Skyrmion Lattice Research Articles

Periodic dynamics of optical skyrmion lattices driven by symmetry

The recently developed concept of optical skyrmions has introduced an exciting dimension to the emerging field of Poincaré engineering in optical lattices. There remains an unexplored territory in investigating system geometries to enhance the versatility of manipulating the topological landscape within optical lattices. Here, we present both experimental and theoretical evidence showcasing the periodic vectorial characteristics of field- and spin-based skyrmion lattices, generated by plasmonic vortices with varying topological charges. Our findings reveal that the geometric symmetry of the system plays a pivotal role in governing the periodic arrangement of these vortex patterns. Building upon this arrangement, the orbital–orbital coupling of plasmonic vortices gives rise to densely packed energy flow distributions, intricately bonded to topological charges. Consequently, this results in the formation of sublattices within the momentum space, each characterized by distinct k-vectors. Skyrmion and meron topologies, driven by the intrinsic spin–orbital coupling, are presented in these lattices. This proposed framework illuminates how symmetry serves as a fundamental tool in the manipulation of optical lattice topologies, opening up new avenues in fields ranging from optical trapping, laser writing, quantum gas microscopy, to electron quantum state control, each of which is poised to benefit from these nontrivial advances.

Probing the Sense of Spin Twisting in Magnetic Skyrmion Lattice by Resonant X-ray Scattering

Probing the Sense of Spin Twisting in Magnetic Skyrmion Lattice by Resonant X-ray Scattering

Skyrmion lattice formation and destruction mechanisms probed with TR-SANS.

Magnetic skyrmions are topologically protected, nanoscale whirls of the spin configuration that tend to form hexagonally ordered arrays. As a topologically non-trivial structure, the nucleation and annihilation of the skyrmion, as well as the interaction between skyrmions, varies from conventional magnetic systems. Recent works have suggested that the ordering kinetics in these materials occur over millisecond or longer timescales, which is unusually slow for magnetic dynamics. The current work investigates the skyrmion ordering kinetics, particularly during lattice formation and destruction, using time-resolved small angle neutron scattering (TR-SANS). Evaluating the time-resolved structure and intensity of the neutron diffraction pattern reveals the evolving real-space structure of the skyrmion lattice and the timeframe of the formation. Measurements were performed on three prototypical skyrmion materials: MnSi, (Fe,Co)Si, and Cu2OSeO3. To probe lattice formation and destruction kinetics, the systems were prepared in the stable skyrmion state, and then a square-wave magnetic field modulation was applied. The measurements show that the skyrmions quickly form ordered domains, with a significant distribution in lattice parameters, which then converge to the final structure; the results confirm the slow kinetics, with formation times between 10 ms and 99 ms. Comparisons are made between the measured formation times and the fundamental material properties, suggesting the ordering temperature, saturation magnetization and magnetocrystalline anisotropy may be driving the timeframes. Micromagnetic simulations were also performed and support a scaling of the kinetics with sample volume, a behavior which is caused by the reconciling of misaligned domains.

Regulating magnetic skyrmions in multiferroic monolayer MnOBr.

Two-dimensional multiferroic materials that exhibit both ferroelectricity and ferromagnetism provide a new platform for the discovery and regulation of magnetic skyrmions. In this study, we utilize first-principles calculations and Monte Carlo simulations to explore the properties and regulation of magnetic skyrmions in a novel multiferroic monolayer, MnOBr. MnOBr exhibits skyrmions without the need for an external magnetic field. Upon applying an external magnetic field, we found the disappearance of labyrinth domains and the formation of a periodic arrangement of the skyrmion lattice. By employing machine learning techniques, we depict a phase diagram of MnOBr under varying magnetic fields and biaxial strain, which provides a detailed depiction of phase transitions of spin textures in monolayer MnOBr. Furthermore, in MnOBr/CdClBr heterostructures, we demonstrate that the creation and annihilation of magnetic skyrmions can be controlled by switching the polarization direction of the Janus CdClBr. These findings show potential applications of MnOBr as a 2D magnetic skyrmion material in spintronic devices.

Unification of Spin Helicity in the Magnetic Skyrmion Lattice of EuNiGe3

In the magnetic skyrmion lattice of non-centrosymmetric EuNiGe3, the original magnetic helicity, determined by the antisymmetric exchange interaction, is reversed, resulting in a unified helicity.

Skyrmion Lattices Phase Driven by Interfacial-Engineered Dzyaloshinskii–Moriya Interaction in Frustrated Antiferromagnetic/Ferroelectric Bilayers

Skyrmion Lattices Phase Driven by Interfacial-Engineered Dzyaloshinskii–Moriya Interaction in Frustrated Antiferromagnetic/Ferroelectric Bilayers

Designing Layered 2D Skyrmion Lattices in Moiré Magnetic Heterostructures

AbstractSkyrmions are promising for the next generation of spintronic and magnonic devices, but their zero‐field stability and controlled nucleation through chiral interactions remain challenging. In this theoretical study, the potential of moiré magnetic heterostructures to generate ordered skyrmion lattices from the stacking‐dependent magnetism in 2D magnets is explored. Heterostructures formed by twisting ultrathin CrBr3 films on top of CrI3 substrates are considered, assuming a moderate interfacial Dzyaloshinskii–Moriya interaction. At large moiré periodicity and appropriate substrate thickness, a moiré skyrmion lattice emerges in the interfacial CrBr3 layer due to the weaker exchange interactions in CrBr3 compared to CrI3. This lattice is then projected to the remaining layers of the CrBr3 film via chiral interlayer exchange fields. By varying the pristine stacking configurations within the ultrathin CrBr3 film, layered ferromagnetic and antiferromagnetic skyrmion lattices without the need for a permanent magnetic field are realized. These findings suggest the possibility of creating ordered skyrmion lattices in moiré magnetic heterostructures, enabling further exploration of their fundamental properties and technological relevance.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet.

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N=-1/2 and antimeron with N=1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N=-1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

A Simulation Study of the Dynamical Control of Optical Skyrmion Lattices through the Superposition of Optical Vortex Beams

Optical skyrmion lattices play an important role in photonic system design and have potential applications in optical transmission and storage. In this study, we propose a novel metasurface approach to calculating the dependence of the multi-beam interference principle and the angular momentum action in the spin–orbit interaction. The metasurface consists of nanopore structures, which are used to generate an optical skyrmion lattice. The superposition of optical vortex beams with circular polarization states is used to evaluate the evolution of the shape of the topological domain walls of the hexagonal skyrmion lattice. Our results show that the distribution of the skyrmion spin vector can be controlled by changing the lattice arrangement from triangular to hexagonal shapes. The distribution of skyrmion number at the microscale is further calculated. Our work has significant implications for the regulation of the shape of topological domain walls of skyrmion lattices, with potential applications in polarization sensing, nanopositioning, and super-resolution microimaging.

Handwritten digit recognition by spin waves in a Skyrmion reservoir

By performing numerical simulations for the handwritten digit recognition task, we demonstrate that a magnetic skyrmion lattice confined in a thin-plate magnet possesses high capability of reservoir computing. We obtain a high recognition rate of more than 88%, higher by about 10% than a baseline taken as the echo state network model. We find that this excellent performance arises from enhanced nonlinearity in the transformation which maps the input data onto an information space with higher dimensions, carried by interferences of spin waves in the skyrmion lattice. Because the skyrmions require only application of static magnetic field instead of nanofabrication for their creation in contrast to other spintronics reservoirs, our result consolidates the high potential of skyrmions for application to reservoir computing devices.

Towards skyrmion crystal stabilization in the antiferromagnetic triangular lattice at ambient conditions

We explore possibilities of stabilizing a skyrmion lattice (SkX) phase in the frustrated antiferromagnetic (AF) Heisenberg model with the Dzyaloshinskii–Moriya interaction on a triangular lattice at ambient conditions. We show that by stacking multiple AF layers and coupling them with strong ferromagnetic (F) interaction the SkX phase stability temperature window can be extended by several times. The transition temperature increase is supported by the increasing number of layers and interlayer interaction and thus room-temperature SkX phase could be achievable by proper tailoring of the multilayer structure. Further, we demonstrate that in the sandwich heterostructure, obtained by inserting a stiff F layer in between two AF layers, the required external magnetic field can be completely replaced by the effective field imposed by the F layer. Thus, one can design a heterostructure with the SkX phase stabilized at relatively high temperatures and zero field - the environment favorable for technological applications.

Author Correction: Asymmetric slow dynamics of the skyrmion lattice in MnSi

Author Correction: Asymmetric slow dynamics of the skyrmion lattice in MnSi

Phase transitions driven by magnetoelectric and interfacial Dzyaloshinskii-Moriya interaction

In this paper, we study phase transitions in a magnetoelectric bilayer with two order parameters using Monte Carlo simulation. We investigate the effects of temperature, magnetoelectric coupling, and anisotropy in the multiferroic bilayer formed by a frustrated antiferromagnetic layer with Heisenberg spins and a triangular lattice ferroelectric layer. We show that magnetic frustration induces creation of skyrmions and a skyrmion lattice at moderate values of Dzyaloshinskii-Moriya interaction and interface magnetoelectric coupling with adjacent ferroelectric layer. The skyrmion crystal is stable up to relatively high temperatures. The effect of anisotropy is to cause only a shift of the critical temperature without changing the type of the phase transition. The phase of the skyrmion lattice becomes more resistant and stable to temperature fluctuations in the case of a highly anisotropic frustrated film.

2D-Perovskite Multiferroics: Interface-Induced Magnetoelectric Effect in Perovskite-Based Multiferroic Superlattices

Multiferroics are materials crucial for energy-efficient scalable electronics. The implementation of an effective combination of ferroic orderings on the nanoscale requires the design of new multiferroic materials. Recently, there have been observations of magnetoelectricity in the antiferromagnetic Ruddlesden-Popper and perovskite oxides with the interfacial Dzyaloshinskii-Moriya interaction. We propose a model for studying magnetic states and magnetoelectric effects in magnetoelectrically coupled antiferromagnetic–ferroelectric bi-layers with the interfacial Dzyaloshinskii–Moriya interaction. The ground magnetic states are calculated for a system on a rectangular lattice, with Heisenberg spins interacting with each other via an antiferromagnetic exchange interaction and a Dzyaloshinskii–Moriya interaction in the absence of an external magnetic field. Our calculations show that the interfacial Dzyaloshinskii-Moriya interaction in the considered system leads to the stabilization of topological skyrmionic states in a zero magnetic field. We explore transformations of magnetic states considering the changes in the in-plane magnetic anisotropy constant and the magnetoelectric coupling parameter. Our findings have shown the possibility of the existence of several magnetic configurations: a skyrmion lattice, a skyrmion state, and a uniform antiferromagnetic ordering realized at a definite ratio of the system parameters. We determine the areas of the phases existence and the conditions required for spin-reorientation phase transitions.

Genetic-tunneling driven energy optimizer for spin systems

Finding the ground state of complex many-body systems, such as magnetic materials containing topological textures, like skyrmions, is a fundamental and long-standing problem. We present here a genetic-tunneling-driven variance-controlled optimization method, that efficiently identifies the ground state of two-dimensional skyrmionic systems. The approach combines a local energy-minimizer backend and a metaheuristic global search frontend. The method is shown to perform significantly better than simulated annealing. Specifically, we demonstrate that for the Pd/Fe/Ir(111) system, our method correctly and efficiently identifies the experimentally observed spin spiral geometry, skyrmion lattice and ferromagnetic ground states as a function of the external magnetic field. To our knowledge, no other optimization method has until now succeeded in doing this. We envision that our findings will pave the way for evolutionary computing in mapping out phase diagrams for spin systems in general.

Three-dimensional neutron far-field tomography of a bulk skyrmion lattice

AbstractMagnetic skyrmions are localized non-collinear spin textures, characterized by an integer topological charge. Commonly observed in thin systems as two-dimensional sheets, in three dimensions skyrmions form tubes that are thought to nucleate and annihilate along their depth on points of vanishing magnetization. However, a lack of techniques that can probe the bulk of the material has made it difficult to perform experimental visualizations of skyrmion lattices and their stabilization through defects. Here we present three-dimensional visualizations of a bulk Co8Zn8Mn4 skyrmion lattice through a tomographic algorithm applied to multiprojection small-angle neutron scattering measurements. Reconstructions of the sample show a disordered skyrmion lattice exhibiting three-dimensional topological transitions through emergent (anti)monopole branching and segmentation defect pathways. Our technique provides insights into skyrmion stabilization and topological transition pathways in a bulk skyrmion lattice, guiding the future development and manipulation of skyrmion materials for spintronic applications.

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3.

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Broadband magnetic resonance spectroscopy in MnSc_2S_4

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc_2S_4 . Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc_2S_4 by THz spectroscopy at 300 mK and in magnetic fields up to 12 T and by broadband microwave spectroscopy at various temperatures up to 50 GHz. We found a single magnetic resonance with frequency linearly increasing in field. The small deviation of the Mn^{2+} ion g-factor from 2, g = 1.96, and the absence of other resonances imply very weak anisotropies and negligible contribution of higher harmonics to the spiral state. The significant difference between the dc magnetic susceptibility and the lowest-frequency ac susceptibility in our experiment implies the existence of mode(s) outside of the measured frequency windows. The combination of THz and microwave experiments suggests a spin gap opening below the ordering temperature between 50 GHz and 100 GHz.

Skyrmion-Excited Spin-Wave Fractal Networks.

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creatingthe magnetic equivalent of a turbulentsea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin-wave interference can precipitate from the chaos. This work uses small-angle neutron scattering (SANS)to capture the dynamics in hybrid skyrmions and investigate the spin-wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-anglescattering intensity, which is present only in the resonancecondition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin-wave emissions and are constrained by the skyrmion lattice. These results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin-wave fractal structure, and demonstrate SANS as a unique tool to probe high-speed dynamics.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.