The Interface between Gd and Monolayer MoS2: A First-Principles Study

We analyze the electronic structure of interfaces between two-, four- and six-layer Gd(0001) and monolayer MoS2 by first-principles calculations. Strong chemical bonds shift the Fermi energy of MoS2 upwards into the conduction band. At the surface and interface the Gd f states shift to lower energy and new surface/interface Gd d states appear at the Fermi energy, which are strongly hybridized with the Mo 4d states and thus lead to a high spin-polarization (ferromagnetically ordered Mo magnetic moments of 0.15 μB). Gd therefore is an interesting candidate for spin injection into monolayer MoS2.

M onolayer transition metal dichalcogenides, especially MoS 2 , have promising prospects in many fields due to their exotic electronic, optical, chemical and thermal properties [1][2][3][4] . Unlike gapless graphene, monolayer MoS 2 has a direct optical band gap of 1.8 eV 5,6 , which is key for field effect transistors, photodetectors and electroluminescent devices [7][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 themselves 10,11 . Based on density functional theory, Gan et al. have shown that the chemical bonds formed at the MoS 2 /TiC interface result in conductive MoS 2 12 and Feng et al. have predicted that the interfacial hybridization in Fe 4 N/MoS 2 superlattices results in magnetic MoS 2 13 . Pb, Au and Ag contacts to monolayer MoS 2 can be used to realize good electron injection 14 . Popov et al., on the other hand, have observed that Au is rather inefficient for electron injection and have proposed Ti as alternative electrode material 15 . Moreover, Chen et al. have demonstrated a n-type Schottky-barrier for the contact between monolayer MoS 2 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) surface 17 . 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 m B /Gd 18 . Moreover, Gd crystallizes in the hcp structure with less than 1% lattice mismatch to MoS 2 and has a low work function of 3.1 eV 19 , thus being able to efficiently inject electrons into the conduction band of MoS 2 . For these reasons, we investigate in the present work, the electronic structure of interfaces between two-, four-and six-layer Gd(0001) and monolayer MoS 2 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 Package 20,21 . For the exchange-correlation potential we use the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof 22 . Due to strong on-site Coulomb repulsion of the localized Gd 4f electrons, the rotationally invariant GGA1U method is employed with U 5 7.7 eV and J 5 0.7 eV 23 . The two-layer Gd/MoS 2 interface is also studied taking into account the spin-orbit coupling (GGA1SOC). In all calculations the Gd 5s, 5p, 6s, 5d, and 4f orbitals are treated as valence states, a C-centered 4 3 4 3 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 25

Results and Discussion
Bulk MoS 2 has a layered 2H structure with space group P6 3 mmc (D 6h point group). The trigonal prismatic coordination of the bulk is maintained in monolayer MoS 2 , whereas the symmetry is reduced to P 6m2 (D 3h point group) due to a loss of inversion symmetry. Gd crystallizes in a hcp structure with space group P6 3 mmc. The optimized geometries of the interfaces between two-and six-layer Gd and monolayer MoS 2 are shown in Fig. 1. The results for the interface between four-layer Gd and monolayer MoS 2 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 MoS 2 are 3.65 and 3.18 Å , respectively, whereas for both the two-and six-layer Gd/MoS 2 interfaces we obtain 11.03 Å (3.68 and 3.18 Å for Gd and MoS 2 ). This means that there is almost no strain. In order to quantify the interaction strength between Gd and MoS 2 , we calculate the binding energy E B 5 E I 2 E M 2 E Gd , where E I , E M , and E Gd represent the total energies of the Gd/MoS 2 interface, monolayer MoS 2 , and the Gd slab, respectively. We obtain per surface Gd atom values of 20.62 and 20.64 eV for the two-and six-layer Gd/MoS 2 interfaces, reflecting substantial bonding. The distance between the S I,F (the first index refers to the layer and the second to the site) and Mo F 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/MoS 2 interface, whereas the corresponding distance for the S I-H and Mo H atoms is larger, namely, 3.17 and 4.69 Å (3.14 and 4.67 Å ).  The density of states (DOS) of pristine monolayer MoS 2 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 4d 3z 2 {r 2 , d xy , d x 2 {y 2 and S 3p states at the conduction and valence band edges is consistent with previous results 26 . Figures 3 and 4 give the DOSs obtained for the two-and sixlayer Gd/MoS 2 interfaces. The majority spin Mo F states at the Fermi energy (E F ) display high 4d 3z 2 {r 2 , d xy , and d x 2 {y 2 DOSs with d yz and d xz admixtures, while the minority spin DOSs are small. The majority spin Mo H DOS at E F is slightly larger than the minority spin DOS (mainly d 3z 2 {r 2 states, followed by d xy , d x 2 {y 2 and d yz , d xz states). Furthermore, the broader peaks in Fig. 3(a) as compared to Fig. 3   moments. Figure 4 demonstrates that for S II the p z DOS is larger than the p x and p y DOSs, similar to pristine monolayer MoS 2 , at the valence band edge, while for S I mainly the p x and p y orbitals contribute. This means that the Gd-S II interaction is weak (large distance). Due to hybridization with the Gd 5d states (details later), some S p states show up at E F , especially majority spin states, which leads to a tiny S magnetic moment (0.01 m B ). It is worth noting that, due to the nonmagnetic nature of MoS 2 , we have set the initial magnetic moments of S and Mo to zero in all calculations. The spatial extension of the spin density in MoS 2 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 Mo F -Gd distance as compared to the Mo H -Gd distance enhances the interaction so that Mo F has a larger magnetic moment of about 0.12 and 0.15 m B (Mo H : 0.07 and 0.10 m B ) in the two-and six-layer Gd/MoS 2 interfaces, respectively.    27 . In the combined systems, although the bands of MoS 2 hybridize with those of Gd they can still be identified, see the red color in Figs. 5(b) and (c). We find E F 0.34 and 0.51 eV, respectively, above the conduction band edge for the majority and minority spin bands, making MoS 2 display a metallic character. Figs. 6(a) and (b) show the DOS for Mo F and Mo H in the two-layer Gd/MoS 2 interface as obtained by GGA1SOC in comparison to simple GGA. We find that the SOC has almost no influence, except for a slight reduction of the d 3z 2 {r 2 DOS.
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/ MoS 2 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 lowenergy electron diffraction 28,29 .
In bulk Gd the unoccupied f states are located 3.6 eV above E F and the occupied f states 8.8 eV below E F , 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 method 30 and is close to the experimental value of 12 eV 31 . The fact that the Gd magnetic moment (7.43 m B ) exceeds 7 m B suggests an induced polarization of other orbitals. We find magnetic moments of 0.02, 0.03 and 0.40 m B for the Gd s, p, and d states, which can be explained by the s-f exchange model 32 . 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/MoS 2 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 20.5 to 0.4 eV (from 20.2 to 0.2 eV) for the two-layer (six-layer) Gd/MoS 2 interface for the surface 33-37 (more pronounced) and interface Gd atoms. Moreover, a strong hybridization between the Gd d, Mo d and S p states appears near E F (see Figs. 3, 4 and 7). The majority and minority spin Gd d DOSs at E F 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 m B . 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 MoS 2 in layer I. The same is found for the I and VI layers in the six-layer Gd/MoS 2 interface, which is consistent with inverse photoemission spectroscopy 37 , 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.

Conclusion
We have investigated the geometry, electronic structure, and magnetism at the interface between Gd(0001) and monolayer MoS 2 . Strong chemical bonds are formed and seriously modify the electronic states of MoS 2 , especially at E F . Interaction with the Gd d states shifts E F into the conduction band and makes MoS 2 metallic. Large magnetic moments appear on the Mo atoms. Moreover, distinct surface/interface Gd d states are formed at E F 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.