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.

Before taking the LTEM image shown in a, the sample has been temporarily tilted to provide an in-plane magnetic field that helps stabilizing the sparse array of antiskyrmions. In b -f the magnetic field remains along the pole direction. It is gradually decreased, as indicated. The scale bar corresponds to 300 nm. directions. In all cases, the texture deforms to a triangular shape but after returning to a perpendicular field, the configurations turn back to the initial elliptical-skyrmion phase shown in e. The scale bar corresponds to 100 nm.

Supplementary Note 1. Preparation of a thin lamella for the Lorentz TEM investigation
In Supplementary Figure 1 Figure 1a). Then we remove a few micrometers from the outside region of Pt using ion beams with a higher current (Supplementary Figure 1b). Thereafter we start to polish both sides of the lamella to remove the damaged portions of the surface using the ion beam at lower currents. The final polishing has been conducted at an energy of 2 keV. At this point the lamella has a thickness of nearly 3 m.
In the next step, in a tilted condition (52° degree with respect to the electron column), we deposited Pt of a few nanometers thickness on both sides of the thicker lamella using an electron beam (Supplementary Figure 1c). The steps of smooth polishing and Pt deposition are required here, because when we lift out the lamella, our lamella must not be damaged by the ion beam (during the following cutting process of the lamella for the process of lifting out, its surface is perpendicular to ion beam). Supplementary Figure 1d shows the deposition of Pt on both sides of the lamella.
To lift out the lamella, first we cut it in an 'L' shape so that one side of the lamella is attached to the bulk sample and the other two sides will be cut by the ion beam. We then attach a nanomanipulator to the sample by depositing Pt (Supplementary Figure 1e) and cut out the remaining part that is attached to the bulk sample. We attach our thicker lamella to a four-arm grid, which is seated perpendicularly to the electron column (Supplementary Figure 1f). The lamella is attached to any of the four arms and a few nanometers of Pt are deposited on the junction between the grid and the sample (Supplementary Figure 1g).
To separate out the lamella from the attached nanomanipulator, we cut the end portion of it with an ion beam (Supplementary Figure 1h). Then we vent out the whole FIB stem and again place the four-arm grid parallel to electron column. After this we tilted the sample by 52°. More Pt is deposited on the surface of the lamella to protect the lamella from the ion beam. Then we thin down both sides of the lamella by cleaning the cross section pattern with lower currents to a few nanometers. The final polishing is done at an energy of 2 keV to remove surface amorphization.
The final film thickness is ~170nm (Supplementary Figure 1i). The surface of the lamella is shown in Supplementary Figure 1j. The left portion has a larger thickness of approximately 400nm and the right part is the portion that has been investigated in the present study.

Supplementary Note 2. Field dependence of a sparse array of individual antiskyrmions
In Fig. 1g-k we have shown that the explained tilted-field protocol allows for the formation of a dense array of antiskyrmions that survives even at zero field. In Supplementary Figure 2 we show how a sparse array of antiskyrmions behaves when the field is decreased without providing an in-plane component. In Supplementary Figure 2f, zero field is reached and the antiskyrmions have disappeared. In contrast to Fig. 1k the system is now in a helical phase.
This shows once again that the observed magnetic textures are metastable and that the type of the stabilized texture strongly depends on the experimental protocol. Two (topologically) distinct spin textures can be metastabilized under the same temperature and magnetic field.

Supplementary Note 3. Observation of elliptical-skyrmions at 150 K and 250 K
In Supplementary Figure 3 we present LTEM images of elliptical-skyrmions at the temperatures 150K and 250K to compliment the presented images for 200K from the main text. We follow the same protocol in each case and observe a similar trend for the metastabilization of ellipticalskyrmions each time.
The only essential difference is that at the highest temperature of 250K the elliptical-skyrmion lattice transitions to the helical state at zero magnetic field (Supplementary Figure 3j), while the lattice is rather periodic at 200K (Fig. 3e of the main text) and 150K (Supplementary Figure   3e). A possible reason is that the strength of the dipole-dipole interaction -the stabilizing mechanism of skyrmionic textures in the present material -is decreased, since the net magnetization decreases with increasing temperature 1 . At the next higher temperature (300K presented in Fig. 1 of the main text) no elliptical-skyrmions have been observed when the presented experimental protocol was used indicating that the DMI has become more important than the dipole-dipole interaction at this temperature.

Supplementary Note 4. Field-tilting effect on elliptical-skyrmions
To investigate if the chirality and the elongation axis of the elliptical-skyrmions is determined by the direction of the in-plane field, we varied the effective tilting direction of the field along different {11} directions (indicated by the angles and in Supplementary Figure 8). Starting from the elliptical-skyrmion lattice shown in Supplementary Figure 8e, tilting along the specified direction and coming back to the pole direction, the magnetic texture always returns to the same configuration. Therefore, in our sample under the presented protocol, the skyrmion chirality is not determined by the in-plane tilting direction.