Introduction

Monolayer transition metal dichalcogenides, especially MoS2, have promising prospects in many fields due to their exotic electronic, optical, chemical and thermal properties1,2,3,4. Unlike gapless graphene, monolayer MoS2 has a direct optical band gap of 1.8 eV5,6, which is key for field effect transistors, photodetectors and electroluminescent devices7,8,9. On the other hand, the low electron mobility hampers high performance applications. Interfaces often are more crucial to nanoelectronics than the involved semiconductors themselves10,11. Based on density functional theory, Gan et al. have shown that the chemical bonds formed at the MoS2/TiC interface result in conductive MoS212 and Feng et al. have predicted that the interfacial hybridization in Fe4N/MoS2 superlattices results in magnetic MoS213. Pb, Au and Ag contacts to monolayer MoS2 can be used to realize good electron injection14. Popov et al., on the other hand, have observed that Au is rather inefficient for electron injection and have proposed Ti as alternative electrode material15. Moreover, Chen et al. have demonstrated a n-type Schottky-barrier for the contact between monolayer MoS2 and Ir(111), Pd(111), or Ru(0001)16.

Clearly, interfaces between semiconductors and metals are critical for future electronic devices based on this new class of materials. In particular, injection of spin-polarized charge from ferromagnets may have a significant technological impact in the area of spintronics. Gd is one of the four room-temperature ferromagnetic metals (Curie temperature 293 K; the others being Fe, Co and Ni). A significant enhancement of the Curie temperature by 29% has been found experimentally at the Gd(0001) surface17. In contrast to transition metals, the ferromagnetic order generated by the localized Gd 4f electrons also polarizes the conduction electrons (Gd 5d and 6s), leading to a large magnetic moment of 7.63 μB/Gd18. Moreover, Gd crystallizes in the hcp structure with less than 1% lattice mismatch to MoS2 and has a low work function of 3.1 eV19, thus being able to efficiently inject electrons into the conduction band of MoS2. For these reasons, we investigate in the present work, the electronic structure of interfaces between two-, four- and six-layer Gd(0001) and monolayer MoS2 by density functional theory, demonstrating great potential for spin injection.

Methods

Our first-principles calculations are performed using the projector-augmented wave method as implemented in the Vienna Ab-initio Simulation Package20,21. For the exchange-correlation potential we use the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof22. Due to strong on-site Coulomb repulsion of the localized Gd 4f electrons, the rotationally invariant GGA+U method is employed with U = 7.7 eV and J = 0.7 eV23. The two-layer Gd/MoS2 interface is also studied taking into account the spin-orbit coupling (GGA+SOC). In all calculations the Gd 5s, 5p, 6s, 5d and 4f orbitals are treated as valence states, a Γ-centered 4 × 4 × 1 k-grid is employed and the plane wave energy cutoff is set to 600 eV. Furthermore, the convergence criterium for the total energy is chosen to be 10−5 eV. The surface unit cell of Gd(0001) has p(3 × 3) periodicity with experimental lattice constant 10.89 Å24, while the surface unit cell of monolayer MoS2 has × R30° periodicity with experimental lattice constant 10.98 Å25. Thus, the mismatch amounts only to 0.83%. The cell volume is relaxed and the ionic positions are optimized, using the conjugated gradient method, until the Hellmann-Feynmann forces on each atom are reduced to less than 0.01 eV/Å. A 15 Å thick vacuum layer ensures decoupling in the slab geometry. Because of strong chemical bonding between Gd(0001) and monolayer MoS2, van der Waals forces are not taken into account.

Results and Discussion

Bulk MoS2 has a layered 2H structure with space group P63mmc (D6h point group). The trigonal prismatic coordination of the bulk is maintained in monolayer MoS2, whereas the symmetry is reduced to (D3h point group) due to a loss of inversion symmetry. Gd crystallizes in a hcp structure with space group P63mmc. The optimized geometries of the interfaces between two- and six-layer Gd and monolayer MoS2 are shown in Fig. 1. The results for the interface between four-layer Gd and monolayer MoS2 turn out to be very similar to those of the six-layer system and thus are not further discussed in the following. According to Fig. 1(e), three S and Mo atoms in each layer sit above the hexagonal (H) hollow sites and nine S and Mo atoms are located above face-centered (F) hollow sites. The optimized lattice constants of Gd and MoS2 are 3.65 and 3.18 Å, respectively, whereas for both the two- and six-layer Gd/MoS2 interfaces we obtain 11.03 Å (3.68 and 3.18 Å for Gd and MoS2). This means that there is almost no strain. In order to quantify the interaction strength between Gd and MoS2, we calculate the binding energy EB = EI − EM − EGd, where EI, EM and EGd represent the total energies of the Gd/MoS2 interface, monolayer MoS2 and the Gd slab, respectively. We obtain per surface Gd atom values of −0.62 and −0.64 eV for the two- and six-layer Gd/MoS2 interfaces, reflecting substantial bonding. The distance between the SI,F (the first index refers to the layer and the second to the site) and MoF atoms, respectively and their nearest Gd neighbors is 2.77 and 4.23 Å (2.76 and 4.21 Å) in the two-layer (six-layer) Gd/MoS2 interface, whereas the corresponding distance for the SI-H and MoH atoms is larger, namely, 3.17 and 4.69 Å (3.14 and 4.67 Å).

Figure 1
figure 1

(a, c) Side view of the charge density difference due to the interaction at the two- and six-layer Gd/MoS2 interfaces. The cyan and yellow isosurfaces (±0.003 e/Å3) represent accumulation and depletion of electrons, respectively. (b, d) Side view of the spin density difference for the two- and six-layer Gd/MoS2 interfaces. The isosurface value is 0.002 e/Å3. Red color indicates cuts through the isosurface. (e) Top view of the optimized two-layer Gd/MoS2 interface.

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The density of states (DOS) of pristine monolayer MoS2 is addressed in Fig. 2(a). The crystal-field splitting of the Mo 4d states in the trigonal prismatic environment of the S atoms is visible. Hybridization between the Mo 4, dxy, and S 3p states at the conduction and valence band edges is consistent with previous results26. Figures 3 and 4 give the DOSs obtained for the two- and six-layer Gd/MoS2 interfaces. The majority spin MoF states at the Fermi energy (EF) display high 4, dxy and DOSs with dyz and dxz admixtures, while the minority spin DOSs are small. The majority spin MoH DOS at EF is slightly larger than the minority spin DOS (mainly states, followed by dxy, and dyz, dxz states). Furthermore, the broader peaks in Fig. 3(a) as compared to Fig. 3(b) reflect more dispersive bands in the two-layer Gd/MoS2 interface. To illustrate the charge transfer, we show the charge density difference between the Gd/MoS2 interfaces and the sum of the isolated Gd and MoS2 subsystems in Figs. 1(a) and (c). Charge accumulates at the Mo atoms and in the Gd-S bond region. The Mo excess electrons populate majority spin states, resulting in enhanced Mo 4d magnetic moments. Figure 4 demonstrates that for SII the pz DOS is larger than the px and py DOSs, similar to pristine monolayer MoS2, at the valence band edge, while for SI mainly the px and py orbitals contribute. This means that the Gd-SII interaction is weak (large distance). Due to hybridization with the Gd 5d states (details later), some S p states show up at EF, especially majority spin states, which leads to a tiny S magnetic moment (0.01 μB). It is worth noting that, due to the nonmagnetic nature of MoS2, we have set the initial magnetic moments of S and Mo to zero in all calculations. The spatial extension of the spin density in MoS2 induced by the contact to Gd is shown in Figs. 1(b) and (d). It mainly extends into the Mo region and is small for S (large change of the Mo DOS). We find that the Mo magnetic moments order ferromagnetically. The shorter MoF-Gd distance as compared to the MoH-Gd distance enhances the interaction so that MoF has a larger magnetic moment of about 0.12 and 0.15 μB (MoH: 0.07 and 0.10 μB) in the two- and six-layer Gd/MoS2 interfaces, respectively.

Figure 2
figure 2

DOS of (a) the Mo and S atoms in pristine monolayer MoS2 and (b) the Gd atoms in bulk Gd.

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Figure 3
figure 3

DOS of the Mo atoms at the F and H sites for the two- and six-layer Gd/MoS2 interfaces.

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Figure 4
figure 4

DOS of the S atoms at the F and H sites for the two- and six-layer Gd/MoS2 interfaces.

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Figure 5(a) shows a band gap of 1.6 eV for pristine monolayer MoS2, consistent with previous GGA calculations27. In the combined systems, although the bands of MoS2 hybridize with those of Gd they can still be identified, see the red color in Figs. 5(b) and (c). We find EF 0.34 and 0.51 eV, respectively, above the conduction band edge for the majority and minority spin bands, making MoS2 display a metallic character. Figs. 6(a) and (b) show the DOS for MoF and MoH in the two-layer Gd/MoS2 interface as obtained by GGA+SOC in comparison to simple GGA. We find that the SOC has almost no influence, except for a slight reduction of the DOS.

Figure 5
figure 5

Band structure of (a) pristine monolayer MoS2 and (b, c) the two- and six-layer MoS2 interfaces. EF = 0 eV.

The red lines correspond to the bands of monolayer MoS2.

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Figure 6
figure 6

DOS (sum of both spin channels) of the Mo atoms at the F and H sites for the two-layer Gd/MoS2 interface: Comparison between the GGA and GGA+SOC methods.

EF = 0 eV.

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The distance between nearest neighbor atoms is 3.60 Å in bulk Gd, while the distances of nearest neighbor atoms in the interface and surface Gd layers, see Figs. 1(a, e) and (c), respectively, are smaller. The very short distance between layers V and VI in the six-layer Gd/MoS2 interface points to a substantial surface relaxation. On the other hand, the distances in the subsurface, see Fig. 1(c), are larger than the bulk value. This variation is consistent with a contraction of the surface layer by 0.085–0.115 Å (~3–4%) and an expansion of the subsurface layer by 0.050–0.075 Å (~1.5–2.5%) as measured by low-energy electron diffraction28,29.

In bulk Gd the unoccupied f states are located 3.6 eV above EF and the occupied f states 8.8 eV below EF, see Fig. 2(b), reflecting an exchange spin splitting of 12.4 eV. This value agrees with results of the full potential linear augmented plane wave method30 and is close to the experimental value of 12 eV31. The fact that the Gd magnetic moment (7.43 μB) exceeds 7 μB suggests an induced polarization of other orbitals. We find magnetic moments of 0.02, 0.03 and 0.40 μB for the Gd s, p and d states, which can be explained by the s-f exchange model32. The total Gd magnetic moments are enhanced in the surface Gd layers by 0.9% and 1.9% for the two- and six-layer Gd/MoS2 interfaces, respectively and reduced by 0.9% and 0.5% in the interface Gd layers. The magnetic moments of the different layers given in Table 1 show no effect for the f states; all changes are carried by the d states. The Gd d DOS in Fig. 7, in contrast to the bulk, shows majority spin states from −0.5 to 0.4 eV (from −0.2 to 0.2 eV) for the two-layer (six-layer) Gd/MoS2 interface for the surface33,34,35,36,37 (more pronounced) and interface Gd atoms. Moreover, a strong hybridization between the Gd d, Mo d and S p states appears near EF (see Figs. 3, 4 and 7). The majority and minority spin Gd d DOSs at EF are different because of an enhancement in the surface and a reduction in the interface Gd layers. In the other Gd layers the Gd magnetic moments are close to the bulk value of 7.43 μB. The Gd f DOSs of layers I and II, respectively, show downward shifts of 0.2 and 0.3 eV for the majority spin states and of 0.3 and 0.4 eV for the minority spin states, relative to the bulk Gd f states, where the different amplitude is due to the interaction with MoS2 in layer I. The same is found for the I and VI layers in the six-layer Gd/MoS2 interface, which is consistent with inverse photoemission spectroscopy37, while for the II, III, IV and V layers the shifts are very small. Gd core-level shifts can be attributed to the different chemical environments of the surface and interface atoms, thus being small in other layers.

Table 1 Gd 5d and 4f magnetic moments (μB) in each layer of the two- and six-layer Gd/MoS2 interfaces, as compared to bulk Gd
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Figure 7
figure 7

DOS of the Gd atoms in the different atomic layers of the two- and six-layer Gd/MoS2 interfaces.

EF = 0 eV.

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Conclusion

We have investigated the geometry, electronic structure and magnetism at the interface between Gd(0001) and monolayer MoS2. Strong chemical bonds are formed and seriously modify the electronic states of MoS2, especially at EF. Interaction with the Gd d states shifts EF into the conduction band and makes MoS2 metallic. Large magnetic moments appear on the Mo atoms. Moreover, distinct surface/interface Gd d states are formed at EF and a clear downward shift of the Gd f states is observed for both the surface and interface, whereas the Gd magnetic moments are enhanced at the surface but reduced at the interface.