application across the sample thickness, the director n(r) rotates to lie perpendicular to the direction of the applied field E in the sample mid-plane, thus deforming our skyrmionic structures from their initial axi-symmetric state to an asymmetric one shown in Fig. 1e. Similar asymmetric skyrmions have been demonstrated in both LCs and chiral magnets [9,37,[44][45][46][47]. Due to their topological stability, the resulting asymmetric skyrmions maintain their topological nature under tunable deformation [9,36,37]. This morphing of the director field with electric field application is not invariant upon reversal of time, which results in a net translational motion upon voltage modulation [36]. Many skyrmions under such energy conversion conditions tend to exhibit long-range interactions and schooling behavior [9]. Vectorized n(r) plots (Fig. 1e), midplane director field schematics displaying the n(r) orientations in the form of nonpolar field lines (Fig. 1f), and numerically-generated polarizing images ( Fig. 1g) are all consistent with experimental images of similar structures under similar conditions (Fig. 1h). These computer simulated polarizing optical microscopy images are generated using a Jones matrix method [36,15] in which the optical properties of the material (Table 1) and the sample thickness are taken as numerical inputs for calculating the resulting polarizing optical microscopy textures that one would expect to see. The material parameters used in these computer simulations presented in Fig. 1 correspond to the experimental values for ZLI-2806 with a CB-15 additive (Table 1). Using two different nematic hosts and both left-and right-handed cholesterics (corresponding to different chiral additives, Table 1) allowed us to assure the broad applicability of our findings to a broad range of chiral nematic material systems. Experimental images and videos were obtained using an Olympus BX-51 upright microscope with a 10x objective and crossed polarizers inserted above and below the sample. For samples with the QL-76 chiral additive, an additional optical filter (obtained from Edmund Optics) was inserted below the sample to enable red-light optical imaging (blocking the short-wavelength blue and green light) and preclude unintentional reaction of the photo-sensitive dopant to the microscope's white light source. A blue-light projection system comprised of an Epson EMP-730 LC Projector's micro-display was coupled to the microscope setup via dichroic mirrors [13,17] that allowed for projection of focused blue-light patterns into the midplane of the sample with tunable polarization capabilities. Images and videos were captured using a chargecoupled device camera purchased from Point Grey Research, Inc and analyzed using ImageJ open source software (National Institute of Health). Positional data for each skyrmion in motion was extracted using the "wrmTrck" plugin for ImageJ and exported to MATLAB for further analysis.

Results and discussion
Through selective optical manipulation using the methods described above for laser tweezer manipulation and blue light photo-patterning, we guide skyrmion collective dynamics by introducing new means of controlling velocity, size, motion directionality, jamming, and reconfigurability of skyrmion assemblies. Due to the fact that these structures are highly energetically favorable and stable within our samples, the skyrmions can be squeezed and morphed, unlike hard colloidal or granular active particles and more like squishy biological cells and organisms that can be crammed together and deformed before regaining their preferred shape. Therefore, we demonstrate highly robust manipulation while the skyrmions are in a non-equilibrium state of motion as they move around obstacles, react to changes in the elastic free-energy landscape due to blue-light exposure, and adapt to these interferences by changing their assemblies and trajectories, as detailed below.

Obstacle-induced jamming and crowded skyrmion motion
First, we utilize the optical laser tweezers to carefully arrange a number of obstacles in the path of skyrmion motion trajectories to investigate the crowding and jamming behavior of active skyrmions. Having high levels of control and tunability over the density and position of obstacles and the number of skyrmions moving through the field of view, we start from relatively high densities of each (Fig. 2, Visualization 2). At motion powered by U = 3.5 V and f = 60 Hz, the skyrmions tend to stick together and form quasi-hexagonally-packed clusters which, in this case, leads to large-scale jamming of mobile skyrmions in-between the obstacles. Consequently, velocity within the skyrmion crowd falls to zero and the jamming state persists over a long period of time on the order of minutes.  We demonstrate, however, that such jamming can be controlled and overcome by tuning skyrmion size via the amplitude of voltage application. We show this using the case of sparser initial skyrmions and obstacles (Fig. 3, Visualization 3), where the jamming still occurs but differently than in the previous case. Once we observe jamming start to occur during the U = 3.5 V motion, we increase the applied field to U = 4 V, which induces more squeezing of the asymmetric skyrmion structures [34] and allows them to compress themselves into closerpacked clusters and overcome the jamming. The clusters at higher voltage, which are comprised of skinnier skyrmions of smaller lateral dimensions, then regain their motion and smoothly traverse through the remaining obstacles.
Instead of being used to induce jamming, the obstacles can also be created in a way that mediates continuous, uninterrupted motion of many skyrmions at once. By organizing the obstacles into channels (Fig. 4, Visualization 4), the skyrmions can be funneled from a dispersed "crowd" into neat single-file lines. Similar to crowds of people passing through security gates (Fig. 1b-d), the skyrmions demonstrate short-range persistence of the directional motion induced by the obstacles (Fig. 4b).

Photo-induced guiding and deflection of skyrmion motion
While laser-induced obstacles provide a precise and persisting means of manipulation, they also require hands-on, one-by one creation that is time consuming on the large scale and are not easily modified or moved. We therefore turn to photo-manipulation to add a temporary and adaptable means of controlling skyrmion motion to our toolbox. We characterize the polarization-dependent response of the LC samples with dynamic skyrmions to blue light exposure when the chiral LC is further mixed with the azobenzene-based dopant QL-76. Upon exposure, the illumination light not only increases the helical pitch of the projected area, but the photoresponsive azobenzene-based dopant molecules likewise tend to orient themselves perpendicular to the polarization of the blue light [48], which we can control with a linear polarizing element in our optical microdisplay projection setup [13]. The result of this reorientation is a region within the sample with changing the in-plane tilt directionality of the in-plane n(r) in the center of the sample (Fig. 5a,b). This is particularly useful for steering skyrmion motion because, upon voltage modulation, they tend to move perpendicular to the direction of the far-field tilt ( Fig. 5c-d), and, thus, along the linear polarization direction.
We demonstrate experimentally, first with a few skyrmions (Fig. 5e,f) and then with many more (Fig. 5g,h), that this in-plane field reorientation induces deflection of motion towards the direction of the polarization. The effect can be understood as resulting from the realignment of the LC director in the cell midplane to orient orthogonally to the linear polarization of illumination light (a common effect for LCs doped with azobenzene-containing dyes [49]), which, in turn, redirects the motion of squirming skyrmions. As skyrmions approach this sample's region of illumination, they slow down from 0.30 µm/s to 0.25 µm/s then, upon overcoming the energetic barrier induced by the blue light, accelerate to 0.36 µm/s within the illumination area. Once outside of the blue-light region, the velocity falls back to the average ~ 0.30 µm/s (Fig. 5e,f). This dynamic behavior can be understood as a combined effect due to both tuning pitch with optical illumination and rotating the cell midplane's director to orient orthogonally to the polarization of the blue illumination light. Our experimental projection setup enables application of various illumination shapes and patterns, which we utilize to show the precise tunability of directional steering. To do this, a pattern was chosen in which a small central channel has no exposure while two semi-circles above and below the channel are exposed to induce in-plane n(r) reorientation (Fig. 6, Visualization 5). As the self-assembled chains move towards the left side of the frame in Fig.  6, one chain in particular travels into the channel then "feels" the exposure near the center of the channel, where the reorientation is arguably the strongest, and then rotates to travel upwards in a trajectory parallel to the direction of the linear polarization of illumination light (Fig. 6).

Reconfiguring skyrmion motion using laser-patterned obstacles and light
We have now developed an experimental system with multifaceted, adjustable properties that can be used to influence skyrmion motion. Next, we investigate how a combination of these semi-permanent and short-term control tools can be used to facilitate new emergent behavior within the collective migration of school-like assemblies. One such example of emergent behavior lies in the dynamic rearrangement of skyrmion chains (Fig. 7, Visualization 6), in this case utilizing both pinned obstacles and the steering mechanism induced by blue-light illumination, with the polarization direction set to be perpendicular to the un-exposed trajectories of motion. In this case, the laser-pinned obstacles act as nucleation sites for the oscillatory motion of chains that elastically attach themselves to the stationary obstacle sites and then swirl and reconfigure their snake-like assemblies, moving in and out of the exposure area and thus individually changing their orientations and motion directions. Finally, we present a demonstration of emergent dynamic behavior featuring patterned exposure, dynamic structures that become obstacles at random by getting stuck on surface defects (laser-induced pinning sites), and an additional unpaired topological defect called an umbilic (Fig. 8, Visualization 7). This elementary-winding-number umbilic is a nonsingular defect in the in-plane n(r) tilt directionality field that is created spontaneously upon voltage application and self-assembles with the twisted structure of the skyrmion core to stabilize the elementary skyrmion in the tilted far-field (Fig. 8c, inset) [37]. In this case, we create the "unpaired" umbilic by exposure to blue light at the transition between the voltage off and on states [17]. Because the unpaired umbilic represents a long-range spatial pattern in the tilt director directionality field, when skyrmions in motion come near the defect, they are deflected and sidetracked according to the direction of the local tilt directionality field, moving orthogonally to it. This likewise has long-range effects on the trajectories of motion, which develop complex swirling pattern that persists over long periods of time ( Fig. 8d-g). During this motion, random skyrmions in motion temporarily get stuck on various pinning sites (marked by red crosses within the experimental images in Fig. 8d,f) and, favorably, can free themselves from the pinning sites and persist with their emergent collective movement. This finding demonstrates that the technique for pinning obstacles with laser tweezers can either be used as a permanent or a temporary means of hindering and adjusting trajectories of motion.
This observation also provides a number of new experimental knobs to turn for controlling and guiding active topological solitons. In particular, one can envisage optical or other types of patterning of the director field in the midplane that can lead to electrically powered transport of LC skyrmions along well-defined pre-programmed trajectories. Although trajectories of motions of similar skyrmions can be defined by real-time scanning infrared laser beams of optical tweezers with velocity that allows for skyrmions following the laser traps without escaping them (Fig. 8h-i), the demonstrated capability of combining ambient-light-based control of electrically powered skyrmion motions ( Fig. 8a-g) can be used over much larger areas and without sophisticated laser tweezer setups. Additionally, it can be combined with the very same laser trap scanning to manipulate skyrmion dynamics in even more versatile ways, for example, to accelerate and re-direct skyrmion motions within localized sample regions (Fig. 8i).

Conclusions
In this work, we have established multifaceted means of control over topological solitons in collective emergent motions by manipulating the velocity, size, directionality, jamming and sorting behavior, and through the reconfigurability of skyrmion assemblies. We have accomplished this by utilizing a combining optical manipulations that have never been used in harmony to enhance this active behavior and uncover new means of experimental control. By selectively pinning topological solitons to the surface alignment layer on the glass substrates using a focused optical laser tweezer setup, we create semi-permanent stationary obstacles around which skyrmions can move smoothly or exhibit jamming behavior or movement reminiscent of crowds of people funneling through security gates. A photo-sensitive chiral additive enables precise steering and accurate manipulation of motion for both individual structures and self-assembled groups of skyrmions upon exposure by tuning the polarization of the blue-light illumination. When these techniques are used together, we gain multifaceted control over trajectories of motion and oscillatory-like behavior such as slithering and swirling of skyrmion chains. As these structures are energetically favorable, easily stabilized, and highly robust in optically anisotropic LC materials, like the ones used in displays, there are many exciting opportunities for applications development and new touch-screen technologies based on emergent responses to external fields and selective manipulation of twisted solitons. The experimental sample fabrication techniques used throughout this study are highly reminiscent of those used in the multi-billion-dollar LC display industry, which can potentially stimulate the translation of our findings to the consumer markets. Previous studies have shown the ability to use specialty experimental systems involving micropatterned substrates [50], thickness gradients, and structured beams of light to control skyrmionic structures in equilibrium conditions [28,35,[50][51][52], however our work enables higher levels of dynamic control using low-intensity unstructured light. These advances add to the experimental toolkit available for controlling active behavior of solitons and promises new complex avenues and compelling possibilities for technological uses for LC skyrmions. From the active matter standpoint, where guiding active particles by microfabricated topographic pathways and other means has been a mission of many recent studies [2,[53][54][55][56], our light-guided active skyrmions can serve as a model system to probe such emergent out-of-equilibrium behavior in new regimes of external control. The dynamic skyrmions in racetrack magnetic memories [25,26] may potentially pin on impurities and defects in crystalline solid films and, therefore, our work on topologically similar LC skyrmions [57] may potentially provide insight into ways of unjamming the moving skyrmions in the contexts of such applications.