L Herrera Diez

F Ummelen

V Jeudy

G Durin

L Lopez-Diaz

R Diaz-Pardo

A Casiraghi

G Agnus

D Bouville

J Langer

B Ocker

R Lavrijsen

H J M Swagten

D Ravelosona

Magnetic domain wall curvature induced by wire edge pinning

Keywords: magnetic micro wires, domain wall curvature, perpendicular magnetic anisotropy

In this study we report on the analysis of magnetic domain wall (DW) curvature due to magnetic field induced motion in Ta/CoFeB/MgO and Pt/Co/Pt wires with perpendicular magnetic anisotropy. In wires of 20µm and 25µm a large edge pinning potential produces the anchoring of the DWs ends to the wire edges which is evidenced as a significant curvature of the DW front as it propagates. As the driving magnetic field is increased the curvature reduces as the result of the system moving away from the creep regime of DW motion, which implies a weaker dependence of the DW dynamics on the interaction between the DW and the wire edge defects. A simple model is derived to describe the dependence of the DW curvature on the driving magnetic field and allows to extract the parameter σ E which accounts for the strength of the edge pinning potential. The model describes well systems with both weak and strong bulk pinning potentials like Ta/CoFeB/MgO and Pt/Co/Pt, respectively. This provides a means to quantify the effect of edge pinning induced DW curvature in magnetic DW dynamics.

Understanding the behaviour of magnetic domain walls (DWs) when transitioning from full films into patterned structures is of great importance for developing nanodevices for DW based technologies 1 . The analysis of DW dynamics in the so called creep regime of motion [2][3][4][5] , where defects play a central role, is a key aspect. In Ta/CoFeB/MgO/Ta films with perpendicular anisotropy bulk defect densities, and therefore depinning fields (H dep ), are relatively low [6][7][8] . In Pt/Co/Pt films, for example, the values of H dep can be more than one order of magnitude higher 2,4,5 . Due to this low bulk pinning potential the DW dynamics can be easily controlled even in full films by artificial pinning imposed through homogeneous material engineering processes, like light ion irradiation [9][10][11] or pre-patterned substrates 12 . Defects generated through micro/nanostructuring can also have a great impact in pristine materials. DW velocities even in micrometer size wires have been found to experience a critical decrease below the creep law dependence at low drive which scales with the wire width 13 . This effect is also accompanied by an increase in the curvature of the DW front and has therefore been attributed to edge pinning. A deeper analysis of the DW curvature in wires is therefore needed in view of miniaturisation for technological applications. In this study we present the analysis of the DW curvature in a series of 20µm wide Ta/CoFeB/MgO/Ta a) Electronic mail: liza.herrera-diez@c2n.upsaclay.fr wires as a function of the magnetic field. The large edge pinning potential defines curvatures that at low drive reach the maximum radius R = w/2, where w is the wire width. We present a simple model that accounts for the variations in DW curvature as a function of the driving magnetic field allowing for the extraction of σ E , a parameter that characterises the strength of the edge pinning potential. We also apply the same analysis to Pt/Co/Pt 25µm wide wires, which present a higher intrinsic bulk pinning potential. The model describes well both systems, which shows that it can be used to asses the strength of edge pinning and its influence in DW dynamics for different bulk pinning potentials. The samples investigated are Si/SiO 2 /Ta (5nm)/Co 20 Fe 60 B 20 (1 nm)/ MgO (2 nm)/Ta (3 nm) films deposited by magnetron sputtering and annealed at 300 • C exhibiting perpendicular magnetic anisotropy. A series of 20µm wires was fabricated by photolithography and ion beam etching. The 25µm wide Pt/Co/Pt wires were fabricated by depositing a stack of Ta (4 nm)/Pt (4 nm)/Co (0.6 nm)/Pt (4 nm) by magnetron sputtering using e-beam lithography. The final wire structure was reached by conducting a lift off process. Table 1 presents the values of saturation magnetisation (M s ), effective perpendicular anisotropy constant (K ef f ), wire width and depinning field (H dep ) for the two types of samples. H dep corresponds to the experimentally determined transition between the creep and depinning regimes of DW motion 4,5,14 . Fig. 1 shows the Kerr microscopy images of the DW In order to gain more insight into this behaviour, let us first consider a DW propagating in a strip as shown in Fig. 2 (a). In this scenario the propagating DW remains straight and the Zeeman energy gain (dE S ) that the system experiences by letting the DW propagate a distance ∆x is the following:

dE s = -2M s • H • t • dA s , ( 1
)
where t is the thickness of the magnetic wire and dA s is the area swept by the DW (see Fig. 2 (a)). Let us now consider again an initial state where the DW is straight and moves by the same amount (∆x). However, the initially straight DW front can now develop a curvature of radius R as it propagates, this straight-to curved DW displacement is depicted in Fig. 2 (b). In this case the Zeeman energy gain is expressed as follows:

dE c = σ • t • dL -2M s • H • t • dA c . (2)
The gain in energy is reduced by the appearance of the first term that accounts for the variation in DW length dL with respect to the initial state where the DW is straight. For a straight DW its length is equal to L = w while for a curved profile L = 2R arcsin( w 2R ). This means that the additional energy cost due to the DW curvature is linked to an increase in DW length equal to dL = 2R• arcsin( w 2R ) -w. The energy gain for a curved wall is also further reduced due to the smaller area swept by the DW. For a straight DW the area is dA S = w • ∆x while for the curved DW it takes the following form:

dA c = w • (∆x -h) + A CS , (3)
where h is the sagitta as indicated in Fig. 2 (b) and A CS is the area of the circular sector which can be expressed as follows:

h = R -R 2 - w 2 4 , (4)
A CS = RL 2 - w 2 • R 2 - w 2 4 . (5)
Using these expressions we can now calculate dE s and compare it to dE c when, for example, the curvature radius is R = 10µm and w = 20µm. It is not surprising to find that if no edge pinning is involved it is more energetically favourable for the DW to remain straight for all applied magnetic fields. Fig. 3 shows the result of this calculation considering the CoFeB parameters informed in Table 1, the energy gain of a straight DW (solid blue line) is always more negative than that of a curved DW (solid green line) in the whole magnetic field range. Up to this moment no edge pinning was considered. As it is known, the curved DW scenario (Fig. 2 (b)) is a strategy to overcome edge pinning. Therefore, in order to accurately compare it to a straight DW scenario (Fig. 2 (a)), this last configuration should also include an energy cost associated with keeping the DW straight in the presence of edge pinning instead of allowing a curvature to appear. In a previous study 13 we have proposed an additional energy term to account for deviations from the creep law that are observed due to a strong edge pinning potential in CoFeB. This term includes the parameter σ E that can be used to quantify the strength of the edge pinning and describes the effect of the pull-back that the DW experiences in a strong edge pinning potential.

In the present case, the increase in DW length observed in curved DWs due to edge pinning is taken into account by the term σ • t • dL. Let us assume that this energy cost due to edge pinning can find its counterpart in the hypothetic straight DW scenario as an increase in the DW energy equal to:

σ • t • dL = dσ • t • w. (6)
In this context the difference in the DW energy between the initial and final states of the straight DW after a displacement ∆x is proposed to be given by dσ = 2σ E . This increment accounts for the effect of having two strong anchoring points of the DW at each wire side but no bending, therefore the expression for dE s takes the form:

dE s = 2σ E • t • w -2M s • H • t • dA s . (7)
The addition of this term shifts dE s towards higher energies producing a crossing with dE c as shown in Fig. 3 (dashed blue line). This crossing is the point where dE s = dE c and defines a field limit (H CL ) for the existence of a DW curvature with radius R. Above this field value, it is more energetically favourable for the DW to remain straight even in the presence of edge pinning. Reordering the terms in dE s = dE c allows to extract the expression for H CL which has the following form: The model presented here is valid up to a maximum curvature of 2/w, however, at low drive higher curvatures are observed for both CoFeB and Pt/Co/Pt. This occurs at magnetic fields below the value needed to depin the DW from the wire edges, even at the expense of a maximum curvature, but well above that needed to overcome pinning at the centre of the wire. In this case, it may be more energetically favourable for a DW to increase its length going from the edges to the centrer of the wire to increase the switched area. In this context, the DW front could take a more triangular shape and exhibit at the centre a curvature smaller than w/2. This effect can be visualized in the wires at the centre of Fig. 2 (a). The description of the curvatures above 2/w (R < w/2) at low drive is not considered in this model. The solid curves representing H CL provide a dividing line between curved and straight DWs in a magnetic field map. As mentioned, the calculation of these curves takes into account the values of K ef f , M s and the width of the wire, while the value of σ E is adjusted to model the results. The values of σ E obtained for CoFeB and Pt/Co/Pt are 1.01x10 -2 N/m and 6.35x10 -2 N/m, respectively. σ E has been introduced in a previous study as a means to quantify the strength of the edge pinning potential in the context of edge-pinning induced deviations from the creep law in CoFeB wires 13 . In this framework, it is particularly interesting to compare σ E to the DW surface tension σ = 4 A ex • K ef f where A ex is the exchange stiffness constant (2.3 x 10 -11 J/m for CoFeB and 1.6x 10 -11 J/m for Pt/Co/Pt). The ratio σ/σ E results in 1.1 an 0.28 for CoFeB and Pt/Co/Pt wires, respectively. It has been proposed 13 that as this ratio decreases the edge pinning potential represented by σ E progressively dominates over the DW surface energy allowing for a DW curvature. However, when comparing values for different materials not only the differences in the intrinsic parameters but also of the bulk pinning potentials need to be taken into account. The effect of the edge pinning potential depends on its relative strength with respect to the bulk pinning potential, intimately related to the value of the depinning field H dep .

H CL = σ E • w -σ • dL 2M s • (w • h -A CS ) . (8)
The measured DW curvatures in CoFeB and Pt/Co/Pt cover a similar range going from those corresponding to R=w /2 down to low values corresponding to a large R (higher than R = w/0.4 ) for nearly straight DWs. However, the magnetic field range over which each curvature is observed is significantly different with respect to H dep , which is marked by red lines in Fig. 4 (a) and (b). In CoFeB at H dep , the maximum DW curvature observed experimentally and also described by the model is 6 x10 -4 m -1 (R = w/1.2 ). The DW curvature is still relatively pronounced and continues to be well beyond the creep regime. Only at fields around 30 mT, three times larger than H dep , do the DWs become relatively straight, showing a maximum curvature of 2 x10 -4 m -1 (R = w/0.4 ). In contrast, the Pt/Co/Pt wires at H dep already show relatively straight DWs with a maximum curvature below 2 x10 -4 m -1 . This can be related to the large differences of about one order of magnitude found in the depinning field for the two materials. This difference also exists in full films and is due to the intrinsic bulk pinning potential that is known to be exceptionally low in CoFeB materials 2,6 . In this context, a relatively small edge pinning potential can already have a large impact on the dynamics in CoFeB while a much larger one is needed to dominate the DW dynamics in Pt/Co/Pt.

Consequently, the edge pinning potential in CoFeB induces a much stronger effect than in Pt/Co/Pt, reflected here in the strong and persisting curvature of the DWs even beyond the creep regime. In contrast, in Pt/Co/Pt a significant DW curvature induced by edge pinning is only observed deep into the creep regime. This model can also be used to extrapolate the effects of edge pinning to narrower wires. Fig. 5 (a) shows the calculated H CL profiles using σ E =1.01x10 -2 N/m, the intrinsic parameters for CoFeB and varying the wire width. The H CL values increase as the wire becomes narrower. The plot in the inset of Fig. 5 (a) shows the H CL values for a DW radius of w /2 as a function of the wire width, here a dramatic increase is observed for narrow wires. This model could therefore allow for the estimation of the effects of edge pinning for a given material and a particular wire edge structure, for example linked to the fabrication process, as the wire width decreases. The estimation could be conveniently done by analysing the DW dynamics at much larger scales.

For wires widths below 5µm, it is interesting to compare this analytical model with micromagnetic simulations. Fig. 5 (b) shows the result for CoFeB wires, filled squares and circles represent the curvatures observed for w =4µm and w =2µm with an maximum edge roughness (M ER ) of 30nm (see supplementary information). The DW curvature follows a similar trend as the analytical model with respect to magnetic field and w. M ER plays a key role, empty squares show the trend obtained for w =4µm and M ER = 80nm which is reflected in a shift of the curvatures at all magnetic fields to significantly higher values. The curvature at 40mT was also evaluated in a wire with very rough edges, M ER =300nm showing a further increase (crossed diamond). This is in line with the conclusions made earlier regarding the effects of the fabrication process in the DW curvature. The curve obtained using the analytical model for w =4µm is shown in Fig. 5 In contrast, for low M ER the effect of varying α is not a dominant feature. This bring the attention to the crucial role of disorder in the DW dynamics in CoFeB. In the present study, perfect wires are simulated, while studies in the literature show that adding a granular structure and an anisotropy distribution to simulate disorder can have a large impact in the DW dynamics. In this context, additional energy dissipation channels appear in the system which could also affect the response to a change in the value of α 11 . A detailed micromagnetic study would be needed to fully characterise these effects. Micromagnetic simulations have also been performed for w =250nm and w =500nm, where the analytical model finds its limit of validity since it is based on the one dimensional(1D) model of DW motion. A dimensionality change may occur from a 2D to a 1D medium for very narrow wires 16 and edge effects can rule over creep dynamics 17 limiting the use of a 1D based model. For w =500nm, M ER =30nm and α =0.015 the internal structure of the DW presents a large number of Bloch lines and an irregular DW front, showing no curvature for either 10mT nor 20mT. A similar behavior is observed for w =250nm (see supplementary information). This confirms the presence of a more complex dynamics at this scale going beyond the 1D model and calls for a more careful theoretical analysis.

In conclusion, we present a simple model to describe the dependence of the DW curvature on the applied magnetic fields in wires with an edge pinning potential. This model allows for the estimation of the magnetic field limit up to which a given DW curvature can be observed and it has been applied to two key spintronics materials with low and high bulk pinning potentials, CoFeB and Pt/Co/Pt. The analysis of the DW curvature also allows for the extraction of the parameter σ E that can be used to compare edge pinning potentials in different devices. The relative strength of the edge pinning potential with respect to the surface tension of the DW (σ/σ E ) together with the differences between the edge and bulk pinning potentials in each material are the key aspects involved in the description of the DW curvature. It has also been shown that this model can be used to extrapolate the effects of edge pinning observed in relatively large wires to smaller dimensions and has a good correspondence with results obtained from micromagnetic simulations. Therefore, this model can be of considerable interest for the understanding and the quantification of the effects of edge pinning in patterned magnetic structures.

FIG. 1 .

 1 FIG. 1. (a) Kerr microscopy images of curved DWs in CoFeB wires. (b) DW curvature in a Pt/Co/Pt wire as a function of the magnetic field.

FIG. 2 .

 2 FIG. 2. Straight DW (a) and DW that transitions between a straight and a curved profile upon displacement (b).

FIG. 3 .

 3 FIG.3. Energy gain dEs (blue line) and dEc (green line) for straight and curved DWs as a function of the applied magnetic field in CoFeB. The straight DW without pinning increases its energy when the term 2σE • t • w is added to account for edge pinning (dotted blue line).

FIG. 4 .

 4 FIG. 4. Domain wall curvature as a function of magnetic field in a 20 µm wide CoFeB wire (a, different colors correspond to the different wires shown in Fig. 1) and in a 25 µm wide Pt/Co/Pt wire. The solid lines are the calculation of HCL

FIG. 5 .

 5 FIG. 5. (a) Calculated HCL profile for σE=1.01x10 -2 N/m (CoFeB) for different wire widths. HCL values corresponding to R=w /2 as a function of the wire width (inset). (b) Comparison with micromagnetic simulations.

TABLE I .

 I Material Width (µm) Ms(A/m) K ef f (J/m 3 ) H dep (mT) Ms, K ef f , the wire width (w) and the depinning fields H dep for the Ta/CoFeB/MgO/Ta and Pt/Co/Pt wires.

	CoFeB	20	8.7x10 5	3.4x10 5	9.7
	Pt/Co/Pt 25	1.4x10 6	1.3x10 6	100.0

  (b), the curvatures are significantly larger than those obtained with micromagnetic simulations even for very large M ER . It is therefore important to highlight that the micromagnetic simulations were made using the experimental values presented in Table 1 while exploring the effect of variations in the Gilbert damping parameter α. The curvatures for w =4µm in open and full squares and the crossed diamond were calculated using α =1, all showing relatively low values. For high M ER , changing α from 1 (crossed diamond) to 0.01 (crossed square) increases significantly the curvature, as seen at 40mT. CoFeB is known to have low values of α in the 0.015 range15 , therefore lower α values not only give curvatures closer to the analytical model but are also more compatible with experimental values.

ACKNOWLEDGMENTS

We gratefully acknowledge financial support from the European Union FP7 and H2020 Programs (MSCA ITN grants No. 608031 and No. 860060), from the French National Research Agency (project ELECSPIN), and Ministerio de Economia y Competitividad of the Spanish Government (project MAT201787072C41P). The authors thank G. van der Jagt for useful comments.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

SUPPLEMENTARY MATERIAL

Information about micromagnetic simulations.


Hugo Henck

Zeineb Ben Aziza

Debora Pierucci

Feriel Laourine

Francesco Reale

Pawel Palczynski

Julien Chaste

Mathieu G Silly

François Bertran

Patrick Le Fevre

Emmanuel Lhuillier

Taro Wakamura

Cecilia Mattevi

Julien E Rault

Matteo Calandra

Abdelkarim Ouerghi
email: abdelkarim.ouerghi@c2n.upsaclay.fr

Electronic band structure of Two-Dimensional WS2/Graphene van der Waals Heterostructures

Keywords:

Combining single-layer two-dimensional semiconducting transition metal dichalcogenides (TMDs) with graphene layer in van der Waals heterostructures offers an intriguing means of controlling the electronic properties through these heterostructures. Here, we report the electronic and structural properties of transferred single layer WS2 on epitaxial graphene using micro-Raman spectroscopy, angle-resolved photoemission spectroscopy measurements (ARPES) and Density Functional Theory (DFT) calculations. The results show good electronic properties as well as well-defined band arising from the strong splitting of the single layer WS2 valence band at K points, with a maximum splitting of 0.44 eV. By comparing our DFT results with local and hybrid functionals, we find the top valence band of the experimental heterostructure is close to the calculations for suspended single layer WS2. . Our results provide an important reference for future studies of electronic properties of WS2 and its applications in valleytronic devices.

I. INTRODUCTION

Two-dimensional (2D) materials, such as graphene, h-BN, phosphorene, and transition metal dichalcogenides (TMDs), are an ideal platform for studying exciting physical properties not attainable in their bulk counterparts [START_REF] Geim | Van der Waals heterostructures[END_REF].

They often exhibit a versatile electronic structure controllable by thickness [START_REF] Li | From Bulk to Monolayer MoS2: Evolution of Raman Scattering[END_REF], surface chemical adsorption, and strain [START_REF] Castro | Biased Bilayer Graphene : Semiconductor with a Gap Tunable by the Electric Field Effect[END_REF]. Of particular interest are the family of TMDs of formula MX2 (M = Mo, W; X=S, Se). They are semiconductor with unique properties in the 2D limit such as indirect to direct band gap transition, large exciton binding energy, well-defined valley degrees of freedom, and spin splitting of the valence band [START_REF] Yang | Long-lived nanosecond spin relaxation and spin coherence of electrons in monolayer MoS2 and WS2[END_REF]. Many efforts have been made to harvest these properties into practical optoelectronic, spintronic, and valleytronic devices [START_REF] He | Probing effect of electric field on photocarrier transfer in graphene-WS_2 van der Waals heterostructures[END_REF].

In addition to homogenous 2D materials, van der Waals (vdW) heterostructures have recently emerged as a novel class of materials, in which different 2D atomic planes are vertically stacked to give rise to distinctive properties and exhibit new structural, chemical, and electronic phenomena [START_REF] Geim | Van der Waals heterostructures[END_REF][START_REF] Froehlicher | Charge Versus Energy Transfer in Atomically Thin Graphene-Transition Metal Dichalcogenide van der Waals Heterostructures[END_REF]. These heterostructures, in contrast with traditional heterostructures, can be designed and assembled by stacking individual 2D layers without lattice parameter constraints. The weak interlayer coupling in vdW heterostructures offers the possibility of combining the intrinsic electronic properties of each individual 2D layers in devices. In particular, WS2/graphene vdW heterostructures are remarkable since they gather the high carrier mobility and broadband absorption of graphene [START_REF] Pallecchi | High Electron Mobility in Epitaxial Graphene on 4H-SiC(0001) via post-growth annealing under hydrogen[END_REF], as well as the direct bandgap and extremely strong light-matter interactions of single layer WS2. The combination of these unusual characteristics led to potential applications in field-effect transistor devices [START_REF] Georgiou | Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics[END_REF] and energy harvesting materials [START_REF] Hu | Advances and Challenges in Metal Sulfides / Selenides for Next-Generation Rechargeable Sodium-Ion Batteries[END_REF]. MX2 single layer, the elementary unit to form ultrathin films by weak stacking, features a novel spin-valley coupled band structure. At the corners of the first Brillouin zone (BZ), the valence (conduction) band has two inequivalent valleys. Owing to the broken inversion symmetry in single layers, the strong spin-orbit coupling (SOC) from the dorbitals of the metal atoms results in a valence band spin splitting at K points, with a magnitude as large as 400 meV in WS2 [START_REF] Ulstrup | Spatially Resolved Electronic Properties of Single-Layer WS2 on Transition Metal Oxides[END_REF][START_REF] Katoch | Giant spin-splitting and gap renormalization driven by trions in single-layer WS$_2$/h-BN heterostructures[END_REF]. The spin-splitting has opposite signs at the K and K' valleys as they are time reversal of each other at the valence band. This spin-valley coupling forms the basis for manipulation of spin and valley degrees of freedom in these 2D semiconductors.

Angle resolved photoemission spectroscopy (ARPES) is one of the most suitable tools to investigate the electronic structure of 2D materials with energy and momentum resolution as well as surface sensitivity [START_REF] Pierucci | Band alignment and minigaps in monolayer MoS2-graphene van der Waals heterostructures[END_REF], [START_REF] Grubišić Čabo | Observation of Ultrafast Free Carrier Dynamics in Single Layer MoS 2[END_REF], [START_REF] Jin | Tuning the electronic structure of monolayer graphene / MoS 2 van der Waals heterostructures via interlayer twist201409[END_REF], [START_REF] Yeh | Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide[END_REF].

There have been a number of ARPES studies either on bulk MX2 samples or few-layer samples prepared by various methods such as exfoliation, chemical vapor deposition (CVD) [START_REF] Forti | Electronic properties of single-layer tungsten disulfide on epitaxial graphene on silicon carbide[END_REF][START_REF] Rossi | Patterned tungsten disulfide/graphene heterostructures for efficient multifunctional optoelectronic devices[END_REF], and epitaxial growth [START_REF] Liu | Elastic Properties of Chemical-Vapor-Deposited Monolayer MoS2 , WS2 , and Their Bilayer Heterostructures[END_REF][START_REF] Dau | Millimeter-scale layered MoSe2 grown on sapphire and evidence for negative magnetoresistance[END_REF]. They all observe sizable splitting in the VB at the K-point, with a size of ∼150 meV for MoS2 and ∼400 meV for WS2 as tungsten induces larger SOC [START_REF] Strategy | Electronic Properties of MoS2-WS2 Heterostructures Synthesized with Two-Step Lateral Epitaxial Strategy[END_REF]. Furthermore, uniform and large-area synthesis of single layer WS2 is an important subject toward applications of 2D materials in various electronic devices [START_REF] Zhang | Vertical heterostructures of layered metal chalcogenides by van der Waals epitaxy[END_REF].

I. METHODS:

Single layer graphene was produced via a two-step process beginning with a starting substrate of 4H-SiC(0001).

Prior to graphitization, the substrate was hydrogen etched (100% H2) at 1550 °C to produce well-ordered atomic terraces of SiC. Subsequently, the SiC sample was heated to 1000 °C and then further heated to 1550 °C in an Ar atmosphere [START_REF] Sediri | Atomically Sharp Interface in an h-BN-epitaxial graphene van der Waals Heterostructure[END_REF][START_REF] Pallecchi | Observation of the quantum Hall effect in epitaxial graphene on SiC(0001) with oxygen adsorption[END_REF][START_REF] Pierucci | Self-organized metalsemiconductor epitaxial graphene layer on off-axis 4H-SiC[END_REF]. WS2/SiO2 samples were grown by chemical vapor deposition (CVD) in a 1" quartz tube furnace. The growth substrate was placed in the center of the furnace and heated to 800 °C. A 25 mg sulfur pellet was placed on a piece of silicon and positioned upstream in the furnace such that its temperature was approximately 150 °C. Carrier gas (500 sccm N2) was used to bring sulfur vapor into the furnace for a 30 min growth period.

The ARPES measurements were conducted at the CASSIOPEE beamline of Synchrotron SOLEIL (Saint-Aubin, France). We used linearly polarized photons of 50 eV and a hemispherical electron analyzer with vertical slits to allow band mapping. The total angle and energy resolutions were 0.25° and 10 meV. All ARPES experiments were done at low temperature (8 K). XPS experiments were carried out on the TEMPO beamline of Synchrotron SOLEIL (Saint-Aubin, France) at room temperature. The photon source was a HU80 Apple II undulator set to deliver linearly polarized light. The photon energy was selected using a high-resolution plane grating monochromator with a resolving power E/ΔE that can reach 15,000 on the whole energy range (45 -1500 eV). During the XPS measurements, the photoelectrons were detected at 0° from the sample surface normal 𝒏 ⃗ ⃗ and at 46° from the polarization vector 𝑬 ⃗ ⃗ .

I. RESULTS AND DISCUSSIONS

In this work, TMD/graphene heterostructures were made from WS2 grown by CVD on SiO2/Si substrates that were then transferred onto graphene/SiC [START_REF] Pierucci | Large area molybdenum disulphide -epitaxial graphene vertical Van der Waals heterostructures[END_REF] (more details about the transfer procedure are given in the supplementary information Section I) [26]. A schematic of WS2 crystal structure is presented in Figure 1(a) where the lattice constants are indicated. The CVD growth of WS2 on SiO2 results in characteristic single-crystal domains shaped as well-defined equilateral triangles [START_REF] Han | Seeded growth of highly crystalline molybdenum disulphide monolayers at controlled locations[END_REF]. These films can be nondestructively transferred to various kinds of substrates as desired. With respect to SiO2 and similar substrates, graphene layer has favorable qualities such as atomic flatness, and homogeneous charge distribution. This should enable direct investigation of the adjacent TMD's intrinsic electronic structure and many-body effects. Graphene layer is often used as a substrate for TMD heterostructures with high device performance [START_REF] Schwierz | Two-dimensional materials and their prospects in transistor electronics[END_REF]. Single layered WS2 flakes were then easily identified by their optical contrast with respect to the graphene substrate (Figure 1 (d) and supplementary information section II and III). Several Raman spectra of WS2 on graphene, collected in different flake positions, are shown in Figure 1(c). These Raman spectra are obtained with 532 nm excitation, which is in resonance with the B exciton absorption peak [START_REF] O'brien | Mapping of Low-Frequency Raman Modes in CVD-Grown Transition Metal Dichalcogenides: Layer Number, Stacking Orientation and Resonant Effects[END_REF][START_REF] Zhao | Lattice dynamics in mono-and few-layer sheets of WS2 and WSe2[END_REF] . Then, beside the first order modes at the Brillouin zone (BZ) center (Γ), the in-plane phonon mode 𝐸 2𝑔 1 at 356 cm -1 and the out-of-plane phonon mode A1g at 418 cm - 1 [START_REF] Kobayashi | Growth and Optical Properties of High-Quality Monolayer WS 2 on Graphite[END_REF][START_REF] Gutie | Extraordinary Room-Temperature Photoluminescence in Triangular WS 2 Monolayers[END_REF], the Raman spectra present a series of overtone and combination peaks. These different contributions are clearly separated using a multi-peak Lorentzian fit (blue lines in Figure 1 (c) top). In particular, the Raman feature around 350 cm -1 is the convolution of several components: the 𝐸 2𝑔 1 (𝛤), the 2 LA (M) mode at 351.7 cm -1 , which is a second-order Raman mode due to LA phonons at the M point of the BZ zone, and the 𝐸 2𝑔 1 (𝑀) mode [START_REF] Molina-Sánchez | Phonons in single-layer and few-layer MoS2 and WS2[END_REF].

Moreover, Raman peaks at 323.7 cm -1 and 297.1 cm -1 are combinations modes, which are attributed to 2𝐿𝐴 (𝑀) -𝐸 2𝑔 2 (𝛤) and the 2𝐿𝐴 (𝑀) -2𝐸 2𝑔 2 (𝛤) modes, respectively. Raman mapping was conducted to investigate the uniformity within the single flake. The 2𝐿𝐴 (𝑀), 𝐸 2𝑔 1 (𝛤) and the A1g (𝛤) modes intensity and position mapping are shows in Figure 1(d) and S2. These Raman modes peak positions and intensity are uniform within the single crystal, indicating that the electronic properties of WS2 are uniform on the graphene substrate. From the frequency difference between the A1g (𝛤) and the 2LA(M), the thickness of the WS2 flakes can be determined [START_REF] Berkdemir | Identification of individual and few layers of WS2 using Raman spectroscopy[END_REF][START_REF] Withers | Electron transport of WS2 transistors in a hexagonal boron nitride dielectric environment[END_REF][START_REF] Bianco | Direct epitaxial CVD synthesis of tungsten disulfide on epitaxial and CVD graphene[END_REF]. An average distance of 65.9 ± 0.1 cm -1 is obtained, as shown in figure S4. This value is consistent with monolayer WS2 as already shown by previous studies [START_REF] Withers | Electron transport of WS2 transistors in a hexagonal boron nitride dielectric environment[END_REF]. For the following experiments, the single layer coverage was estimated to be around 20% of the total area of the sample.

The high quality of the WS2 transferred on graphene layer allows investigating the electronic structure by X-ray photoelectron spectroscopy (XPS) and ARPES. Both the feasible large-area synthesis and the reliable film transfer process can promise that WS2 ultrathin films will pave a route to many applications of 2D materials and vdW heterostructure. XPS is used to determine the chemical composition and stoichiometry of the WS2 films transferred on the graphene. The C-1s XPS spectrum of WS2/graphene heterostructure, collected at h=340 eV, is shown in Figure 2(a). The C-1s spectrum showed three components at 283.9, 284.7, and 285.1 eV in binding energy (BE).

These components correspond to the SiC bulk (labeled SiC), the graphene layer (labeled G), and the interface layer (labeled I), respectively. The G peak was fitted by a sum of a Gaussian function convoluted with a Doniach-Sunjic line shape with an asymmetry factor  of 0.09 and a FWHM of 0.4 eV. The low value of the FWHM indicates that only one core level peak was present and thus the carbon atoms had a unique chemical environment. Moreover, no structure appeared at 286.7 eV in the C-1s XPS spectrum, usually attributed to the contamination and/or oxidation, this means even if the samples were annealed at 300 °C, the WS2/graphene layers were very inert and did not show any contamination after WS2 transfer process.

The W-4f and S-2p XPS peaks deconvolution shown in Figure 2(b) and (c), present the standard WS2 stoichiometry.

The WS2 is well fitted by a doublet peaks at BE of 33.4 eV, 35.6 eV, corresponding to W-4f7/2, W-4f5/2 core energy levels (4f5/2: 4f7/2 ratio of 0.75) [START_REF] Mao | Ferromagnetism in exfoliated tungsten disulfide nanosheets[END_REF], respectively (Figure 2 corresponding to S-W bonding, and confirms the presence of WS2. The absence of the oxygen content [START_REF] Li | Enhanced electrochromic performance of WO3 nanowire networks grown directly on fluorine-doped tin oxide substrates[END_REF][START_REF] Barrera | Solution synthesis of fewlayer 2H MX2 (M = Mo, W; X = S, Se)[END_REF] in these samples is a result of high quality of the interface in this hybrid hetero-structure, particularly in light of the Raman characteristics that are comparable to high quality WS2 (see above and supplementary information section II and ref [START_REF] Gao | Large-area synthesis of high-quality and uniform monolayer WS2 on reusable[END_REF]).

The electronic structure was also probed using ARPES measurements. The WS2 flakes are relatively well spaced on the graphene substrate, ensuring, thanks to the small spot size (50×50 m 2 ), the mapping of a single flake. SiC [START_REF] Pierucci | Band alignment and minigaps in monolayer MoS2-graphene van der Waals heterostructures[END_REF]. Then, the n-type doping, close to 9×10 12 cm -2 , of pristine graphene was not modified by the formation of the heterostructure. This confirms, as shown also by the work function measurement (see supplementary information Figure S8), that there was no significant charge transfer between the 2D materials. However, if we look more in detail at the momentum distribution curves (MDCs) shown in figure 2 (f) a less dispersive behavior of the peaks are present around ED. Then, the presence of gap-like feature at the K point (already present in the pristine graphene) cannot be completely excluded [START_REF] Zhou | Substrate-induced bandgap opening in epitaxial graphene[END_REF]. However, a more detail study of this feature goes beyond the scope of this paper. From a linear fitting of the MDCs a Fermi velocity v F ~ 1.05 × 10 6 m/s was also determined.

It is obvious that also the sharp and intense structure of -bands confirms the high structural quality of WS2 / graphene heterostructure. Differently from our previous work on MoS2/graphene layer and from Diaz et al. [START_REF] Pierucci | Band alignment and minigaps in monolayer MoS2-graphene van der Waals heterostructures[END_REF][START_REF] Diaz | Interface properties of CVD grown graphene transferred onto MoS2[END_REF] no signature of interlayer hybridization and mini-gaps opening [START_REF] Diaz | Direct observation of interlayer hybridization and Dirac relativistic carriers in graphene/MoS₂ van der Waals heterostructures[END_REF] is present on the π-band of graphene. The absence of this superperiodicity effects probably is related to the mismatch angle between the WS2 flake and the graphene underlayer. In the following discussions regarding the ARPES data, we will focus mostly on the split of the valence band feature at the K-point of the WS2 (Figures 3). In particular, in order to gain more insight on the electronic structure of WS2, we performed first principles electronic structure calculations on an isolated WS2 monolayer using the QUANTUM ESPRESSO code [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF][START_REF] Andreussi | Advanced capabilities for materials modelling with Quantum ESPRESSO[END_REF] and PBE [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] and HSE06 [START_REF] Krukau | Influence of the exchange screening parameter on the performance of screened hybrid functionals[END_REF] hybrid functionals within the adaptive compressed exchange [START_REF] Lin | Adaptively Compressed Exchange Operator[END_REF] implementation. More technical details are given in the supplemental materials (section IV). Figure 3(a) shows the measured band structure around the K valley. The top of the valence band at the K point is mostly formed by planar dxy and dx2-y2 orbital of tungsten, while at the  point the band is mostly composed by W dz orbitals and S pz orbitals.

The observation of a single valence band at  with a higher binding energy than at K also excludes the contribution from bilayer or trilayer WS2: in bilayer TMD systems, the valence band near  shows a bonding/anti-bonding splitting that would be observable by ARPES as two bands, in contrast to what is seen here [START_REF] Yeh | Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide[END_REF]. The maximum of the valence band is located at the K point (-1.8 eV, which is 0.3 eV higher than at  point). Since the band gap of single WS2 is 2.27 eV [START_REF] Raja | Coulomb engineering of the bandgap and excitons in two-dimensional materials[END_REF], these measurements indicate that our sample is heavily electron doped, which is consistent with previous reports. [START_REF] Ulstrup | Spin and valley control of free carriers in single-layer WS2[END_REF] The electronic structure in the -2 eV to -3 eV binding energy range is globally in good agreement with our electronic structure calculations (Figures 3(b) and (c)), although the energy separation between the top of the valence band at K and  is slightly underestimated in PBE (Figure 3 (b)). In both theory and experiments the valence band maximum at the  point is located at higher binding energies than that at the K-point, the energy separation between the two being 0.20 eV in experiments (Figure 3(b) and (c)), 0.17 eV in PBE and 0.20 eV in HSE Figure 3 (c). The measured spin-orbit splitting at K is about 440 meV. Our theoretical calculations for the isolated WS2 monolayer lead to splittings of 440 meV (PBE) and 551 meV (HSE06 on top of PBE).

Moreover, an analysis of the curvature of the bands from the ARPES measurements also allows us to deduce the effective mass of the single layer WS2 forming the heterostructure. We determined an experimentally derived hole effective mass of 0.4 m0 (upper band) and 0.5 m0 (lower band) (where m0 is the free electron mass) at K, and a hole effective mass of 1.7 m0 at . These values agree very well with the PBE calculated bands, suggesting that many body effects are not important close to the top of the valence band at K.

Finally, the gap between the two highest energy valence bands and the bands at lower energies is substantially underestimated in PBE. The inclusion of the exchange interaction within the HSE06 functional on top of the PBE geometry corrects both errors but leads to a somewhat too large spin-orbit coupling.

Although we cannot include explicitly the interaction with the substrate as we miss the structural orientation between WS2 and graphene, it seems that the measured ARPES data agrees well with the bands of an isolated single layer with PBE geometry and electronic structure obtained with the inclusion of the exchange interaction. In particular the exchange interaction seems to improve the agreement not only for the top of the valence band at zone center but also for the electronic structure in the binding energy region below -3 eV.

IV. CONCLUSIONS

In summary, we have studied the electronic structure of single layer WS2 on epitaxial graphene. We found that this heterostructure gives rise to sharp bands, in particular for the WS2 VBM near the  and K points. We directly observe the strong spin splitting of the upper VB and its value are in excellent agreement with the PBE DFT calculations. Our ARPES measurements on the heterostructure showed graphene and WS2 largely retained their original electronic structure and, in particular suspended WS2 monolayer is a good approximation of the electronic properties close to the top of the valence band. Finally, we determined experimentally spin-orbit splitting. Our results provide an important reference for future studies of electronic properties of WS2 and their applications in spintronic and valleytronic devices

  (b)) and confirmed by micro-Raman spectroscopy (Figure 1 (c) and (d)). The optical image in Figure 1(b) shows large (lateral size about 50 μm) triangular flakes of WS2 on the graphene layer. The graphene underlayer used in this study was obtained by annealing 4H-SiC(0001) (see Methods). After the transfer of WS2 onto graphene, an annealing process at T = 300 °C for 60 minutes in UHV was used to further clean the surface and interface of the WS2/graphene heterostructure. To investigate the structural properties of the WS2 flakes micro-Raman and photoluminescence (PL) spectroscopy were used (Figure 1 (c) and

  (b)). The sulfur S-2p peak (Figure 2(c)) consists of a single doublet (S 2p3/2 at a BE = 163 eV and a 2p1/2:2p3/2 ratio of 0.5 and spin-orbit splitting of 1.19 eV)

Figure 2 (

 2 d) shows the photoelectron intensity as a function of energy and k-momentum around the normal emission. This is a good measure of the band structure of WS2 around Γ. The zero of binding energy (i.e. the Fermi level) was determined by fitting the leading edge of the graphene layer at the same photon energies and under the same experimental conditions. Beside the typical dispersion of the π bands of graphene around -6 to -8 eV (most intense band), a new set of bands is visible at the Γ point of the BZ, which is the signature of WS2 valence band. In the spectra, the most distinct features include the valence band maximum (VBM) at . The full width at half maximum (FWHM) of WS2 band branches is about 80 meV as shown by Energy distribution curves (EDC) in FigureS7) extracted from the ARPES map of Figure2(d) at the  point. The sharpness of the different bands can be attributed to the high quality of the transferred flake. Figure 2(e) shows the measured band structure corresponding to the graphene underlayer. The single and robust Dirac cone confirms that the graphene monolayer at the heterostructure preserves the Dirac linear dispersion and the massless relativistic character of the graphene carriers close to the Fermi level. The Dirac point (ED) is located at 0.40 eV below the Fermi level as in the case of pristine graphene on

Figure captions:Figure 1 :

 1 Figure captions:

Figure 2 :

 2 Figure 2: High resolution XPS and ARPES of WS2/graphene heterostructures: a) C-1s and b) W-4f , (e) S-2p core levels at h = 340 eV.d) ARPES map of WS2/graphene heterostructure around the  point in the K high symmetry direction of WS2 Brillouin zone, e) Band structure of the graphene layer in the heterostructure at the K high symmetry direction, f) corresponding momentum distribution curves (MDCs) of figure (e).

Figure 3 :

 3 Figure 3: a) ARPES map of single layer WS2 along the K high symmetry directions, b) and c) Comparison between ARPES map and DFT calculations (PBE and HSE06 respectively).

Acknowledgements: We acknowledge support from the Agence Nationale de la Recherche (ANR) under grants Labex Nanosaclay and H2DH (ANR-15-CE24-0016), from the Region Ile-de-France in the framework of C'Nano IdF (nanoscience competence center of Paris Region). Labex Nanoscalay belongs to the public funded Investissements d'Avenir program managed by ANR.