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The search for manganese incorporation in MoSe2 monolayer epitaxially grown on graphene

The introduction of magnetism in two-dimensional (2D) materials represents an intense field of research nowadays and the quest to reach above-room-temperature ordering temperatures is still underway. Intrinsic ferromagnetism was discovered in 2017 in CrI3 and Cr2Ge2Te6 in the monolayer form with low Curie temperatures. An alternative method to introduce magnetism into conventional 2D materials is substitutional doping with magnetic impurities similarly to three-dimensional diluted magnetic semiconductors. The case of Mn-doped transition metal dichalcogenide (MoS2, MoSe2, WS2, WSe2) monolayers is very interesting because combining out-of-plane ferromagnetism and valley contrast leads to ferrovalley materials. In this work, we focus on the incorporation of Mn in MoSe2 by molecular beam epitaxy on graphene which has been rarely addressed up to now. By using a multiscale characterization approach, we demonstrate that Mn atoms are incorporated into the MoSe2 monolayer up to 5 atomic percent. However, when incorporated into the film, Mn atoms tend to diffuse to the grain edges forming undefined MoxMnySez phase at grain boundaries after completion of the MoSe2 monolayer. This segregation leaves the crystalline and electronic structure of MoSe2 unmodified. Above 5%, the saturation of Mn content in MoSe2 leads to the formation of epitaxial MnSe clusters.


Introduction
Spintronics aims at exploiting the spin degree of freedom of electrons and led to very important achievements in data storage and sensor industries [1]. To date, only ferromagnetic metals were used in elementary devices like spin valves or magnetic tunnel junctions preventing easy electrical control of magnetic properties. The emergence of dilute magnetic semiconductors (DMS) where ferromagnetism is mediated by charge carriers offered the opportunity to electrically control their magnetic properties [2]. For instance, the Curie temperature [3] and magnetic anisotropy [4] of Mn-doped GaAs could be tuned by applying an electric field. However, those materials still suffer today from low Curie temperatures [5] and remain difficult to stabilize due to the very low solubility of magnetic impurities like Mn in conventional semiconductors like GaAs, GaN or Ge [6].
In parallel, the field of 2D semiconductors like transition metal dichalcogenides (TMD) of formula MX 2 (M = Mo, W and X = S, Se) and others has grown considerably in the last decade for their exceptional optical and electrical properties [7,8]. In order to turn these materials magnetic, it is natural to explore the incorporation of magnetic atoms like Mn which exhibits the largest spin moment among transition metals. Molecular beam epitaxy (MBE) has been the principal tool to grow DMS [9]. Due to the lack of lattice matched substrates, the method to grow epitaxial TMD monolayers either by MBE or chemical vapor deposition is the van der Waals (vdW) epitaxy [10]. In this regime, the weak vdW interaction between the substrate and the TMD releases the lattice matching constraint and makes possible the growth of fully relaxed TMD monolayers. If the substrate is single crystalline, the weak vdW interaction is sufficient to ensure the epitaxial growth of the TMD and obtain good crystalline quality. The substrates are usually vdW materials like graphene [11,12] or mica [13,14] but passivated surfaces like Se-passivated GaAs also give very good epitaxial growths [15,16].
To date, Mn doping has been little investigated in TMD monolayers. Early theoretical work predicted long-range ferromagnetism in Mn-doped TMD monolayers [17]. When Mn substitutes Mo or W and for concentrations less than 5%, the ferromagnetic coupling between Mn spins is mediated by the antiferromagnetic exchange interaction between the localized d states of Mn and the delocalized p states of chalcogen atoms. In MoSe 2 , Mn atoms are expected to carry a spin moment of 1.27µ B and introduce gap states close to the Fermi level and at the bottom of the conduction band. However very few experimental achievements have been reported so far [13,[18][19][20]. In Ref. [19], the authors raised an important issue related to the high reactivity of Mn atoms. During growth, when Mn atoms or precursors are in direct contact with the SiO 2 substrate, they tend to react with oxygen atoms and not to incorporate into MoS 2 . The use of a vdW substrate like graphene is more suitable to achieve Mn doping. In Ref. [20], the authors developed another growth method on SiO 2 called solid phase epitaxy where Mn atoms are not in direct contact with the SiO 2 substrate. It allows the incorporation of Mn atoms into MoSe 2 without evidence of Mn clustering. However the exact position of Mn atoms in MoSe 2 could not be resolved. In Refs. [20] and [19], the authors do not provide magnetic measurements and there is no direct proof of efficient magnetic doping and ferromagnetism in Mn doped MoS 2 and MoSe 2 . In contrast, in Refs. [13] and [18], the authors report temperature dependent magnetic measurements of Mn doped MoSe 2 multilayers grown on mica and Mn doped MoS 2 nanostructures respectively. As long as parasitic magnetic signals from the substrate can be neglected, the authors observe the coexistence of a strong paramagnetic signal at low temperature and a very soft ferromagnetic signal persisting up to 100 K. However, in both works, Mn atoms could not be accurately located in MoSe 2 and MoS 2 probably because it is challenging from a technical point of view. Hence, the exact origin of ferromagnetism is not clearly stated. It can originate from substitutional doping of Mn atoms or to any Mn-rich phase in the form of Mo x Mn y Se z or Mo x Mn y S z due to Mn segregation.
In this work, we study the MBE growth of Mo 1−x Mn x Se 2 monolayers by co-evaporating all three elements in ultra high vacuum (UHV) conditions on a graphene substrate. By using a multiscale characterization approach, we conclude that the Mn solubility in MoSe 2 monolayer is extremely low. In optimized growth conditions for MoSe 2 , Mn atoms spontaneously segregate at the MoSe 2 grain edges during the growth forming an undefined Mo x Mn y Se z phase at grain boundaries. As a consequence, the crystal and electronic structures of MoSe 2 are almost unaffected by the incorporation of Mn atoms. Moreover, above 5%, α-MnSe(111) clusters appear at the surface of the film.

Sample growth and crystal structure
Mo 1−x Mn x Se 2 monolayers were grown by MBE on a graphitized 6H-SiC(0001) substrate in a UHV chamber with a base pressure of 5 × 10 −10 mbar. For scanning transmission electron microscopy (STEM) observations, the films were deposited in the same conditions on a graphene layer grown by CVD on platinum which allows for their transfer on TEM grids by an electrochemical method [21]. The CVD graphene on platinum is polycrystalline with 10 µm-large singlecrystalline domains. We assume that, in the middle of a domain, the growth proceeds the same as on epitaxial graphene on SiC. This assumption is reasonable since the graphene layer is screening the substrate underneath and the surface chemistry (which is critical for the growth and Mn incorporation) is of van der Waals type in both cases.
Before the growth, the substrate was thermally cleaned in the MBE chamber at a temperature of 750°C for 15 min. The growth temperature was 500°C. Molybdenum and selenium are respectively evaporated by an electron gun evaporator and an effusion cell. The direct Se flux measured at the sample position using a retractable Bayard-Alpert gauge was between 1 × 10 −6 and 2×10 −6 mbar. The Mo deposition rate, measured with a quartz balance, was 1.1 Å/min. Note that these growth conditions (temperature and depostion rates) were optimized to obtain the best crystalline quality of MoSe 2 monolayers on graphene.
Considering the low Mn concentrations (<10%), manganese cannot be incorporated during the whole duration of the MoSe 2 monolayer growth because the required flux would be too low to be under control. Here, Mn is evaporated with an electron gun evaporator at a stable rate of 0.75 Å/min. We thus used a sequential incorporation of manganese (typically in 2 or 3 times regularly spaced in time) during the growth of MoSe 2 . We studied six different Mo 1−x Mn x Se 2 samples with compositions x = 0; 0.01; 0.025; 0.05; 0.075 and 0.1 respectively. The Mn content was calibrated by Rutherford Backscattering measurements [13]. Post-growth annealing was performed at 750°C during 15 min under Se flux to improve the crystalline quality [21]. Finally, the as-grown monolayers were coated by a 15 nm-thick amorphous Se protecting layer to avoid their oxidation in air during their transfer to the characterization techniques except for transmission electron microscopy.
The crystal structure of Mo 1−x Mn x Se 2 monolayers was monitored in-situ by Reflection High Energy Electron Diffraction (RHEED). The different RHEED patterns obtained for the 6 samples are displayed in Figure 1. They clearly exhibit an anisotropic character with different patterns along the [100] and [110] crystal directions. Considering the initial RHEED pattern of graphene also shown in Figure 1, we can conclude that the Mo 1−x Mn x Se 2 monolayers are all in epitaxial relationship with graphene regardless the Mn concentration. Moreover, RHEED patterns only exhibit thin streaks up to 2.5% of Mn. Bright spots (highlighted by white arrows in Figure 1) appear in the RHEED patterns for Mn compositions of 5% and above. From the lateral position of the spots compared to the one of MoSe 2 streaks, we deduce a lattice spacing of 3.85 Å. It corresponds to the interplanar distance of the cubic phase of MnSe shown in Figure 2a.
As shown in Figure 2b, the position of the diffraction spots can be well explained by the presence of cubic MnSe clusters at the surface of MoSe 2 or bare graphene with (111)  orientation. From the RHEED patterns, their epitaxial relationship with MoSe 2 (resp. graphene) is MnSe(422)||MoSe 2 (100) (resp. Gr(100)). The presence of twin MnSe clusters on MoSe 2 is due to the presence of MoSe 2 twin grains as expected for the epitaxial growth of MoSe 2 on graphene [21,22]. The presence of twin MnSe clusters on graphene is also expected due to the six-fold symmetry of the graphene surface.
Grazing incidence X-ray diffraction measurements were performed using a SmartLab Rigaku diffractometer equipped with a copper rotating anode beam tube (λ K α = 1.54 Å) and operated at 45 kV and 200 mA. A parabolic mirror and a parallel in-plane collimator with a 0.5°resolution was used in the primary optics and a second parallel collimator was used in the secondary one. Parasitic radiations were eliminated by a K β filter inserted on the detector side. The results are shown in Figure 3 for 3 different Mn concentrations: 0%; 2.5% and 5%. All the measurements were done with the selenium capping on top.
According to the radial scans along the SiC(h00) direction in Figure 3a and along the SiC(hh0) direction in Figure 3b, the incorporation of Mn up to a concentration of 5% does not affect the MoSe 2 crystal structure. The (100), (110) and (200) Bragg peaks of MoSe 2 remain unchanged when increasing the Mn content. In the same way, the azimutal scans of the MoSe 2 (110) Bragg peak in Figure 3c show that the mosaic spread of MoSe 2 grains is unaffected by the incorporation of Mn. It remains in the 6°-8°range. In the 5% Mn sample, we could not detect the presence of MnSe by X-ray diffraction which might be due to the small size of the MnSe clusters at the sample surface as shown by STEM in the following.

Scanning transmission electron microscopy
After their transfer on a TEM grid, Mo 1−x Mn x Se 2 monolayers are observed by angular dark field scanning transmission electron microscopy (ADF-STEM). STEM measurements have been carried out using a double Cs-corrected FEI Ultimate at 80 kV. ADF-STEM images were acquired using a convergence semi-angle of 22 mrad and collecting scattering larger than 50 mrad. Here, we stress the fact that we observe by ADF-STEM the same epitaxial relationship between CVD graphene and MoSe 2 lattices as the one between epitaxial graphene on SiC and MoSe 2 lattices observed by RHEED and X-ray diffraction in Section 2 and by k-PEEM in Section 4.2.
We first focus on the sample containing 1% of Mn. Low and high magnitude STEM images of this sample are shown in Figures 4a and 4b respectively. We observe the nearly completion of the MoSe 2 monolayer in dark grey. Black and light grey areas correspond to uncovered graphene and to the second MoSe 2 monolayer respectively. In Figure 4b, we note the presence of dark spots at Se sites which correspond to Se vacancies. The atomic details are shown in the Z -contrast (Z being the atomic number) image of Figure 4c. Mo, Se and Se vacancy sites are clearly identified in the intensity profile of Figure 4e by their relative Z -contrast. The creation of Se vacancies is a known effect due to electron irradiation during the STEM observations. As the amount of Se vacancies observed in this sample containing Mn was equivalent to that routinely observed in undoped samples, we consider that there is no impact of Mn doping on Se sites.
STEM observations at several positions on the sample did not show the presence of clusters at the surface of the sample. Moreover a thorough analysis in the inner parts of MoSe 2 single crystalline grains did not show the presence of Mn atoms in substitution of Mo except one shown in the Z -contrast image of Figure 4d. In the intensity profile of Figure 4f, the relative Z -contrast at each atomic position allowed us to detect the presence of one impurity atom substituting Mo, supposed to be a Mn atom according to its relative intensity.
A second sample containing 5% of Mn was also studied by STEM and the results are shown in Figure 5. In Figure 5a and b, the low and high magnitude STEM images exhibit several features. First, we find again the nearly completion of one MoSe 2 monolayer in dark grey. Black and light grey areas correspond to uncovered graphene and to the second MoSe 2 monolayer respectively. In this sample, we also observe a high density of nanoparticles at the surface of MoSe 2 .
In Figure 5a, nanoparticles have a diameter of 10 to 20 nm and in Figure 5b, smaller nanoparticles with a diameter of 1 nm can be detected. Those nanoparticles correspond to MnSe clusters also detected by RHEED in the Mo 0.95 Mn 0.05 Se 2 sample. This is confirmed by the electron energy loss spectroscopy (EELS) map at the Mn L-edge shown in Figure 5c: all the clusters are Mn-rich. However, since the STEM sample was not capped with amorphous selenium, the MnSe clusters are fully oxidized as demonstrated by the elemental EELS map at the O K-edge in Figure 5d. Again, it was not possible to detect Mn atoms substituting Mo in MoSe 2 single crystalline domains.

Scanning tunneling microscopy and spectroscopy
In order to elucidate the position of Mn atoms, we have analyzed by STM/STS at 8 K two similar samples with a nominal Mn doping level of 5% Mn. The MoSe 2 coverage was around 1 ML and the amorphous selenium coating layer was first removed in vacuum by a soft annealing at around 200°. Compared to the case of undoped (bare) MoSe 2 layers grown using the same technique and growth conditions [11,23], large scale images (not shown) reveal two kinds of parasitic structures in the Mn doped samples. The first one is a sparse distribution of small three-dimensional grains with a typical height of 3 nm corresponding to the MnSe clusters detected by RHEED and STEM. The second one consists in small patches (a few nanometers in lateral size) of a two-dimensional unidentified phase attached to the semiconducting MoSe 2 islands. Its apparent height is 0.4 nm, much smaller than the one measured on semiconducting MoSe 2 monolayer islands (0.7-0.8 nm). We shall not discuss these structures in this section, which is devoted to the Mn doping of the semiconducting 2H TMD. We simply notice that these phases (clusters and patches) may incorporate a significant amount of the deposited Mn, which would naturally explain the discrepancy between the rather high nominal Mn doping of the TMD layer and the fairly low concentration of Mn found in the TMD flakes as shown in the following. We recall that a homogeneous doping of 2H-MoSe 2 by 5% should result in a mean spacing of ≈1.5 nm between Mn atoms.  Figure 6a is an overview of a TMD flake for the doped sample. The morphology of the flakes is indeed quite similar to the one observed in undoped layers [11,23]. The monolayer of MoSe 2 (1L-MoSe 2 ) island has a shape approximately triangular. A second layer (2L-MoSe 2 ) grows on top of the first layer. In both layers we observe the characteristic triangular pattern of mirror twin boundaries (TB) which have been studied previously by STM/STS [24,25]. Actually, the only difference we can see with bare MoSe 2 samples is the presence of atomic size features which accumulate close to the edges (and grain boundaries as well) and decorate the 1L-MoSe 2 grains. Some of these accumulation areas are indicated by the green ellipses in Figure 6a. Similar features are observed on 2L-MoSe 2 , which are occasionally found farther apart from the edges (blue ellipse in Figure 6a). Figure 6b and c present images taken at positive and negative biases of the same area on another 1L-MoSe 2 flake. With these biases, we probe electronic states located close to the bottom of the conduction band and to the top of the valence band of (bulk) 1L-MoSe 2 in Figures 6b  and 6c respectively. In the two images, we can see objects with sub-nanometer sizes (examples are indicated by the green ellipse) along the edges of the flake. All these structures exhibit a similar contrast (apparent height and size) for the two biases shown in Figure 6b and c, and more generally for all the different biases we have used in the measurements (typically from +1.2 V to −2.3 V). This indicates that all these objects have the same origin. Since they were not observed in bare MoSe 2 samples, we ascribe the structures (some of them circled in green) shown in Figure 6b and c to Mn atoms incorporated in the TMD matrix. Note that inside the flake, more than 5 nm away from the edges, the TMD seems to be quite homogeneous (except for the unavoidable TB). This homogeneous contrast in the interior of the 1L-MoSe 2 was verified at different positions and using different biases. This is in good agreement with ADF-STEM observations in the middle of CVD graphene domains far from grain boundaries. It supports the fact that the MBE growth of Mo 1−x Mn x Se 2 on CVD graphene and epitaxial graphene on SiC are similar. In the same way, we found exactly the same result in vanadium doped WSe 2 [26] where STM and ADF-STEM observations are also comparable in the middle of graphene grains.
From our own experience and from published works, we know that variable bias imaging allows for the detection of isoelectronic substitutional atoms in TMD layers, such as O on S/Se sites [27] or Mo on W sites [28,29]. We expect that the incorporation of non-isoelectronic dopants such as Mn in MoSe 2 , would give rise to a larger perturbation in the local electronic structure of the TMD matrix, and thus to a contrast (on the nanometer size) that should be easily observed using STM, as recently achieved in WSe 2 flakes doped with V atoms [26]. The presence of such a contrast at the edge and its absence inside the island suggests that Mn atoms are only present close to the boundaries of the flakes.
The fact that Mn atoms are only present close to the edges of 1L-MoSe 2 , and that they tend to accumulate there, is not favorable for STS studies. Indeed, it is difficult to extract from these data information about the electronic structure of isolated Mn atoms in a MoSe 2 matrix, which is the situation considered in theoretical studies [17,[30][31][32]. It is known [33,34] that there is a strong upwards band bending which develops at the edges of semiconducting TMD layers deposited on graphene (or graphite). This band bending of typically 300 meV extends 5 nm away from the edge for bare MoSe 2 [34]; it corresponds to the area where Mn dopants accumulate. As a consequence, the location (in energy) of the valence and conduction band edges at the defect site are quite uncertain. In addition, in-gap edge states (which eventually pin the Fermi level) are observed at the boundaries of bare semiconducting TMDs [33,34]. Despite these limitations, we have nevertheless performed STS studies on several Mn agglomerates on 1L and 2L-MoSe 2 layers. One example is shown in Figure 6d for a Mn agglomerate in a 1L-MoSe 2 flake. We have taken a series of spectra along the pink line in the top panel. This line starts on a clean MoSe 2 area. It first crosses a TB, and then enters the agglomerate highlighted with the green box. The conductance map obtained from this series of spectra is displayed in the bottom panel of Figure 6d. The dark blue area corresponds to the bandgap of the MoSe 2 layer. The TB gives a significant density of states within this bandgap as expected [24,25]. For distances between 5 and 7 nm, a strong upwards band bending is seen when approaching the Mn agglomerate. On the Mn agglomerate (green boxed area), we see a set of discrete in-gap states, located on both sides of the Fermi level E F (here E F corresponds to zero sample bias). The highest occupied (lowest empty) in-gap states are located at −0.4 eV below (+0.2 eV above) E F respectively. We find that Mn dopants generally give rise to both occupied and empty in-gap states (with different binding energies depending on the local configurations) for the different areas we have probed by STS. Such in-gap states both in occupied and empty states are actually predicted by ab-initio calculations [17,[30][31][32]. However, for the reasons quoted above, those STS results may not be directly compared with such calculations.

X-ray photoemission spectroscopy
XPS measurements were performed under ultrahigh vacuum with an X-ray microprobe (beam size of 100 µm) photoelectron spectrometer (PHI 5000 VersaProbe-II) fitted with a monochromatic Al K α source (hν = 1486.7 eV). The photoelectron take-off angle was 45°and the overall energy resolution 0.6 eV for high resolution core level spectra. The C 1s peak, commonly used for energy referencing, overlaps with a Se Auger line and becomes hard to identify when the sample is poorly covered by adventitious carbon [35]. Therefore the energy scale was calibrated by shifting the Si 2p peak, coming from the SiC substrate. The decomposition of the core-level line shape into individual bonding-state components was done with the CasaXPS software, using the sum of 30% Lorentzian and 70% Gaussian line-shapes and Shirley background subtraction. The spin-orbit splitting was set to 3.1 eV for Mo 3d, 0.9 eV for Se 3d and 11.5 eV for Mn 2p. In the particular case of Mn 2p, we considered a Lorentzian asymmetric line-shape according to Ref. [36] and a linear background due to a poor peak intensity caused by a low photoionization cross section [37] and a small amount of atoms combined with a strong inelastic background from the nearby Se Auger lines.
Prior to the XPS analysis, the samples were heated at 350°C under UHV in order to remove the Se capping layer and leave a clean surface suitable for the measurements. Figure 7a shows the series of Mn 2p spectra with increasing doping concentration. The series of corresponding valence band spectra is presented in Figure 7b. The Mo 3d and Se 3d core-level spectra of the 5% Mn doped sample are displayed in Figures 7c and 7d respectively. The red-dashed ellipses point out the absence of Mo or Se oxide in the sample as expected from the preparation protocol. The Mo and Se binding energies are compatible with previous results on MoSe 2 monolayers [20]. The series of Mn spectra shows an increased Mn 2p intensity upon increasing nominal concentration, evidencing that the effective Mn incorporation within the MoSe 2 layer keeps on increasing when increasing the initial Mn content. The Mn 2p 3/2 main peak corresponds to a 641 eV binding energy i.e. 2 eV larger than for metallic Mn which is indicative of oxidized Mn. Since oxygen is not found in the survey spectra (not shown), and Se has a higher electronegativity than Mn, we can conclude that at least a significant fraction of Mn is incorporated in the form of MnSe compounds. The series of valence band spectra, which reveals a monotonic shift of the valence band maximum away from the Fermi level upon increasing of the nominal Mn concentration (from 0.35 up to 0.57 eV for 1% to 10% Mn doping, respectively). This shift is equivalent to n-type doping or more generally, can be attributed to the occupation of additional electronic states in the bandgap of MoSe 2 at room temperature. However, n-type doping of MoSe 2 can be ruled out since we do not observe a clear rigid shift of Mo 3d and Se 3d core-level spectra towards lower binding energies as expected upon n-type doping. The electronic states responsible for the shift of the valence band maximum may thus originate from another phase than MoSe 2 present in the sample as shown in the following.

k-resolved photoemission electron microscopy
The k-PEEM analysis was performed using a NanoESCA MkI spectro-microscope (ScientaOmicron) [38,39] in ultra-high vacuum conditions and at ambient temperature. A He-I cold cathode lamp (hν = 21.1 eV) was used as a laboratory, vacuum-ultra-violet (VUV) excitation source impinging the sample in an off-normal direction, namely at an angle of 65°with respect to the sample normal. Momentum-resolved images were acquired over the first Brillouin zone (k x , k y = ±1.8 Å −1 ). The high energy resolution momentum images were recorded at a spectrometer pass energy of 50 eV and a 1 mm diameter entrance slit of the imaging spectrometer (equivalent to an overall energy resolution of ≈0.2 eV), and with low-noise, event-counting detection allowing enhanced sensitivity for precise upper valence band analysis. The calibration of the k-space scale was done by measuring the known reciprocal lattice distances of a freshly prepared Cu(111) single crystal surface with identical PEEM settings as applied to the MoSe 2 samples. Figure 8a shows the angular image of the 1-ML MoSe 2 sample containing 5% of Mn recorded at a binding energy of 1.58 eV. It shows the K points of both MoSe 2 and graphene layers which are perfectly aligned confirming the epitaxial growth of the MoSe 2 monolayer on graphene. The full band structure was then generated from the series of angular images recorded from −0.5 to 5 eV binding energies. Figure 8b shows a cut along the K-Γ-K direction. The band structure clearly shows the monolayer character of the doped MoSe 2 layer, with the valence band maximum located at the K point, ≈250 meV above the Γ point. A curvature analysis of the Γ and K bands reveals similar hole effective masses compared to the undoped sample (respectively 2.73m 0 and 1.03m 0 , m 0 being the electron mass). The valence band spectra at the K and Γ points are shown in Figures 8c and 8d respectively for the undoped and 5%-doped layers. The spectra are almost identical highlighting the fact that the valence band shift observed by XPS is not related to the MoSe 2 layer. Finally we also recorded the band structures of the 2.5% and 7.5% Mn doped MoSe 2 monolayers (not shown). They are almost identical to the band structure as the undoped layer at the resolution limit of the setup as if Mn incorporation had no effect on the electronic properties of MoSe 2 .

Discussion
Based on our multiscale sample analysis, we draw in this section conclusions about the incorporation of Mn in MoSe 2 monolayers. First, RHEED, STEM and STM demonstrated the presence of MnSe clusters for Mn concentrations above 5%. Below this concentration, Mn atoms are incorporated in the MoSe 2 monolayer as shown by XPS measurements. Hence this 5% concentration represents an upper limit for the incorporation of Mn atoms in MoSe 2 . Then, by electron and X-ray diffraction, we can conclude that the crystal structure of MoSe 2 remains unchanged upon Mn doping. The same conclusion can be drawn regarding the electronic structure: the Mo and Se core level spectra in XPS measurements and the electronic band structure measured by k-PEEM are very similar to those of bare MoSe 2 . Those conclusions are confirmed by STEM observations where the inner part of MoSe 2 single crystalline grains do not show the presence of Mn atoms (except for one area where we could fortuitously detect one Mn atom substituting Mo). The answer is then given by STM/STS measurements where we clearly see that incorporated Mn atoms tend to diffuse to the edge of the MoSe 2 grains leaving their inner part intact.
Therefore, Mn atoms accumulate at grain edges to form an undefined Mo x Mn y Se z phase which, at the completion of one monolayer, is located at grain boundaries. The spontaneous decomposition between pure MoSe 2 and a Mn-rich phase was also referred to as spinodal nanodecomposition in DMS [6]. In magnetic measurements, it is highly probable that any de-tected signal on such samples would exclusively come from this Mn-rich phase. Finally, the valence band shift detected upon Mn incorporation in XPS is probably due to the occupation of in-gap states (as shown by STS) or by the presence of the MnSe clusters. In summary, the growth conditions by MBE to obtain high crystalline quality MoSe 2 monolayers systematically lead to the segregation of Mn dopants to the grain edges and to the formation of MnSe clusters above 5% when grain edges are saturated. The resulting Mn solubility in MoSe 2 is thus extremely low. Lowering the growth temperature would probably limit the diffusion of Mn atoms but would result in poor quality MoSe 2 layer since the optimized growth conditions for the epitaxy of MoSe 2 on graphene are within a very narrow window for the growth temperature and deposition rates. Mndoping of MoSe 2 by MBE might not be the good strategy to obtain a well-defined Mo 1−x Mn x Se 2 diluted magnetic semiconductor. One possible explanation is the absence of stable MnSe 2 twodimensional phase: the 1T-MnSe 2 phase, predicted ferromagnetic [40], is thermodynamically unstable. This situation is at odd with vanadium doping because the 1T-VSe 2 phase is stable and might be easily incorporated into MoSe 2 or WSe 2 as recently shown [26]. Moreover, substitutional vanadium doping of WSe 2 was recently reported by several groups either theoretically [41] or experimentally [42,43] showing very promising ferromagnetic properties.

Conclusion
We have grown Mo 1−x Mn x Se 2 monolayers with x ≤ 0.1 by MBE on graphene using the optimized growth conditions for MoSe 2 . By using a multiscale characterization approach including in-situ RHEED, X-ray diffraction, STEM, STM/STS, XPS and k-PEEM, we could study the incorporation of Mn in MoSe 2 . The combination of all these techniques allowed us to conclude about the extremely low solubility of Mn in MoSe 2 . During MBE growth, Mn dopants segregate at the grain edges forming undefined Mo x Mn y Se z phase at grain boundaries. The crystal and electronic structure of MoSe 2 grains remain unchanged upon Mn doping. Above 5% of Mn, epitaxial cubic MnSe clusters start forming at the surface of the film. Finally, Mn doping of MoSe 2 by MBE might not be the most suitable strategy to achieve a diluted MoSe 2 :Mn magnetic semiconductor.