Skyrmion Lattice Research Articles

Skyrmion soliton motion on periodic substrates by atomistic and particle based simulations

Abstract We compare the dynamical behavior of magnetic skyrmions interacting with square and triangular defect arrays just above commensuration using both atomistic and particle-based models. Under applied drives, the initial motion is a kink traveling through the pinned skyrmion lattice. For the square defect array, both models agree well and show a regime in which the soliton motion is locked along 45°. The atomistic model also produces locking of a soliton along 30°, which is absent in the particle-based model. For the triangular defect array, the atomistic model exhibits 30° soliton motion over a wide region of external current values. In contrast, the particle-based model gives 45° soliton motion over a small range of external driving force values. The difference arises because the nondeforming particle model facilitates meandering skyrmion orbits while the deformable atomistic model enables stronger skyrmion-skyrmion interactions that reduce the meandering. Our results indicate that soliton motion through pinned skyrmion lattices on a periodic substrate is a robust effect.

Spin Spiral State at a Ferromagnetic Gd Vacuum Interface.

Centrosymmetric bulk magnets made of layered Gd intermetallics had been discovered recently to exhibit helical spin spirals with a wavelength of ≈2 nm that transform into skyrmion lattices at certain magnetic fields. Here we report on the observation of a spin spiral state at the Gd(0001) surface. Spin-polarized scanning tunneling microscopy images show striped regions with a periodicity of about 2nm. These stripes rearrange upon application of an external magnetic field, thereby unambiguously confirming their magnetic origin. Density functional theory calculations explain that competing exchange interactions in the surface layer of Gd(0001) together with a magnetovolume fine-tuning of the exchange interaction to the next Gd layer favor a chiral 2nm conical spin spiral at the surface, arising as a general behavior of the Gd monolayer.

Reentrant multiple-q magnetic order and a “spin meta-cholesteric” phase in Sr3Fe2O7

Topologically nontrivial magnetic structures such as skyrmion lattices are well known in materials lacking lattice inversion symmetry, where antisymmetric exchange interactions are allowed. Only recently, topological multi-q magnetic textures that spontaneously break the chiral symmetry, for example, three-dimensional hedgehog lattices, were discovered in centrosymmetric compounds, where they are instead driven by frustrated interactions. Here we show that the bilayer perovskite Sr3Fe2O7, previously believed to adopt a simple single-q spin-helical order, hosts two distinct types of multi-q spin textures. Its ground state represents a novel multi-q spin texture with unequally intense spin modulations at the two ordering vectors. This is followed in temperature by a new “spin meta-cholesteric” phase, in which the chiral symmetry is spontaneously broken along one of the crystal directions, but the weaker orthogonal modulation melts, giving rise to intense short-range dynamical fluctuations. Shortly before the transition to the paramagnetic state, vortex-crystal order spanned by two equivalent q vectors emerges. This renders Sr3Fe2O7 an ideal material to study transitions among multiple-q spin textures in a centrosymmetric host.

Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices.

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.

Spin Wave Chiral Scattering by Skyrmion Lattice in Ferromagnetic Nanotubes

Spin Wave Chiral Scattering by Skyrmion Lattice in Ferromagnetic Nanotubes

Real-Space Topology-Engineering of Skyrmionic Spin Textures in a van der Waals Ferromagnet Fe3GaTe2.

Realizing magnetic skyrmions in two-dimensional (2D) van der Waals (vdW) ferromagnets offers unparalleled prospects for future spintronic applications. The room-temperature ferromagnet Fe3GaTe2 provides an ideal platform for tailoring these magnetic solitons. Here, skyrmions of distinct topological charges are artificially introduced and engineered by using magnetic force microscopy (MFM). The skyrmion lattice is realized by a specific field-cooling process and can be further erased and painted via delicate manipulation of the tip stray field. The skyrmion lattice with opposite topological charges (S = ±1) can be tailored at the target regions to form topological skyrmion junctions (TSJs) with specific configurations. The delicate interplay of TSJs and spin-polarized device current were finally investigated via the in situ transport measurements, alongside the topological stability of TSJs. Our results demonstrate that Fe3GaTe2 not only serves as a potential building block for skyrmion-based spintronic devices, but also presents prospects for Fe3GaTe2-based heterostructures with the engineered topological spin textures.

Exotic Spin Excitations in a Polar Magnet VOSe_{2}O_{5}.

Magnetic resonance dynamics has been studied for a polar magnet VOSe_{2}O_{5}, which hosts several nontrivial magnetic phases including Néel-type skyrmion lattice (SkL). In both cycloidal and SkL spin states, two excitation modes active to oscillating magnetic field B_{ν}⊥c and one mode active to B_{ν}∥c are identified. The subsequent micromagnetic simulations well reproduce the observed selection rules and relative resonance frequencies, which allows the unambiguous assignment of the spin oscillation manner for each mode. Interestingly, the IC-2 phase with a potential double-q character was found to host similar excitation modes as the SkL state. We also discovered the existence of the novel B' phase with four modes active to B_{ν}⊥c. The present results provide a fundamental basis for the comprehensive understanding of resonant spin dynamics in polar magnets, and highlight VOSe_{2}O_{5} as a unique material platform to host a rich variety of nontrivial spin excitations.

Magnetostriction related to skyrmion-lattice formation in chiral magnet FeGe

The B20 type chiral magnet FeGe exhibits the formation of skyrmion-lattice (SkL) phases in the vicinity of the magnetic ordering temperature. The SkL is a magnetic superlattice composed of vortex-type topological spin objects, and it has experimentally been known that its formation requires the existence of an intermediate (IM) phase between SkL and the paramagnetic (PM) phases. We take interest in how the crystal lattice experiences the formation of these topological spin texture. In this study, we observed the so-called spin–orbit coupling induced magnetostriction related to these topological spin texture formation, in addition to the ac magnetization anomalies. The temperature and magnetic field dependences of the lattice parameter reflected the transformation of phases, such as helimagnetic (HM), SkL, IM, conical (CM), and PM phases. In the PM region, a phase characterized as gaseous skyrmions was detected similarly to the case of the same B20 type MnSi. Furthermore, the HM, CM, and IM phases were also divided into two regions. Thus, the precise phase diagram near Tc was reconstructed from the prospect of the magnetostriction such that we demonstrated that the stabilization of skyrmions needs a finite magnetic field.

Meron-Mediated Phase Transitions in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy: Successive Transformation of the Hexagonal Skyrmion Lattice into the Square Lattice and into the Tilted FM State.

I revisit the well-known structural transition between hexagonal and square skyrmion lattices and subsequent first-order phase transition into the tilted ferromagnetic state as induced by the increasing easy-plane anisotropy in quasi-two-dimensional chiral magnets. I show that the hexagonal skyrmion order first transforms into a rhombic skyrmion lattice, which, adjusts into a perfect square arrangement of skyrmions ("a square meron-antimeron crystal") within a narrow range of anisotropy values. These transitions are mediated by merons and anti-merons emerging in the boundaries between skyrmion cells; energetically unfavorable anti-merons annihilate, whereas pairs of neighboring merons merge. The tilted ferromagnetic state sets in via mutual annihilation of oppositely charged merons; as an outcome, it contains bimeron clusters (chains) with the attracting inter-soliton potential. Additionally, I demonstrate that domain-wall merons are actively involved in the dynamic response of the square skyrmion lattices. As an example, I theoretically study spin-wave modes and their excitations by AC magnetic fields. Two found resonance peaks are the result of the complex dynamics of the domain-wall merons; whereas in the high-frequency mode the merons rotate counterclockwise, as one might expect, in the low-frequency mode merons are instead created and annihilated consistently with the rotational motion of the domain boundaries.

Rolling Motion of Rigid Skyrmion Crystallites Induced by Chiral Lattice Torque.

Magnetic skyrmions are topologically protected spin textures with emergent particle-like behaviors. Their dynamics under external stimuli is of great interest and importance for topological physics and spintronics applications alike. So far, skyrmions are only found to move linearly in response to a linear drive, following the conventional model treating them as isolated quasiparticles. Here, by performing time and spatially resolved resonant elastic X-ray scattering of the insulating chiral magnet Cu2OSeO3, we show that for finite-sized skyrmion crystallites, a purely linear temperature gradient not only propels the skyrmions but also induces continuous rotational motion through a chiral lattice torque. Consequently, a skyrmion crystallite undergoes a rolling motion under a small gradient, while both the rolling speed and the rotational sense can be controlled. Our findings offer a new degree of freedom for manipulating these quasiparticles toward device applications and underscore the fundamental phase difference between the condensed skyrmion lattice and isolated skyrmions.

Dynamic transition and Galilean relativity of current-driven skyrmions.

The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields1-3. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding4-6, resulting in the conduction electrons exhibiting the topological Hall effect (THE)7. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated8,9. The resulting emergent electrodynamics dictate the magnitude of the THE by the relative motion of SkL and conduction electrons. Here we report the emergent electrodynamics induced by SkL motion in Gd2PdSi3, facilitated by its giant THE10,11. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, in which the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE may be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity-current profile, which shows the inertial-like motion of the SkL in the creep regime, appearing as the current hysteresis of the skyrmion velocity.

Multidimensional dynamic control of optical skyrmions in graphene–chiral–graphene multilayers

Abstract Optical skyrmions are topological quasiparticles with a complex vectorial field structure. Their associated characteristics of ultra-small, ultra-fast and topological protection have great application prospects in high density data storage, light matter interaction and optical communication. At present, the research of optical skyrmions is still in its infancy, where the construction and flexible regulation of different topological textures are current research hotspot. Here, we combine the twist degree of freedom of materials and optical skyrmions. Based on graphene–chiral–graphene multilayers structure, we demonstrate the field mode symmetry and hybridization to form Bloch-type graphene plasmons skyrmion lattice. At the same time, by changing chirality parameter, the Fermi energy of graphene and the phase of incident light, multidimensional control of Bloch-type optical skyrmions can be realized. Our work demonstrated that the properties of materials provide the additional dimensions to regulate the topological states, and the combination of different materials structures provides the possibility for dynamic construction and manipulation of multiple topological states, which is expected to find applications in integrated nanophotonics devices.

Emergence and transformation of polar skyrmion lattices via flexoelectricity

As analogies to magnetic skyrmions, polar skyrmions in ferroelectric superlattices and multilayers have garnered widespread attention for their non-trivial topology and novel properties like negative capacitance and nonlinear optical effect. So far, they have only been theoretically predicted to be able to assemble ordered hexagonal skyrmion lattices (SkLs) in ferroelectric thin films. Here, based on phase-field simulations, we report the critical roles of flexoelectricity playing in the stabilization and transformation of polar SkLs. Different polar SkL patterns can emerge in the ferroelectric thin films, including tetragonal-SkL, and hexagonal-SkLs with diverse orientations, as summarized by phase diagrams. These emergent SkL states are attributed to the material anisotropy modified by the flexoelectric effect. Interestingly, we further found that the hexagonal-SkLs can be rotated by applying strain gradient or in-plane electric field to the films. Moreover, a nonreciprocal bending response of tetragonal-SkL is also induced by the flexoelectric effect. Our results provide useful guidelines for the implementation of polar skyrmion lattices in experiments.

Dynamic Behavior of Above-Room-Temperature Robust Skyrmions in 2D Van der Waals Magnet.

Magnetic skyrmions are swirl-like spin configurations that present topological properties, which have great potential as information carriers for future high-density and low-energy-consumption devices. The optimization of skyrmion-hosting materials that can be integrated with semiconductor-based circuits is the primary challenge for their industrialization. Two-dimensional van der Waals ferromagnets are emerging materials that have excellent carrier mobility and compatibility with integrated circuits, making them an ideal candidate for spintronic devices. Here, we report the realization of skyrmions at above room temperature in the 2D ferromagnet Fe3GaTe2. The thickness tunability of their skyrmion size and the formation of the skyrmion lattice are revealed. Furthermore, we demonstrate that the skyrmions can be moved by a low-density current at room temperature, together with an apparent skyrmion Hall effect, which is consistent with our quantitative micromagnetic simulation. Our work offers a promising 2D material platform for harnessing magnetic skyrmions in practical device applications.

Melting and freezing of a skyrmion lattice

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices (SkL) in systems of small, medium, and large sizes with the number of skyrmions ranging from 103to over 105. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of SkLs. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the SkL. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.

Achiral hard bananas assemble double-twist skyrmions and blue phases.

Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.

Solid–liquid transition in a skyrmion matter

We report Monte-Carlo studies of the orientational order and melting of a 2D skyrmion lattice containing more than one million spins. Two models have been investigated, a microscopic model of lattice spins with Dzyaloshinskii–Moryia interaction that possesses skyrmions, and the model in which skyrmions are treated as point particles with repulsive interaction derived from a spin model. They produce similar results. The skyrmion lattice exhibits a sharp one-step transition between solid and liquid phases on temperature and the magnetic field. This solid–liquid transition is characterized by the kink in the magnetization. The field-temperature phase diagram is computed. We show that the application of the field gradient to a 2D system of skyrmions produces a solid–liquid interface that must be possible to observe in experiments.

Embedded Skyrmion Bags in Thin Films of Chiral Magnets.

Magnetic skyrmions are topologically nontrivial spin configurations that possess particle-like properties. Earlier research has mainly focused on a specific type of skyrmion with topological charge Q = -1. However, theoretical analyses of 2D chiral magnets have predicted the existence of skyrmion bags-solitons with arbitrary positive or negative topological charge. Although such spin textures are metastable states, recent experimental observations have confirmed the stability of isolated skyrmion bags in a limited range of applied magnetic fields. Here, by utilizing Lorentz transmission electron microscopy, the extraordinary stability of skyrmion bags in thin plates of B20-type FeGe is shown. In particular, it is shown that skyrmion bags embedded within a skyrmion lattice remain stable even in zero or inverted external magnetic fields. A robust protocol for nucleating such embedded skyrmion bags is provided. The results agree perfectly with micromagnetic simulations and establish thin plates of cubic chiral magnets as a powerful platform for exploring a broad spectrum of topological magneticsolitons.

Detailed dynamics of a moving magnetic skyrmion lattice in MnSi observed using small-angle neutron scattering under an alternating electric current flow

Detailed dynamics of a moving magnetic skyrmion lattice in MnSi observed using small-angle neutron scattering under an alternating electric current flow

Phonon softening and atomic modulations in EuAl4

EuAl4 is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in EuAl4. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at TCDW=142 K, freezes out in an atomic displacement mode described by the superspace group Immm(00γ)s00. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl4 is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl4 and ThCr2Si2-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism. Published by the American Physical Society 2024