Introduction

Two-dimensional (2D) layered materials have drawn remarkable scientific and engineering interest due to their marvelous electronic, optical, and thermal properties1,2,3,4, especially their dimensionality-correlated quantum phenomena5,6,7, such as superconductivity, topological properties, and magnetism8,9,10,11,12,13. More specifically, 2D materials are promising candidates for next-generation memory and computation technologies as Moore’s law approaching its limits14. How to precisely tune the properties of 2D materials is a key factor for their applications. In this regard, great efforts focusing on their atomic flat interface and chemical-bond-free van der Waals (vdW) gap, such as intercalating guest atoms and building 2D heterostructures, have been attempted to generate a variety of properties in recent years. For example, many 2D heterostructures15,16,17,18 had been constructed successfully through direct growth or pick-and-lift methods. Various heterostructures have been revealed with unusual properties and are promising for electrical and quantum applications in the future19,20,21. Alternatively, the chemical-bond-free vdW gaps permit the insertion of guest species. Especially, the intercalated 3d-transition metals (TM) could introduce a variety of extraordinary electronic and magnetic properties compared to their parent 2D material22,23,24,25,26,27,28. For example, it is well known that TaS2 turns into ferromagnet when Fe atoms are intercalated29.

However, the ultrathin heteroatoms-intercalated 2D materials are difficult to be obtained. Although chemical vapor deposition (CVD) is known as the most effective method in 2D materials synthesis4, the precursor vapor pressure always varies in the furnace, resulting in phase separation when synthesizing heteroatoms-intercalated 2D materials. Also, mechanical exfoliation is hard to achieve UHI-2DMs because of the strong interlayer interaction30. Despite success demonstrated in experiments to intercalate 2D materials with Fe, Cu, Co and so on31 based on chemical vapor transport (CVT)32,33,34,35 and solvent intercalation30,36, present available methods are difficult to synthesize atomically thin materials with controllable amount of intercalation. Flux-assisted growth (FAG)37, developed by our group, has been proved as a universal method to synthesize complicated 2D materials with multi-elements within the layer. However, whether complicated 2D materials with heteroatoms in the van der Waals gap can be synthesized by this method or not is still unclear.

In this work, we applied the FAG approach37 to synthesize UHI-2DMs with a controllable amount of intercalation. The thermodynamic stability window of UHI-2DMs, revealed by density functional theory (DFT) calculations, is quite narrow, leading to difficulties in CVD synthesis. In contrast, the FAG approach follows flux-crystallization mechanism via which a homogeneous precursor flux with precisely controlled stoichiometry is provided, and the confined space can kinetically suppress vertical direction growth. Therefore, the evolved FAG can synthesize UHI-2DMs with controlled intercalated components. Through this ingenious FAG method, UHI-2DMs with ferromagnetic (FM) or antiferromagnetic (AFM) properties (V1/3NbS2, Cr1/3NbS2, Mn1/3NbS2, Fe1/3NbS2, Co1/3NbS2, Co1/3NbSe2, Fe1/3TaS2) were successfully prepared. Fe1/4TaS2 was also successfully synthesized to demonstrate the capacity of this FAG approach to precisely control the intercalant concentration. The selected area electron diffraction (SAED) indicates that the host 2D materials are homogeneous intercalated by TMs with specific superlattice, as \(\sqrt{3}\)a × \(\sqrt{3}\)a and 2a × 2a superlattice appears for the Fe1/3TaS2 and Fe1/4TaS2 sample, respectively. Cross-sectional scanning transmission electron microscopy (STEM) unambiguously substantiates the intercalated TMs distributed in the vdW gaps of host 2D material. Moreover, the other UHI-2DMs can be synthesized in prospect, such as Ni/Cu/Pd/Ag/Pt intercalated 2D materials24,38,39,40,41,42,43,44,45.

Results and discussion

Controlled growth of UHI-2DMs

As depicted in Fig. 1a and Supplementary Fig. 1, here various UHI-2DMs, successfully synthesized by FAG, are demonstrated. The host 2D materials were composed by metal (Nb and Ta) and chalcogen (S and Se). The pink triangles mark the ultrathin heteroatoms homogeneous intercalations have been realized in FAG method, and the blue triangles indicate other possible guest heteroatoms24,38,39,40,41,42,43,44,45. The FAG synthesis processes are schematically exhibited in Fig. 1b. In brief, synthesis processes are in three steps, mixing, melting, and precipitating (see “Methods” section for more details), following the flux-crystallization mechanism. Because the flux-crystallization growth can provide uniform flux with precisely controlled stoichiometry, the ratio of guest TM atoms can be easily controlled. More importantly, the confined space is conducive to suppress vertical direction growth kinetically. Thus, FAG method has unique advantages in controlling thickness. (Supplementary Table 2).

Fig. 1: Synthesis processes and mechanisms of UHI-2DMs (Ultrathin heteroatoms-intercalated 2D layered materials) on mica through FAG (Flux-assisted growth) approach.
figure 1

a A bridged periodic table of various UHI-2DMs. The metal (Nb and Ta) and chalcogen (S and Se) combined into parent 2D materials. The heteroatoms that have been successfully intercalated into the parent 2D materials by this method are noted by pink triangles. Other possible guest heteroatoms are noted by blue triangles. b Schematic of FAG synthesis processes. Step 1, mix. Step 2, melt. Step 3, precipitate. c The phase diagrams of synthesized FexTaS2, where the stable range of the formation of Fe1/3TaS2 and Fe1/4TaS2 are marked as pink and blue areas, respectively. μS, μFe, and μTa present the chemical potential of S, Fe, and Ta, respectively. d, e the thickness (d) and lateral size (e) distribution of as-synthesized UHI-2DMs. Avg presents the average layer number and lateral size of UHI-2DMs in d and e, respectively.

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As demonstrated in Fig. 1c and Supplementary Fig. 2, the formation energy of FexTaS2 and other by-products are calculated. It is clear that the formation ranges for both Fe1/3TaS2 and Fe1/4TaS2 are very narrow and sensitive to the concentration of each element. Thus, they can only be synthesized when Fe/Ta/S ratio is strictly controlled, which can be easily met by our FAG method. To demonstrate the capability and generality of our FAG approach in synthesizing intercalated 2D material, growth statistics in thickness and lateral size of UHI-2DMs are shown in Fig. 1d, e. Interestingly, the thickness can be controlled to the thinnest (2 L, two host 2D material layers with one intercalated TM layer) and the lateral size can be up to hundreds of micrometers, promising for properties study and device applications. Note that the layer number of UHI-2DMs is defined as the number of the host 2D material. The detailed growth statistics are shown in Supplementary Figs. 3–13.

Precise regulation of interlayer atoms

UHI-2DMs are the ultrathin layered materials with TM arraying ordered in the vdW gap, where the ordering always strongly links with TM concentration (Fig. 2a). To our best knowledge, it is the first time that UHI-2DMs are directly grown with bottom-up assembly. As optical microscopy (OM) images shown in Fig. 2b, these synthesized UHI-2DMs appear as triangular or hexagonal morphology with lateral size up of hundreds of micrometers and sharp edges, indicating their high crystal quality. Especially, the thickness can be downsized to 2 L, which is the thinnest thickness of the intercalated structure30.

Fig. 2: Structural and chemical analysis of typical as-synthesized UHI-2DMs.
figure 2

a Simplified atomic structure of heteroatom-intercalated TaS2 in side view and top view with different heteroatom concentrations. b Optical microscopy images of different UHI-2DMs (V1/3NbS2, Cr1/3NbS2, Mn1/3NbS2, Fe1/3NbS2, Co1/3NbS2, Co1/3NbSe2, Fe1/3TaS2 and Fe1/4TaS2). c Transmission electron microscopy (TEM) image of Fe1/3TaS2 and the corresponding energy dispersive X-ray spectroscopy (EDS) element mapping. d High-resolution X-ray photoelectron spectroscopy (XPS) of intercalated Fe 2p spectra. e, f selected area electron diffraction (SAED) patterns of Fe1/3TaS2 (e) and Fe1/4TaS2 (f). g, h EDS (g) and Raman spectra (h) of Fe1/3TaS2 and Fe1/4TaS2. The colored areas of wathet blue and pale yellow in Raman spectra present Fe* 2a × 2a superstructure and Fe* \(\sqrt{3}\)a × \(\sqrt{3}\)a superstructure, respectively. The gray areas mark phonon modes for different superlattices. Scale bars: b 50 μm; c 1 μm.

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In order to confirm tunable intercalation concentration, FexTaS2 was used as an example in this section. As characterized by transmission electron microscopy (TEM) elemental mapping (Fig. 2c), the uniform color contrast verifies that Fe atoms are intercalated successfully and distributed homogeneously through the host TaS2. In addition, the peak position together with the peak shape of Fe in the high-resolution X-ray photoelectron spectroscopy (XPS) spectrum (Fig. 2d) confirms the positive valence state of the intercalated Fe atoms. This also means that there is a strong interaction between the host 2D material and the intercalated TM46,47.

Since the element ratio of the as-synthesized product is the same as the precursors, the ultrathin FexTaS2 flakes with different Fe ratio could be obtained by simply adjusting the element ratio of the precursor bulk crystal. As shown in Fig. 2e, f, selected area electron diffraction (SAED) patterns of FexTaS2 samples exhibit superlattice spots which are absent in the corresponding pristine parent 2D material (Supplementary Fig. 14). The main spots belong to the host TaS2, while the faint spots are resulted from the intercalated Fe atoms. Different Fe superlattice means different Fe ordering and concentration (Supplementary Fig. 15). The sample displaying with \(\sqrt{3}\)a × \(\sqrt{3}\)a and 2a × 2a superlattices (where a is the basic lattice constant of host 2D materials) is corresponding to Fe1/3TaS2 and Fe1/4TaS2, respectively, which is further confirmed by the energy dispersive X-ray spectroscopy (EDS) results (Fig. 2g). The same phenomenon was found in other UHI-2DMs (Supplementary Figs. 16, 17). Figure 2h shows the typical Raman spectra of as-synthesized FexTaS2. There is a sharp peak around 140 cm−1 in the Fe1/3TaS2 sample, which is the fingerprint of Fe* \(\sqrt{3}\)a × \(\sqrt{3}\)a superstructure30. For the Fe1/4TaS2 sample, a broader and less intense Raman features around 120 cm−1 appear, which is a characteristic of Fe* 2a × 2a superstructure32. The as-synthesized materials show significant differences from parent 2D materials, indicating successful intercalations. In addition, the A1g mode of these two intercalated samples displays redshift around 10 cm−1 compared with host TaS2, which means a charge transfer from Fe to the host lattice (Supplementary Fig. 18)48, consistent with XPS results. This provides a basis for material property regulation.

Uniformity of interlayer atoms

The homogeneity of TMs in host 2D materials is very important, which determines the properties and device applications. Thus, position-dependent Raman spectra and SAED were applied to evaluate the phase homogeneity of UHI-2DMs. As shown in Supplementary Figs. 19–23, the peaks from intercalation at different areas in Raman spectra have similar peak intensity and position. SAED collected in different regions of one flake present identical pattern superlattice spots and orientation. These strong evidences indicate the structural homogeneity of the as-synthesized UHI-2DMs. Note that, the slight deviations in atomic proportions from EDS results were derived from the bulk precursors. In fact, the FexTaS2 precursors grown by CVT themselves exist composition deviations (Supplementary Fig. 24).

Besides, the UHI-2DMs present excellent air-stable. After 30 days exposure in air, the color and morphology of the intercalated sample does not change compared with the fresh one (Supplementary Fig. 25). These characterizations prove the high crystalline quality of UHI-2DMs synthesized by this FAG method and also prove the capability of FAG to regulate the components exactly.

Atom superlattice structure of UHI-2DMs

To further reveal the detailed atom superlattice structure of as-synthesized UHI-2DMs materials, we selected Mn1/3NbS2 as a representative for atomic resolution scanning transmission electron microscopy-high-angle annular dark field (STEM-HAADF) image considering the proper mass difference between Mn and Nb. Such difference can be reflected in suitable contrast of STEM-HAADF atomic image effectively. As shown in Fig. 3a and Supplementary Fig. 26, the (001) plane of Mn intercalated 2H-type NbS2 with no obvious defect or lattice deformation is presented, indicating the high crystallinity after intercalating. The corresponding fast Fourier transform (FFT) pattern shows two concentric sets of diffraction spots (Fig. 3b). The main spots highlighted by white circles belong to the host 2H-type NbS2, corresponding to the (110) planes with interplanar crystal spacing of 0.28 nm. The faint spots at (1/3,1/3,0)-type positions presenting a \(\sqrt{3}\)a × \(\sqrt{3}\)a superlattice are resulted from the intercalated Mn atoms (highlighted by orange circles)29,33,47. The atom model (Fig. 3c) is used to demonstrate the superlattice structure with the intercalated Mn atoms. Furthermore, high-resolution cross-sectional STEM-HAADF (vertical to the edge of the hexagon film) was performed to verify the distribution of TMs in the vdW gaps of host 2D material (Supplementary Fig. 27). It is clear that the Mn atoms homogeneously intercalate in the vdW gaps of NbS2 (Fig. 3d) and no apparent defects can be observed, even though in a fairly large field of view (Supplementary Figs. 28, 29). The corresponding atom intensity profile (Fig. 3e) and cross-sectional EDS mapping (Supplementary Fig. 30) also confirm the presence of additional layers of Mn atoms between the NbS2 layers. A slightly larger Nb-Nb distance along the c axis (0.63 nm for Mn1/3NbS2, and 0.60 nm for 2H-NbS2.) can be attributed to the intercalation of Mn atoms (Supplementary Fig. 31)39. The corresponding FFT pattern from the cross-sectional [01\(\bar{1}\)0] zone axis (Fig. 3f) indicates a homogeneous intercalation phase. To further show the atomic structure of the intercalated materials, the corresponding simulated image and atom model are presented (Fig. 3g–i). All these data show the high crystallinity of synthesized UHI-2DMs with highly ordered intercalated guest atoms.

Fig. 3: Structural characterization of Mn1/3NbS2.
figure 3

a High-magnification scanning transmission electron microscopy-high-angle annular dark field (STEM-HAADF) image. Zone axis [0001]. b, c Corresponding fast Fourier transform (FFT) pattern (b) and atom model (c) of Mn1/3NbS2. d Cross-sectional STEM image of Mn1/3NbS2. e Atom intensity profiles as outlined in the aqua dashed line in (d). Red arrows indicate the signal of Mn atoms. Zone axis [01\(\bar{1}\)0]. f The corresponding FFT pattern of (d). g–i Enlarged STEM image (g) corresponding to the regions highlighted with red boxes (~2 × 2 nm) in d, and the corresponding simulated image (h), atom model (i), respectively. Scale bars: a 2 nm; b 3 nm−1; d 1 nm; f 3 nm−1; g 0.5 nm.

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Magnetic properties of UHI-2DMs

Then, the magnetic properties of as-synthesized UHI-2DMs were tested to tell the effect of guest atoms on the property tuning in 2D structure. These layered intercalated compounds have attracted intense interest due to their modulated complicated ferromagnetism or antiferromagnetism for the past forty years49. Firstly, the magnetic properties of as-synthesized UHI-2DMs were examined through superconducting quantum interference device (SQUID). As shown in Supplementary Fig. 32 and Supplementary Table 3, the magnetic ordering temperatures drew from SQUID was comparable to their reported bulk crystals22,23,24, and completely different from their host 2D materials. The soliton lattice of Cr1/3NbS2 in thick sample was observed through SQUID measurement because that part of the chiral helimagnetic structure is transformed into ferromagnetic arrays under external magnetic field (Supplementary Fig. 33). It confirms that this direct synthesis method could induce highly ordered intercalation structures and robust magnetic properties.

Then, Fe1/3TaS2 is chosen to examine the thickness-related magneto-transport properties by standard Hall bar devices as well, as shown in Fig. 4a. Firstly, properties of pristine 2D TaS2 are characterized, presenting typical superconducting properties with superconducting transition temperature (Ts) ~3 K (Supplementary Fig. 34, 35), consistent with previous reports12.

Fig. 4: Magnetic properties characterization of Fe1/3TaS2.
figure 4

a Optical micrograph with standard Hall bar device and side view of heterostructure schematic. b–e Hall resistivity (b, d) and magnetic resistivity (c, e) of 3 L and 18 L Fe1/3TaS2 respectively, at various temperatures. μ0H is the applied magnetic field. Note that these curves were vertically shifted for clarity. f Magnetic phase diagram for Fe1/3TaS2 of thickness versus temperature. The dashed line highlights the interphase boundary. g Hall resistivity and magnetic resistivity for 18 L Fe1/3TaS2 with the external field parallel and perpendicular to the c-axis, respectively. h The relationships between θM and θH with two constants (K1 = 0.334 and K2 = −0.119) of magnetic anisotropy energy according to the Stoner–Wohlfarth model. \({\theta }_{M}\) and \({\theta }_{H}\) are the tilt angles for magnetization \(M\) and \({\mu }_{0}H\) with the normal direction of the sample surface respectively. Inset: angle-dependent magnetoresistance with the magnetic field rotates in the plane perpendicular to the direction of current. Rxx and Rxy are labeled as red and cyan curves, respectively. i Temperature-dependent longitudinal resistivities of Fe1/3TaS2 with different thicknesses.

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We then evaluated the magnetic order of 2D Fe1/3TaS2 samples by simultaneously monitoring the longitudinal resistivity (ρxx) and transverse Hall resistivity (ρxy) as a function of external magnetic field (H) and temperature (T) respectively (Fig. 4b–e). The external magnetic field, μ0H, was applied perpendicular to the sample plane (out-of-plane). The curves of Fe1/3TaS2 devices with different thicknesses all present hysteretic behavior which belongs to the anomalous hall effect (AHE). Besides, ρxx and ρxy of samples with various thicknesses (3 L, 4 L, 6 L, 18 L, 33 L) show similar behavior (Supplementary Fig. 36), which suggests layer-independent magnetic ordering temperature in Fe1/3TaS2. Due to the damage to the samples during transfer, the thinnest nanosheet (2 L) cannot be tested in this work. Curie temperature (Tc), which is defined as the onset temperature of non-zero ρxy occurring at zero external magnetic field in ρxy-μ0H plots, is estimated around 19 K. It is widely observed in 2D ferromagnets that the Tc monotonously decreased with the decrease of thickness8,50,51. In contrast, the Tc value of 2D Fe1/3TaS2 samples almost does not vary with thickness (Fig. 4f) and is comparable to the Tc for bulk crystal. The results are roughly consistent with previous work, where robust magnetic properties are realized in 2D FexTaS2 by a solvent intercalation method30. Note that, the MR and ρxy of samples present broad features which may be caused by intercalation disorder. As discussed before, the defect of 2D Fe1/3TaS2 samples may root in the composition variation in bulk precursor because of the one-to-one mechanism52. More efforts will be made to synthesize a perfectly constructed precursor, which might be crucial for FAG method to circumvent such disorder.

The layer-independent Tc may be attributed to the pinning effect53 or complicated magnetic domain structure caused by the intercalant disorder30 and the exchange interaction associated with the weak interlayer coupling in 2D nature54,55. The great coercivity in these atomically thin samples is also a signal of the pinning effect or complicated magnetic domain. To further explain the layer-independent Tc, magneto crystalline anisotropy (MCA) was also examined. The ρxy and MR curves with the external field applied parallel to the c-axis (H‖c) were compared with those in which the external field is applied perpendicular to the c-axis (H⊥c) (Fig. 4g). Only H∥c profiles are hysteretic, which suggests an easy axis along c and strong out-of-plane MCA in few-layer Fe1/3TaS2. To further determine the orientation of the magnetic easy axis in Fe1/3TaS2, angle-dependent AHE measurements (Fig. 4h) and quantitative analysis of magnetic anisotropy energy (inset) were performed with the phenomenological Stoner–Wohlfarth model56. Details of the fitting procedure are described in the Method section. The θM–θH data directly fall into the region of θM  < θH. By calculation, the magnetic anisotropy constants K1 and K2 at 2 K are 0.334 M J m−3 and −0.119 M J m−3, respectively, confirming the out-of-plane magnetic easy axis. The large MCA in Fe1/3TaS2 raises the anisotropy-stabilized long-range ferromagnetism in ultrathin Fe1/3TaS2, which is probably the reason for unchanged Tc.

Besides, the resistance increased with the temperature rising under a magnetic field of 0 Oe, also manifesting a typical metallic feature with good crystallinity (Fig. 4i and Supplementary Fig. 37). Then, DFT calculations were performed to investigate the electronic and magnetic properties of the Fe1/3TaS2 with various thicknesses (Fig. 5 and Supplementary Fig. 38). Taking the 3 L Fe1/3TaS2 slab model for example. As shown in Fig. 5a, the illustration of the difference of charge density confirms that electrons would transfer from the Fe atoms to the host TaS2 layers after intercalation, which is consistent with the above analysis of the peak shift in the Raman spectra. According to the orbital-projected DOS (Fig. 5c), significant splitting occurs between the spin-up states (far below the Fermi level) and spin-down states for the orbital from Fe atoms. And it is obvious that the \({d}_{{z}^{2}}\) orbitals of Fe are fully occupied, while the rest d orbitals of Fe are partially occupied by the majority-spin electrons. Thus, the local magnetic moments on the Fe sites are around 4 \({\mu }_{B}\), which is consistent with the calculated result (3.518\({\mu }_{B}\)). Then, focusing on the states around the Fermi surface, it is obvious that p-d hybridization occurs between the delocalized p orbitals of S atoms and the localized d orbitals of Fe/Ta atoms (Fig. 5c, d), where the illustration of the spin density (Fig. 5b) further affirms the delocalization of the p electrons of S atoms. Therefore, the long-range magnetic interaction among Fe atoms could be mediated by such p-d hybridization, which turns out to be the ferromagnetic ordering in the Fe layer in the current system.

Fig. 5: The theoretical calculation of Fe1/3TaS2.
figure 5

a, b The illustrations of the charge density difference (a) and spin density (b) of 3 L Fe1/3TaS2. The red and green regions indicate charge accumulation and depletion, respectively. The iso-surface of charge density difference is set as 0.02 eV/Å3 and that of spin density is set as 0.001 electron/Å3. c, d The DFT-calculated density of states projected on Fe/S atoms (c) and Ta/S atoms (d) of 3 L Fe1/3TaS2, respectively, where the Fermi levels (EF) are set as 0 and highlighted by the gray dotted line.

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Besides, the magneto-transport properties of Fe1/4TaS2 and Cr1/3NbS2 samples were tested as well. As shown in Supplementary Fig. 39, the magnetic behaviors of Fe1/4TaS2 are totally different from Fe1/3TaS2. This indicates that one can precisely regulating the concentration of atoms to achieve different magnetic properties through FAG method, which is crucial for tailoring magnetic properties and the development of spintronic devices. For the Cr1/3NbS2 crystal (Supplementary Fig. 40), the saturated critical magnetic field was detected in the longitudinal resistance (Rxx) curve, presenting the transition from chiral soliton lattice to forced ferromagnetic state. Besides, the transverse Hall resistance (Rxy) show the ab-plane easy axis since AHE is observed when H⊥c57,58,59,60.

In summary, we have synthesized eight kinds of UHI-2DMs successfully via a universal FAG method. The intercalated components can be regulated precisely in stoichiometric ratio and the thickness of UHI-2DMs down to the thinnest limit of the intercalated compounds can be realized, due to the homogeneous flux of the components and the confined space of FAG method. The magnetic properties could be induced by intercalated Fe atoms, proving that intercalation is an effective strategy to engineer the quantum properties of 2D materials. The as-synthesized Fe1/3TaS2 sample presented ferromagnetism with layer-independent magnetic ordering temperature, indicating that intercalation might introduce some unique properties in 2D materials. In a word, our work provides an idea for direct synthesis of heteroatoms-intercalated ultrathin 2D materials, in which the atoms type and intercalation amount can be tuned, promising to exploit a class 2D materials with tailored properties. Besides, this method might also be promising for synthesizing some unconventional intercalated compounds to explore exotic chemical and physical properties.

Methods

Growth of UHI-2DMs by FAG

The precursor crystals were grown by CVT method28. Fluxes such as KCl and KI were used to decrease the melting points of the reacting materials and to assist the crystallization of UHI-2DMs. In brief, the precursor crystals mixed with flux were sandwiched between two pieces of mica compressed by a homemade setup. The setup contains two pieces of rounded stainless steel of 6 cm in length and 1.8 cm in width and three screws. The pressure is around 1.7 × 105 Pa. Then the setup was thermal treated in Ar or Ar/H2 atmosphere for flux-crystallization proceeds. The detailed growth parameters and synthesis descriptions are shown in Supplementary Table 4.

Sample characterization

The morphology and thickness of UHI-2DMs were characterized by Optical microscope (OM, Olympus CX41) and an atomic force microscope (ICON, Veeco/Bruker) under the atmospheric environment. Raman spectra (iHR 500) were performed under 532 nm laser excitation at room temperature. XPS (250Xi, Thermo Scientific Escalab) was used to characterize the chemical composition and chemical states of the samples. Quantum Design MPMS3 SQUID Magnetometer was used to measure the magnetic properties of as-synthesized UHI-2DMs. The detailed phases and atomic structure characterizations are shown in Supplementary Figs. 41–51.

STEM sample preparation and characterization

UHI-2DMs were transferred onto copper grids for STEM characterizations by Poly (methyl methacrylate) (PMMA) (950 PMMA A4, Micro Chem) assisted method. The samples were spin-coated with homemade PMMA and then etched with 3% hydrofluoric acid (HF). Then, the PMMA/sample layer was peeled off, rinsed with deionized water, and transferred to copper grids. Finally, acetone and isopropanol were used to remove the PMMA. STEM-HAADF images, HRTEM, EDS analysis, SAED, and mapping were performed using a FEI Themis Z at 300 kV and JEM-2100F TEM operating at 200 kV equipped with Oxford Aztec EDS system. The cross-sectional specimens were prepared by focused ion beam using a standard lift-out procedure. Image simulations were performed with the QSTEM software.

Device fabrication and electrical measurements

Fe1/3TaS2 of different thicknesses were transferred on 285-nm SiO2/Si using PMMA-assisted wet-transfer method, and selected to fabricate Hall bar devices. We determined the layer number of the flakes with an atomic force Microscope. Laser direct writing lithography and e-beam evaporation of Ti/Au (10 nm/40 nm) were used. The transport measurements were carried out in a superconducting magnet with helium-3 cryostat. The xx- and xy-resistances of Fe1/3TaS2 were derived from four-terminal measurements using SR830-DSP lock-2 in amplifier, with an alternating excitation current of 2–20 μA.

Magnetic anisotropy energy analysis based on the Stoner–Wohlfarth model

Normally, in a ferromagnetic system with a rhombohedral structure, the free energy \(F\) of its magnetic moment can be described with the Stoner–Wohlfarth model in consideration of the orientation of the magnetic easy axis as follows:

$$F={K}_{1}\, {\sin }^{2}\, {\theta }_{M}-{\mu }_{0}{HM}\cos \left({\theta }_{H}-{\theta }_{M}\right)$$
(1)

where \({K}_{1}\) is the first-order constant of magnetic anisotropic energy to determine the magnetic easy axis; \({\mu }_{0}H\) is the applied magnetic field; and \({\theta }_{M}\) and \({\theta }_{H}\) are the tilt angles for magnetization \(M\) and \({\mu }_{0}H\), respectively (the normal direction of the sample plane is defined as 0° for the tilt angles). As described in Eq. (1), at the equilibrium state with the minimum free energy \(F\), θM should satisfy the following equation:

$$\frac{\partial F}{\partial {\theta }_{{{\rm{M}}}}}=0=2{K}_{1}\sin {\theta }_{{{\rm{M}}}}\cos {\theta }_{{{\rm{M}}}}-{\mu }_{0}{HM}\sin({\theta }_{{{\rm{H}}}}-{\theta }_{{{\rm{M}}}})$$
(2)

We calculate \({\theta }_{{{\rm{M}}}}\) as a function of θH using the following formula:

$${\theta }_{{{\rm{M}}}}({\theta }_{{{\rm{H}}}})=\arccos \left(\frac{{R}_{{AHE}}^{s}({\theta }_{{{\rm{H}}}})}{{R}_{{AHE}}^{s}({\theta }_{{{\rm{H}}}}=0)}\right)$$
(3)

The relationship between \({\theta }_{{{\rm{H}}}}\) and \({\theta }_{{{\rm{M}}}}\) reflects the direction of the magnetic easy axis, where \({\theta }_{{{\rm{M}}}}\)  < \({\theta }_{{{\rm{H}}}}\) means that the magnetization tends in the out-of-plane orientation.

In the above discussion, we use the first-order constant \({K}_{1}\) to successfully describe the magnetic anisotropy energy and the resulting magnetization direction. However, the \({K}_{1}\) value can only determine whether the magnetic easy axis is in the in-plane or out-of-plane orientation. To precisely determine the canted angle of the magnetic easy axis, the free energy in the Stoner–Wohlfarth model can be extended to have both constants \({K}_{1}\) and \({K}_{2}\), as shown below:

$$F={K}_{1}\, {\sin }^{2}\, {\theta }_{{{\rm{M}}}}+{K}_{2}\, {\sin }^{4}\, {\theta }_{{{\rm{M}}}}-{\mu }_{0}{HM}\cos \left({\theta }_{{{\rm{H}}}}-{\theta }_{{{\rm{M}}}}\right)$$
(4)

where \({K}_{1}\) and \({K}_{2}\) are the first- and second-order constants for magnetic anisotropic energy, respectively. Within this model, the canted angle of the magnetic easy axis can be described in a specific way. \({K}_{1}\) > 0 and 0 > \({K}_{2}\) >\(-\frac{{K}_{1}}{2}\) means that the magnetization tends in the out-of-plane orientation.

Density functional theory calculations

The first principle calculations were through the Vienna Ab Initio Simulation package (VASP)61, where the projector-augmented-wave method62,63 was applied. For the exchange-correlation functional, the generalized-gradient approximation (GGA) of the Perdew-Burke-Ernzerhof type64 was chosen. The energy cutoff was set as 500 eV. And the criteria of the convergence for the ionic relaxation loop and electronic SC-loop were 0.01 eV/Å and 10−6 eV, respectively.

To investigate the dependence of the electronic and magnetic properties of FeTa3S6 on thickness, we built three structure models, including the bulk, layered structure with 2 L and 3 L (Details can be found in Supplementary Information). The k-point meshes were 8 × 8 × 4, and 8 × 8 × 1 for bulk and slab models, correspondingly. Moreover, vacuum layers of 20 Å were added along the c direction in slab models.

To investigate the stable region of FeTa3S6 in the phase diagrams, we used the similar method which was reported in previous studies65. We first determined the possible byproducts during the synthesis of the FeTa3S6, including seven binary compounds (FeS, FeS2, Fe3S4, Ta2S, Ta3S2, TaS2, and TaS3), and one ternary compound (FeTa4S8). Then, we calculated their enthalpies of formation. For each plot shown in Supplementary Fig. 2, the chemical potentials of two of the three elements (Fe, Ta, and S) were chosen as the independent variables, and the value of the rest was set as 0. Under the constraint of the growth conditions (Details can be found in Supplementary Information), the phase diagrams of FeTa3S6 could be obtained.

For all the bulk models involved, the lattice constants were set as the experimental results. The Liechtenstein method66 was adopted for the GGA + U calculations, where U (4 eV) and J (0.7 eV) were added to the d orbitals of Fe atoms. Furthermore, the most stable magnetic type for each magnetic structure was consistent with experimental observations (Details can be found in Supplementary Table 1).