Structure and Magnetism of EuS on Bi2Se3(0001)

The rocksalt‐type ferromagnetic (FM) insulator EuS (bulk TC = 17 K) grown on Bi2Se3 with well‐matched (111) plane of the film and (0001) plane of the substrate is studied. The system may feature magnetic proximity effect breaking the time‐reversal symmetry and opening a bandgap in the metallic topologically protected surface state of Bi2Se3. The experimental X‐ray diffraction studies are combined with ab initio calculations to resolve contradictory results concerning the enhancement of the TC up to 300 K and the degree of induced magnetization in the system. It is concluded that previous studies relied on idealized and unconfirmed structure models. Herein, it is shown by surface X‐ray diffraction (SXRD) with ab initio calculations that a two double layer‐thick EuS film grows with a sharp interface and without chemical intermixing in a single domain state in an FCC‐type stacking on the Bi2Se3(0001) surface in which the topmost layer is metallic, thereby lifting polarity. A large pz‐orbital‐derived top‐layer sulfur magnetic moment of 0.6 μB is found, whereas for europium, μEu = 6.9 μB throughout the film is found. No magnetization within the first Bi2Se3 quintuple layer is found. The calculation of the exchange parameters Jij indicates a complex FM and antiferromagnetic ordering between europium and sulfur with a maximum Néel temperature of 226 K.

concentrations largely exceeding bulk limits. [22][23][24][25][26] This approach, by which the magnetic proximity is exploited to establish FM order in the TI has been shown to be very successful in the case of Fe deposited on x ¼ 9% Mn-doped Bi (1Àx) Mn x Te, [27] where T C was reported to be as high as room temperature. However, as shown by several investigations, we have published in the recent past during the course of this project, direct surface deposition of metals in general involves an uncontrolled reaction at the interface which modifies the near surface geometric and electronic structure. [24,25,[28][29][30] In consequence, for the controlled preparation of a structurally homogeneous and sharp interface, deposition of an (anti) FM or FM insulator film is a promising route.
In this respect, the FM insulator EuS is a primary candidate to serve as an adsorbate. Bulk EuS is a ferromagnet with T C ¼ 17 K and its crystal structure (cubic rocksalt type with lattice parameter a 0 ¼ 5.968 Å at 298.15 K) fits well for an almost lattice matched growth with its (111) plane parallel to the (0001) surface of Bi 2 Se 3 (4.22 vs 4.14 Å, respectively). Consequently, the epitaxial system EuS/Bi 2 Se 3 (0001) has already been investigated in the past.
Proximity-induced ferromagnetism with T C in the 20 K range has been reported for EuS deposited on undoped Bi 2 Se 3 [31] using magnetotransport measurements. An excess magnetic moment as compared with that which can be expected from the magnetic moment of Eu 2þ ions alone (11.3 vs 7 μ B per Eu 2þ ion) was observed. This was attributed to the induced magnetization in Bi 2 Se 3 , either by magnetization of the bismuth atoms or of the electron gas of the topological surface state (TSS). Subsequently, a theoretical study by Eremeev et al. [32] challenged the interpretations of the study by Wei et al. [31] The calculations were based on the structure model in which the interfacial Eu 2þ ions are located in the face-centered cubic (FCC)-type site of the Se-terminated Bi 2 Se 3 (0001) surface. As pointed out in the study by Eremeev et al., [32] the very localized 4f electronic states of the rare-earth ion Eu 2þ are not capable to provide an efficient proximity effect and the induced magnetic moment within the TI is negligibly small. The only interaction between EuS and Bi 2 Se 3 originates from the overlap between the TSS with the topologically trivial metallic interface states. The latter originate from EuS adsorption-induced band bending. An alternative interpretation for the results in the study by Wei et al. [31] was given by assuming some diffusion of europium across the interface replacing bismuth and/or selenium.
More recently, experimental works [33,34] have reported the enhancement of the magnetization within the top Bi 2 Se 3 quintuple layer (QL), enhancement of T C of the EuS film to T C % 300 K and a very strong out of plane magnetic anisotropy, [33] the latter being a prerequisite for breaking time reversal symmetry. It has been suggested that in addition to the strong spin orbit coupling in Bi 2 Se 3, it is the penetration of the TSS into the EuS film, which is responsible for the T C enhancement in EuS resulting from Ruderman-Kittel-Kasuya-Yosida (RKKY)-type exchange interaction.
Despite intense discussion regarding the proximity-induced magnetization in the epitaxial EuS/Bi 2 Se 3 system, theory up to now relies on the interface structure model in which europium atoms of the first EuS (double) layer are located in the FCC-type threefold hollow sites formed by the topmost selenium atoms, i.e., they are located above the third-layer selenium atoms.
Further layers are stacked such as to continue the FCC-stacking. Until now, it is not clear whether this model is correct. Transmission electron microscopy images [33] indicated very good epitaxial growth but a detailed atomic structure could not be derived. As already noted in the study by Wei et al., [31] a clearcut understanding of the proximity-induced interface magnetism would require the in-depth analysis of the interface structure. To this end, we have carried out a synchrotron radiation X-ray diffraction study of the EuS/Bi 2 Se 3 (0001) interface.

Growth Characterization of EuS/Bi 2 Se 3 (0001)
Prior to the surface X-ray diffraction (SXRD) experiments growth of EuS on Bi 2 Se 3 (0001) was characterized by low-energy-electron diffraction (LEED) and scanning tunneling microscopy (STM). The experiments were conducted in an ultrahigh vacuum (UHV) chamber equipped with standard surface characterization tools. The (0001) surface of the bulk Bi 2 Se 3 single crystal was cleaned by repeated Ar þ -ion sputtering (E kin ¼ 1 keV) followed by annealing at about 480 C for about 30 min. Surface cleanliness and surface morphology were characterized by Auger electron spectroscopy (AES) and STM.
The LEED pattern shown in Figure 1a recorded at an electron energy of E ¼ 30 eV is typical for the well ordered and smooth Bi 2 Se 3 (0001) surface prepared by this procedure. [22,23] We have selected an electron energy so as to maximize the contrast between symmetry in-equivalent first-order reflections. According to the threefold symmetry of the Bi 2 Se 3 (0001) surface (plane group p3m1), two sets of reflections are observed, the stronger set being highlighted by the circles, the weaker one by the arrows.
EuS deposition was subsequently carried out in situ by evaporation of 3 N EuS powder from a well-degassed Knudsen cell heated up to 870 C. At this temperature, growth of one EuS double layer (DL) requires a deposition time of about 1 h. Here and in the following, we define as one DL one single sheet consisting of one europium and one sulfur layer, which is the building block of the cubic rocksalt EuS structure along Figure 1. LEED patterns shown in an inverse contrast of a) pristine and b) EuS covered Bi 2 Se 3 (0001) surface. Electron energies in electron volts are listed below the panels. EuS deposition leaves the threefold symmetric (1 Â 1) surface lattice metric unchanged indicating the formation of a wellordered EuS overlayer lattice matched to the substrate. The two sets of symmetry-related spots are highlighted by circles and arrows, respectively. The uppermost spot appears stronger than the two equivalent one due to some tilting of the crystal. For details see text.
www.advancedsciencenews.com www.pss-b.com the bulk [111] direction. During deposition, the pressure remained in the 10 À9 mbar range. After deposition, the sample was annealed at 460 C for about 15 min to improve the longrange order of the film. Chemical characterization was carried out by AES, which showed that the differentiated S-KLL transition peak-to-peak amplitude at E ¼ 152 eV is about as intense as those of the Bi-NOO transitions (E ¼ 96 and 101 eV). AES spectra of Bi 2 Se 3 are discussed in detail in the study by Roy et al. [23] Due to the low sensitivity of the Eu-N 45 O 23 N 67 and the N 45 O 67 N 67 AES transition near 109 and 120 eV [35] and their overlap with Bi-NOO peaks, they could not be determined unambiguously. Nevertheless, X-ray photoemission spectroscopy (XPS) using a Mg Kα X-ray source showed the presence of europium in the deposited film.
A LEED pattern of an approximately three DL-thick EuS film is shown in Figure 1b recorded at E ¼ 44 eV. As compared with those observed for the pristine surface, the spots are not notably broadened, only the signal-to-background ratio has become smaller. As in the case of the pristine sample, the LEED pattern exhibits a threefold symmetry. The observation of the threefold symmetry for such a thick EuS film, where scattering by the substrate is negligible, is an important result. It proves that the EuS film adsorbs in a preferential way on the threefold symmetric Bi 2 Se 3 (0001) surface rather than forming two mutually 60 -rotated domains which would result in a sixfold symmetric LEED pattern.
The surface morphology was investigated by STM. Figure 2a shows a 800 Â 800 nm 2 STM image (U ¼ 1 V, I ¼ 200 pA) of the three DL-thick EuS film (the same sample as used for the LEED experiments). The profile along the white line is plotted in Figure 2b. The morphology of the film surface is characterized by laterally 10-30 nm-sized islands homogeneously covering the 500 nm wide terraces of the substrate surface, whose step morphology remains unaltered upon EuS deposition. Steps on . Islands are about 1 nm high corresponding to three EuS DLs which at this coverage fill the majority of the surface. Some fraction of single-layer and DL EuS islands grow on the complete film. c) 300 Â 480 nm 2 STM image of the sample recorded in the vicinity of step edges. Islands align along the upper step edges more uniformly than on terraces. The line profile d) highlights different islands differing in height by 0.35 nm, i.e., one DL which is the building block during growth.
www.advancedsciencenews.com www.pss-b.com the Bi 2 Se 3 (0001) surface are 0.96 nm high corresponding to the thickness of one QL, the basic building block of the Bi 2 Se 3 bulk crystal. [22,23] The vacancy island which the linescan crosses is about 1 nm deep, very closely corresponding to the thickness of three DLs along the [111] direction bulk EuS ( ffiffi ffi 3 p Â 0.5968 ¼ 1.034 nm). In addition, some islands grown on this layer have a height of about 0.6 and 1.0 nm, corresponding to two and three DLs, respectively. These observations suggest that growth of EuS takes place in units of one DL, about 0.35 nm thick. This model is supported by the zoom-in image (300 Â 480 nm 2 ) with the same tunneling parameters and a profile along the line is shown in Figure 2c,d, respectively. The islands fully cover the surface leaving the morphology of the surface (e.g., the V-shaped morphology of the step edges) unchanged. Closer inspection suggests that the islands located directly along the step edges are well aligned in some contrast to those on the terraces. The profile along the line confirms the conclusions that the growth of the film occurs in Eu─S DL. Islands along the line have a height which are multiples of 0.35 nm.

Structure of EuS/Bi 2 Se 3 (0001)
SXRD experiments were conducted at the beamline SIXS of the Synchrotron Soleil in St. Aubin (France) using an UHV diffractometer equipped with a preparation chamber. The EuS/Bi 2 Se 3 (0001) sample was prepared in the same way as done in the home laboratory. Prior to the SXRD experiments, surface chemistry and long-range order were investigated by AES and LEED, yielding the same results as discussed earlier. As no superstructure is formed upon deposition of the EuS film, the SXRD structure determination is based on the analysis of the intensity distribution along the (1 Â 1) integer-order crystal truncation rods (CTRs) in the same way as done for the majority of surface/interface systems studied during the SPP1666 project. In the following, the basics of the CTR SXRD analysis are shortly outlined:

SXRD and CTRs
To outline the basic principle of the structure analysis in Figure 3a, a schematic of the reciprocal space in an a*-c* section is shown together with the corresponding crystal model in (b) which is "semi-infinite" along the c-axis. As a consequence of the crystal termination, in addition to the bulk Bragg points (spheres), there exist rods normal to the sample surface which are represented by thin solid lines. These rods are referred to as "CTRs." They were already theoretically predicted by v.Laue, [37] but the first clear-cut experimental verification took until 1986 published by Robinson. [38] The analytic treatment shows that in the case of a bulk truncated crystal the intensity along the CTRs varies by roughly five orders of magnitude between the in-phase bulk Bragg positions at integer l and the antiphase condition half way between the bulk Bragg reflections. Consequently, at the antiphase condition, where the reflected intensity of a semi-infinite FCC-type crystal is calculated to be equal to that of a quarter of a monolayer, adsorption of foreign species commensurate with the substrate lattice substantially modifies the total reflected intensity.
The structure factor amplitude of a primitive crystal can be written as a semi-infinite sum over the lattice planes from À∞ to zero with f S being the atomic scattering amplitude of the substrate atoms. The finite penetration of the X-ray beam was neglected. The latter, expressed by an effective absorption factor exp½Àμ ⋅ n ⋅ d (with d being the layer spacing and μ the absorption coefficient) lifts the divergence of the lattice sum at the bulk Bragg conditions at integer l. We have explicitly considered www.advancedsciencenews.com www.pss-b.com only the summation along the z-direction (surface normal) and included the contributions along the a and b directions in the "Laue factors" g(h) and g(k). [37] Adsorption of any species as well as relaxations of the substrate being commensurate with the substrate lattice can be simulated by coherent addition of F CTR with the adsorbate amplitude to give the total scattering amplitude (F tot ) which can be expressed by with the atomic scattering factor f ad of the adsorbate and its fractional coverage θ j . The summation runs over all atoms j within the (1 Â 1) surface unit cell.

Atomic Structure of EuS/Bi 2 Se 3 (0001)
For the data collection, we used a wavelength of λ ¼ 0.103 nm (E ¼ 12.0 keV) of the beam incident at an angle of α i ¼ 0.5 to the sample surface. Integrated intensities (I obs ) were recorded using a 2D pixel detector in two different ways by successive conventional transverse (ω-) scans at a given q z and by direct line scans along q z , the momentum transfer along the reciprocal c* direction normal to the surface. Both data sets give the same results. The I obs were derived from the raw data and converted to structure factor magnitudes (jF obs j) using the program "Binoculars" as outlined in the study by Drnec et al. [39] In the following, we refer to the data derived from transverse ω-scans. Figure 4 shows the intensity distribution along five symmetry independent CTRs which were obtained by symmetry averaging from in total ten CTRs. Symbols represent the jF obs j together with their (1σ) standard deviations derived from the quadrature sum of the statistical and the systematic error as outlined, e.g., in the study by Robinson and Tweet. [40] We find the reproducibility of symmetry equivalent jF obs ðHKLÞj being equal to about 10%. The data set consists of in total 951 data points separated by 0.05 reciprocal lattice units (rlu) along q z with a maximum q z of 15.45 rlu along the (20 L) rod. We refer to the lattice of the Bi 2 Se 3 crystal with a 0 ¼ b 0 ¼ 4.14 Å, and c 0 ¼ 28.65 Å, respectively.
The jF obs j were fitted using the Program "Prometheus" adapted to include the CTR analysis. [41] Due to the high symmetry of the structure (plane group p3m1) in which all atoms occupy high-symmetry sites (Wyckoff sites 1a, 1b, and 1c), only the z-parameters of the atomic sites are free parameters in addition to an overall scale factor and the Debye parameter (B ¼ 8πU, with U being the isotropic mean square displacement amplitude) representing static and dynamic disorders. [42] The structure of the pristine Bi 2 Se 3 ð0001Þ surface has been thoroughly investigated in our group in the past. [22,23] Comparison of the data in Figure 4 with those published in the sudies by Roy et al. [22,23] evidences that the overall shape of the CTRs is strongly modified upon EuS adsorption.
The best fit of the jF calc ðHKLÞj to the jF obs ðHKLÞj is represented by the solid line in Figure 4. The fit quality is quantified by the unweighted residuum (R U ) (R U ¼ P jjF obs j À jF calc jj= P jF obs j. Here, F obs and F calc are the experimental and calculated structure factors, respectively. The summation runs over all data points.) and by the Goodness of Fit (GOF) parameter (GOF ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1=ðN À PÞ ⋅ P ½ðI obs À I calc Þ 2 =σ 2 p , with: I ¼ jFj 2 , σ ¼ standard deviations of the data points, N ¼ number of data points, P ¼ number of parameters.) for which R U ¼ 0.17 and GOF ¼ 1.21 is obtained, respectively. These values can be considered as fairly good and direct-eye inspection of Figure 4 also indicates that the fit follows the data in detail.
The structure model derived from the fit is schematically shown in Figure 5. We have considered the first QL of the Bi 2 Se 3 substrate only, all deeper layers were treated as bulk like.  . Experimental (symbols) and calculated (lines) structure factor magnitudes (jF obs j, jF calc j) along five symmetry independent CTRs. The fit corresponds to the structure model discusses using Figure 5. Atoms are represented by differently colored spheres as shown in the legend. Numbers refer to interatomic and interlayer distances in Ångstrøms. The most important result is that EuS grows with first-layer europium atoms located in the threefold hollow ("FCC") site above the third-layer selenium atom. The following selenium layer also continues the FCC-type stacking.
We have analyzed the structure in very detail by setting different occupancy factors (Θ) for the different layers while simultaneously relaxing the z-coordinates and the atomic displacement parameters (ADPs), here given by the Debye parameter (B). [42] Figure 6 shows a contour plot of the GOF parameter versus the fractional occupancy of the first DL growing by FCC and/ or hexagonal close packed (HCP)-type stacking. It is clearly evident that the first DL follows the FCC stacking and covering about Θ FCC 70% of the surface area. The fit quality achieved for different models such as HCP-type or mixed growth is distinctly worse. From the variance of the GOF, we estimate that the accuracy of the occupancy determination is in the 10-20 percentage point regime. The GOF minimum is approximately at Θ HCP ¼ 15% HCP occupancy, which however appears as not being significant.
Furthermore, no atomic exchange between europium and bismuth as well as intercalation of europium into the first van der Waals (vdW) gap is found (at least within the uncertainty estimated). In this respect, the EuS/Bi 2 Se 3 interface is distinctly different to many other metallic adsorbates where extensive alloying with bismuth has been found, such as, in the case of iron, gold, silver, and chromium. [24,25,28,30] The second DL (fractional occupancy % 45%) grows on the first one in a FCC-type stacking, although the HCP-type stacking cannot be ruled out based on the XRD analysis alone, as it yields almost the same GOF and very similar structural z-parameters. This is because of the low occupancy and the very large ADPs (see the following paragraphs). As will be shown later, theory favors the FCC stacking having a lower total energy. The HCP-type stacking of the second DL would not come as a surprise and we recall that stacking faults at the surface of ultrathin films of bulk rocksalt-type insulators growing along the polar [111] direction have been reported in the past. One example is the rocksalt-type CoO on Ir(001). [43] The stacking fault, there in detail induced by a switch from the bulk-like FCC stacking to the Wurtzite-type stacking was inferred to turn the insulating film to metallic, thereby contributing to the depolarization of the polar structure. [44] Vertical relaxations are important within the EuS film and the first QL of the substrate albeit being small. For the latter, a value of d 12 ¼ 1.54 AE 0.12 Å is found, which corresponds to a À3% contraction relative to the bulk value of d ¼ 1.587 Å. [23] Spacings between deeper layers are also little affected and only d 23 , which is equal to 2.10 AE 0.05 versus 1.94 Å in the bulk, exhibits an expansion outside the experimental uncertainty.
Within the EuS film, we observe strong relaxations. In bulk EuS, the distance between consecutive europium and sulfur layers is equal to 1.722 Å, whereas we find 1.79 AE 0. 16    Simultaneously with atomic relaxations the Debye parameters (B) were refined. For atoms within the EuS film they are in the range between B ¼ 10 and 15Å 2 corresponding to isotropic mean-squared displacement amplitudes of U ¼ 0.13 and 0.19Å 2 , respectively. These very high values can only be related to static disorder rather than to thermal disorder which is typically in the B ¼ 0.5-1 Å 2 range.
We recall that the CTR analysis is sensitive to the structure of the overlayer atoms relative to the (1 Â 1) surface unit cell. This corresponds to a projection of all adlayer atomic sites within the experimental coherence length (several hundred nanometers) into the (1 Â 1) surface unit cell. [45] STM images in Figure 2 show isolated EuS islands rather than a film completely covering the substrate surface. Based on this observation, we may tentatively suggest that due to the high surface-to-volume ratio of the islands, the large fraction of atoms located near the island rims locally relax laterally. In consequence, these are not in perfect registry with the (1 Â 1) surface unit cell. This scenario is referred to as "mesoscopic misfit" (MM) and has been observed in many nanoislands systems. [45][46][47]

Ab Initio Calculations
To elucidate the experimental findings, we resort to a density functional theory (DFT) approach to describe electronic and magnetic properties of the EuS/Bi 2 Se 3 ð0001Þ interface. The approach is a self-consistent relativistic full-potential Green function method based on the multiple-scattering theory and provides an adequate description of bulk materials, surface, interfaces, and real-space clusters. [48][49][50] The goal of our simulations is to study 2 DL of EuS on Bi 2 Se 3 ð0001Þ. The structure model, derived by SXRD, serves as input for our calculations, which are carried out within a generalized gradient approximation (GGA) of the DFT. [51] To eliminate the polarity of the EuS surface, dangling bonds at the S-terminated side of the slab were passivated by hydrogen atoms as suggested Eremeev et al. [32] The strongly localized Eu 4f electrons are treated within the GGAþU approach. [52] The effective Hubbard parameter U Ã ¼ U À J ¼ 5 eV was chosen to ensure the binding energy of Eu 4f states to be in agreement with available photoemission experiments. [53,54] To verify the value of U Ã , we calculated various magnetic properties of EuS bulk. The obtained magnetic moment μ theory Eu ¼ 6.93 μ B and the Curie temperature T theory C ¼ 15.3 K are in good agreement with experimental results, μ exp Eu % 7μ B and T exp C ¼ 16.3 K, respectively. [55] The EuS/Bi 2 Se 3 ð0001Þ interface was simulated with a symmetric supercell consisting of six Bi 2 Se 3 QLs, four EuS DLs (placed by two on both sides of the Bi 2 Se 3 slab), and four vacuum QLs. The vacuum layers were represented by empty (Z ¼ 0) Wigner-Seitz cells. The angular momentum cutoff for the Green function expansion was chosen to be l max ¼ 3. For the integration over the Brillouin zone (BZ), we used an improved tetrahedron method with a 20 Â 20 Â 6 mesh in the full BZ. [56] As the stacking of the second EuS DL relative to the that of the first one adjacent of the Bi 2 Se 3 ð0001Þ surface ("FCC" vs "HCP") could not unambiguously determined by SXRD total energy calculations were carried out, indicating that the FCC stacking is energetically more favorable than the HCP stacking by 0.4 eV per unit cell. At first view, this suggests that the FCC stacking is favored, but we recall that gowth of ultrathin adlayers on a substrate crystal is a highly nonequilibrium process, so that a HCP-type stacking cannot be excluded a priori. Therefore, we studied both stacking sequences and compare their impact on the electronic and magnetic properties of the film.
To describe the magnetic properties of the two DL thick EuS/Bi 2 Se 3 ð0001Þ system the exchange parameters between magnetic moments were calculated using the magnetic force theorem as implemented within the multiple scattering theory. [57,58] Due to the lack of itinerant electrons, the magnetic interaction is not expected to be of long-range order. Therefore, any magnetic configuration can be used as a reference. As EuS is known to be an FM insulator, we chose this type of ordering for the estimate of the exchange coupling parameters JðRÞ.
The magnetic moment of Eu atoms (μ Eu ) is primarily determined by the occupied 4f electrons in the majority spin channel ( Figure 7) and is equal to μ Eu ¼ 6.9 μ B . We find a strong magnetic moment for the surface sulfur atom being equal to μ Se ¼ 0.6 μ B originating from the unpaired S-p z states at the film surface (see topmost panels in Figure 7). This scenario bears close resemblance with the oxygen-p z -derived magnetic moment in polar ZnO. [59,60] Magnetic moments for top-layer sulfur are almost identical for FCC-and HCP-type stacking of the second DL.
The surface sulfur possesses a large density of states (DOS) in the vicinity of the Fermi level (E F ) indicating a metallic surface and eliminating the polarity. It should be emphasized that this does not depend on whether the surface sulfur atoms are passivated by hydrogen or not. As Bi 2 Se 3 is known to have natural defects such as Se vacancies etc. acting as n-doping, we considered both the undoped (pristine) and the n-doped case. The natural n-doping in Bi 2 Se 3 leads to an energetic shift of the DOS by %0.3-0.4 eV toward the conduction band. In our calculations, n-doping is considered by a small concentration of Se vacancies either within the coherent potential approximation [61,62] or by shifting the DOS toward the conduction bands. Both approaches provide very similar results.
Exchange coupling parameters ( J ij ) for both FCC-and HCP-stacking models as well as for undoped and n-doped Bi 2 Se 3 are shown in Figure 4 versus the interatomic distance (D) between atomic pairs. First of all, the overall behavior of the J ij is that increasing D decreases the J ij rapidly while being oscillatory in nature, typical for the RKKY interaction. [63] Furthermore, large magnetic exchange parameters are only observed for the second (top) EuS DL, whereas they are almost negligible for the first (interface) DL. Therefore, the magnetic coupling between europium moments is FM in nature www.advancedsciencenews.com www.pss-b.com (i.e., J EuÀEu > 0) but very weak (see black open and filled symbols in Figure 8). This is almost independent on the Bi 2 Se 3 doping state as the DOS related to the itinerant electrons is almost constant within the corresponding energy range. Furthermore, the magnetic interaction between the localized europium 4f electrons is primarily mediated by itinerant 5d states, which are almost unoccupied in this system. In consequence, J EuÀEu is nearly identical in both stacking sequences and for both EuS DLs. Based on the random phase approximation, we estimated the Curie temperature (T C ) of the europium subsystem-while eliminating the exchange coupling with sulfur-and found T C ¼ 2 À 3 K for both stacking sequences and almost independent on doping (the sulfur is excluded from the consideration). Magnetic coupling between sulfur (J SÀS ) and between europium and sulfur (J EuÀS ) is strongly affected by doping (see open and filled symbols in Figure 4, respectively). The most interesting result of the calculations is the large magnetic moment of sulfur in the surface EuS DL. As pointed out previously, the sulfur magnetic moment is generated by the unpaired S-p z electrons. Depending on the doping state, the nearest neighbor exchange parameter J SÀS is either negative ( J SÀS ¼ À6.5 meV) or positive (J SÀS ¼ þ4.0 meV), for undoped and doped Bi 2 Se 3 , respectively. It is, however, almost independent on the stacking sequence.
Thus, for the undoped case, the sulfur moments order antiparallel to each other, whereas they are parallel due to the n-doping. For the latter case, T C was found to be 194 and 198 K for the FCC and HCP stackings, respectively. As Bi 2 Se 3 samples are naturally n-doped, the parallel orientation of the moments should be observed in experiment. The sulfur magnetic moments do not significantly differ depending on doping: μ ¼ 0.58 μ B versus 0.60 μ B in the undoped case. The origin for the strong dependency of the sign of J SÀS on the doping state are variations of the DOS near E F induced by doping where the sulfur moments are becoming more localized and the interaction between them is getting more short range.
Nearest neighbor exchange parameters between sulfur and europium are positive and strong in the case of undoped Bi 2 Se 3 : J Eu-S ¼ 9.4 and 7.5 meV for FCC and HCP stacking, respectively. Note that, this is opposite in sign to J SÀS . Europium moments in the interfacial EuS layer are weakly coupled to the Eu moments in the surface layer and try to order parallel to each other. As the Eu-Eu interaction is very weak, it is difficult to maintain a certain stable magnetic order for the Eu i moments. The estimated Néel temperature (T N ) for the FCC-and HCP-stacking model in the absence of doping is T N ¼ 210 and 226 K, respectively. www.advancedsciencenews.com www.pss-b.com

Conclusions
In summary, we have carried out a combined experimental and theoretical study of a 2 DL thick EuS film and its interface to the Bi 2 Se 3 (0001) surface. EuS grows in a single domain state with europium of the first EuS DL on the FCC sites on the Bi 2 Se 3 (0001) surface, i.e., above the third-layer selenium atoms of the first QL. The second DL continues the FCC-type stacking. The electronic structure of the EuS film is characterized by a metallic surface DL lifting polarity, whereas the magnetic interaction is dominated by the RKKY interaction. Most importantly, we find that there is a strong p z -orbital-derived magnetic moment (%0.6 μ B ) for the top-layer sulfur atoms due to the dangling bonds, which is not quenched upon passivation by hydrogen. Magnetic coupling parameters J ij are weak between europium atoms, but strong (4-9 meV) between sulfur and sulfur and between europium and sulfur magnetic moments. The magnetic interaction between sulfur magnetic moments is strong, extended over several coordination spheres and can establish a certain magnetic order in the system: an antiferromagnetic order in the absence of n-doping and the FM one under n-doping, which is natural for Bi 2 Se 3 samples. Critical temperatures were estimated within the range of 194-226 K depending on the doping and on the type of stacking (either FCC or HCP) sequences. In real experiments, the value of the critical temperature can be higher due to presence of various defects, which could be responsible for a certain magnetic order as it was already found in other systems. [59,60,[64][65][66][67] Acknowledgements

Conflict of Interest
The authors declare no conflict of interest.