Skyrmion Structure Research Articles

Cylindrical defect structures formed by chiral nematic liquid crystals in quasi-one-dimensional systems.

Blue phases are three-dimensional self-assembly structures of liquid crystals with a lattice of line defects. They have attracted considerable interest as photonic materials. It is well known that blue phases occur in cholesteric liquid crystals (CLCs) under certain thermodynamic conditions; however, recent studies have indicated that confining surfaces may induce distinctive structural changes. For example, in a previous study, a quasi-two-dimensional (Q2D) confinement system was investigated with the aid of numerical calculations, and a stable Q2D Skyrmion structure was attained. Here, we performed molecular simulations to investigate the CLC phase behavior at the molecular scale for a quasi-one-dimensional (Q1D) nanotube system. Various morphological behaviors of CLCs were observed by changing the temperature and the radius of the nanotubes. In particular, we discovered a self-assembled structure with cylindrical (or ring-like) defects rather than lines by introducing a novel local orientation analysis. Our simulation results show that the self-assembly of CLCs offers a guide to control the intensity in Q1D systems and fundamental knowledge for their application to optical devices.

Artifacts in magnetic force microscopy under in-plane applied magnetic field: Magnetic bubble as a case study

The study of magnetic bubble configuration in Co/Ni multilayers circular dots under in-plane magnetic field enlightens two magnetic force microscopy (MFM) measurement artifacts. We demonstrate that any tilt of the magnetic field producing out-of-plane field component due to the inhomogeneity of the MFM set up strongly affects the shape and size of the magnetic bubble independently of the in-plane field component intensity. Furthermore, MFM signal variations for in-plane magnetic field larger than 0.1 Tesla can only be understood considering MFM tip magnetization rotation. These two artifacts can have strong impact on MFM images and need to be carefully checked for reliable results in imaging skyrmionic structures with MFM under-field.

Vortex and skyrmionic patterns in chiral p-wave superconducting systems

In the framework of the microscopic Bogoliubov-de Gennes theory, we study the spatial configurations of topological defects in chiral p-wave superconducting systems. Besides the quantized vortex states with pointlike cores, the coreless single or multiple skyrmionic structures with the topological charge Q=2 and several types of the skyrmion-vortex coexisting modes can remain stable in the bulk system. Interestingly, the multiskyrmionic patterns containing several separated skyrmionic chains can be obtained at an appropriate flux, accompanied with half-quantum vortex-antivortex pairs in one component of the order parameter. Further, more complex skyrmionic states with Q=6 can also take place when the external magnetic flux becomes stronger.

Smectic Liquid-Crystalline Structure of Skyrmions in Chiral Magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) Thin Film.

The organizing of magnetic skyrmions shows several forms similar to atomic arrays of solid states. Using Lorentz transmission electron microscopy, we report the first direct observation of a stable liquid-crystalline structure of skyrmions in chiral magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) thin film, caused by magnetic anisotropy and chiral surface twist. Elongated skyrmions are oriented and periodically arranged only in the ⟨110⟩ directions, whereas they exhibit short-range order along the ⟨001⟩ directions, indicating a smectic skyrmion state. In addition, skyrmions possess anisotropic interaction with an opposite sign depending on the crystal orientation, in contrast to existing isotropic interaction.

Spatial configurations of topological defects in mesoscopic p-wave superconducting squares

In the framework of the microscopic Bogoliubov-de Gennes theory, we study the spatial configurations of topological defects under high external magnetic field in mesoscopic p-wave superconducting square systems. Besides the multivortex state with four conventional vortices, two novel types of multiskyrmionic states containing four separated coreless skyrmions with the topological charge Q = 2 or Q = 3 can be obtained as the ground states, accompanied with the half-quantum vortex-antivortex pair in one or two components of the order parameter. Moreover, when the superconducting pairing interaction is enlarged, more complex single or multiple skyrmionic structures as well as the skyrmion-vortex coexisting modes can remain (meta-)stable in the mesoscopic chiral sample.

Controlling skyrmion bubble confinement by dipolar interactions

Large skyrmion bubbles in confined geometries of various sizes and shapes are investigated, typically in the range of several micrometers. Two fundamentally different cases are studied to address the role of dipole-dipole interactions: (I) when there is no magnetic material present outside the small geometries and (II) when the geometries are embedded in films with a uniform magnetization. It is found that the preferential position of the skyrmion bubbles can be controlled by the geometrical shape, which turns out to be a stronger influence than local variations in material parameters. In addition, independent switching of the direction of the magnetization outside the small geometries can be used to further manipulate these preferential positions, in particular with respect to the edges. We show by numerical calculations that the observed interactions between the skyrmion bubbles and structure edge, including the overall positioning of the bubbles, can be explained by considering only dipole-dipole interactions.

Thermal creation of skyrmions in ferromagnetic films with perpendicular anisotropy and Dzyaloshinskii-Moriya interaction

We study theoretically, via Monte Carlo simulations on lattices containing up to 1000×1000 spins, thermal creation of skyrmion lattices in a 2D ferromagnetic film with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. At zero temperature, skyrmions only appear in the magnetization process in the presence of static disorder. Thermal fluctuations violate conservation of the topological charge and reduce the effective magnetic anisotropy that tends to suppress skyrmions. In accordance with recent experiments, we find that elevated temperatures assist the formation of skyrmion structures. Once such a structure is formed, it can be frozen into a regular skyrmion lattice by reducing the temperature. We investigate topological properties of skyrmion structures and find the average skyrmion size. Energies of domain and skyrmion states are computed. It is shown that skyrmion lattices have lower energy than labyrinth domains within a narrow field range.

An effect of the Gilbert damping constant on the skyrmion Hall effect

We investigate the skyrmion Hall effect using the Landau-Lifshitz-Gilbert (LLG) equation and the Thiele equation, respectively. Then, we find that these methods give different values for the ratio of in-plane skyrmion velocity components when the Gilbert damping constant is relatively small. Since the Thiele equation is derived from the LLG equation by assuming that the skyrmion structure does not change and behaves like a rigid body, the above result suggests that this assumption does not hold when the Gilbert damping constant is relatively small. Therefore, we conclude that the Thiele equation can not describe the systems precisely under the relatively small Gilbert damping constant due to the distortion of the skyrmion structure and that it is mandatory to solve the LLG equation numerically in order to investigate the skyrmion Hall effect accurately. This result is very important since the Gilbert damping constants of metal materials are generally very small.

Resolving Internal Magnetic Structures of Skyrmions by Lorentz Electron Ptychography

Resolving Internal Magnetic Structures of Skyrmions by Lorentz Electron Ptychography

Tetragonal Superstructure of the Antiskyrmion Hosting Heusler Compound Mn1.4PtSn.

Skyrmions in non-centrosymmetric magnets are vortex-like spin arrangements, viewed as potential candidates for information storage devices. The crystal structure and noncollinear magnetic structure together with magnetic and spin–orbit interactions define the symmetry of the skyrmion structure. We outline the importance of these parameters in the Heusler compound Mn1.4PtSn which hosts antiskyrmions, a vortex-like spin texture related to skyrmions. We overcome the challenge of growing large micro-twin-free single crystals of Mn1.4PtSn, which has proved to be the bottleneck for realizing bulk skyrmionic/antiskyrmionic states in a compound. The use of 5d-transition metal, platinum, together with manganese as constituents in the Heusler compound such as Mn1.4PtSn is a precondition for the noncollinear magnetic structure. Because of the tetragonal inverse Heusler structure, Mn1.4PtSn exhibits large magneto-crystalline anisotropy and D2d symmetry, which are necessary for antiskyrmions. The superstructure in Mn1.4PtSn is induced by Mn-vacancies, which enable a ferromagnetic exchange interaction to occur. Mn1.4PtSn, the first known tetragonal Heusler superstructure compound, opens up a new research direction for properties related to the superstructure in a family containing thousands of compounds.

Skyrmion-generated spinmotive forces in inversion broken ferromagnets

We present an analytical study on the spinmotive force (SMF) generated by translational motion of magnetic skyrmion. A SMF refers to an electrical voltage induced by dynamical magnetic textures, which reflects the spatiotemporal variation of the magnetization. The dynamics of a skyrmion thus can be detected by a SMF measurement, which may play an important role in future skyrmion-based technologies. We find the dependence of the SMF on skyrmion structure (e.g., skyrmion or anti-skyrmion, N\'{e}el or Bloch type, and the polarity of the skyrmion core) and Rashba and Dresselhaus spin-orbit couplings (SOCs). To this end, we derive explicit formulae for the spin-dependent electric fields originating from the two SOCs. Our findings offer a comprehensive understanding of the phenomenon and an estimation of the electrical voltage signal associated with a moving skyrmion for a given experiment.

Orientation-dependent current-induced motion of skyrmions with various topologies

We study the current-driven motion of metastable localized spin structures with various topological charges in a (Pt$_{1-x}$Ir$_{x}$)/Fe bilayer on a Pd(111) surface by combining atomistic spin model simulations with an approach based on the generalized Thiele equation. We demonstrate that besides a distinct dependence on the topological charge itself the dynamic response of skyrmionic structures with topological charges $\mathrm{Q} = -1$ and $\mathrm{Q}= 3$ to a spin-polarized current exhibits an orientation dependence. We further show that such an orientation dependence can be induced by applying an in-plane external field, possibly opening up a new pathway to the manipulation of skyrmion dynamics.

Observation of emergent momentum\u2013time skyrmions in parity\u2013time-symmetric non-unitary quench dynamics

Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time ({cal{P}}{cal{T}})-symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of {cal{P}}{cal{T}} symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.

Skyrmions and composite vortex states in three-component Bose–Einstein condensates with spin–orbit coupling

Stable and metastable vortex states in two-dimensional three-component Bose–Einstein condensates are studied in the presence of spin–orbit coupling. The ground states exhibit two skyrmion structures which respectively correspond to the d-skyrmion in antiferromagnetic or the F-skyrmion in ferromagnetic condensates. The half skyrmion and full skyrmion can be controlled by changing the strength of the spin–orbit coupling. We also find a stable composite vortex state which is associated to mixing of the ferromagnetic and antiferromagnetic manifolds.

Superfluid spin transport in ferro- and antiferromagnets

This paper focuses on spin superfluid transport, observation of which was recently reported in antiferromagnet Cr$_2$O$_3$ [Yuan et al., Sci. Adv. 4, eaat1098 (2018)]. This paper analyzes the role of dissipation in transformation of spin current injected with incoherent magnons to a superfluid spin current near the interface where spin is injected. The Gilbert damping parameter in the Landau-Lifshitz-Gilbert theory does not describe dissipation properly, and the dissipation parameters are calculated from the Boltzmann equation for magnons scattered by defects. The two-fluid theory is developed similar to the two-fluid theory for superfluids. This theory shows that the influence of temperature variation in bulk on the superfluid spin transport (bulk Seebeck effect) is weak at low temperatures. The scenario that the results of Yuan et al. are connected with the Seebeck effect at the interface between the spin detector and the sample is also discussed. The Landau criterion for an antiferromagnet put in a magnetic field is derived from the spectrum of collective spin modes. The Landau instability starts in the gapped mode earlier than in the Goldstone gapless mode, in contrast to easy-plane ferromagnets where the Goldstone mode becomes unstable. The structure of the magnetic vortex in the geometry of the experiment is determined. The vortex core has the skyrmion structure with finite magnetization component normal to the magnetic field. This magnetization creates stray magnetic fields around the exit point of the vortex line from the sample, which can be used for experimental detection of vortices.

Anatomy of Skyrmionic Textures in Magnetic Multilayers.

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real-space spin configuration. Here, two advanced X-ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]n multilayers. First, by using ptychography, a high-resolution diffraction imaging technique, the 2D out-of-plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X-ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth-dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole-dipole interactions together with the external magnetic field play an important role in stabilizing sub-100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X-ray-based approach opens the door for in-depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.

Towards an Effective Theory of Skyrmion Crystals

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of $B, D\neq0$, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by $D$ and $B$. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc.

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.

Topological Hall effect for electron scattering on nanoscale skyrmions in external magnetic field

We consider topological Hall effect (THE) in thin ferromagnetic films due to electron scattering on magnetic skyrmions in the presence of the relatively strong external magnetic field. We account for the effect of the magnetic field on a skyrmion structure and describe the hallmarks of THE differentiating it from ordinary and anomalous Hall effects. We have found that, although in typical ferromagnets the variation of magnetic field in the range 1-5 T substantially affects the skyrmion size, THE changes rather weakly remaining quite robust. Therefore, the magnitude of THE is primarily determined by the skyrmions sheet density $n_{sk}$, being comparable to the magnitude of the ordinary Hall effect (OHE) at $n_{sk}=10^{11}$ cm$^{-2}$. The sign of THE is opposite to that of OHE for skyrmions with positive vorticity, while for antiskyrmions the signs are the same.

Realization of artificial skyrmion in CoCrPt/NiFe bilayers**Project supported by the National Key Research and Development Program of China (Grant No. 2018YFF01010701), the National Natural Science Foundation of China (Grant No. 51332003), and the Sichuan Science and Technology Program, China (Grant No. 2018G20140).

Skyrmion, as a quasi-particle structure, has attracted much attention due to its potential applications in future spintronic devices. Artificial skyrmion structure has aroused great interest as it can be stabilized at room temperature, without needing to incorporate materials with Dzyaloshinskii–Moriya interaction (DMI) into it. In this paper, it is found that the artificial skyrmion structure can be realized in CoCrPt/NiFe bilayers by micromagnetic simulations. The critical magnetic field of the core decreases as the diameter of the NiFe soft magnetic layer increases. The artificial skyrmion has excellent topological protection, and the critical magnetic field of plane is about 76 mT (760 Oe, 1 Oe = 79.5775 A·m−1). The external magnetic field plays a key role in determining the core diameter of the skyrmion, and the artificial skyrmion can be realized in CoCrPt/Cu/CoCrPt/NiFe four-layer with a diameter of 13 nm.