# Determining the Proximity Effect Induced Magnetic Moment in Graphene by
Polarized Neutron Reflectivity and X-ray Magnetic Circular Dichroism

R. O. M. Aboljadayel<EMAIL_ADDRESS>Cavendish Laboratory, Physics
Department, University of Cambridge, Cambridge CB3 0HE, United Kingdom.  C. J.
Kinane  ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science
and Innovation Campus, Oxon, OX11 0QX, United Kingdom.  C. A. F. Vaz  Swiss
Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland  D. M.
Love  Cavendish Laboratory, Physics Department, University of Cambridge,
Cambridge CB3 0HE, United Kingdom.  R. S. Weatherup  Department of
Engineering, University of Cambridge, Cambridge CB3 0FA, United Kingdom.  P.
Braeuninger-Weimer  Department of Engineering, University of Cambridge,
Cambridge CB3 0FA, United Kingdom.  M.-B. Martin  Department of Engineering,
University of Cambridge, Cambridge CB3 0FA, United Kingdom.  A. Ionescu
Cavendish Laboratory, Physics Department, University of Cambridge, Cambridge
CB3 0HE, United Kingdom.  A. J. Caruana  ISIS Facility, STFC Rutherford
Appleton Laboratory, Harwell Science and Innovation Campus, Oxon, OX11 0QX,
United Kingdom.  T. R. Charlton  ISIS Facility, STFC Rutherford Appleton
Laboratory, Harwell Science and Innovation Campus, Oxon, OX11 0QX, United
Kingdom.  J. Llandro  Cavendish Laboratory, Physics Department, University of
Cambridge, Cambridge CB3 0HE, United Kingdom.  P. M. S. Monteiro  Cavendish
Laboratory, Physics Department, University of Cambridge, Cambridge CB3 0HE,
United Kingdom.  C. H. W. Barnes  Cavendish Laboratory, Physics Department,
University of Cambridge, Cambridge CB3 0HE, United Kingdom.  S. Hofmann
Department of Engineering, University of Cambridge, Cambridge CB3 0FA, United
Kingdom.  S. Langridge<EMAIL_ADDRESS>ISIS Facility, STFC
Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Oxon,
OX11 0QX, United Kingdom.

###### Abstract

We report the magnitude of the induced magnetic moment in CVD-grown epitaxial
and rotated-domain graphene in proximity with a ferromagnetic Ni film, using
polarized neutron reflectivity (PNR) and X-ray magnetic circular dichroism
(XMCD). The XMCD spectra at the C K-edge confirms the presence of a magnetic
signal in the graphene layer and the sum rules give a magnetic moment of up to
$\sim\,0.47\,\mu$B/C atom induced in the graphene layer. For a more precise
estimation, we conducted PNR measurements. The PNR results indicate an induced
magnetic moment of $\sim$ 0.53 $\mu$B/C atom at 10 K for rotated graphene and
$\sim$ 0.38 $\mu$B/C atom at 10 K for epitaxial graphene. Additional PNR
measurements on graphene grown on a non-magnetic Ni9Mo1 substrate, where no
magnetic moment in graphene is measured, suggest that the origin of the
induced magnetic moment is due to the opening of the graphene’s Dirac cone as
a result of the strong C pz-3d hybridization.

Graphene, XMCD, PNR, magnetism, heterostructures

###### pacs:

##  I Introduction

Graphene is a promising material for many technological and future spintronic
device applications such as spin-filters,1, 2, 3, 4, 5, 6, 7 spin-valves and
spin field-effect transistors due to its excellent transport properties.8, 9
Graphene can have an intrinsic charge carrier mobility of more than 200,000
cm2V-1s-1 at room temperature (RT),10 and a large spin relaxation time as a
result of its long electron mean free path and its negligible spin-orbit and
hyperfine couplings.2, 11

Manipulating spins directly in the graphene layer has attracted great
attention as it opens new ways for using this 2D material in spintronics
applications.2, 12 This has been realized via various approaches such as
through the proximity-induced effect,13, 14, 15, 16, 2 chemical doping of the
graphene surface 11 or through a chemically-induced sublattice.17 Here, we
report the feasibility of the first method in utilizing the exchange coupling
of local moments between graphene and a ferromagnetic (FM) material to induce
a magnetic moment in graphene.

Graphene is a zero-gap semiconductor because the $\pi$ and $\pi^{*}$ bands
meet at the Fermi energy ($E$F), at the corner of the graphene’s Brillouin
zone ($K$ points), i.e. at degenerate points forming the Dirac point ($E$D),
where the electronic structure of these bands can be described using the
tight-binding model.18, 19 However, the adsorption of graphene on a strongly
interacting metal distorts its intrinsic band structure around $E$D. This is a
result of the overlap of the graphene’s valence band with that of the metal
substrate due to the breaking of degeneracy around $E$D in a partially-filled
d-metal, as discussed in the universal model proposed by Voloshina and
Dedkov.20 Their model was supported by density functional theory calculations
and proven experimentally using angle-resolved photoemission spectroscopy.18,
20, 21, 22, 23, 24, 25 Furthermore, a small magnetic signal was detected in
the X-ray magnetic circular dichroism (XMCD) spectra of the graphene layer in
proximity with a FM transition metal (TM) film, suggesting that a magnetic
moment is induced in the graphene.13, 2, 26, 27 However, no direct
quantitative analysis of the total induced magnetic moment has been reported.

It is widely accepted that graphene’s C atoms are assembled in what is known
as the top-fcc configuration on top of close-packed (111) surfaces, where the
C atoms are placed on top of the atoms in the first and third layers of the TM
substrate.20, 22, 23 The strength of the graphene-TM interaction is influenced
by the lattice mismatch, the graphene-TM bond length and the position of the d
orbital of the TM relative to EF. Therefore, a Ni(111) substrate was used as
the FM since it has a small lattice mismatch of -1.2%, a bond length of $2.03$
Å and their d orbitals are positioned $\sim 1.1$ eV below EF (i.e. forming
$\pi-$d hybrid states around the $K$ points).20, 21, 22, 28 Epitaxial and
rotated-domain graphene structures were investigated since rotated graphene is
expected to interact more weakly with the TM film underneath. This is a result
of the loss of epitaxial relationship and a lower charge transfer from the TM
due to missing direct Nitop$-$C interaction and the smaller region covered by
extended graphene layer as a result of the 3∘ rotation between the graphene
and Ni .29, 22, 30, 31 Therefore, a smaller magnetic moment is expected to be
induced in rotated-domain graphene.

We have studied the structural, magnetic and electronic properties of
epitaxial- and rotated-domain graphene grown on Ni films, confirmed the
presence of a magnetic moment in graphene by element-specific XMCD and
measured the induced magnetic moment at 10 K and 300 K for rotated and
epitaxial graphene using polarized neutron reflectivity (PNR).

To our knowledge, our attempt is the first reported approach in using PNR and
XMCD sum rules combined to estimate the total induced magnetic moment in
graphene. This is due to the thinness of graphene which is close to the
resolution of the PNR technique, and the difficulty in processing the XMCD C
K-edge signal due to the contribution of the carbon contamination in the
beamline optics. We attribute the presence of an induced magnetic moment in
graphene to the hybridization of the C pz orbital with the 3d bands of the TM,
which is supported by additional PNR measurements on graphene grown on a non-
magnetic Ni9Mo1(111) substrate, where no magnetic moment is detected in the
graphene layer.

##  II Results and Discussion

###  II.1 Raman Spectroscopy Measurements

In order to evaluate the quality, number of graphene layers, the doping and
defect density in the grown graphene samples we used Raman spectroscopy, which
is a non-destructive technique known to be particularly sensitive to the
structural and electronic properties of graphene.32, 33 For these
measurements, the graphene layer was first transferred by a chemical etching
process from the metallic film onto a Si substrate with a thermally oxidized
SiO2 layer similar to that reported in Ref [34]. This was done to avoid loss
in the resonance conditions due to the strong chemical interaction between the
graphene $\pi$ orbital and the d-states of Ni and Ni9Mo1 which also alters the
graphene’s pz orbitals (see Experimental section for further details).

Figure 1: Room temperature Raman spectroscopy measurements taken at three
different regions (1-3) after transferring the graphene from (a) the epitaxial
Ni and (b) rotated Ni samples to a Si/SiO2 wafer, showing the graphene’s
characteristic peaks. The dashed vertical lines separate the regions of the
different peaks.

Figure 1 shows the Raman scans taken at three different regions of the
graphene after being transferred from the Ni films (see Section IV.2 of the
Experimental Section). All the spectra possess the D, G, D’, D+D” and 2D
peaks.35, 36 Although all the 2D peaks shown in Figure 1 were fitted with
single Lorentzians, they have relatively broad full-width at half-maximum
(FWHM). The average FWHM of the 2D peak of epitaxial and rotated-domain
graphene transferred from the Ni film are 40.8 cm-1 and 46.2 cm-1,
respectively. Furthermore, the spectra of both samples show a high ID/IG ratio
(average of 1.49 for epitaxial graphene and 2.35 for rotated graphene). The
variation in the spectra of each sample, presence of second order and defect-
induced peaks, the large FWHM of the 2D peak and the high ID/IG ratio could be
a result of the chemical etching and transfer process (see the Sample
Preparation section) or the chemical doping from the HNO3 used to etch the
metallic films. Therefore, it is difficult to estimate the number of graphene
layers based on the position of the G and 2D peaks and I2D/IG ratio. However,
the SEM scan and LEED diffraction pattern in Figure 7 (a) and (c),
respectively, show a single epitaxial graphene layer grown on Ni(111). The
broader FWHM of the 2D and the higher average I2D/IG ratio in the rotated
graphene compared to the epitaxial structure could be attributed to the
formation of more defective or turbostratic (multilayer graphene with relative
rotation between the layers) graphene as a result of the occasional overlap of
the graphene domains.37 The Raman spectra for the graphene/Ni9Mo1 sample, as
well as the full list of the peak positions and the 2D average FWHM of all the
measured samples is provided in the supplementary material (SI).

###  II.2 X-ray Magnetic Circular Dichroism (XMCD)

Figure 2: X-ray absorption spectra for circular polarized light and the areas
used to apply the sum rules for the rotated graphene/Ni sample measured at 300
K: (a) and (b) XMCD and XAS spectra for Ni L2,3-edge. (c) and (d) XMCD and XAS
spectra for the graphene layer. The vertical and horizontal dashed lines in
(a) indicate the maximum integration range over the L2,3 peak and the values
used for the calculation of $m_{o}$ and $m_{s}$, respectively.

The X-ray absorption spectra ($\mu$XAS) and the XMCD response ($\mu$XMCD) at
the Ni L2,3-edge in the rotated graphene/Ni sample are shown in Figure 2. The
spectra show no sign of oxidation, proving that graphene acts as a good
passivation layer against oxidation.38, 39 The region between the L3 and L2
edges with a constant negative intensity is known as the diffuse magnetism
region, $\mu$diff, and it has been observed and reported for Co, Ni and Fe
XMCD spectra.40, 41 $\mu$diff is expected to arise as a result of the opposite
spin directions for the 4s and 3d electrons, interstitial and sp-projected
magnetic moments, and the fact that it couples antiferromagnetically to the
sample’s total magnetic moment in 3d elements, except for Mn.40 Although
$\mu$diff has been reported to contribute to about $-7\%$ to the total
magnetic moment in Ni,42, 40 since the sum rule does not account for
$\mu$diff, the integration range over the L3 was stopped just before $\mu$diff
for the calculation of the orbital magnetic moment, $m_{o}$, and the spin
magnetic moment, $m_{s}$ (858.7 eV). On the other hand, the main L3 peak and
the shoulder, $\mu$shoulder, are due to multiple initial-states configuration,
$3d^{8}$ and $3d^{9}$, respectively, and therefore they were accounted for in
the sum rule calculations.40

Although the non-resonant contribution was subtracted from the $\mu_{+}$ and
$\mu_{-}$ spectra, a higher background is measured at the post-edge ($E>880$
eV). This tail has been 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
$\mu$B/Ni atom and 0.625 $\mu$B/Ni atom, respectively, and thus $m_{total}$ is
0.709 $\mu$B/Ni atom (see the SI for the expressions for $m_{o}$, $m_{s}$ and
$m_{total}$ at the L-edge). Considering the 20$\%$ accuracy of the XMCD
technique in estimating the magnetic moments of materials, the results
obtained for Ni is consistent with the values reported in the literature. 43,
44

The C K-edge spectra for the rotated graphene/Ni sample are shown in Figure 2
(c) and (d). For the C K-edge, higher sources of errors are expected in the
XMCD estimation attributed to the difficulty of applying the sum rules to the
C K-edge spectra in comparison with that for Ni L2,3-edge. For instance,
various studies have been reported for Ni 13, 42, 45, 23, 43, 46, 47 which can
be used as references for our measurements, but the application of the sum
rules has not been reported for graphene before. Also, the number of holes,
$n_{h}$, has not been measured for C previously. Moreover, the gyromagnetic
factor ($g$) of the graphene was found to be different depending on the
underlying substrate,48, 49, 50 and it has not been reported for graphene on
Ni. It is also noteworthy to mention the difficulty associated with measuring
the C K-edge due to the C contamination of the optical elements which appear
as a significant reduction in the incoming intensity at this particular
energy.

Nonetheless, we can obtain an upper limit to the orbital moment of the
graphene layer by integrating the modulus of the dichroic signal,
$|\mu_{XMCD}|$, which is shown in Figure 2 (c), red curve. Although the
magnetic dichroism response is expected mainly at the peak corresponding to
the 1s$\rightarrow\pi^{*}$ transition as a result of the C pz$-$Ni 3d
hybridization,13 a small magnetic signal is observed at the
1s$\rightarrow\sigma^{*}$ transition peak as well; a similar behaviour was
reported for graphene/2 ML Co/Ir(111).24 The calculated upper bound $m_{o}$
for graphene is 0.062 $\mu$B/C atom using $n_{h}=4$; which corresponds to an
$m_{s}$ of 0.412 $\mu_{B}$/C atom, using $g=2.3$, which is the value reported
for graphene grown on SiC.48 Therefore, $m_{total}$ of the rotated-domain
graphene grown on Ni is $\sim$0.474 $\mu_{B}$/C atom (see the SI for the
expressions of $m_{o}$, $m_{s}$ and $m_{total}$ at the K-edge).

Despite the large uncertainties expected for the estimated graphene moments,
the XMCD results demonstrate the presence of magnetic polarization in
graphene. For more precise, quantified and independent estimates, we turn to
PNR.

###  II.3 Polarized Neutron Reflectivity

PNR experiments were carried out to measure the magnetic properties of each
layer of the samples individually and to determine the value of the induced
magnetic moment in graphene quantitatively.

The PNR results for the rotated-domain graphene/Ni(111) and epitaxial
graphene/Ni(111) samples, measured at 10 K and 300 K, are displayed in Figures
3 and 4, respectively. Panel (a) for each figure shows the Fresnel
reflectivity profiles and panels (b) and (c) the spin asymmetry
($SA=[R_{+}-R_{-}]/[R_{+}+R_{-}]$, where $R_{+}$ and $R_{-}$ are the spin-up
and spin-down neutron specular reflectivities, respectively). $SA$ scales with
the magnetic signal. A flat $SA$ line at zero, shown as a blue dashed line,
represents no net magnetic induction present in the system. Panel (d) displays
the nuclear scattering length density (nSLD), for the sample structure. This
structure is shared at both temperatures in the co-refinement, and panel (e)
shows the magnetic scattering length density (mSLD) for each temperature.

Figure 3: PNR Model 9: consists of a Ni layer split into two regions for the
rotated graphene/Ni sample with a magnetic dead-layer at the substrate
interface and continuous magnetic moment variation up to the graphene layer
which is allowed to be magnetic. (a) Fresnel reflectivity for 10 K and 300 K,
(b) and (c) show the spin asymmetries, (d) is the nuclear scattering length
density (nSLD) profile and (e) the magnetic scattering length density (mSLD)
profile. The grey banded regions around the SLD lines are the 95% Bayesian
confidence intervals. Figure 4: Ni layer split into two regions for the
epitaxial graphene/Ni sample (a) Fresnel reflectivity for 10 K and 300 K, (b)
and (c) show the spin asymmetries, (d) is the nuclear scattering length
density (nSLD) profile and (e) the magnetic scattering length density (mSLD)
profile.

The fitting procedure is fully described in the SI, which contains the various
models used to fit the rotated graphene/Ni sample. The 10 K and 300 K data
shown in Figures 3 and 4 were fitted simultaneously with a shared nSLD and
independent mSLD. The bulk of the fitting model selection was done on the
rotated graphene/Ni sample. The study presented in the SI show the importance
of prior knowledge of the sample properties to obtain the best PNR fit to
estimate the induced magnetic moment in graphene. We used the information
obtained from the structural characterizations (SEM and Raman spectroscopy) to
obtain a lower bound on the graphene layer thickness. The fit tends to shrink
the graphene thickness to less than one monolayer, if unrestrained, which does
not agree with the SEM and Raman scans (refer to SI). This could be due to the
limited $Q$ (wavevector transfer) range measured in the time available for the
experiment, as the fit is found to rely strongly on the high $Q$ statistics.
It should be noted that in model 9 shown in Figure 3 the magnetic moment of
the graphene layer was allowed to fit to zero, but the analysis always
required a non-zero value for the magnetic moment to obtain a good fit with
low uncertainty, which is consistent with the XMCD results. The unrestrained
graphene thickness models are shown in the SI. It is noteworthy that the
improvement in the figure of merit ($\chi^{2}$) for the unconstrained to the
constrained graphene thickness are within the error bar of each other.
However, the results show that the graphene thickness has only a subtle
influence, if any, on the amount of the induced magnetization as can be
deduced from the values of the measured magnetic moments. To get greater
certainty on the model selection given the data we used a nested sampler51, 52
to calculate the Bayesian evidence taking into account the structural
information, providing a high degree of confidence in the final fit model as
shown in the SI.

Additional scenarios were also tested. For example, oxidation of the Ni layer
and the formation of Ni-carbide were examined by embedding an intermediate NiO
and Ni2C layer, respectively, at the interface between the Ni and graphene,
but this lead to poorer fits and the best results, shown in Figures 3 and 4,
were achieved using a simpler model: Substrate/a FM layer split into two
regions/graphene (see the modelling methodology in the SI).

The results of the fits to the PNR data are summarised in Table 1.
Interestingly, it is the rotated-domain graphene rather than the epitaxially
grown graphene that has the largest induced magnetic moment, counter to the
initial hypothesis that the coupling between the graphene and Ni(111) would be
weaker in the rotated-domain case. The greater uncertainty in the values of
the moment obtained for the graphene in the epitaxial case can be attributed
to the Bayesian analysis being sensitive to the reduced count time and short
$Q$ range that the epitaxial Ni was measured with, due to finite available
beam time. Both Ni(111) samples have the full Ni moment at 10 K, which is only
slightly reduced at 300 K. This reduction is associated with a magnetic
gradient across the Ni(111) film. In the rotated-domain sample, this gradient,
as shown in Figure 3 (d), starts with a magnetic moment close to the bulk nSLD
of Ni (9.414 x 10${}^{-6}\,$Å-2) and reduces in size towards the surface, and
is required in order to fit the lower $Q$ features and allow the higher $Q$
features to converge, paramount to getting certainty on the thin graphene
layers. The mSLD consequently also has a gradient that oppositely mirrors the
nSLD at 300 K and reaches the full moment for Ni (0.6 $\mu_{B}$/Ni atom
equivalent to an mSLD = 1.4514 x 10${}^{-6}\,$Å-2) near the surface and being
slightly reduced near the substrate. The Ni(111) used for the epitaxial
graphene, displays a much weaker gradient, being almost uniform across the Ni
thickness but has the same general trends. We attribute the origin of the
difference in the nSLD profiles to the fact that the samples were deposited at
different times, following the growth recipe described in the Sample
Preparation section.

The Ni9Mo1 sample was used to clarify whether the induced magnetic moments in
graphene are due to the C pz-3d hybridization which result in opening the
Dirac cone, as postulated in Refs. [23, 2, 28, 18, 20], or because of
electron transfer (spin doping) and surface reconstruction, which distorts the
d band of the TM as for fullerene/non-magnetic TM, as proposed in Refs. [53,
54, 55]. For this purpose, a Ni9Mo1 film was used with the aim of preserving
the fcc crystal structure of Ni while suppressing its magnetization, as
suggested in Ref. [56]. Since the Ni is doped by 10$\%$ only, the lattice
mismatch and bond length to graphene are expected to be similar to that for
graphene/Ni(111) sample, but the d-orbital position is considerably
downshifted with respect to EF. The growth procedure and the structural
properties of the sample is discussed in detail in the Experimental Section.

Figure 5: Ni9Mo1 split into two regions for the graphene/Ni9Mo1 sample. (a) Fresnel reflectivity for 10 K and 300 K, (b) and (c) show the spin asymmetries, (d) is the nuclear scattering length density (nSLD) profile and (e) the magnetic scattering length density (mSLD) profile. Table 1: Summary of the PNR results for the rotated graphene/Ni, epitaxial graphene/Ni and graphene/Ni9Mo1 samples using model 9: sapphire/a FM layer split into two regions/graphene. The values in the parenthesis are the lower and upper 95% Bayesian confidence limits.57 | FM Layer1 + FM layer2 | Graphene
---|---|---
Sample |  Temperature |  Thickness |  Magnetic Moment |  Thickness | Magnetic Moment
|  [K] |  [nm] |  [$\mu_{B}$/atom] |  [nm] | [$\mu_{B}$/atom]
Rotated Gr/Ni |  10 K |  $80.6(80.2,81.3)$ |  $0.60(0.60,0.61)$ |  $0.86(0.81,1.04)$ | $0.53(0.52,0.54)$
300 K |  $0.57(0.56,0.57)$ | $0.53(0.51,0.54)$
Epitaxial Gr/Ni |  10 K |  $77.5(77.1,78.0)$ |  $0.61(0.60,0.61)$ |  $0.92(0.2,1.2)$ | $0.38(0.12,0.50)$
300 K |  $0.579(0.575,0.583)$ | $0.2(0.0,0.5)$
Gr/Ni9Mo1 |  10 K |  $75.0(74.0,76.4)$ |  $0.064(0.056,0.071)$ |  $0.84(0.80,1.00)$ | $0.12(0.07,0.17)$
300 K |  $0.003(-0.004,0.01)$ | $0.02(0.001,0.05)$

The results of the PNR measurements of the graphene/Ni9Mo1 sample are shown in
Figure 5. Again there is a gradient across the Ni9Mo1 film. At 10 K a small,
but detectable spin splitting and a minute variation in the $SA$ are observed.
Surprisingly, a higher magnetization is detected in graphene
($0.12\,(0.07,0.17$) $\mu$B/C atom) than in the Ni9Mo1 film
($0.064\,(0.06,0.07$) $\mu$B/C atom), but the 95% confidence intervals
indicate that we are not sensitive to this to a degree to say for sure given
the Q range and counting statistics in the data. All we can ascertain is that
there is a small moment in the Ni9Mo1 and a non zero moment in the graphene.
At 300 K, both the alloy and the graphene have effectively zero moment within
the 95% confidence intervals. The origin of the small residual moment at 10 K
could arise from clusters of unalloyed Ni throughout the layer that become
ferromagnetic at low temperature, which then polarize the graphene as per the
Ni(111) samples. At 300 K, no magnetic moment in the Ni9Mo1 and graphene are
detected. Therefore, the results support the hypothesis of the universal
model, whereby the measured induced magnetic moment in graphene is due to the
opening of the ED rather than the distortion of the d band. This is because no
magnetic moment is detected in the Ni9Mo1 nor in the graphene layer.

The PNR fits have shown that at 10 K a magnetic moment of $\sim 0.53\,\mu$B/C
atom ($\sim 0.38\,\mu$B/C atom) was induced in the rotated-domain (epitaxial)
graphene grown on Ni films. These results indicate larger moments than
previously reported.26, 13 In Ref. [26], Mertins et al. estimated the
magnetic moment of graphene to be $0.14\pm 0.3\,\mu$B/C atom when its grown on
a hcp Co(0001) film. They obtained this value by comparing the XMCD
reflectivity signal of graphene to that of the underlayer Co film.26 Weser et
al. suggested a similar value ($0.05-0.1\,\mu$B/C atom) for the magnetic
moment induced in a monolayer of graphene grown on a Ni(111) film.13 However,
their assumption was based on comparing the graphene/Ni system with other C/3d
TM structures, such as a C/Fe multilayer with 0.55 nm of C,58 and carbon
nanotubes (CNTs) on a Co film,59 where a magnetic moment of 0.05 $\mu$B/C atom
and 0.1 $\mu$B/C atom was estimated, respectively. Nonetheless, it is
difficult to compare graphene-based heterostructures with other C
allotropes/TM systems. This is because the Dirac cone is a characteristic
feature of graphene and CNTs of the carbon allotropes. Therefore, one cannot
exclude that a different mechanism other than the break of degeneracy around
ED may be responsible for the magnetic moment detected in the C layer of a
C/Fe multilayer system. On the other hand, for the CNTs/Co heterostructure,
although Dirac cones exist in CNTs, a direct quantitative analysis of the
induced magnetic moment was not possible from the MFM images reported in Ref.
[59]. In contrast, PNR provides a direct estimation of the induced magnetic
moment in graphene.

##  III Conclusion

In summary, we have successfully grown graphene by chemical vapor deposition
(CVD) on different TM substrates. Induced magnetic moment in rotated-domain
graphene as a result of the proximity effect in the vicinity of a FM substrate
was detected by element-specific XMCD measurements at the C K-edge. PNR
experiments were carried out to determine the magnitude of the magnetic moment
detected by XMCD. Although a higher magnetic moment was expected to be induced
in epitaxial graphene/Ni sample, the PNR results indicate the epitaxial
graphene film had a magnetic moment of $\sim 0.38\,\mu$B/C atom as compared to
the rotated-domain graphene $\sim 0.53\,\mu$B/C atom. Both values are higher
than those predicted in other studies.13, 58, 59 PNR measurements on
graphene/Ni9Mo1 support the universal model proposed by Voloshina and Dedkov
that the induced magnetic moment in graphene arises as a result of the opening
of the graphene’s Dirac cone as a result of the strong C pz-Ni 3d
hybridization. Our PNR provides the first quantitative estimation of the
induced magnetization in graphene by PNR.

##  IV Experimental Section

###  IV.1 Sample Preparation

The sample preparation procedure involved two stages; the growth of the TM
films using magnetron sputtering and the growth of graphene by CVD.

The TM films were deposited at RT on 1 mm thick Al2O3(0001) substrates using a
CEVP magnetron sputtering chamber with a base pressure of 1.2 - 2 $\times$
10-8 mTorr. The thick substrates were used to reduce the possibility of sample
deformation which could affect the reflectivity measurements. The deposition
of the TM films was performed using 99.9% pure Ni and Ni9Mo1 targets. A DC
current of 0.1 A and a constant flow of pure Argon of 14 sccm were used to
grow 80 nm of highly textured Ni(111) and Ni9Mo1(111) films at a rate of 0.02
nm s-1 in a plasma pressure of 2 mTorr (3 mTorr for Ni9Mo1). Figure 6 shows
the X-ray diffraction (XRD) measurements of the deposited films acquired with
a Bruker D8 Discover HRXRD with a Cu K$\alpha$ monochromatic beam (40 kV, 40
mA). The scans show highly textured pure films oriented in the [111] direction
for Ni and Ni9Mo1 films.

Figure 6: X-ray diffraction measurements (scanning range of 40∘ \- 53∘) of
highly textured films: (a) Al2O3(0001)/Ni(111) and (b)
Al2O3(0001)/Ni9Mo1(111).

The samples were then transferred into a CVD system for the growth of graphene
directly on Ni(111) and Ni9Mo1(111) films on $\sim$ 2 cm $\times$ 2 cm
substrates. Growth recipes similar to those reported by Patera et al. 29 were
adapted to obtain epitaxial and rotated-domain graphene directly on the Ni
film. For the Ni9Mo1 film, rotated-domain graphene was grown by first
introducing pure H2 gas at a rate of 200 sccm to the CVD chamber with a base
pressure of 2.7 $\times$ 10-6 mbar. Then, the CVD growth chamber was heated to
650 ∘C for 12 minutes and the sample was then exposed to C2H4 with a flow rate
of 0.24 sccm and 40 minutes before it was cooled down to RT in vacuum. This
approach reduces any oxidized TM back to a clean metallic surface before the
growth of graphene.

Figure 7: SEM images at 1 kV showing the graphene domains for (a) epitaxial
graphene/Ni and (b) rotated graphene/Ni and (c) The LEED diffraction pattern
of epitaxial graphene on a Ni(111) substrate at 300 eV. The red circle in (b)
highlights a single graphene domain with a diameter of $\sim 0.25\,\mu$m.

The SEM images shown in Figure 7 illustrate the structure of epitaxial and
rotated graphene on Ni with a surface coverage of $\sim 70\%-90$%. Figure 7
(a) shows a homogenous monolayer of graphene on Ni. The darker grey regions in
Figure 7 (b) are the differently oriented graphene domains, whereas the bright
areas in Figure 7 (a) and (b) are the bare Ni film. The low-energy electron
diffraction (LEED) in Figure 7 (c) shows the graphene’s hexagonal pattern
epitaxially grown on the Ni(111) substrate. The ($1\times 1$) grown graphene
structure is confirmed since no additional diffraction spots are observed in
the LEED pattern.

###  IV.2 Raman Spectroscopy Measurements

RT Raman scans were taken at three different regions of each sample using a
532 nm excitation laser wavelength ($50\times$ objective lens and
$\sim\,1\,\mu$m laser spot size). Before the measurements, the graphene was
first transferred by a chemical etching process from the metallic films onto a
Si substrate with a 300 nm thermally oxidized SiO2 layer. This approach
overcome the fact that closely lattice-matched films lead to a loss in the
resonance conditions for observing Raman spectra as a result of the strong
chemical interaction between the graphene $\pi$ orbital and the d-states of Ni
and Ni9Mo1 which also alters the graphene’s pz orbitals. Furthermore, the
increase in the C$-$C bond length to match the lattice of the FM leads to
significant changes in the graphene’s phonon spectrum.22, 60 For the transfer
process, the samples were cleaved into $\sim$ 5 mm $\times$ 5 mm squares and
HNO3, diluted to 5% for Ni9Mo1 and 10% for Ni, was used to etch the metallic
films slowly while preserving the graphene layer.

###  IV.3 X-ray Magnetic Circular Dichroism (XMCD)

We carried out element selective XMCD measurements to detect and distinguish
the magnetization in the graphene from that of the FM layer. The XMCD
experiments were performed at 300 K at the SIM end station of the Swiss Light
Source (SLS) at the Paul Scherrer Institut (PSI), Switzerland, using total
electron yield (TEY) detection mode with 100% circularly polarized light. The
rotated-domain graphene/Ni sample was set to an incident angle of 30∘ from the
incoming X-ray beam. An electromagnet was fixed at 40∘ 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 magnetization along the beam
direction. It was then reduced to 0.085 T during the X-ray absorption
spectroscopy measurements. The intensity of the incident X-ray beam was
measured with a clean, carbon free, gold mesh placed just before the sample
position. This is particularly important for normalizing the signal at the C
K-edge due to the presence of carbon on the surface of the X-ray optical
components.

###  IV.4 Polarized Neutron Reflectivity

The PNR measurements were conducted at 10 K and 300 K, under an in-plane
magnetic field of 0.5 T, using the Polref instrument at ISIS spallation
neutron source (UK). The fitting of the data was done using the Refl1D 61
software package with preliminary fits done in GenX.62 Although Ni is
ferromagnetic at RT, the 10 K measurements are expected to provide a better
estimation of the induced magnetic moment due to the lower thermal excitations
of the electron spin at low temperature. Both the 10 K and 300 K data sets
were fitted simultaneously to provide further constraint to the fits. This is
analogous to the isotropic contrast matching 63, 64 used in soft matter
neutron reflectivity experiments. This is very important in this case due to
the attempt to measure a thin layer of graphene within a limited total Q range
for PNR. The PNR is sensitive to only part of the broad fringe from the
graphene layer which acts as an envelope function on the higher frequency
fringes from the thicker Ni layer underneath (the modelling methodology is
discussed in detail in the SI).

Acknowledgements

We would like to thank the ISIS Neutron and Muon Source for the provision of
beam time (RB1510330 and RB1610424). The data is available at the following
DOIs https://doi.org/10.5286/ISIS.E.RB1510330 and
https://doi.org/10.5286/ISIS.E.RB1610424. Part of this work was performed at
the Surface and Interface Microscopy (SIM) beamline of the Swiss Light Source
(SLS), Paul Scherrer Institut (PSI), Villigen, Switzerland.

Other data presented in this study are available from the corresponding author
upon request.

## References

  * Karpan  _et al._ [2007] V. M. Karpan, G. Giovannetti, P. A. Khomyakov, M. Talanana, A. A. Starikov, M. Zwierzycki, J. van den Brink, G. Brocks, and P. J. Kelly, Physical Review Letters 99 (2007).
  * Weser  _et al._ [2011] M. Weser, E. N. Voloshina, K. Horn, and Y. S. Dedkov, Physical Chemistry Chemical Physics 13, 7534 (2011).
  * Zhang  _et al._ [2015] J. Zhang, B. Zhao, Y. Yao, and Z. Yang, Scientific Reports 5, 1 (2015).
  * Högl  _et al._ [2020] P. Högl, T. Frank, K. Zollner, D. Kochan, M. Gmitra, and J. Fabian, Physical Review Letters 124, 136403 (2020).
  * Meng  _et al._ [2013] J. Meng, J. J. Chen, Y. Yan, D. P. Yu, and Z. M. Liao, Nanoscale 5, 8894 (2013).
  * Song and Dai [2015] Y. Song and G. Dai, Applied Physics Letters 106 (2015).
  * Xu  _et al._ [2018] J. Xu, S. Singh, J. Katoch, G. Wu, T. Zhu, I. Žutić, and R. K. Kawakami, Nature Communications 9, 2 (2018).
  * Hill  _et al._ [2006] E. W. Hill, A. K. Geim, K. Novoselov, F. Schedin, and P. Blake, IEEE Transactions on Magnetics 42, 2694 (2006).
  * Semenov  _et al._ [2007] Y. G. Semenov, K. W. Kim, and J. M. Zavada, Applied Physics Letters 91, 153105 (2007).
  * Sze and Ng [2006] S. M. Sze and K. K. Ng,  _Physics of Semiconductor Devices_ (Wiley, 2006).
  * Pi  _et al._ [2010] K. Pi, W. Han, K. M. McCreary, A. G. Swartz, Y. Li, and R. K. Kawakami, Physical Review Letters 104, 187201 (2010).
  * Zhang  _et al._ [2018] Y. Zhang, X. Sui, D. L. Ma, K. K. Bai, W. Duan, and L. He, Physical Review Applied 10, 1 (2018).
  * Weser  _et al._ [2010] M. Weser, Y. Rehder, K. Horn, M. Sicot, M. Fonin, A. B. Preobrajenski, E. N. Voloshina, E. Goering, and Y. S. Dedkov, Applied Physics Letters 96, 012504 (2010).
  * Leutenantsmeyer  _et al._ [2016] J. C. Leutenantsmeyer, A. A. Kaverzin, M. Wojtaszek, and B. J. van Wees, 2D Materials 4, 014001 (2016).
  * Wang  _et al._ [2015] Z. Wang, C. Tang, R. Sachs, Y. Barlas, and J. Shi, Physical Review Letters 114, 016603 (2015).
  * Haugen  _et al._ [2008] H. Haugen, D. Huertas-Hernando, and A. Brataas, Physical Review B 77, 115406 (2008).
  * Tuan and Roche [2016] D. V. Tuan and S. Roche, Physical Review Letters 116, 106601 (2016).
  * Dedkov and Voloshina [2015] Y. Dedkov and E. Voloshina, Journal of Physics: Condensed Matter 27, 303002 (2015).
  * Fal’ko [2007] V. Fal’ko, Nature Physics 3, 151 (2007).
  * Voloshina and Dedkov [2014] E. N. Voloshina and Y. S. Dedkov, Materials Research Express 1 1, 035603 (2014).
  * Voloshina and Dedkov [2011] E. Voloshina and Y. Dedkov, in  _Physics and Applications of Graphene - Experiments_, Vol. 499 (InTech, 2011) pp. 75–78.
  * Dahal and Batzill [2014] A. Dahal and M. Batzill, Nanoscale 6, 2548 (2014).
  * Dedkov and Fonin [2010] Y. S. Dedkov and M. Fonin, New Journal of Physics 12, 125004 (2010).
  * Vita  _et al._ [2014] H. Vita, S. Böttcher, P. Leicht, K. Horn, A. B. Shick, and F. Máca, Physical Review B \- Condensed Matter and Materials Physics 90, 1 (2014).
  * Marchenko  _et al._ [2015] D. Marchenko, A. Varykhalov, J. Sánchez-Barriga, O. Rader, C. Carbone, and G. Bihlmayer, Physical Review B \- Condensed Matter and Materials Physics 91, 1 (2015).
  * Mertins  _et al._ [2018] H. C. Mertins, C. Jansing, M. Krivenkov, A. Varykhalov, O. Rader, H. Wahab, H. Timmers, A. Gaupp, A. Sokolov, M. Tesch, and P. M. Oppeneer, Physical Review B 98, 1 (2018).
  * Mendes  _et al._ [2019] J. B. Mendes, O. Alves Santos, T. Chagas, R. Magalhães-Paniago, T. J. Mori, J. Holanda, L. M. Meireles, R. G. Lacerda, A. Azevedo, and S. M. Rezende, Physical Review B 99, 1 (2019).
  * Karpan  _et al._ [2008] V. M. Karpan, P. A. Khomyakov, A. A. Starikov, G. Giovannetti, M. Zwierzycki, M. Talanana, G. Brocks, J. van den Brink, and P. J. Kelly, Physical Review B 78, 195419 (2008).
  * Patera  _et al._ [2013] L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, ACS nano , 7901 (2013).
  * Weatherup  _et al._ [2014] R. S. Weatherup, H. Amara, R. Blume, B. Dlubak, B. C. Bayer, M. Diarra, M. Bahri, A. Cabrero-Vilatela, S. Caneva, P. R. Kidambi, M. B. Martin, C. Deranlot, P. Seneor, R. Schloegl, F. Ducastelle, C. Bichara, and S. Hofmann, Journal of the American Chemical Society 136, 13698 (2014).
  * Kozlov  _et al._ [2012] S. M. Kozlov, F. Viñes, and A. Görling, Journal of Physical Chemistry C 116, 7360 (2012).
  * Wang  _et al._ [2008] Y. Y. Wang, Z. H. Ni, Z. X. Shen, H. M. Wang, and Y. H. Wu, Applied Physics Letters 92 (2008), 10.1063/1.2838745, arXiv:0801.4595 .
  * Chilres  _et al._ [2013] I. Chilres, L. A. Jauregui, W. Park, H. Cao, and Y. P. Chen, in  _New Developments in Photon and Materials Research_, edited by J. I. Jang (Nova Science Publishers, Incorporated, 2013) Chap. 19, pp. 553–595.
  * Reina  _et al._ [2008] A. Reina, H. Son, L. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, The Journal of Physical Chemistry C 112, 17741 (2008).
  * Malard  _et al._ [2009] L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, Physics Reports 473, 51 (2009).
  * Ferrari and Basko [2013] A. C. Ferrari and D. M. Basko, Nature Nanotechnology 8, 235 (2013).
  * Cabrero-Vilatela  _et al._ [2016] A. Cabrero-Vilatela, R. S. Weatherup, P. Braeuninger-Weimer, S. Caneva, and S. Hofmann, Nanoscale 8, 2149 (2016).
  * Martin  _et al._ [2015] M.-B. Martin, B. Dlubak, R. S. Weatherup, M. Piquemal-Banci, H. Yang, R. Blume, R. Schloegl, S. Collin, F. Petroff, S. Hofmann, J. Robertson, A. Anane, A. Fert, and P. Seneor, Applied Physics Letters 107, 012408 (2015).
  * Dlubak  _et al._ [2012] B. Dlubak, M.-B. Martin, R. S. Weatherup, H. Yang, C. Deranlot, R. Blume, R. Schloegl, A. Fert, A. Anane, S. Hofmann, P. Seneor, and J. Robertson, ACS nano 6, 10930 (2012).
  * O’Brien and Tonner [1994] W. L. O’Brien and B. P. Tonner, Physical Review B 50, 12672 (1994).
  * Eriksson  _et al._ [1992] O. Eriksson, A. M. Boring, R. C. Albers, G. W. Fernando, and B. R. Cooper, Physical review. B, Condensed matter 45, 2868 (1992).
  * O’Brien  _et al._ [1994] W. L. O’Brien, B. P. Tonner, G. R. Harp, and S. S. P. Parkin, Journal of Applied Physics 76, 6462 (1994).
  * Eriksson  _et al._ [1990] O. Eriksson, B. Johansson, R. C. Albers, A. M. Boring, and M. S. S. Brooks, Physical Review B 42, 2707 (1990).
  * Vaz  _et al._ [2008] C. Vaz, J. Bland, and G. Lauhoff, Reports on Progress in Physics 71, 056501 (2008).
  * Nakajima  _et al._ [1999] R. Nakajima, J. Stöhr, and Y. U. Idzerda, Physical Review B 59, 6421 (1999).
  * Chen  _et al._ [1990] C. T. Chen, F. Sette, Y. Ma, and S. Modesti, Physical Review B 42, 7262 (1990).
  * Söderlind  _et al._ [1992] P. Söderlind, O. Eriksson, B. Johansson, R. C. Albers, and A. M. Boring, Physical Review B 45, 12911 (1992).
  * Menezes  _et al._ [2017] N. Menezes, V. S. Alves, E. C. Marino, L. Nascimento, L. O. Nascimento, and C. Morais Smith, Physical Review B 95, 1 (2017).
  * Song  _et al._ [2010] Y. J. Song, A. F. Otte, Y. Kuk, Y. Hu, D. B. Torrance, P. N. First, W. A. De Heer, H. Min, S. Adam, M. D. Stiles, A. H. MacDonald, and J. A. Stroscio, Nature 467, 185 (2010).
  * Semenikhin  _et al._ [2020] P. V. Semenikhin, A. N. Ionov, and M. N. Nikolaeva, Technical Physics Letters 46, 186 (2020).
  * Skilling [2004] J. Skilling, AIP Conference Proceedings 735, 395 (2004), https://aip.scitation.org/doi/pdf/10.1063/1.1835238 .
  * McCluskey  _et al._ [2020] A. R. McCluskey, J. F. K. Cooper, T. Arnold, and T. Snow, Machine Learning: Science and Technology 1, 035002 (2020).
  * Ma’Mari  _et al._ [2015] F. A. Ma’Mari, T. Moorsom, G. Teobaldi, W. Deacon, T. Prokscha, H. Luetkens, S. Lee, G. E. Sterbinsky, D. A. Arena, D. A. MacLaren, M. Flokstra, M. Ali, M. C. Wheeler, G. Burnell, B. J. Hickey, and O. Cespedes, Nature 524, 69 (2015).
  * Pai  _et al._ [2010] W. W. Pai, H. T. Jeng, C. M. Cheng, C. H. Lin, X. Xiao, A. Zhao, X. Zhang, G. Xu, X. Q. Shi, M. A. Van Hove, C. S. Hsue, and K. D. Tsuei, Physical Review Letters 104, 1 (2010).
  * Moorsom  _et al._ [2014] T. Moorsom, M. Wheeler, T. Mohd Khan, F. Al Ma’Mari, C. Kinane, S. Langridge, D. Ciudad, A. Bedoya-Pinto, L. Hueso, G. Teobaldi, V. K. Lazarov, D. Gilks, G. Burnell, B. J. Hickey, and O. Cespedes, Physical Review B - Condensed Matter and Materials Physics 90, 1 (2014).
  * Hansen  _et al._ [1958] M. Hansen, R. P. Elliott, and F. A. Shunk,  _Constitution of Binary Alloys_ (McGraw-Hill, New York, 1958) p. 1305.
  * Kienzle  _et al._ [2011] P. Kienzle, J. Krycka, N. Patel, and I. Sahin, https://bumps.readthedocs.io/en/latest/ (2011), accessed: (28-09-2021).
  * Mertins  _et al._ [2004] H.-C. Mertins, S. Valencia, W. Gudat, P. M. Oppeneer, O. Zaharko, and H. Grimmer, Europhysics Letters (EPL) 66, 743 (2004).
  * Céspedes  _et al._ [2004] O. Céspedes, M. S. Ferreira, S. Sanvito, M. Kociak, and J. M. D. Coey, Journal of Physics: Condensed Matter 16, L155 (2004).
  * Allard and Wirtz [2010] A. Allard and L. Wirtz, Nano Letters 10, 4335 (2010).
  * Kienzle  _et al._ [2017] P. Kienzle, B. Maranville, K. O’Donovan, J. Ankner, N. Berk, and C. Majkrzak, https://www.nist.gov/ncnr/reflectometry-software (2017), accessed: (28-09-2021).
  * Björck and Andersson [2007] M. Björck and G. Andersson, Journal of Applied Crystallography 40, 1174 (2007).
  * Majkrzak  _et al._ [2003] C. F. Majkrzak, N. F. Berk, and U. A. Perez-Salas, Langmuir 19, 7796 (2003).
  * Koutsioubas [2019] A. Koutsioubas, Journal of Applied Crystallography 52, 538 (2019).