Azadirachta indica) is a tree from the Meliaceae family native to India, where it is considered as one of the most important plants worldwide. The anticancer effects of neem oil on breast cancer cells have been recently reported; however, its in vivo effects have not been studied. This prompted us to investigate the protective effects of neem oil on 7,12-dimethylbenz(a)anthracene (DMBA)-induced breast cancer in high-fat/sucrose-fed Wistar rats. Juvenile female Wistar rats were treated either with neem oil at a dose of 3 mL/kg body weight at 3 different frequencies, 2 times/week (Neem 1), 4 times/week (Neem 2), and every day (Neem 3), or with tamoxifen (3.3 mg/kg body weight), starting 1 week prior to DMBA treatment and lasting 12 weeks. Incidence, burden, volume, and histological analysis of mammary tumors were measured. Further toxicological parameters have been assessed. No tumors were detected in rats from the normal group, while all the rats from the negative control group (100%) developed mammary tumors. The regular consumption of neem oil at a dose of 3 mL/kg (2 or 4 times/week) significantly (p < 0.01) and in a dose-dependent manner reduced tumor incidence (80%), burden [35.78% (2 times/week) and 36.09% (4 times/week)], and weight. Neem consumption protected rats against DMBA-induced breast hyperplasia, with an optimal effect when taken 4 times weekly. Interestingly, all the animals that received a daily dose of 3 mL/kg died at the third week of the experiment. Further, animals that took the neem oil 4 times per week developed hepatotoxicity, evidenced by an increase of liver wet weight, transaminase (ALT and AST) activity, and histological abnormalities in liver. This study brings insight into the use of neem oil, which is greatly appreciated in traditional medicine. In summary, we demonstrated for the first time that the regular consumption of neem oil prevents breast cancer, but its excessive consumption is toxic.Neem ( Cancer is a growing health problem affecting millions of people worldwide. In 2012, it was estimated that 32.6 million people were suffering from cancer, and it is predicted that 18.5% of the world's population will likely develop cancer before the age of seventy-five . VariousBreast cancer continues to be an enigmatic challenge for researchers and is one of the most threats and a major cause of mortality in women worldwide . TreatmeAzadirachta indica) is a tropical or subtropical fast-growing evergreen with oblique leaves and stout trunk of timber values with insect-repellant properties [50 of 10 μl/ml and 20 μl/ml, respectively. According to the same authors, the neem oil induced apoptosis and cell cycle arrest at G0/G1 phase in both cell types. However, the in vivo effects of neem oil have not been studied, although it is being used increasingly in Cameroonian traditional system. We therefore analyze the in vivo anti-mammary cancer effects of neem oil.Neem anthracene (DMBA) (purity ≥ 95%) was purchased from Sigma-Aldrich . Tamoxifen citrate (Mylan®) was purchased from MYLAN SAS .Azadirachta indica L.) were harvested in Maroua  in June 2017 around 11:30 a.m. The plant was localized at the geographical coordinates of N10° 35.487' East and E0 14° 18.910' altitude with a “ESTREX” global positioning system. The city of Maroua is in the Sudano-Sahelian agroecological zone, characterized by two seasons: wet (June to September) and dry (October to May). Annual rainfall ranges between 800 and 1000 mm. Annual mean temperature is 298 C, with a maximum of 39 8C in March and minimum of 17 8C in January. This botanical sample was identified and authenticated by M. Victor Nana, a taxonomist at the National Herbarium of Cameroon (HNC-IRA), by comparison to the specimens deposited under the voucher number 4447 SRFK.The seeds of neem  was collected in a clean plastic flask after filtering with a Whatman N°2 filter paper constituting our neem oil.Fifty prepubertal female Wistar rats, aged 35-40 days at the beginning of experiment and weighing around 45-65 g, were supplied by the breeding facility of the Laboratory of Animal Physiology, University of Yaounde I . These rats were housed in plastic cages in groups of five at room temperature. The animals had free access to a standard (SD) or high-fat high-sucrose (HFHS) chow  and wateHousing of animals and all experiments were approved by the Cameroon Institutional National Ethic Committee, which adopted all procedures recommended by the European Union on the protection of animals used for scientific purposes . i.p.). On the one hand, blood samples were collected in anticoagulant (EDTA) tubes for hematological analysis; on the other hand, they were collected in dried tubes and centrifuged at 600 × g for 15 min at 4°C for biochemical analysis. Furthermore, the skin was dissected out to expose mammary tumors and all tumors were removed, counted, and weighed. A 1 mm precision sliding caliper (IGAGING®) was used to measure the size of tumors. Afterward, the formula from Faustino-Rocha et al. [π/6) was used to calculate the tumor volume. Estrogen target organs were also removed and weighed. Finally, all these organs were fixed in 10% neutral formalin solution for histomorphology.Thirty-five (35) female rats were acclimatized for 10 days and randomly assigned at age of 50-55 days into 7 groups of 5 animals each. At the beginning of the experiment, animals were divided into two groups: rats fed with standard (n = 5) and high-fat/sucrose (n = 30) diet. Animals received the following treatment schedule: the rats fed with standard diet (SD) served as normal control 1 (NOR-1) and received the vehicle (cotton oil) throughout the experiment. Regarding animals fed with HFHS, group 1 served as normal control 2 (NOR-2) and received the vehicle (cotton oil); group 2 served as negative control (DMBA) and also received the vehicle; group 3 (positive control) received tamoxifen (Mylan®) at the dose of 3.3 mg/kg dissolved in cotton oil. The remaining groups were treated with neem oil at a dose 3 mL/kg  at 3 different frequencies: 2 times/week (Neem 1), 4 times/week (Neem 2), and every day (Neem 3). All treatments were administered via intragastric gavage one week before DMBA administration, once a day around 2:00 p.m., and lasted for 3 months. Breast tumors were induced in group 2 to group 6 of animals that received HFHS by a single subcutaneous dose of DMBA (50 mg/kg) dissolved in 1 ml of cotton oil, while normal group (NOR-1 and NOR-2) received cotton oil only. Experimental rats were weighed weekly and palpated twice a week to check the development of mammary tumors from the first day of acclimatization until the end of the experiment. Tumorous latency (time of tumor appearance) was recorded. On days 1 and 84 of treatment, fasting glycaemia was measured using whole capillary blood obtained from the tip of the tail. The sacrifice and autopsy of either animals that died during the experiment or those that became moribund were carried out. At the end of the 3-month treatment, all survivors were sacrificed after a 12 h overnight nonhydric fasting under valium and ketamine anesthesia  and alanine transaminase (ALT) activities were measured as previously reported , 15 usinDifferent hematological parameters were evaluated using a Mindray BC-2800 Auto Hematology Analyzer from Shenzhen Mindray Bio-Medical Electronics Co., Ltd. These are white blood cell (WBC) count, lymphocytes, monocytes, granulocytes, red blood cell (RBC) count, hematocrit, hemoglobin, mean corpuscular volume (MCV), mean corpuscular hemoglobin (MCH), mean corpuscular hemoglobin concentration (MCHC), and platelets.Results are presented as means ± standard deviation (SEM) for each experimental group. Statistical analysis of data with GraphPad Prism software version 6.00 (GPW6-242831-RBMZ-03274) was performed using the one-way analysis of variance (ANOVA) followed by Dunnett's post hoc test for multiple comparisons. Statistical significance of differences was considered at a p value < 0.05.The body weight change of animals during the 12 weeks of experiment is represented in rd week of the experiment.It is important to notice that all the animals treated with a daily dose of 3 mL/kg of neem oil died before the 3th day of treatment.3, those of Neem 1 (with a mean volume about 700 cm3) and Neem 2 (with a mean volume about 300 cm3) decreased. Interestingly, the animals that received tamoxifen showed a significant (p < 0.001) lower tumor volume from day 49 until the end of the experiment with an average tumor volume of 150 cm3 as compared to DMBA group.In this study, tamoxifen significantly (p < 0.001) decreased average tumor weight as compared to DMBA control group . The neeThe tamoxifen significantly (p < 0.01) decreased the endometrium height but did not induce significant change in the vaginal epithelial height. The regular consumption of neem oil induced a significant decrease in endometrium height (p < 0.001) as well as the vaginal epithelial height (p<0.05 with Neem 1 and p<0.001 with Neem 2).No statistical significance was observed between normal and DMBA groups in all measured parameters except for a significant (p < 0.001) increase in red blood count (RBC) and platelets level in the DMBA as compared to normal group . TamoxifThe mammary gland microarchitectures of rats from normal group showed normal acini surrounded by a small amount of fibrous conjunctive tissue . Rats thOn the other hand, histological abnormalities such as sinusoid dilatation, vascular congestion, and inflammation were observed in the liver of animals that took neem oil 4 times/week, as compared to the liver of normal animals. No significant alteration was observed in the microarchitecture of kidneys.Azadirachta indica) have been shown to inhibit the growth of cancer cells through several mechanisms [ in vivo antitumor effects of neem oil, based on its reported anticancer effects on breast cancer cells [ in vivo anticancer effects of neem oil observed in this study. Preclinical studies have shown compelling evidence suggesting that the anticancer effects of neem are mediated through modulation of multiple cellular processes. Numerous bioactive compounds have been isolated from neem oil and could explain the chemopreventive and anticancer therapeutic efficacy of A. indica. There are essentially triterpenoids and steroids: nimbin, nimbinin, nimbidic acid, salannin, meliantriol, azadirone, epoxyazadiradione, azadiradione, gedunin, 7-deacetyl-gedunin, meldenin, salannin-lactone, nimbin-lactone, vepinin, nimbidinin, nimbinene, nimbandiol, 3-deacetylsalannin, salannol, 6-o-acetyl-nimbandiol, 1,3-diacetyl-vilasinin, and 6-deacetyl nimbinene [Despite the improvement in the diagnosis and treatment of breast cancer, it remains a major health issue for women . Existinchanisms . The preer cells . It was er cells , which der cells . Nimbolier cells . These cimbinene . In factimbinene . It is pGiven that neem-based preparations have been consumed for several millennia, the normal consumption of neem products can be regarded as absolutely safe . It is a in vitro anticancer effects reported, we demonstrated for the first time that the regular consumption of neem oil prevents breast cancer in rats, but its excessive consumption is toxic.In summary, the regular consumption of neem oil at a dose of 3 mL/kg (2 or 4 times/week) significantly reduced tumor incidence (80%), burden, and mass in a dose-dependent manner. Neem consumption protected rats against DMBA-induced breast hyperplasia. However all the animals that received a daily dose of 3 mL/kg died at the third week of the experiment. Further, animals which took neem oil 4 times a week presented a hepatotoxicity. This study brings new insight into the use of neem oil, which is greatly appreciated in traditional medicine. In line with the previous


A suspended monolayer graphene has only about 2.3% absorption rate in visible and infrared band, which limits its optoelectronic applications. To significantly increase graphene’s absorption efficiency, a tunable dual-band and polarization-insensitive coherent perfect absorber (CPA) is proposed in the mid-infrared regime, which contains the silicon array coupled in double-layers graphene waveguide. Based on the FDTD methods, dual-band perfect absorption peaks are achieved in 9611 nm and 9924 nm, respectively. Moreover, due to its center symmetric feature, the proposed absorber also demonstrates polarization-insensitive. Meanwhile, the coherent absorption peaks can be all-optically modulated by altering the relative phase between two reverse incident lights. Furthermore, by manipulating the Fermi energies of two graphene layers, two coherent absorption peaks can move over a wide spectrum range, and our designed CPA can also be changed from dual-band CPA to narrowband CPA. Thus, our results can find some potential applications in the field of developing nanophotonic devices with excellent performance working at the mid-infrared regime. As a crucial issue for nanophotonics and optoelectronics, efficient light-matter interaction has widely caused concerns in recent years , 2, partMore specifically, among these devices based on graphene, optical absorber takes an important role in the field of developing advanced optoelectronic devices, such as solar energy-trapping devices and emitters. Recently, due to the unique attributes of graphene, some absorbers based on graphene have been reported. Moreover, as mentioned above, most of these absorbers are focused on the terahertz and infrared regimes, because graphene with special processes can excite SPPs, leading to the strong light-graphene interactions in these wavelengths . For insImportantly, coherent perfect absorber (CPA), which is another way to control and strengthen the optical absorption of graphene, has attracted great attention due to the all-optical modulation features , 28. DepIn this paper, we design and study a tunable dual-band and polarization-insensitive CPA in the mid-infrared band, which contains a silicon array coupled in double-layers graphene waveguide. The physical mechanism of the designed CPA is analyzed by the scattering matrix. Meanwhile, the features of proposed CPA are demonstrated by the finite-difference time-domain (FDTD) simulations. When the incident light is illuminated into the silicon array, since the plasmonic resonances on the double continuous graphene films can be emerged due to the mechanism of guided-mode resonance, then the coupling effect between them results in the perfect dual-band absorption peaks, which are achieved in 9611 nm and 9924 nm, respectively. Moreover, due to its center symmetric feature, the proposed absorber also demonstrates polarization-insensitive. Furthermore, most of the reported graphene-based absorbers are manipulated by only changing the properties of graphene through an electrostatic field, magnetic field, or chemical doping, which are the causes of additional losses and also make the devices more complicated. For our proposed CPA, the coherent absorptions can be all-optically modulated by altering the relative phase between two reverse incident lights, which improves the absorber’s adjustability and does not increase the complexity of the structure. Meanwhile, by manipulating the Fermi energies of two graphene layers, two coherent absorption peaks can move over a wide spectrum range, and our designed CPA can also be changed from dual-band CPA to narrowband CPA. Therefore, our work provides a very promising way with convenience and sensitivity for potential applications include switches, all-optical logical devices, and coherent photodetectors.x-direction) and width (y-direction) of every silicon square in the array are both set as w = 80 nm, as shown in Fig. x-direction and y-direction are p = 160 nm, and the thickness (z direction) of silicon square is h = 100 nm. Moreover, the thicknesses of the silica spacer and substrate are d1 = 75 nm and d2 = 150 nm, respectively. I1 and I2, as two coherent incident lights, are simultaneously irradiated on the proposed CPA from two contrary directions, as shown in Fig. I1 and I2 is I2 = αI1 exp(iφ + ikz), where α, φ, and z are the relative amplitude, phase difference, and phase reference point between I1 and I2, respectively. O1 and O2 are the emergent lights scattering from the bottom and top of proposed CPA. Furthermore, the thicknesses of two graphene films are both set as 0.34 nm in our simulations, and the conductivities of two graphene films are both computed within the local random phase approximation as follows [T = 300K is the room temperature and Ef is the Fermi energy. Meanwhile, the intrinsic relaxation time is described as υf is the Fermi velocity and μ = 10000cm2V−1s−1 is the carrier mobility. For our proposed structure, the Fermi energies of the upper and lower graphene films are assumed as Ef1 = 0.66eV and Ef2 = 0.31eV, respectively.As illustrated in Fig.  follows :1\documx- and y-directions, and perfectly matched layer is applied along the z-direction including both the top and bottom of the proposed device. Moreover, we utilize the non-uniform mesh to compute the simulation results, where the minimum mesh size inside the graphene layer equals 0.1 nm and gradually increases outside the graphene film to cut down on the storage space and computing time.In the simulation, we utilize the 3D FDTD method for the numerical calculation. Meanwhile, periodic boundary conditions are applied along the I1 in the z-direction. Since the graphene-based CPA is in the symmetry environment, the combined reflection and transmission coefficients can be expressed as r = η and t = 1 + η, respectively, where η is the self-consistent amplitude related to the graphene hybrid waveguide. Thus, the absorption is derived as A = 1 − |r|2 − |t|2 =  − 2η2 − 2η. The condition of maximum absorption is ∂A/∂η = 0  and we get Amax = 0.5. In our simulation, when only one incident beam I1 vertically illuminates on the proposed absorber, due to the plasmonic resonances on the double graphene films, which are emerged by incident light through the silicon array for the mechanism of guided-mode resonance, then the coupling effect between the double graphene films leads to the dual-band absorption peaks, as demonstrated in Fig. Firstly, in order to clearly explain the physical mechanism, we investigate the absorption of proposed CPA under normal illumination of only one incident beam I1 and I2 vertically incident on the proposed structure from opposite sides, the schematic diagram is shown in Fig. O1 and O2 can also be assumed as the intensities of emergent lights from the bottom and top of the proposed CPA. The relationship between the incident lights and emergent lights is demonstrated by the scattering matrix:Then, when r11 = r22 =  − 0.5 and t12 = t21 = 0.5), by considering the relationship I2 = αI1 exp(iφ + ikz) with z = 0, the coherent absorption Aco of the proposed graphene-based CPA is express as [When the incoherent absorption limit is satisfied π to 2Nπ.Thus, according to Eq. , Aco canφ = 0 and α = 1 are coherent illuminated on the proposed structure, dual-band perfect absorption peaks can be achieved in λ1 = 9611 nm and λ2 = 9924 nm, respectively. Moreover, compared with the absorption under the illumination of only one incident beam, the absorption of the proposed graphene-based CPA has been significantly enhanced. It is worth noting that due to its center symmetric feature, the proposed CPA also demonstrates polarization-insensitive. As shown in Fig. p or s polarization, the absorption spectrum remains the same.As illustrated in Fig. To clearly demonstrate the features of proposed CPA, we illustrate the magnetic fields around the double-layers graphene waveguide at the wavelengths of absorption peaks. As described in Fig. φ, as illustrated in Fig. α of coherent incident lights is set as 1, and the other structural parameters are kept as the same as that in Fig. φ from 0 to π, two absorption peaks at 9611 nm and 9924 nm decrease continuously from 0.982 and 0.993 to almost 0, respectively. Thus, the modulation contrast can be as high as 34.8 dB and 35.2 dB at the two coherent absorption peaks with different φ, which shows a significant all-optical modulation property.Next, for the sake of displaying all-optical modulation characteristics, we demonstrate the coherent absorption of proposed absorber with different phase differences εi and ki  are the permittivities and wave vectors of the silicon array-graphene waveguide (i = 1), silica layer (i = 2), graphene film (i = 3), and silica substrate (i = 4), respectively. dg is the thickness of graphene. Thus, by properly manipulating the Fermi energies of two graphene films, the features of plasmonic modes sustained by two graphene films could be significantly and independently controlled. As seen in Fig. Ef1 of upper-layer graphene remains unchanged and the Fermi energy Ef2 of lower-layer graphene decreases from 0.31 to 0.27 eV, the absorption peak at λ1 red-shifts and keeps the value almost unchanged, while the absorption peak at λ2 reduces rapidly and even disappears under Ef2 = 0.27 eV, as shown in Fig. Ef2 increases from 0.31 to 0.37 eV, the absorption peak at λ1 reduces rapidly and almost disappears under Ef2 = 0.37 eV, while the absorption peak at λ2 blue-shifts and keeps the value almost unchanged. Thus, the dual-band proposed perfect absorber can be changed to narrow-band perfect absorber by separately altering the Ef2. On the other hand, when Ef2 remains unchanged and Ef1 increases from 0.62 to 0.72 eV, both two absorption peaks blue-shifts and keeps their values almost unchanged over a wide wavelength range, which demonstrates a significantly tunable characteristic. Compared with the other absorbers based on the discrete graphene patterns, it is worth noting that two graphene films of the proposed CPA are in the continuous form, which is more convenient to get excellent tunability.In the following, for our four layers (silicon array-graphene waveguide/silica layer/graphene film/silica substrate) system, combined with continuous boundary conditions and the Maxwell equations, the dispersion relation can be expressed as :4\documw is increased, dual-band absorption peaks are both red-shifted due to the increment of effective resonance wavelength of localized plasmon mode. Moreover, the filling factor will increase with w, which further reinforces the intensity of field enhancement and concentration between neighboring silicon square and inside graphene. Thus, the absorption efficiency will firstly increase with w. However, with the continuous increment of filling factor, too many areas of graphene will be covered by silicon squares. As a result, the absorption efficiency will subsequently decrease with the increment of w. Then, as shown in Fig. p, because the resonant wavelength of localized plasmon mode becomes larger. Furthermore, it is noted that the resonant frequency of the plasmonic mode supported by the lower-layer graphene strongly depends on the separation distance d1. As shown in Fig. d1 is increased, the nearfield coupling strength between the upper- and lower-layer resonance modes will become more and more weak, which lead the dual-band absorption peaks eventually to degenerate into one peak. Meanwhile, we also investigate the absorption of proposed CPA with different dielectric array. As shown in Fig. 2 array (nT = 2.9) or the GaSb array (nG = 3.8) is not better than the one with silicon array. Moreover, it is worth noting that the wavelengths of absorption peaks are red-shifted with the increment of the refractive index of the dielectric array.In addition, we investigate the influences of different structure parameters on the optical absorption of proposed CPA, as shown in Fig. As mentioned before, most reported graphene-based perfect absorbers are polarization-sensitive and focused on the narrowband or broadband perfect absorbers, dual-band graphene-based perfect absorbers are seldom investigated in the mid-infrared regime. In this paper, we have designed a tunable dual-band and polarization-insensitive CPA in the mid-infrared regime, and the corresponding absorption features are discussed by using the scattering matrix and FDTD simulation, which illustrate that dual-band perfect absorption peaks are achieved in 9611 nm and 9924 nm, respectively. Moreover, due to its center symmetric feature, the proposed CPA also exhibits polarization-insensitive. Meanwhile, the coherent absorption peaks can be all-optically modulated by altering the relative phase between two reverse incident lights. Furthermore, by manipulating the Fermi energies of two graphene layers, two coherent absorption peaks can move over a wide spectrum range, and our designed CPA can also be changed from dual-band CPA to narrowband CPA. On the other hand, for the proposed CPA, subwavelength metamaterials based on silicon squares can be integrated for the current CMOS technology, and chemical vapor deposition (CVD) grown graphene can be transferred over the silica layer using standard transfer techniques . Moreove


Carbon allotropes with their dispersive electron states at the Fermi level and a small spin-orbit coupling are not an obvious candidate for ferromagnetism. Here we show that the origin of ferromagnetism in hydrogenated epitaxial graphene with a relatively high Curie temperature (>300 K) lies in the formation of curved specific carbon site regions in the graphene layer, induced by the underlying Si-dangling bonds and by the hydrogen bonding. Hydrogen adsorption is therefore more favourable at only one sublattice site, resulting in a localized state at the Fermi energy that can be attributed to a pseudo-Landau level splitting. This  This indicates that the observed peaks in the DOS can be assigned to pseudo-Landau levels (PLLs). It is worth to note that the H-induced PLLs are not only caused by ”mechanical” strain  and, hence, a pseudo-magnetic field. Using a Fermi velocity of 1.0 × 106 ms−1, the resulting pseudo-magnetic field extracted from the fit is ∼250 T and its value increases for higher hydrogen coverage and vice versa. This is in agreement with previous theoretical results [The adsorbed H atom breaks a π bond and slightly pulls out the carbon atom below due to a covalent bond interaction. This carbon atom changes its hybridization state from speference . The corous work  as arisious work , the consymmetry ,39. As isymmetry ,41, strun = 0) will split into two states; filled state (spin up) and empty state (spin down) denoted by red and blue lines in From the value of the pseudo-magnetic field, it is noteworthy that the magnetic length  SiC superstructure. Our calculation results for the isosurface of the spin density distribution of four hydrogen adsorbed atoms, occupying an A sublattice at the corners of the quasi – (6×6) SiC superstructure, are shown in The attached hydrogen atoms (remarked by arrows in the figure) are separated from each other by ∼1.7 nm, and, as clearly seen, the localized electron states extend over a few graphene unit cells around the H atoms. The long-range magnetic coupling is therefore attributed to these connected regions of spin-polarized quasi-localized states.n = 0 gives rise to two exchange split states lying in a band gap which is defined by the energy difference between the PLLs n = 1 and n = −1. The bandwidth of the filled (spin up) band is ~0.1 eV and the empty (spin down) band is almost flat. This is in agreement with Ref. [n = 0 which is ~200 meV. This value is well above kBT (kB is the Boltzmann constant) at room temperature.Very unexpectedly, experimental results of hydrogenated epitaxial graphene show room- temperature ferromagnetism ,43. Howeith Ref. , therefo2 to sp3 hybridization. In order to avoid this, we compress the (√3×√3)R30◦ SiC by 7% instead of stretching it. This leads to a very high coverage of hydrogen (∼12%) atoms in the unit cell and therefore it was replaced by a (4×4) graphene cell, commensurate with a (2√3×2√3)R30◦ SiC substrate, while keeping the 7% compression of the substrate to get the commensurability between the two lattices. This was also used for epitaxial two-layer graphene on the Si-face of SiC by Gao and Tosatti [In the previous sections, the origin of the room-temperature ferromagnetic property of hydrogenated graphene on SiC was, for simplicity, discussed excluding the effect of the SiC substrate and buffer layer in the electronic structure calculations, just to indicate the connection between the role of local strain and the existence of pseudo-Landau levels. So far, a ferromagnetic behaviour is reported only for hydrogenated graphene, which is grown on a SiC substrate ,43. So i Tosatti . Adding From the side view of the structure in The spin unrestricted calculated band structure of epitaxial graphene and hydrogenated epitaxial graphene on SiC are shown in n = 0. In the geometry we utilized, the hydrogen coverage is ∼3%; this leads to the observation of a filled (majority spin) pseudo-Level n = 0 at about 0.3 eV below the Fermi energy at the K point. This value may decrease if the hydrogen coverage is less and vice versa [n = −1 decreases when the hydrogen coverage is reduced since it is related to the pseudo-magnetic field.However, it is very likely to be attributed to Coulomb interactions between the localized electrons of the Si-dangling bonds. Looking more closely, while no spin polarization was obtained for the graphene π-electrons, each localized state attributed to the Si-dangling bonds ,46 splitn = 0 could play a role leading to an increase in the exchange splitting of this latter and hence gives rise to a larger magnetic moment.In addition, the calculated total magnetic moment without the SiC nor the buffer layer contribution but with the simulated effective electron doping as discussed in 3.2, is 0.5 μB per H adatom. This value is smaller than the one obtained when the Si-dangling bonds of the buffer layer are present in 3.3, which is 0.7 μB per H adatom. This indicates that Coulomb interactions between localized Si-dangling bond states and the quasi-localized PLL n = 0 give rise to long-range ferromagnetic coupling. The relative high Curie temperature is obtained due the narrow bandwidth of these states formed in a bulk energy gap leading to a high magnon stiffness. Furthermore, Coulomb interactions between the pseudo-Landau level and the Si-dangling bond states can lead to an increase of the total magnetic moment. The presence of localized electron states close to the Fermi level is evidenced by photoemission spectroscopy measurements, which also indicates the p-doping of epitaxial graphene due to hydrogenation.In conclusion, our electronic structure calculations in combination with published experimental results provides a coherent picture to understand the observed room-temperature ferromagnetism in hydrogenated epitaxial graphene on SiC. We have theoretically shown that specific carbon sites, due to the presence of Si-dangling bonds in the underlying buffer layer, result in a quasi (6×6)SiC superstructure of epitaxial graphene, favouring one sublattice site hydrogen occupation. The chemical modification of the graphene layer by H adatoms and strain-like effects generate a pseudo-magnetic field and consequently localized pseudo-Landau levels in the electron density of states. Extended spin-polarized electron states from the pseudo-Landau level


Standard photocurrent measurements on a graphene/WTe2 phototransistor reveal a pronounced photocurrent enhancement (a photoresponsivity ~8.7 A/W under 650 nm laser illumination). Transport and photocurrent mapping suggest that both photovoltaic and photothermoelectric effects contribute to the enhanced photoresponse of the hybrid system. Our results help to enrich the understanding of new and emerging device concepts based on 2D layered materials.Heterostructures based on two-dimensional (2D) materials have sparked wide interests in both fundamental physics and applied devices. Recently, Dirac/Weyl semimetals are emerging as capable functional materials for optoelectronic devices. However, thus far the interfacial coupling of an all-semimetal 2D heterostructure has not been investigated, and its effects on optoelectronic properties remain less well understood. Here, a heterostructure comprising of all semi-metallic constituents, namely graphene and WTe The absence of dangling bonds on the surfaces of vdWs materials enables the creation of high-quality hetero-interfaces without the constraints of lattice matching and processing compatibility6. Indeed, vdWs heterostructures have been realized using different combinations of 2D materials, including metallic graphene7, insulating boron nitride (BN)8 and semiconducting transition metal dichalcogenides (TMDCs)10. While interesting electronic and optical properties of these 2D materials are being investigated, peculiar physics at the hetero-interfaces are attracting ever growing attentions14. Elucidating the interfacial effects and coupling mechanisms for different types of heterostructures and constituents compounds will provide important guidelines for developing functional 2D materials heterostructures.Heterostructures based on van der Waals (vdWs)-bonded layered materials have opened new avenues for fundamental scientific studies and applied devices21. Graphene is, strictly speaking, an exemplary 2D Dirac semimetal. Owing to its unique physical properties, e.g. mono-atomic thickness, universal optical absorption and gate tunable Fermi level, a variety of remarkable optoelectronic devices have been demonstrated by forming different types of graphene heterostructures. For instance, stacking graphene with semiconductors can form a versatile Schottky-type metal-semiconductor junction that is widely used in photodetection, solar energy collection and Schottky diode, etc26. Graphene-hexagonal boron nitride (hBN) heterostructure, as a paradigm of semimetal-insulator junction, offers a huge potential application in the fabrication of atomically thin field-effect transistors, resonant tunneling transistors and diodes29. In addition, due to the work function difference, graphene is usually doped by 3D metal contact, which can effectively improve the performance of graphene-based photodetectors34. Although considerable amount of work has focused on graphene heterostructures, graphene-semimetal heterostructures  have remained less well studied37.In addition to conventional semiconductor and metal materials, Dirac/Weyl semimetals are emerging as capable functional quantum materials for optoelectronic and photonic applications2 is investigated. WTe2 is chosen to form an all-semimetal 2D heterostructure as it belongs to an emerging class of Weyl semimetal with significant relevance to optics and photonics42. In addition to providing potentially better metallic contact than commonly used 3D metals43, study of the fundamental properties of such heterostructures may yield new insights into the design and optimization of 2D materials based nanodevices. Here, we study the interfacial transport and photoresponse of all-semimetal graphene and WTe2 heterostructure. Multi-fold of photocurrent enhancement, with a photoresponsivity ~8.7 A/W under 650 nm laser illumination, is observed in the graphene/WTe2 hybrid device. Transport and photocurrent mapping suggest that both photovoltaic and photothermoelectric effects contribute to the enhancement of photocurrent. Our experimental results, provide new insights in the design of photonic functional vdWs heterostructures.In this work, the optoelectronic properties of a hetero-interface formed by semimetal graphene and WTe2 heterostructure. Few-layer WTe2 flakes were mechanically exfoliated onto the SiO2/Si substrate. Chemical vapor deposition (CVD) grown monolayer graphene was then transferred onto the WTe2 flakes using the polymethyl methacrylate (PMMA) supported procedures (see Methods for details). Optical contrast measurements were first used to identify the thickness of WTe2 and graphene samples, and further characterizations were conducted by Raman spectroscopy, as shown in Supplementary Figure 2 sample well coincide with its Td structure, confirming its semimetallic nature44. Figure 2 stack. From the height profile of the WTe2 flake on the substrate, the thickness of it is estimate to be ∼8 nm, corresponding to ~10 layers of WTe2. The heterostructure devices are prepared by a standard photolithography procedure (see Methods for details). Since thin WTe2 flakes tend to degrade in ambient environment45, a fatigue test of the graphene/WTe2 film was conducted through optical contrast and Raman spectroscopy, in which the hybrid film showed no discernible change after 11 days of exposure in ambient conditions . Figure 2 device. The graphene channel is about 30 × 35 μm. The quality of the heterostructure device is confirmed by Raman spectroscopy again. As shown in Fig. 2 agree well with the previous results46, confirming no significant perturbation to either material during the fabrication processes.Figure 2 heterostructure and to provide insights into the hybridization of the all-semimetal interface, we conducted standard photocurrent measurements with a focused 650 nm continuous wave laser in vacuum (<10−5 Torr) at room temperature. Figure 2 heterostructure and a pure graphene control sample with the same design  and external quantum efficiency (EQE) are the key figure-of-merit that are used to evaluate the performance of a photodetector. R is defined as the photocurrent at unit incident optical power and is given by:Iph is the photocurrent and Popt is the incident light power on the effective area of the photodetectors. Apparently, high photoresponsivity indicates a large photocurrent can be achieved under relatively low incident illumination power. On the other hand, EQE characterizes the effectiveness of conversion of photons to electrons and is defined as:h is Planck’s constant, c the velocity of light, e is the electronic charge and λ is the wavelength of the incident power. To compare with other devices, we measured the power-dependent photocurrent of the graphene/WTe2 hybrid device at 650 nm . Such a shift in transfer curve is compatible with the previously discussed Fermi level pinning effect, when considering the work function for graphene and WTe2 are 4.5 eV and 4.39 eV, respectively39. It should be noted that the rather small work function mismatch (~0.1 eV) would lead to a built-in field that is weak and easily screened by impurity at the interface. The inset of Fig. 2 interface as stipulated by the difference in work function.To shed lights on the photocurrent enhancement at the semimetal interface, it should be noted that due to the requirement of continuity of Fermi level, the difference in work function between metallic materials  and graphene can drive a charge transfer process, resulting in an inhomogeneous doping profiles (built-in field) along graphene, which is capable of separating light-induced electron-hole (e-h) pairs. To confirm such a ‘photovoltaic’ picture, transfer characteristics of the graphene/WTe2 heterostructure, we fabricated a staggered graphene/WTe2 heterostructure device as shown in Fig. I-V) characteristic of the staggered graphene/WTe2 device . As shown in Fig. 2 junction, which further confirm the important role of the interfacial effects in the heterostructure system. Clearly, the photocurrent enhanced area in Fig. 33. Therefore, photothermoelectric effect is considered to be another contributing factor to the photocurrent, which results from local heating of the graphene and WTe2 junction due to the incident laser58. On one hand, inhomogeneous doping profiles of the graphene and WTe2 junction as mentioned above, give different Seebeck coefficients at the junction. On the other hand, considering graphene’s excellent (up to 5000 Wm−1 K−1) and WTe2’s rather poor (~3 Wm−1 K−1) thermal conductivities60, we assume that heat is accumulated in the graphene and WTe2 junction when illuminated by light, which leads to a temperature gradient across the device. Then, a thermoelectric photocurrent was induced due to the different Seebeck coefficients and temperature gradient. Considering the small electron capacity and large light-induced changes in electron temperature in graphene, the photothermoelectric effect may play as important a role as in the photovoltaic effect. Investigation of photocurrent generation as a function of layer thickness therefore would yield more insights into the interfacial charge transfer dynamics but is beyond the scope of the current study.To further elaborate the photocurrent generation mechanism of the graphene/WTe2 flakes with monolayer graphene. The photocurrent investigation suggests that, despite the all-semimetal nature of the heterostructure (by graphene and few-layer WTe2), the interfacial effects can effectively separate the photo-induced electron-hole pairs and lead to pronounced photocurrent enhancement, both due to photovoltaic and photothermoelectric effects. A photoresponsivity ~8.7 A/W is obtained for the heterostructure device under 650 nm laser illumination. These results advance the understanding of fundamental properties of all-semimetal heterostructures and provide guidelines for designing novel photonic devices.In conclusion, we demonstrated an all-semimetal vdWs heterostructure device through the integration of few-layer WTe2 flakes and transferred them onto a highly doped Si wafer capped by a 285-nm-thick SiO2 layer. Thickness of the exfoliated WTe2 flakes was measured by means of optical contrast and Raman spectra.A standard mechanical exfoliation method was employed to isolate few-layer WTe2 flakes. The PMMA was immediately removed using hot acetone (60 °C).A 0.5 cm × 0.5 cm CVD grown monolayer graphene coated with PMMA on copper was immersed in ammonium persulfate for 3 h and deionized water for 30 min, respectively. Subsequently, the graphene film supported by PMMA was transferred onto the WTe2 stacks through a shadow mask by electron beam evaporation. The graphene/WTe2 channel was patterned using photolithography procedure and oxygen plasma etching.The source and drain electrodes  were deposited on top of the graphene/WTeThe Raman spectroscopy measurements were carried out using a Horiba Jobin Yvon LabRAM HR-800 Raman spectrometer with a 514 nm argon ion laser. Surface morphology of the films was studied using atomic force microscopy (AFM) .−5 Torr) at room-temperature. The photocurrent mapping was performed in a custom data collecting system with a 532 nm continuous wave laser generator, a mechanical chopper, a source meter (Keithley 2612B), and a lock-in amplifier . The transport characterization of the staggered device was measured under vacuum at 24 K for suppressing the outside interference.For photoresponse characterization, the 650 nm laser beam is guided through an optical fiber with a FC/PC ferrule and is subsequently incident onto the channel of the devices without focusing. The beam at the device was measured to be Gaussian-shaped with a diameter of about 300 μm. The electrical measurements were conducted using a semiconductor parameter analyzer (Keithley 4200) in a closed cycle cryogenic probe station under vacuum (<10Supplementary Information


The influence of hydrogen overflow was decreased and the current response was enhanced because the modified graphene extended the potential range of the electrode. The Gr/l-cysteine/gold electrode showed high electrochemical conductivity, producing a marked increase in anodic peak currents (vs. the glass carbon electrode (GCE) and boron-doped diamond (BDD) electrode). The calculated detection limits are 1.15, 0.30, and 1.42 µg/L, and the sensitivities go up to 0.18, 21.69, and 152.0 nA·mm−2·µg−1·L for, respectively, the BDD electrode, the GCE, and the Gr/l-cysteine/gold electrode. It was shown that the Gr/l-cysteine/gold-modified electrode is an effective means for obtaining highly selective and sensitive electrodes to detect trace levels of cadmium.Cadmium(II) is a common water pollutant with high toxicity. It is of significant importance for detecting aqueous contaminants accurately, as these contaminants are harmful to human health and environment. This paper describes the fabrication, characterization, and application of an environment-friendly graphene (Gr)/ Cadmium (Cd) has long been recognized as one of the most notable toxic heavy metals to ecosystems and human health ,2. It waConventional spectrometric measurements for metals include atomic absorption spectrophotometry (AAS) ,7,8, indTo address this issue, several nanoparticles have been modified on the surface of electrode based on nanotechnology, which has demonstrated exciting prospects in both chemical and optical determination of Cd(II) over the past decades. A variety of electrode surface modifications have been explored to increase sensitivity for metal detection. Sensitive, environment-friendly, and efficient determinations of heavy metal have been developed by grafting various kinds of nanomaterials onto the surface of electrodes. Platinum and gold electrodes in different forms and sizes have been widely used as backing material in electrochemical analysis due to their excellent electron transfer kinetics. However, they have been limited to detection in a positive potential range for most heavy metals due to the low hydrogen overvoltage that reduces the cathodic potential window, while the stripping peak of cadmium is comparatively negative. Platinum and gold electrodes can be combined with various nanoparticles and have a wide potential range.2-bonded carbon atoms [Carbon-based electrodes, such as the glass carbon electrode (GCE), the boron-doped diamond (BDD) electrode, and the graphene-modified electrode, have a wide working potential range to make extensive analyses, low background currents to obtain high sensitivity, and stable structures to overcome harsh chemical environments. Graphene, a new type of environmental film, has also shown high hydrogen overpotential, which can suppress the hydrogen overflow on a gold electrode. Graphene is a 2D nanomaterial of spon atoms ,17. Moreon atoms ,19. Sincon atoms  and exceon atoms ,23,24,25l-cysteine was selected as the linker between graphene and gold microelectrode as it provides fast electron transfer for electrochemical detection and amino group that can potentially join with graphene by dehydration-condensation reaction. The boron-doped diamond (BDD) electrode and the glass carbon electrode (GCE) were also examined for Cd measurements, and the results were compared with that of the Gr/l-cys/Au electrode.In this paper, graphene was modified on a gold electrode via a self-assembled method based on thiols and related molecules, which provided a way to perform Cd detection in a negative potential range . We trie2+ in 3% nitric acid) was purchased from the China National Research Centre for Certified Reference Material. Cadmium samples were carefully diluted from the stock solution with double-distilled water. Carboxyl graphene (2 mg/L) was from Nanjing XFNANO Materials Tech Co., Ltd. . Dichloroethane (EDC) and N-Hydroxysuccinimide (NHS) were purchased from Sigma-Aldrich . Sodium acetate and glacial acetic acid were obtained from Xilong Tech Co., Ltd. . Ferricyanide solution (0.5 mM) was added into 0.1 M KCl solution.The purities of all reagents were in analytical grade except those stated separately. Double distilled water (18 MΩ·cm) was used to prepare for samples. Cadmium standard stock solution  using a three-electrode system based on a microelectrode chip. For comparison, traditional electrochemical bulk electrodes were used, while the glassy carbon electrode and the boron-doped diamond electrode (3 mm in diameter) served as the working electrode, the platinum disk electrode (3 mm in diameter) served as a counter electrode, and Ag/AgCl (saturated KCl) served as the reference electrode.Field-emission scanning electron microscope  produced by Hitachi  was used to check the morphologies of the graphene.2SO4 until a stable curve was obtained. The gold microelectrode was dipped in 20 µL of 10 mM l-cysteine (C2H7NS) solution for 6 h at 4 °C. The l-cysteine-modified gold electrode was obtained after 6 h of immersion. The modified gold microelectrode was washed with deionized water and dried in air for 24 h. Then, a mixed solution of NHS and EDC was applied into the carboxyl graphene (GN–COOH) solution for 15 min at 4 °C. Three microliters of the graphene-mixed solution was dispensed on the surface of the l-cysteine-modified gold microelectrode for 12 h at 25 °C. The hydroxyl group of the GN–COOH bond with the amino group of l-cysteine on the Au microelectrode with those steps. Finally, the carboxyl graphene (GN–COOH)-modified gold microelectrode was modified with l-cysteine as shown in The ring-disk microelectrode chip contains a gold working microelectrode, a platinium counter electrode. The microelectrode was prepared by the MEMS technique. The gold-working electrode was fabricated by standard optical lithography and a lift-off process with a diameter of 3 mm. Before modification, the gold microelectrode was cleaned in 0.01 M HDifferential pulse stripping voltammetry (DPSV) was applied to detect trace levels of cadmium under an optimized condition. All solutions were stored in a 20-mL Teflon bottle. DPSV parameters were optimized such that cadmium was deposited for 360 s at −1.1 V in 0.1 M acetate buffer (pH 4.50). The DPSV of electrodeposit metal was performed in the potential range of −1.1 to 0.5 V. The samples were homogeneous medium via stirring during the deposition steps, and the magnetic stirrer turned off for 120 s to equipoise prior to the DPSV scan.l-cysteine/Au electrode are shown in l-cysteine composite is rougher and sheets of graphene are clear in the edge of electrode. There are some thin folds on the surface in the center of the electrode. The electrochemical properties of different gold electrodes were characterized by CV. l-cys/Au, Gr/l-cys/Au, and Gr/l-cys/Au electrodes in solution containing 0.5 mM Fe(CN)33− and 0.1 M KCl. Compared with the CV curve of the bare gold electrode (curve a), an obviously increased redox current was obtained by the l-cysteine-modified gold electrode (curve b). After the chemical bond between GN–COOH and l-cysteine layer, the redox current of Gr/l-cysteine/Au electrode (curve c) decreases compared with the l-cysteine/Au electrode. It can be seen from the reduced redox current that electron transfer was inhibited by the graphene layer. Reduction of GN–COOH to rGN–COOH (curve d) increases the conductivity of the catalyst. The existence of rGN–COOH results in a stronger combination of cadmium with the modified electrode. The subsequent stripping of cadmium was therefore kinetically harder, and the stripping potential became more negative. However, this potential shift brings about fierce hydrogen evolution, which may damage the deposition layer. Consequently, the rG/l-cys/Au electrode cannot be applied to Cd detection.The typical SEM images of Gr/l-cys/Au on the surface is shown in 2 to H2O2 at the gold surface depending on the pH of the medium, which easily occurred in acidic media [l-cys/Au electrode. Such behavior was due to the fabrication of graphene on the gold electrode and the graphene-modified gold electrode can be used in cadmium determination.The influence of oxygen on the voltammetric behaviors of the bare gold electrode and the Gr/ic media . It can l-cys/Au electrode. As the pre-concentration time increased from 120 to 840 s, the peak currents for Cd2+ at pH 4.50 linearly increased, owing to the increased amount of cadmium ion on the Gr/l-cys/Au electrode. However, the stripping currents tended to slightly deviate from the linear region after 360 s, as shown in In order to investigate the influence of the deposition time and pH value of the detection solution, experiments were designed with 10 µg/L Cd(II) by DPSV to identify the current response on the Gr/l-cys/Au (B) electrodes drawn by AFM. The height profile of one layer’s is about 120 nm along the line across the membrane surface. It is believed that 2D graphene sheets combined to create an interconnected framework. The overlap of graphene can greatly enhance the specific surface area of the Gr/l-cys/Au electrode and can give the unfolded graphene a significant character to capture metal ions during deposition time in aqueous phase [The thickness of the one layer was measured by atomic force microscope (AFM). us phase .l-cysteine composite-modified electrodes generated improved the electrochemical character in a solution containing 0.5 mM ferri/ferrocyanide and 0.1 M KCl. The redox current decreased when the amount of GN–COOH loading increased from 3 to 9 µL, indicating that adding more GN–COOH to the electrode surface could diminish the electrochemical sensitivity of modified gold electrode. Graphene incorporation into l-cysteine is crucial for improving the electrochemical properties of the composite. One graphene layer displayed the best sensitivity, stability, and firm combination.l-cysteine was used to connect the electrode surface with the graphene by a self-assembly process. Calibration samples of deionized water (DW) were used to test the analytical performance of our method. Samples were spiked with 0, 5, 10, 15, and 20 µg/L cadmium(II) from standard stock solutions. The resulting calibration plots are linear over a range from 5 to 20 µg/L, with correlation coefficients exceeding 0.95 (To detect trace levels of Cd(II), DPSV is used because of its high sensitivity and linearity . To incring 0.95 . The anal-cysteine nanocomposite-modified gold electrode was compared to the GCE and the BDD electrode in similar systems for measuring trace levels of Cd(II). l-cys/Au electrode, the glass carbon electrode, and the boron-doped diamond electrode. The sensitivities go up to 0.18, 21.69, and 152.0 nA·mm−2·μg−1·L for, respectively, the BDD electrode, the GCE, and the Gr/l-cys/Au electrode. The sensitivity of the Gr/l-cys/Au electrode was higher than the other carbon-based electrodes, and the detection limit of the proposed method was comparable to other electrochemical detection methods. It was thus shown that the Gr/l-cys/Au-modified electrode is an effective method for obtaining highly selective and sensitive electrodes for detecting trace levels of cadmium.Furthermore, carbon-based electrodes have obtained significant attention in previous reports because of its environmental-friendly effect and high sensitivity, especially the GCE, the BDD electrode, and the graphene ,32. A val-cysteine film was successfully modified on gold microelectrode, and the structure of the microelectrode chip demonstrated the fabrication of this composite electrode. The Gr/l-cysteine/gold electrode showed microelectrode behavior and yielded a high, steady current. The electrochemical characteristics of the microelectrode during modifications were investigated by cyclic voltammetry in [l-cysteine gold microelectrode, the GCE, and BDD electrode for Cd(II) determination are linear with a range from 5 to 20 µg/L, with correlation coefficients exceeding 0.95. The Gr/l-cysteine gold microelectrode showed the highest sensitivity compared with the bare glassy carbon and boron-doped diamond due to the use of graphene and microelectrodes. In addition to the present work, this modified microelectrode can also be used for the detection of other trace metals that have lower deposition potentials than cadmium.In this work, the gold disk microelectrodes with the sensing diameter of 3 mm were fabricated by the MEMS technique on a glass wafer. The novel Gr/metry in . The rep


CuNi alloy foils are demonstrated to be one of the best substrates for synthesizing large area single‐crystalline graphene because a very fast growth rate and low nucleation density can be simultaneously achieved. The fast growth rate is understood to be due the abundance of carbon precursor supply, as a result of the high catalytic activity of Ni atoms. However, a theoretical understanding of the low nucleation density remains controversial because it is known that a high carbon precursor concentration on the surface normally leads to a high nucleation density. Here, the graphene nucleation on the CuNi alloy surfaces is systematically explored and it is revealed that: i) carbon atom dissolution into the CuNi alloy passivates the alloy surface, thereby drastically increasing the graphene nucleation barrier; ii) carbon atom diffusion on the CuNi alloy surface is greatly suppressed by the inhomogeneous atomic structure of the surface; and iii) a prominent increase in the rate of carbon diffusion into the bulk occurs when the Ni composition is higher than the percolation threshold. This study reveals the key mechanism for graphene nucleation on CuNi alloy surfaces and provides a guideline for the catalyst design for the synthesis of graphene and other 2D materials. It was observed that the nucleation density of graphene decreases monotonically when the Ni composition in the CuNi alloy increases from 0% to 30%. The decreased nucleation density of graphene on CuNi alloy is attributed to two factors: (i) the passivation of the CuNi alloy surface by both nickel and carbon atoms leads to an increased nucleation barrier; and (ii) the Ni content in the alloy increases the barrier for surface diffusion and changes the diffusion behavior of carbon atoms from surface diffusion to the bulk diffusion when the content of Ni in the alloy is higher than the percolation threshold, 19.9%. In addition, the secondary ion mass spectrometry (SIMS) measurements clearly show that more C atoms can be found in the deep bulk of the CuNi alloy when the Ni content of the alloy is increased, supporting our theoretical prediction.Figure85Ni15 alloy surface has the largest grain size, demonstrating the highest growth rate of graphene on Cu85Ni15. For alloys with a Ni composition less than 15%, the growth rate of graphene increases with the Ni composition. However, for alloys with Ni content larger than 15%, an increase in the Ni composition leads to reduced grain sizes or slower growth rates. Figure 95Ni5, Cu90Ni10, Cu85Ni15, and Cu75Ni25 after 10 min of growth at a temperature of 1050 °C. It can be clearly seen that graphene domains grown on Cu85Ni15 have larger sizes than those grown on Cu95Ni5 or Cu90Ni10, while a further increase of Ni content to 25% (Cu75Ni25) leads to smaller graphene grains. The fast growth of graphene on Cu85Ni15 can be attributed to the efficient decomposition of CH4 on the surface and the extra carbon supply dissolved near the substrate surface, while the slower growth rate at larger Ni content was attributed to the loss of the carbon precursors from the surface through carbon bulk diffusion along the very long Ni chains inside the alloy when the Ni content exceeds the percolation threshold, 19.9%.The grain size and nucleation density of graphene on different CuNi alloy surfaces are shown in 4 flow can also affect the nucleation density of graphene, but the effect is much smaller compared with the composition of CuNi alloy . Moreover, the decrease of graphene nucleation density on CuNi alloy with the increase of Ni composition is not dependent on the carbon flow.In sharp contrast to the growth rate, the nucleation density of graphene keeps decreasing as the Ni composition increases from 0% to 30%  is the energy of a metal substrate with an adsorbed C atom on its surface, E(M) is the energy of the metal substrate, and EG is the energy of a C atom in graphene.The nucleation of graphene starts from the self‐assembly of the carbon precursors  on a substrate surface. To understand the nucleation process, we first calculated the formation energy of a single C atom on CuNi alloy surfaces. The formation energy of a C atom on an alloy surface is defined asFigureThe theoretical calculations above demonstrate that the formation of a graphene sheet on the CuNi alloy surface becomes less favorable at a low carbon concentration when the Ni composition is at some point between 25% and 50%. This is consistent with our experimental observation that no nucleation of graphene was found on the CuNi alloy with Ni content larger than 30%.ω* is the attachment rate of C atoms into a cluster of critical size, Γ = [G*/(3πkTN*2)]1/2 is the Zeldovich factor, N1 is the concentration of C atoms, k is the Boltzmann constant, T is the temperature, and G* is the nucleation energy.ω* = N*edgep(νexp(−Eb/kT)), where N*edge is the number of attachment sites of the 2D nucleus. For a sp2 network structure, N*edge ∼ (6 × N*)1/2, and ν = 1013 s−1. Eb is the barrier for attaching a C atom to the graphene, which can be estimated as the diffusion barrier of a C atom on the alloy surface as the graphene edge on the metal substrate is very active. Thus, we can rewrite Equation According to classical 2D nucleation theory, the nucleation rate of graphene can be written asN1), the diffusion barrier Eb, as well as the nucleation barrier G*.Therefore, under a fixed growth temperature, the nucleation rate is mainly determined by C atom concentration (E(NC) is the formation energy of the carbon cluster on the substrate from a C atom in graphene, Δµ is the chemical potential difference of a carbon atom in the feedstock and in the graphene, and N is the number of carbon atoms in the cluster. To form a graphene nucleus, the carbon clusters need to be greater than the nucleation size, N*, and their formation energy needs to overcome the nucleation barrier, G*. Based on the crystal nucleation theory, the nucleation barrier and nucleation size of the graphene nucleus can be viewed as the maximum point  of the curve of Gibbs free energy (G) versus cluster size (N).[[qv: 9a]]As the graphene nucleation starts from the formation of a carbon cluster, calculating the Gibbs free energy of formation of the carbon cluster is essential to obtain the nucleation barrier of graphene. The Gibbs free energy of formation of the carbon cluster on a metal substrate can be obtained by using the following equation[[qv: 9b]]E(CN), of the graphene nucleus under a fixed chemical potential difference Δµ can be obtained by[[qv: 9b]]E0 is a term of constant for a specified metal, it can be regarded as the energy difference between sp2 hybridized C in a perfect graphene and in the carbon cluster; Eedge is the formation energy of each edge atom, and √(6N) represents the number of edge atoms.The formation energy, E(CN) in Equation By replacing N*, and the nucleation barrier, G*, can be obtained by assuming dG/dN = 0, and thusThe nucleation size, G*, on the metal surface is determined by Eedge under a fixed chemical potential Δµ. According to Equation Eedge can be obtained by calculating the formation energy of a carbon cluster. Based on this argument, the nucleation of graphene on different CuNi alloy surface can be compared by calculating the formation energy of a carbon cluster.Therefore, the nucleation barrier, 24, is selected. The formation energy of C24 on a transition metal surface can be calculated by using a similar definition to that of the single atom given by Equation E(C24@M) is the energy of a C24 cluster on a metal substrate.In this study, a typical carbon cluster, C24 cluster on the four pure alloy surfaces  surface is 13.16 eV, and it decreases to 12.81 eV when the Ni composition of CuNi alloy is 11%. Then, formation energy is further decreased to 11.39 eV when the Ni content is increased to 25%, as shown by the black line in Figure 24. Such an increased reactivity of the alloy surface caused by Ni doping has also been reported in previous studies.Constrained by the size of the theoretical model, only Cu100) and three CuNi(100) surfaces with Ni composition of 11%, 16%, and 25% are considered in our calculation. We first studied the formation of a Ces Figure3a. The0 and thr24 on CuNi alloy surfaces by taking the effect of dissolved carbon atoms into account. In our calculations, the effect of carbon solubility in CuNi alloy is simulated by adding some additional carbon atoms in the most energetically stable adsorption sites on the alloy surfaces. As shown in Figure 24 on the CuNi/C surface were found to be greatly increased  surface (13.16 eV).However, it should be noted that a higher Ni content in the CuNi alloy normally leads to a faster dissolution of carbon atoms and a higher binding energy of the dissociated carbon atoms. Although the dissolution of carbon atoms in Cu is negligible, their solubility in Ni is much higher.d Figure c. For ex24 increases from 13.16 to 15.26 eV, demonstrating that the doping of Ni content into the Cu bulk could passivate the Cu(100) surface. Another contribution to the surface passivation stems from the dissolved carbon atoms, for example, the formation energy of C24 on the (100) surface of Ni2C is 6.31 eV higher than that on the Ni(100) surface. This means carbon dissolution can considerably passivate the Ni atoms.The increase of the formation energy can be understood by considering the passivation of the CuNi alloy surface atoms from both the Ni atoms and the dissolved carbon atoms. As shown in Figure S2 (Supporting Information), by replacing the sublayer Cu atoms with Ni atoms, the formation energy of C24 on the CuNi/C surfaces show a tendency to first rise and then decrease, and thus have a peak at a Ni composition of ≈15%. This demonstrates that the passivation of the CuNi alloy surface has a maximum at a Ni composition of ≈15%, further increase of Ni content makes the alloy surface less passivated.The calculations clearly demonstrate that carbon dissolution into the CuNi alloy can effectively passivate the alloy surface, leading to greatly increased graphene nucleation barriers. It is interesting that the formation energies of C75Ni25 is lower than that on the Cu85Ni15 surface because the former has a lower nucleation barrier than the latter one.Above calculation explains very well the decreased nucleation density of graphene on CuNi alloys with Ni composition varying from 0% to 15% because a high nucleation barrier always contributes to a low nucleation density. However, it cannot explain why the nucleation density on Cu87.5Ni12.5 and Cu75Ni25 to represent typical alloys without and with a very long chain of adjacent Ni atoms penetrating into the bulk, respectively. As the percolation threshold of a face centered cubic (fcc) material is ≈19.9%,87.5Ni12.5, and alloys with Ni composition larger than 19.9% can be represented by that of Cu75Ni25.According to Equation 87.5Ni12.5 is shown by the blue line in Figure87.5Ni12.5, the calculated highest diffusion barrier is 2.83 eV , while the bulk diffusion has a barrier of 1.43 eV only. This demonstrates that the decomposed carbon atoms on the alloy surface can relatively quickly diffuse into the bulk of the alloy, which will greatly reduce the concentration of the carbon precursor on the surface. Therefore, although the higher Ni composition leads to a relatively fast feedstock decomposition and thus high C concentration,Although the surface diffusion is very similar, the carbon diffusion into CuFigure19–1023 atoms cm−3 near the surface of the alloy and this rises sharply with an increase in the relative Ni content. The C atom concentration drops greatly in the bulk of the alloy, indicating that the system is far from thermal equilibrium and the carbon atom concentration inside the bulk was not saturated when the experiments were carried out. In Cu95Ni5, the C concentration is as low as 1019 atoms cm−3. Considering that there are ≈1023 atoms cm−3 in the material, the proportion of the dissolved C in the bulk of Cu95Ni5 is as low as 10−4. This demonstrates that relatively few C atoms have diffused from the surface to the bulk. However, the dissolved C in the bulk of Cu75Ni25 alloy is ≈10 times higher, demonstrating the faster diffusion of C atoms from the surface to the bulk in this case. The SIMS images of depth profile clearly show that the C dissolution in the Cu75Ni25 alloy is much higher (with more bright points) than those in other alloys.The time of flight (TOF)‐SIMS depth profile analysis is performed to study the C dissolution in CuNi alloys under the same condition of graphene growth procedure. As shown in 75Ni25 surface could be lower than that on the Cu85Ni15. Although graphene on Cu75Ni25 has lower nucleation barrier and the feedstock can be dissociated faster, the number of C atoms involved in the graphene nucleation is less than that on the Cu85Ni15 surface because some of the dissociated C atoms diffuse quickly into the bulk. This greatly decreases the graphene nucleation rate and thus leads to a lower nucleation density at high Ni content.Combined the theoretical calculations with the experimental observations, we conclude that the surface diffusion of C atoms dominates for the CuNi alloy with low Ni composition (Ni% < 19.9%) while bulk diffusion of C atoms becomes dominant when the Ni composition of the alloy is higher than the percolation threshold, (Ni% > 19.9%). Based on this argument, we can explain why the nucleation density of graphene on CuIn summary, against our intuition, we have found that the nucleation density of graphene on CuNi alloy surface always decreases with an increase in the Ni content, although systems with a high Ni content have a fast carbon feedstock decomposition. Such a “contradictory” phenomenon has been explained by our theoretical calculations. For CuNi alloy with low Ni composition (<19.9%), the decreased nucleation density can be attributed to the greatly increased nucleation barrier caused by carbon and Ni passivation to the Cu surface, together with the increased diffusion barrier of carbon atoms on the alloy surface. For CuNi alloy with high Ni composition (>19.9%), in addition to the two factors mentioned above, the fast diffusion of surface C atoms into the bulk through the continuous Ni chains in the alloy results in a rapid loss of the surface atoms and which greatly decreases the nucleation density.Experimental Details—Preparation of CuNi Binary Substrate: A 6 cm × 6 cm Cu foil  was first electrochemically polished with a current density of ≈0.3 A cm−2 for 90 s, then annealed at 1050 °C in a mixture of Ar/H2 (400/100 sccm) for 2 h followed by electroplated with a current density of ≈0.01 A cm−2. A Ni film with a certain thickness was deposited on the Cu foil at a rate of 200 nm min−1. The polishing solution was a mixture of 500 mL of water, 250 mL of ethanol, 250 mL of orthophosphoric acid, 50 mL of isopropyl alcohol, and 5 g of urea. The electrolytic solution consisted of 1 L of water, 280 g of NiSO4⋅6H2O, 8 g of NiCl2⋅6H2O, 4 g of NaF, and 30 g of H3BO3.Experimental Details—Characterization of CuNi Surface: X‐ray diffraction (XRD) and electron backscattered diffraction (EBSD) are employed to analyze the crystallinity and surface morphology of metal substrate. The XRD spectra shows that grains in the CuNi foil have a wide range of crystallographic orientations before annealing but a strong (100) texture is developed after high temperature annealing . It could also be observed that Cu and Ni were completely interdiffused to each other to form a uniform CuNi alloy. However, the density of the grain boundaries did not increase obviously with the increasing Ni content. The EBSD image showed that the average grain size on Cu95Ni5, Cu85Ni15 and Cu75Ni25 surfaces was ≈200–500 µm . Longer pregrowth annealing under Ar/H2 flow could help in the production of CuNi (100) facets while mitigating surface roughness and grain boundary (GB) migration. The uniform orientation of CuNi alloy after polishing and annealing is helpful to improve the nucleation density and quality of single crystalline graphene.Experimental Details—Graphene Growth: CuNi alloy foils containing 5–15 at% Ni  were used as substrates. Prior to growth, the CuNi foils were cleaned by hydrochloric acid, acetone, isopropanol, and deionized water to remove the surface oxide and organic impurity. The CuNi substrate was then loaded into a quartz tube with a diameter of 50 mm. The substrates were annealed at 1050 °C 2 h in a H2 and Ar flow (H2/Ar = 50/1000 sccm) at atmosphere pressure to further increase its surface flatness and grain size. Then, 80–120 sccm methane (0.5% CH4 diluted in Ar), 15 sccm H2, and 300 sccm Ar were fed into the CVD system. Millimeter‐sized graphene domains could be obtained even after exposure to methane for only about ≈5–10 min. After that, the substrates cooled down to room temperature in a mixed Ar/H2 flow.Experimental Details—SIMS Measurements: SIMS can provide detailed chemical information of the surface and subsurface of a material with high‐accuracy depth profiling. In this study, TOF‐SIMS (ION‐TOF GmbH TOF.SIMS5) depth profile analysis was performed to further test the component of alloys and the carbon dissolution in CuNi alloys. It could be observed that Cu and Ni were completely interdiffused to each other to form CuNi alloy foils with the atomic proportions determined by the amount of the deposited Ni film at high temperature annealing. The SIMS measurement provided more decisive information to understand the local nucleation feature and growth conditions on CuNi alloy. Surface enrichment of carbon was detected on the CuNi alloy after the substrate was exposed to methane for few minutes. The surface concentration of carbon reached 1 × 1022–1 × 1023 atoms cm−3 and raised with the increasing of the proportion of Ni content  slab and a vacuum layer of 15 Å were used along the z direction . Also, a four‐layer Ni (or Cu) slab with the same vacuum was used to calculate the formation energy of C24 on the substrate.2 of the PBE functional.k‐points selected. A plane‐wave basis kinetic energy cut‐off of 400 eV was used in all the calculations.Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package,The authors declare no conflict of interest.SupplementaryClick here for additional data file.


Here, we report on the observation and manipulation of individual magnetic moments in graphene open-shell nanostructures on a gold surface. Using scanning tunneling spectroscopy, we detect the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect. We find near-by spins coupled into a singlet ground state and quantify their exchange interaction via singlet-triplet inelastic electron excitations. Theoretical simulations picture how electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Extra hydrogen atoms bound to radical sites quench their magnetic moment and switch the spin of the nanostructure in half-integer amounts. Our work demonstrates the intrinsic π-paramagnetism of graphene nanostructures.Turning graphene magnetic is a promising challenge to make it an active material for spintronics. Predictions state that graphene structures with specific shapes can spontaneously develop magnetism driven by Coulomb repulsion of  π-magnetism in graphene systems has been predicted but remains an experimental challenge. Here the authors report the discovery of unpaired electron spins localized in certain sites of graphene nanoribbons, and the measurement of their coupling by inducing singlet-triplet excitations with a scanning tunneling microscope. Generally, magnetism is associated to a large degree of electron localization and strong spin–orbit interaction. Both premises are absent in graphene, a strongly diamagnetic material. The simplest method to induce magnetism in graphene is to create an imbalance in the number of carbon atoms in each of the two sublattices, what, according to the Lieb’s theorem for bipartite lattices2, causes a spin imbalance in the system. This can be done by either inserting defects that remove a single pz orbital6 or by shaping graphene with zigzag (ZZ) edges8. However, magnetism can also emerge in graphene nanostructures where Lieb’s theorem does not apply10. For example, in π-conjugated systems with small band gaps, Coulomb repulsion between valence electrons forces the electronic system to reorganize into open-shell configurations11 with unpaired electrons  localized at different atomic sites. Although the net magnetization of the nanostructures may be zero, each radical state hosts a magnetic moment of size μB, the Bohr magneton, turning the graphene nanostructure paramagnetic. This basic principle predicts, for example, the emergence of edge magnetization originating from zero-energy modes in sufficiently wide ZZ14 and chiral16 graphene nanoribbons (chGNRs).Among the many applications predicted for graphene, its use as a source of magnetism is the most unexpected one, and an attractive challenge for its active role in spintronic devices19 hide the weak paramagnetism of radical sites20. Scanning probe microscopies can spatially localize the source states of magnetism19, but they require both atomic-scale resolution and spin-sensitive measurements. Here we achieve these conditions to demonstrate that atomically defined graphene nanostructures can host localized spins at specific sites and give rise to the Kondo effect22, a many-body phenomenon caused by the interaction between a localized spin and free conduction electrons in its proximity. Using a low-temperature scanning tunneling microscope (STM) we use this signal to map the spin localization within the nanostructure and to detect spin–spin interactions.The experimental observation of spontaneous magnetization driven by electron correlations is still challenging, because, for example, atomic defects and metal impurities in the graphene structures23. We deposited the organic molecular precursors 2,2′-dibromo-9,9′-bianthracene  surface by cross-dehydrogenative coupling of adjacent chiral GNRs (chGNRs)ene Fig.  on a cleene Fig.  to produ11 surfacIn Fig. I/dV) on the three types of junctions. Spectra on the bright sites of Type 1 and 2 junctions show very pronounced zero-bias peaks 34. The more pronounced signal for either particle tunneling (over ZZ) or for hole tunneling (over PC) indicates the spins system lies out of particle-hole symmetry point, with EF closer to the corresponding singly unoccupied or singly occupied (SO) state, respectively. Hence, the gap between dI/dV peaks in Fig. Junctions with two bright regions (Type 3) show different low-energy features: two peaked steps in dmeV Fig. . The ste31, one obtains the exchange coupling J = 2.7 (9.9) meV for the upper (lower) spectrum.Interestingly, the spectral gap in Type 3 junctions increases with the length of the connecting ribbons. In Fig. I/dV signal measured in Type 3 junctions. This supports that this signal is an intrinsic effect of junction edge sites, rather than caused by defects or other atomic species.To explain the emergence of localized spins, we simulated the spin-polarized electronic structure of chGNR junctions using both density functional theory (DFT) and mean-field Hubbard (MFH) models (see Supplementary Notes π-electrons as described within a tight-binding (TB) model  and lowest unoccupied (LU) molecular states of the nanostructure. Due to the large degree of localization , and exchange coupled as schematically illustrated in Fig. π-sextet rule to the close-shell structure of Fig. The origin of the spontaneous magnetization can be rationalized by considering the effect of Coulomb correlations between del Fig. . The spidel Fig. . These aI/dV spectra found over Type 3 junctions  substrate has the general trend of hole-doping GNRs43, which in some systems caused depopulation of the mid-gap states37. The band structure of the  chGNR and, in particular, the proximity of the VB to EF, is a crucial aspect to stabilize the electron population of the GNR junction on the surface and hence, for the survival of their magnetic ground state.Open shell configurations of extended + ion sputtering and subsequent annealing to 730 K. The molecular precursor  was sublimated at 170 °C from a Knudsen cell onto the clean Au(111) substrate kept at room temperature. Then the sample was first annealed at 200 °C for 15 min in order to induce the polymerization of the molecular precursors by Ullmann coupling, then the sample was annealed at 250 °C for 5 min to trigger the cyclodehydrogenation to form chiral graphene nanoribbons (chGNRs). A last step annealing at 350 °C for 1 min created nanostructure junctions. A tungsten tip functionalized with a CO molecule was used for high-resolution images. All the images in the manuscript were acquired in constant height mode, at very small voltages, and junction resistances of typically 20 MΩ. The dI/dV signal was recorded using a lock-in amplifier with a bias modulation of Vrms = 0.1 mV  operated at 1.2 K with a magnetic field up to 3 T was used to measure the temperature and magnetic field dependence of the Kondo resonance, while other experiments were done with a home made STM operating at 5 K. Both setups allow in situ sample preparation and transfer into the STM. The Au(111) substrate was cleaned in UHV by repeated cycles of Ne mV Fig.  and Vrms44 of DFT. Exchange and correlation (XC) were included within either the local (spin) density approximation (LDA)45 or the generalized gradient approximation (GGA)46. We used a 400 Ry cutoff for the real-space grid integrations and a double-zeta plus polarization (DZP) basis set generated with an 0.02 Ry energy shift for the cutoff radii. The molecules, represented with periodic unit cells, were separated by a vacuum of at least 10 Å in any direction. The electronic density was converged to a stringent criterion of 105. The force tolerance was set to 0.002 eV/Å. To complement the DFT simulations described above we also performed simulations based on the MFH model, known to provide a good description for carbon π-electron systems48.We performed calculations with the SIESTA implementationSupplementary InformationPeer Review File


These findings show that atomic-scale control of hydrogen adsorption on graphene can give rise to a robust magnetic order.The origin of the ferromagnetism in metal-free graphitic materials has been a decade-old puzzle. The possibility of long-range magnetic order in graphene has been recently questioned by the experimental findings that point defects in graphene, such as fluorine adatoms and vacancies, lead to defect-induced paramagnetism but no magnetic ordering down to 2 K. It remains controversial whether collective magnetic order in graphene can emerge from point defects at finite temperatures. This work provides a new framework for understanding the ferromagnetism in hydrogenated graphene, highlighting the key contribution of the spin-polarized pseudospin as a “mediator” of long-range magnetic interactions in graphene. Using first-principles calculations of hydrogenated graphene, we found that the unique ‘zero-energy’ position of H-induced quasilocalized states enables notable spin polarization of the graphene’s sublattice pseudospin. The pseudospin-mediated magnetic interactions between the H-induced magnetic moments stabilize the two-dimensional ferromagnetic ordering with Curie temperatures of T Several experiments showed that the ferromagnetic order in graphitic materials originates from the carbon π-electron systems rather than from magnetic impurities15. Further studies have shown that point defects in graphitic materials contribute to carbon-based ferromagnetism21. Recently, proximity-induced ferromagnetism25 was also demonstrated for a single-layer graphene placed on an insulating magnetic substrate. Despite decades of research on carbon-based magnetism, it remains unclear under what conditions long-range magnetic order can emerge from point defects in graphitic materials. Contrary to the previous notion that graphene ferromagnetism arises from defect-induced magnetic moments21, Nair et al.5 recently demonstrated that point defects in graphene, such as fluorine adatoms and vacancies, lead to notable paramagnetism but no magnetic ordering down to liquid helium temperatures. The maximum response of the induced paramagnetism was limited to one moment per approximately 1,000 carbon atoms. The lack of collective magnetic order in graphene was attributed to the absence of long-range magnetic interactions between the well-separated magnetic moments5, with the implication that previously reported room-temperature ferromagnetism in graphitic materials27 might originate from undetected magnetic impurities or particles.The two-dimensional (2D) magnetism in graphene has attracted considerable attention because of its exceptional promise in graphene-based spintronics11 have provided direct evidence that individual hydrogen atoms adsorbed on graphene induce magnetic moments, creating opportunities for atomic-scale control of graphene ferromagnetism12. As in the graphene systems with fluorine adatoms or carbon vacancies5, however, the magnetic response in hydrogenated graphene is limited because the phase separation into pure graphene and fully hydrogenated graphene  parts is thermodynamically more stable28. The ferromagnetism at reasonably high temperatures in such a magnetically dilute system thus requires long-range magnetic interactions between the H-induced magnetic moments, as well as controlled hydrogenation of graphene under non-equilibrium conditions.Recent scanning tunneling microscope experimentsσ-bond formation effectively induces a “vacancy” in the π-electron system31, creating a quasilocalized state occupied by an electron33 and an associated magnetic moment  calculations, we show that hydrogenated graphene not only hosts H-induced localized spins but also responds to them by forming spin-polarized pseudospin as a “mediator” of long-range magnetic interactions in graphene. In hydrogenated graphene, it is well-known that the C–H ent Fig. . The H-iDR, which arises from the overlap between the wavefunctions of “vacancies”, leads to ferromagnetic (FM) interaction between “vacancies” in the same sublattices18. Because of the slow decay of the wavefunctions, the interaction range is relatively large  In addition to the “conventional” magnetic interactions based on the wavefunction overlap, we show that “unconventional” long-range interactions exist that involve a delocalized “mediator” between the localized spins  interaction is FM for a pair of “vacancies” in the same sublattice Figure rge Fig. . For tworge Fig. , the eleTo distinguish the long-range “mediated” magnetic interaction from the direct exchange interaction, we performed DFT calculations of hydrogenated graphene using judiciously chosen H-adatom positions  in the first term denotes the H pairs of a given type, and i on the A sublattice can take either 1 (spin up) or –1 (down). The spin-polarized DFT calculations were performed in the Sz = S subspace; thus, m(1)} and {m(2)}, for which some of the FM-coupled  pairs in {m(1)} were changed to the AFM-coupled  pairs in {m(2)} (Supplementary Table Nflip), the energy difference is given by where the symbol , with an energy gain proportional to Figure A and HB in graphene. The spin ground state has 18, where |HA| and |HB| are the number of H adatoms at the graphene’s A and B sublattices. Assuming an antiparallel net magnetization on opposite sublattices at finite temperatures, the low-energy graphene state for the occupied electrons is characterized by the spin-up t* = 3.3 eV in the DFT calculations 〉 and 〈mB(T)〉, at temperature T are calculated self-consistently (Methods). We define two characteristic temperatures, B is the Boltzmann constant, and nH is the atom percentage of H adatoms. Figure F for the different probabilities, PA and PB, of having HA and HB on the graphene layer. The magnetization per H adatom is 35. A slight imbalance with PA = 0.51 and PB = 0.49, for example, induces m = 0.02 μB/atom, which corresponds to the magnetization per weight of 0.1 Am2/kg at nH = 1 at. % β has the critical exponent β = 0.5, regardless of PA and PB , the Tc is determined by competition between the FM and AFM interactions38, i.e., A through the direct exchange interaction, and the same SPPS simultaneously stabilizes the spin-down HB through the superexchange interaction. The FM and AFM interactions thus “cooperate”, rather than compete, in hydrogenated graphene.We note that the AFM interaction contributes to  compete ; the spiH ~ 1 at. %. The “cooperativeness” of the FM and AFM interactions contributes to the high Tc. The realization of the robust 2D ferromagnetism in such a magnetically and electrically dilute system is unusual; the 2D magnetism in hydrogenated graphene is described by mean-field theory owing to the intrinsic long-range nature of the SPPS-mediated interactions. Our new finding of the mechanism underlying graphene ferromagnetism should have enormous implications for understanding and atomic-scale control of graphene-based magnetism, which is an important step toward bringing the vision described in “Painting magnetism on a canvas of graphene (ref.12)” closer to reality.In summary, we have shown that the SPPS-mediated, long-range magnetic interactions give rise to a robust magnetic order in hydrogenated graphene, which can be stable even at room temperature for the H concentration of n39) to DFT, as implemented in the Vienna ab-initio Simulation Package40. The DFT calculations employed the projector augmented wave method42 with an energy cutoff of 500 eV for the plane-wave part of the wave function. For the Brillouin zone integration, we used a Γ-centred grid containing enough k points, as dense as the 60 × 60 grid for the two-atom unitcell of graphene.We calculated total energies and spin densities of partially hydrogenated graphene using the generalized gradient approximation  or the number of the C atoms in a supercell with |Λ| = 96, 150, 216, 300, 384, 432, and 864 } =  and {m(2)} = , were considered. Then, from Eq. To extract the interaction strength of the long-range AFM interaction B is the Boltzmann constant, and nH is the H concentration, A = PB, A ≠ PB, it gradually increases in magnitude with increasing T. From the condition of no net magnetization on each sublattice at Tc, we obtained We used a mean-field approximation with Supplementary Information