Since Geim and Novoselov initially reported [1] the successful fabrication of graphene by the transparent tape exfoliation technique in 2004, there has been a continuous attempt to identify two-dimensional (2D) materials with superior characteristics. In the realm of contemporary materials research, atomic-level thickness layered van der Waals materials are suitable as a broad class of materials with excellent physical properties [2], and they are now gaining popularity among scientists. The van der Waals force interaction within the interlayer of layered 2D materials is a typical weak coupling interaction. In particular, with the discovery of boronene [3], MoS₂ [4], and black phosphorus [5], single or multiple-layer 2D layered materials, the interest in 2D semiconductor layered materials, and their relative heterostructures have been intensively studied. Yet, another essential attribute of materials, magnetic properties, has been of interest and is absent from many 2D van der Waals materials. For example, graphene [6], a band-gapless, nonmagnetic 2D material, impedes its employment in spintronic devices. Hence, researchers are hopeful of discovering a series of 2D stacked magnetic materials.

Low-dimensional ferromagnetic semiconductors are urgently required to construct the next-generation of nanoscale spintronic devices. In recent years, there are some 2D half-metallic materials, for example, monolayer Mxene [7, 8] and multiferroic nanosheets ACr₂S₄ [9] (A = Li, Na, K Rb). The transition-metal trichalcogenides (TMTC), another class of typical layered van der Waals materials that possess both magnetic properties and a unique layered structure, have also attracted the interest of the public [10]. They are coupled between layers by weak van der Waals interactions; for instance, MnPS₃ has excellent physicochemical properties and is easy to prepare [11, 12]. In addition, the materials of this structure display diverse electronic properties, some as semiconducting and others as insulating, and they also have unique magnetic properties. As a potential candidate for 2D magnetic layered van der Waals materials, it has become the focus of recent research. In particular, as a member of the family of layered van der Waals materials, crystalline Cr-based transition metal trichloride has attracted significant interest. For example, the Curie temperature of CrSiTe₃ [13], one of the transition metal trisulfide materials, increases as the number of layers decreases. It is reported to be a well-known 2D ferromagnetic [14] semiconductor because both the block and monolayer exhibit different magnetic ground states. In addition, it has been reported [15] that the Curie temperature of CrI₃ is 45 K. Being a multilayer van der Waals insulator, its Curie temperature drops as the number of layers reduces, and it is also regarded as an excellent 2D ferromagnetic material. In recent years, Cr₂Ge₂Te₆ has also been selected by researchers because of its van der Waals geometry, intrinsic ferromagnetism, and higher Curie temperature than CrI₃. It has been stated [16] that V. Carteaux produced the first bulk of Cr₂Ge₂Te₆ in 1995. In 2017, a ferromagnetic monolayer, Cr₂Ge₂Te₆, with a Curie temperature of 61 K, in experimental, was exfoliated [17]. 2D layered Cr₂Ge₂Te₆ [18] of novel electronic, magnetic, optical, optoelectronic, piezoelectric, and thermoelectric properties are easily compatible with nanoelectronic devices. It was even reported [17] that ferromagnetism exists in the new Cr₂Ge₂Te₆ atomic layer and that the Curie temperature can be easily regulated by modulating the applied magnetic field. This finding suggests Cr₂Ge₂Te₆ is an ideal candidate for the study of 2D magnetic phenomena and spintronic device materials. On the other hand, the focus of research on this type of 2D layered van der Waals magnetic materials will also significantly advance our understanding of the magnetic properties of low-dimensional materials, which, when combined with their rich electronic and optical properties, will open up numerous application possibilities for 2D magnetoelectric and magneto-optical applications.

In particular, research on intrinsically magnetic semiconductors with high Curie temperatures, large band gaps, and high carrier mobility is of extraordinary significance for developing the next-generation of ultra-miniaturized, highly integrated spintronics and magneto-optics devices. Nevertheless, it is challenging to have long-range ordered ferromagnetic and semiconducting properties in 2D materials [19], thus hoping that the substrate material can be tuned by some conventional modifications to produce magnetic properties. In the past decades, many modifications, such as magnetic doping [20], nonmagnetic doping [21], or hole doping [22], have been used in an attempt to introduce long-range ordered ferromagnetic sequences in semiconductors. Functional adsorption is one of the most traditional techniques to modulate the electronic and magnetic properties of the material effectively. Many efforts have previously been devoted to studying metal atom interactions in 2D materials inducing magnetic for applications in spintronics. Particularly, graphene-like 2D materials interact with magnetic atoms to produce half metal, and this modulation has been considered as an effective and interesting means of application to spintronics. Some theoretical studies have shown that the adsorption of metal atoms on the graphene sheets significantly increases the Curie temperature up to 438 K [23]. The adsorption of transition metal atoms on the surface of black phosphorus also effectively modulates its electronic and magnetic properties [24]. It was reported that a strong orbital coupling between GaSe monolayer and transition metals was found to produce 100% spin-polarized currents [25]. A recent study also found that monolayer Cr₂Ge₂Te₆ nanosheet interacted with alkali metals, enhancing their ferromagnetism and exhibiting half-metallic properties [26]. Therefore, the combination of 2D layered van der Waals materials, intrinsic ferromagnetism, half-metallic properties, and adsorption will likely provide a good platform for applying new low-dimensional magnetic materials in the field of spintronics.

Using first-principles calculation, we want to examine the electronic and magnetic properties of 3d transition metals adsorbed on monolayer Cr₂Ge₂Te₆ nanosheet. We found that 3d transition metals adsorbed on the substrate Cr₂Ge₂Te₆ significantly change the magnetic moments of the system. Except for Ti and Cr adsorbed, the Curie temperature of the adsorption system (TM = Sc, V, Mn, Fe, Co, Ni, Cu, and Zn) is significantly enhanced by a factor of two, with an enhancement of Curie temperature increasing rate over to 200%. Based on the optimized structure of the adsorbed system, we analyzed the geometry, electronic structure, spin density of states, magnetic moments, and Curie temperature of the ten-absorbed system for first-principles calculation. We found that the adsorption energy changes significantly as the 3d transition metal is adsorbed at different positions. The degree of interaction between the transition metal atoms and monolayer Cr₂Ge₂Te₆ significantly differs at different adsorption positions. We also found that the 3d transition metals change the electronic properties of the absorbed system, especially Cr₂Ge₂Te₆@Ti and Cr₂Ge₂Te₆@Fe become metallic. At the same time, the Sc, V, Co, Ni, and Cu absorbed systems show half-metallic. In addition, we found that the adsorption of 3d transition metals can significantly increase the Curie temperature of the system. Therefore, the present study reveals that the monolayer Cr₂Ge₂Te₆ can change its electronic structure and magnetic properties by adsorption of 3d transition metal atoms, thus predicting the unlimited application prospects of monolayer 2D Cr₂Ge₂Te₆ ferromagnet in the next-generation of functional spintronic devices.

Our density functional theory (DFT) calculations were performed using Vienna ab initio Simulation Package [27, 28]. The projector augmented wave formalism (PAW) [29, 30] describes the ion-electron potential. The exchange of correlation functions during the simulations is mainly handled by the generalized gradient approximation (GGA) [31] and is parameterized by the Perdew-Burke-Ernzerhofer (PBE) parameterization. Projection-enhanced wave functions have also been used to describe the electron-ion potential [27, 32]. The kinetic cut-off energy of the plane wave basis group is set as 400 eV. We set the condition of full convergence at ion relaxation as long as the total energy is less than 10^–5 eV and the force on each atom is less than 0.01 eV/Å when the lattice constant, as well as the atomic positions, will be the most stable state of complete relaxation. To eliminate the interaction between periodic boundaries, we simulated the properties of the monolayer Cr₂Ge₂Te₆ using a 20 Å thick slab model in the z-direction. In addition, to fully characterize the van der Waals interactions between the adsorbed 3d transition metal and the monolayer Cr₂Ge₂Te₆, a DFT-D3 correction method [33, 34] with the Grimme scheme is used to perform the whole system study calculations. We adopted the 2 × 2 supercell structure for monolayer Cr₂Ge₂Te₆ with one transition metal. Besides, the Brillouin zone k-point mesh of 3 × 3 × 1 is used for optimizing, and a denser 8 × 8 × 1 k-point mesh is used for electronic structure computations. Here, we analyzed these results by utilizing the PBE + U functional to describe the high correlations between the electrons in the d shell. The on-site interactions U e f f are represented by the equation, U e f f = U − J , where U and J stand for the on-site Hubbard Coulomb and exchange parameters, respectively. U has been assigned values of 3.00 eV for Cr and 2.50 eV for other 3d transition metal atoms, respectively [35–38]. The values of J have been set to be 0.90 eV for Cr and 0.00 eV for 3d transition metals [39, 40]. Additionally, we computed the band structure of the monolayer Cr₂Ge₂Te₆ in a unit cell with and without the PBE + U. The Monte Carlo (MC) simulation based on the Ising model [41] was used to estimate the Curie temperature of the monolayer Cr₂Ge₂Te₆ and single-layer Cr₂Ge₂Te₆ absorbed transition metals.

It is known from previous studies [42] that there is a large van der Waals gap in the structure of bulk Cr₂Ge₂Te_6, and the interlayer interactions are pretty weak, so it is possible to extract 2D Cr₂Ge₂Te₆ nanosheet by experimental peeling. Therefore, before studying the adsorption of transition metal atoms by the substrate monolayer Cr₂Ge₂Te₆, we first investigated the structural, electronic, and magnetic properties of the monolayer Cr₂Ge₂Te₆. Supplementary Figure S1A shows the top and side views of a monolayer Cr₂Ge₂Te₆ supercell (2 × 2). Cr₂Ge₂Te₆ is a hexagonal lattice structure. Each layer can be considered an octahedral CrTe₆ at the edge of the hexagonal lattice and a Ge dimer in the center [43]. After structural optimization, there are 40 atoms in the supercell (2 × 2) with lattice constants of a = b = 13.65 Å, α = 120°, and a bond length of 2.78 Å between the Cr atom and the nearest neighboring Te atom. Our calculated results are in agreement with previous literature [18]. The spin-polarized band structure shown in Supplementary Figure S1B explains the electronic properties of monolayer Cr₂Ge₂Te₆. It reveals that the monolayer Cr₂Ge₂Te₆ is a semiconductor whose band gap in the spin-down channel is indirect, with the valence band in the Γ point being the top of the valence band (VBM) and the bottom of conduction band (CBM) located in the Κ point, and the value of band gap in the spin-down channel is 0.52 eV; In the spin-up channel, we can see that the VBM is located at Γ point, while the CBM is located between K point and M point, and its indirect band gap value is 0.31 eV, which is consistent with the results of the literature [18, 44]. Supplementary Figure S1C shows the total density of states of the monolayer Cr₂Ge₂Te₆. We can see that near the Fermi surface, both the conduction band and the valence band are asymmetric in both spin channels, and the VBM in the spin-up channel is closer to the Fermi surface than its VBM in the spin-down energy band, while the CBM in the spin-up channel is closer to the Fermi surface than that in the spin-down channel, which also indicates that both the conduction band and the valence band edges near the Fermi surface are fully spin-polarized. Thus the band gap in the spin-up channel is smaller than that in the spin-down channel, implying that Cr₂Ge₂Te₆ is a bipolar magnetic semiconductor [45]. In addition, the contribution of the Cr atom in the spin-up is significantly larger than that in the spin-down, while the density of states of Te atoms is in the conduction band, where the electronic density of states in the spin-up is significantly larger than that in the spin-down. In addition, the valence band edge is mainly contributed by Te atoms, and at the conduction band edge, it is contributed primarily by Cr and Te atoms [18]. The spin polarization at the Fermi surface is also caused by the interaction between Cr and Te atoms. The valence band top is occupied by the p orbital of the Te atom, while the hybridized orbital of the d orbital of the Cr atom and the p orbital of the Te atom occupies the conduction band bottom.

To confirm the magnetic ground state of the most stable monolayer Cr₂Ge₂Te₆ nanosheet, we have calculated two different magnetic configurations for monolayer Cr₂Ge₂Te₆ nanosheet, i.e., ferromagnetic (FM) and antiferromagnetic (AFM) states. The energy difference (∆E) is defined as the difference between the energy of AFM and FM per cell, that is ∆E = E _AFM −E _FM , where E A F M and E F M represent the total energy of the antiferromagnetic Cr₂Ge₂Te₆ and the ferromagnetic Cr₂Ge₂Te₆ nanosheet. ∆E = 55.25 meV, showing that a 2D Cr₂Ge₂Te₆ has a higher energy per unit cell in AFM than in the FM state, which is more stable than in the AFM state. In addition, the literature [46] reported that the magnetic properties of Cr₂Ge₂Te₆ are mainly derived from the local magnetic moments on the Cr atomic sites; therefore. After calculations, we obtained the magnetic moment of the monolayer Cr₂Ge₂Te₆ as 24.00 µ_B, and the magnetic moment of each Cr atom is about 3.37 µ_B. This result is consistent with the literature [47]. We used Monte Carlo simulations to obtain the Curie temperature of the monolayer Cr₂Ge₂Te₆. The Monte Carlo simulation calculates the monolayer Cr₂Ge₂Te₆ nanosheet with a supercell of 20 × 20 × 1 to minimize the periodic reduction constraint. Each simulation was cycled for at least 10⁵ steps to ensure the overall structure reached equilibrium at each temperature. As shown in Supplementary Figure S1D, the magnetic moment of the monolayer Cr₂Ge₂Te₆ start to decrease sharply at about 87 K. indicating a Curie temperature of about 87 K for the monolayer Cr₂Ge₂Te₆ nanosheet.

Previous work has shown [18] that low-dimensional materials are sensitive to external stimuli, which helps us investigate the adsorption system’s fundamental properties. After studying the electronic properties and magnetic properties based on monolayer Cr₂Ge₂Te₆, we selected transition metal (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) atoms and monolayer Cr₂Ge₂Te₆ nanosheet for the analytical study of the adsorption mechanism. Studying this class of transition metal adsorption will be a good guide for applying 2D magnetic materials in spintronic devices. We selected 2 × 2 supercell monolayer Cr₂Ge₂Te₆ as substrates for the adsorbing 3d transition metals from Sc atoms to Zn atoms sequentially. To find the most favorable adsorption sites, as shown in Figures 1A–C, we considered three locations where the monolayer Cr₂Ge₂Te₆ nanosheet adsorb the transition metal atoms. They are positions A (Cr-top), B (Te-top), and C (Ge-top), respectively. The adsorption distance (d) is the distance between 3d transition metal atoms and the substrate surface atoms, as shown in Figure 1D. To evaluate the interaction between the substrate and 3d transition metals, we calculated the adsorption energy of the adsorption system. We used the adsorption energy to describe the absorption stability with the following equation: E a d s = E C r 2 G e 2 T e 6 @ T M − E C r 2 G e 2 T e 6 + E T M , where, E C r 2 G e 2 T e 6 @ T M , E C r 2 G e 2 T e 6 , and E T M are the total energy of 3d transition metal deposited on the monolayer Cr₂Ge₂Te₆ and the energy of the bare monolayer Cr₂Ge₂Te₆ and 3d transition metal, respectively. According to the definition, it is evident that when the value of adsorption energy E a d s is greater, then the more robust the interaction between 3d transition metal and monolayer Cr₂Ge₂Te₆, the more stable adsorption of the transition metal. After structural relaxation and static calculations for the structures of the monolayer Cr₂Ge₂Te₆ adsorbing transition metal at each of the three different sites, we obtained their respective adsorption energies E a d s and adsorption distances d.

Figure 2A shows the calculated adsorption energy at three positions after complete structural relaxation. All adsorption energies at all positions are negative, except for the Cr adsorbed at the Cr-top position and Ti atoms adsorbed at the Ge-top site. The adsorption energies are negative, indicating that this reaction is exothermic, suggesting the monolayer Cr₂Ge₂Te₆ can adsorb transition metals at three different positions, indicating that these adsorption systems are stable. Still, the interaction strength between the transition metal and the substrate differs from 3d transition metals. For the adsorption of Mn and Zn, there is no significant difference in the adsorption energies at the three different sites. Still, the adsorption energy of the Cr₂Ge₂Te₆@Mn fluctuating between −0.55 and −0.66 eV, is larger than that of the Cr₂Ge₂Te₆@Zn, indicating that the interaction strength in Cr₂Ge₂Te₆@Mn is stronger than that of the Cr₂Ge₂Te₆@Zn. For the systems adsorbed Sc, Ti, V, Cr, Fe, Co, Ni, and Cu, their adsorption energies significantly changed at different adsorption positions, implying the strength of interaction between 3d transition metals and the substrate was quite different. Similarly, from Supplementary Table S1, the adsorption distances of 3d transition metals adsorbed at different positions have significantly different variations. Cr₂Ge₂Te₆@Sc has relatively high adsorption energy, indicating a strong interaction between the Sc atoms and the substrate. However, for the Cr₂Ge₂Te₆@Zn, the adsorption distance fluctuates around 2.92 Å. In contrast, the adsorption energies at all three positions are small and almost negligible, indicating minimal interaction between the Zn atoms and the substrate material. On the other hand, for the adsorption systems of Ti, V, Cr, Mn, Fe, Co, Ni, and Cu, the adsorption distance and adsorption energies obviously differ significantly at three different positions. For example, for the Cr₂Ge₂Te₆@Fe, we found that the value of the adsorption energy −1.65 eV at the Cr-top position is considerably larger than that of −0.39 eV at the Te-top position. At the same time, its adsorption distance of 1.20 Å is much larger than that of 2.79 Å at the Te-top position, indicating that the adsorption of Fe atoms at the Cr-top position is more stable than that at the Te-top position. More stable the absorption and their interactions are stronger.

We can determine the best adsorption site based on the minimum adsorption energy after structural relaxation. In Cr₂Ge₂Te₆@Fe, Co adsorbed at the Te-top position was significantly shifted and moved above the Cr atom, so the best adsorption site for the transition metal Co is at the Cr-top position. Similarly, we found that the Zn also moved from the Te-top site to the Ge-top site, so the best adsorption site for Zn is at the Ge-top position. Also, Cr₂Ge₂Te₆@Ni has a similar trend, having the Te-top position as the adsorption site. As a result (shown in Supplementary Table S1, S2), three categories may be used to group the best adsorption site for the ten absorption systems. The optimum adsorption site for Ti, V, Fe, Co, and Cu is at the Cr-top position (A site); the best adsorption site for Cr and Ni is at the Te-top position (B site); and the best adsorption site for Sc, Mn, and Zn is located at the Ge-top position (C site). Figure 2B shows the adsorption distance d at the best adsorption site. The Cr₂Ge₂Te₆@Zn has the smallest negative value of adsorption energy at −0.07 eV. As we all know, the outermost shell of the Zn atom is in an entire electron state. The Zn binds to the monolayer Cr₂Ge₂Te₆ through weak interaction, most likely as physical adsorption. Except for Zn absorbed, the E _ads values of the other absorption system are pretty large, ranging from −2.54 to −0.66 eV, indicating a strong bonding between 3d transition metals and the substrate. For Ti, V, Cr, Mn, Fe, Co, Ni, and Cu absorbed, the higher the negative values of the adsorption energy and, at the same time, the smaller their adsorption distance d, indicating strong bonding, most likely by chemical interaction. The adsorption energies of the adsorbed Sc and Ni atoms are the highest, reaching −2.14 and −2.54 eV, respectively, indicating that the bonding between Sc and Ni atoms and monolayer Cr₂Ge₂Te₆ is the strongest. For the adsorption system, the stability of 3d transition metal adsorption: Cr₂Ge₂Te₆@Ni > Cr₂Ge₂Te₆@Sc > Cr₂Ge₂Te₆@Co > Cr₂Ge₂Te₆@Cu > Cr₂Ge₂Te₆@V > Cr₂Ge₂Te₆@Fe > Cr₂Ge₂Te₆@Ti = Cr₂Ge₂Te₆@Cr > Cr₂Ge₂Te₆@Mn > Cr₂Ge₂Te₆@Zn. In addition, except for Sc, Ti, and V absorbed, the trend of adsorption energy change is consistent with the trend of its adsorption distance d change. In conclusion, by adsorbing 3d transition metals at various places, we determined that the optimal adsorption sites for various transition metals are situated at various locations. In general, the greater the negative value of their adsorption energy and the shorter the adsorption distance, the easier and stronger the mutual interaction between the substrate material and the transition metals.

Figure 3 depicts the spin-polarized band structure of the adhered nanosheet. As is evident, the transition metal has a considerable influence on the electronic structure of the monolayer Cr₂Ge₂Te₆ nanosheet of the substrate material. The half-metallic attribute of a material is that it exhibits metallic qualities and semiconductor or insulator properties for electrons with two distinct spin orientations. When the spin polarization rate is 100%, the material is half-metallic, meaning that the energy band in the spin-up channel is metallic while the energy band in the opposite spin direction is non-metallic. For Cr₂Ge₂Te₆@Sc, V, Cr, Co, Ni, and Cu, the spin-up energy bands cross the Fermi level showing the metallic. In contrast, the spin-down energy bands have band gaps, indicating that the spin-down energy bands are semiconducting in nature, suggesting that these systems become half metallic and supply 100% of the spin-polarized current due to their spin polarizabilities 100% at the Fermi level. For the half metallic adsorption systems, their corresponding half metallic gaps (E_g) were computed. The half metallic gap is the minimum between the lowest energy of spin-up (down) conduction bands in relation to the Fermi level and the greatest energy of spin-up (down) valence bands in absolute values. And the results showed that in the Cr₂Ge₂Te₆@Sc, V, Cr, Co, Ni, and Cu, half metallic gaps, E_g were 40.82, 121.14, 24.56, 100.78, 46.33, and 118.06 meV, indicating the half metallic of these adsorption systems is relatively stable. For the Cr₂Ge₂Te₆@Sc (Figure 3A), the spin-down channel retains the band structure of the pristine Cr₂Ge₂Te₆. The substrate material has acquired electrons because the spin-up energy band is heavily hybridized, and its conduction band is moved downward relative to intrinsic Cr₂Ge₂Te₆. With Cr₂G₂Te₆@V and Co, the spin-down exhibits a similar pattern; the spin-down energy band is visibly moved down relative to the intrinsic Cr₂G₂Te₆, and the spin-up is evidently annihilated, showing that 3d transition metal and the substrate have a strong interaction. As shown in Figures 3B, F, the Cr₂Ge₂Te₆@Ti and Fe have similar energy band structures, but their spin-up energy bands are more severely destroyed, indicating more intense energy band hybridization. Both the spin-up and spin-down energy bands exhibit metallic properties with conductivity, indicating the transition from semiconducting to metallic of the system. In the Cr₂G₂Te₆@Mn (Figure 3E), although the spin-down and spin-up valence bands preserve most of the intrinsic energy bands, the conduction bands exhibit notable change, suggesting that the Mn interacts with the substrate quite significantly. Yet, both spin-up and spin-down energy bands preserve the semiconductor character, with a very narrow band gap of 0.07 eV and 0.65 eV, respectively, showing that the entire system offers the semiconducting. Cr₂G₂Te₆@Zn (Figure 3J) preserves the intrinsic Cr₂G₂Te₆ energy band in both the spin-down and spin-up energy bands, indicating a very weak interaction and monolayer Cr₂G₂Te₆. It still exhibits semiconducting, with a band gap of about 0.18 eV in the spin-up and 0.48 eV in the spin-down. We also find that the energy band is slightly shifted downward, showing that Cr₂G₂Te₆ receives electrons. Hence, monolayer Cr₂G₂Te₆ energy bands are significantly hybridized with 3d transition metal except for Zn absorbed. As such, according to the interaction between the transition metal and the substrate material, it can be divided into four categories: half metal (Cr₂Ge₂Te₆@Sc, Cr₂Ge₂Te₆@V, Cr₂Ge₂Te₆@Cr, Cr₂Ge₂Te₆@Co, Cr₂Ge₂Te₆@Ni, and Cr₂Ge₂Te₆@Cu); metal (Cr₂Ge₂Te₆@Ti and Cr₂Ge₂Te₆6@Fe); semiconductor (Cr₂Ge₂Te₆@Mn and Cr₂Ge₂Te₆@Zn).

After that, we investigate the density of states of the adsorbed system, shown in Supplementary Figure S2. It should come as no surprise that the density of states is found to be asymmetric. In Cr₂Ge₂Te₆@Sc, the spin-up energy band near the Fermi level comes mostly from the 3d orbitals of Sc and partially from the 3d orbitals of Cr. In Cr₂Ge₂Te₆@V, the density of states near the Fermi energy level is predominantly provided by the 3d orbitals of V. Moreover, a portion of the density of states comes from the 3d orbitals of the Cr atom that is close as well as the p orbitals of the Ge atom. It should be noted that the formation of half metal in Cr₂Ge₂Te₆@Co and Cu is exactly the same as in Cr₂Ge₂Te₆@V. In contrast, the half-metallic of Cr₂Ge₂Te₆@Ni is mostly due to the contribution of the 3d orbitals of Cr. Notably, Cr₂Ge₂Te₆@Cr exhibits half-metallic properties, mainly coming from the d orbitals of the Cr in the substrate. Its VBM in the spin-down channel results from the hybridization of the 3d orbitals of both the substrate and the adsorbed Cr and the p orbitals of the Ge atom. In Cr₂Ge₂Te₆@Ti and Fe, their metallic properties are mainly derived from the mutual hybridization between the Cr 3d orbitals, the Ge p orbitals, and the transition metal 3d orbitals. In both Cr₂Ge₂Te₆@Mn and Cr₂Ge₂Te₆@Zn, the conduction band bottom and valence band top at the Fermi plane are mainly contributed by the 3d orbitals of Cr atoms and partly by the p orbitals of Ge.

In order to get a comprehensive comprehension of the shifts in charge transfer that occur between 3d transition metals and monolayer Cr₂Ge₂Te₆, we carried out the differential charge density, as shown in Figure 4. We discovered that, with the exception of the charge that was transferred between the Zn and the monolayer Cr₂Ge₂Te₆, which was a very small amount, there was a large charge transfer in all of the other absorption systems. In addition, we used Bader charge [48] analysis to investigate the flow and magnitude of transferred charge between 3d transition metals and the monolayer Cr₂Ge₂Te₆. As shown in Supplementary Table S2, there is almost no charge transfer between Zn atom and the substrate, exactly in agreement with Figure 4J, indicating that the substrate material and transition metal interact weakly, matching the bandstructure (Figure 3J) and the very small adsorption energy (−0.07 eV). The charge transferred between Co and monolayer Cr₂Ge₂Te₆ is significantly more than that transferred in Cr₂G₂Te₆@Zn, as shown in Figure 4G. And the loss of charge accumulates near the Co, while the accumulation of charge clearly occurs at the surface of the monolayer Cr₂Ge₂Te₆, as well as slightly partial charge accumulation in the intermediate Cr atomic layer, indicating that strong chemical interaction between the Co atoms and monolayer Cr₂Ge₂Te₆, and a roughly 0.21 e loss of Co by Bader analysis. Furthermore, the charge transfer that occurs between Sc, Ti, V, Mn, Fe, and Cu and monolayer Cr₂Ge₂Te₆ is even much stronger, with charge loss occurring clearly around the 3d transition metals and charge accumulation apparently still present in the adsorbed intermediate region as well as around the surface and interlayer of monolayer Cr₂Ge₂Te₆. This suggests that the connection between the transition metals Sc, Ti, V, Mn, Fe, and Cu atoms and monolayer Cr₂Ge₂Te₆ is relatively robust and most likely involves chemisorption. Furthermore, in the Cr₂Ge₂Te₆@Cr and @Ni systems, the loss of charge occurs mainly around 3d transition metals, and electron accumulation is evident not only at the surface atoms of monolayer Cr₂Ge₂Te₆ but also more very evident on the Cr atom of the intermediate layer, suggesting equally strong hybridization in the absorbed system. In accordance with the Bader charge analysis, we conduct quantitative research to determine the magnitude of the charge that is transmitted from the transition metal to the single layer Cr₂Ge₂Te₆. We discover that the number of transferred charges between Zn and monolayer Cr₂Ge₂Te₆ is very low, coming in at just 0.04 e, which suggests that the interaction between Zn and the substrate is relatively weak. Strong contact exists between monolayer Cr₂Ge₂Te₆ and the remainder of the 3d transition metals. The substrate Cr₂Ge₂Te₆ function as an acceptor to take up the lost electrons by the 3d transition metals. Just shown in Supplementary Table S2, the number of electrons transferred from Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu to monolayer Cr₂Ge₂Te₆ is 0.76, 0.65, 0.83, 0.71, 0.64, 0.40, 0.21, 0.54, and 0.39 e, respectively, indicating a significant increase in the number of charges transferred. This result lines up perfectly with the findings about the adsorption energy.

After that, we began to investigate how the adsorption of three-dimensional transition metals might affect the magnetic properties of a single layer of Cr₂Ge₂Te₆. In order to investigate the magnetic ground state of the monolayer Cr₂Ge₂Te₆ adsorbed with 3d transition metals, we took into account the four magnetic states that are depicted in Figures 5A–D. These states are, in order, ferromagnetic state, Néel-antiferromagnetic state, Stripy-antiferromagnetic state, and Zigzag-ferromagnetic state, respectively. As can be seen in Table 1, the ferromagnetic state is significantly lower after the adsorption of 3d transition metal compared to the other three magnetic states. This suggests that the monolayer Cr₂Ge₂Te₆ absorbed with 3d transition metals is still relatively resistant in the ferromagnetic state. The ferromagnetic state is unaffected by the adsorption of 3d transition metals since it is an intrinsic magnetic state of the monolayer Cr₂Ge₂Te₆. In addition, we defined the energy difference between the Néel-antiferromagnetic and ferromagnetic states as ∆E ₁: ∆ E 1 = E N e e l − A F M − E F M (1) where E (Neel-AFM) and E F M are the total energy of the absorbed system in the Néel-antiferromagnetic state and in the ferromagnetic state of the adsorbed transition metal, respectively. The energy difference of the ten absorbed systems is 1.50, 0.18, 0.41, 0.21, 0.52, 0.32, 0.33, 0.32, 0.37, and 0.34 eV, respectively. Clearly, there is a significant rise in the energy differences for adsorbed 3d transition metals. In an example, the energy difference of Cr₂Ge₂Te₆@Sc is about 1.50 eV, which is more than six times greater than the energy difference (∆E ₁ = 221.01 meV) of the pristine monolayer Cr₂Ge₂Te₆. Because of this, the results above indicate that the ferromagnetic state is the most stable for the absorbed system. Furthermore, the ferromagnetic state of the absorbed system is noticeably more stable when compared to the ferromagnetic state of the monolayer Cr₂Ge₂Te₆.

In the ferromagnetic state, the supercell 2 × 2 monolayer Cr₂Ge₂Te₆ with 8 Cr atoms, is expected to have a total magnetic moment of 24.00 µ_B. Furthermore, we calculated the magnetic moments of Cr near the optimal adsorption site (denoted by M_Cr) and the magnetic moments of the transition metals in the Cr₂Ge₂Te₆@TM adsorption system (represented by M_TM) separately. The findings are presented in Figure 5E. From Table 1, we can see that when 3d transition metals are absorbed, the magnetic moments of Cr near the optimal adsorption site do not vary, mainly in the range of 3.33–3.58 µ_B, which is significantly higher than 3.37 µ_B for monolayer Cr₂Ge₂Te₆. Among them, with the adsorption of V and Cu, the M_Cr reached a maximum of 3.58 µ_B; however, the M_Cr changed the least after adopting Mn, coming to 3.33 µ_B. On the other hand, we calculated the magnetic moments M_TM of the transition metals in the Cr₂Ge₂Te₆@TM adsorption system. And the results showed that from Sc to Zn atoms, the magnetic moments M_TM were 1.78, 1.88, 2.97, 3.34, 4.83 4.83, 2.86, 1.85, 0.11, 0.00和0.00 µ_B. The results are consistent with the results of Supplementary Figure S3. The 3d transition metals affect the magnetic properties of the adsorption system. In addition, we also calculated the total magnetic moments for the ten absorbed systems, as shown in Figure 5E. We discovered that the total magnetic moment first goes through an increase, then slightly decreases after the Cr adsorption, and then continues to increase again after Fe adsorption, all the way to the Zn, where the total magnetic moment falls; however, the decrease in the total magnetic moment for the Ni atom adsorption is greater than that for Cu atom adsorption. As we all know, the 4s orbitals from Sc to V are full of electrons, and the outermost 3d orbitals are unfilled with the number of electrons 3.00, 4.00, and 5.00 e. The total magnetic moments of the Cr₂Ge₂Te₆@Sc, Ti, and V systems are all integers, rising to 27.00, 28.00, and 29.00 µ_B in that sequence. This may be explained by the fact that the number of electrons in the outermost layer is connected to the total magnetic moments. When the Sc is absorbed, the total magnetic moments of Cr₂Ge₂Te₆@Sc increase by 3.00 µ_B, which coincides with the number of 4 s, 3d orbital electrons. In addition, from Mn to Co, the 4 s orbital is full of electrons, and the outermost 3d orbital is unfilled, with 5.00, 6.00, and 7.00 e, respectively. The total magnetic moments of the adsorbed systems of Cr₂Ge₂Te₆@Mn, Cr₂Ge₂Te₆@Fe, and Cr₂Ge₂Te₆@Co are also integers, decreasing linearly from a magnetic moment of 29.00 µ_B–27.00 µ_B, which is also related to the number of electrons in the outermost 3d orbitals. As we all know, the outermost 3d orbitals of Mn are arranged in 5.00 e. When Mn is adsorbed, the total magnetic moment of the Cr₂Ge₂Te₆@Mn reaches 29.00 µ_B. This is precisely 5.00 µ_B more than the total magnetic moment of the monolayer Cr₂Ge₂Te₆ without the adsorbed transition metal, which is 24.00 µ_B. This is due to the fact the outermost 3d orbitals of Mn have five unpaired electrons. Compared to 24.00 µ_B of the monolayer Cr₂Ge₂Te₆, the total magnetic moment of the Cr₂Ge₂Te₆@Fe is 28.00 µ_B, an increase of 4.00 µ_B. This can be interpreted as the Fe has 6 electrons in the outermost 3d orbitals but only 4 unpaired electrons. Compared to 29.00 µ_B for the Cr₂Ge₂Te₆@Mn, the total magnetic moment of the Cr₂Ge₂Te₆@Fe is reduced by 1.00 µ_B, and the total magnetic moment of the Cr₂Ge₂Te₆@Co adsorption system is reduced to 27.00 µ_B, which is likely to be the same reason. Since the 3d orbital of Cu is in the full electron state and the 4 s orbital is half full with only one electron, the total magnetic moment of the Cr₂Ge₂Te₆@Cu increases to 25.00 µ_B. Compared to 24.00 µ_B for a single layer of Cr₂Ge₂Te₆, the total magnetic moment of the Cr₂Ge₂Te₆@Cu increases by only 1 µ_B. Obviously, the magnetic moment of Zn, whose outermost 3d orbitals are in the full electron state, is zero; hence the total magnetic moment of the Cr₂Ge₂Te₆@Zn does not change.

On the other hand, we estimate the density of states of Cr₂Ge₂Te₆@TM shown in Figure 6. The total magnetic of the adsorption system is greater, the more asymmetric the spin-polarized density of states. It is noticeable that the spin-polarized density of states asymmetry becomes more and more pronounced with the absorption of Sc and V, indicating that Cr₂Ge₂Te₆@V has a greater total magnetic moment than that of Cr₂Ge₂Te₆@Sc. Similarly, the Cr₂Ge₂Te₆@Mn has a greater spin-polarized density of states asymmetry than the Cr₂Ge₂Te₆@Cu system, indicating a bigger total magnetic moment. While the asymmetry of the spin-polarized density of states of Cr₂Ge₂Te₆@Ni and Cr₂Ge₂Te₆@Zn is significantly weaker, so the total magnetic moments of these two transition metal adsorption systems are also the smallest. In order to investigate more progressively the origin of the total magnetic moment and magnetism of Cr₂Ge₂Te₆@TM, we also calculated the spin density distribution by the following equation: Δ ρ = ρ ↑ − ρ ↓ (2)

Where Δ ρ is the spin density of Cr₂Ge₂Te₆@TM, ρ ↑ is the spin density in spin up and ρ ↓ is the spin density of spin down. Supplementary Figure S3 shows that the total magnetic moment mainly comes from the Cr of monolayer Cr₂Ge₂Te₆ and partly from the adsorbed 3d transition metals. In Cr₂Ge₂Te₆@Sc, Ti, V, Cr, Mn, Fe, and Co, the total magnetic moment mainly comes from transition metals; while for the adsorbed Ni, Cu, and Zn, the total magnetic moment is mainly derived from the Cr distribution of monolayer Cr₂Ge₂Te₆. This result also agrees with the M_TM results of previously calculated transition metal magnetic moments.

In spintronic devices, the Curie temperature influences the transition temperature from ferromagnetic to paramagnetic and the stability of the ferromagnetic sequence. Calculating the Curie temperature of each adsorption system using Monte Carlo simulation is the next step to directly evaluate whether the ferromagnetic state coupling of the adsorbent system is improved. According to the literature [49, 50], based on the energy difference calculated above and Ising model simulations, we obtain the following expression for the spin exchange parameter J, J = Δ E 1 2 N Z S 2 (3) where N represents the number of magnetic atoms, Z represents the number of nearest neighbor magnetic atoms of Cr atoms, and ∆E ₁ is the energy difference between the Néel-antiferromagnetic and ferromagnetic states that we calculated earlier. As shown in Figure 5F, the Curie temperatures of Cr₂Ge₂Te₆@Ti and Cr are slightly lower, around 150 K, while the Curie temperatures of other transition metal adsorption systems typically exceed 200 K. However, compared to that of the monolayer Cr₂Ge₂Te₆, the adsorption of 3d transition metals result in a significant increase in the Curie temperature of Cr₂Ge₂Te₆@TM and an improvement in the ferromagnetic coupling. According to the Goodenough-Kanamori rules [165,166], the ferromagnetic state coupling of monolayer Cr₂Ge₂Te₆ is the product of superexchange interaction and direct exchange interaction.

Since the bond length between Cr-Cr of the Cr₂Ge₂Te₆@TM system is relatively large, about 4.10 Å and the direct exchange interaction is mainly by the direct electron hopping of two adjacent Cr atoms showing the antiferromagnetic coupling, their direct exchange interaction is relatively weak. It is well knowledge that the superexchange contact will have a greater propensity to display ferromagnetic coupling. The superexchange interaction in the adsorbed system is generated by the Te atom acting as an intermediate anion. Since the bond angle of Cr-Te-Cr is mostly around 90°, this results in a more powerful superexchange interaction. Hence, the struggle between the two exchange interactions leads to the dominance of superexchange interactions in the adsorption system, which shows ferromagnetic coupling as a consequence. In view of this, the adsorption of 3d transition metals by the monolayer Cr₂Ge₂Te₆ leads to the enhancement of the ferromagnetic state. After that, we also define the Curie temperature increasing rate ε for the adsorption system by equation, ε = Τ c C r 2 G e 2 T e 6 @ T M − Τ c C r 2 G e 2 T e 6 Τ c C r 2 G e 2 T e 6 × 100 % (4)

According to our calculation, the Curie temperature enhancement ratio of Cr₂Ge₂Te₆@TM reaches 224%, 68%, 277%, 85%, 367%, 207%, 207%, 190%, 242%, and 224%, respectively. All adsorbed transition metals improved their Curie temperatures by a factor of 2, with the exception of Ti and Cr atoms, whose adsorption Curie temperature improvement was less than 100%, suggesting that transition metals may dramatically increase their Curie temperatures.

In addition, we study how the electric field modulates the electrical characteristics of the adsorption system. According to earlier research, the Cr₂Ge₂Te₆@Mn system is a semiconductor; thus, we choose this system as an example and apply a positive electric field, that is, an electric field directed from the Cr₂Ge₂Te₆ to the adsorbed atoms. We discovered that the application of an additional positive electric field has a considerable influence on the electronic properties of the Cr₂Ge₂Te₆@Mn, particularly the spin-polarized electronic states of the monolayer Cr₂Ge₂Te₆. The calculated projected spin-up and spin-down band structures of the Cr₂Ge₂Te₆@Mn adsorption system under 0.10 and 0.60 V/Å electric fields are shown in Figures 7A, B, respectively. After applying the electric field, the spin-up energy band extended all the way to the Fermi level, whereas the spin-down energy band remained semiconducting. This caused a spin-polarization current with a spin-polarization rate of 100% at the Fermi level. In addition, compared to the energy band of the intrinsic monolayer Cr₂Ge₂Te₆, the conduction band in the spin-up channel of Cr₂Ge₂Te₆@Mn moves increasingly downward with an increasing positive electric field, suggesting that as its magnitude increases, the electric field increasingly impacted the conduction band in the spin-up channel. Consequently, the applied positive electric field transforms Cr₂Ge₂Te₆@Mn from a semiconductor to a half-metal, suggesting that the applied electric field has a distinct benefit in managing the electronic and magnetic properties of the absorbed system. In other words, as seen in Figure 7C, the applied positive electric field causes more charges initially localized in a certain energy band to shift in relative positions. Once the energy band at these positions crosses the Fermi energy level under the influence of the electric field, the materials also transform into a half-metal, i.e., one spin-up electronic state moves downward across the Fermi plane, while the electric field has little effect on the other spin-down electronic state, thus achieving a modulation of the electronic and magnetic properties of the absorbed system.

In conclusion, based on first-principles calculation, the electronic and magnetic properties of the monolayer Cr₂Ge₂Te₆ absorbed with 3d transition metal atoms have been investigated. Based on the calculated absorption energy, equilibrium absorption distance, and charge redistribution, the monolayer Cr₂Ge₂Te₆ absorbed Zn via a weak interaction. At the same time, the rest of the 3d transition metals are fascinated with the substrate via a strong interaction. Our results show that Cr₂Ge₂Te₆@TM can possess different electronic properties. We found that the adsorption of Ti and Fe leads to a transformation from semiconductor to metal. While in Cr₂Ge₂Te₆@Sc, V, Co, Ni, and Cu, one of their spin energy bands appears to be metallic, the other spin energy band remains semiconductor, so the absorption realizes the changes from semiconductor to half metal. Furthermore, the ferromagnetic coupling is the most stable state in Cr₂Ge₂Te₆@TM, and their respective Curie temperatures are greatly enhanced by adsorption, demonstrating that adsorption may effectively boost the ferromagnetic state of monolayer Cr₂Ge₂Te₆. This relates to the outcome of the competition between direct exchange and superexchange. This research demonstrates a feasible method for not only modifying the electrical characteristics of the monolayer Cr₂Ge₂Te₆ but also enhancing their ferromagnetic stability. We are certain that this method can be experimentally achieved in the near future, which will considerably ease the deployment of CGT in nanoelectronic and spintronic devices.