Velocity Enhancement by Synchronization of Magnetic Domain Walls

Data-driven exploration of swarmalators with second-order harmonics

We explore the dynamics of a swarmalator population comprising second-order harmonics in phase interaction. A key observation in our study is the emergence of the active asynchronous state in swarmalators with second-order harmonics, mirroring findings in the one-dimensional analog of the model, accompanied by the formation of clustered states. Particularly, we observe a transition from the static asynchronous state to the active phase wave state via the active asynchronous state. We have successfully delineated and quantified the stability boundary of the active asynchronous state through a completely data-driven method. This was achieved by utilizing the enhanced image processing capabilities of convolutional neural networks, specifically, the U-Net architecture. Complementing this data-driven analysis, our study also incorporates an analytical stability of the clustered states, providing a multifaceted perspective on the system's behavior. Our investigation not only sheds light on the nuanced behavior of swarmalators under second-order harmonics, but also demonstrates the efficacy of convolutional neural networks in analyzing complex dynamical systems.

Amplitude responses of swarmalators

Swarmalators are entities that swarm through space and sync in time and are potentially considered to replicate the complex dynamics of many real-world systems. So far, the internal dynamics of swarmalators have been taken as a phase oscillator inspired by the Kuramoto model. Here we examine the internal dynamics utilizing an amplitude oscillator capable of exhibiting periodic and chaotic behaviors. To incorporate the dual interplay between spatial and internal dynamics, we propose a general model that keeps the properties of swarmalators intact. This adaptation calls for a detailed study, which we present in this paper. We establish our study with the Rössler oscillator by taking parameters from both chaotic and periodic regions. While the periodic oscillator mimics most of the patterns in the previous phase oscillator model, the chaotic oscillator brings some fascinating states.

Solvable model of driven matter with pinning

We present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls.

Swarmalators with delayed interactions

We investigate the effects of delayed interactions in a population of "swarmalators," generalizations of phase oscillators that both synchronize in time and swarm through space. We discover two steady collective states: a state in which swarmalators are essentially motionless in a disk arranged in a pseudocrystalline order, and a boiling state in which the swarmalators again form a disk, but now the swarmalators near the boundary perform boiling-like convective motions. These states are reminiscent of the beating clusters seen in photoactivated colloids and the living crystals of starfish embryos.

Attractive and repulsive interactions in the one-dimensional swarmalator model

We study a population of swarmalators, mobile variants of phase oscillators, which run on a ring and have both attractive and repulsive interactions. This one-dimensional (1D) swarmalator model produces several of collective states: the standard sync and async states as well as a splaylike "polarized" state and several unsteady states such as active bands or swirling. The model's simplicity allows us to describe some of the states analytically. The model can be considered as a toy model for real-world swarmalators such as vinegar eels and sperm which swarm in quasi-1D geometries.

Swarmalators on a ring with uncorrelated pinning

We present a case study of swarmalators (mobile oscillators) that move on a 1D ring and are subject to pinning. Previous work considered the special case where the pinning in space and the pinning in the phase dimension were correlated. Here, we study the general case where the space and phase pinning are uncorrelated, both being chosen uniformly at random. This induces several new effects, such as pinned async, mixed states, and a first-order phase transition. These phenomena may be found in real world swarmalators, such as systems of vinegar eels, Janus matchsticks, electrorotated Quincke rollers, or Japanese tree frogs.

Antiphase synchronization in a population of swarmalators

Swarmalators are oscillatory systems endowed with a spatial component, whose spatial and phase dynamics affect each other. Such systems can demonstrate fascinating collective dynamics resembling many real-world processes. Through this work, we study a population of swarmalators where they are divided into different communities. The strengths of spatial attraction, repulsion, as well as phase interaction differ from one group to another. Also, they vary from intercommunity to intracommunity. We encounter, as a result of variation in the phase coupling strength, different routes to achieve the static synchronization state by choosing several parameter combinations. We observe that when the intercommunity phase coupling strength is sufficiently large, swarmalators settle in the static synchronization state. However, with a significant small phase coupling strength the state of antiphase synchronization as well as chimeralike coexistence of sync and async are realized. Apart from rigorous numerical results, we have been successful to provide semianalytical treatment for the existence and stability of global static sync and the antiphase sync states.

Diverse behaviors in non-uniform chiral and non-chiral swarmalators

We study the emergent behaviors of a population of swarming coupled oscillators, dubbed swarmalators. Previous work considered the simplest, idealized case: identical swarmalators with global coupling. Here we expand this work by adding more realistic features: local coupling, non-identical natural frequencies, and chirality. This more realistic model generates a variety of new behaviors including lattices of vortices, beating clusters, and interacting phase waves. Similar behaviors are found across natural and artificial micro-scale collective systems, including social slime mold, spermatozoa vortex arrays, and Quincke rollers. Our results indicate a wide range of future use cases, both to aid characterization and understanding of natural swarms, and to design complex interactions in collective systems from soft and active matter to micro-robotics.

Pinning in a system of swarmalators

We study a population of swarmalators (swarming/mobile oscillators) which run on a ring and are subject to random pinning. The pinning represents the tendency of particles to stick to defects in the underlying medium which competes with the tendency to sync and swarm. The result is rich collective behavior. A highlight is low dimensional chaos which in systems of ordinary, Kuramoto-type oscillators is uncommon. Some of the states (the phase wave and split phase wave) resemble those seen in systems of Janus matchsticks or Japanese tree frogs. The others (such as the sync and unsteady states) may be observable in systems of vinegar eels, electrorotated Quincke rollers, or other swarmalators moving in disordered environments.

Swarmalators on a ring with distributed couplings

We study a simple model of identical "swarmalators," generalizations of phase oscillators that swarm through space. We confine the movements to a one-dimensional (1D) ring and consider distributed (nonidentical) couplings; the combination of these two effects captures an aspect of the more realistic two-dimensional swarmalator model. We discover several collective states which we describe analytically. These states imitate the behavior of vinegar eels, catalytic microswimmers, and other swarmalators which move on quasi-1D rings.

Domain wall motion driven by a wide range of current in coupled soft/hard ferromagnetic nanowires

Racetrack memory with the advantages of small size and high reading speed is proposed based on current-induced domain wall (DW) motion in a ferromagnetic (FM) nanowire. Walker breakdown that restricts the enhancement of DW velocity in a single FM nanowire can be depressed by inter-wire magnetostatic coupling in a double FM nanowire system. However, this magnetostatic coupling also limits the working current density in a small range. In the present work, based on micromagnetic calculation, we have found that when there is a moderate difference of magnetic anisotropy constant between two FM nanowires, the critical current density for triggering the DW motion can be reduced while that for breaking the inter-wire coupling can be enhanced significantly to a magnitude of 1013 A m-2, which is far above the working current density in current electronic devices. The manipulation of working current density is relevant to the modification of DW structure and inter-wire magnetostatic coupling due to the difference of the anisotropy constants between the two nanowires and paves a way to develop racetrack memory that can work in a wide range of current.

Multiple Walker breakdowns in magnetic multilayers

Herein, we report an exotic domain-wall dynamics showing double Walker breakdowns in magnetic multilayer films composed of two magnetic layers. Such multiple Walker breakdowns are attributed to the internal magnetic dipole field, which is antisymmetric on the domain walls of the lower and upper magnetic layers. A micromagnetic simulation shows four phases of the domain-wall dynamics, which result in a phase diagram with the phase boundaries of the double Walker breakdown fields. Such double Walker breakdowns lead to two minima in the variation of the domain-wall velocity, as often observed experimentally.

Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures

The design of complex, competing effects in magnetic systems-be it via the introduction of nonlinear interactions^1-4, or the patterning of three-dimensional geometries^5,6-is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states⁷, ultrafast chiral domain wall dynamics^8-10 and spin textures with new spin topologies^7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography^12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall¹⁴. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials¹⁵, unconventional computing^2,16, particle trapping^17,18 and magnetic imaging¹⁹.

Collective behavior of swarmalators on a ring

We study the collective behavior of swarmalators, generalizations of phase oscillators that both sync and swarm, confined to move on a one-dimensional (1D) ring. This simple model captures the essence of movement in two or three dimensions, but has the benefit of being solvable: most of the collective states and their bifurcations can be specified exactly. The model also captures the behavior of real-world swarmalators which swarm in quasi-1D rings such as bordertaxic vinegar eels and sperm.

Emergent behavior in an adversarial synchronization and swarming model

We consider a red-versus-blue coupled synchronization and spatial swarming (i.e., swarmalator) model that incorporates attraction and repulsion terms and an adversarial game of phases. The model exhibits behaviors such as spontaneous emergence of tactical manoeuvres of envelopment (e.g., flanking, pincer, and envelopment) that are often proposed in military theory or observed in nature. We classify these states based on a large set of features such as spatial densities, synchronization between clusters, and measures of cluster distances. These features are used to study the influence of coupling parameters on the expected presence of these states and the-sometimes sharp-transitions between them.

Synchronization and spatial patterns in forced swarmalators

Swarmalators are particles that exhibit coordinated motion and, at the same time, synchronize their intrinsic behavior, represented by internal phases. Here, we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. The system represents, for example, a swarm of fireflies in the presence of an external light source that flashes at a fixed frequency. If the spatial movement is ignored, the dynamics of the internal variables are equivalent to those of Kuramoto oscillators. In this case, the phases tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here, we show that in a system of swarmalators, the force also shifts the phases and angular velocities leading to synchronization with the external frequency. However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero at a critical intensity that depends on the model parameters. In the regime of zero correlation, the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, different patterns emerge, with the particles spiraling or splitting in two clusters centered at opposite sides of the stimulus' location. The spiral and two-cluster patterns are stable and active. The two clusters slowly rotate around the source while exchanging particles, or separate and collide repeatedly, depending on the parameters.