Skyrmion Lattice Research Articles

Position-dependent stability and lifetime of the skyrmion state in nickel-substituted Cu2OSeO3

We report spatially resolved small-angle neutron-scattering measurements of the conical and skyrmion states of a bulk single crystal of nickel-substituted ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$, with a nominal concentration of Ni of 14%. We observe a significant spatial dependence of the structure of these magnetic states, characterized by increased disorder and misalignment with respect to the applied field as we approach the edge of the sample. Remarkably, the edge skyrmion state is also characterized by an extended stability towards lower temperatures. Surprisingly, in the same region of the sample, the metastable skyrmion state did not show simple decay. Instead, only a fraction of the scattered intensity appeared to decay, and the intensity therefore did not approach zero during our measurements. We suggest that the increased local disorder and the coexistence of conical and skyrmion states, induced by demagnetization effects at the edge of the sample, are responsible for the increased stability of this skyrmion state. We also infer that the unclear metastable behavior of the skyrmion lattice at the edge of the sample is due to the local geometry of the sample, which induces coexistence of different skyrmion states whose lifetimes are superimposed and difficult to separate in the data.

Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2

Magnetic skyrmions were thought to be stabilised only in inversion-symmetry breaking structures, but skyrmion lattices were recently discovered in inversion symmetric Gd-based compounds, spurring questions of the stabilisation mechanism. A natural consequence of a recent theoretical proposal, a coupling between itinerant electrons and localised magnetic moments, is that the skyrmions are amenable to detection using even non-magnetic probes such as spectroscopic-imaging scanning tunnelling microscopy (SI-STM). Here SI-STM observations of GdRu2Si2 reveal patterns in the local density of states that indeed vary with the underlying magnetic structures. These patterns are qualitatively reproduced by model calculations which assume exchange coupling between itinerant electrons and localised moments. These findings provide a clue to understand the skyrmion formation mechanism in GdRu2Si2.

Plasmonic Skyrmion Lattice Based on the Magnetoelectric Effect.

The physical mechanism of the plasmonic skyrmion lattice formation in a magnetic layer deposited on a metallic substrate is studied theoretically. The optical lattice is the essence of the standing interference pattern of the surface plasmon polaritons created through coherent or incoherent laser sources. The nodal points of the interference pattern play the role of lattice sites where skyrmions are confined. The confinement appears as a result of the magnetoelectric effect and the electric field associated with the plasmon waves. The proposed model is applicable to yttrium iron garnet and single-phase multiferroics and combines plasmonics and skyrmionics.

Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer

Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI2. Our first-principles and Monte Carlo simulations reveal that the anisotropies of the short-range symmetric exchange, when combined with magnetic frustration, can lead to an emergent chiral interaction that is responsible for the predicted topological spin structures. The proposed mechanism finds a prototypical manifestation in two-dimensional magnets, thus broadening the class of materials that can host spontaneous skyrmionic states.

Skyrmion lattice creep at ultra-low current densities

Magnetic skyrmions are well-suited for encoding information because they are nano-sized, topologically stable, and only require ultra-low critical current densities jc to depin from the underlying atomic lattice. Above jc skyrmions exhibit well-controlled motion, making them prime candidates for race-track memories. In thin films thermally-activated creep motion of isolated skyrmions was observed below jc as predicted by theory. Uncontrolled skyrmion motion is detrimental for race-track memories and is not fully understood. Notably, the creep of skyrmion lattices in bulk materials remains to be explored. Here we show using resonant ultrasound spectroscopy—a probe highly sensitive to the coupling between skyrmion and atomic lattices—that in the prototypical skyrmion lattice material MnSi depinning occurs at {j}_{c}^{* } that is only 4 percent of jc. Our experiments are in excellent agreement with Anderson-Kim theory for creep and allow us to reveal a new dynamic regime at ultra-low current densities characterized by thermally-activated skyrmion-lattice-creep with important consequences for applications.

Particle-size dependent structural transformation of skyrmion lattice

Magnetic skyrmion is a topologically protected particle-like object in magnetic materials, appearing as a nanometric swirling spin texture. The size and shape of skyrmion particles can be flexibly controlled by external stimuli, which suggests unique features of their crystallization and lattice transformation process. Here, we investigated the detailed mechanism of structural transition of skyrmion lattice (SkL) in a prototype chiral cubic magnet Cu2OSeO3, by combining resonant soft X-ray scattering (RSXS) experiment and micromagnetic simulation. This compound is found to undergo a triangular-to-square lattice transformation of metastable skyrmions by sweeping magnetic field (B). Our simulation suggests that the symmetry change of metastable SkL is mainly triggered by the B-induced modification of skyrmion core diameter and associated energy cost at the skyrmion-skyrmion interface region. Such internal deformation of skyrmion particle has further been confirmed by probing the higher harmonics in the RSXS pattern. These results demonstrate that the size/shape degree of freedom of skyrmion particle is an important factor to determine their stable lattice form, revealing the exotic manner of phase transition process for topological soliton ensembles in the non-equilibrium condition.

Mixed topology ring states for Hall effect and orbital magnetism in skyrmions of Weyl semimetals

Skyrmion lattices as a novel type of chiral spin states are attracting increasing attention, owing to their peculiar properties stemming from real-space topological properties. At the same time, the properties of magnetic Weyl semimetals with complex $k$-space topology are moving into the focus of research in spintronics. We consider the Hall transport properties and orbital magnetism of skyrmion lattices imprinted in topological semimetals, by employing a minimal model of a 2D mixed Weyl semimetal which, as a function of the magnetization direction, exhibits two Chern insulator phases separated by a Weyl state for an an in-plane magnetization direction. We find that while the orbital magnetization is topologically robust and Hall transport properties are very sensitive to the details of the spin distribution in accordance to the behavior expected from the recently discovered chiral Hall effect[1], their behavior in the region of the Chern insulator gap is largely determined by the properties of the so-called mixed topology ring states, emerging in domain walls that separate the skyrmion core from the ferromagnetic background. In particular, we show that these localized ring states possess a given orbital chirality which reverses sign as a function of the skyrmion radius, thereby mediating a smooth switching dynamics of the orbital magnetization of the skyrmion lattice. We speculate that while the emergent ring states can possibly play a role in the physics of Majorana states, probing their properties experimentally can provide insights into the details of skyrmionic spin structures.

Magnetic Direct-Write Skyrmion Nanolithography.

Magnetic skyrmions are stable spin textures with quasi-particle behavior and attract significant interest in fundamental and applied physics. The metastability of magnetic skyrmions at zero magnetic field is particularly important to enable, for instance, a skyrmion racetrack memory. Here, the results of the nucleation of stable skyrmions and formation of ordered skyrmion lattices by magnetic force microscopy in (Pt/CoFeSiB/W)n multilayers, exploiting the additive effect of the interfacial Dzyaloshinskii-Moriya interaction, are presented. The appropriate conditions under which skyrmion lattices are confined with a dense two-dimensional liquid phase are identified. A crucial parameter to control the skyrmion lattice characteristics and the number of scans resulting in the complete formation of a skyrmion lattice is the distance between two adjacent scanning lines of a magnetic force microscopy probe. The creation of skyrmion patterns with complex geometry is demonstrated, and the physical mechanism of direct magnetic writing of skyrmions is comprehended by micromagnetic simulations. This study shows a potential of a direct-write (maskless) skyrmion (topological) nanolithography with sub-100 nm resolution, where each skyrmion acts as a pixel in the final topological image.

Robust metastable skyrmions with tunable size in the chiral magnet FePtMo3N

Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $\beta$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K. The magnetic field-induced redistribution of the SANS intensity showed that the helical structure transforms to a lattice of skyrmions at $\sim$13~mT at temperatures just below $T_{\text C}$. Our key observation is that the skyrmion state in FePtMo$_3$N is robust against field cooling down to the lowest temperatures. Moreover, once the metastable state is prepared by field cooling, the skyrmion lattice exists even in zero field. Furthermore, we show that the skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample temperature and can be continuously tuned between 120 and 210~nm. This offers new prospects in the control of topological properties of chiral magnets.

Late stages in the ordering of magnetic skyrmion lattices

The late-stage ordering of interacting magnetic skyrmions is studied numerically through extensive Langevin molecular dynamics simulations. Defining skyrmion displacements that change the connectivity of cells obtained in a Voronoi tesselation as events, we investigate event histograms as a function of the time elapsed since preparing the system as well as the histograms of consecutive events as a function of the time separating these two events. These histograms, which provide unique insights into the transient properties during the ordering process of skyrmion matter, show a characteristic behavior that allows the Magnus-force dominated regime, where the Magnus force accelerates the relaxation process, to be distinguished from the noise-dominated regime, where the Magnus force enhances the effects of thermal noise. In the Magnus-force dominated regime the different histograms display power-law tails with exponents that depend on the strength of the Magnus force.

Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons: comment.

We comment on a recent paper entitled "Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons" [Opt. Express28, 10322 (2020)10.1364/OE.384718] and disprove the assertion that Bloch-type skyrmions exist in the magnetic field of surface plasmon polaritons.

Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons: reply.

This is a Reply to the Comment by Meiler, Frank, and Giessen directed to a recent paper "Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons" [Opt. Express28, 10320 (2020)10.1364/OE.384718] regarding to the existence of Bloch-type skyrmions in the magnetic field of surface plasmon polaritons.

Dynamic susceptibility of skyrmion clusters in Co/Pt nanodots

We study the dynamic susceptibility of skyrmion clusters in Co/Pt nanodots using micromagnetic simulations. For this, we investigate the dynamic response of the skyrmions to a small magnetic field pulse applied parallel to the dot axis. Skyrmions exhibit a main resonance peak associated with the skyrmions' breathing mode, which is closely linked to the average radius of the skyrmions. Furthermore, we find that non-trivial secondary modes appear when the cluster size increases. These results can be used as a detection and characterization mechanism for skyrmion lattices in confined systems.

Site-substitution effect on skyrmion phases of Cd2+-Cu2OSeO3 nanocrystallites

The past decade has seen a significant uptick in research interest to study the materials that can host magnetic skyrmion lattices. The curiosity of such materials is mainly driven by the technological applications of emergent skyrmion lattices that manifest a whirlpool-like spins arrangement. Insulating Cu2OSeO3 reported to host magnetic skyrmion lattices below 60 K and considered as a potential candidate for exploring this new phase of materials. Here in this article, we propose a new synthesis process to grow the Cd2+-substituted Cu2OSeO3 nanocrystallites with variable sizes ranging over 50–200 nm. The proposed method consists of only a single-step heat treatment of 12 h, which is cost-effectivethan the routine solid-state process that requires a rigorous 15–20 days of heat treatment. By employing X-ray diffraction (XRD), transmission electron microscopy (TEM), energy dispersive X-ray analysis (EDX), X-ray photoelectron spectroscopy (XPS), and isothermal magnetization (M-T) measurements, we present a comparative investigation of the structural, electronic and magnetic properties of pristine and Cd2+-substituted Cu2OSeO3 nanocrystallites. As non-magnetic substitution can alter the fundamental magnetic interactions, therefore, Cd2+-Cu2OSeO3 nanocrystallites offer a new methodology to control the magnetic skyrmion phases and its stability.

Ground-state phases and spin textures of spin–orbit-coupled dipolar Bose–Einstein condensates in a rotating toroidal trap* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11475144 and 11047033), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2019203049 and A2015203037), the University Science and Technology Foundation of Hebei Provincial Department of Education, China (Grant No. Z2017056), Science

We investigate the ground-state phases and spin textures of spin–orbit-coupled dipolar pseudo-spin-1/2 Bose–Einstein condensates in a rotating two-dimensional toroidal potential. The combined effects of dipole–dipole interaction (DDI), spin–orbit coupling (SOC), rotation, and interatomic interactions on the ground-state structures and topological defects of the system are analyzed systematically. For fixed SOC strength and rotation frequency, we provide a set of phase diagrams as a function of the DDI strength and the ratio between inter- and intra-species interactions. The system can show rich quantum phases including a half-quantum vortex, symmetrical (asymmetrical) phase with quantum droplets (QDs), asymmetrical segregated phase with hidden vortices (ASH phase), annular condensates with giant vortices, triangular (square) vortex lattice with QDs, and criss-cross vortex string lattice, depending on the competition between DDI and contact interaction. For given DDI strength and rotation frequency, the increase of the SOC strength leads to a structural phase transition from an ASH phase to a tetragonal vortex lattice then to a pentagonal vortex lattice and finally to a vortex necklace, which is also demonstrated by the momentum distributions. Without rotation, the interplay of DDI and SOC may result in the formation of a unique trumpet-shaped Bloch domain wall. In addition, the rotation effect is discussed. Furthermore, the system supports exotic topological excitations, such as a half-skyrmion (meron) string, triangular skyrmion lattice, skyrmion–half-skyrmion lattice, skyrmion–meron cluster, skyrmion–meron layered necklace, skyrmion–giant-skyrmion necklace lattice, and half-skyrmion–half-antiskyrmion necklace.

Lattice Solutions in a Ginzburg\u2013Landau Model for a Chiral Magnet

We examine micromagnetic pattern formation in chiral magnets, driven by the competition of Heisenberg exchange, Dzyaloshinskii–Moriya interaction, easy-plane anisotropy and thermodynamic Landau potentials. Based on equivariant bifurcation theory, we prove existence of lattice solutions branching off the zero magnetization state and investigate their stability. We observe in particular the stabilization of quadratic vortex–antivortex lattice configurations and instability of hexagonal skyrmion lattice configurations, and we illustrate our findings by numerical studies.

Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings.

Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications1-4. Skyrmions have so far been observed in a variety of magnets that exhibit nearly parallel alignment for neighbouring spins, but theoretically skyrmions with anti-parallel neighbouring spins are also possible. Such antiferromagnetic skyrmions may allow more flexible control than conventional ferromagnetic skyrmions5-10. Here, by combining neutron scattering measurements and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattice is stabilized in MnSc2S4 through anisotropic couplings. The observed lattice is composed of three antiferromagnetically coupled sublattices, and each sublattice is a triangular skyrmion lattice that is fractionalized into two parts with an incipient meron (half-skyrmion) character11,12. Our work demonstrates that the theoretically proposed antiferromagnetic skyrmions can be stabilized in real materials and represents an important step towards their implementation in spintronic devices.

Skyrmion and tetarton lattices in twisted bilayer graphene

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moir\`e unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.

Angle Dependence of the Magnetic Phase Diagram in Cubic Chiral Antiferromagnet EuPtSi

The magnetic-field-induced A-phase for H ∥ [111] in cubic chiral antiferromagnet EuPtSi has been recently identified as a skyrmion lattice phase. We examined precise magnetic-field angle dependence...

Topological energy barrier for skyrmion lattice formation in MnSi

We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in small domains, each of which consisting of hundreds of skyrmions, and with an activation barrier of several eV.