Origin of Giant Rashba Effect in Graphene on Pt/SiC

1. Introduction

Induced spin-orbit coupling in graphene is still actively investigated topic since it opens a way to realize quantum Hall effects in graphene [1,2,3,4]. It is known that a strong spin–orbit coupling is a necessary condition for observing spin Hall effects, quantum anomalous Hall effect, spin galvanic effect, spin Edelstein effect, giant Rashba effect, spin-transfer and spin-orbit torque effects, spin interference effect, etc.

Giant Rashba splitting in graphene on Au monolayer was reported earlier in several experimental papers [5,6,7,8,9,10,11], and was clearly supported by the density functional theory (DFT) calculations of Gr/Ni system with intercalated Au clusters [9] and tight-binding calculations of graphene on top of a gold monolayer in the hcp configuration [12]. The giant spin splitting was observed for Au-intercalated graphene on SiC substrate [8], but authors concluded that sizable spin splittings become giant (∼100 meV) only near avoided-crossing gap.

At the same time, platinum is the most used nonmagnetic metal in spintronics because it is characterized by spin-polarized $5d$ states at the Fermi level, resulting in a high intrinsic spin Hall effect [13]. Furthermore, it was shown that graphene monolayer on Pt(111) surface [7] and on Ir(111) with intercalated Pt monolayer between graphene and Ir [14] exhibits pronounced spin-polarized Dirac cone-like $\pi$ states.

However, the systems of graphene on metal substrates cannot be directly applied for future electronics or spintronics. In this regards, graphene systems on semiconductor substrates, such as graphene on silicon carbide (SiC) with intercalated metal, are more promising for applications [15,16,17,18,19,20]. The possibility of intercalation of monolayer of noble metals underneath a graphene on SiC, such as Au and Pt, was shown in Refs. [8,16,17,21]. Also, in the work [22] it was predicted that in a system graphene/Pt/SiC with nanodots of ferromagnetic metals atop it, a reversible magnetization of ferromagnetic nanodots can be realized by applying a spin-current due to spin-orbit torque effect.

It is known that high temperature annealing of 6H-SiC(0001) surface leads to formation of $(6\sqrt{3}\times 6\sqrt{3})R30$° reconstruction. Wherein, carbon layer at the surface is strongly bonded to the substrate and is called a zero-layer graphene (ZLG) [23,24,25]. Intercalation of various metals is a widely used method for transformation of zero-layer to quasi-freestanding graphene monolayer [21,26,27].

In the current work, we synthesize graphene system on SiC substrate with intercalated Pt submonolayer to evaluate the influence of corrugation at nanoscale on induced spin-orbit coupling in graphene. For this purpose intercalation of Pt atoms underneath ZLG was carried out. In contrast to the intercalation of 0.5 ML Au [9], a single ordered phase of graphene on Pt was achieved with a low atomic density in Pt monolayer. This made it possible to combine different research methods and interpret the results within single-phase system.

2. Materials and Methods

Synthesis and photoemission experiments were carried out in situ in ultra-high vacuum conditions in the setup Nanolab at the Resource Center “Physical Methods of Surface Investigation” of Saint Petersburg State University Research park. The samples were investigated by X-ray photoelectron spectroscopy (XPS), angle-resolved photoelectron spectroscopy (ARPES) using a VG Scienta R4000 hemispherical energy analyzer with spin Mott detector. A narrow-band high-intensity source of ultraviolet radiation VUV 5k and an X-ray radiation source with an Al anode with monochromators were used as excitation sources. The photoelectron spectra of the core levels were decomposed into spectral components by fitting procedure. The line shape of Si 2p and C 1s spectra was defined by Gaussian/Lorentzian product formula with mixing parameters of 0 and 0.5, respectively [28]. The asymmetry parameter for the graphene peak of C 1s spectra was 0.12. Raw data are shown in figures by circles along with the best-fit spectra, the corresponding components and the background. For analysis of crystalline and atomic structure we used low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM).

Semi-insulating wafers of 6H-SiC(0001) purchased from TankeBlue Semiconductor Co. Ltd. (part number W26S0P-CPF) were used in the experiment. We provided deposition of 1.5 Å of Pt on the pristine surface of SiC(0001) with zero-layer graphene on top, and then the system was annealed at $T=1100$$°$during 1 hour. The amount of deposited Pt was controlled by a quartz microbalance. The sample temperature was determined using Keller CellaTemp PA 20 AF 2/C pyrometer with the emissivity set to 0.6 for 60° off-normal angle. The base pressure was below $2·{10}^{-10}$ mbar during the experiment.

First-principles calculations were performed using the OpenMX code which provides a fully relativistic DFT implementation with localized pseudoatomic orbitals [29,30] and norm-conserving pseudopotentials [31]. The exchange correlation energy in the PBE version of generalized gradient approximation was employed [32]. The accuracy of the real-space numerical integration was specified by the cutoff energy of 300 Ry, the total energy convergence criterion was 3·10⁻⁵ eV. The k-mesh for Brillouin zones of $8\times 8$ and $9\times 9$ supercells were specified as $1\times 1\times 1$ mesh. The basis functions were taken as C6.0–s2p2d1 and Pt7.0–s3p2d2f1 (the pseudopotential cutoff radius is followed by a basis set specification). The interfaces were modeled by periodic slabs consisting of one Pt atomic layer covered by graphene monolayer. The unit cell drawings were produced by VESTA software [33].

3. Results and discussion

Firstly, zero-layer graphene on SiC(0001) was synthesized at the temperature of about $T=1250$$°\mathrm{C}$. Figure 1 shows the C 1s and Si 2p core levels spectra before and after Pt intercalation. Deconvolution of the photoelectron spectra into components by a fitting procedure is presented. The C 1s spectrum of ZLG (Figure 1(a)) has a characteristic shape with three components: two components S1 (284.7 eV) and S2 (285.5 eV), corresponding to the carbon in ZLG, and the component of bulk carbon (denoted by (B)) in the SiC compound (283.8 eV). The Si 2p spectrum (Figure 1(b)) presents one broad peak at the binding energy of 101.7 eV which is in accordance with the previous results [23,34,35]. However, the Si spin-orbit coupling doublet ($2p_{1/2}$ and $2p_{3/2}$) is not resolved, so the one asymmetric peak is obtained during the fitting procedure. It should be noted that initial ZLG is assisted by a small amount of graphene monolayer (see a low-intensity component at 284.6 eV in Fig.1(a)). But as we will show below, this part of the surface is inert to intercalation process.

After Pt deposition and subsequent annealing at $T=1100$$°\mathrm{C}$ we observed the changes of the XPS spectra. First of all, they are followed by decreasing of the ZLG components and bulk component of carbon atoms in the SiC and increasing of the graphene component at 284.4 eV of binding energies. That means the transformation of ZLG into graphene monolayer by intercalation process. Secondly, the spectral components corresponding to Si and C atoms in the bulk SiC are both shifted by 0.9 eV towards lower binding energies. This effect can be explained by different surface band bending in the system due to the Pt atoms influence on the interface [36].

In order to study the depth location of underlying layers, it is necessary to carry out additional analysis of the XPS data with angular resolution, in which photoelectron spectra are taken at different emission angles. Analyzing the angular dependences of XPS core level intensities of the elements, it is possible to determine the relative positions of the layers in depth (see for example supplemental material of Ref. [37]). Figure 2 shows the changes of the C 1s, Pt 4f and Si 2p spectra measured at photoemission angles of 0° and 60° relative to the surface normal. The intensity ratios of the selected components for these two angles give us an understanding of the relative depth location. A more surface-sensitive spectrum corresponds to a larger photoemission angle. Therefore, comparing the $I_{{60}^{°}}/I_{0^{°}}$ intensity ratios for the C 1s graphene component, Pt 4f components and Si 2p bulk component (the numerical values of the ratios are shown in the Figure 2), we conclude that graphene is located above the Pt submonolayer, while the latter is localized between graphene and SiC substrate. It proves the intercalation of Pt underneath ZLG on SiC.

LEED image in Figure 3(a) shows formation of ZLG on SiC with ($6\sqrt{3}\times 6\sqrt{3}$) and ($5\times 5$) reconstructions [38]. Blurred moire pattern of graphene appeares after Pt intercalation (Figure 3(b)). ZLG reconstruction is no more visible proving intercalation of Pt atoms between ZLG and SiC substrate. Observation of SiC ($1\times 1$) diffraction spots up to high kinetic energies ($\sim 200$ eV) evidences about good crystal quality of the substrate after intercalation. Notably, the measured period of superstructure $\sim (5\times 5)$ ($\sim 1.2$ nm$\times 1.2$ nm) by STM method perfectly agrees with predicted one for 0° rotation angle between graphene and Pt layer [39].

To analyse the electronic structure of the system the ARPES intensity maps were measured before and after Pt deposition (Figure 3(c-f)). Due to the fact that the electronic structure of ZLG does not have intense electronic states near the Fermi level, even a small amount of graphene layer will contribute to the signal in ARPES spectra. As the result, the initial surface was characterized by presence of the graphene Dirac cone typical for graphene on SiC with n-doping and the Dirac point energy position at about 0.42 eV below the Fermi level (see Figure 3(d)) [23]. However, the graphene coverage was much less than ZLG one according to XPS data analysis.

After Pt intercalation a new Dirac cone is clearly visible on ARPES data in Figure 3(e,f). This cone is related to the intercalated graphene monolayer that was formed by ZLG transformation. It is shifted above the Fermi level (p-doping) due to Pt intercalation. At the same time, the initial Dirac cone remains unchanged. The band structure in the $\overline{\mathrm{\Gamma }\mathrm{K}}$ direction is shown in Figure 3(c). The $\pi$ and $\sigma$ graphene states are observed, and Pt bands are slightly visible near the Fermi level.

Spin structure of intercalated graphene system was measured by spin-ARPES at k_‖ values marked by blue arrows in Figure 3(c). The spin-resolved photoemission spectra are shown in Figure 4 for the in-plane Rashba spin component (S_y). The spin splitting of 200 meV (±50 meV) is observed for all measured spectra in the wide range of the binding energies. Such experimentally discovered value of spin splitting is unprecedentely giant for graphene systems and we will provide an explanation for this effect.

STM measurements were performed to provide more information about atomic structure of the surface. Only one well-ordered structure at large nanometer scales has been resolved, namely the structure of periodic triangular shaped defects (Figure 5). The periodicity of the superstructure is ∼(5×5) relative to graphene lattice. 2D fast Fourier transform (2D FFT) image shown on the inset of panel (b) also reveals the superstructure spots. Notably, a corrugation of about 0.2–0.3 Å was measured by STM, which is in a good agreement with the value reported for graphene on Pt(111) surface with vacancies in the topmost layer [37,40]. The observation of corrugation of a comparable magnitude after intercalation of an incomplete Pt monolayer is evidence that a rarefied platinum layer with holes is formed under graphene. In order to show the presence of a corrugated graphene lattice, we performed 2D FFT filtering of the image and presented it in a 3D view with illumination. The 2D-FFT image displays six spots corresponding to the superstructure, while the graphene structure is visible in the 3D image.

To analyze the causes of giant Rashba spin-orbit coupling phenomena and interpret obtained experimental data, we address to DFT calculations. In this regard, it should be noted that we were unable to find published information about experimental spin-orbit splittings in graphene with the energies above 100 meV. Similar experimental splitting values were obtained earlier, but only as a result of the interplay between exchange and spin-orbit couplings [10,11]. Moreover, DFT calculations had significant differences with the experimental results either in the magnitude of the spin-orbit splitting or in the atomic structure of graphene and the underlying layer. Due to impossibility to take into account all peculiarities of the real system structure in calculations and necessity to achieve experimental values of the spin splitting, unrealistic surface models are usually used. In our case of single-phase system, we have opportunity to provide the calculations of rather realistic simple model unit cells that might shed some light on the complex origin of the observed giant Rashba phenomenon. Single-phase system with a rarefied Pt layer with voids makes it possible to theoretically simplify the system as if it were intercalated by single Pt atoms. The first one is a model of Gr/Pt interface with flat layers (Figure 6(a)). The splitting close to 100 meV was obtained at a distance of ∼2.8 Å that is less than equilibrium distance for Gr/Pt(111) system (∼3.3-3.4 Å) [37,41]. But even such a close distance is not enough to obtain a splitting value which is comparable with the experimental one. It’s worth considering that further approchement of graphene and Pt layer leads not only to an increase in the splitting, but also to the destruction of the Dirac cone due to strong hybridization with Pt 5d states. In the second model, we check the influence of graphene corrugation near the average Gr-Pt distance of ∼2.8 Å . The graphene corrugation was obtained after structure optimization of Gr(8×8)/Pt interface with the equilibrium distance of ∼3.3 Å. Since the splitting increased slightly compared to the previous case, even though the carbon atoms now have different distances to the Pt layer, we can conclude that the average distance between graphene and Pt layer and the number of Pt atoms play a major role. In order to reduce this average distance without bringing the entire graphene and platinum closer together, we made a point defect in the form of an additional Pt atom under graphene and provide structural optimization of this system. In this case due to the formation of a "hat-like" structure in graphene above this Pt atom, some of carbon atoms have a very small distance to the nearest platinum atom (∼2.3 Å), which should increase the spin-orbit coupling induced in graphene. Besides, it should be noted that the structural optimization leads to the fact that the flat areas became even closer to the Pt layer (∼2.5 Å). As it turned out, such a defect enhanced the splitting to a value ∼170 meV. Notably, graphene Dirac dispersion is not destroyed. Within the experimental resolution we have a good agreement between this model and the experiment. Thus, important features revealed for the first time in the calculations are: the possibility of graphene corrugation in a large-scale unit cell with a flat substrate and graphene pinning effect in case of point defects in the form of Pt atoms under graphene.

Without any doubt, the unit cells used in calculations have too small lateral parameters and a model of the system based on STM data should have an unit cell with minimal dimensions (15x15) with a periodic arrangement of voids and a quasi-periodic arrangement of Pt atoms between them. For this reason our DFT calculations cannot fully take into account the complex structure of the real surface and a challenging task of large unit cells calculations should be solved to establish completely the role of nanometer-scale unit cells in giant Rashba effect. However, despite the described limitations, we believe that the performed calculations of model unit cells give a good enough idea of the possible cause of the giant Rashba splitting in the considered system, which consists in reduction of the average distance between carbon and platinum atoms due to the appearance of an ordered network of platinum clusters and voids under graphene.

4. Conclusions

Our study of Pt-intercalated graphene on SiC substrate revealed an ordered single-phase consisting of graphene on rarefied Pt layer with triangular-shaped voids. Corrugated graphene on such Pt layer has a giant spin splitting value of about 200 meV. Theoretical model with additional platinum atoms under graphene shows a decrease in the distance between graphene and Pt layer atoms as a result of the pinning effect and the corrugation of graphene at the sites of point defects. It is supposed that a more complex interface between graphene and intercalated noble metal layer with pinning defects underlies the giant Rashba effect.