Structure analysis. We utilized a transmission electron microscope that is double Cs-corrected and is equipped with energy-dispersive X-ray spectroscopy (EDS) to accurately reconstruct the lattice structure. The crystals were sectioned by focused ion beam (FIB) along three crystal planes indexed as (001), (10), and (100), as depicted in the schematic image in Supplementary Figs. 3a - 3d. Figure 1 displays the high-angle annular dark-field images captured using scanning transmission electron microscopy mode (HAADF-STEM) and the corresponding EDS atomic resolution mapping of FGT samples having different Tc values of 160, 210, and 230 K. The HAADF-STEM images are suitable for identifying all ions based on their size and electronic states since the Ge and Te anions are much larger than the Fe cations. Moreover, the HAADF-STEM images are in good agreement with the cartoon of the crystal structure along the (10) plane, and the planes of (100) and (001) are also consistent with the structure (see Supplementary Figs. 3(e)-(j)). Additionally, the Fe-1 and Fe-2 sites are identifiable, where Fe-2 is positioned on the same layer with the Ge ions.
Elementary distribution analysis. Elementary mappings obtained through EDS for the intermediate-Tc and high-Tc crystals (Fig. 1(b) and (c)) indicate the presence of three distinct kinds of defects. Firstly, an additional layer of weaker spots between two Te-sublayers was observed in the Te mapping towards (10) plane, and such Te ions were also observed along the (100) plane. Based on the lattice cartoon of Ge and Te ions along (100) and (10) planes, it was found that the substitution of Te occurred on the Ge sites. Secondly, the Ge mapping demonstrated the doping of a few Ge on the Te sites. Thirdly, a Fe intercalation layer was clearly observed within the van der Waals gap in the Fe mapping towards both (10) and (100) planes. The HAADF-STEM image also confirmed the presence of such intercalation layer within the van der Waals gap. However, no occupation of Ge or Te on Fe sites was detected.
In the low-Tc crystal as shown in Fig. 1(a), both HAADF-STEM and EDS images demonstrated the absence of Fe-intercalation, while the antisite defects of Ge and Te anions were observed. The antisite of Te and Ge was found in both high-Tc and low-Tc crystals, indicating that it was not the main factor that modulated Tc in different samples. On the other hand, the additional layer of Fe ion not only contributed to the carriers of FGT, but also modified the magnetic coupling, thus inducing peculiar magnetic ordering.
Density functional theory calculations on the defects. The application of density functional theory (DFT) was utilized to reveal the underlying cause of Fe intercalation and its effects on the Curie temperature in FGT. The primary origin of intercalated Fe can be attributed to the segregation of Fe ions from their original sites to the interlayer region, resulting in the creation of Fe vacancies at those sites. This process can be facilitated by the presence of additional atoms, such as Te or Ge, that fill these Fe vacancies, leading to the formation of antisite defects. Formation enthalpies of several vacancies, antisite defects, and their various combinations, including Fe3+ (VFe3+), Fe2+ (VFe2+), Ge (VGe), and Te (VTe) vacancies, TeGe antisites, bare Fe intercalation (Fe3+xGeTe2), as well as combinations of Fe3+xGeTe2 with GeFe3+, GeFe2+, TeFe3+, and TeFe2+ antisites, were examined in our calculations. Figures 2a-2c and Supplementary Fig. 5 illustrate their formation enthalpies as a function of Fe, Ge, and/or Te chemical potentials. VFe2+ (red) and Fe3+xGeTe2 (blue) exhibit the lowest formation enthalpies among all considered defects in Fe deficient and rich limits, respectively, as shown in Fig. 2a. Nevertheless, the combination of VFe2+ and Fe3+xGeTe2 (VFe2+ + Fe3+xGeTe2) has a higher formation enthalpy under both Fe deficient and Fe rich limits, indicating that it is less likely to be the source of Fe intercalation. Although this combination can intrinsically introduce intercalated Fe atoms, it requires additional energy gain for stabilization.
A potential method for stabilization involves occupying the Fe vacancy with Ge or Te atoms, resulting in the formation of antisite defects. In the Te-rich regime, the formation enthalpy of the Te/Ge antisite (Te substituting Ge) lies within a range of -0.3 to 2.0 eV (as shown in Fig. 3b), which is the most energetically favored among all considered antisite defects. This is consistent with the most frequently observed Te substitution at Ge sites in our experiments (as depicted in Fig. 1). The substituted Ge atoms have a propensity to occupy Fe3+ sites instead of Fe2+ sites, as the filling of the former site (Fe3+) provides an additional energy gain of at least 0.8 eV (as shown in Fig. 2c and Supplementary Fig. 5). Therefore, we may infer that the introduction of intercalated Fe atoms is most likely facilitated by the formation of TeGe and GeFe3+ antisite defects in FGT. This process could be regulated, in principle, by controlling the supplying ratio of Te.
Incorporating the TeGe antisite defect and/or Fe intercalation presents an opportunity to further adjust the magnetic properties and spin exchange couplings of FGT. Upon considering the TeGe antisite defects, an intralayer and interlayer ferromagnetic (FM) state becomes the most energetically favored magnetic configuration (Fig. 2d-g and Supplementary Fig. 6). This state is more stable by 14 meV/Fe than the antiferromagnetic (AFM) order, and is consistent with the observed FM behavior in FGT samples where TeGe antisite is commonly present. As illustrated in Fig. 2g, the FM state remains the ground state when the intercalated Fe is situated in the interlayer region sandwiched by FGT free of TeGe antisite defects. However, in the presence of both TeGe antisite and Fe intercalation, a ferrimagnetic order (FiM, Fig. 2e) emerges, where the intercalated Fe sublayers are AFM coupled with adjacent FGT layers, and this configuration is energetically favored. This local AFM coupling can potentially give rise to an exchange bias effect in the high-Tc samples with both TeGe antisite and Fe intercalation.
Fe intercalation modified exchange couplings. Incorporation of Fe intercalation would furnish additional magnetic moments and exchange paths, thus reinforcing magnetic couplings along the interlayer direction in FGT. To assess the tunability of the Curie temperature, we computed the spin-exchange coupling (SEC) parameters based on a Heisenberg model, which are indicated with dashed arrows in different colors in Fig. 3a and listed in Supplementary Table 1. Monte Carlo simulations were executed with an anisotropic Heisenberg (AH) model (refer to the Methods for elaboration). Local magnetic moments of Fe atoms along the easy magnetization axis, as disclosed by Monte Carlo simulations, were depicted in Fig. 3b for FGT with defects. Based on the derived SEC parameters and the easy axis single-ion anisotropy, a Tc value of 148 K was obtained in FGT with TeGe antisite defects, which is in close proximity to the experimental value of 160 K of low-Tc ferromagnetic samples. As the magnetic couplings within FGT layers are predominantly determined by the intrinsic FGT exchange couplings and TeGe antisite defects, we further considered a J7 to describe the spin exchange between the intercalated Fe and the Fe atoms in the adjacent FGT layers. Our calculations demonstrated that the value of J7 is highly adjustable, ranging from -3.0 to 15.9 meV/Fe, depending on the density of the intercalated Fe atoms (Supplementary Table 2). Due to the augmented number of exchange paths and enlarged J7 value, Tc elevates from 160 to 250 K with an increase in Fe intercalation density (Fig. 3b), indicating that Fe intercalation is an exceptionally efficient method of enhancing Tc in FGT.
The magnetic characteristics of three distinct samples with varying Tc were assessed through measurements of the anomalous Hall effect. The magnetic field was applied along the c-axis, and the FGT flakes were transferred onto pre-patterned Ti/Au electrodes under an inert atmosphere, as illustrated in Fig. 3(c) and 3(d). The temperature dependent normalized anomalous Hall resistivity (ρAHE) was determined from the ρAHE-H curves in Supplementary Figure 7, as shown in Fig. 3(e). The ρAHE-T curves approached zero at temperatures of 160 K, 210 K, and 230 K for the low-Tc, intermediate-Tc, and high-Tc samples, respectively, indicating the same Tc as the bulk crystals.
Exchange bias effect. Our density functional theory (DFT) calculations of FGT, incorporating both TeGe antisite and Fe intercalation, indicate that intercalated Fe atoms could induce local antiferromagnetic (AFM) coupling between intercalated Fe sublayers and adjacent FGT layers, resulting in an exchange bias effect in the high-Tc samples. To investigate this effect, we analyzed the Hall resistance hysteresis loops for both high and low-Tc samples, as shown in Supplementary Fig. 8. The low-Tc crystal exhibited a typical anomalous Hall effect (AHE) of ferromagnetism under zero-field-cooling (ZFC), as displayed in Supplementary Fig. 8a, while the ordinary Hall effect was relatively weak as a flat Hall resistance (Rxy) at large magnetic field (H). The coercive fields Hc were almost the same at 160 mT for both positive and negative sweeping directions, comparable to the previous report on FGT29. To study the effect of magnetization history on the hysteresis loops, we also examined nine consecutive Hall resistivity loops at 2 K immediately after field-cooling (FC) by applying a magnetic field of 14 T along the c-axis above the Tc (see Supplementary Fig. 8b). The Hall resistance loops of the low-Tc samples were independent of sweeping history or cooling field, and the Hc was fixed at about 160 mT.
In the case of the high-Tc samples, as demonstrated in Fig. 4a-4d and Supplementary Fig. 8e-8g, the hysteresis loops of Hall resistance exhibit a perfectly square shape with no intermediate state, consistent with the Stoner-Wohlfarth model. Notably, the magnetization reversal process is observed to have an asymmetric shape, with the center of the hysteresis loop shifted from zero field by a certain value, resulting in different coercive fields Hc1 and Hc2. This asymmetric Rxy hysteresis loop is a typical behavior of the exchange bias effect, which is essentially attributed to the interfacial coupling between a ferromagnetic (FM) layer and an adjacent antiferromagnetic (AFM) layer30.
The exchange bias effect exhibited by the high-Tc samples is noteworthy for its FC dependent behavior. When the system is subjected to ZFC, a fixed coercive field is observable on the negative side of Hc2 for all loops. Conversely, the positive side of Hc1 fluctuates with sweeping history, leading to a variable HE within a broad range from -162 to 89 mT. The ZFC exchange bias effect is atypical, yet consistent with previous research into gating induced exchange bias effect in FGT21. Once exposed to FC of a high magnetic field (±14 T), as illustrated in Fig. 4c and 4d, the exchange bias field displays greater stability than those obtained from ZFC. With a negative field cooling (-14 T), the coercive fields are almost biased to the positive side, whereas applying a positive FC of 14 T causes the coercive fields to shift to the negative side, in line with a negative exchange bias effect. As a result, the exchange field (HE) is primarily fixed at 89 mT for -14 T FC and -72 mT for 14 T FC.
Moreover, the antiferromagnetic (AFM) coupling has the ability to increase the coercive fields of the high-Tc sample to approximately 640 mT, which is significantly higher than that of the low-Tc sample (±160 mT). This intensification of magnetic coupling from the low-Tc crystals is evident in the square-shaped hysteresis loops of Hall resistance and the enhanced Hc of the high-Tc FGT. However, unlike the conventional training effect observed in FM/AFM bilayer systems31, there is always a fluctuation of HE, as discussed in detail in Supplementary note V. Therefore, identifying the relationship between the local atomic structure and the AFM coupling within the FM ordering is crucial to uncover the source of the exchange bias effect.
In essence, it can be concluded that Fe intercalation is responsible for the emergence of the exchange bias effect in the high-Tc samples. In the low-Tc crystal, all magnetic moments at Fe-1 and Fe-2 sites are ferromagnetically coupled, whereas the intercalated Fe may locally induce antiferromagnetic coupling to adjacent layers. The pinning effect of the FM/AFM interface on the FM domain is crucial in achieving the exchange bias effect. It is worth noting that the intercalated Fe is not uniformly filled but randomly distributed at interstitial sites. Thus, the FM/AFM interface is more likely to be the pinning sites. By gradually ramping up the high magnetic fields to 14 T while cooling, the magnetic moment in the AFM component overcomes its exchange energy to align along H, and the AFM coupling at the FM/AFM interface can be well-defined. Consequently, the exchange bias effect is turned from negative to positive, as shown in Fig. 4(e) and 4(f) for 14 T and -14 T cooling, respectively. When under ZFC, FM/AFM interfaces (center) can be spontaneously generated after the FM transition, although the polarization is randomly distributed for each interface due to the random formation of the ferromagnetic domain. The polarization direction of the FM domain can be well-aligned under relatively low field sweeping (900 mT), while the AFM can hardly be reoriented. Thus, the pinning effect still exists, resulting in the exchange bias effect.
To summarize, we have established a connection between the magnetism and structure of Fe3GeTe2 with varying Curie temperature using electrical transport measurements, STEM, and first-principles calculations. Our results demonstrate the presence of an exchange bias effect in high-Tc samples, indicating the existence of a ferromagnetic and antiferromagnetic interface at the center, while this effect is absent in low-Tc samples. Atomic-resolution scanning transmission electron microscopy and energy-dispersive X-ray spectroscopy imaging provide element-resolved atomic structure information of Fe3GeTe2 in real-space and confirm the presence of Fe intercalation on interstitial sites in the van der Waals gap in high-Tc samples. First-principles calculations further support the notion that the Fe-intercalation layer can lead to local antiferromagnetic coupling for the exchange bias effect, thus significantly enhancing both antiferromagnetic coupling and Tc. The discovery of the Fe-intercalation layer provides a mechanism for enhancing Tc and Hc in Fe3GeTe2, namely, the hidden antiferromagnetic ordering due to the Fe-intercalation. It also offers a path to control Tc and Hc in Fe3GeTe2 by manipulating the external magnetic coupling within the inter-layer ferromagnetic system, which is promising for the development of spintronic devices.