Magnetic effects in sulfur-decorated graphene

The interaction between two different materials can present novel phenomena that are quite different from the physical properties observed when each material stands alone. Strong electronic correlations, such as magnetism and superconductivity, can be produced as the result of enhanced Coulomb interactions between electrons. Two-dimensional materials are powerful candidates to search for the novel phenomena because of the easiness of arranging them and modifying their properties accordingly. In this work, we report magnetic effects in graphene, a prototypical non-magnetic two-dimensional semi-metal, in the proximity with sulfur, a diamagnetic insulator. In contrast to the well-defined metallic behaviour of clean graphene, an energy gap develops at the Fermi energy for the graphene/sulfur compound with decreasing temperature. This is accompanied by a steep increase of the resistance, a sign change of the slope in the magneto-resistance between high and low fields, and magnetic hysteresis. A possible origin of the observed electronic and magnetic responses is discussed in terms of the onset of low-temperature magnetic ordering. These results provide intriguing insights on the search for novel quantum phases in graphene-based compounds.

Due to the two-dimensional nature and Dirac fermionic behaviour of charge carriers, the electronic and magnetic properties of graphene can be easily modified, making it one of the most appealing materials for a variety of disparate applications [1][2][3][4] . Such easiness to access novel regimes has shifted the focus in the graphene research from graphene itself to the modification of graphene, providing an exciting and versatile platform for realization of novel phenomena and device functionality 5 . One of such efforts is to induce magnetic effects in graphene. Indeed a growing number of studies ranges from theoretical predictions on the intrinsic ferromagnetism or spin ordering [6][7][8][9][10][11][12] to experimental probes of defect/impurity-induced local magnetic moments [13][14][15][16][17][18][19][20] . However, these magnetic moments are induced by the change of local crystal structure, e. g., carbon vacancies and deformations from sp 2 to sp 3 -type crystal structure, and hence, they have been identified as spin-1/2 paramagnets 21 . On the other hand, magnetic ordering can be realized in graphene when decorated with sulfur. Upon doping with sulfur, stacked graphene layers, i.e., graphite, exhibit ferromagnetism, which has been claimed to coexist with superconductivity 22,23 .
In this work, we have combined two different but complementary probes such as angle-resolved photoemission spectroscopy (ARPES) to study the evolution of the graphene band structure upon sulfur introduction and magneto-transport to explore the electro-magnetic properties of the graphene/sulfur (G/S) system. Figure 1A shows the procedure adopted to prepare the G/S samples. First, graphene samples are grown epitaxially on n-doped 6 H-SiC(0001) and undoped 4 H-SiC( ) 0001 surfaces by silicon sublimation method, as detailed elsewhere [24][25][26] . The graphene sample and a piece of sulfur are then sealed in a glass ampule, with a vacuum of 10 −6 Torr. The ampule is annealed at 230 °C in a furnace for 60 hours, while the pressure inside the ampule increased by vapourized sulfur was ~360 Torr. The presence of sulfur in the samples is confirmed by the observation of: a) sulfur 2 p core electrons in the photoemission spectra and b) Auger electrons corresponding to the sulfur LMM transition in the Auger electron spectroscopy (AES) spectra 27 . The concentration of sulfur is determined by AES and the value of sulfur/carbon ratio is 1/9.
Changes in the electronic structure are monitored by ARPES experiments. Figure 1B,C show ARPES intensity maps as a function of energy and momentum for as-grown graphene (G) and G/S samples. Data are taken at 10 K, near the Brillouin zone corner K, along the black line shown in the inset. In line with previous reports [28][29][30] , the Dirac energy, E D , of the G sample lies ~0.35 eV below the Fermi energy, E F , due to the formation of a Schottky barrier 31 . Two most obvious effects resulting from the introduction of sulfur are: a) broadening of the ARPES spectra; and b) small shift of E D towards E F . The former suggests that sulfur introduces disorder and the latter indicates charge transfer between sulfur and the graphene layer. More specifically, E D is estimated by the minimum of the integrated ARPES intensity (Fig. 1D), a quantity proportional to the one-dimensional density of states, or the full width at half maximum (FWHM) of the momentum distribution curves (MDCs, momentum spectra at constant energy shown in the inset of Fig. 1D) that shifts towards E F by ± 67 6 meV with introduction of sulfur. This signifies a decrease of the carrier concentration by 17% from . × A closer look at the energy distribution curves (EDCs, energy spectra at constant momentum k F indicated by the vertical blue lines in Fig. 1B,C) reveals a surprising depletion of states at E F ( Fig. 2A). This is a typical signature of energy gap opening at E F . The temperature dependence of the EDCs for the G/S sample is shown in Fig. 2B. As the temperature T is lowered, a clear depletion of states at E F or a shift of the leading edge toward higher binding energy is observed. This is clearly in striking contrast to the G sample (Fig. 2C), where, as previously reported 32 , no gap is observed when measured below 45 K. The magnitude of the energy gap is determined by the leading edge of the EDCs with respect to E F through the standard procedure 33 of fitting the first derivative of each energy spectrum with a Gaussian function. The temperature dependence of the gap is summarized in Fig. 2D. The gap develops below a transition temperature ± T 30 10 K c with a maximum shift of . ± . 4 1 0 6 meV at 10 K and appears to be independent from the substrate. The different T-dependence of G/S from G excludes the possibility of thermal smearing as the origin of the depletion of states at E F . Several mechanism can be accounted for the gap opening from superstructures [34][35][36] and charge-or spin-density wave 37 to magnetic ordering 38 and superconductivity 39 . The lack of replica (shadow) bands corresponding to the additional periodicities, however, makes the formation of the former two less likely scenarios. Indeed, considering the sulfur/carbon ratio present in our G/S sample, one would expect the gap opening at a momentum of 0.3 ~ 0.4 Å −1 , which is far away from 0.05 Å −1 where the energy gap is observed (Fig. 1C). Magnetism and superconductivity are certainly appealing scenarios also in view of the report of coexisting ferromagnetism and superconductivity in sulfur-doped graphite 22 .
To gain better insight on the origin of the gap opening, we have performed magneto-transport measurements (Figs 3 and 4). In each case, the introduction of sulfur strongly modifies the response of the G sample. Especially, the resistance R of G/S gradually deviates and sharply increases with respect to the one of the G sample with lowering T (Fig. 3A). Figure 3B displays a ln(R) versus − / T 1 2 curve for the same data 40 . The linear T-dependence observed at low temperatures is typical of disordered systems in the variable range hopping regime (VRH) [40][41][42] , consistent with an increase in the disorder of the G/S sample as discussed in Fig. 1C. This is qualitatively different from that of G (inset of Fig. 3B), where the linearity is not well defined due to the curvature in the whole T range.
In Fig. 4, we show the low-temperature magneto-resistance (R versus external magnetic field H) for both samples. The most striking difference is the behaviour of the magneto-resistance at low fields, where its complete reversal is observed upon sulfur introduction. This reversal can be explained with a transition from a weak antilocalization regime to a weak localization regime as previously reported for pure graphene 43,44 . For this case, intervalley scattering is turned on, thus causing an increase in R near zero field. While the magneto-resistance of the G sample (Fig. 4A) is positive (increasing R upon increasing H) over the whole field range, the magneto-resistance of the G/S sample (Fig. 4B) shows a crossover at ~5 T from positive at high fields to negative (decreasing R upon increasing H) at low fields, similar to the case of weak localizations. We note, however, that the crossover field is three orders of magnitude higher than the previous results for weak localizations, where   the strength of localization is suppressed very quickly in the presence of magnetic field 43 . Instead, the negative magneto-resistance at low fields is reminiscent of fluorinated graphene 45 , identified as a spin-1/2 paramagnet 21 .
The magneto-resistance near H = 0 T reveals another surprising phenomena of G/S, magnetic hysteresis with coercive fields of 0.12 T and 0.02 T (defined to be half the distance between the two peaks denoted by green and blue dashed lines in Fig. 4D). On the other hand, the G sample measured under the same condition (Fig. 4C) shows one order of magnitude smaller hysteretic effect with a coercive field of 0.003 T, likely induced by a remnant field of the superconducting magnet used for the measurements. Hysteresis in the magneto-resistance normally indicates the formation of magnetic domains or the existence of a magnetic granular system. The domains or grains change polarity above a given coercive field, creating a remanence in the signal. In the case of the G/S sample, the observed hysteresis persists in high fields up to 5 T, suggesting very large magnetic anisotropy and/or saturation fields. The observed magnetic hysteresis in the disordered system (broad ARPES spectrum in Fig. 1C along with the Fig. 3B) requires that magnetic moments are correlated with electronic states of graphene in the presence of sulfur.
One of the plausible origins of the observed magnetic moments is magnetized sulfur atoms. Our first principles calculations for G/S (Fig. 5A) suggest that a non-magnetic sulfur atom, after being trapped in between graphene and the buffer layer (a carbidic layer in between graphene and the SiC substrate whose crystal structure is the same as graphene, but π bands are absent due to the interactions with the substrate) exhibits spin-polarized states via the interaction with the buffer layer (see the spin density map in Fig. 5B, where the red and blue iso-surfaces correspond to spin up and down, respectively) exhibiting a magnetic moment of 0.63 μB. This can result in indirect exchange interactions analogous to the Ruderman-Kittel-Kasuya-Yosida interactions in metals driving the spin-dependent VRH 46,47 . Within this picture, spin-dependent hopping between neighbouring sublattices costs an energy J leading to the opening of a gap in the electronic spectra below a certain temperature 38,47  what the double-exchange mechanism expects 50 . Such spin-dependent VRH and energy gap opening are exactly demonstrated in the temperature-dependence of magneto transport signals (Figs 3 and 4) and energy spectra (Fig. 2B,D).
It is interesting to note that similar behaviour has been observed at the interface between LaAlO 3 and SrTiO 3 51,52 . This interface is a quasi-two-dimensional metallic layer that presents ferromagnetic order and large negative magneto-resistance 51 . In this case, electronic charge separation has been suggested as the main ingredient for the appearance of the novel behaviour 52 . At the G/S sample, it is clear that sulfur removes electrons from the graphene layer (Fig. 1D). This similarity suggests that depending on the nature of the charge transfer between sulfur and carbon, nanoscale inhomogeneities are created, leading to nanoscopic droplets with different electronic and magnetic properties, similar to the LaAlO 3 /SrTiO 3 interfaces [52][53][54] . However, we should stress the stark contrast between these layered oxides and G/S: G/S is metallic not insulating, and hence electronic screening should be more efficient 55 , Coulomb interactions weaker, and therefore the observed behaviour is even more surprising. In conclusion, we have revealed an unusual response to temperature and magnetic field from a material that consists of non-magnetic and light elements such as carbon and sulfur. The results here presented place graphene/ sulfur as another appealing system where magnetic ordering can be realized in graphene and carbon-based materials in general, and suggest the appealing possibility to realize novel phenomena such as ferromagnetic quantum Hall effect 56 for graphene-based spintronic devices operated not only by temperature and doping, but also by magnetic field.

Methods
Experiments. High-resolution ARPES experiments were performed at beamlines 10.0.1 and 12.0.1 of the Advanced Light Source at Lawrence Berkeley National Laboratory using 50 eV photons, with energy and momentum resolutions of 9 meV and 0.01 Å −1 , respectively. The magneto-transport properties were measured in a Van-der-Pauw geometry for the G/S and G samples using a custom-built cryogenic vacuum probe equipped with a 10 T superconducting magnet.
Calculations. Ab initio total energy calculations were performed with a plane-wave basis set 57 using the Vienna Ab-initio Simulation Package (VASP) [58][59][60] . The exchange-correlation of electrons was treated within the generalized gradient approximation (GGA) as implemented by Perdew-Berke-Enzelhof 61 . The crystal structure is simulated by using the supercell slab approach with vacuum region which separates the two surfaces (top and bottom surfaces). The bottom one is passivated by hydrogens to remove the lone pair of the SiC substrate. The k point sampling is (9 × 9 × 1). The structural optimisation and spin-polarized calculation were performed.