Quasi 2D electronic states with high spin-polarization in centrosymmetric MoS2 bulk crystals

Time reversal dictates that nonmagnetic, centrosymmetric crystals cannot be spin-polarized as a whole. However, it has been recently shown that the electronic structure in these crystals can in fact show regions of high spin-polarization, as long as it is probed locally in real and in reciprocal space. In this article we present the first observation of this type of compensated polarization in MoS2 bulk crystals. Using spin- and angle-resolved photoemission spectroscopy (ARPES), we directly observed a spin-polarization of more than 65% for distinct valleys in the electronic band structure. By additionally evaluating the probing depth of our method, we find that these valence band states at the point in the Brillouin zone are close to fully polarized for the individual atomic trilayers of MoS2, which is confirmed by our density functional theory calculations. Furthermore, we show that this spin-layer locking leads to the observation of highly spin-polarized bands in ARPES since these states are almost completely confined within two dimensions. Our findings prove that these highly desired properties of MoS2 can be accessed without thinning it down to the monolayer limit.

shows the comparison of ARPES spectrum along ΓK direction to the corresponding calculation of bulk projected band structure for 2H-MoS 2 and 3R-MoS 2 . The broadening of the valence band around the Γ point is a good indication for the delocalization of these states in the out-of-plane (ΓA) direction. The high dispersion is a result of the 3D bulk-like character of these states in contrast to the quasi 2D valence band around the K point, which is discussed in the main article.
In figure 2 we analyze the contribution by the band structure of 2H-MoS 2 and 3R-MoS 2 quantitatively. Fig. 2 a)-c) show the ARPES spectra and DFT calculations that we discuss in the main article including markers that indicate the position of the energy distribution curves (EDCs), which are shown in Fig. 2 d)-f). The figures also show a least squares fit with the bulk projected band structure of the 2H and 3R-phase. Our DFT (film) calculations show no evidence for surface states in these energy-and momentum-regions. The fitted curve in Fig. 2 d) and f) are in good agreement with the data and show only 6.5% (d) and 0% (f) contribution of 3R. The fit in Fig. 2 e) to the data does not properly reproduce the data. Nevertheless, the agreement of the band structure of 2H-MoS 2 here is also by far better. The only point in the ARPES spectrum that seems to agree better with the calculations for the bulk projectet band structure of 3R-MoS 2 is highlighted with an arrow. However, our film calculations (main article) show a surface state in exactly this region.
In addition to the ARPES data we analyze the reflectivity spectrum in Fig. 3 by fitting a linear combination of reference spectra from Ref. 1 to our data. One can see that the sligtly different shape of the peak in our data at 2 eV compared to the 2H reference spectrum is compensated by a 8.7% portion of the 3R phase in the least squares fit. This, however, might as well be an artifact of the experimental setup since the shape of this peak is known to be asymmetric even for pure 2H-MoS 2 . 2 In summary we find no clear indication of the existence of a different phase in our sample and with the methods that we employed it is safe to assume 10% of 3R-MoS 2 as an upper limit. Figure 4 shows a calculation that estimates the effect of a mixed crystal phase on the spin-polarization that is observed in photoemission. As we discussed in the main article the observed polarization in 2H-MoS 2 is obscured by its alternating sign from one layer to the next. Consequently the initial spin-polarization that one can relate to the experimental observation depends on the probing depth, which we cannot reliably determine. Therefore we plotted the initial spin-polarization of the bands in 2H-MoS 2 that we can conclude from observing 65% in photoemission for several probing depths. In the main article we estimated 4Å inelastic mean free path (IMFP) according to the minimum of the universal curve for photoemission. The blue curve Fig. 4 shows that for an IMFP of 4Å, observing 65% spin-polarization corresponds to a fully spin-polarized initial state in each layer, which is in perfect agreement with our DFT calculations. Even for a possible contamination of our sample by up to 10% 3R-MoS 2 we still can conclude that the 2H-layers are at least 95% spin-polarized.
The plot also shows that assuming the minimum probing depth can only underestimate the initial polarization since a larger IMFP further conceals it. A further argument for the low IMFP is that the curve for 5Å exceeds 100% . This is due to the fact that at this probing depth even with fully polarized monolayers the contribution of the opposing layers is to strong to observe 65% polarization as we did. In this case 23% of the 3R-MoS 2 could explain our observation, which is unlikely as we have shown.
One can see in figure 4 that for an IMFP of 4Å (blue curve) our observation of 65% spin-polarization perfectly matches our DFT calculations, which show fully polarized layers in a pure 2H-MoS 2 crystal. If, however, the sample was in fact partially composed of 3R-MoS 2 , whose spin-polarization does not alternate throughout the layers and is therefore independent of the probing depth, then already a lower degree of polarization in 2H-MoS 2 could explain our results. At a higher probing depth (yellow and red curve) the polarization of the 2H-phase is more obscured by the contribution of deeper layers. Therefore, in this case an even higher spin-polarization of the 2H-MoS 2 monolayers has to be assumed to explain our results.