Acoustic Skyrmionic Mode Coupling and Transferring in a Chain of Subwavelength Metastructures.

Skyrmions, a stable topological vectorial textures characteristic with skyrmionic number, hold promise for advanced applications in information storage and transmission. While the dynamic motion control of skyrmions has been realized with various techniques in magnetics and optics, the manipulation of acoustic skyrmion has not been done. Here, the propagation and control of acoustic skyrmion along a chain of metastructures are shown. In coupled acoustic resonators made with Archimedes spiral channel, the skyrmion hybridization is found giving rise to bonding and antibonding skyrmionic modes. Furthermore, it is experimentally observed that the skyrmionic mode of acoustic velocity field distribution can be robustly transferred covering a long distance and almost no distortion of the skyrmion textures in a chain of metastructures, even if a structure defect is introduced in the travel path. The proposed localized acoustic skyrmionic mode coupling and propagating is expected in future applications for manipulating acoustic information storage and transfer.

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets.

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Asymmetric Magnon Frequency Comb.

We theoretically show the asymmetric spin wave transmission in a coupled waveguide-skyrmion structure, where the skyrmion acts as an effective nanocavity allowing the whispering gallery modes for magnons. The asymmetry originates from the chiral spin wave mode localized in the circular skyrmion wall. By inputting two-tone excitations and mixing them in the skyrmion wall, we observe a unidirectional output magnon frequency comb propagating in the waveguide with a record number of teeth (>50). This coupled waveguide-cavity structure turns out to be a universal paradigm for generating asymmetric magnon frequency combs, where the cavity can be generalized to other magnetic structures that support the whispering gallery mode of magnons. Our results advance the understanding of the nonlinear interaction between magnons and magnetic textures and open a new pathway to exploring the asymmetric spin wave transmission and to steering the magnon frequency comb.

"Polymerization" of Bimerons in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy.

We re-examine the internal structure of bimerons, which are stabilized in easy-plane chiral magnets and represent coupled states of two merons with the same topological charge |1/2| but with opposite vorticity and the polarity. We find that, in addition to the vortices and antivortices, bimerons feature circular regions which are located behind the anti-vortices and bear the rotational sense opposite to the rotational sense chosen by the Dzyaloshinskii-Moriya interaction. In an attempt to eliminate these wrong-twist regions with an excess of positive energy density, bimerons assemble into chains, and as such exhibit an attracting interaction potential. As an alternative to chains, we demonstrate the existence of ring-shaped bimeron clusters of several varieties. In some rings, bimeron dipoles are oriented along the circle and swirl clockwise and/or counterclockwise (dubbed "roundabouts"). Moreover, a central meron encircled by the outer bimerons may possess either positive or negative polarity. In other rings, the bimeron dipoles point towards the center of a ring and consequently couple to the central meron (dubbed "crossings"). We point out that the ringlike solutions for baryons obtained within the Skyrme model of pions, although driven by the same tendency of the energy reduction, yield only one type of bimeron rings. The conditions of stability applied to the described bimeron rings are additionally extended to bimeron networks when bimerons fill the whole space of two-dimensional samples and exhibit combinations of rings and chains dispersed with different spatial density (dubbed bimeron "polymers"). In particular, bimeron crystals with hexagonal and the square bimeron orderings are possible when the sides of the unit cells represent chains of bimerons joined in intersections with three or four bimerons, respectively; otherwise, bimeron networks represent disordered bimeron structures. Moreover, we scrutinize the inter-transformations between hexagonal Skyrmion lattices and disordered bimeron polymers occuring via nucleation and mutual annihilation of merons within the cell boundaries. Our theory provides clear directions for experimental studies of bimeron orderings in different condensed-matter systems with quasi-two-dimensional geometries.

Dynamics of Elliptical Magnetic Skyrmion in Defective Racetrack.

Recently, it has been reported that the skyrmion Hall effect can be suppressed in an elliptical skyrmion-based device. Given that defects are unavoidable in materials, it is necessary and important to investigate the dynamics of an elliptical skyrmion in a defective racetrack device. In this work, the current-driven dynamics of an elliptical skyrmion in a defective racetrack device are systematically studied using micromagnetic simulations. The system energy analysis reveals that the magnetic parameters of the circular defect play critical roles in determining the type (repulsive or attractive) and the magnitude of the force on the elliptical skyrmion. The simulated trajectories show that the primary motion modes of the elliptical skyrmion in the defective racetrack can be divided into four types, which are dependent on the values of the Dzyaloshinskii-Moriya interaction (DMI) constant Dd, the perpendicular magnetic anisotropy constant Kd, the magnitude of the driving current density J, and the size d of the defect. Further investigation of the motion-mode phases of the skyrmion reveals the synthetic effects of Dd, Kd, J, and d. Finally, the minimum depinning current density J, which linearly depends on the parameters of Dd and Kd, is obtained for a skyrmion completely pinned in the defect. Our findings give insights into the dynamics of an elliptical skyrmion in the presence of a defect with different magnetic parameters in a racetrack device and may be useful for performance enhancement of skyrmion-based racetrack memory devices.

Electron-Assisted Generation and Straight Movement of Skyrmion Bubble in Kagome TbMn6Sn6.

Topological magnetic textures are promising candidates as binary data units for the next-generation memory device. The precise generation and convenient control of nontrivial spin topology at zero field near room temperature endows the critical advantages in skyrmionic devices but is not simultaneously integrated into one material. Here, in the Kagome plane of quantum TbMn6Sn6, the expedient generation of the skyrmion bubbles in versatile forms of lattice, chain, and isolated one by converging the electron beam, where the electron intensity gradient contributes to the dynamic generation from local anisotropy variation near spin reorientation transition (SRT) is reported. Encouragingly, by utilizing the dynamic shift of the SRT domain interface, the straight movement is actualized with the skyrmion bubble slave to the SRT domain interface forming an elastic composite object, avoiding the usual deflection from the skyrmion Hall effect. The critical contribution of the SRT domain interface via conveniently electron-assisted heating is further theoretically validated in micromagnetic simulation, highlighting the compatible application possibility in advanced devices.

Topological aspects of multi-kantiferromagnetism in cubic rare-earth compounds.

We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focusing on the series of cubicRCu compounds, whereR= Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically non-trivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of(ππ0)antiferromagnetism with the possibility for various multi-kconfigurations. Motivated by general trends in these materials, we discuss the possible existence of topologically non-trivial winding in real and reciprocal space in the class ofRCu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties inRCu systems promises access to advanced functionalities.

Reconfigurable Skyrmion-Based Logic Gates: Versatile Design and Full-Scale Implementation.

Herein, we investigate the behavior of skyrmions within a racetrack design incorporating voltage-controlled magnetic anisotropy (VCMA) gates. Our analysis encompassed multiple forces, including spin currents and anisotropy gradients induced by bias voltages. As a result, the efficient control of skyrmion dynamics was achieved across various VCMA gate configurations. Building upon these findings, we propose an efficient approach to reconfigurable skyrmion logic (RSL) in a thin antiferromagnetic (AFM) film through a versatile design. Our RSL harnesses the selective integration of VCMA, spin-polarized currents, and skyrmion-skyrmion (sky-sky) interactions to implement multiple logic gates, including AND, OR, XOR, NOT, NAND, XNOR, and NOR. The design brings a significant advantage with its simplified fabrication process, making the implementation of the RSL practical and accessible for various applications. Furthermore, the RSL enables seamless dynamic switching between logic gates, thereby enhancing its multifunctionality. Additionally, the strategic incorporation of sky-sky interactions and skyrmion-edge repulsion prominently facilitates the realization of complex gates, such as NAND, XNOR, and NOR gates, that typically require intricate design efforts. Hence, this streamlined integration of RSL, coupled with its adaptability to changing computational needs, underscores its potential as a practical solution for implementing high-functionality skyrmion-based logic gates.

Thermal Stability of Skyrmion Tubes in Nanostructured Cuboids.

Magnetic skyrmions in bulk materials are typically regarded as two-dimensional structures. However, they also exhibit three-dimensional configurations, known as skyrmion tubes, that elongate and extend in-depth. Understanding the configurations and stabilization mechanism of skyrmion tubes is crucial for the development of advanced spintronic devices. However, the generation and annihilation of skyrmion tubes in confined geometries are still rarely reported. Here, we present direct imaging of skyrmion tubes in nanostructured cuboids of a chiral magnet FeGe using Lorentz transmission electron microscopy (TEM), while applying an in-plane magnetic field. It is observed that skyrmion tubes stabilize in a narrow field-temperature region near the Curie temperature (Tc). Through a field cooling process, metastable skyrmion tubes can exist in a larger region of the field-temperature diagram. Combining these experimental findings with micromagnetic simulations, we attribute these phenomena to energy differences and thermal fluctuations. Our results could promote topological spintronic devices based on skyrmion tubes.

Raman Shifts in Two-Dimensional van der Waals Magnets Reveal Magnetic Texture Evolution.

Two-dimensional (2D) van der Waals magnets comprise rich physics that can be exploited for spintronic applications. We investigate the interplay between spin-phonon coupling and spin textures in a 2D van der Waals magnet by combining magneto-Raman spectroscopy with cryogenic Lorentz transmission electron microscopy. We find that when stable skyrmion bubbles are formed in the 2D magnet, a field-dependent Raman shift can be observed, and this shift is absent for the 2D magnet prepared in its ferromagnetic state. Correlating these observations with numerical simulations that take into account field-dependent magnetic textures and spin--phonon coupling in the 2D magnet, we associate the Raman shift to field-induced modulations of the skyrmion bubbles and derive the existence of inhomogeneity in the skyrmion textures over the film thickness.

Direct Observation of Room-Temperature Magnetic Skyrmion Motion Driven by Ultra-Low Current Density in Van Der Waals Ferromagnets.

The recent discovery of room-temperature ferromagnetism in 2D van der Waals (vdW) materials, such as Fe3GaTe2 (FGaT), has garnered significant interest in offering a robust platform for 2D spintronic applications. Various fundamental operations essential for the realization of 2D spintronics devices are experimentally confirmed using these materials at room temperature, such as current-induced magnetization switching or tunneling magnetoresistance. Nevertheless, the potential applications of magnetic skyrmions in FGaT systems at room temperature remain unexplored. In this work, the current-induced generation of magnetic skyrmions in FGaT flakes employing high-resolution magnetic transmission soft X-ray microscopy is introduced, supported by a feasible mechanism based on thermal effects. Furthermore, direct observation of the current-induced magnetic skyrmion motion at room temperature in FGaT flakes is presented with ultra-low threshold current density. This work highlights the potential of FGaT as a foundation for room-temperature-operating 2D skyrmion device applications.

Dynamic Motion of Polar Skyrmions in Oxide Heterostructures.

Polar skyrmions have been widely investigated in oxide heterostructures due to their exotic properties and intriguing physical insights. However, the field-driven motion of polar skyrmions, akin to that of the magnetic counterpart, remains elusive. Herein, using phase-field simulations, we demonstrate the dynamic motion of polar skyrmions with integrated external thermal, electrical, and mechanical stimuli. External heating reduced the spontaneous polarization, while an applied electric field decreased the skyrmion size and weakened the interactions between the skyrmions. Together, the skyrmion motion barrier is significantly reduced from 40 to 2 eV under 9 V at 500 K. An applied mechanical force transformed the skyrmions into a c-domain region near the indenter center under the electric field, providing the space and driving force needed for the motion of the skyrmions. This study confirms that polar skyrmions can move like particles and provides concrete design principles for polar skyrmion-based electronic devices.

Chiral Skyrmions Interacting with Chiral Flowers.

The chiral nature of active matter plays an important role in the dynamics of active matter interacting with chiral structures. Skyrmions are chiral objects, and their interactions with chiral nanostructures can lead to intriguing phenomena. Here, we explore the random-walk dynamics of a thermally activated chiral skyrmion interacting with a chiral flower-like obstacle in a ferromagnetic layer, which could create topology-dependent outcomes. It is a spontaneous mesoscopic order-from-disorder phenomenon driven by the thermal fluctuations and topological nature of skyrmions that exists only in ferromagnetic and ferrimagnetic systems. The interactions between the skyrmions and chiral flowers at finite temperatures can be utilized to control the skyrmion position and distribution without applying any external driving force or temperature gradient. The phenomenon that thermally activated skyrmions are dynamically coupled to chiral flowers may provide a new way to design topological sorting devices.

Skyrmion transport and annihilation in funnel geometries.

Using atomistic simulations, we have investigated the transport and annihilation of skyrmions interacting with a funnel array under a current applied perpendicular to the funnel axis. We find that transport without annihilation is possible at low currents, when the motion is dominated by skyrmion-skyrmion interactions and skyrmions push each other through the funnel opening. Skyrmion annihilation occurs for higher currents when skyrmions in the upper half of the sample exert pressure on skyrmions in the bottom half of the sample due to the external current. Upon interacting with the funnel wall, the skyrmions undergo a size reduction that makes it easier for them to pass through the funnel opening. We find five phases as a function of the applied current and the size of the funnel opening: (i) pinned, (ii) transport without annihilation, (iii) transport with annihilation, (iv) complete annihilation, and (v) a reentrant pinning phase that only occurs for very narrow openings. Our findings provide insight into how to control skyrmion transport using funnel arrays by delineating regimes in which transport of skyrmions is possible as well as the conditions under which annihilation occurs.

Nontraditional Movement Behavior of Skyrmion in a Circular-Ring Nanotrack.

Magnetic skyrmions are considered promising candidates for use as information carriers in future spintronic devices. To achieve the development of skyrmion-based spintronic devices, a reasonable and feasible nanotrack is essential. In this paper, we conducted a study on the current-driven skyrmion movement in a circular-ring-shaped nanotrack. Our results suggest that the asymmetry of the inside and outside boundary of the circular ring changed the stable position of the skyrmion, causing it to move like the skyrmion Hall effect when driven by currents. Moreover, the asymmetric boundaries have advantages in enhancing or weakening the skyrmion Hall effect. Additionally, we also compared the skyrmion Hall effect from the asymmetric boundary of circular-ring nanotracks with that from the inhomogeneous Dzyaloshinskii-Moriya interaction. It was found that the skyrmion Hall effect in the circular ring is significantly greater than that caused by the inhomogeneous Dzyaloshinskii-Moriya interaction. These results contribute to our understanding of the skyrmion dynamics in confined geometries and offer an alternative method for controlling the skyrmion Hall effect of skyrmion-based devices.

Skyrmion motion under temperature gradient and application in logic devices.

Under the presence of temperature gradient (TG) on a nanotrack, it is necessary to investigate the skyrmion dynamics in various magnetic systems under the combined effect of forces due to magnonic spin transfer torque(µSTT),thermal STT (τSTT), entropic difference(dS),as well as thermal induced dipolar field (DF). Hence, in this work, the dynamics of skyrmions in ferromagnets (FM), synthetic antiferromagnets (SAF), and antiferromagnets (AFM) have been studied under different TGs and damping constants (αG). It is observed thatαGplays a major role in deciding the direction of skyrmion motion either towards the hotter or colder side in different magnetic structures. Later, FM skyrmion based logic device is proposed that consists of a cross-coupled nanotrack, where the skyrmions on horizontal and vertical nanotrack are controlled by exploiting TG and electrical STT (eSTT), respectively by taking the advantages of thermal induced skyrmion Hall effect (SkHE). The proposed device performs AND and OR logic functionalities simultaneously, when the applied current density is2×1011Am-2.Moreover, the proposed device is also able to exhibit the half adder functionality by tuning the applied current density to3×1011Am-2.The total energy consumption for AND and OR logic operation and half adder are 33.63 fJ and 25.06 fJ, respectively. This paves the way for the development of energy-efficient logic devices with ultra-high storage density.

All-Electrical 9-Bit Skyrmion-Based Racetrack Memory Designed with Laser Irradiation.

Racetrack memories with magnetic skyrmions have recently been proposed as a promising storage technology. To be appealing, several challenges must still be faced for the deterministic generation of skyrmions, their high-fidelity transfer, and accurate reading. Here, we realize the first proof-of-concept of a 9-bit skyrmion racetrack memory with all-electrical controllable functionalities implemented in the same device. The key ingredient is the generation of a tailored nonuniform distribution of magnetic anisotropy via laser irradiation in order to (i) create a well-defined skyrmion nucleation center, (ii) define the memory cells hosting the information coded as the presence/absence of skyrmions, and (iii) improve the signal-to-noise ratio of anomalous Hall resistance measurements. This work introduces a strategy to unify previous findings and predictions for the development of a generation of racetrack memories with robust control of skyrmion nucleation and position, as well as effective skyrmion electrical detection.

Reversible Phase Transition between Vortex Lattice and Hexagonal Polar Skyrmion Crystals.

Polar skyrmions in oxide heterostructures have recently attracted extensive interest due to their unique physical properties and potential applications. Here, we report the formation of the vortex lattice and the nanoscale polar skyrmion crystals with two-dimensional hexagonal symmetry in PbTiO3/SrTrO3 (PTO/STO) superlattices. Under an increasing external field, the system transitions from a vortex lattice phase to hexagonal polar skyrmion crystals (PSkC). The formation and annihilation process of the polar skyrmion crystals resemble the structural phase transition observed in atomic crystals. A temperature-electric field topological phase diagram is constructed, demonstrating stabilization of the vortex lattice and polar skyrmion crystals in a wide temperature and electric-field range. This study demonstrates the potential of manipulating the topological phase transition and its long-range order through an external field.

Skyrmion-Bubble Bundles in an X-Type Sr2 Co2 Fe28 O46 Hexaferrite above Room Temperature.

Magnetic skyrmions are spin swirls that possess topological nontriviality and are considered particle-like entities. They are distinguished by an integer topological charge Q. The presence of skyrmion bundles provides an opportunity to explore the range of values for Q, which is crucial for the advancement of topological spintronic devices with multi-Q properties. In this study, a new material candidate, Sr2 Co2 Fe28 O46 hexaferrite of the X-type, which hosts small dipolar skyrmions at room temperature and above is presented. By exploiting reversed magnetic fields from metastable skyrmion bubbles at zero fields, skyrmion-bubble bundles with different interior skyrmion/bubble numbers, topological charges, and morphologies at room temperature are incorporated. These experimental findings are consistently supported by micromagnetic simulations. These results highlight the versatility of topological spin textures in centrosymmetric uniaxial magnets, thereby paving the way for the development of room-temperature topological spintronic devices with multi-Q characteristics.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.