Bloch-type Skyrmions Research Articles

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.

Bloch Lines Constituting Antiskyrmions Captured via Differential Phase Contrast.

Much scientific capital has been directed toward exotic magnetic spin textures called Bloch lines, that is, Néel-type line boundaries within domain walls, because their geometry promises high-density magnetic storage. While predicted to arise in high-anisotropy magnets, bulk soft magnets, and thin films with in-plane magnetization, Bloch lines also constitute magnetic antiskyrmions, that is, topological antiparticles of skyrmions. Most domain walls occur as Bloch-type or Néel-type, in which the magnetization rotates parallel or perpendicular to the domain wall across its profile, respectively. The Bloch lines' Néel-type rotation and their minute size make them difficult to directly measure. This work utilizes differential phase contrast (DPC) scanning transmission electron microscopy (STEM) to measure the in-plane magnetization of Bloch lines within antiskyrmions emergent in a non-centrosymmetric Heusler magnet with D2d symmetry, Mn1.4 Pt0.9 Pd0.1 Sn, in addition to Bloch-type skyrmions in an FeGe magnet with B20-type crystal structure to benchmark the DPC technique. Both in-focus measurement and identification of Bloch lines at the antiskyrmion's corners are provided.

Giant Topological Hall Effect and Superstable Spontaneous Skyrmions below 330 K in a Centrosymmetric Complex Noncollinear Ferromagnet NdMn2Ge2.

Skyrmions with topologically nontrivial spin textures are promising information carriers in next-generation ultralow power consumption and high-density spintronic devices. To promote their further development and utilization, the search for new room temperature skyrmion-hosting materials is crucial. Considering that most of the previous skyrmion-hosting materials are noncollinear magnets, here, the detection of the topological Hall effect (THE) and the discovery of skyrmions at room temperature are first reported in a centrosymmetric complex noncollinear ferromagnet NdMn2Ge2. Below 330 K, the compound can host stable Bloch-type skyrmions with about 75 nm diameter in a wide window of magnetic field and temperature, including zero magnetic field and room temperature. Moreover, the skyrmions can induce a giant topological Hall effect in a wide temperature range with a maximum value of -2.05 μΩ cm. These features make the compound attractive for both fundamental research and potential application in novel spintronic devices.

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

A skyrmion is a topologically protected soliton with a spin structure on the micro/nano scale that has promising applications in magnetic information storage and spintronics devices. This study focuses on the optical skyrmion lattice structures created in the surface plasmon polaritons (SPPs) field. Both the Néel-type optical skyrmion lattice formed by the electric field vector and Bloch-type optical skyrmion lattice formed by the magnetic field vector are generated via exciting a hexagonal grating structure on the metal surface with six Gaussian optical spots. Such a multiple-spot excitation can be realized through tightly focusing a specially designed complex field with a high NA lens. Through introducing the phase difference of the excitation beams to shift the SPP standing waves, the shape and position of the optical skyrmion lattice can be dynamically controlled. Both the electric field vector and magnetic field vector are evaluated quantitatively based on the electric and magnetic field obtained by finite difference time domain (FDTD) simulation to demonstrate the validity and capability of the proposed technique.

Robust cycloid crossover driven by anisotropy in the skyrmion host GaV4S8

We report on the anomalous magnetization dynamics of the cycloidally-modulated spin textures under the influence of uniaxial anisotropy in multiferroic $\mathrm{GaV_4S_8}$. The temperature and field dependence of the linear ac susceptibility [$\chi_{1\omega}^{\prime}(T,H)$], ac magnetic loss [$\chi_{1\omega}^{\prime\prime}(T,H)$], and nonlinear ac magnetic response [$M_{3\omega}(T,H)$] are examined across the magnetic phase diagram in the frequency range $f = 10-10000$ Hz. According to recent theory, skyrmion vortices under axial crystal symmetry are confined along specific orientations, resulting in enhanced robustness against oblique magnetic fields and altered spin dynamics. We characterize the magnetic response of each spin texture and find that the dynamic rigidity of the N\'eel skyrmion lattice appears enhanced compared to Bloch-type skyrmions in cubic systems, even in the multidomain state. Anomalous $M_{3\omega}$ and strong dissipation emerge over the same phase regime where strong variations in the cycloid pitch were observed on lowering temperature in recent small-angle neutron scattering experiments [White et al., Phys. Rev. B 97, 020401(R) (2018)]. Here, we show that strong anisotropy also drives an extended crossover of the zero-field cycloid texture in $\mathrm{GaV_4S_8}$. The frequency dependence of these dynamic signatures is consistent with that of a robust anharmonic spin texture exhibiting a correlated domain arrangement. The results underpin the essential role of magnetic anisotropy in enhancing the rigidity of topological spin textures for diverse applications.

Elliptical Bloch skyrmion chiral twins in an antiskyrmion system

Skyrmions and antiskyrmions are distinct topological chiral spin textures that have been observed in various material systems depending on the symmetry of the crystal structure. Here we show, using Lorentz transmission electron microscopy, that arrays of skyrmions can be stabilized in a tetragonal inverse Heusler with D2d symmetry whose Dzyaloshinskii-Moriya interaction (DMI) otherwise supports antiskyrmions. These skyrmions can be distinguished from those previously found in several B20 systems which have only one chirality and are circular in shape. We find Bloch-type elliptical skyrmions with opposite chiralities whose major axis is oriented along two specific crystal directions: [010] and [100]. These structures are metastable over a wide temperature range and we show that they are stabilized by long-range dipole-dipole interactions. The possibility of forming two distinct chiral spin textures with opposite topological charges of ±1 in one material makes the family of D2d materials exceptional.

Observation of Magnetic Skyrmion Bubbles in a van der Waals Ferromagnet Fe3GeTe2.

Two-dimensional (2D) van der Waals (vdW) magnetic materials have recently been introduced as a new horizon in materials science, and they enable potential applications for next-generation spintronic devices. Here, in this communication, the observations of stable Bloch-type magnetic skyrmions in single crystals of 2D vdW Fe3GeTe2 (FGT) are reported by using in situ Lorentz transmission electron microscopy (TEM). We find the ground-state magnetic stripe domains in FGT transform into skyrmion bubbles when an external magnetic field is applied perpendicularly to the (001) thin plate with temperatures below the Curie temperature TC. Most interestingly, a hexagonal lattice of skyrmion bubbles is obtained via field-cooling manipulation with magnetic field applied along the [001] direction. Owing to their topological stability, the skyrmion bubble lattices are stable to large field-cooling tilted angles and further reproduced by utilizing the micromagnetic simulations. These observations directly demonstrate that the 2D vdW FGT possesses a rich variety of topological spin textures, being of great promise for future applications in the field of spintronics.

Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet.

Geometrically frustrated magnets can host complex spin textures, leading to unconventional electromagnetic responses. Magnetic frustration may also promote topologically nontrivial spin states such as magnetic skyrmions. Experimentally, however, skyrmions have largely been observed in noncentrosymmetric lattice structures or interfacial symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustrated centrosymmetric triangular-lattice magnet Gd2PdSi3 We observed a giant topological Hall response, indicating a field-induced skyrmion phase, which is further corroborated by the observation of in-plane spin modulation probed by resonant x-ray scattering. Our results may lead to further discoveries of emergent electrodynamics in magnetically frustrated centrosymmetric materials.

Spin-wave mediated interactions for majority computation using Skyrmions and spin-torque nano-oscillators

Recent progress in all-electrical nucleation, detection and manipulation of magnetic skyrmions has unlocked the tremendous potential of skyrmion-based spintronic devices. Here, we show via micromagnetic simulations that the stable magnetic oscillations of STNO radiate spin waves (SWs) that can be scattered in the presence of skyrmions in the near vicinity. Interference between SWs emitted by the STNO and SWs scattered by the skyrmion gives rise to interesting dynamics that leads to amplification or attenuation of STNO’s magnetic oscillations. In the presence of strong Dzyaloshinskii-Moriya interaction (DMI), the amplified magnetic oscillations evolve into a new skyrmion. These interactions between skyrmions and STNOs are found to be identical for both Neel-type and Bloch-type skyrmions, and are not observed between domain walls and STNOs. These findings offer a novel perspective in processing information using single skyrmions and we propose a 3-bit majority gate for logic applications.

Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid He3−A

We investigate torsional chiral magnetic effect (TCME) induced by skyrmion-vortex textures in the A phase of the superfluid $^3$He. In $^3$He-A, Bogoliubov quasiparticles around point nodes behave as Weyl fermions, and the nodal direction represented by the $\ell$-vector may form a spatially modulated texture. $\ell$-textures generate a chiral gauge field and a torsion field directly acting on the chirality of Weyl-Bogoliubov quasiparticles. It has been clarified by G. E. Volovik [Pi'sma Zh. Eksp. Teor. Fiz. {\bf 43}, 428 (1986)] that, if the $\ell$-vector is twisted, the chiral gauge field is responsible for the chiral anomaly, leading to an anomalous current along ${\ell}$. Here we show that, even for non-twisted $\ell$-vector fields, a torsion arising from $\ell$-textures brings about contributions to the equilibrium currents of Weyl-Bogoliubov quasiparticles along ${\rm curl}{\ell}$. This implies that while the anomalous current appears only for the twisted (Bloch-type) skyrmion of the $\ell$-vector, the extra mass current due to TCME always exists regardless of the skyrmion type. Solving the Bogoliubov-de Gennes equation, we demonstrate that both Bloch-type and N\'{e}el-type skyrmions induce chiral fermion states with spectral asymmetry, and possess spatially inhomogeneous structures of Weyl bands in the real coordinate space. Furthermore, we discuss the contributions of Weyl-Bogoliubov quasiparticles and continuum states to the mass current density in the vicinity of the topological phase transition. In the weak coupling limit, continuum states give rise to backflow to the mass current generated by Weyl-Bogoliubov quasiparticles, which makes a non-negligible contribution to the orbital angular momentum. As the topological transition is approached, the mass current density is governed by the contribution of continuum states.

High-resolution combined tunneling electron charge and spin transport theory of Néel and Bloch skyrmions

Based on a combined charge and vector spin transport theory capable of imaging noncollinear magnetic textures on surfaces with spin-polarized scanning tunneling microscopy (SP-STM), the high-resolution tunneling electron charge and coupled spin transport properties of a variety of N\'eel- and Bloch-type skyrmions are investigated. Axially symmetric skyrmions are considered within the same topology class characterized by a vorticity value of $m=1$, and their helicities are varied by taking $\gamma=0$ and $\pi$ values for the N\'eel skyrmions and $\gamma=-\pi/2$ and $\pi/2$ values for the Bloch skyrmions. Depending on the orientation of the magnetization of the STM tip as well as on the helicity and the time-reversal of the skyrmionic spin structures, several relationships between their spin transport vector components, the in-plane and out-of-plane spin transfer torque and the longitudinal spin current, are identified. The magnitudes of the spin transport vector quantities show close relation to standard charge current SP-STM images. It is also demonstrated that the SP-STM images can be used to determine the helicity of the skyrmions. Moreover, the modified spin polarization vectors of the conduction electrons due to the local chirality of the complex spin texture are incorporated into the tunneling model. It is found that this effect modifies the apparent size of the skyrmions. These results contribute to the proper identification of topological surface magnetic objects imaged by SP-STM, and deliver important parameters for current-induced spin dynamics.

Magnetostatics of magnetic skyrmion crystals

Magnetic skyrmion crystals are topological magnetic textures arising in the chiral ferromagnetic materials with Dzyaloshinskii–Moriya interaction. The magnetostatic fields generated by magnetic skyrmion crystals are first studied by micromagnetic simulations. For Néel-type skyrmion crystals, the fields will vanish on one side of the crystal plane, which depend on the helicity; while for Bloch-type skyrmion crystals, the fields will distribute over both sides, and are identical for the two helicities. These features and the symmetry relations of the magetostatic fields are understood from the magnetic scalar potential and magnetic vector potential of the hybridized triple-Q state. The possibility to construct magnetostatic field at nanoscale by stacking chiral ferromagnetic layers with magnetic skyrmion crystals is also discussed, which may have potential applications to trap and manipulate neutral atoms with magnetic moments.

Azimuthal spin-wave excitations in magnetic nanodots over the soliton background: Vortex, Bloch, and Néel-like skyrmions

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Continuous mapping of the SW spectrum between these states is realized with gradual change of the out-of-plane magnetic anisotropy and Dzyaloshinskii-Moriya exchange interaction (DMI). Our study shows lifting of the SW frequencies degeneracy and change in systematics of the frequency levels. The change is induced by a geometrical Berry phase, that is present for the dot-edge localized SWs in a vortex state and vanishes in skyrmion states. Furthermore, channeling of the azimuthal SWs localized at the skyrmion edge is present and induces large frequency splitting. This is attributed to DMI induced nonreciprocity, while coupling of the breathing and gyrotropic modes is related to soliton motion. Finally, an efficient coupling of the dynamic magnetization in the skyrmion state to uniform magnetic field in nanodots with non-circular symmetry is shown.

Micromagnetic simulation of the ground states of Ce-Fe-B amorphous nanodisks

Using 3D micromagnetics package OOMMF, the ground states of Ce2Fe14B amorphous nanodisks with different dimensions, initial magnetization states and magnetocrystalline anisotropy constants (K) in zero external field were investigated. The simulations indicate that the disk size is the decisive factor in determining magnetic configurations. A diagram is constructed to bring out the dependence of the different equilibrium states on the disk thickness and diameter. When the ratio of thickness (T) to diameter (D) is smaller than 1, the vortex state is energetically more favorable than other states and the eigenfrequency of vortex approximately proportional to (T/D)1/2. A variety of magnetization distributions of ground states for different anisotropy strengths is obtained. The result shows the magnetocrystalline anisotropy not only shrinks or broadens the vortex core but also induces an out-of-plane magnetization component both at the edge and the center of disks. When the K strength reaches a threshold value, there is a transition from vortex state to Bloch-type Skyrmion state which suggests the possibility of Skyrmion in rare-earth materials. In addition, in the system with specific aspect ratio and low intrinsic anisotropy, the vortex domain can always be sustained under various initial conditions. Meanwhile, the existence of stable vortex domain is found by experimentation in amorphous Ce-Fe-B ribbons which is in good agreement with the simulation result.

Mapping the magnetization fine structure of a lattice of Bloch-type skyrmions in an FeGe thin film

Bloch-type magnetic skyrmions are nanoscale vortex-like spin objects that form densely packed lattice arrangements in B20-type chiral magnets in the presence of a magnetic field. Here, we use off-axis electron holography, in combination with an iterative model-based reconstruction algorithm, to study the geometries of the projected in-plane magnetization distributions of individual skyrmions in an FeGe thin film as a function of applied magnetic field. We compare our results with micromagnetic simulations and find a departure from magnetic chirality in the transition regions between adjacent skyrmions when they are in lattice arrangements.

Micromagnetic investigations of Néel- and Bloch-type skyrmion dynamics induced by spin Hall effect of cap layers

We investigate the spin-injection driving of skyrmion domains on a wire using micromagnetic simulations. We find that both Néel- and Bloch-type skyrmion domains are driven in oblique directions when the spin current is injected into the vertical axis of the skyrmion domains. The driving direction is analyzed from the magnetized direction and the domain-wall structure of the skyrmion domains.

Current-Induced Nucleation and Annihilation of Magnetic Skyrmions at Room Temperature in a Chiral Magnet.

A magnetic skyrmion is a nanometer-scale magnetic vortex carrying an integer topological charge. Skyrmions show a promise for potential application in low-power-consumption and high-density memory devices. To promote their use in applications, it is attempted to control the existence of skyrmions using low electric currents at room temperature (RT). This study presents real-space observations for the current-induced formation and annihilation of a skyrmion lattice (SkL) as well as isolated skyrmions in a microdevice composed of a thin chiral magnet Co8 Zn9 Mn3 with a Curie temperature, TC ≈ 325 K, above RT. It is found that the critical current for the manipulation of Bloch-type skyrmions is on the order of 108 A m-2 , approximately three orders of magnitude lower than that needed for the creation and drive of ferromagnetic (FM) domain walls in thin FM films. The in situ real-space imaging also demonstrates the dynamical topological transition from a helical or conical structure to a SkL induced by the flow of DC current, thus paving the way for the electrical control of magnetic skyrmions.

Spin excitation spectrum in a magnetic nanodot with continuous transitions between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states

We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves and breathing modes in various stable magnetization states and helps to understand the rich spin excitation spectrum on the skyrmion background.

Skyrmion dynamics under uniaxial anisotropy

Broadband microwave spectroscopy has been performed on single-crystalline GaV$_4$S$_8$, which exhibits a complex magnetic phase diagram including cycloidal, N\'eel-type skyrmion lattice, as well as field-polarized ferromagnetic phases below 13 K. At zero and small magnetic fields two collective modes are found at 5 and 15 GHz, which are characteristic of the cycloidal state in this easy-axis magnet. In finite fields, entering the skyrmion lattice phase, the spectrum transforms into a multi-mode pattern with absorption peaks near 4, 8, and 15 GHz. The spin excitation spectra in GaV$_4$S$_8$ and their field dependencies are found to be in close relation to those observed in materials with Bloch-type skyrmions. Distinct differences arise from the strong uniaxial magnetic anisotropy of GaV4S8 not present in so-far known skyrmion hosts.