# Néel-type skyrmion in WTe2/Fe3GeTe2 van der Waals heterostructure

Jul 31, 2020

### Thickness characterization of WTe2 and FGT

Before we show the proximity effect of the heterostructures, we first determine the properties of WTe2 and FGT separately. The 1T’ crystal structure of WTe2 (Fig. 1a) has been confirmed in the previous work31. Atomic force microscopy was adopted to measure the thickness of this material as shown in Fig. 1b, c. It shows that the single-layer (1L) WTe2 on the SiO2/Si substrate has a height of about 1.1 nm. The transport data of 1L WTe2 are given in Supplementary Note 1, Supplementary Fig. 1. Bulk FGT consists of weakly bonded Fe3Ge layers that alternate with two Te layers with a space group P63 mmc as shown in Fig. 1a (bottom). For FGT, the 1L thickness is 0.8 nm11. This thickness is used to determine the number of layers for FGT as shown in Fig. 1d, e. As shown in Fig. 1f–i, the Curie temperature decreases from ~200 to ~100 K when the thickness of FGT goes down from 60L to 4L. The perpendicular magnetic anisotropy is well preserved for FGT with thickness down to seven layers. For the thin FGT samples with seven layers and four layers, hexagonal boron nitride (h-BN) thin flakes are used for protection from effects of the ambient conditions.

### Topological Hall effect in WTe2/FGT heterostructure

WTe2 has one of the largest spin–orbit coupling among the transition metal dichalcogenides32. At the interface, the terminated atoms in WTe2 are the same as those in FGT: two layers of heavy Te atoms are coupled through the 5p orbital, where the strong spin–orbit interaction from WTe2 could play a significant role in reorganizing the spin polarizations in FGT. Such effect can be captured by transport measurements in thin films, and the transport data of h-BN/WTe2/FGT heterostructures are shown in Fig. 2 with h-BN serves as the protection layer (Supplementary Note 2). For the h-BN/1L WTe2/4L FGT sample (sample A) as shown in Fig. 2a, b, the longitudinal resistivity increases when temperature goes down from room temperature (Supplementary Note 3, Supplementary Fig. 2). The Curie temperature for this device is below 150 K, which is close to that of a 4L FGT on SiO2/Si sample. Topological Hall is a spin-chirality-driven Hall effect, i.e., the spin chirality induces a finite contribution to the Hall response. In our case, dips and peaks near the magnetic phase transition edge, which signal the presence of the topological Hall effect, show up below 100 K as shown in Fig. 2c. For example, at 50 K there is a dip or peak at a field strength  ~±975 Oe as indicated by the dashed lines (Supplementary Note 4, Supplementary Figs. 3 and 4). Different from this sample where the interfacial coupling has been reflected through the topological Hall effect, a 2L WTe2/30L FGT heterostructure (sample B) shows the perpendicular magnetic anisotropy is well preserved in FGT when the temperature is below 180 K in the Fig. 2e, indicated by the square loop of the Hall resistivity. However, within an intermediate temperature range (180–200 K), the hysteresis loops differ in having transitions in steps. For example, at 190 K, the Hall resistivity suddenly jumps from the low saturation value to an intermediate level and then changes linearly. Finally, it saturates to the high saturation value at a relatively high positive field. The reversed trace does the opposite as expected. A possible explanation for this behavior is the formation of labyrinthine domain structures in FGT which results in multi domains12, and this will be confirmed later. Compared to the sample A as shown in Fig. 2a–c, the sample B as shown in Fig. 2d, e with a much thicker FGT flakes measures the averaged transport signal which may lead to the smearing out of the topological Hall signal at the interface, which will be discussed later. In the following part, we utilize L-TEM to directly investigate the domain structures in 2L WTe2/40L FGT and 2L WTe2/30L FGT heterostructures, the latter of which is similar to sample B and we also confirm a large DMI at the interface.

### Experimental observation of Néel-type skyrmions with L-TEM

Lorentz microscopy allows us to obtain direct magnetic domain structural images of thin magnetic films based on the fact that electrons experience a Lorentz force when traveling in a magnetic field. Compared to other techniques33, L-TEM, as one of the most direct methods to observe magnetic domain structures, domain walls and skyrmions, affords the advantage of a spatial resolution below 5 nm. The contrast formed in L-TEM is traditionally explained from the deflection of electrons due to the Lorentz force. For the Néel-type skyrmions, no contrast could be observed in the L-TEM image if the sample is not tilted because the intensity change caused by the Lorenz force at any point in the Néel-type skyrmion is compensated or canceled. After tilting the sample, dark-bright contrast could be formed in the L-TEM image34 due to the contributions from both the outside and the core of the Néel-type skyrmion as schematically shown in Fig. 3a. The skyrmion lattice was observed in a 2L WTe2/40L FGT heterostructure at 180 K for the rotating angle α = 30° (Fig. 3b) in de-focused and focused images. From under focus to over focus, the skyrmions transform from white on the top and dark in the bottom to the opposite contrasts. These are consistent with the Néel-type nature of the skyrmions (Supplementary Note 5, Supplementary Fig. 5). One hexagonal skyrmion lattice is indicated with the dashed lines. The field dependence of a single skyrmion in the WTe2/30L FGT (similar to sample B for the transport measurements) is shown in Fig. 3c when a field changes from 540 to 660 Oe at 94 K. The Néel-type skyrmion is well developed at a field of 540 and 600 Oe along the z direction, having dark on the top side and bright in the bottom. The size is estimated to be  ~150 nm (more information about the skyrmion size of  ~150 nm at 100 K and  ~80 nm at 197 K can be found in Supplementary Note 6, Supplementary Fig. 6). However, we failed to resolve any domain structure in 1L WTe2/4L FGT samples (similar to sample A) using L-TEM. This may be due to the small sheet magnetization in the thin film, which requires higher beam exposure to resolve; however, this already exceeds the tolerance of our samples, beyond which, unrecoverable damages occur. L-TEM measurements of WTe2/FGT heterostructures with varied FGT thicknesses suggest the DMI only penetrates to a finite depth of FGT (Supplementary Note 7, Supplementary Fig. 7). To further understand how this interfacial DMI penetrates through the FGT layers, we have carried out simulations as shown in Fig. 3d. For FGT away from the interface, it enters the ferromagnetic phase as shown in the vertical profile in the yz plane.

### Experimental evidence of WTe2 induced DMI

The strong perpendicular magnetic anisotropy favors out-of-plane magnetization, which makes the spin polarization in the FGT form the domain in the up or down directions. Figure 4b shows the magnetic domain images for the 30L FGT thin flake without WTe2 (see Fig. 4a). The film exhibits labyrinth domains at 94 K and 0 Oe. When the in-plane field is tuned to the opposite direction, the contrast of domain edge completely switches the sign as shown in the cases of a tilt angle of α = −20° and α = 21°.

The formation and structure of domain walls are usually a result of the interplay between exchange interaction, magnetic anisotropy and dipolar interaction. Reducing the thickness of the FGT flakes decreases the dipolar interaction, thus, perpendicular magnetic anisotropy leads to a stabilized single domain14. Meanwhile, the exchange interaction term here includes DMI, which is a noncollinear exchange interaction that favors a chirally rotating magnetic structure of a specific rotational direction. By comparing the WTe2/FGT and the nearby FGT regions, the magnetic domain difference shows the interfacial coupling contributes to a strong DMI.

For the WTe2/FGT heterostructure, there is no contrast when α = 0° as shown in Fig. 4c, which is an evidence for the Néel-type domains. When α ≠ 0°, we have observed this well aligned and stripe-like domains with a domain width w = 290 nm at 0 T, which is sharply different from the domain structure of the FGT flake shown in Fig. 4b, having a much smaller domain width. In this case, the DMI is largely enhanced28 for this heterostructure from the interfacial Te atoms coupling. A phenomenological model defines the dependence of the domain width w on the domain wall energy δW by35

$$w=beta frac{4pi {delta }_{{rm{W}}}}{{M}_{{rm{s}}}^{2}},$$

(1)

here the domain wall energy δW is related to exchange stiffness A, effective anisotropy constant Keff, and DMI constant D by ({delta }_{{rm{W}}}=4sqrt{A,{K}_{{rm{eff}}}}-pi | D|)36. β is a phenomenological fitting parameter and taken to be 0.31 for FGT35. A domain width of 290 nm leads to a domain wall energy δw = 0.77 mJ m−2 including the DMI term (Supplementary Note 8, Supplementary Fig. 8). In the case of pristine FGT without considering DMI, the domain wall energy is simply expressed as 4(sqrt{A,{K}_{{rm{eff}}}}). Then by comparing these two domain wall energies with and without the DMI contribution, we obtain a DMI energy D = 1.0 mJ m−2 in our system, which is comparable to the previous value in heavy metal/ferromagnet thin film systems27 (Supplementary Note 9, Supplementary Fig. 9). One can compare D to the critical value Dc, which is required to stabilize chiral Néel domain wall27,37

$$| {D}_{{rm{c}}}| =frac{4}{pi }sqrt{frac{A}{{K}_{{rm{eff}}}}}{K}_{{rm{d}}},$$

(2)

where when the magnetostatic or stray field energy constant Kd = 2(pi {M}_{{rm{s}}}^{2}) is large, the critical value for the Néel type domain is larger. Thus, Dc is estimated to be ~0.1 mJ m−2, so that D > Dc and chiral Néel textures are expected. Compared to the transport measurements which take the averaged transport signal of the few nanometers of FGT coupled to the WTe2 near the interface, and other FGT layers away from the interface, L-TEM helps confirm the DMI from the Néel-type skyrmion captured at the WTe2/FGT interface since the uncoupled FGT layers in a single uniform domain contribute no contrast (Supplementary Note 10, Supplementary Figs. 10 and 11).