Chiral Skyrmions Research Articles

Chiral Skyrmion and Skyrmionium States Engineered by the Gradient of Curvature

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose a new mechanism to stabilize chiral N\'{e}el skyrmion states relying on the \textit{gradient} of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers $\pm 1$ and a skyrmionium state with a winding number $0$. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii--Moriya interaction. The latter emerges due to the gradient of the local curvature at a bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables one to reduce a magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii--Moriya interaction.

Modeling the Shape of Axisymmetric Skyrmions in Magnetic Multilayers

We present a comprehensive micromagnetic model of isolated axisymmetric skyrmions in magnetic multilayers with perpendicular anisotropy. Most notably, the essential role of the internal dipolar field is extensively considered with a minimum amount of assumptions on the magnetization profiles. The tri-dimensional structure of the multilayered skyrmions is modeled by their radial profiles in each layer. We first compare the results of the model against a full micromagnetic description in Cartesian coordinates. Our model combines information on both layer-dependent size and chirality of the skyrmions. We also provide a convenient criterion in order to characterize the stability of skyrmions against anisotropic elongations that would break their cylindrical symmetry, which allows to confirm the stability of the determined solutions. Because this model is able to treat magnetization configurations twisted through the thickness of multilayered skyrmions, it can provide predictions on any potential hybrid chirality in skyrmions due to the interplay of Dzyaloshinskii-Moriya and dipolar interactions in multilayers. We finally apply the results of our model to the description of the current-driven dynamics of hybrid chiral skyrmions. Using the Thiele formalism, we show that we can predict the forces exerted on the multilayered skyrmions by vertical spin-polarized currents, which provides a method to conform hybrid skyrmion chiralities and spin-current injection geometries in order to optimize skyrmion motion in multilayers, to the aim of maximizing the current-induced velocity, or canceling the skyrmion Hall angle.

Electric Field-Induced Creation and Directional Motion of Domain Walls and Skyrmion Bubbles.

Magnetization dynamics driven by an electric field could provide long-term benefits to information technologies because of its ultralow power consumption. Meanwhile, the Dzyaloshinskii-Moriya interaction in interfacially asymmetric multilayers consisting of ferromagnetic and heavy-metal layers can stabilize topological spin textures, such as chiral domain walls, skyrmions, and skyrmion bubbles. These topological spin textures can be controlled by an electric field and hold promise for building advanced spintronic devices. Here, we present an experimental and numerical study on the electric field-induced creation and directional motion of topological spin textures in magnetic multilayer films and racetracks with thickness gradient and interfacial Dzyaloshinskii-Moriya interaction at room temperature. We find that the electric field-induced directional motion of chiral domain wall is accompanied by the creation of skyrmion bubbles at certain conditions. We also demonstrate that the electric field variation can induce motion of skyrmion bubbles. Our findings may provide opportunities for developing skyrmion-based devices with ultralow power consumption.

Single Chiral Skyrmions in Ultrathin Magnetic Films.

The stability and sizes of chiral skyrmions in ultrathin magnetic films are calculated accounting for the isotropic exchange, Dzyaloshinskii–Moriya exchange interaction (DMI), and out-of-plane magnetic anisotropy within micromagnetic approach. Bloch skyrmions in ultrathin magnetic films with B20 cubic crystal structure (MnSi, FeGe) and Neel skyrmions in ultrathin films and multilayers Co/X (X = Ir, Pd, Pt) are considered. The generalized DeBonte ansatz is used to describe the inhomogeneous skyrmion magnetization. The single skyrmion metastability/instability area, skyrmion radius, and skyrmion width are found analytically as a function of DMI strength . It is shown that the single chiral skyrmions are metastable in infinite magnetic films below a critical value of DMI , and do not exist at . The calculated skyrmion radius increases as increases and diverges at , whereas the skyrmion width increases monotonically as increases up to without any singularities. The calculated skyrmion width is essentially smaller than the one calculated within the generalized domain wall model.

Writing skyrmions with a magnetic dipole

We demonstrate numerically, through energy minimization on large spin lattices, that one can write skyrmions in a thin magnetic film with a magnetic dipole of a few tens of nanometer in size. Nucleation of non-chiral skyrmions as well as chiral skyrmions formed by the Dzyaloshinskii-Moriya interaction has been investigated. Analytical model is developed that agrees with the numerical results. It is shown that skyrmions can be written through a number of scenarios that depend on the experimental technique and parameters of the system. In one scenario, which branches into subscenarios of different topology, the magnetic dipole on approaching the film creates a skyrmion-antiskyrmion pair. As the dipole moves closer to the film, it induces collapse of the antiskyrmion and creation of a non-zero topological charge due to the remaining skyrmion. In a different scenario, the dipole moving parallel to the film nucleates a skyrmion at the boundary and then drags it inside the film. Possible implementations of these methods for writing topologically protected information in a magnetic film are discussed.

Temperature dependence of the Dzyaloshinskii-Moriya interaction in Pt/Co/Cu thin film heterostructures

Magnetic materials that exhibit chiral domain walls are of great interest for spintronic devices. In this work, we examine the temperature-dependent behavior of the Dzyaloshinskii-Moriya interaction (DMI) in Pt/Co/Cu thin film heterostructures. We extract the DMI strength, D, from static domain spacing analysis between 300 K and 500 K and compare its temperature dependence to that of the magnetic anisotropy, Ku, and saturation magnetization, Ms. Consistent with expected scaling in thin films, Ms exhibits Bloch-law temperature scaling and Ku scales as Ms2.1±0.1. However, D varies more strongly with temperature than expected, scaling as D∝Ms4.9±0.7, indicating that interfacial DMI is more sensitive to thermal fluctuations than bulk magnetic properties. We suggest that this may be related to the temperature dependence of locally induced magnetic moments in the Pt underlayer and the 3d-5d orbital interactions at the interface. While we observe stable domain widths in the studied temperature range, a strongly temperature dependent DMI may have significant consequences for potential devices based on the chiral domain wall or skyrmion motion.

Homogeneous and heterogeneous nucleation of skyrmions in thin layers of cubic helimagnets

Formation of isolated chiral skyrmions by homogeneous and heterogeneous nucleation has been studied in thin layers of cubic helimagnets via elongation of torons and chiral bobbers, correspondingly. Both torons and bobbers are localized in three dimensions, contain singularities, and according to the theoretical analysis within the standard phenomenological models can exist as metastable states in saturated and modulated phases of noncentrosymmetric ferromagnets. Their elongation into the defect-free skyrmion filament is facilitated by small anisotropic contributions making skyrmion cores negative with respect to the surrounding parental state. We show that isolated magnetic torons pose the same problem of compatibility with a surrounding phase as the torons in confinement-frustrated chiral nematics [I. Smalyukh et al., Nature Mater 9, 139-145 (2010)]. We underline the distinct features of magnetic and liquid-crystals torons and calculate phase diagrams indicating their stability regions.

Hybrid chiral domain walls and skyrmions in magnetic multilayers.

Noncollinear spin textures in ferromagnetic ultrathin films are currently the subject of renewed interest since the discovery of the interfacial Dzyaloshinskii-Moriya interaction (DMI). This antisymmetric exchange interaction selects a given chirality for the spin textures and allows stabilizing configurations with nontrivial topology including chiral domain walls (DWs) and magnetic skyrmions. Moreover, it has many crucial consequences on the dynamical properties of these topological structures. In recent years, the study of noncollinear spin textures has been extended from single ultrathin layers to magnetic multilayers with broken inversion symmetry. This extension of the structures in the vertical dimension allows room temperature stability and very efficient current-induced motion for both Néel DWs and skyrmions. We show how, in these multilayered systems, the interlayer interactions can actually lead to hybrid chiral magnetization arrangements. The described thickness-dependent reorientation of DWs is experimentally confirmed by studying demagnetized multilayers through circular dichroism in x-ray resonant magnetic scattering. We also demonstrate a simple yet reliable method for determining the magnitude of the DMI from static domain measurements even in the presence of these hybrid chiral structures by taking into account the actual profile of the DWs. The existence of these novel hybrid chiral textures has far-reaching implications on how to stabilize and manipulate DWs, as well as skymionic structures in magnetic multilayers.

Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants

Extended numerical simulations enable to ascertain the diffusive behavior at finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers exhibiting symmetric - Heisenberg - as well as antisymmetric - Dzyaloshinskii-Moriya - exchange interactions. The Brownian motion of walls and skyrmions is shown to obey markedly different diffusion laws as a function of the damping parameter. Topology related skyrmion diffusion suppression with vanishing damping parameter, albeit already documented, is shown to be restricted to ultra-small skyrmion sizes or, equivalently, to ultra-low damping coefficients, possibly hampering observation.

Manipulation of skyrmion motion by magnetic field gradients

Magnetic skyrmions are particle-like, topologically protected magnetisation entities that are promising candidates as information carriers in racetrack memory. The transport of skyrmions in a shift-register-like fashion is crucial for their embodiment in practical devices. Here, we demonstrate that chiral skyrmions in Cu2OSeO3 can be effectively manipulated under the influence of a magnetic field gradient. In a radial field gradient, skyrmions were found to rotate collectively, following a given velocity–radius relationship. As a result of this relationship, and in competition with the elastic properties of the skyrmion lattice, the rotating ensemble disintegrates into a shell-like structure of discrete circular racetracks. Upon reversing the field direction, the rotation sense reverses. Field gradients therefore offer an effective handle for the fine control of skyrmion motion, which is inherently driven by magnon currents. In this scheme, no local electric currents are needed, thus presenting a different approach to shift-register-type operations based on spin transfer torque.

Stability of axisymmetric chiral skyrmions

We examine topological solitons in a minimal variational model for a chiral magnet, so-called chiral skyrmions. In the regime of large background fields, we prove linear stability of axisymmetric chiral skyrmions under arbitrary perturbations in the energy space, a long-standing open question in physics literature. Moreover, we show strict local minimality of axisymmetric chiral skyrmions and nearby existence of moving soliton solutions for the Landau–Lifshitz–Gilbert equation driven by small spin transfer torques.

Nanoscale control of perpendicular magnetic anisotropy, coercive force and domain structure in ultrathin Ru/Co/W/Ru films

Development of fast and energy-efficient spintronic devices requires novel nanoscaled materials with controllable magnetic properties. Here we show that the introduction of an ultrathin W interlayer between Co and Ru in Ru/Co/Ru films enables to preserve perpendicular magnetic anisotropy (PMA) and dramatically reduce the coercive force and size of magnetic domains. We find that the Ru/Co/W/Ru films with up to 0.35 nm of the nominal thickness of W have robust PMA. The observed formation of a dendritic domain structure with small domains having homochiral Néel domain walls is an indicator of the interfacial Dzyaloshinskii-Moriya interaction appearing in trilayers with asymmetrical interfaces. The inversion-symmetry-broken Ru/Co/W/Ru films are a potential host for nucleation and manipulation of non-trivial spin textures like chiral domain walls and skyrmions.

Chirality-induced antisymmetry in magnetic domain wall speed

In chiral magnetic materials, numerous intriguing phenomena such as built-in chiral magnetic domain walls (DWs) and skyrmions are generated by the Dzyaloshinskii–Moriya interaction (DMI). The DMI also results in asymmetric DW speeds under an in-plane magnetic field, which provides a useful scheme to measure the strength of the DMI. However, recent findings of additional asymmetries such as chiral damping have inhibited the unambiguous determination of the DMI strength, and the underlying mechanism of overall asymmetries comes under debate. Here, we experimentally investigate the nature of the additional asymmetry by extracting the DMI-induced symmetric contribution from the DW speed. Our results reveal that the additional asymmetry has a truly antisymmetric nature with the typical behavior governed by the DW chirality. In addition, the antisymmetric contribution alters the DW speed by a factor of 100, dominating the overall variation in DW speed. Thus, experimental inaccuracies can be largely removed by calibration with such antisymmetric contributions, enabling the standard DMI measurement scheme.

Emergence and magnetic-field variation of chiral-soliton lattice and skyrmion lattice in the strained helimagnet Cu2OSeO3

We demonstrate emergence of both the chiral soliton lattice and skyrmion lattice and investigate their magnetic-field variation in the strained ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$ thin plate by means of small-angle resonant soft x-ray scattering. The tensile strain stabilizes a helical spin structure with the modulation vector along the strain direction. Consequently, when increasing the field perpendicular to the modulation vector, it undergoes large shrinkage and higher-order diffraction peaks are also observed, which is in accord with a typical feature of the chiral soliton lattice. The skyrmion lattice also appears in the presence of tensile strain but is elongated along the strain direction in reciprocal space. The magnetic-field dependence of the modulation vector along the strain direction agrees with the theoretical model quantitatively, while that along other directions does not. The agreement, however, becomes worse at lower temperatures, which may be attributed to the large potential barrier for skyrmion annihilation.

Investigation of the Dzyaloshinskii-Moriya interaction and room temperature skyrmions in W/CoFeB/MgO thin films and microwires

Recent studies have shown that material structures, which lack structural inversion symmetry and have high spin-orbit coupling can exhibit chiral magnetic textures and skyrmions which could be a key component for next generation storage devices. The Dzyaloshinskii-Moriya Interaction (DMI) that stabilizes skyrmions is an anti-symmetric exchange interaction favoring non-collinear orientation of neighboring spins. It has been shown that materials systems with high DMI can lead to very efficient domain wall and skyrmion motion by spin-orbit torques. To engineer such devices, it is important to quantify the DMI for a given material system. Here, we extract the DMI at the Heavy Metal/Ferromagnet interface using two complementary measurement schemes, namely, asymmetric domain wall motion and the magnetic stripe annihilation. By using the two different measurement schemes, we find for W(5 nm)/Co20Fe60B20(0.6 nm)/MgO(2 nm) the DMI to be 0.68 ± 0.05 mJ/m2 and 0.73 ± 0.5 mJ/m2, respectively. Furthermore, we show that this DMI stabilizes skyrmions at room temperature and that there is a strong dependence of the DMI on the relative composition of the CoFeB alloy. Finally, we optimize the layers and the interfaces using different growth conditions and demonstrate that a higher deposition rate leads to a more uniform film with reduced pinning and skyrmions that can be manipulated by spin orbit torques.

Compactness results for static and dynamic chiral skyrmions near the conformal limit

We examine lower order perturbations of the harmonic map problem from $$\mathbb {R}^2$$ to $$\mathbb {S}^2$$ including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform background state. Energy functionals of this type arise in the context of magnetic systems without inversion symmetry. In the almost conformal regime, where these perturbations are weighted with a small parameter, we examine the existence of relative minimizers in a non-trivial homotopy class, so-called chiral skyrmions, strong compactness of almost minimizers, and their asymptotic limit. Finally we examine dynamic stability and compactness of almost minimizers in the context of the Landau–Lifshitz–Gilbert equation including spin-transfer torques arising from the interaction with an external current.

Observation of stable N\xe9el skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy

Néel skyrmions are of high interest due to their potential applications in a variety of spintronic devices, currently accessible in ultrathin heavy metal/ferromagnetic bilayers and multilayers with a strong Dzyaloshinskii–Moriya interaction. Here we report on the direct imaging of chiral spin structures including skyrmions in an exchange-coupled cobalt/palladium multilayer at room temperature with Lorentz transmission electron microscopy, a high-resolution technique previously suggested to exhibit no Néel skyrmion contrast. Phase retrieval methods allow us to map the internal spin structure of the skyrmion core, identifying a 25 nm central region of uniform magnetization followed by a larger region characterized by rotation from in- to out-of-plane. The formation and resolution of the internal spin structure of room temperature skyrmions without a stabilizing out-of-plane field in thick magnetic multilayers opens up a new set of tools and materials to study the physics and device applications associated with chiral ordering and skyrmions.

Topological spin Hall effect in antiferromagnetic skyrmions

The topological Hall effect (THE), as one of the primary manifestations of non‐trivial topology of chiral skyrmions, is traditionally used to detect the emergence of skyrmion lattices with locally ferromagnetic order. In this work we demonstrate that the appearance of non‐trivial two‐dimensional chiral textures with locally anti‐ferromagnetic order can be detected through the spin version of the THE – the topological spin Hall effect (TSHE). Utilizing the semiclassical formalism, here used to combine chiral antiferromagnetic textures with a density functional theory description of the collinear, degenerate electronic structure, we follow the real‐space real‐time evolution of electronic SU(2) wavepackets in an external electric field to demonstrate the emergence of sizeable transverse pure spin current in synthetic antiferromagnets of the Fe/Cu/Fe trilayer type. We further unravel the extreme sensitivity of the TSHE to the details of the electronic structure, suggesting that the magnitude and sign of the TSHE in transition‐metal synthetic antiferromagnets can be engineered by tuning such parameters as the thickness or band filling. Besides being an important step in our understanding of the topological properties of ever more complex skyrmionic systems, our results bear great potential in stimulating the discovery of antiferromagnetic skyrmions.

Imaging and manipulation of skyrmion lattice domains in Cu2OSeO3

Nanoscale chiral skyrmions in noncentrosymmetric helimagnets are promising binary state variables in high-density, low-energy nonvolatile memory. Skyrmions are ubiquitous as an ordered, single-domain lattice phase, which makes it difficult to write information unless they are spatially broken up into smaller units, each representing a bit. Thus, the formation and manipulation of skyrmion lattice domains is a prerequisite for memory applications. Here, using an imaging technique based on resonant magnetic x-ray diffraction, we demonstrate the mapping and manipulation of skyrmion lattice domains in Cu2OSeO3. The material is particularly interesting for applications owing to its insulating nature, allowing for electric field-driven domain manipulation.

Direct observation of the skyrmion Hall effect

The well-known Hall effect describes the transverse deflection of charged particles (electrons or holes) in an electric-current carrying conductor under the influence of perpendicular magnetic fields, as a result of the Lorentz force. Similarly, it is intriguing to examine if quasi-particles without an electric charge, but with a topological charge, show related transverse motion. Chiral magnetic skyrmions with a well-defined spin topology resulting in a unit topological charge serve as good candidates to test this hypothesis. In spite of the recent progress made on investigating magnetic skyrmions, direct observation of the skyrmion Hall effect in real space has, remained elusive. Here, by using a current-induced spin Hall spin torque, we experimentally observe the skyrmion Hall effect by driving skyrmions from creep motion into the steady flow motion regime. We observe a Hall angle for the magnetic skyrmion motion as large as 15 degree for current densities smaller than 10 MA/cm^(2) at room temperature. The experimental observation of transverse transport of skyrmions due to topological charge may potentially create many exciting opportunities for the emerging field of skyrmionics, including novel applications such as topological selection.