Phase-tunable growth of FeTe crystals
Figure 1 schematically illustrates the setup of the ambient pressure CVD system for the growth of FeTe crystals on SiO2/Si substrates. Briefly, ferrous chloride (FeCl2) and tellurium (Te) powders were used as reactants. During the CVD process, the Ar and H2 mixture carries a certain amount of tellurium vapor at a fixed heating temperature of tellurium source (TTe) to react with evaporated FeCl2 at different growth temperatures (Tgrowth) to produce different phases. Details about the sample synthesis are provided in the Methods section. As shown in Supplementary Fig. 1, the tetragonal FeTe belongs to P4/nmm space group owning a layered structure in which Fe atom layer and the double slabs of Te atom layers are interlaced in the interlayer direction (Supplementary Fig. 1a). While hexagonal FeTe has a non-layered structure that belongs to P63/mmc space group. This structure can be regarded as the closed-packed Fe atomic planes alternatively occupying the octahedral vacancies created by the AB-stacked Te atomic planes (Supplementary Fig. 1b).
One of the most important features of FeTe is its phase tunability which originates from the formation energy difference between the hexagonal and tetragonal phases in FeTe13,14. Theoretical calculations have predicted that the hexagonal FeTe is the most thermodynamically favorable phase16,19,21. Thus, the growth temperature in the CVD process is essential to realize the phase transition. We found that the phase of FeTe was sensitive to its growth temperature (Tgrowth). As shown in Fig. 1, at a relatively high temperature, hexagonal FeTe will be the dominant phase. Decreasing Tgrowth will lead to the formation of tetragonal FeTe. A clear trend can be seen from the following optical images (Fig. 2a, d; Supplementary Fig. 2a–c). Notably, square-shaped FeTe crystals with an edge size of about 40 μm were obtained at a Tgrowth of 530 °C (Fig. 2a). At 550 °C, the obtained nanosheets remain square-like, with slightly increased thickness estimated by the optical contrast (Supplementary Fig. 2a). However, a mixed square and hexagonal shapes were observed at 570 °C with decreased edge length (Supplementary Fig. 2b). When Tgrowth was further increased to 590 °C, the resulting FeTe nanoplates exhibited a homogeneous triangular shape with maximum domain sizes exceeding 60 μm (Fig. 2d). Further increasing Tgrowth to 610 °C yielded thicker nanoplates again (Supplementary Fig. 2c). It should be pointed out that, the domain sizes and flake thickness of FeTe crystals do not simply increase with temperature. Actually, the obtained FeTe samples by CVD method at different temperatures always show a distribution with different grain size and thickness (Supplementary Fig. 2d, e). The phase evolution of FeTe flakes from tetragonal to hexagonal highly relies on Tgrowth (Supplementary Fig. 2f). These results further prove that maintaining a relatively high temperature is essential for obtaining the thermodynamically stable hexagonal FeTe phase. Similarly, the reported literatures have also shown that the temperature and amount of precursor have a key role for phase transformations in 2D materials22,23,24,25.
Structural characterization of FeTe crystals
Further characterizations were performed to investigate the morphology and composition of the as-obtained FeTe crystals. The atomic force microscopy (AFM) image in Fig. 2b shows an individual tetragonal FeTe flake with a thickness of 3.6 nm. As for hexagonal FeTe, the thickness can be tailored down to 2.8 nm (Fig. 2e), which is extremely thin for a non-layered material. Figure 2c shows the Raman spectra of the as-grown tetragonal FeTe flakes. Two obvious Raman peaks were located at 130 and 152 cm−1, corresponding to the Eg and A1g modes of tetragonal FeTe, which are in good accordance with the previous studies26. A similar result with different peak positions was also observed in the Raman spectra of the hexagonal FeTe crystal (Fig. 2f). Supplementary Figure 3 shows optical images and corresponding Raman intensity maps for tetragonal and hexagonal FeTe flakes, respectively, suggesting the high crystallinity and uniformity of the FeTe crystals. In addition to Raman characterization, X-ray photoelectron spectroscopy (XPS) was used to analyze the chemical composition of the as-grown FeTe nanosheets. The XPS spectra and analysis (Supplementary Figs. 4 and 5) demonstrate both tetragonal and hexagonal phase FeTe nanosheets are reasonably stoichiometric, without oxidation or any residual chlorine.
To probe the atomic structural differences of CVD grown tetragonal and hexagonal-shaped FeTe crystals, aberration-corrected scanning transmission electron microscopy–annular dark field (STEM-ADF) imaging was applied. The image contrast in STEM-ADF image is intimately tied to the Z atomic number varying approximately as Z1.6–1.7, and thereby the Z-contrast STEM image is widely employed to identify the atomic structures in 2D materials27,28. The FeTe crystals were transferred from the SiO2/Si substrate to TEM grids, as shown in Supplementary Fig. 6, through a surface-energy-assisted transfer protocol29,30. The transfer details are provided in the “Methods” section. A typical atomic-resolution STEM-ADF image of the tetragonal shaped FeTe crystal along the  zone axis was depicted in Fig. 3a. Following the intuitive STEM image, it can be seen that in line with the macroscopically manifested tetragonal crystal. The tetragonal FeTe crystals comply with a P4g wallpaper group symmetry. The in-plane Te–Te and Fe–Fe bonds are estimated to be ~3.0 Å, as verified by the zoom-in STEM image (Fig. 3b). No discernible extended defects are spotted in the STEM images confirming that the as-grown tetragonal shaped FeTe crystals are highly crystalline. In addition, the corresponding fast Fourier transform (FFT) pattern reveals a singlet set of spots which further corroborate the high crystallinity of the crystal (Fig. 3c). Apparently, it is a typical layered material where the interlayer bonding is raised by weak Te–Te interaction. The Fe and Te elemental distribution as suggested by the energy-dispersive X-ray spectroscopy (EDS) mapping (Fig. 3d, e) is homogenous throughout the entire crystal, and the chemical stoichiometry is calculated as FeTe.
In stark contrast to the tetragonal shaped FeTe crystal, the STEM image (Fig. 3f) of hexagonal-shaped FeTe crystal reveals an in-plane six-fold symmetry along the  zone axis. The in-plane Te–Te or Fe–Fe bond is calculated as 3.8 Å according to the enlarged STEM image (Fig. 3g). In parallel, no structural defects or stacking faults are observed throughout the flakes suggesting that the hexagonal-shaped FeTe crystal is highly crystalline. The single crystallinity is further verified by the corresponding hexagonal-shaped FFT pattern (Fig. 3h), where only one set of spots can be observed. Structurally, closed-packed Te atomic planes take periodic ABAB stacking order, and the closed-packed Fe atomic planes alternatively occupy the octahedral vacancies created by the AB-stacked Te atomic planes. In other words, the hexagonal-shaped FeTe takes a periodic ACBC stacking registry, where the small and capital letters represent Fe and Te closed-packed atomic planes, respectively. Hence, the hexagonal-shaped FeTe is no longer a layered material. The chemical composition of hexagonal-shaped FeTe crystal was further analyzed by EDS mapping (Fig. 3i, j). The elemental distribution of Fe and Te elements is uniform and homogeneous. In addition, the chemical stoichiometry of Fe and Te is ~1:1.
Magnetoelectric characterization of FeTe samples on SiO2/Si substrate
Although magnetic signal can be directly detected by bulk-sensitive techniques, such as vibrating sample magnetometer (VSM) and superconducting quantum interference device (SQUID), magnetoelectric measurement is more suitable to characterize the weak magnetism from low dimensional nanoflakes2,12. For instance, bulk-sensitive techniques inevitably detect the signal from magnetic contaminations, because ultrathin samples’ weak magnetic signal is often comparable or even weaker than that of contaminations obtained from various sources, such as substrate, glue, magnetic particles from laboratory environment. Supplementary Fig. 7 shows the optical images of tetragonal and hexagonal FeTe Hall-bar devices with different thicknesses, which were fabricated directly onto the SiO2/Si substrates and well-protected by the hexagonal boron nitride (h-BN) capping layer. We should note that tellurides are susceptible to ambient degradation. Generally, our FeTe crystals can survive in the air for only half an hour (Supplementary Fig. 8). So, FeTe samples were always immediately moved to an Ar glove box after the growth process. The glove box (Supplementary Fig. 9) is equipped with an optical microscope with very long-distance objectives, a spin coater, a heating stage and other elements required for the PMMA coating and h-BN encapsulation process. The details are described in the “Methods” section. We reduced the exposure time of FeTe samples in the air as much as possible to avoid the degradation. Figure 4a depicts the temperature-dependent longitudinal sheet resistance (RT) of tetragonal FeTe devices with the thicknesses of 32, 19, and 5 nm, respectively. A clear change of resistance was observed at all three thicknesses, corresponding to the paramagnetic (PM) to AFM phase transition. The TN gradually decreases from 70 to 45 K as the thickness decline, which is consistent with its weak interlayer coupling6. Both the linear Hall effect (black curve in Fig. 4c) and temperature-dependent magnetic moment results (Supplementary Fig. 10) in the 32 nm tetragonal FeTe device confirmed the AFM behavior with TN ~ 70 K, below which the spontaneous magnetization of FeTe lattice exceeds over the thermal fluctuation-induced net magnetic moment31.
Figure 4b shows the RT of hexagonal FeTe devices with thicknesses 30, 12, and 4 nm. The phase transition from non-magnetic (NM) to ferromagnetic (FM) phase was observed at a Tc ~ 220 K for 30 nm, Tc ~ 215 K for 12 nm and Tc ~ 170 K for 5 nm, respectively. The ferromagnetism was further confirmed by the Hall measurement. As for the thick hexagonal FeTe (30 nm), the anomalous Hall effect (AHE) observed clearly at 1.5 K within ±0.5 T magnetic field range (red curve in Fig. 4c). With the temperature increases from 1.5 to 220 K, the temperature-dependent saturation moment and the coercive field (Hc) gradually decrease, above which the AHE vanishes (Fig. 4d). As the thickness declined, Fig. 4e presents the typical AHE hysteresis loops for both 30 and 4 nm hexagonal FeTe devices measured at 100 K within ±0.5 T magnetic field range. Hc develops from 0.13 to 0.44 T while the saturated jump of |∆Rxy| suppresses from 1.58 to 0.2 Ω when the thickness decrease from 30 to 4 nm. Supplementary Fig. 11 shows the temperature-dependent AHE hysteresis loops for a 4 nm hexagonal FeTe device. A smaller Hc with a larger saturated resistance was observed as the temperature gradually rises. As shown in Fig. 4f, the coercive field gradually shrank as the temperature rises and varnished when the temperature is higher than Tc ~ 170 K, supporting the Tc of 4 nm hexagonal FeTe device is ~170 K.
Insight of the origin of magnetic order in FeTe crystals
Density-functional theory calculations were carried out to determine the magnetic ground state of the hexagonal FeTe. Schematic top and side views of the hexagonal FeTe structure are shown in Fig. 5a, b. Our non-magnetic calculation reveals lattice constants a = 3.90 Å and c = 5.36 Å, which are comparable with the STEM (Fig. 3g) and electron diffraction (Supplementary Fig. 12) values of 3.8 and 5.2 Å measured at room temperature, respectively. However, if Fe cations are allowed to have local magnetic moments, lattice constant a elongates to roughly 4.2 Å regardless of its long-range magnetic ordering. Together with the TC of ~220 K (Fig. 4b), these results suggest the structure observed in STEM is, most likely, a non-magnetic but not a paramagnetic hexagonal FeTe. In terms of the tetragonal phase, however, the measured value of a = 3.0 Å is closer to our theoretical value of Néel AFM phase of a = 2.90 Å, but much larger than the non-magnetic value of a = 2.71 Å. An Néel AFM configuration can mostly simulate properties of the corresponding paramagnetic phase, which implies local magnetic moments of the tetragonal phase persist at room temperature, consistent with previous calculations and experiment measurements16. In light of this, we can infer that the tetragonal and hexagonal phases are, most likely, paramagnetic and non-magnetic, respectively at room temperature and during the synthesis process (Fig. 5g).
We first consider a local magnetic moment picture for the ferromagnetism of the hexagonal phase. Significant magnetostriction was observed in the FM–FM (both intra- and interlayer FM, a = 4.23 Å, c = 5.81 Å) and FM–AFM (intralayer FM and interlayer AFM, a = 4.19 Å, c = 5.83 Å) configurations, which are yet to be confirmed by low-temperature STEM experiments. Details of all considered magnetic orders are available in Supplementary Fig. 13. Among these configurations, the FM–AFM order (Fig. 5c) is, however, over 20 meV/Fe more favored than other orders for a perfect hexagonal FeTe (Supplementary Table 1). A structural distortion further lowers the energies of all magnetic orders (on the order of 100 meV/Fe). As a result of the distortion, lattice constant c shows a considerable shrink from roughly 5.8 to 5.45 Å (Fig. 5b), associated with a stretched lattice constant b (from 4.19 to 4.29 Å) and an increased angle α (from 120.0° to 121.4°) (Fig. 5a). The broken in-plane three-fold symmetry aside, the distorted structure primarily leads to a much shorter interlayer Fe–Fe distance, from 2.9 to 2.73 Å, and thus enhances their FM direct exchange through the formed interlayer Fe–Fe bonding. Such enhanced direct exchange favors the FM–FM order, with strongly enhanced FM J1 and J3 (Supplementary Fig. 14 and Supplementary Table 2), in a slightly distorted structure (Fig. 5d; Supplementary Table 1). As a result, the FM–FM order is over 7 meV/Fe more favored than other magnetic configurations in the distorted structure (Supplementary Table 1). The comparison of intact and distorted lattices suggests an energetic competition between the interlayer Fe–Fe bonding and the lifted energy in the distorted lattice, which are associated with the change of interlayer magnetism. This thus implies a likely magnetoelastic effect, up to 1% for in-plane and 6% for out-of-plane, potentially observable in the hexagonal FeTe under certain conditions of temperature, external strain and magnetic field. These results also indicate that the structural distortion might have a paramount role in the observed ferromagnetism.
Spin-exchange parameters for both the undistorted and distorted structures are listed in Supplementary Fig. 14 and Supplementary Table 2, which predict a Tc value around 290 K using Metropolis Monte Carlo (MC) simulation in a 3-layer 3D Ising lattice. Given the fact that MC simulation of the Ising model usually overestimates Tc two or three times32, the hexagonal phase is expected to have a Tc value around 100–150 K in consideration of the Heisenberg local exchange picture, substantially lower than the measured value of ~220 K. This low Tc value indicates another mechanism may corporately result in such a high Tc value of 220 K. Stoner ferromagnetism mechanism is another likely reason for the FM. Non-magnetic calculations were performed to calculate the DOSs using the FM relaxed geometries. Figure 5e, f shows the plots of the total d-orbital DOSs of the undistorted and distorted structures, respectively, both of which meet the Stoner criterion, i.e., (U′/N)ρ(Edf) > 1, compellingly indicating the Stoner ferromagnetism in this metallic system. In addition, the distorted structure shows a larger (U′/N)ρ(Edf) value (1.95) than that of the undistorted structure (1.55), evidencing a stronger Stoner ferromagnetism in distorted FeTe (see Supplementary Fig. 15 for details). The Stoner FM could also explain the coexistence of the high Tc of 220 K and the non-magnetic state observed at RT. In summary of these results, we conclude that the hexagonal phase exhibits a Heisenberg plus Stoner FM below 220 K, NM above RT and, most likely, NM between 220 K and RT, as illustrated in Fig. 5g.