Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks.

Magnetic skyrmion is a nanosized magnetic whirl with nontrivial topology, which is highly relevant for applications on future memory devices. To enable the applications, theoretical efforts have been made to understand the dynamics of individual skyrmions in magnetic nanostructures. However, directly imaging the evolution of highly geometrically confined individual skyrmions is challenging. Here, we report the magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of several skyrmion sizes by using Lorentz transmission electron microscopy. In contrast to the conventional skyrmion lattice in bulk, a series of skyrmion cluster states with different geometrical configurations and the field-driven cascading phase transitions are identified at temperatures far below the magnetic transition temperature. Furthermore, a dynamics, namely the intermittent jumps between the neighboring skyrmion cluster states, is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrmion cluster states.

Quantification of Magnetic Surface and Edge States in an FeGe Nanostripe by Off-Axis Electron Holography.

Whereas theoretical investigations have revealed the significant influence of magnetic surface and edge states on Skyrmonic spin texture in chiral magnets, experimental studies of such chiral states remain elusive. Here, we study chiral edge states in an FeGe nanostripe experimentally using off-axis electron holography. Our results reveal the magnetic-field-driven formation of chiral edge states and their penetration lengths at 95 and 240 K. We determine values of saturation magnetization M_{S} by analyzing the projected in-plane magnetization distributions of helices and Skyrmions. Values of M_{S} inferred for Skyrmions are lower by a few percent than those for helices. We attribute this difference to the presence of chiral surface states, which are predicted theoretically in a three-dimensional Skyrmion model. Our experiments provide direct quantitative measurements of magnetic chiral boundary states and highlight the applicability of state-of-the-art electron holography for the study of complex spin textures in nanostructures.

Interaction of Individual Skyrmions in a Nanostructured Cubic Chiral Magnet.

We report direct evidence of the field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high-resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of an external magnetic field the character of such long-range skyrmion interactions changes from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skyrmion-edge distances as a function of the applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. The important role of demagnetizing fields and the internal symmetry of three-dimensional magnetic skyrmions are discussed in detail.

Enhanced Stability of the Magnetic Skyrmion Lattice Phase under a Tilted Magnetic Field in a Two-Dimensional Chiral Magnet.

The magnetic skyrmion is a topologically stable vortex-like spin texture that offers great promise as information carriers for future spintronic devices. In a two-dimensional chiral magnet, it was generally considered that a tilted magnetic field is harmful to its formation and stability. Here we investigated the angular-dependent stability of magnetic skyrmions in FeGe nanosheets by using high-resolution Lorentz transmission electron microscopy (Lorentz TEM). Besides the theoretically predicted destruction of skyrmion lattice state by an oblique magnetic field as the temperature closes to its magnetic Curie temperature Tc ∼ 278 K, we also observed an unexpected reentry-like phenomenon at the moderate temperatures near the border between conical and skyrmion phase, Tt ∼ 240 K. This behavior is completely beyond the theoretical prediction in a conventional two-dimensional (2D) system. Instead, a three-dimensional (3D) model involving the competition between conical phase and skyrmions is likely to play a crucial role.

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.

Direct Imaging of a Zero-Field Target Skyrmion and Its Polarity Switch in a Chiral Magnetic Nanodisk.

A target Skyrmion is a flux-closed spin texture that has twofold degeneracy and is promising as a binary state in next generation universal memories. Although its formation in nanopatterned chiral magnets has been predicted, its observation has remained challenging. Here, we use off-axis electron holography to record images of target Skyrmions in a 160-nm-diameter nanodisk of the chiral magnet FeGe. We compare experimental measurements with numerical simulations, demonstrate switching between two stable degenerate target Skyrmion ground states that have opposite polarities and rotation senses, and discuss the observed switching mechanism.

Thermal conductivity of a single Bi0.5Sb1.5Te3 single-crystalline nanowire.

Single-crystalline Bi0.5Sb1.5Te3 nanowires were fabricated by a template-assisted pulsed electrodeposition technique; the thermal conductivity of a single Bi0.5Sb1.5Te3 nanowire of different diameters was characterized through a self-heating 3 ω method. The temperature-dependent resistance measurements prove the semiconductor behavior of the nanowires. The extremely low thermal conductivity of the nanowires was found compared with the corresponding bulk, and the Umklapp peaks shift to a higher temperature as the decreasing nanowire's diameter decreases, which qualitatively agrees with the theoretical calculations based on the Callaway model. The boundary scattering plays an important role in the reduction of the thermal conductivity and in the shift of the Umklapp peak of the Bi0.5Sb1.5Te3 nanowires.

Control of morphology and formation of highly geometrically confined magnetic skyrmions.

The ability to controllably manipulate magnetic skyrmions, small magnetic whirls with particle-like properties, in nanostructured elements is a prerequisite for incorporating them into spintronic devices. Here, we use state-of-the-art electron holographic imaging to directly visualize the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in the range of 45-150 nm. We find that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticities in a nanostripe that are absent in both thin films and bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We perform a theoretical analysis based on a three-dimensional general model of isotropic chiral magnets to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices.

Critical phenomenon of the near room temperature skyrmion material FeGe.

The cubic B20 compound FeGe, which exhibits a near room temperature skyrmion phase, is of great importance not only for fundamental physics such as nonlinear magnetic ordering and solitons but also for future application of skyrmion states in spintronics. In this work, the critical behavior of the cubic FeGe is investigated by means of bulk dc-magnetization. We obtain the critical exponents (ß = 0.336 ± 0.004, γ = 1.352 ± 0.003 and ß = 5.276 ± 0.001), where the self-consistency and reliability are verified by the Widom scaling law and scaling equations. The magnetic exchange distance is found to decay as r(-4.9), which is close to the theoretical prediction of 3D-Heisenberg model (r(-5)). The critical behavior of FeGe indicates a short-range magnetic interaction. Meanwhile, the critical exponents also imply an anisotropic magnetic coupling in this system.

Edge-mediated skyrmion chain and its collective dynamics in a confined geometry.

The emergence of a topologically nontrivial vortex-like magnetic structure, the magnetic skyrmion, has launched new concepts for memory devices. Extensive studies have theoretically demonstrated the ability to encode information bits by using a chain of skyrmions in one-dimensional nanostripes. Here, we report experimental observation of the skyrmion chain in FeGe nanostripes by using high-resolution Lorentz transmission electron microscopy. Under an applied magnetic field, we observe that the helical ground states with distorted edge spins evolve into individual skyrmions, which assemble in the form of a chain at low field and move collectively into the interior of the nanostripes at elevated fields. Such a skyrmion chain survives even when the width of the nanostripe is much larger than the size of single skyrmion. This discovery demonstrates a way of skyrmion formation through the edge effect, and might, in the long term, shed light on potential applications.

Electrical probing of field-driven cascading quantized transitions of skyrmion cluster states in MnSi nanowires.

Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future spintronic devices. To enable such applications, particular attention has been focused on the properties of skyrmions in highly confined geometries such as one-dimensional nanowires. Hitherto, it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here, we achieve this by measuring the magnetoresistance in ultra-narrow MnSi nanowires. We observe quantized jumps in magnetoresistance versus magnetic field curves. By tracking the size dependence of the jump number, we infer that skyrmions are assembled into cluster states with a tunable number of skyrmions, in agreement with the Monte Carlo simulations. Our results enable an electric reading of the number of skyrmions in the cluster states, thus laying a solid foundation to realize skyrmion-based memory devices.