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Author(s):
Lehtinen, P. O. & Foster, Adam S. & Ayuela, A. & Krasheninnikov, A.
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Title:
Magnetic Properties and Diffusion of Adatoms on a Graphene Sheet
Year: 2003
Version: Final published version
Please cite the original version:
Lehtinen, P. O. & Foster, Adam S. & Ayuela, A. & Krasheninnikov, A. & Nordlund, K. &
Nieminen, R. M.. 2003. Magnetic Properties and Diffusion of Adatoms on a Graphene
Sheet. Physical Review Letters. Volume 91, Issue 1. 017202/1-4. ISSN 0031-9007
(printed). DOI: 10.1103/physrevlett.91.017202.
Rights: © 2003 American Physical Society (APS). This is the accepted version of the following article: Lehtinen, P.
O. ; Foster, Adam S. ; Ayuela, A. ; Krasheninnikov, A. ; Nordlund, K. ; Nieminen, R. M.. 2003. Magnetic
Properties and Diffusion of Adatoms on a Graphene Sheet. Physical Review Letters. Volume 91, Issue 1.
017202/1-4. ISSN 0031-9007 (printed). DOI: 10.1103/physrevlett.91.017202, which has been published in
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Magnetic Properties and Diffusion of Adatoms on a Graphene Sheet
P. O. Lehtinen,
1
A. S. Foster,
1
A. Ayuela,
1
A. Krasheninnikov,
2
K. Nordlund,
2
and R. M. Nieminen
1
1
Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, 02015, Finland
2
Accelerator Laboratory, University of Helsinki, P.O. Box 43, FIN-00014 Helsinki, Finland
(Received 22 January 2003; published 30 June 2003)
We use ab initio methods to calculate the properties of adatom defects on a graphite surface. By
applying a full spin-polarized description to the system we demonstrate that these defects have a
magnetic moment of about 0:5
B
and also calculate its role in diffusion over the surface. The magnetic
nature of these intrinsic carbon defects suggests that it is important to understand their role in the
recently observed magnetism in pure carbon systems.
DOI: 10.1103/PhysRevLett.91.017202 PACS numbers: 75.75.+a, 68.43.Bc, 75.70.Rf
As the techniques for growth and preparation of carbon
nanostructures have developed, the list of feasible appli-
cations has seen rapid increases [1,2]. However, concur-
rent to this growth of technological possibilities has been
an increase in the demand for atomic-scale understanding
of the processes which determine carbon nanostructure
properties. Studies of radiation effects [3] in graphite
and other carbon nanostructures and experiments on as-
grown nanotubes [4,5] have demonstrated that intrinsic
carbon defects are a common phenomenon in standard
samples. Understanding the properties of these defects
has become an essential part of such diverse processes in
carbon materials such as strain [6], lithium storage in
nanotube based batteries [7], catalytic growth [8], junc-
tions [9], and quantum dot creation [5,10]. Possibly even
more importantly, the recent experimental demonstra-
tions of magnetism in pure carbon systems [11–15]
have ignited speculation that carbon could offer the tan-
talizing prospect of a zero-gap, high-temperature, ferro-
magnetic semiconductor. Several studies have speculated
that intrinsic carbon defects could be responsible for the
observed magnetic properties [11]. Experimentally the
role of these defects is just being explored [16], yet theo-
retical analysis lags somewhat behind.
One of the most common defects to be created is the
carbon vacancy-adatom pair [3], and therefore it is im-
portant to study the influence this kind of defect will have
on the surface physical and electronic structure. For ex-
ample, defect evolution is mainly determined by the
mobility of vacancies and interstitials at the surface.
Defects either disappear by recombination with defects
of opposite character or cluster with defects of similar
character, and the temperature dependence of these pro-
cesses is determined by defect mobility. From experi-
ments, in general the adatom is expected to be much
more mobile in the bulk and at the surface [3] than the
vacancy, and therefore its mobility is the rate determining
factor. Hence, for example, knowledge of adatom migra-
tion properties is crucial in nanotube growth processes
[8]. Some previous first principle theoretical studies have
considered adsorption [8,17] and diffusion [18] of a car-
bon adatom on a graphene sheet, yet the results were
markedly different, and none of them fully implemented
the generalized gradient approximation (GGA), known to
provide better accuracy for studying surface adsorption
and diffusion [19,20]. Also, none of these studies system-
atically considered the influence of the spin density prop-
erties of the adsorbed adatom. In this Letter we study the
adsorption energy and diffusion of carbon adatoms on a
graphene sheet using first principles techniques and
demonstrate that these defects are highly mobile and
magnetic.
All the calculations have been performed using the
plane wave basis
VASP [21,22] code, implementing the
spin-polarized density functional theory (DFT) and
the GGA of Perdew and Wang [23] known as PW91. We
have used projector augmented wave (PAW) potentials
[24,25] to describe the core (1s
2
) electrons, with the 2s
2
and 2p
2
electrons of carbon considered as valence elec-
trons. A kinetic energy cutoff of 400 eV was found to
converge the total energy of our systems to within meV.
All calculations were also converged to meV in total
energy with respect to the k-point sampling of the
Brillouin zone. To determine the applicability of this
method to study carbon based systems we initially
studied bulk graphite and diamond using both the PAW
and the more standard ultrasoft pseudopotential (UPP)
methods. We found no significant difference between
PAW and UPP, and both gave excellent agreement with
experimentally determined structural parameters for
both graphite and diamond. This gave us confidence that
VASP and the PAW method are reliable and flexible enough
to move to more complex carbon systems.
Initially calculations with the single graphite layer
were made using a 50 atom slab, but all properties were
also tested with larger 72 and 98 atom slabs. A single
layer of graphite provides both a good model of the
graphite surface, since the interactions between layers
are only weak van der Waals, and a good model of a
nanotube surface due to the similarity in bonding [6,8].
For the 50 atom slab the total energy was converged to
meV with a Monkhorst-Pack [26] k-point mesh of 3
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3 1 ( included), and a distance between slab images of
18.3 A
˚
. The adatom was initially positioned over an
asymmetric position on the surface, and the whole system
was allowed to relax fully. The diffusion paths were
calculated in a static approximation using the nudged
elastic band method [27,28].
The equilibrium position (Fig. 1) of the adatom was
found to be in a bridgelike structure, between two surface
carbon atoms. This geometry is similar to previous local
density approximation (LDA) calculations [8,17,18] on a
similar surface. The perpendicular distance of the adatom
to the graphite surface is 1.87 A
˚
. The adsorption energy of
the defect was found by moving the adatom far from the
surface until total energy convergence, and once again
fully relaxing the surface to find the difference in energy.
Note that the ground state for the isolated carbon atom is
a triplet state, and we use this as a reference for our
adsorption energies (to compare with adsorption energies
referenced to the singlet state, 1.26 eV should be added to
the values). The adsorption energy was found to be1.40 eV
(1.37 eV for the 72 atom slab). This is similar to the 1.2 eV
[18] and 1.78 eV [8] found in finite cluster LDA studies,
but smaller, even when comparing with the singlet refer-
ence adsorption energy of 2.66 eV, than the 3.30 eV found
in previous periodic LDA works [17]. We also considered
adsorption of an adatom directly on top of a surface
carbon and found this to be over 1.0 eV higher in energy
than the bridge structure.
In contrast to previous studies, we used fully spin-
polarized DFT in our calculations and found that the
ground state for the adsorbed adatom has a magnetic
moment of 0:45
B
. Earlier finite cluster LDA calculations
[18] also found a magnetic ground state for an adatom
adsorbed on graphite, but they considered only a triplet
solution, rather than the full unrestricted spin solution.
If we restrict our system to zero spin ground state only
(S 0), then the total energy is 35.5 meV higher than the
magnetic configuration. Figure 2(a) shows clearly that the
spin-polarized density occupies p orbitals of the adatom.
The magnetic properties of the C adatom on graphene can
be explained via a simple counting argument. Both the
two bonded atoms on the surface, as well as the adatom,
present a different hybridization: the surface atoms at-
tached to the adatom have a sp
2
-sp
3
hybridization while
the adatom stays sp
2
like, as seen in the model of Fig. 2(b).
Concerning the adatom, the counting of the four carbon
electrons is as follows: two electrons participate in the
covalent bond with the graphene carbons. From the two
remaining electrons, one goes to the dangling sp
2
bond,
and another is shared between the sp
2
bond and the p
z
orbital. This p
z
orbital is orthogonal to the surface
orbitals due to symmetry and cannot form any bands,
remaining localized and therefore spin polarized. The
dangling sp
2
bond will also probably be very slightly
spin polarized, but this effect is negligibly small and
cannot be seen in Fig. 2(a). Recent results on other sur-
faces [29–31] demonstrated that this behavior is typical
for low-dimensional systems. The half electron of the p
z
orbital provides the magnetization of around 0:5
B
.In
addition the sp
2
-sp
3
hybridization of the graphene carbon
linked to the adatom decides the adsorption energetics
of the adatom. Hence this counting discussion would
be also relevant for the energetics in nanotubes, where
the sp
2
-sp
3
hybridization, although influenced by
tube curvature, would again determine the adsorption
energies [32].
We want to point out that the magnetic state is not
dependent on the size of the cell, since it is consistently
the ground state for the 50, 72, and 98 atom slabs. We can
also consider how the difference between paramagnetic
FIG. 1. The adatom equilibrium bridgelike position (0) and
the diffusion path (0 –9) from the (a) top and the (b) side. The
arrows mark the magnetic transition point where the magnetic
moment vanishes.
FIG. 2 (color). (a) The spin density in e=
A
3
of a plane normal
to the surface through the center of the adatom when the
adatom is at the equilibrium position. The adatom is at (0,0).
(b) A schematic diagram of the bond orbitals at the equilibrium
position in a plane through the adatom and the two surface
carbons. Note that this schematic is a projection, and that the
blue p orbital is orthogonal to the adatom-surface bonds.
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(S 0) and ferromagnetic energies varies as a function of
the cell size. When increasing the cell size, the difference
oscillates, with a variation larger than the coupling in
metallic multilayers [33], typically of the order of
few meV. This oscillatory behavior points to a RKKY
interaction [33] between the adatoms via the graphene
surface. In the range of sizes where we are working (50–
98 atoms), the zero coupling limit has not been reached
yet, which indicates that the defects with a surface con-
centration of around 1% are still coupled. Although fur-
ther calculations are needed in order to refine this issue,
the ferromagnetic-paramagnetic energy difference can be
ascribed to a Curie temperature of 100– 200 K.
The adatom diffusion path is an almost straight line
between equivalent sites bridging two surface carbon
atoms. Figure 1 shows that the minimum energy path is
slightly shifted into the interstitial space in the surface
and also slightly nearer the surface than the equilibrium
site. The spin-polarized diffusion barrier (see Fig. 3) is
0.47 eV. This result contrasts with Heggie et al. [18] who,
using LDA and a finite cluster, predicted a diffusion path
via an on-top site, with a barrier of only 0.1 eV. Note that
the migration energy in bulk graphite may also contain
contributions from other diffusion processes due to the
presence of a ‘‘surface’’ on either side of the adatom.
However, diffusion through the graphene layer, even via
an interstitialcy mechanism, is predicted to have a barrier
of over 4 times the value we predict for in-plane diffusion
[3], hence migration along the graphene plane will domi-
nate. During the diffusion the magnetic moment vanishes
and this point is marked with an arrow in Fig. 1, and it
occurs at position 3 in Fig. 3. The spin density at this point
is 5 orders of magnitude smaller than for the equilibrium
position— effectively zero. To check that the transition
from magnetic to nonmagnetic configuration was not an
artifact, we reran positions 3 and 4 directly with a large
initial magnetic ‘‘kick.’’ In both cases the nonmagnetic
configuration remained the ground state.
When considering the transition state of the diffusion,
the simple counting argument discussed previously must
be modified. Electron counting would predict a magnetic
moment of 1
B
, while the calculations show no spin
polarization. At the transition point the adatom has
only one direct bond to the surface and the hybridization
changes to sp like. This means there is now two free p
orbitals into which the extra electron goes and they are
also free to align with the surface orbitals forming
bands. The result is a much more delocalized density
and the magnetism is destroyed. The ground state during
diffusion is once again magnetic at position 7, as the
adatom moves to an equivalent bridgelike adsorption
site at position 9. The spin restricted diffusion barrier
was only 0.43 eV, although the diffusion path remains
very similar. In both cases we see that the predicted
diffusion barriers are small, and, as expected from ex-
periments [3], adatoms are highly mobile on the surface.
The physical consequences of the magnetic nature of
this defect for the adsorption and diffusion processes
are not huge — changes of only tenths of an eV between
magnetic and nonmagnetic cases. However, the fact that
this common intrinsic carbon defect is magnetic suggests
that it is highly probable that it plays a role in the
magnetism observed experimentally in several pure car-
bon systems [11,13,14]. In these experiments great
care was taken to eliminate magnetic impurities from
the system, yet residual magnetism was observed.
Speculation was made that intrinsic carbon defects could
be responsible, and here we have shown that a specific
intrinsic carbon defect is magnetic.
The nature of these defects means that they are readily
accessible to detection by magnetic experimental tech-
niques such as electron spin resonance (ESR). The lines of
the ESR spectra will originate from the nuclear spin in
carbon, and further structure will appear as extra lines,
probably around the first and above the last lines in the
spectra. These
13
C ESR satellite spectra may contain
information about the adatom interaction with the gra-
phene. In an effort to make some predictions with regard
to possible signals generated by these defects we have
applied the Karplus-Fraenkel relation [34,35]. We first
integrated the spin density in spheres of increasing radii
around the relevant atoms. In the adatom the magnetiza-
tion increases until it saturates to the cell value. Around
the nearest carbons to the adatom, the magnetization
shows a negative minimum around 0.7 A
˚
, close to
half the distance to the adatom, followed by a sharp
increase due to contributions from the adatom. This mini-
mum corresponds to a negative spin polarization with
respect to the adatom, i.e., they are antiferromagnetically
coupled, although the polarization values are very small.
This follows the trends found in magnetic semiconductors
[36]. From these values we can then estimate a rough
FIG. 3. Calculated energy barrier for diffusion of the adatom
in the spin-polarized and the spin restricted case (S 0). The
data points are fitted with a cubic spline.
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picture for the hyperfine coupling constant. Using a sp
2
interpretation, the calculated hyperfine coupling con-
stants a
c
are 2.32 and 2:02 G for the adatom and its
nearest neighbors, respectively. In addition, as the adatom
and next neighbor atoms are in a ratio of 1:2, the signal
change with the temperature will follow the same
proportion.
The possibility of identifying and controlling the mag-
netic properties of carbon systems via careful preparation
seems within grasp. The high mobility of the adatoms
means that at high temperatures they should be more or
less immediately annihilated by recombination, and their
magnetic influence should be removed. Also, the calcu-
lations predict that the adatoms will diffuse as nonmag-
netic species, only becoming magnetic at the equilibrium
position. However, some clustering of adatoms is likely to
occur, pinning the adatoms and producing some residual
magnetism even at high temperatures. The exact magnetic
nature of adatom clusters is not immediately clear,
although it has been shown that Al adatoms retain their
magnetism even for an infinite chain [30]. Further studies
of the magnetic properties of larger defect clusters are in
progress.
This work is supported by the Academy of Finland
through its Centers of Excellence Program (2000 –2005).
We are grateful to the Center for Scientific Computing,
Espoo, for use of its computational resources. The
LEV00
code [37] was used for the calculation of density maps.
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