Detection of Topological Spin Textures via Nonlinear Magnetic Responses.

Topologically nontrivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation race-track memory and unconventional computing. A major challenge for these applications and the investigation of nanoscale magnetic structures in general is the realization of suitable detection schemes. We study magnetic disclinations, dislocations, and domain walls in FeGe and reveal pronounced responses that distinguish them from the helimagnetic background. A combination of magnetic force microscopy (MFM) and micromagnetic simulations links the response to the local magnetic susceptibility, that is, characteristic changes in the spin texture driven by the MFM tip. On the basis of the findings, which we explain using nonlinear response theory, we propose a read-out scheme using superconducting microcoils, presenting an innovative approach for detecting topological spin textures and domain walls in device-relevant geometries.

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.

Relaxation Dynamics of Zero-Field Skyrmions over a Wide Temperature Range.

The promise of magnetic skyrmions in future spintronic devices hinges on their topologically enhanced stability and the ability to be manipulated by external fields. The technological advantages of nonvolatile zero-field skyrmion lattice (SkL) are significant if their stability and reliability can be demonstrated over a broad temperature range. Here, we study the relaxation dynamics including the evolution and lifetime of zero-field skyrmions generated from field cooling (FC) in an FeGe single-crystal plate via in situ Lorentz transmission electron microscopy (L-TEM). Three types of dynamic switching between zero-field skyrmions and stripes are identified and distinguished. Moreover, the generation and annihilation of these metastable skyrmions can be tailored during and after FC by varying the magnetic fields and the temperature. This dynamic relaxation behavior under the external fields provides a new understanding of zero-field skyrmions for their stability and reliability in spintronic applications and also raises new questions for theoretical models of skyrmion systems.

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.

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.

High field magnetic transport measurements of FeGe thin plates.

Magnetic skyrmions have garnered considerable attention due to their topological properties and potential applications in information storage. These unique structures can be found in chiral magnets, including well-known compounds like MnSi and FeGe with a B20-type crystal structure. In this study, we utilized Lorentz transmission electron microscopy to investigate the influence of magnetic skyrmions on the Hall effect in FeGe under low magnetic fields. Additionally, we examined the magnetoresistance (MR) and Hall effect of FeGe under a high magnetic field of 28 T. Our findings reveal distinct mechanisms governing the MR at low and high temperatures. Notably, the anomalous Hall effect plays a significant role in the Hall resistivity observed at low magnetic fields. Meanwhile, the contribution of the skyrmion-induced topological Hall signal in the FeGe is ignorable. Furthermore, by employing a two-carrier model and fitting the carrier concentration of FeGe under high magnetic fields, we demonstrate a transition in the dominant carrier type from electrons to holes as the temperature increases. These results contribute to a deeper understanding of the intrinsic magnetic properties of FeGe.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

The hyperfine magnetic fields and the effect of high pressure on the magnetic transition temperatures of the noncentrosymmetric FeRhGe2compound (B20).

Hyperfine parameters and the pressure dependence of the magnetic transition temperatures of FeRhGe2have been investigated. Sample has been prepared using high pressure-high temperature synthesis technique. FeRhGe2consists of two B20 structure phases with close lattice constants. The phase separation stays constant in the temperature range 4-300 K. The magnetic transition temperaturesTc1= 213 K andTc2= 135 K of FeRhGe2slightly increases with pressure in the range 0-4.5 GPa. We have compared this pressure dependence with some others compounds in the family Fe1-xRhxGe. The two phases in FeRhGe2have slightly different values of the hyperfine magnetic fields.

Extracting weak magnetic contrast from complex background contrast in plan-view FeGe thin films.

The desire to design and build skyrmion-based devices has led to the need to characterize magnetic textures in thin films of functional materials. This can usually be achieved through the Lorentz transmission electron microscopy (LTEM) and the Lorentz scanning transmission electron microscopy (LSTEM) in thin film cross-section and single crystal specimens. However, direct imaging of the magnetic texture in plan-view samples of thin (< 50 nm) films has proved to be challenging due to the complex "background" contrast associated with the microstructure and defects, as well as contributions from bending of the specimens. Using a mechanically polished 35 nm plan-view FeGe thin film, we have explored three methods to extract magnetic contrast from the complex background contrast observed; (1) background subtraction in defocused LTEM images, (2) frequency filtered CoM-DPC reconstructed from LSTEM datasets and 3) registration of 4D-STEM datasets acquired at different tilt angles. Using these methods, we have successfully implemented real space imaging of both the helical phase and skyrmion phase. The ability to understand nanoscale magnetic behavior from plan-view thin films is a fundamental step towards development of highly integrated spin electronics.

Dislocation-Driven Relaxation Processes at the Conical to Helical Phase Transition in FeGe.

The formation of topological spin textures at the nanoscale has a significant impact on the long-range order and dynamical response of magnetic materials. We study the relaxation mechanisms at the conical-to-helical phase transition in the chiral magnet FeGe. By combining macroscopic ac susceptibility measurement, surface-sensitive magnetic force microscopy, and micromagnetic simulations, we demonstrate how the motion of magnetic topological defects, here edge dislocations, impacts the local formation of a stable helimagnetic spin structure. Although the simulations show that the edge dislocations can move with a velocity up to 100 m/s through the helimagnetic background, their dynamics are observed to disturb the magnetic order on the time scale of minutes due to randomly distributed pinning sites. The results corroborate the substantial impact of dislocation motions on the nanoscale spin structure in chiral magnets, revealing previously hidden effects on the formation of helimagnetic domains and domain walls.

Determining Surface Terminations and Chirality of Noncentrosymmetric FeGe Thin Films via Scanning Tunneling Microscopy.

Scanning tunneling microscopy was used to study the surfaces of 20-100 nm thick FeGe films grown by molecular beam epitaxy. An average surface lattice constant of ∼6.8 Å, in agreement with the bulk value, was observed via scanning tunneling microscopy, low energy electron diffraction, and reflection high energy electron diffraction. Each of the four possible chemical terminations in the FeGe films were identified by comparing atomic-resolution images, showing distinct contrast with simulations from density functional theory calculations. A detailed study of the atomic layering order and registry across step edges allows us to uniquely determine the grain orientation and chirality in these noncentrosymmetric films.