Introduction

Two-dimensional van der Waals (2D vdW) materials with long-range ferromagnetic orders presenting diverse novel phenomena1,2,3,4,5 show promise for fundamental physics and device applications6,7. Among these materials, Fe3GeTe2 (FGT) has drawn particular attention due to its strong perpendicular magnetic anisotropy and long-range ferromagnetic order ranging from bulk crystals down to monolayers8,9,10,11. More importantly, the Curie temperature (TC) of FGT atomic layers is controllable via electrostatic gating or patterned microstructures12,13. In conjunction with these novel properties, magnetic domain structures have been recently investigated in 2D vdW FGT. Complex magnetic domain structures, including labyrinthine domain structures10, bubble domains14, double-walled domains15, and spike-like domains16, have been observed via magnetic force microscopy. Recent investigations of FGT via Lorentz transmission electron microscopy (LTEM) with the application of a magnetic field have led to the discovery of skyrmions. The magnetic field and temperature play a crucial role in skyrmion generation and stability. Rapid cooling below TC with a proper magnetic field has led to field-free skyrmions being observed not only in non-centrosymmetric magnet FeGe17 and MnSi18 but also in centrosymmetric magnet MnNiGa19,20. Unfortunately, such thermal manipulations of skyrmions in 2D vdW magnets remain elusive. Meanwhile, these field-free skyrmions provide an easy way to identify the spin configurations of skyrmions regardless of the application of a magnetic field.

Very recently, Néel-type skyrmions supported by interfacial Dzyaloshinskii–Moriya interactions were discovered in FGT heterostructures21,22. Simultaneously, Bloch-type skyrmions stabilized by magnetic dipole interactions have also been reported in FGT nanosheets23. As theoretically predicted, Bloch-type magnetic twists usually emerge in centrosymmetric magnets with competition between dipole interactions and uniaxial magnetic anisotropy, as reported in Mn-Ni-Ga24, Ni2MnGa25, Fe3Sn226, and 2D vdW Cr2Ge2Te627. In centrosymmetric FGT with a space group of P63/mmc, Néel-type skyrmions in previous reports seem to be a subject of controversy. Thus, direct identification of the spin configurations of skyrmions in 2D vdW FGT deserves further investigation.

In this work, the generation and sustainability of Bloch-type skyrmions in a zero magnetic field over a wide temperature range in 2D vdW FGT were directly demonstrated via LTEM. By tuning the value of the external magnetic field, the highest-density hexagonal skyrmion lattice emerges after reducing the magnetic field to zero. Micromagnetic simulation reveals that compared with stripe domains, the highest-density skyrmion lattice has stronger total energy, indicating that it is in a metastable state. In addition, we found that the field-free Bloch-type skyrmions in FGT can also exhibit no contrast when the tilt angle is zero but present a reversed magnetic contrast at a high tilt angle. On the basis of our experiments, we discuss the possible mechanisms for this disappearing magnetic contrast.

Materials and methods

Sample synthesis

High-quality Fe3GeTe2 single crystals were grown using the Te self-flux method from a mixture of pure elements Fe (99.99%), Ge (99.9999%), and Te (99.995%) with a composition of Fe2GeTe428. The mixture was then sealed in an evacuated quartz tube and heated to 1000 °C. The melt was held at 1000 °C for 3 h and then cooled slowly to 680 °C at a rate of 1 °C/h, and the excess Te flux was removed by spinning the tube. The typical size of the single crystals was ~5 × 5 × 0.2 mm, with a cleavable layer in the ab plane. The composition of the single-crystal FGT was further checked by scanning energy dispersive X-ray spectroscopy, confirming that the atomic ratio was ~3:1:2 (Fig. S1).

Lorentz TEM measurement

The nanosheets for Lorentz TEM observation were fabricated from a single crystal by using a focused iron beam. The magnetic domain was directly observed by using a Tecnai F20 in Lorentz TEM mode and a JEOL 2100F Lorentz TEM, both equipped with liquid nitrogen and low-temperature holders (~90 K) to study the temperature dependence of the magnetic textures. The objective lens was turned off when the sample holder was inserted, and the perpendicular magnetic field was induced to the nanosheet by increasing the objective lens in a small increment. For tilting experiments, the crystalline orientation of the nanosheets was first checked by selected-area electron diffraction (SAED) to ensure compliance along the [001] direction. After marking the value of this angle, a series of tilting experiments were performed. In addition, the specific field cooling (FC) manipulation is shown as follows. First, the sample was heated higher than the Curie temperature TC ~ 150 K. Second, the perpendicular magnetic field was applied by increasing the objective lens current gradually in a very small increment. Third, the temperature of the sample was cooled gradually from 150 K to 93 K. Finally, at 93 K, the small perpendicular magnetic field was turned off.

Micromagnetic simulations

Micromagnetic simulation was performed via the Object Oriented MicroMagnetic Framework (OOMMF) code based on the LLG function29. The slab was 2000 × 2000 × 100 nm with a rectangular mesh of size 5 × 5 × 5 nm. The saturation magnetization was chosen as Ms = 2.23 × 105 A/m at 100 K, and the magnetic anisotropy constant Ku was 0.5 × 105 J/m3. To make analytic progress, we considered an initially random spin state as the paramagnetic state. A field cooling procedure was performed as follows. Initially, the slab was set as a random state, and an external field was applied along the z-axis. After that, the perpendicular field was reduced to zero, and the slab was relaxed to an equilibrium state with each step of 30 ns.

Results

The 2D vdW FGT is a ferromagnet with a strong uniaxial magnetic anisotropy and an easy axis along the c-axis, while it exhibits absolute isotropic characteristics in the ab plane30. Owing to competition between the uniaxial magnetic anisotropy and magnetic dipole interaction, stripe domains separated by Bloch walls spontaneously stabilized without an external magnetic field, as schematically shown in Fig. 1a. In Fig. 1b, c, we show the magnetic domain at 93 K along two orthogonal imaging directions. The corresponding crystalline orientation and crystal structure were examined by using SAED and scanning transmission electron microscopy with high-angle annular dark-field atomic resolution, which coincides with previous reports23,31. In the case of the bc plane, the magnetic contrast induced by the spins inside the domain formed alternating dark or bright stripes, which were further identified by the line profile of magnetic contrast. For magnetic domains observed in the ab plane, the flake was tilted to reduce the diffraction contrast and induce magnetic contrast, which is similar to an approach reported in the previous work23. Clearly, the LTEM contrast is only generated by the domain wall, resulting in bright–dark or dark–bright stripes, as verified by the line profile shown in Fig. 1c. The different magnetic domains in the two orthogonal imaging planes demonstrate that the strong magnetocrystalline anisotropy of FGT persists despite additional shape anisotropy terms arising in the cross-section TEM sample. It is noteworthy that with decreasing width of the domain wall, the magnetic contrast in the ab plane gradually vanished, which will be discussed later.

Fig. 1: Magnetic domains of 2D vdW FGT due to uniaxial anisotropy.
figure 1

a Schematics of magnetic domains and the corresponding simulated LTEM images projected on the (100) and (001) imaging planes. Stripe domains with antiparallel spins are separated by Bloch walls due to uniaxial anisotropy. b, c Magnetic stripes observed along the [100] direction and [001] direction, respectively. The flake rotates slightly to reduce the diffraction effect. A line profile across the stripe domains is consistent with the imaging plane projection in a. The corresponding SAED and STEM HAADF images are shown on the right side.

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The evolution of the magnetic stripe as a function of temperature and magnetic field in the bc plane was studied in the Supporting Information (Fig. S2); here, we focus on the magnetic domain in the ab plane. The flake along the [001] direction was tilted to reduce the diffraction contrast and induce magnetic contrast. Figure 2a–c shows the magnetic domain as a function of temperature observed via LTEM under a zero field. As the temperature decreases to 147 K, slightly below Tc ~ 150 K, magnetic stripes emerge. Upon further cooling, the stripes become wider and more distinctive (Fig. S3). The period of the domain as a function of temperature is shown in Fig. 2h. With the application of an external magnetic field, the stripes gradually transformed into bubbles (details seen in Supporting Information, Fig. S4). In Fig. 2d–f, we show the temperature-dependent LTEM images of bubbles at temperatures ranging from 147 K to 93 K under their corresponding critical magnetic field. Clearly, the critical magnetic field increases with decreasing temperature (Fig. S5). Simultaneously, the size of bubbles represents a similar variation, as shown in Fig. 2i. The magnetic domain texture is further analyzed with magnetic properties in FGT, as shown in Fig. 2g. The a.c. susceptibility measurements in the H//c and H//ab directions were performed to identify the magnetic transition. For the 150 K transition, the peak in each direction appears, which is related to the Curie temperature. In contrast, at the 118 K transition, the peak only appears in the black curve (in the ab plane) but remains almost absent in the H//c direction. Interestingly, the period of the magnetic stripe exactly represents a significant change above 118 K and gradually remains constant at lower temperatures. The varied periodicity may result from the pinned magnetic domain wall32 or a spin-flop transition14, which needs further investigation.

Fig. 2: Temperature dependence of the magnetic domain.
figure 2

a–c Representative underfocused LTEM images of the stripe domain when the temperature decreases from 150 K to 90 K at zero external magnetic field. d–f Magnetic bubbles obtained at their corresponding temperature in a–c with the critical magnetic field. g The imaginary part of the temperature-dependent a.c. susceptibility under zero magnetic field. Oscillate a.c. field (4 Oe) is applied in the H//ab and H//c directions. h Temperature dependence of domain periodicity obtained from a to c. i The corresponding sizes and critical magnetic field of magnetic bubbles calculated from d to f.

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To obtain a field-free skyrmion lattice with the highest density, we tuned the magnitude of the cooling field (HCF), as shown in Fig. 3a–c. The detailed cooling procedure and specific LTEM images are shown in the Methods and Fig. S6. When the magnetic field is lower than 100 Oe or higher than 700 Oe, a stripe emerges. With the magnetic field increasing from 100 Oe to 700 Oe, the size of skyrmions first decreases and then increases (Fig. 3g). Meanwhile, the density of skyrmions represents an inverse variation reaching a maximum value at HCF ~ 400 Oe (Fig. 3b). A stronger magnetic field will force nucleation sites to agglomerate, thereby reducing skyrmion density and enlarging skyrmion size. Clearly, the skyrmion density is apparently enhanced via FC manipulation compared with the random distribution induced solely by the magnetic field. In addition, the spin configuration of field-free skyrmions is further analyzed, which represents dark to bright or bright to dark rings in the underfocused images identified with Bloch-type domain walls separating the spin-up and spin-down domains23.

Fig. 3: Variation in the magnetic state at room temperature at different magnetic fields after FC manipulation.
figure 3

a–c Representative underfocused LTEM images of skyrmion bubbles taken at 93 K after a field cooling manipulation. Micromagnetic simulations of the domain field cooling process as a function of magnetic fields of 100 Oe (d), 400 Oe (e), and 800 Oe (f). g Magnetic field-dependent mean size and density of skyrmion bubbles obtained from LTEM data. h The calculated mean size and density of skyrmions under different magnetic fields. i Field dependence of the energy terms in the simulation after a field cooling process.

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To understand the mechanism stabilizing the skyrmion lattice after field cooling, we performed micromagnetic simulation via the OOMMF code. The input magnetic parameters were used as reported in previous work23. In this approach, we take a random spin configuration as the paramagnetic state. Figure 3d–f shows the representative remanent state after the field cooling manipulation. The variation in the size and density of the skyrmions is the same as that observed in the LTEM experiments, as shown in Fig. 3h. At HCF = 400 Oe, the skyrmions with a homogeneous circular shape are closely packed, forming hexagonal lattice skyrmions. As the magnetic field varies, individual skyrmions stretch to deform the lattice arrangement. The corresponding formation of these spin configurations in centrosymmetric magnets should originate from the competition of the exchange energy, the magnetic anisotropy energy, and the demagnetizing energy, as shown in Fig. 3i. As the external magnetic field increases, the strength of the dipole interaction exhibits a reversal variation compared with the other two interactions, reaching a minimum value at HCF = 400 Oe. Owing to the high density of skyrmions, an increasing number of domain walls reduces the demagnetizing energy; however, it simultaneously gives rise to the exchange energy. Meanwhile, various magnetic moments deviate from the easy axis, resulting in an increasing uniaxial magnetocrystalline anisotropy. The magnetic field-dependent total energy is obtained; obviously, it represents a maximum value with the highest density of skyrmions, which indicates that, compared with the stripe domain, the thermal-equilibrium skyrmion lattice is in a metastable state.

Figure 4 represents the externally applied temperature (T)–magnetic field (H) phase diagram with the ZFC process and FC process measured by systematic Lorentz TEM observations at various T and B. The formation and annihilation magnetic field for skyrmions are plotted by white dashed lines. As shown in Fig. 4a, the phase diagram for skyrmions is limited. The magnetic field to generate skyrmions increases with decreasing temperature. After FC manipulation, the high-density yellow-colored area with zero-field skyrmions covers the entire temperature range toward TC, as shown in Fig. 4b.

Fig. 4: Experimental phase map of the magnetic domain as a function of magnetic field and temperature based on the LTEM observation.
figure 4

a The flake was cooled to a specific temperature, and then an external magnetic field was applied. b An external magnetic field was applied and then slowly cooled down. The points represent different magnetic states: hollow triangle - stripe, dot - skyrmion and hollow rectangle - ferromagnetic state.

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On the basis of field-free skyrmions, we further investigate the spin configuration observed in the FGT flake at various oblique angles, as shown in Fig. 5. The parameter α is defined as the angle between the electron beam direction and the [001] direction of the flake. Based on the direct LTEM observation, at a zero-degree tilt, no magnetic contrast appeared in the defocused LTEM image. With increasing oblique angles, the magnetic contrast gradually appeared. At α = 7°, the sharp contrast of dark to bright or bright to dark rings in the images identified with Bloch domain walls, which is further demonstrated by the line scan positions for contrast profiles of a single skyrmion with two peaks clearly observed in the bottom of Fig. 5b. At a higher tilting angle ~±20°, the skyrmion represents half-black/half-white magnetic contrast and a reversal contrast with reversing tilting direction. This can be easily distinguished from the contrast profile. Clearly, only one peak was observed at a high tilted angle (±20°), and the intensity of the profile represents mirror symmetry with a reversing tilting angle. The same experiment was performed on the magnetic stripe domain, as shown in Fig. S7.

Fig. 5: Field-free skyrmions under different tilt angles.
figure 5

Underfocused LTEM images of field-free skyrmions taken at a defocus value of ~1 mm with tilting angle of 19° (a), 7° (b), 0° (c) and −20° (d) with respect to [001] direction. Skyrmion lattice was obtained after a field cooling with the magnetic field applied at 0°. A single skyrmions at oblique angles and corresponding experimentally measured magnetic contrast profile are shown in the bottom row.

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Discussion

We now discuss the possibility that leads to the varied observations of magnetic contrast in the FGT thin plate. LTEM is sensitive to the in-plane magnetic component, which further induces the phase shift of the electron beam. Note that magnetic contrast was not observed at the zero tilt because of the symmetric deflection of magnetic texture, such as in a Néel type skyrmion33,34, which can result from a small magnetization35 or a narrow domain wall36 of a Bloch-type twist. Based on the above observation, we exclude the existence of a Néel-type magnetic domain in the FGT flake. Through magnetization curve measurements, the saturation magnetization of FGT is calculated to be 0.275 T (100 K), which is approximately 3.6 times smaller than that in Mn-Ni-Ga (300 K). Such small magnetization makes it difficult to detect the magnetic contrast.

Another possible reason can be induced from a very thin domain wall, too narrow to be detected by LTEM, which has been reported in a uniaxial centrosymmetric crystal La1.2Sr1.8(Mn1 - yRuy)2O7 with Bloch-type bubbles36. For a 2D vdW FGT, as shown in Fig. 1a, the magnetic contrast in the ab plane is only generated by the domain wall. With a large magnetic anisotropy ratio Q = Ku/Kd = 16.4 ≫ 1 (Ku is defined as the uniaxial anisotropy coefficient, while Kd is the stray field energy coefficient), the thickness of the domain wall was estimated as 2.5 nm16. Accompanied by the crystalline diffraction contrast along the [001] direction, it becomes more difficult to observe such a thin magnetic domain. However, when the flake was slightly tilted to reduce diffraction contrast, the magnetization component of the domain wall perpendicular to the beam path caused Lorentz deflection, leading to a visible magnetic domain texture. However, a large defocus value (~1 mm) was still used to make the magnetic contrast distinguishable due to a small magnetization. With a higher tilt angle (α = ±20°) (Fig. 5a, d), the in-plane components of the core and peripheral out-of-plane spins mainly contribute to inducing magnetic contrast. When we reverse the tilting direction, the in-plane components of spins also reverse their direction, thus resulting in an opposite magnetic contrast. Notably, our previous observation of the magnetic domain in FGT was also performed at a small tilt angle, which was not mentioned in the previous work. To date, tilting samples via LTEM is considered evidence for the identification of Bloch- or Néel-type magnetic structures. For the Néel-type magnetic structure, the LTEM images represent no magnetic contrast at zero tilting. A similar phenomenon may exist in Bloch-type magnetic twisting inside a thin domain wall. In this case, the magnetic texture in FGT deserves further investigation via a three-dimensional (3D) electron tomography technique or LTEM observation assisted by an in-plane magnetic field37.

Conclusions

In summary, a controllable cooling field-induced field-free skyrmion was investigated in 2D vdW FGT. An appropriate cooling field exists to generate the highest-density skyrmions, which indicates that the magnetic field plays a crucial role in the generation of skyrmions. Theoretical simulations have demonstrated that the field-free skyrmion lattice is in a metastable state. We also examined the stability of the skyrmion lattice in FGT over a wide range of temperatures and magnetic fields, including its zero-field manifestation. On the other hand, we found that field-free Bloch-type skyrmions in FGT can also represent no contrast when the tilt angle is zero, which results from the thin domain wall. Our results can support a further understanding of the spin configuration of skyrmions in 2D vdW materials.