Interplay between quantum anomalous Hall effect and magnetic skyrmions.

SignificanceQuantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK), as two typical topological states in momentum (K) and real (R) spaces, attract much interest in condensed matter physics. However, the interplay between these two states remains to be explored. We propose that the interplay between QAHE and SK may generate an RK joint topological skyrmion (RK-SK), characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Furthermore, the emerging external field-tunable CBS in RK-SK could create additional degrees of freedom for SK manipulations, beyond the traditional SK. Meanwhile, external field can realize a rare topological phase transition between K and R spaces. Our work opens avenues for exploring unconventional quantum states and topological phase transitions in different spaces.

Raman Shifts in Two-Dimensional van der Waals Magnets Reveal Magnetic Texture Evolution.

Two-dimensional (2D) van der Waals magnets comprise rich physics that can be exploited for spintronic applications. We investigate the interplay between spin-phonon coupling and spin textures in a 2D van der Waals magnet by combining magneto-Raman spectroscopy with cryogenic Lorentz transmission electron microscopy. We find that when stable skyrmion bubbles are formed in the 2D magnet, a field-dependent Raman shift can be observed, and this shift is absent for the 2D magnet prepared in its ferromagnetic state. Correlating these observations with numerical simulations that take into account field-dependent magnetic textures and spin--phonon coupling in the 2D magnet, we associate the Raman shift to field-induced modulations of the skyrmion bubbles and derive the existence of inhomogeneity in the skyrmion textures over the film thickness.

Skyrmion based majority logic gate by voltage controlled magnetic anisotropy in a nanomagnetic device.

Magnetic skyrmions are topologically protected spin textures and they are suitable for future logic-in-memory applications for energy-efficient, high-speed information processing and computing technologies. In this work, we have demonstrated skyrmion-based 3 bit majority logic gate using micromagnetic simulations. The skyrmion motion is controlled by introducing agatethat works on voltage controlled magnetic anisotropy. Here, the inhomogeneous magnetic anisotropy behaves as a tunable potential barrier/well that modulates the skyrmion trajectory in the structure for the successful implementation of the majority logic gate. In addition, several other effects such as skyrmion-skyrmion topological repulsion, skyrmion-edge repulsion, spin-orbit torque and skyrmion Hall effect have been shown to govern the logic functionalities. We have systematically presented the robust logic operations by varying the current density, magnetic anisotropy, voltage-controlled gate dimension and geometrical parameters of the logic device. The skyrmion Hall angle is monitored to understand the trajectory and stability of the skyrmion as a function of time in the logic device. The results demonstrate a novel method to achieve majority logic by using voltage controlled magnetic anisotropy which further opens up a new route for skyrmion-based low-power and high-speed computing devices.

Experimental Realization of a Skyrmion Circulator.

Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.

Targeted Writing and Deleting of Magnetic Skyrmions in Two-Terminal Nanowire Devices.

Controllable writing and deleting of nanoscale magnetic skyrmions are key requirements for their use as information carriers for next-generation memory and computing technologies. While several schemes have been proposed, they require complex fabrication techniques or precisely tailored electrical inputs, which limits their long-term scalability. Here, we demonstrate an alternative approach for writing and deleting skyrmions using conventional electrical pulses within a simple, two-terminal wire geometry. X-ray microscopy experiments and micromagnetic simulations establish the observed skyrmion creation and annihilation as arising from Joule heating and Oersted field effects of the current pulses, respectively. The unique characteristics of these writing and deleting schemes, such as spatial and temporal selectivity, together with the simplicity of the two-terminal device architecture, provide a flexible and scalable route to the viable applications of skyrmions.

Kinetics of Magnetic Skyrmion Crystal Formation from the Conical Phase.

The particle-like magnetic skyrmion or skyrmion lattice (SkX) formation has promoted strong application and fundamental science interests. Despite extensive research, the kinetic of the SkX development is much less understood because of the ultrafast spin rotation and high sensitivity to external perturbations. Here, using in situ Lorentz transmission electron microscopy, we successfully measured the dynamics of SkX formation from the conical phase with precise control of both the temperature and the magnetic field. We discovered that the Avrami equation can accurately describe the transition process with an initial Avrami constant around 1, suggesting that the rate-limiting step for the quasiparticle lattice formation is one-dimensional heterogeneous nucleation of individual skyrmions. A modified Arrhenius rate law is established, with an energy barrier that has a square-root dependence on temperature and a quadratic dependence on the magnetic field. This study paves the way toward precise and predictable manipulation of topological spin structures.

Surface acoustic wave controlled skyrmion-based synapse devices.

Magnetic skyrmions, which are particle-like spin structures, are promising information carriers for neuromorphic computing devices due to their topological stability and nanoscale size. In this work, we propose controlling magnetic skyrmions by electric-field-excited surface acoustic waves in neuromorphic computing device structures. Our micromagnetic simulations show that the number of created skyrmions, which emulates the synaptic weight parameter, increases monotonically with increases in the amplitude of the surface acoustic waves. Additionally, the efficiency of skyrmion creation is investigated systemically with a wide range of magnetic parameters, and the optimal values are presented accordingly. Finally, the functionalities of short-term plasticity and long-term potentiation are demonstrated via skyrmion excitation by a sequence of surface acoustic waves with different intervals. The application of surface acoustic waves in skyrmionic neuromorphic computing devices paves a novel approach to low-power computing systems.

Mechanisms of Skyrmion and Skyrmion Crystal Formation from the Conical Phase.

Real-space topological magnetic structures such as skyrmions and merons are promising candidates for information storage and transport. However, the microscopic mechanisms that control their formation and evolution are still unclear. Here, using in situ Lorentz transmission electron microscopy, we demonstrate that skyrmion crystals (SkXs) can nucleate, grow, and evolve from the conical phase in the same ways that real nanocrystals form from vapors or solutions. More intriguingly, individual skyrmions can also "reproduce" by division in a mitosis-like process that allows them to annihilate SkX lattice imperfections, which is not available to crystals made of mass-conserving particles. Combined string method and micromagnetic calculations show that competition between repulsive and attractive interactions between skyrmions governs particle-like SkX growth, but nonconservative SkX growth appears to be defect mediated. Our results provide insights toward manipulating magnetic topological states by applying established crystal growth theory, adapted to account for the new process of skyrmion mitosis.

Real-Space Observation of Topological Defects in Extended Skyrmion-Strings.

Exotic topological spin textures such as emergent magnetic monopole/anti-monopoles (hedgehog/anti-hedgehog) in the metastable extended skyrmion-strings attract much attention to the fundamental physics owing to their novel electromagnetic properties. However, the direct imaging of such spin textures is lacking. Here, we report the real-space observation of emergent magnetic monopoles involved in extended skyrmion-strings by Lorentz transmission electron microscopy (TEM) in combination with micromagnetic simulations. The in-plane extended skyrmion-strings are observed directly by Lorentz TEM to accompany the topological hedgehog-like defect, where the skyrmion-string terminates or merges with another skyrmion-string, as well as the surface-related defects where skyrmion-string bends 90° and ends on the surface. We also demonstrate the transformation of a metastabilized lattice of out-of-plane short skyrmion-strings into an in-plane array of extended skyrmion-strings by tuning the magnitude of oblique fields in a room-temperature helimagnet, revealing the stability of such topological spin textures and the possibility to control them.

Creation of Magnetic Skyrmion Bubble Lattices by Ultrafast Laser in Ultrathin Films.

Magnetic skyrmions are topologically nontrivial spin textures which hold great promise as stable information carriers in spintronic devices at the nanoscale. One of the major challenges for developing novel skyrmion-based memory and logic devices is fast and controlled creation of magnetic skyrmions at ambient conditions. Here we demonstrate controlled generation of skyrmion bubbles and skyrmion bubble lattices from a ferromagnetic state in sputtered ultrathin magnetic films at room temperature by a single ultrafast (35 fs) laser pulse. The skyrmion bubble density increases with the laser fluence, and it finally becomes saturated, forming disordered hexagonal lattices. Moreover, we present that the skyrmion bubble lattice configuration leads to enhanced topological stability as compared to isolated skyrmions, suggesting its promising use in data storage. Our findings shed light on the optical approach to the skyrmion bubble lattice in commonly accessible materials, paving the road toward the emerging skyrmion-based memory and synaptic devices.

Stable Magnetic Skyrmion States at Room Temperature Confined to Corrals of Artificial Surface Pits Fabricated by a Focused Electron Beam.

Stable confinement of elemental magnetic nanostructures, such as a single magnetic domain, is fundamental in modern magnetic recording technology. It is well-known that various magnetic textures can be stabilized by geometrical confinement using artificial nanostructures. The magnetic skyrmion, with novel spin texture and promise for future memory devices because of its topological protection and dimension at the nanometer scale, is no exception. So far, skyrmion confinement techniques using large-scale boundaries with limited geometries such as isolated disks and stripes prepared by conventional microfabrication techniques have been used. Here, we demonstrate an alternative technique confining skyrmions to artificial nanostructures (corrals) built from surface pits fabricated by a focused electron beam. Using aberration-corrected differential phase contrast scanning transmission electron microscopy, we directly visualized stable skyrmion states confined at a room temperature to corrals made of artificial surface pits on a thin plate of Co8Zn8Mn4. We observed a stable single-skyrmion state confined to a triangular corral and a unique transition into a triple-skyrmions state depending on the perpendicular magnetic field. Furthermore, we made an array of stable single-skyrmion states by using concatenated triangular corrals. Artificial control of skyrmion states with the present technique should be a powerful way to realize future nonvolatile memory devices using skyrmions.

Current-Driven Motion of Domain Boundaries between Skyrmion Lattice and Helical Magnetic Structure.

To utilize magnetic skyrmions, nanoscale vortex-like magnetic structures, experimental elucidation of their dynamics against current application in various circumstances such as in confined structure and mixture of different magnetic phases is indispensable. Here, we investigate the current-induced dynamics of the coexistence state of magnetic skyrmions and helical magnetic structure in a thin plate of B20-type helimagnet FeGe in terms of in situ real-space observation using Lorentz transmission electron microscopy. Current pulses with various heights and widths were applied, and the change of the magnetic domain distribution was analyzed using a machine-learning technique. The observed average driving direction of the two-magnetic-state domain boundary is opposite to the applied electric current, indicating ferromagnetic s-d exchange coupling in the spin-transfer torque mechanism. The evaluated driving distance tends to increase with increasing the pulse duration time, current density (>1 × 109 A/m2), and sample temperature, providing valuable information about hitherto unknown current-induced dynamics of the skyrmion-lattice ensemble.

Strongly correlated oxides for energy harvesting.

We review recent advances in strongly correlated oxides as thermoelectric materials in pursuit of energy harvesting. We discuss two topics: one is the enhancement of the ordinary thermoelectric properties by controlling orbital degrees of freedom and orbital fluctuation not only in bulk but also at the interface of correlated oxides. The other topic is the use of new phenomena driven by spin-orbit coupling (SOC) of materials. In 5d electron oxides, we show some SOC-related transport phenomena, which potentially contribute to energy harvesting. We outline the current status and a future perspective of oxides as thermoelectric materials.

Selective Chemical Vapor Deposition Growth of Cubic FeGe Nanowires That Support Stabilized Magnetic Skyrmions.

Magnetic skyrmions are topologically stable vortex-like spin structures that are promising for next generation information storage applications. Materials that host magnetic skyrmions, such as MnSi and FeGe with the noncentrosymmetric cubic B20 crystal structure, have been shown to stabilize skyrmions upon nanostructuring. Here, we report a chemical vapor deposition method to selectively grow nanowires (NWs) of cubic FeGe out of three possible FeGe polymorphs for the first time using finely ground particles of cubic FeGe as seeds. X-ray diffraction and transmission electron microscopy (TEM) confirm that these micron-length NWs with ∼100 nm to 1 µm diameters have the cubic B20 crystal structure. Although Fe13Ge8 NWs are also formed, the two types of NWs can be readily differentiated by their faceting. Lorentz TEM imaging of the cubic FeGe NWs reveals a skyrmion lattice phase under small applied magnetic fields (∼0.1 T) at 233 K, a skyrmion chain state at lower temperatures (95 K) and under high magnetic fields (∼0.4 T), and a larger skyrmion stability window than bulk FeGe. This synthetic approach to cubic FeGe NWs that support stabilized skyrmions opens a route toward the exploration of new skyrmion physics and devices based on similar nanostructures.

Magnetic Skyrmion Formation at Lattice Defects and Grain Boundaries Studied by Quantitative Off-Axis Electron Holography.

We use in situ Lorentz microscopy and off-axis electron holography to investigate the formation and characteristics of skyrmion lattice defects and their relationship to the underlying crystallographic structure of a B20 FeGe thin film. We obtain experimental measurements of spin configurations at grain boundaries, which reveal inversions of crystallographic and magnetic chirality across adjacent grains, resulting in the formation of interface spin stripes at the grain boundaries. In the absence of material defects, we observe that skyrmions lattices possess dislocations and domain boundaries, in analogy to atomic crystals. Moreover, the distorted skyrmions can flexibly change their size and shape to accommodate local geometry, especially at sites of dislocations in the skyrmion lattice. Our findings provide a detailed understanding of the elasticity of topologically protected skyrmions and their correlation with underlying material defects.

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets.

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Mirroring Skyrmions in Synthetic Antiferromagnets via Modular Design.

Skyrmions are promising for the next generation of spintronic devices, which involves the production and transfer of skyrmions. The creation of skyrmions can be realized by a magnetic field, electric field, or electric current while the controllable transfer of skyrmions is hindered by the skyrmion Hall effect. Here, we propose utilizing the interlayer exchange coupling induced by the Ruderman-Kittel-Kasuya-Yoshida interactions to create skyrmions through hybrid ferromagnet/synthetic antiferromagnet structures. An initial skyrmion in ferromagnetic regions could create a mirroring skyrmion with an opposite topological charge in antiferromagnetic regions driven by the current. Furthermore, the created skyrmions could be transferred in synthetic antiferromagnets without deviations away from the main trajectories due to the suppression of the skyrmion Hall effect in comparison to the transfer of the skyrmion in ferromagnets. The interlayer exchange coupling can be tuned, and the mirrored skyrmions can be separated when they reach the desired locations. Using this approach, the antiferromagnetic coupled skyrmions can be repeatedly created in hybrid ferromagnet/synthetic antiferromagnet structures. Our work not only supplies a highly efficient approach to create isolated skyrmions and correct the errors in the process of skyrmion transport, but also paves the way to a vital information writing technique based on the motion of skyrmions for skyrmion-based data storage and logic devices.

Skyrmion crystal phases in Kondo lattice model on triangular lattices.

Very often the magnetic skyrmions (topologically protected spin textures) form a triangular crystal in chiral magnets. Here we study the effect of itinerant electrons on the structure of skyrmion crystal (SkX) on triangular lattice using Kondo lattice model in the large coupling limit and treating the localized spins as classical vectors. To simulate the system, we employ hybrid Markov Chain Monte Carlo method (hMCMC) which includes electron diagonalization in each MCMC update for classical spins. We present the low-temperature results for12×12system at electron densityn=1/3which show a sudden jump in skyrmion number reducing the size of the skyrmions when we increase the hopping strength of the itinerant electrons. We find that this high skyrmion number SkX phase is stabilized by a combined effect: lowering of density of states at electron fillingn=1/3and also pushing the bottom energy states further down. We show that these results hold for larger24×24system using traveling cluster variation of hMCMC. We expect that itinerant triangular magnets might exhibit the possible transition between low-density to high-density SkX phases by applying external pressure.

Local Manipulation of Skyrmion Nucleation in Microscale Areas of a Thin Film with Nitrogen-Ion Implantation.

Precise manipulation of skyrmion nucleation in microscale or nanoscale areas of thin films is a critical issue in developing high-efficient skyrmionic memories and logic devices. Presently, the mainstream controlling strategies focus on the application of external stimuli to tailor the intrinsic attributes of charge, spin, and lattice. This work reports effective skyrmion manipulation by controllably modifying the lattice defect through ion implantation, which is potentially compatible with large-scale integrated circuit technology. By implanting an appropriate dose of nitrogen ions into a Pt/Co/Ta multilayer film, the defect density was effectively enhanced to induce an apparent modulation of magnetic anisotropy, consequently boosting the skyrmion nucleation. Furthermore, the local control of skyrmions in microscale areas of the macroscopic film was realized by combining the ion implantation with micromachining technology, demonstrating a potential application in both binary storage and multistate storage. These findings provide a new approach to advancing the functionalization and application of skyrmionic devices.

Experimental demonstration of skyrmionic magnetic tunnel junction at room temperature.

Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last decade, while electrical detection compatible with semiconductor processes has not been achieved, and this is considered one of the most crucial gaps regarding the use of skyrmions in real applications. Here, we report the direct observation of nanoscale skyrmions in CoFeB/MgO-based magnetic tunnel junction devices at room temperature. High-resolution magnetic force microscopy imaging and tunneling magnetoresistance measurements are used to illustrate the electrical detection of skyrmions, which are stabilized under the cooperation of interfacial Dzyaloshinskii-Moriya interaction, perpendicular magnetic anisotropy, and dipolar stray field. This skyrmionic magnetic tunnel junction shows a stable nonlinear multilevel resistance thanks to its topological nature and tunable density of skyrmions under current pulse excitation. These features provide important perspectives for spintronics to realize high-density memory and neuromorphic computing.