Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.


Details of sample synthesis and preparation
The FeGe single crystals were grown by the chemical vapour transport method with iodine as the transport agent. 1 Magnetometry measurements were performed to characterise the bulk single crystal FeGe sample. The Curie temperature of the sample T C , defined as the S1 point of greatest slope in a plot of the magnetisation M versus temperature, was found to be 280.5 K. Figure S1 illustrates the stages used to prepare the device-like structures (as described in Materials and Methods). The dumbbell structures were prepared so that the central constriction was the width of a single skyrmion. Surrounding the device-like structures a dark band is visible at the edges between the FeGe structures and Pt coating that is likely to be a damaged surface layer created by the implantation of Ga + ions during sample preparation. This is approximately 15 nm in depth at each surface, estimated by measuring the thickness of the dark bands. The central constrictions were measured to be 75, 77 and 64 ± 3 nm in the three device-like shapes, comparable to the helical length of 70 nm in FeGe. The device-like structures were created to limit any skyrmion lattice that does form to 2 − 3 skyrmions by 4 − 5 skyrmions. Two simple blocks were also prepared with similar dimensions to allow a comparison of skyrmion behaviour in a less complex structure under the same experimental conditions. The plane of the sample lies close to (011) with the long axis of the sample corresponding to [111] and the short axis corresponding to [211]. The thickness of the device-like structures was determined using energy filtered imaging to be 73 ± 6 nm. 2

Electron Microscopy
The thinned cross-section of FeGe device-like structures was mounted in a Gatan liquid nitrogen cooled model 636 transmission electron microscope (TEM) holder and examined in an FEI Titan 3 TEM equipped with a Lorentz lens. The specimen was initially mounted in a magnetic field-free condition and a calibrated external magnetic field was applied out of the plane of the specimen using the objective lens of the TEM. To observe magnetic contrast in the TEM, a phase imaging technique is required, and these are only sensitive to the inplane components of the magnetic flux density arising from local magnetisation within the S2 specimen. Bloch skyrmions appear as bright or dark areas of contrast when imaged away from the focus depending on defocus and orientation of applied magnetic field. The helical phase can be characterised using defocused imaging, but the field polarised and cone phases cannot be distinguished from each other as there is no net in-plane component of magnetic field for either when an out-of-plane magnetic field is applied. Lorentz TEM (LTEM) image series were acquired at 90 K and 263 K with an applied external magnetic field varying between 0 mT and ±310 mT. Hysteresis experiments were conducted at 90 K, 219 K and 245 K and were imaged using LTEM. Images were energy filtered using a 10 eV Gatan Tridiem imaging filter and were acquired on a 2048 × 2048 pixel CCD. At each change of magnetic field within the hysteresis loop, the LTEM image was refocused before adjusting the defocus to 200 µm for each image acquired. The changes in applied magnetic field also give rise to subtle tilts of the electron beam causing diffraction contrast to move across the image so that some of the shapes appear dark in some of the images.

FIB damage of specimen surfaces
Focused ion beam milling is inherently damaging to the specimen surfaces, leaving both an amorphous layer and an ion implanted layer deeper into the specimen. 3 The specimen preparation method for these small device-like structures allows us to examine some of the surface layers in cross-section and explore the impact of these surface layers on the magnetic spin structures that are experimentally observed. Bright-field TEM images reveal a dark band at the surface of the FeGe nanostructures where surface modification has occurred due to sample preparation in the FIB. Intensity line traces were taken across each edge as shown in Figure S2(a) and (b) and the surface layer thickness was measured from the observed reduction in intensity as shown in Figure S2 6 has revealed that only the outermost 4 nm of the surface is amorphous, and that a strong signal from implanted gallium is observed using STEM-EDX to a depth of at least 17 nm into the surface, which would correspond to the observed thickness of the dark surface ('damage') layers observed in these specimens, particularly on the surfaces with lowest damage (3 and 6). When considering the magnetic properties at the surfaces of the specimen, we can observe that the helical phase magnetic contrast is observed to continue into the dark layer specimen. LTEM does not allow a detailed analysis of the magnetic contrast very close to the surfaces because overlapping contrast is observed at the edges from mean inner potential differences between the FeGe and Pt layer.

Mask generation for Micromagnetic Simulations
In order to construct the specimen geometry in the simulations, we start from a standard bright-field LTEM image, taken close to the image plane where little magnetic contrast is observed which allows the boundary between the Pt and FeGe to be clearly defined (see Figure S9(a)). A gaussian blur is used ( Figure S9(b)) before an adaptive local histogram equalisation is applied to each image ( Figure S9(c)), and intensity thresholding is then used to resolve a clear boundary ( Figure S9(d) and (e)) which can be used to construct a mask defining the simulation geometry, using the software package scikit-image 7 (Figure S9(f)).
By pipelining the processing of the experimental images in this way, we ensure that there is      Figure S5: Unprocessed LTEM images of the device-like structures at 245 K under an applied external magnetic field cycled from 0 mT to −313 mT and then to +310 mT before returning to 0 mT. S10 Figure S6: High-pass filtered LTEM images of the device-like structures at 90 K under an applied external magnetic field cycled from 0 mT to −313 mT and then to +310 mT before returning to 0 mT. S11 Figure S7: High-pass filtered LTEM images of the device-like structures at 219 K under an applied external magnetic field cycled from 0 mT to −313 mT and then to +310 mT before returning to 0 mT. S12 Figure S8: High-pass filtered LTEM images of the device-like structures at 245 K under an applied external magnetic field cycled from 0 mT to −313 mT and then to +310 mT before returning to 0 mT. Figure S9: Mask generation process for simulation geometry (a) Bright field TEM image of block 1, (b) a gaussian blur is applied to smooth any sharp variations in intensity, (c) the image is limited in range to improve the accuracy of contour generation; the contours are shown in (d). (e) a single contour is selected to generate the mask (f) used for simulations. S14