Spin injection and magnetoresistance in MoS2-based tunnel junctions using Fe3Si Heusler alloy electrodes

Recently magnetic tunnel junctions using two-dimensional MoS2 as nonmagnetic spacer have been fabricated, although their magnetoresistance has been reported to be quite low. This may be attributed to the use of permalloy electrodes, injecting current with a relatively small spin polarization. Here we evaluate the performance of MoS2-based tunnel junctions using Fe3Si Heusler alloy electrodes. Density functional theory and the non-equilibrium Green’s function method are used to investigate the spin injection efficiency (SIE) and the magnetoresistance (MR) ratio as a function of the MoS2 thickness. We find a maximum MR of ~300% with a SIE of about 80% for spacers comprising between 3 and 5 MoS2 monolayers. Most importantly, both the SIE and the MR remain robust at finite bias, namely MR > 100% and SIE > 50% at 0.7 V. Our proposed materials stack thus demonstrates the possibility of developing a new generation of performing magnetic tunnel junctions with layered two-dimensional compounds as spacers.

In this work, we focus on the spin transport properties of Fe 3 Si/MoS 2 /Fe 3 Si MTJs. An illustration of the structure of a 3-monolayer MoS 2 junction is presented in Fig. 1(a). We first investigate the electronic properties of the interface between Fe 3 Si and MoS 2 by using density functional theory (DFT). Then, by combining DFT with the non-equilibrium Green's function (NEGF) method for transport, we are able to analyze the dependence of the transmission coefficient on the MoS 2 thickness at zero bias. The spin-injection efficiency (SIE), η, and the magnetoresistance (MR) ratio for different MoS 2 layer thicknesses are then calculated. We obtain a maximum MR ratio of ~300% with a SIE of ~80% for a junction comprising only three MoS 2 monolayers. The details of the electronic transport are explained thoroughly by looking closely at the k -resolved transmission coefficients at the Fermi level, E F . Finally, we further investigated the SIE and the MR ratio as a function of the bias voltage. Interestingly, both remain robust as the bias potential is increased.

Results and Discussion
The details of the relaxed structure at the interface are presented in Fig. 1(c). In the D0 3 structure (Fm m 3 ) the A, B and C sites of Fe 3 Si are occupied by Fe ions, while Si is placed at the remaining octahedral-coordinated D site. By comparing the binding energy, E b , we can conclude that it is more energetically favorable to terminate the Fe 3 Si surface with A and C sites. In this case E b = −1.13 eV per surface atom, indicating covalent bonding with MoS 2 . The shortest S-Fe bond length is found to be 2.09 Å, while the average separation between the top layer of Fe 3 Si and the bottom Mo layer is 3.49 Å [this is taken from the Mo plane -see Fig. 1(c)]. The equilibrium distance between the Fe and the S closest planes is 1.90 Å, while the MoS 2 inter-layer distance is 6.15 Å.
We start our analysis by looking at the spin-resolved transmission coefficients, T σ (E) (σ = ↑, ↓), for all the systems studied in the parallel (P) and anti-parallel (AP) configuration. For the 1L-MoS 2 junction the transmission of the P configuration shows a metallic-like behaviour for both spin channels [see Fig. 2(a). This is due to the strong hybridization between the Fe(A,C) and the S atoms at the interface, resulting in the metallization of the MoS 2 monolayer. Metallization of thin MoS 2 barriers is confirmed by the projected density of states (PDOS) presented in Fig. 3(a), where one can clearly see that the PDOS of the Mo atoms at the surface is different from that of bulk MoS 2 and displays a small spin polarization. Such result is consistent with previous studies using Fe electrodes 18 . As presented in Fig. 3(c), one can see that the minority-spin PDOS of the interface Fe(A,C) atoms increases significantly around the Fermi energy, as compared to those in the bulk-like region. This means that   Increasing the MoS 2 thickness reduces the transmission of both the P and AP configurations for all the spin channels, as shown in Fig. 2(c,d). As the spacer thickness is increased to 3 monolayers [see Fig. 3(b)], the PDOS of the Mo atoms located in the middle of the junction becomes almost identical to that of bulk MoS 2 , indicating that the metallization extends only to the layers adjacent to the electrodes. Remarkably, T ↓ (E F ) decreases faster than T ↑ (E F ), as it will be discussed in more detail later. When compared to the 1L-MoS 2 junction, T ↓ (E F ) for the 3L-, 5L-, 7L-and 9L-MoS 2 junction is reduced by about two, four, six and seven orders of magnitude, respectively. This demonstrates the tunneling transport regime. Notably the drop in transmission is much more evident in the energy region [−0.3, 0.3] eV. This is significantly smaller than the DFT local spin-density approximation bandgap of bulk MoS 2 (~1.8 eV), indicating that the electrodes screening plays a dramatic role in determining the bandgap of the spacer in the junction. A similar behaviour has been already observed for transition metals electrodes 16,18 . The zero-bias transport properties of Fe 3 Si/MoS 2 /Fe 3 Si junctions with different tunnel barrier thicknesses are summarized in Table 1.
The calculated SIE and MR ratio for all the junctions studied are presented in Fig. 4(a,c), respectively. In the P configuration, the SIE increases with thickness up to 5 monolayers, reaching a plateau at η ∼ 80%, while that of the AP is low and does not change much (note that in a perfectly symmetric junction the SIE in the AP configuration must vanish). This suggests that there is an optimal layer thickness for injecting spins into MoS 2 . Note that the SIE is negative, −50.17%, for the 1L-MoS 2 junction due to the large T ↓ (E F ). This reflects the spin-polarization of the DOS of the electrodes; ρ with ρ σ F being the DOS at E F for the spin σ [see Fig. 2(a)].
The MR ratio [see Fig. 4(b)] increases significantly from ~100% to ~300% as the MoS 2 spacer thickness is enlarged from one to three layers. It remains at about 300% for the 5-monolayer junction and then decreases to about 150% and 120% for 7 and 9 MoS 2 monolayers, respectively. In summary, the MR ratio exhibits a maximum at 300% for certain spacer thicknesses, namely for the 3L-and 5L-MoS 2 junctions. Our results are compared to previous studies of MoS 2 -based MTJs in Table 2. We predict a MR value larger than that obtained for Fe 3 O 4 17 , Co 20 , Ni 20 and Py 15 electrodes and slightly larger than that for Fe 18 . However, it should be noted that for 7L-and 9L-MoS 2 junctions, our results demonstrate that the MR values with Fe 3 Si electrodes become less than that of previous studies 18 using Fe electrodes.
The bias dependence of the SIE and the MR ratios both characterize the MTJs quality in practical applications. These are defined as their corresponding linear response quantities, with T σ (E) and G being replaced by the spin-polarized and the total current, respectively. Our results for voltages up to 0.7 V are presented in Fig. 4(b,d) for the 1L-, 3L-and 5L-MoS 2 junctions. Except for the 1L-MoS 2 case, the SIEs in the P configuration increase with increasing the applied bias, whereas the opposite is observed in the AP one. Note that at finite bias the junction symmetry is broken and the SIE for the AP case may differ from zero, but the actual sign depends on the bias polarity. Interestingly in the P configuration the SIE increases to a maximum at high voltage for the 3L-MoS 2 junction, whereas it remains roughly constant and then decreases for the 5L-MoS 2 one. Finally the SIE of the 1L-MoS 2 junction follows the behaviour of the 3L-MoS 2 one, but starts from a negative value at V = 0. A more detailed discussion of the spin-polarized I-V curves can be found in the Supplementary Information.
The most interesting feature of Fig. 4(d) is that the MR ratios gradually decrease under the application of a bias voltage. Already at 0.1 V the MR is reduced by approximately 25%, 10% and 18% for the 1L-MoS 2 , 3L-MoS 2 and 5L-MoS 2 junctions, respectively. Note that such percentage changes are calculated as the decrease from the zero-bias MR value. This needs to be compared with what found in MoS 2 -based MTJs with Fe electrodes, for which the MR drop is of the order of ~80% 18,19 .
In order to understand the different MR ratios presented before, in Fig. 5(a,b) we show the k -resolved transmission coefficients at E F for the 1L-MoS 2 and 5L-MoS 2 junctions. In general in the P configuration the transmission profile in the 2D Brillouin zone orthogonal to the transport direction follows somehow closely the  distribution of open channels in the electrodes [see Fig. 5(c)]. This is much more evident for the 1L-MoS 2 junction, confirming that in case of MoS 2 metallization the MR is entirely dominated by the electronic structure of the electrodes. As expected for the AP configuration the transmission profile is a sort of convolution of that of the two spin channels in the P one.
Moving our attention to the 5L-MoS 2 junction the situation becomes somehow more complex. The most striking feature is the appearance of regions of low transmission in the Brillouin zone, which are present for both spin channels regardless of the electrodes configuration. In particular such regions are concentrated around the k z = 0, and k y = ±π/2a y axes. This behaviour can be explained by looking at Fig. 5(d), where we show the smallest MoS 2 complex wave-vector, κ, in the direction of the transport for any given transverse k . Note that κ is essentially the wave-function decay coefficient across the barrier, so that the highest transmission is expected for the smallest κ. From the figure one can clearly see that the regions of small transmission identified in Fig. 5(b) correspond to those where κ is large, and that the transmission is maximized at the edge of the Brillouin zone in the k x direction. Importantly, from the transmission plots it emerges that in the regions of high transmission both spin channels are present, so that a clear spin filtering is not in action in this material system. Thus, increasing the barrier thickness has the sole effect of changing the distribution of the k wave-vectors contributing to the conductance. This in general changes the MR. However, since both spin channels are transmitted across the k regions filtered by the barrier, the MR does not increase significantly with the layer thickness.
Certainly our theoretical predictions now need to be passed to the experimental scrutiny. On the one hand we are confident that, should epitaxial junctions be made, the MR and SIE will be large. On the other hand, it might be the case that the fabrication process produces interdiffusion at the Fe 3 Si/MoS 2 interface, which will

Conclusion
In conclusion we have demonstrated that magnetic tunnel junctions based on Fe 3 Si Heusler alloy electrodes and MoS 2 spacers may present advantages over the most conventional choices based on transition metals permalloy.
In particular we have shown that the junctions, comprising only three MoS 2 monolayers, display a spin injection efficiency of the order of 80% and a MR ratio of 300%. These are both robust as the bias potential is increased, so that our proposed junctions can sustain a large current with significant spin polarization. Thus magnetic tunnel junctions constructed with 2D barriers appear promising for realizing current-operated spin devices.

Methods
MoS 2 is sandwiched in between the Fe 3 Si electrodes, so that its cleavage plane binds to the (100) surface of Fe 3 Si. Commensurability is obtained by aligning the Fe 3 Si cubic cell with the planar 2 3 × cell of MoS 2 and requires a uniform stretch of the Fe 3 Si in plane lattice constants by about 5% (Fe 3 Si becomes slightly orthorhombic). We have tested that such small strain on Fe 3 Si does not affect its electronic structures significantly (see the Supplementary Information). The final cell describing the scattering region comprises a variable number of MoS 2 monolayers and two cells of Fe 3 Si at each side. Note that 3 atomic layers of Fe 3 Si (1.5 cells) are enough to screen out the perturbation of MoS 2 at the interface 40 . As a matter of notation we denote as nL-MoS 2 junction in which the MoS 2 spacer is n monolayers thick. Each cell is then fully relaxed by using the DFT code SIESTA 41 , with basis set, exchange-correlation functional, real-space mesh cutoff and k-point grid identical to those used for the transport calculations. Note that Siesta is the DFT engine of Smeagol. The relaxation is performed by conjugate gradient until the residual forces on each atom are below 0.01 eV/Å, while the in-plane lattice parameters are kept to those of MoS 2 .
The quantum transport calculations have been performed by employing a combination of the non-equilibrium Green's function technique (NEGF) based on density functional theory (DFT) as implemented in the SMEAGOL 42,43 package. For all calculations we have used the local spin density approximation (LSDA) 44 to the exchange-correlation functional. The valence electrons are described by using a local double-ζ plus polarization basis set. The atomic core electrons are modelled with norm-conserving relativistic Troullier-Martin pseudopotentials 45 . We have determined that convergence is achieved by using a real-space integration with a mesh cutoff of 300 Ry and a k-space grid of 8 × 10 × 1 points. The transmission spectra and the current are then computed over a 80 × 100 × 1 grid (see the Supplementary Information).
The fundamental quantities that characterize spintronics devices are the MR ratio and the SIE. The low-bias MR ratio is defined as MR = 100%