Skyrmion Helicity Research Articles

Anomalous Hall effect sensitive to magnetic monopoles and skyrmion helicity in spin–orbit coupled systems

Magnetic textures, such as skyrmions and domain walls, engender rich transport phenomena, including anomalous Hall effect and nonlinear response. In this work, we discuss an anomalous Hall effect proportional to the net magnetic monopole charge and dependent on the skyrmion helicity that occurs by a skew scattering in a noncentrosymmetric two-dimensional magnet. This mechanism, which arises from the spin–orbit interaction (SOI), gives rise to a finite anomalous Hall effect in a ferromagnetic domain wall whose spins rotate in the xy plane despite no out-of-plane magnetic moment. We show that the presence and absence of the monopole contribution is related to crystal symmetry, which gives a guideline for finding candidate materials beyond the Rashba model. The results demonstrate the rich features arising from the interplay of SOI and magnetic textures, and their potential for detecting various magnetic textures in micrometer devices.

Modulation of skyrmion helicity by competition between Dzyaloshinskii-Moriya interaction and magnetic frustration

Modulation of skyrmion helicity by competition between Dzyaloshinskii-Moriya interaction and magnetic frustration

Dynamics of hybrid magnetic skyrmion driven by spin–orbit torque in ferrimagnets

Precise control of skyrmion dynamics is essential for the future spintronic device design based on the magnetic skyrmions. In this work, we propose a scheme to implement hybrid magnetic skyrmions (HMS) in ferrimagnets and we study the dynamics of the HMS driven by spin–orbit torque. It is revealed that the skyrmion Hall effect depends on the skyrmion helicity and the net angular momentum (δs), allowing the effective modulation of the HMS motion through tuning Dzyaloshinskii–Moriya interaction and δs. Moreover, the Magnus force for finite δs suppresses the transverse motion and enhances the longitudinal propagation, resulting in the decrease in Hall angle accompanying faster dynamics than that in antiferromagnets. Thus, the Hall effect can be suppressed through selecting suitable materials to better control the HMS motion. Finally, we propose a convenient skyrmion diversion scheme through modulating the helicity and Hall angle of the HMS, benefiting the future spintronic device design.

Universal Quantum Computation Based on Nanoscale Skyrmion Helicity Qubits in Frustrated Magnets.

We propose a skyrmion-based universal quantum computer. Skyrmions have the helicity degree of freedom in frustrated magnets, where twofold degenerated Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction. We construct a qubit based on them. A skyrmion must become a quantum-mechanical object when its size is of the order of nanometers. It is shown that the universal quantum computation is possible based on nanoscale skyrmions in a magnetic bilayer system. The one-qubit quantum gates are materialized by controlling the electric field and the spin current. The two-qubit gate is materialized with the use of the Ising-type exchange coupling. The merit of the present mechanism is that external magnetic field is not necessary. Our results may open a possible way toward universal quantum computation based on nanoscale topological spin textures.

Electric field manipulation of spin chirality and skyrmion dynamic.

The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange interaction that stabilizes spin chirality. One scientific and technological challenge is understanding and controlling the interaction between spin chirality and electric field. In this study, we investigate an unconventional electric field effect on interfacial DMI, skyrmion helicity, and skyrmion dynamics in a system with broken inversion symmetry. We design heterostructures with a 3d-5d atomic orbital interface to demonstrate the gate bias control of the DMI energy and thus transform the DMI between opposite chiralities. Furthermore, we use this voltage-controlled DMI (VCDMI) to manipulate the skyrmion spin texture. As a result, a type of intermediate skyrmion with a unique helicity is created, and its motion can be controlled and made to go straight. Our work shows the effective control of spin chirality, skyrmion helicity, and skyrmion dynamics by VCDMI. It promotes the emerging field of voltage-controlled chiral interactions and voltage-controlled skyrmionics.

Combined Magnetic Imaging and Anisotropic Magnetoresistance Detection of Dipolar Skyrmions (Adv. Funct. Mater. 4/2023)

Detecting a Single Skyrmion In article number 2207770, Haifeng Du, Lingyao Kong, and his co-workers combine Lorentz-transmission electronic microcopy with anisotropic magnetoresistance detection on single dipolar skyrmions. This study reveals magnetic field, skyrmion helicity, and skyrmion counts dependence on magnetoresistance and promotes the reading functions of skyrmionic devices.

Skyrmion helicity: Quantization and quantum tunneling effects

We derive the quantization of magnetic helicity in the solid-state and demonstrate tunable macroscopic quantum tunneling, coherence, and oscillation for a skyrmion spin texture stabilized in frustrated magnets. We also discuss the parameter space for the experimental realization of quantum effects. Typically, for a skyrmion of 5 nm radius, quantum tunneling between two macroscopic states with distinct helicities occurs with an inverse escape rate within seconds below 100 mK, and an energy splitting in the MHz regime. Feasibility of quantum tunneling of an ensemble of magnetic spins inspires new platforms for quantum operations utilizing topologically protected chiral spin configurations.

Magnetic Skyrmions with Unconventional Helicity Polarization in a Van Der Waals Ferromagnet.

Skyrmion helicity, which defines the spin swirling direction, is a fundamental parameter that may be utilized to encode data bits in future memory devices. Generally, in centrosymmetric ferromagnets, dipole skyrmions with helicity of -π/2 and π/2 are degenerate in energy, leading to equal populations of both helicities. On the other hand, in chiral materials where the Dzyaloshinskii-Moriya interaction (DMI) prevails and the dipolar interaction is negligible, only a preferred helicity is selected by the type of DMI. However, whether there is a rigid boundary between these two regimes remains an open question. Herein, the observation of dipole skyrmions with unconventional helicity polarization in a van der Waals ferromagnet, Fe5- δ GeTe2 , is reported. Combining magnetometry, Lorentz transmission electron microscopy, electrical transport measurements, and micromagnetic simulations, the short-range superstructures in Fe5- δ GeTe2 resulting in a localized DMI contribution, which breaks the degeneracy of the opposite helicities and leads to the helicity polarization, is demonstrated. Therefore, the helicity feature in Fe5- δ GeTe2 is controlled by both the dipolar interaction and DMI that the former leads to Bloch-type skyrmions with helicity of ±π/2 whereas the latter breaks the helicity degeneracy. This work provides new insights into the skyrmion topology in van der Waals materials.

Magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets: effect of skyrmion helicity oscillation

A theoretical study on the interplay of frustrated skyrmion and magnons should reveal new physics and future experiment designs. In this study, we investigate the magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets based on micromagnetic simulations, focusing on the effect of skyrmion helicity oscillation. The oscillation speed and Hall angle of the frustrated skyrmion depending on the magnon intensity and damping constant are simulated, which demonstrates that the skyrmion helicity oscillation effectively suppresses Hall motion. The elastic scattering theory reveals that the helicity oscillation affects the scattering cross-section of injected magnons, which in turn effectively modulates the skyrmion Hall motion. This study provides a comprehensive understanding of magnon-skyrmion scattering in frustrated magnets, thus benefiting future spintronic and magnonic applications.

Stimulated Nucleation of Skyrmions in a Centrosymmetric Magnet.

Understanding the dynamics of skyrmion nucleation and manipulation is important for applications in spintronic devices. In this contribution, the spin textures at magnetic domain-boundaries stimulated by application of in-plane magnetic fields in a centrosymmetric kagome ferromagnet, Fe3Sn2, with thickness gradient are investigated using Lorentz transmission electron microscopy. Switching of the in-plane magnetic field is shown to induce a reversible transformation from magnetic stripes to skyrmions, or vice versa, at the interface between differently oriented domains. Micromagnetic simulations combined with experiments reveal that the rotatable anisotropy and thickness dependence of the response to the external in-plane field are the critical factors for the skyrmion formation. In addition, it is shown that the helicity of skyrmions can also be controlled using this dynamic process. The results suggest that magnetic materials with rotatable anisotropy are potential skyrmionic systems and provides a different approach for nucleation and manipulation of skyrmions in spintronic devices.

Stability of skyrmion formation and its abnormal dynamic modes in magnetic nanotubes

We studied the stability of skyrmion formation and its abnormal dynamic motions in magnetic nanotubes with perpendicular magnetic anisotropy with respect to the tube surface. Unlike planar geometry, skyrmions, which are formed in an elliptical shape, are stabilized, to a greater or lesser degree, by the curved geometry, depending on the sign of the Dzyaloshinskii-Moriya Interaction (DMI) constant. The positive and negative signs of the DMI constant play a crucial role in the formation of skyrmions on the curved surface. These effects become stronger as the diameter of the tube decreases, quantitatively evidencing that the curvature-induced DM-like interaction also contributes to the stability of skyrmion formation. The dynamic modes of the skyrmion in the tubes are found to be as follows: two in-plane gyration modes in the counterclockwise (CCW) and clockwise (CW) rotation senses, and one out-of-plane breathing mode. On the other hand, in contrast to the planar geometry, the initial CCW gyration motion turns out to be a linear translational motion in the circumferential direction of the tube for cases where the strength of axial AC magnetic fields is greater than a threshold field strength. The direction of the translational motions is determined by the skyrmion helicity governed by the sign of the interfacial DMI constant. This work provides further physical insight into the static and dynamic properties of skyrmions formed in curved-geometry systems and also suggests its potential application to information processing devices.

Controlled transformation of skyrmions and antiskyrmions in a non-centrosymmetric magnet.

Control of topological spin textures in magnetic systems may enable future spintronic applications. Magnetic field pulses can switch the vortex polarity1 or the winding number of magnetic bubbles2. Thermal energy can reverse the helicity of skyrmions3 and induce the transformation between meron and skyrmion by modifying the in-plane anisotropy4,5. Among the various topological spin textures, skyrmions6,7 and antiskyrmions8-10 are nanometric spin-whirling structures carrying integer topological charges (N) of -1 and +1 (refs. 7,11,12), respectively, and can be observed in real space8,13. They exhibit different dynamical properties under current flow14-18, for example, opposite signs for the topological Hall effect. Here we observe, in real space, transformations among antiskyrmions, non-topological (NT) bubbles and skyrmions (with N of +1, 0 and -1, respectively) and their lattices in a non-centrosymmetric Heusler magnet, Mn1.4Pt0.9Pd0.1Sn, with D2d symmetry. Lorentz transmission electron microscopy images under out-of-plane magnetic fields show a square lattice of square-shaped antiskyrmions near the Curie temperature and a triangular lattice of elliptically deformed skyrmions with opposite helicities at lower temperatures. The clockwise and counter-clockwise helicities of the skyrmions originate from Dzyaloshinskii-Moriya interactions with opposite signs along the [100] and [010] directions, respectively. A variation of the in-plane magnetic field induces a topological transformation from antiskyrmions to NT-bubbles and to skyrmions, which is accompanied by a change of the lattice geometry. We also demonstrate control of the helicity of skyrmions by variations of the in-plane magnetic field. These results showcase the control of the topological nature of spin configurations in complex magnetic systems.

Dynamics of deformed skyrmions and helicity reversal in composite spin valve pillar

We have investigated and reported the presence of deformed skyrmions in a composite spin valve pillar in the absence of Dzyaloshinskii–Moriya interaction and external magnetic field. When spin wave parameters are tuned in the high-frequency microwave range, distorted skyrmions are nucleated from magnetic stripe domains. We report the possibility of reversal of skyrmion helicity by the proper change of free layer magnetization orientation. Our investigation predicts the possibility of skyrmion based read-write memory devices and data transmission.

Magnetoelectric effect and orbital magnetization in skyrmion crystals: Detection and characterization of skyrmions

Skyrmions are small magnetic quasiparticles, which are uniquely characterized by their topological charge and their helicity. In this Rapid Communication, we show via calculations how both properties can be determined without relying on real-space imaging. The orbital magnetization and topological Hall conductivity measure the arising magnetization due to the circulation of electrons in the bulk and the occurrence of topologically protected edge channels due to the emergent field of a skyrmion crystal. Both observables quantify the topological Hall effect and distinguish skyrmions from antiskyrmions by sign. Additionally, we predict a magnetoelectric effect in skyrmion crystals, which is the generation of a magnetization (polarization) by application of an electric (magnetic) field. This effect is quantified by spin toroidization and magnetoelectric polarizability. The dependence of the transverse magnetoelectric effect on the skyrmion helicity fits that of the classical toroidal moment of the spin texture and allows to differentiate skyrmion helicities: it is largest for Bloch skyrmions and zero for Neel skyrmions. We predict distinct features of the four observables that can be used to detect and characterize skyrmions in experiments.

Skyrmion electrical detection with the use of three-dimensional Topological Insulators/Ferromagnetic bilayers

The effect of the magnetic skyrmion texture on the electronic transport properties of the TI surface state coupled to a thin-film FM is numerically investigated. It is shown that both Bloch (vortex) and Néel (hedgehog) skyrmion textures induce additional scattering on top of a homogeneous background FM texture which can modify the conductance of the system. The change in conductance depends on several factors including the skyrmion size, the dimensions of the FM and the exchange interaction strength. For the Néel skyrmion, the result of the interaction strongly depends on the skyrmion number Nsk and the skyrmion helicity h. For both skyrmion types, significant change of the resistance can be achieved, which is in the order of kΩ.

Spin-wave spectroscopy of the Dzyaloshinskii-Moriya interaction in room-temperature chiral magnets hosting skyrmions

Propagation character of spin wave was investigated for chiral magnets FeGe and Co-Zn-Mn alloys, which can host magnetic skyrmions near room temperature. On the basis of the frequency shift between counter-propagating spin waves, the magnitude and sign of Dzyaloshinskii-Moriya (DM) interaction were directly evaluated. The obtained magnetic parameters quantitatively account for the size and helicity of skyrmions as well as their materials variation, proving that the DM interaction plays a decisive role in the skyrmion formation in this class of room-temperature chiral magnets. The propagating spin-wave spectroscopy can thus be an efficient tool to study DM interaction in bulk single-phase compounds. Our results also demonstrate a function of spin-wave diode based on chiral crystal structures at room temperature.

Controlling skyrmion helicity via engineered Dzyaloshinskii–Moriya interactions

Single magnetic skyrmion dynamics in chiral magnets with a spatially inhomogeneous Dzyaloshinskii–Moriya interaction (DMI) is considered. Based on the relation between DMI coupling and skyrmion helicity, it is argued that the latter must be included as an extra degree of freedom in the dynamics of skyrmions. An effective description of the skyrmion dynamics for an arbitrary inhomogeneous DMI coupling is obtained through the collective coordinates method. The resulting generalized Thiele equation is a dynamical system for the center of mass position and helicity of the skyrmion. It is found that the dissipative tensor and hence the Hall angle become helicity dependent. The skyrmion position and helicity dynamics are fully characterized by our model in two particular examples of engineered DMI coupling: half-planes with opposite-sign DMI and linearly varying DMI. In light of the experiment of Shibata et al (2013 Nat. Nanotechnol. 8 723) on the magnitude and sign of the DMI, our results constitute the first step toward a more complete understanding of the skyrmion helicity as a new degree of freedom that could be harnessed in future high-density magnetic storage and logic devices.

Stability of topological charge of magnetic skyrmion configurations

We analyze the topological charge of a skyrmion qs, and the corresponding Hall conductivity σxy, which can serve as an electrical read-out for skyrmion-based memory. We derived the general form of the Dzyaloshinskii–Moriya (DM) interaction for any arbitrary orientation of the DM vector D. Based on the DM interaction energy, we obtained the dependence the skyrmion helicity angle γ on the orientation of D. We showed via general mathematical arguments, the topological nature of the skyrmionic charge qs, and its independence of γ and specific details of the interior of the skyrmion (e.g., its core size). Finally, we showed via numerical micromagnetics the stability of qs under varying applied B-fields till the annihilation field, despite the drastic reduction in the skyrmion core size.

Two-dimensional skyrmion lattice in a nanopatterned magnetic film

We study the possibility of a two-dimensional (2D) skyrmion crystal stabilization in a magnetic film with perpendicular anisotropy in the absence of Dzyaloshinskii-Moriya interaction by creating the regular array of blind holes or stubs. By micromagnetic simulation we demonstrate that skyrmions can be stable in the patterned films with the parameters of ordinary materials such as CoPt, FePt, or FePd. The skyrmion lattices can be initialized in the system by simple magnetization in the uniform external magnetic field. At the zero external field the skyrmion helicity depends on the geometry of the blind hole or stub but also can be tuned by applying the field. The suggested method makes it possible to create dense enough (with the period less than 100 nm) skyrmion lattices which are important to carry out transport measurements.

Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling

Chirality--that is, left- or right-handedness--is an important concept in a broad range of scientific areas. In condensed matter, chirality is found not only in molecular or crystal forms, but also in magnetic structures. A magnetic skyrmion is a topologically stable spin vortex structure, as observed in chiral-lattice helimagnets, and is one example of such a structure. The spin swirling direction (skyrmion helicity) should be closely related to the underlying lattice chirality via the relativistic spin-orbit coupling. Here, we report on the correlation between skyrmion helicity and crystal chirality in alloys of helimagnets Mn(1-x)Fe(x)Ge with varying compositions by Lorentz transmission electron microscopy and convergent-beam electron diffraction over a broad range of compositions (x = 0.3-1.0). The skyrmion lattice constant shows non-monotonous variation with composition x, with a divergent behaviour around x = 0.8, where the correlation between magnetic helicity and crystal chirality changes sign. This originates from continuous variation of the spin-orbit coupling strength and its sign reversal in the metallic alloys as a function of x. Controllable spin-orbit coupling may offer a promising way to tune skyrmion size and helicity.