Determining the Proximity Effect Induced Magnetic Moment in Graphene by Polarised Neutron Reflectivity and X-ray Magnetic Circular Dichroism
R. O. M. Aboljadayel, D. M. Love, C. A. F. Vaz, R. S. Weatherup, P. Braeuninger-Weimer, M.-B. Martin, A. Cabrero-Vilatela, A. Ionescu, C. J. Kinane, T. R. Charlton, J. Llandro, P. M. S. Monteiro, C. H. W. Barnes, S. Hofmann, S. Langridge
DDetermining the Proximity Effect Induced Magnetic Moment inGraphene by Polarised Neutron Reflectivity and X-ray MagneticCircular Dichroism
R. O. M. Aboljadayel, ∗ D. M. Love, C. A. F. Vaz, R. S. Weatherup, P. Braeuninger-Weimer, M.-B. Martin, A. Cabrero-Vilatela, A.Ionescu, † C. J. Kinane, T. R. Charlton, J. Llandro, P. M. S.Monteiro, C. H. W. Barnes, S. Hofmann, and S. Langridge Cavendish Laboratory, Physics Department,University of Cambridge, Cambridge CB3 0HE, United Kingdom. Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland Department of Engineering, University of Cambridge,Cambridge CB3 0FA, United Kingdom. ISIS Facility, STFC Rutherford Appleton Laboratory,Harwell Science and Innovation Campus,Oxon, OX11 0QX, United Kingdom. (Dated: January 26, 2021)
Abstract
We report the magnitude of the induced magnetic moment in CVD-grown epitaxial and rotated-domain graphene as a result of the proximity effect in the vicinity of the ferromagnetic substratesCo and Ni, using polarised neutron reflectivity (PNR). Although rotated-domain graphene is knownto interact weakly with the ferromagnetic underlayer in comparison with the epitaxial graphene,the PNR results indicate an induced magnetic moment of ∼ µ B /C atom at 10 K for bothstructures. The origin of the induced magnetic moment is found to be due to the opening of thegraphene’s Dirac cone as a result of the strong C p z -3 d hybridisation, which was confirmed byadditional PNR measurements using a non-magnetic Ni Mo and Cu substrates. We validated ourPNR fitting models using the Bayesian uncertainty analysis and corroborated the results by X-raymagnetic circular dichroism measurements. ∗ [email protected] † [email protected] a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n . INTRODUCTION Graphene is a promising material for many technological and future spintronic deviceapplications such as spin-filters [1, 2], spin-valves and spin field-effect transistors due to itsexcellent transport properties [3, 4]. A single layer graphene can have an intrinsic chargecarrier mobility of more than 200,000 cm /Vs at room temperature (RT) [5], and a large spinrelaxation time as a result of its long electron mean free path and its negligible spin-orbitand hyperfine couplings [2, 6].Manipulating spins directly in the graphene layer has attracted great attention as it opensnew ways for using this 2D material in spintronics applications [2, 7]. This has been realisedvia various approaches such as through the proximity-induced effect [2, 8–11], chemicaldoping of the graphene surface [6] or through a chemically-induced sublattice [12]. Here, wereport the feasibility of the first method in utilising the exchange coupling of local momentsbetween graphene and a ferromagnetic (FM) material to induce a magnetic moment ingraphene.Graphene is a zero-gap semiconductor because the π and π ∗ bands meet at the Fermienergy ( E F ), at the corner of the graphene’s Brillouin zone ( K points), i.e. at degeneratepoints forming the Dirac point ( E D ), where the electronic structure of these bands can bedescribed using the tight-binding model [13, 14]. However, the adsorption of graphene on astrongly interacting metal distorts its intrinsic band structure around E D . This is a resultof the overlap of the graphene’s valence band with that of the metal substrate due to thebreak of degeneracy around E D in a partially-filled d -metal [2, 13, 15–17]. Thus, in theproximity of a FM-TM an induced magnetic moment in graphene is expected, as discussedin the universal model proposed by Voloshina and Dedkov [18].It is widely accepted that graphene’s C atoms are assembled in what is known as thetop- fcc configuration on top of close-packed (111) films, where the C atoms are placed ontop of the atoms in the first and third layers of the TM substrate [15, 16, 18]. The strengthof the graphene-TM interaction is influenced by the lattice mismatch, the graphene-TMbond length and the position of the d orbital of the TM relative to E F . Therefore, Ni(111)and Co(111) substrates were used since they have a small lattice mismatch of -1.2% forNi(111) and -1.6% for Co(111), a bond length of 2 . − .
16 ˚A and their d orbitals arepositioned ∼ . − . E F (i.e. forming π - d hybrid states around the K points)216–20]. Epitaxial and rotated-domain graphene structures were investigated since rotatedgraphene is expected to interact more weakly with the TM film underneath due to the lossof epitaxial relationship and a lower charge transfer from the TM due to missing directNi top -C interaction [21]. Therefore, a smaller magnetic moment is expected to be inducedin rotated-domain graphene.We have studied the structural, magnetic and electronic properties of epitaxial- androtated-domain graphene grown on Ni and Co films, confirmed the presence of magneticmoment in graphene by element-specific XMCD and measured the induced magnetic momentof ∼ µ B /C at 10 K for both samples using PNR. We then validated the PNR fittingmodels and studied the correlation between the fitted parameters using Bayesian uncertaintyanalysis.This paper is organised as follows: We first give a description of the sample prepara-tion and their properties in Section II and Section III, and the X-ray magnetic dichroism(XMCD) results are discussed in Section IV. In Section V, we present the polarised neutronreflectivity (PNR) measurements and the Bayesian uncertainty analysis. The additionalPNR experiments on graphene/Ni Mo and graphene/Cu are discussed in Section VI. Wealso compare our results with those reported in the literature for graphene on Ni and forother carbon-based films on transition-metal (TM) substrates [8, 22, 23].Although graphene/FM interfaces have been previously investigated using XMCD, nodirect quantitative analysis of the induced magnetic moment in graphene was carried out[2, 8]. Therefore, to our knowledge, our attempt is the first reported approach in using PNRand XMCD sum rules to estimate the induced magnetic moment in graphene. This is dueto the thinness of graphene which is close to the resolution of the PNR technique, and thedifficulty in processing the XMCD C K -edge signal due to the contribution of the carboncontamination in the beamline optics. We also prove that the measured induced magneticmoment in graphene is due to the hybridisation of the C p z orbital with the 3 d bands ofthe TM by carrying out additional PNR measurements on non-magnetic Ni Mo (111) andpolycrystalline Cu substrates. 3 I. SAMPLE PREPARATION
The sample preparation procedure involved two stages; the growth of the TM films usingmagnetron sputtering and the growth of graphene by chemical vapour deposition (CVD).
A. Growth of the transition metal films
The TM films were deposited at RT on 1 mm thick Al O (0001) substrates using a CEVPmagnetron sputtering chamber with a base pressure of 1.2 - 2 × − mTorr. The thicksubstrates were used to reduce the possibility of sample deformation which could affect thereflectivity measurements. The deposition of the TM films was performed using 99.9% pureNi and Co targets. A DC current of 0.1 A and a constant flow of pure Argon of 14 sccmwere used to grow 80 nm of highly textured Ni(111) and Co(111) films at a rate of 0.02nm/s in a plasma pressure of 2 mTorr. B. Growth of graphene by CVD
The samples were then transferred into a CVD system for the growth of graphene directlyon Ni(111) and Co(111) films on ∼ × et al . [21] were adapted to obtain epitaxial and rotated-domaingraphene directly on the Ni film. For the Co film, rotated-domain graphene was grown byfirst introducing H gas at a rate of 180 sccm to the CVD chamber with a base pressure of2.7 × − mbar. Then, the CVD growth chamber was heated to 630 ◦ C for 12 minutes andthe sample was then exposed to C H with a flow rate of 0.63 sccm for 60 minutes before itwas cooled down to RT in vacuum. This approach reduces any oxidised TM back to cleanNi or Co film before the growth of graphene.The SEM images shown in Figure 1 illustrate the structure of epitaxial and rotatedgraphene on Ni and Co with a surface coverage of ∼ − ×
1) grown graphene structure4
IG. 1. SEM images at 1 kV showing the graphene domains for (a) epitaxial graphene/Ni and (b)rotated graphene/Ni and at 2 kV for (c) rotated graphene/Co. (d) The LEED diffraction patternof epitaxial graphene on a Ni(111) substrate at 300 eV. The red circle in (b) highlights a singlegraphene domain with a diameter of ∼ . µ m. is confirmed since no additional diffraction spots are observed in the LEED pattern. III. RAMAN MEASUREMENTS
The quality, number of graphene layers, the doping and defect density in the growngraphene samples were investigated using Raman spectroscopy with a 532 nm excitationlaser wavelength (50 × objective lens and ∼ µ m laser spot size). Graphene has two maincharacteristic peaks in the Raman spectra, a first-order Raman scattering (RS) G peak at ∼ − , corresponding to a single phonon excitation in the first Brillouin zone (BZ),located at the frequency of the in-plane longitudinal optical ( LO ) and transverse optical( T O ) phonon branches at the Γ point [24, 25]; and a second-order (double-resonance) RS2 D peak at ∼ − in which two phonons are excited in the scattering process. The5S for the 2 D line is known as an inter-valley process and is usually used as an indication ofa perfect crystalline honeycomb-like structure [25, 26]. On the other hand, the G peak is agraphite-like line which can be observed in different carbon-based materials [26]. Graphenealso possesses other second-order RS peaks such as D+D” located at ∼ − and 2 D’ at ∼ − and disorder-induced peaks such as D at ∼ − and D’ at ∼ − [25, 27].For the Raman measurements, the graphene was first transferred by a chemical etchingprocess from the metallic films onto a Si substrate with a 300 nm thermally oxidised SiO layer similar to that reported in Ref. [28]. This is because closely lattice-matched films leadto a loss in the resonance conditions for observing Raman spectra as a result of the strongchemical interaction between the graphene π orbital and the d -states of Co and Ni, whichalso alters the graphene’s p z orbitals. Furthermore, the increase in the C-C bond length tomatch the lattice of the FM leads to significant changes in the graphene’s phonon spectrum[16, 24]. For the transfer process, the samples were cleaved into ∼ × , diluted to 10% (for Ni) and 20% (for Co), was used as the chemical reagent toetch the metallic films slowly while preserving the graphene layer.Single-layer graphene is known to have three characteristic features; I D / I G ratio > D peak fitted with a single Lorentzian with a full-width at half-maximum (FWHM)less than 40 cm − [29]. Furthermore, I D / I G is usually used as an indicator of defectspresent in graphene, which increases with the increase of disorder in the graphene structure FIG. 2. Room temperature Raman spectroscopy measurements taken after transferring thegraphene from (a) the epitaxial Ni, (b) rotated Ni, and (c) rotated Co samples to a Si/SiO wafer, showing the graphene’s characteristic peaks. The dashed vertical lines separate the regionsof the different peaks. I D / I G ratio. Also, the D peakwas reported to change in shape, position and width by increasing the number of graphenelayers, while the G peak is downshifted with increasing the number of graphene layers,but upshifted with increasing the doping level [25]. Moreover, the width of the 2 D peakincreases with the number of graphene layers [27, 30–32]. Therefore, we assess the qualityof our transferred graphene based on these features.RT Raman scans were taken at three different regions of each sample where all spectrapossess the D , G , D’ , D + D” and 2 D peaks as shown in Figure 2. The variation in thespectra suggests spatial inhomogeneities in our samples. However, this could also be aresult of the chemical etching and transfer process. Although all the 2 D peaks shown inFigure 2 were fitted with single Lorentzians, they have relatively broad FWHM. The widewidth of the FWHM could be attributed to a high defect density, or to doping from theHNO used to etch the metallic films. The average FWHM of the 2 D peak of epitaxialgraphene transferred from the Ni film is 40.81 cm − . However, the high D’ peak shown inFigure 2 (a) indicates a highly defective graphene structure, which is also confirmed by thehigh I D / I G ratio (average of 1.49). Hence, it is difficult to estimate the number of graphenelayers based on the position of the G and 2 D peaks and I D / I G ratio. However, the SEM scanand LEED diffraction pattern in Figure 1 (a) and (d), respectively, show a single epitaxialgraphene layer grown on Ni(111). For the rotated domain graphene transferred from theNi(111) surface (Figure 2 (b)), the average FWHM of the 2 D peak (46.17 cm − ) and thehigh average I D / I G ratio (2.35) suggest the formation of massively defective or turbostratic(multilayer graphene with relative rotation between the layers) graphene as a result of theoccasional overlap of the graphene domains [29].The Raman spectra of the graphene deposited on Co are shown in Figure 2 (c). Theaverage FWHM of the 2 D peak for spectrum 1 and 2 is 40.11 cm − , whereas the FWHMfor spectrum 3 is 63.19 cm − which confirm the spatial inhomogeneity seen in the SEM scan(Figure 1 (c)). The average I D / I G ratio of 0.47 (i.e. < .
5) and the 2 D peaks with FWHM ∼
50 cm − suggest a few-layer graphene system [29]. However, the very low average I D / I G ratio (0.09) and the fact that only the blue spectrum (number 3) has a small D’ shouldersuggest that good-quality few-layer graphene with low defect density was grown on the Cofilm.Although a few-layer graphene system was grown on Co, we can infer that there are less7han five layers in total since it was reported that only the Raman spectrum of graphenewith up to five layers could be distinguished from that of graphite [32]. Furthermore, ourresults show a higher disorder level in the graphene transferred from the Ni films comparedto that transferred from Co which agree with Patera et al. , where many defects, associatedwith Ni, were found trapped in the graphene lattice [21]. A full list of the peak positionsand the 2 D average FWHM of all the measured samples is provided in the supplementalmaterials. IV. X-RAY MAGNETIC CIRCULAR DICHROISM (XMCD)
We carried out element selective XMCD measurements to detect and distinguish themagnetisation in the graphene from that of the FM layer. The XMCD experiments wereperformed at 300 K at the SIM-end station at PSI using total electron yield (TEY) detectionmode with 100% circularly polarised light. The rotated-domain graphene samples were setto an incident angle of 30 ◦ from the incoming X-ray beam. An electromagnet was fixed at40 ◦ to the incoming X-ray beam and a magnetic field of 0.11 T was applied for 30 seconds in-plane to the surface of the samples to align the film magnetisation along the beam direction.It was then reduced to 0.085 T during the X-ray absorption spectroscopy (XAS) and XMCDmeasurements. The intensity of the incident X-ray beam was measured with a clean, carbonfree, gold mesh placed just before the sample position. This is particularly important fornormalising the signal at the C K -edge due to the presence of carbon on the surface of theX-ray optical components. Here, µ XAS = 12 ( µ + + µ − ) , (1)and µ XMCD = µ + − µ − , (2)where µ + and µ − are the absorption coefficients parallel and antiparallel to the light prop-agation vector, respectively, normalised to a common value [33].According to the sum rules, XAS and XMCD spectra can be used to determine the 3 d orbital angular momentum < L z > and the spin angular momentum < S z > for the L -edge8sing the following expressions [34, 35]: < L z > = − n h · (cid:82) L + L ( µ + − µ − ) dE (cid:82) L + L ( µ + + µ − + µ XAS ) dE , (3) < S z > = − n h · (cid:82) L ( µ + − µ − ) dE − (cid:82) L ( µ + − µ − ) dE (cid:82) L + L ( µ + + µ − + µ XAS ) dE (cid:16) < T z > < S z > (cid:17) . (4)Here, n h = (10 − n d ) is the number of holes in the 3 d states, whereas n d is the electronoccupation number of the 3 d states. L + L represent the integration range over the L and L edges and < T z > , which is the expectation value of the magnetic dipole operator,is known to be very small in TMs and hence it was ignored [36].In (2), µ XMCD is corrected for the light degree of polarisation, P , and the light’s incidentangle, θ . Therefore, it was multiplied by a factor 1 P cos θ [37], where θ is measured withrespect to the sample’s surface, while µ XAS remains unchanged [38].By correcting µ XMCD for P and θ , and substituting (2) and (1) into (3) and (4) with A and B being the first and second integrals in the numerator, respectively, and 3 C as thedenominator, < L z > and < S z > can be re-written as [34]: < L z > = − n h P cos θ (cid:16) A + BC (cid:17) (5)and < S z > = − n h P cos θ (cid:16) A − B C (cid:17) . (6)The orbital magnetic moment, m o , is equal to < L z > , whereas the spin magnetic moment, m s , is given by m s = 2 < S z > [35]. Therefore, the total magnetic moment ( m total ) of thesample can be estimated as m total = m o + m s [35, 39, 40]:In contrast, since the XMCD at the K -edge measures the transitions from a non-spin-split s orbital to p orbital, only m o can be obtained [41]: m o = n h P cos θ (cid:82) K µ XMCD (cid:82) K µ XAS , (7)For the K -edge, n h becomes equal to 6 − n p , where n p is the electron occupation numberin the 2 p bands [42]. Since m s = 2 m o / ( g − g is the gyromagnetic factor [43], m total can be estimated for the K -edge.Figure 3 shows the XAS and XMCD spectra at 300 K for the graphene/Co samplemeasured at the Co L -edge and C K -edge. The Co spectra show no sign of oxidation9nd this proves that graphene acts as a good passivation layer against oxidation [44, 45].The region between the L and L with a constant negative intensity is known as the diffusemagnetism region, µ diff , and it has been observed and reported for Co, Ni and Fe XMCDspectra [33, 46]. µ diff is expected to arise as a result of the opposite spin directions for the4 s and 3 d electrons, interstitial and sp -projected magnetic moments, and the fact that itcouples antiferromagnetically to the sample’s total magnetic moment in 3 d elements, exceptfor Mn [33]. Although µ diff has been reported to contribute to about −
4% and −
7% tothe total magnetic moment in Co and Ni, respectively [33, 47], since the sum rule doesnot account for µ diff , the integration range over the L was stopped just before µ diff forthe calculation of m o and m s (858.7 eV for the Ni sample and 787.2 eV for Co). On theother hand, the main L peak and the shoulder, µ shoulder , are due to multiple initial-statesconfiguration, 3 d and 3 d , respectively, and therefore they were accounted for in the sumrule calculations [33].The calculated < L z > and < S z > of the Co layer obtained by using (5) and (6) are 0.057 µ B and 0.21 µ B , respectively. Therefore, the total magnetic moment is m total =0.48 µ B / Coatom, which is lower than the previously reported values of ∼ µ B for bulk Co [35, 48].The reduced calculated values are attributed to the fact that the Co magnetisation couldnot be saturated with the applied field of 0.11 T, as confirmed by the SQUID magnetometrymeasurements shown in Figure 4 (a), taken with the magnetic field applied in-plane (0 ◦ )and out-of-plane (90 ◦ ) to the sample. The shape of the hystereses and the size of thecoercivities of both measurements show that the easy axis is in-plane, whereas the reducedsample moments measured by the SQUID may be due to the error arising from measuringthe sample’s dimensions accurately. However, the measurements prove that the magneticfield of 0.11 T applied at the start of the XMCD experiments was insufficient to saturate orto prevent the strong demagnetisation of the Co film as can be seen from Figure 4 (c).We can obtain an upper limit to the orbital moment of the graphene layer by integratingthe modulus of the dicrhoic signal, | µ XMCD | , which is shown in Figure 3 (c), red curve. Eventhough the dichroic contrast and thus the magnetic moment for the Co film are significantlyreduced, the XMCD signal of the C K -edge (Figure 3 (c)) gives a clear indication that amagnetic moment has been induced in the graphene. Furthermore, although the magneticdichroism response is expected mainly at the peak corresponding to the 1 s → π ∗ transitionas a result of the C p z - Co 3 d hybridisation [8], a small magnetic signal is observed at the10 IG. 3. Absorption spectra for circular polarised light and the areas used to apply the sum rules forthe graphene/Co sample measured at 300 K: (a) and (b) XMCD and XAS spectra for Co L -edge.(c) and (d) XMCD and XAS spectra for the graphene layer. s → σ ∗ transition peak as well.The m o value was estimated to be 0.012 µ B /C atom for the C K -edge using n h = 4. m s is then calculated to be 0.08 µ B /C atom, using g = 2 .
3, which is the value reported forgraphene grown on SiC [49]. Therefore, m total of the graphene grown on Co is 0.092 µ B /Catom. If one corrects for the partial saturation of the Co magnetisation, one obtains anupper value for the graphene magnetic moment µ total = 0 . × . .
48 = 0 . µ B /C atom.11igher sources of errors are expected in the XMCD estimation attributed to the difficultyof applying the sum rules to the C K -edge spectra in comparison with that for Co and Ni L -edge. For instance, various studies have been reported for Co and Ni [8, 15, 35, 47, 48, 50–53]which can be used as references for our measurements, but the application of the sum ruleshas not been reported for graphene before. Also, n h has not been measured for C previously.Moreover, the g -value of the graphene was found to be different depending on the underlyingsubstrate [49, 54, 55], but it has not been reported for graphene on Ni nor on Co substrates.It is also noteworthy to mention the difficulty associated with measuring the C K -edge dueto the C contamination of the optical elements which appear as a significant reduction inthe incoming intensity at this particular energy.The µ XMCD and µ XAS of the Ni L -edge in the rotated graphene/Ni sample and itscorresponding graphene top layer are shown in Figure 5. It is clear from the XMCD spectrumthat µ shoulder is more pronounced in Ni than in Co due to the extra electrons in the d band.Furthermore, although the non-resonant contribution was subtracted from the µ + and µ − spectra, a higher background is measured at the post-edge ( E >
880 eV). This tail hasbeen excluded from the sum rules as it is considered part of the non-resonant contribution.The calculated m o and m s are 0.084 µ B /Ni atom and 0.625 µ B /Ni atom, respectively, andthus m total is 0.709 µ B /Ni atom. Considering the 20% accuracy of the XMCD techniquein estimating the magnetic moments of materials, the results obtained for Ni is consistent FIG. 4. SQUID measurements showing the hysteresis loops obtained with the field applied parallel(0 ◦ ) and out-of-plane (90 ◦ ) to (a) graphene/Co and (b) graphene/Ni samples. (c) Zoom-in view ofthe 300 K SQUID measurements where the field is applied parallel to the surface of the graphene/Niand graphene/Co samples. The dotted vertical line marks the position of 0.11 T. IG. 5. Absorption spectra for circular polarised light and the areas used to apply the sum rulesfor the rotated graphene/Ni sample measured at 300 K: (a) and (b) XMCD and XAS spectra forNi L -edge. (c) and (d) XMCD and XAS spectra for the graphene layer. with the values reported in the literature [48]. The slight reduction in the magnetic momentdetected by the SQUID (Figure 4 (b)) could be attributed to the same reasons discussedabove for the graphene/Co sample.The C K -edge spectra for the graphene/Ni sample are shown in Figure 5 (c) and (d).The calculated m o for graphene is 0.034 µ B / C atom using n h = 4. Therefore, m total for thegraphene grown on Ni is estimated to be 0.227 µ B /C atom.13espite the large uncertainties expected for the estimated graphene moments, the XMCDresults demonstrate the presence of magnetic polarisation in graphene. For more preciseestimates, we turn to PNR. V. POLARISED NEUTRON REFLECTIVITY AND THE BAYESIAN UNCER-TAINTY ANALYSIS
PNR experiments were carried out to measure the magnetic properties of each layer ofthe samples individually and to determine the value of the induced magnetic moment ingraphene quantitatively. The measurements were conducted at 10 K and under an appliedmagnetic field of 0.5 T, using the Polref instrument at ISIS (UK), while the fitting of thedata was done using GenX [56]. Although both Ni and Co are ferromagnetic at RT, the10 K measurements are expected to provide a better estimation of the induced magneticmoment due to the lower thermal excitations of the electron spin at low temperature.The results for the PNR measurements, the corresponding scattering length density (SLD)profiles and the spin asymmetry ( SA = [ R + − R − ] / [ R + + R − ], where R + and R − are thespin-up and spin-down neutron specular reflectivity, respectively) are shown in Figure 6 forthe epitaxial graphene/Ni, rotated graphene/Ni and rotated graphene/Co. The results of thefits to the PNR data are summarised in Table I. For epitaxial and rotated-domain graphenegrown on Ni, the PNR fits indicate a slightly thicker epitaxial graphene with a higher errorcompared to the rotated-domain graphene, which reflects the low relative accuracy of thegraphene’s thickness estimation expected from a reflectivity technique. However, the resultsshow that the graphene thickness has only a subtle, if any, influence on the amount of theinduced magnetisation as can be deduced from the values of the measured magnetic momentslisted in Table I.The fitting procedure was started by pinning the thickness ( d ), roughness ( σ ) and density( ρ ) of the layers to the values obtained from XRR measurements (data not shown) whilefitting the remaining parameters: magnetic moment, instrument resolution, background andthe incident intensity ( I ). The XRR fitted parameters were then allowed to vary withinrestricted limits as they tend to drift to unrealistic values if no boundaries are set. All thevariables were regularly reset to ensure that the fitting routine converged to the same results.Furthermore, fixing the magnetic moment of graphene to zero yielded unrealistic values for14 IG. 6. PNR data (open symbol and line) and fits (solid line), the corresponding SLD profile(insets) and the spin asymmetry for the epitaxial graphene/Ni (a,d), rotated graphene/Ni (b,e)and rotated graphene/Co (c,f), measured at 10 K and with an in-plane magnetic field of 0.5 T. the thickness and roughness of the graphene layer (which does not agree with the SEM andRaman scans) and poorer fits, especially in the low- and mid- Q range ( ∼ .
025 - 0.080 ˚A -1 ),as shown in Figure 7 for the epitaxial graphene/Ni sample. This agrees with the XMCDresults and confirm the consistency of the PNR fits shown in Figure 6 which indicate aninduced magnetic moment in the graphene layer.Additional scenarios were also tested. For example, the oxidation of the TM layer and TABLE I. Summary of the PNR results.FM Layer GrapheneSample Thickness Magnetic Moment Thickness Magnetic Moment(nm) ( µ B /atom) (nm) ( µ B /atom)Epitaxial Ni(111) 77 . ± .
25 0 . ± .
02 0 . ± .
05 0 . ± . . ± .
30 0 . ± .
01 0 . ± .
20 0 . ± . . ± .
29 1 . ± .
01 1 . ± .
18 0 . ± . IG. 7. The PNR data (open symbol and line), fits (solid line) and the spin asymmetry (inset)for the epitaxial graphene/Ni obtained by pinning the magnetic moment in graphene to zero. Theinset table lists the deduced thickness and roughness for the graphene layer. the formation of TM-carbide was examined by embedding an intermediate TM-oxide andTM-carbide layer at the interface between the TM and graphene, but this lead to poorer fits(see supplemental materials) and the best results, shown in Figure 6, were achieved using asimple model: Sapphire/a single layer of TM film/graphene.Although Co has a higher magnetic moment than Ni, the PNR fits indicate that a similarmagnetic moment is induced in the graphene whether grown on Co or as rotated and epitaxialgraphene on Ni. This can be attributed to the larger lattice mismatch between the grapheneand Co than with the Ni surface.The PNR fits have shown that a magnetic moment of ∼ µ B /C was induced in thegraphene grown on Ni and Co films. These results indicate larger moments than the valuepreviously predicted by Weser et al. , who suggested that the induced magnetic moment fora graphene monolayer grown on a Ni(111) film would be between 0 . − . µ B /C atom[8]. Their assumption was based on comparing the graphene/Ni system with other C/3 d TM structures, such as a C/Fe multilayer [22], and carbon nanotubes (CNTs) on a Co film[23], where a magnetic moment of 0.05 µ B and 0.1 µ B /C atom was estimated, respectively.16n the former study [22], the magnetic moment of a C/Fe multilayer system with 0.55nm of C was measured. However, the Dirac cone is a characteristic feature in graphene andCNTs. Therefore, we suggest that a different mechanism other than the break of degeneracyaround E D may have been responsible for the magnetic moment detected in the C layer inRef. [22], hence, making it difficult to compare graphene-based heterostructures with otherC allotropes/TM systems. On the other hand, although Dirac cones exist in CNTs, a directquantitative analysis of the induced magnetic moment was not possible from the MFMimages reported in Ref [23]. In contrast, PNR provides a direct estimation of the inducedmagnetic moment in graphene.We performed Bayesian uncertainty analysis of the graphene/Ni PNR measurementsusing the Refl1D and Bumps software [57, 58]. This was done to test the validity of thefitting models, understand the correlation between the fitted parameters and hence provethe reliability of the PNR results.The Bayesian analysis shown in Figure 8 were simulated using sapphire/Ni/Ni/graphenemodel (the addition of the second Ni layer is discussed below). The reflectivity curvespresented in Figure 8 (a) were normalised to that of the sapphire substrate, to eliminate thesubstrate contribution, thus easily highlighting the features associated with the thin films.The residual graph shown in the inset illustrates the difference between the theoretical modeland the measured data, where the fits resulted in a small spread of data of ± .
06 from theorigin. Furthermore, the analysis yielded a similar structural contribution of the SLD tothat shown in Figure 6, while suggesting a higher magnetisation in the graphene.The graph presented in Figure 8 (b) show the correlation between the fitted parameters.To read the graph and understand the relation between two parameters, a line is drawnvertically for the first parameter, while drawing a horizontal one for the second parameter.The shape inside the box at intersection of the two lines indicates the relation between theparameters. The oval rounded shape shows no correlation between the fitted parameters andthat both are at the most probable value. The distorted oval shape reflects some kind ofcorrelation between the different fitted parameters. For instance, there is an approximatelylinear relationship between the density of C and the roughness of the first Ni layer (
Ni1rhoM ). However, “
C interface M below ” shows a complicated relation to all other fittedparameters likely due to the constraints applied to the fits.These cross-correlation plots are mainly used to understand whether or not the model used17
IG. 8. Bayesian simulations for rotated domains graphene grown on Ni measured at 10 K withan applied of 0.5 T. (a) The PNR reflectivity curves normalised to that of the sapphire substrate.The insets show the corresponding residuals and the resultant SLD profile. (b) The correlationsimulation of the fitted parameters. (c) The population histogram and probability distribution ofthe fitted PNR parameters. is over-determined i.e., if the number of parameters used is the minimum set of parametersneeded to describe the data. Therefore, we are intentionally over-parameterising the Ni layerto obtain the details in the graphene (i.e. whether the effect we are observing is happeningin the Ni or the graphene layer). Here, the Ni layer is artificially broken into two layers(Ni1 and Ni2) and the model was run to find the minimum value. This was done to showthe strong linear correlation between the thicknesses of the Ni layers. Curiously, we also18bserve a weak correlation between
C density and
Ni2 thickness . This is likely to be dueto the fact that as the carbon density is varied, some of it creates alterations in the SLDprofile indistinguishable from the changes of the
Ni2 thickness .The population histogram series show the probability distribution for each of the fittedparameters for the rotated Gr/Ni sample at 10 K with an applied field of 0.5 T (Figure 8 (c)).The shaded yellow region represents the 68% confidence interval (one standard deviationaround the mean value), while the green line is the highest probability provided that theparameter is fixed at the maximum likelihood value. The histogram and the probabilitydistribution should have a maximum shape for all the parameters of a model to be fullyconverged, which is the case for our simulation.
VI. PNR MEASUREMENTS OF THE GRAPHENE/Ni Mo (111) ANDGRAPHENE/Cu SAMPLES Further PNR experiments were carried out to clarify whether the results are merely dueto the C p z -3 d hybridisation as postulated in Ref. [8, 20] or because of the chemical bondsbetween the C and TM atoms, as for fullerene/non-magnetic TM as proposed in Ref. [59].For this purpose, a Ni Mo film was used with the aim of preserving the fcc crystal structureof Ni while suppressing its magnetisation, as suggested in Ref. [60]. Since the Ni is dopedby 10% only, the lattice mismatch and bond length to graphene are expected to be similarto that for graphene/Ni(111) sample, but the d -orbital position is considerably downshiftedwith respect to E F . See supplemental materials for the sample preparation procedure andits structural properties.The results of the PNR measurements of the Ni Mo /graphene sample are shown in Figure9. A small, but detectable spin splitting and a minute variation in the spin asymmetry areobserved. Surprisingly, a higher magnetisation is detected in graphene (0 . ± . µ B )than in the Ni Mo film (0 . ± . µ B ), which can be attributed to the small residualmoment of the Ni Mo . Since a small magnetic moment persisted in Ni Mo (111) at 10 K,the measurements were repeated using a non-magnetic TM, Cu.As expected, no induced magnetic moment was detected in graphene (results not shown).This is because, firstly, Cu is a non-magnetic TM, and secondly because the weak interactionbetween the graphene and the Cu surface atoms will not open up the graphene’s Dirac cone.19 IG. 9. (a) The PNR data (open symbol and line) and fits (solid line) for the Ni Mo /graphenesample and the corrresponding SLD (inset). (b) The spin asymmetry of the fit. Therefore, we conclude that the measured induced magnetic moment in graphene is due tothe strong C p z -TM 3 d hybridisation. VII. CONCLUSION
In summary, we have successfully grown graphene by CVD on different TM substrates.Induced magnetic moment in rotated-domain graphene as a result of the proximity effectin the vicinity of a FM substrate was detected by element-specific XMCD measurementsat the C K -edge. PNR experiments were carried out to determine the amount of mag-netic moment detected by XMCD. Although a higher magnetic moment was expected tobe induced in epitaxial graphene/Ni sample, the PNR results indicate similar magnetic mo-ment of ∼ . µ B /C atom induced in both structures which is about five times higher thanthe values predicted in other studies [8, 22, 23]. Furthermore, using Co film, which is astronger FM but has a larger lattice mismatch with the graphene layer compared to Ni,induced equivalent magnetic moment to that measured in graphene/Ni samples. AdditionalPNR measurement on non-magnetic Cu film confirms that the induced magnetic momentin graphene arises as a result of the opening of the graphene’s Dirac cone due to the strongC p z -Ni 3 d hybridisation. Therefore, our study is considered the first reported attempt to20stimate the induced magnetisation in graphene by PNR. Appendix A: Supplementary Material1. Preparation of the graphene/Ni Mo (111) sample A 80 nm thick Ni Mo (111) film was deposited at RT on a 1 mm thick Al O (0001)substrate using a CEVP magnetron sputtering from a 99.9% pure Ni Mo target. A constantDC current of 0.1 A with a constant flow of 14 sccm of pure Argon gas were used to growthe film at a rate of 0.02 nm/s in a plasma of 3 mTorr.The Ni Mo (111) film was then transferred into a CVD chamber for the growth ofgraphene. Pure H gas was introduced to the CVD at a flow rate of 200 sccm and thesample was then heated to 650 ◦ C, again for 12 minutes before introducing C H at a rate of0.24 sccm for 40 minutes and then cooled down to RT to produced rotated-domain grapheneon Ni Mo (111).
2. Preparation of the graphene/Cu sample
The Cu film was deposited on a clean 0.5 mm thick Al O (0001) substrate using a thermalevaporator with a base pressure of 3 . × − mbar. The growth parameters were tuned toevaporate a 950 nm thick film with an evaporation rate of 0.2 nm/s. The growth recipe ofgraphene on the Cu film is described in Ref. [61].
3. Raman Measurements
A transfer method similar to that used for the graphene/Ni and graphene/Co was usedfor the graphene/Ni Mo (111) sample before taking the Raman measurements. However,the HNO was diluted to 5% for Ni Mo . On the other hand, no transfer procedure wasdone for the graphene grown on Cu due to the large lattice mismatch between the grapheneand Cu ( ∼ . Mo film and for graphene/Cu sample. Theaverage peaks positions and the average 2 D FWHM of all the samples are listed in Table II.21
IG. 10. Room temperature Raman spectroscopy measurements for (a) transferred graphene fromthe Ni Mo (111) film and (b) graphene/Cu sample, showing the graphene’s characteristic peaks.The dashed vertical lines indicate regions for the different peaks. Due to the high I D’ of the Raman spectra for the graphene transferred from Ni Mo (Figure 10 (a)), an argument similar to that used for the graphene transferred from Ni(111)can be applied here to explain the spectra. However, the wide spatial variation across thesurface of the sample, which could be attributed to formation of occasional strong Mo − Cbonding between the graphene and the Ni Mo film, makes it difficult to assess the qualityof the graphene grown on Ni Mo based on the 2 D FWHM.Figure 10 (b) shows the two main characteristic peaks of pristine graphene; G and 2 D ,while the missing defect induced-peaks from all the three spectra and the I D / I G of about2 (except for the blue spectrum) reveal that graphene with low defect density was grown onthe Cu film. Furthermore, the broad FWHM of the 2 D peaks is an indicative of a few-layergraphene as the 2 D peak is known to broaden with the number of graphene layers due tothe splitting of phonon bands [25]. The noisy spectra is attributed to the background of thecoupled polycrystalline Cu substrate [63].
4. PNR Models
Figure 11 to Figure 13 show the PNR fits, their corresponding SLD and spin asymmetryof the various models tested to find the best model for fitting the PNR data for the epitaxial22
ABLE II. The results of the Raman measurements summarising the average peaks positions and2 D FWHM for graphene transferred from rotated Co, rotated Ni, epitaxial Ni and Ni Mo and forgraphene/Cu sample.Sample D (cm − ) G (cm − ) D’ (cm − ) D + D” (cm − ) 2 D (cm − ) 2 D FWHM(cm − )Rotated Co 1349.6 1586.9 1621.7 2457.8 2692.3 40.1Rotated Ni 1346.3 1590.7 1624.8 2464.2 2681.9 46.2Epitaxial Ni 1344.6 1590.7 1623.1 2462.6 2682.6 40.8Ni Mo O /Ni/NiC. graphene/Ni sample. The value of the fit figure of merit ( χ ), and the fitted parameterswere used to assess the goodness-of-the fits. For example, Figure 11 shows the resultsobtained from fitting the data using a model with a NiC at the top layer instead of graphene(i.e. Al O /Ni/NiC). This yielded a poor fit with a χ = 21 . Q range. It also estimated a reduced number density23 IG. 12. The 10 K PNR data fits, the corresponding SLD profile and spin asymmetry for theepitaxial graphene/Ni(1111) using the model: Al O /Ni/NiC/Gr. of 0.04 ˚A for the graphene layer instead of 0.114 ˚A .In Figure 12, we tested the formation of carbide interdiffusive layer at the interfacebetween the Ni and graphene (i.e Al O /Ni/NiC/Gr). As with the previous model, thesimulation does not fit the reflectivity fringes in the mid- and high- Q ranges. However,although the value estimated with this model for the graphene number density agrees withthe literature, it gave unrealistic values for its thickness (0.01 nm, which is the minimum ofthe fitting range) and roughness (0.25 nm, which is the maximum of the fitting range) anda very high χ value of 28.4.Figure 13 shows the results obtained from testing the presence of a NiO layer at theinterface between the Ni and graphene. 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