Since the discovery of graphene,^[1–3] extensive interests in two-dimensional (2D) materials have been inspired. In recent years, a number of other 2D materials were discovered, such as honeycomb boron nitride,^[4] layered transition metal dichalcogenides,^[5] black phosphorus,^[6] and Mexene.^[7] The 2D materials exhibit a variety of intriguing electronic and magnetic properties such as quantum spin Hall effect,^[8] valleytronics,^[9] and ferromagnetism,^[7] which make the 2D materials promising for wide applications in the next-generation of electronic and spintronic devices.

In 2D systems, it was believed that the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin–Wagner theorem.^[10] However, magnetic anisotropy can counteract these thermal fluctuations and enable the long-range magnetic order. Recently, the 2D ferromagnetism has been demonstrated in Cr₂Ge₂Te₆ and CrI₃ monolayers,^[11,12] and the magnetic anisotropy comes from the anisotropic superexchange interaction and large spin–orbital coupling of the I atom.^[13] However, the Curie temperature (T_C) of Cr₂Ge₂Te₆ and CrI₃ monolayers is quite low (< 60 K), which hampers the practical applications in spintronic devices at room temperature. FeBr₃ monolayer with the same crystal structure as that of CrI₃ was predicted to have higher T_C ∼ 150 K,^[14] but it is still far below the room temperature. Recently, VSe₂ monolayer was discovered to possess strong ferromagnetic (FM) ordering above room temperature.^[15] Nevertheless, VSe₂ monolayer is metallic, which may cause extra energy dissipation of spintronic devices. Furthermore, all these materials belong to van der Waals crystals, so each monolayer is electronically saturated, which leads to weak interaction with the neighboring monolayers or substrate. For real applications, it is necessary to place the 2D FM materials on certain substrates, but the van der Waals interaction between the 2D FM materials and substrates makes the heterostructure unstable. Therefore, exploring new 2D FM materials which are semiconducting, have high T_C, and can chemically bind to a substrate is of both fundamental interest and application merit.

In this paper, we proposed a new family of 2D FM semiconductors combined with TaX (X = S, Se, or Te) monolayer and Al₂O₃(0001) substrate based on first-principles calculations. Analyses of the electronic structures reveal that the TaX monolayers are ferromagnetic with a spin moment of 3 μ_B and undergo a metal-to-insulator transition when they are placed on the Al₂O₃(0001) substrate. The induced band gaps are remarkable, ranging from 188 meV to 303 meV. Furthermore, the magnetic states near the Fermi energy are localized within the TaX monolayers and exhibit 100% spin polarization.

To model the Al₂O₃(0001) substrate, we constructed a slab with 18 atomic layers (thickness of ∼11Å), along with a vacuum of 15Å between adjacent slabs. Then we put a TaX (X = S, Se, or Te) monolayer on Al₂O₃(0001). The atomic structure and electronic properties were calculated with density functional theory (DFT) as implemented in the Vienna ab-initio simulation package.^[16,17] The interaction between the valence electrons and ionic cores was described within the framework of the projector augmented wave (PAW) method.^[18,19] The Perdew–Burke–Ernzerhof type generalized gradient approximation was used for the exchange–correlation potentials.^[20] The energy cutoff for the plane wave basis expansion was set to 500 eV. The 2D Brillouin zone was sampled by a 27 × 27 k-grid mesh. The atomic positions were fully relaxed with a criterion that requires the force on each atom to be smaller than 0.01 eV/Å.

As mentioned above, the VSe₂ monolayer is ferromagnetic with T_C above the room temperature. On the other hand, the spin–orbit coupling (SOC) leads to interesting phenomena in low-dimensional materials.^[21] Therefore, we choose TaX₂ (X = S, Se or Te) monolayers (see Fig. 1(a)), which are the isovalent counterpart of the VSe₂ monolayer and the SOC effect of the Ta-5d orbital is much stronger than that of the V-3d orbital. However, the TaX₂ monolayers are electronically saturated, so it has only a van der Waals interaction with the substrate. To activate the chemical activity of the TaX₂ monolayers, we remove one anion layer, resulting in buckled honeycomb structure TaX monolayers, as shown in Fig. 1(b). Then we place the TaX monolayers on Al₂O₃(0001) substrate, as shown in Fig. 1(c). Here, we choose the Al₂O₃(0001) surface as the substrate, because it is widely used as the substrate to support low-dimensional materials in experiments.^[22–24] Bulk Al₂O₃ is an insulator with a band gap of ∼9 eV, while the band gap of the Al₂O₃(0001) surface is reduced by about 1 eV due to the surface states.^[25,26] From the density of states in Fig. 1(d), the calculated band gap of Al₂O₃(0001) is 4.6 eV, which is smaller than the experimental value but close to the previous theoretical calculation result.^[27] It should be noticed that, in the experimental process of fabrication, the growth condition must be controlled delicately, so that the Ta layer grows on Al₂O₃(0001) first and then the X layer grows to form a honeycomb TaX monolayer.

Fig. 1.

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Fig. 1. (color online) The top view (top panels) and side view (bottom panels) of atomic structures of (a) TaX2 monolayer, (b) TaX monolayer, and (c) TaX/Al2O3. The blue, brown, purple, and red spheres represent Ta, X (S, Se, or Te), Al, and O atoms, respectively. d1, d2, and d3 denote the Ta–X, X–O, and Ta–Al bond lengths, respectively. Δh indicates the buckling distance of the TaX monolayer. (d) Density of states (DOS) of the Al2O3(0001) surface. The Fermi energy is set to be the zero point of energy.

We firstly study the properties of freestanding TaX monolayers. As listed in Table 1, the optimized lattice constant ranges from 3.1Å to 3.3Å. The Ta–Te bond length is significantly larger than the other two because of the larger atomic size of the Te atoms. The TaX monolayers keep buckling with buckling distances ranging from 1.65Å to 2.00Å, as listed in Table 1. All the TaX monolayers are magnetic and the magnetic moments are smaller than 1 μ_B. In addition, the magnetic moments increase slightly from TaS to TaTe, which may be attributed to the increasing lattice constants from TaS to TaTe. In addition, the TaX monolayers are metallic, as seen from the band structures in Fig. 2. For TaS and TaSe monolayers, there is a hole pocket at the M point in the majority spin channel, and an electron pocket between the M and Γ points in the minority spin channel. For the TaTe monolayer, the dispersions of the electronic bands near the Fermi energy (E_F) are much more complex than the other two cases, especially in the minority spin channel. Clearly, removing one anion layer from the TaX₂ monolayers induces spin polarization but retains the metallic character.^[28,29]

Fig. 2.

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	Fig. 2. (color online) Band structures of freestanding (a) TaS, (b) TaSe, and (c) TaTe monolayers. The black and red curves stand for bands in majority and minority spin channels, respectively. The horizontal dashed lines indicate the Fermi energy.

Table 1.

Table 1.

Table 1. The magnetic moments (MS in μB), Bader charges (ρ in e), and structural properties of freestanding and Al2O3(0001) supported TaX (X = S, Se, or Te) monolayers. a (in Å) indicates the lattice constant of the freestanding TaX monolayers. d1, d2, and d3 (in Å) denote the Ta–X, X–O, and Ta–Al bond lengths, respectively, as marked in Fig. 1. The lattice constants are adjusted to match those of Al2O3(0001) (4.76Å) when the TaX monolayers are placed on the substrate. The binding energy (Eb in eV) between the TaX monolayer and Al2O3(0001) is defined as Eb = E(TaX) + E(Sub) − E(TaX/Sub), where E(TaX), E(Sub), and E(TaX/Sub) are the total energies of freestanding TaX, pure Al2O3(0001) substrate, and the combined system, respectively. . Free standing On substrate a d1 Δh MS ρTa ρX d1 d2 d3 Δh MS Eb ρTa ρX TaS 3.10 2.43 1.65 0.88 –0.77 0.77 2.97 2.29 2.17 1.08 3 2.13 –1.33 1.56 TaSe 3.16 2.57 1.81 0.90 –0.61 0.61 3.02 2.29 2.32 1.25 3 1.88 –1.26 1.48 TaTe 3.31 2.77 2.00 0.94 –0.37 0.37 3.11 2.30 2.55 1.48 3 1.94 –1.16 1.36

Table 1. The magnetic moments (MS in μB), Bader charges (ρ in e), and structural properties of freestanding and Al2O3(0001) supported TaX (X = S, Se, or Te) monolayers. a (in Å) indicates the lattice constant of the freestanding TaX monolayers. d1, d2, and d3 (in Å) denote the Ta–X, X–O, and Ta–Al bond lengths, respectively, as marked in Fig. 1. The lattice constants are adjusted to match those of Al2O3(0001) (4.76Å) when the TaX monolayers are placed on the substrate. The binding energy (Eb in eV) between the TaX monolayer and Al2O3(0001) is defined as Eb = E(TaX) + E(Sub) − E(TaX/Sub), where E(TaX), E(Sub), and E(TaX/Sub) are the total energies of freestanding TaX, pure Al2O3(0001) substrate, and the combined system, respectively. .

When the TaX monolayers are placed on Al₂O₃(0001), the Ta atoms prefer the hollow sites comprised of three surface O atoms and the anion X atoms take the atop sites of the surface Al atoms, as shown in Fig. 1(c). Note that the lattice constant of Al₂O₃(0001) (4.76Å) is much larger than that of the freestanding TaX monolayers, so the substrate imposes a large extensive constraint on the TaX monolayers. Consequently, the Ta–X bond lengths increase significantly, and the buckling distances decrease obviously, as listed in Table 1. The Ta atoms bind strongly to the surface O atoms of Al₂O₃(0001), with short Ta–O bonds (∼2.3Å). In addition, the interactions between the anion X atoms and Al atoms are also quite strong, resulting in short X–Al bonds ranging from 2.17Å to 2.55Å. Obviously, the TaX monolayers are chemically stuck on the Al₂O₃(0001) substrate, which results in large binding energies around 2 eV as listed in Table 1. Therefore, the TaX monolayers are stable on the Al₂O₃(0001) substrate, and the combined system TaX/Al₂O₃(0001) could be regarded as an entire entity with the 2D FM states existing on the topmost layer.

It is instructive to see how the electronic and magnetic properties are modified by the Al₂O₃(0001) substrate. Firstly, we find that the magnetic moment increases to 3 μ_B for all cases, similar to the phenomenon found in other materials with epitaxial strain from the substrate.^[30,31] This can be attributed to the significant changes of the charge states of the Ta and X atoms as shown in Table 1. Clearly, based on the Bader charge division scheme,^[32] the Ta atoms loose more electrons and the X atoms gain more electrons compared to the situation in the freestanding monolayers. Consequently, the change of charge states leads to the change of magnetic states.^[33] Furthermore, the spin moments are mainly contributed by the Ta atoms, so the spin density distributes almost completely around the Ta atoms, as shown for the case of the TaTe/Al₂O₃(0001) in Fig. 3(a).

Fig. 3.

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Fig. 3. (color online) (a) Spin density of TaTe/Al2O3(0001) with cutoff of ±0.3 e/Å3. Top panel: parallel to the surface and crossing the Ta atoms; bottom panel: perpendicular to the TaTe monolayer and crossing one of the Ta–Te bonds. (b)–(d) Band structures of (a) TaS/Al2O3(0001), (b) TaSe/Al2O3(0001), and (c) TaTe/Al2O3(0001). The black and red curves stand for bands in majority and minority spin channels, respectively. The horizontal dashed lines indicate the Fermi energy.

Interestingly, all the TaX/Al₂O₃(0001) become semiconductors, as shown by the band structures in Figs. 3(b)–3(d), which indicates that metal-to-insulator transition is induced by the substrate. The band gaps are quite remarkable, 303.5 meV, 188.4 meV, and 235.4 meV for TaS/Al₂O₃(0001), TaSe/Al₂O₃(0001), and TaTe/Al₂O₃(0001), respectively. The TaS/Al₂O₃(0001) and TaSe/Al₂O₃(0001) have indirect band gaps, while TaTe/Al₂O₃(0001) is a direct-gap semiconductor. This difference originates from the different sizes of the anion atoms, which result in different bond lengths and buckling distances as listed in Table 1. Furthermore, the bands near E_F are completely from the majority spin channel, while the valence bands in the minority spin channel are far below the E_F and bring about a large band gap in the minority spin channel. Therefore, the carriers excited by temperature or from doping exhibit 100% spin polarization.

To reveal the atomic-orbital contributions to the band structures, we plot the projected density of states (PDOS) of the Ta-5d orbitals and X-s and X-p orbitals in Fig. 4. Because of the local C_3v symmetry (see Fig. 1(c)), the d orbitals split into three groups: d_xy/x²−y², d_xz/yz, and d_z², while the p orbitals split into two groups: p_x/y and p_z. From Fig. 4, it can be seen that the states within 1.5 eV below the E_F in the majority spin channel are contributed from all components of the Ta-5d orbitals, only with little contributions from the anion atoms. The states from 0.5 eV to 2 eV above the E_F in the majority spin channel originate from d_xy/x²−y² and d_xz/yz, and are dominated by the latter. Similarly, the states from 0 eV to 3 eV in the minority spin channel are also contributed from the Ta-5d orbitals. This is understandable because the Al₂O₃(0001) substrate is a wide-gap insulator, so its states are far way from E_F. Therefore, the spin current and electron current will localize within the TaX monolayers when the TaX/Al₂O₃(0001) systems are used in spintronic devices. This is a good feature to keep the currents from contaminations caused by the substrate.

Fig. 4.

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	Fig. 4. (color online) Projected density of states (PDOS) on d orbitals of the Ta atom (top panels) and s and p orbitals of the anion atoms (bottom panels) for (a) TaS/Al2O3(0001), (b) TaSe/Al2O3(0001), and (c) TaTe/Al2O3(0001). The vertical dashed lines indicate the Fermi energy. d±2, d±1, and d0 stand for the dxy+(x2−y2), dxz+yz, and dz2 orbitals, respectively. p±1 stands for the px+y orbital.

In summary, we investigated the electronic and magnetic properties of the TaX (X = S, Se or Te) monolayer in freestanding cases and supported by the Al₂O₃(0001) substrate based on first-principles calculations. We found that both freestanding and substrate supported TaX monolayers are ferromagnetic. The TaX monolayers are chemically bound on the Al₂O₃(0001) substrate with stable atomic structures. Interestingly, the freestanding TaX monolayers are metallic, while the substrate supported TaX monolayers are semiconductors with band gaps of 188–303 meV. Since the Al₂O₃(0001) substrate is a wide-gap insulator, the states near the E_F are contributed by the TaX monolayers especially the Ta atom. Therefore, TaX/Al₂O₃(0001) can be regarded as a 2D FM semiconductor. Our study paves the way to engineering 2D FM materials that are promising for practical applications in spintronics devices.