Chemical Physics Letters 541 (2012) 70–74
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Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Magnetism in graphene induced by hydrogen adsorbates
Željko Šljivančanin a,⇑, Richard Balog b, Liv Hornekær b
a
b
Vinča Institute of Nuclear Sciences (020), RS-11001 Belgrade, Serbia
Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, DK-8000 Aarhus C, Denmark
a r t i c l e
i n f o
Article history:
Received 31 January 2012
In final form 11 May 2012
Available online 1 June 2012
a b s t r a c t
Applying density functional theory we studied magnetism in partially hydrogenated graphene. We
demonstrated that the difference in the number of H atoms adsorbed on two graphene sublattices g
can be used as a parameter to predict stability of hydrogen structures on graphene. All favorable structures with even number of H atoms are non-magnetic, with g equal to zero. Favorable structures with
odd number of H adsorbates have g equal to one, giving rise to a total magnetic moment of 1 lB . Structures with higher g, including recently proposed graphone, are thermodynamically unfavorable and
kinetically unstable at room temperature.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
After isolation of a single graphene layer in 2004 [1] the investigation of fundamental physical and chemical properties, as well
as possible technological applications of this truly two-dimensional material has become one of the main topics in nanoscience
and nanotechnology [2–5]. Most of the research efforts have been
focused on electronic properties of graphene with the aim of using
graphene as a key material in fast post silicon nanoelectronics.
However, the direct application of graphene as field-effect transistor requires the opening of a finite band-gap. The most promising
strategies include cutting graphene into nanoribbons [6,7] and
graphene hydrogenation [8]. The prospects of engineering magnetism in graphene-based materials [5,9,10,6] open another research
topic highly relevant for possible technological applications since
understanding of fundamental magnetic properties in systems
without d and f electrons is expected to facilitate design of novel
magnetic and spintronic devices. Experimental characterization
and manipulation of graphene is however extremely challenging,
which creates tremendous difficulties in tailoring graphene’s properties towards desired functionalities. Therefore experimental
results on magnetism in graphene are still rather scarce. Only
recently Wang et al. [11] measured magnetization hysteresis loops
in graphene samples and observed room-temperature ferromagnetism. The dominant presence of ferromagnetism in graphene samples is also reported in experiments of Matte et al. [12].
Ideal graphene is a two-dimensional non-magnetic crystal with
two carbon atoms, Ca and Cb, in the basis. According to Lieb’s
theorem [13], in a bipartite lattice any imbalance in number of sites
belonging to each of two sublattices leads to a magnetic ground
⇑ Corresponding author.
E-mail address: [email protected] (Ž. Šljivančanin).
0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.cplett.2012.05.043
state. Hence, the observed magnetism in graphene is attributed to
the presence of impurities, edges or structural defects which
produce such an imbalance [14,5,9]. In several recent computational studies it has been demonstrated that chemisorption of H
atoms leads to the magnetism in graphene [9,15,16]. The adsorption
of a single hydrogen atom gives rise to quasi-localized states in
vicinity of the adsorbate, accompanied with a magnetic moment
of 1 lB [9]. The magnetic properties of H dimers adsorbed on graphene have been thoroughly investigated by computational methods
based on density functional theory (DFT) [15–17]. Non-vanishing
spin density is observed only when both H atoms are adsorbed on
the same graphene sublattice. The calculated magnetic moment of
2 lB is in full agreement with Lieb’s theorem. However, several recent experimental and theoretical investigations of H dimers on
graphite or graphene [18,19,15,16,10,20] have identified ortho(O-) and para-dimers (P-dimers) as the two most stable diatomic
H configurations on these substrates. They are nearly degenerate
in energy and both are non-magnetic with H atoms chemisorbed
on C sites belonging to the two different sublattices. Combining
scanning tunneling microscopy (STM) with DFT calculations we
previously demonstrated that other dimer structures observed in
experiments were also non-magnetic [20]. In all these configurations g is equal to zero. The magnetic structures with both H atoms
chemisorbed on the same sublattice, and thus non-zero g are considerably less favorable. Similarly, DFT studies show that the most
stable clusters with four or six H adatoms on graphene are also
non-magnetic [17]. Small clusters containing an odd number of H
adsorbates have also been studied. DFT calculations show that
favorable trimer and pentamer structures induce in the graphene
lattice a total magnetic moment of only 1 lB per cluster. Yet, in a recent Letter Zhou et al. [21] predicted the existence of a new stable
graphene-based material, graphone, with ferromagnetic properties.
This hypothetical two-dimensional material was proposed as a
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Ž. Šljivančanin et al. / Chemical Physics Letters 541 (2012) 70–74
(a)
0.50
1.15
M=2
0.00
M=0
0.00
M=1
0.43
(b)
1.70
M=3
Figure 1. Selected configurations of H dimers (a) and trimers (b) on graphene, together with the values of their total magnetic moment M given in lB . The structures with
high M (left panels) transform to more stable ones with lower M (right panels) by diffusion of H atoms. The total energies (relative to the energies of more favorable
structures) and the activation energies along the corresponding transition paths are presented in the middle panels. The H and C atoms are depicted as blue and gray spheres,
respectively. All energies are in eV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(a)
(c)
(b)
0.43
2.00
0.00
Figure 2. (a) Graphone and (c) the structure formed after diffusion of the H atom (indicated by the red arrow) to the neighboring C site. (b) The activation energy for H
diffusion, and the relative energies (in eV) of two configurations. The surface unit cell used in the calculations is marked by black rhombuses. The color coding of atoms is the
same as in Figure 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(a )
(e)
(b)
(c)
(d)
2.00
3.76
6.36
Figure 3. (a) Graphone and the structures formed after diffusion to the neighboring C sites of (b) one, (c) three and (d) eight H atom within the super cell; (e) the schematic
plot of their relative total energies (in eV per super cell). The surface unit cell used in the calculations is marked by black rhombuses. The color coding of atoms is the same as
in Figure 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
stable form of hydrogenated graphene. Graphone is a semi-hydrogenated realization of graphene having every Ca-atom (or equivalently every Cb-atom) throughout the sheet covered by a hydrogen
atom. It is described as a semiconductor with a small indirect band
gap. The fully hydrogenated graphene in which both carbon atoms
are covered by hydrogen is termed graphane and is a well-described
Ž. Šljivančanin et al. / Chemical Physics Letters 541 (2012) 70–74
2. Methods
Our calculations were done using the ultrasoft pseudopotentials
[27,28] and supercell approach, as implemented in the DACAPO code
[29,30]. The electron wave functions and augmented electron density were expanded in plane waves with cutoff energies of 25 and
140 Ry, respectively. For the exchange–correlation functional we
used the GGA-PW91 form [31]. The structure and total energies
of H clusters with one, two and three atoms were calculated by
modeling the surface with rhombohedral, periodically repeated
graphene sheets having a 6 6 surface unit cell with 72 carbon
atoms, and separated by 15 Å of vacuum. The Chadi–Cohen scheme
[32] with six special points was used for sampling of the surface
Brillouin zone. Graphone was described in a 4 4 rhombohedral
cell with 15 Å of vacuum between periodically repeated carbon
sheets. The corresponding Brillouin zone is sampled applying the
Chadi–Cohen scheme with eighteen special points. The optimized
lattice constant of graphone was found to be 1.46 Å compared to
1.42 Å for graphene [20]. All atoms were relaxed using the Broyden–Fletcher–Goldfarb–Shanno algorithm [33]. The activation
energies for diffusion of H atoms were calculated employing the
nudged elastic band method [34]. The effect of the quantum tunneling of H atoms has not been considered in the present Letter
since recent investigations demonstrated that its contribution to
the H diffusion can be safely neglected at room temperature [35].
The H binding energies are calculated relative to the energy of an
isolated H atom.
energy gain of 1.15 eV is accompanied with suppression of magnetism in the graphene lattice.
For hydrogen trimers the highest total magnetic moment of 3 lB
is obtained for trimer configurations with all three H atoms adsorbed on the same graphene sublattice. Yet, these structures are
not thermodynamically favorable since the H binding energy per
adsorbate is by 0.6 eV smaller than in the trimers identified as
the most favorable [17]. In Figure 1b we show an example of a
trimer structure with magnetic moment M ¼ 3 lB (left panel). This,
structure is unstable against diffusions of H atoms which transforms it to the trimer with M ¼ 1 lB (right panel) and total energy
as much as 1.70 eV lower than the energy of the initial configuration. The activation energy for diffusion of the H atom to the neighboring C site is 0.43 eV, as depicted in the middle panel in Figure 1b.
In general, trimers with a total magnetic moment of 3 lB are unstable against diffusions of H atoms which transform them into more
favorable structures. A systematic study of small H clusters on
graphene is presented in Ref. [17]. The results of our calculations
agree very well with similar studies of other groups [15,16,36,37].
Graphone, presented in Figure 2a, can be considered as an infinite H cluster composed of closely packed M-dimers [21]. Graphone
has been proposed to be thermally stable at room temperature
based on molecular dynamics (MD) simulations [21]. In the present
Letter we have complemented these MD simulations with manual
searches for low-barrier decomposition pathways for the graphone.
The result of these calculations is shown in Figure 2. According to
our calculations, H atom diffusion over the C–C bond to a neighboring C site is characterized by a low energy barrier of only 0.43 eV.
We find the resulting structure to be 2.00 eV more stable than the
initial graphone structure, as shown in Figure 2. The huge energy
release reflects that graphone is immensely unstable which is causing the low diffusion energy barrier. In fact, if the same H diffusion
event is considered at low H coverage, i.e. for a single H atom on
graphene, where the process is thermo-neutral, a barrier of
1.14 eV is found [18]. Different stages of graphone decomposition
realized by diffusion of H atoms to the neighboring C sites are examined by comparison of the total energies of four structures in Figure
3. The total energy of graphone (Figure 3a) is 2.00 eV per unit cell
higher than the energy of the structure in Figure 3b. By diffusion
of additional two H atoms this structure transforms to the adsorption configuration depicted in Figure 3c which is lower in energy
by further 3.76 eV per unit cell. Finally, the configuration with the
same number of H adsorbates on both graphene sublattices
(Figure 3d), produced by diffusion of additional five H atoms, is as
Even though the most energetically favorable hydrogen dimers
on graphite or graphene are all non-magnetic [18,19,15,16,10,20]
this does not exclude the formation of magnetic dimer configurations such as the meta-dimer (M-dimer) depicted in Figure 1a
[17]. This structure induces a total magnetic moment in graphene
of 2 lB, as expected according to Lieb’s theorem. The binding energy of the H atoms in the meta dimer structure is similar to the
binding energy of two hydrogen monomers, making it 1.15 eV less
stable than the most stable dimer structures. Furthermore, the Mdimer is unstable at room temperature, since H diffusion to the
neighboring C site occurs along the pathway with the activation
energy of only 0.50 eV (see middle panel in Figure 1a). The high
low stability
3. Results and discussion
1.6 Fig. 3d
binding energy (eV/H)
insulator [22,23]. In the proposed graphone, electrons localized at
non-hydrogenated carbon atoms are unpaired, producing local
magnetic moments. The moments are ferromagnetically coupled
with the Curie temperature estimated in the range between 278
and 418 K [21]. This finding was followed by a number of computational studies focused on various aspects of this hypothetical material [24–26].
In the present Letter we demonstrate that H structures at graphene can be classified according to the value of the g parameter,
defined as the difference in number of hydrogenated Ca and Cbatoms. In all thermodynamically favorable H structures on graphene
g is as small as possible. Furthermore, we investigate the kinetic stability of adsorbate structures with high total magnetic moments and
show that these undergo transitions to more stable configurations
with smaller magnetic moments along pathways with energy barriers lower than 0.5 eV. The hypothetical material graphone is a thermodynamically very unfavorable form of partially hydrogenated
graphene which is also kinetically unstable at room temperature.
The manuscript is organized as follows. In Section 2 we describe
the computational approach used in the present Letter. The results
and discussion are presented in Section 3, which is followed by the
summary of main results and concluding remarks given in Section 4.
high stability
72
II
1.4 O-dimer
H3
P-dimer
Fig. 3c
1.2
1
Fig. 3b
VI
Fig. 3a
(graphone)
0.8
monomer
0
0.2
low-spin
0.4
0.6
η/N
0.8
H3
M-dimer
1
high-spin
Figure 4. The H binding energy as a function of g/N, N is number of H adsorbates
per unit cell. The H clusters are labeled according to the notation used in Ref. [17].
Ž. Šljivančanin et al. / Chemical Physics Letters 541 (2012) 70–74
73
Figure 5. The iso-contours of the spin densities at 0.5 Å above the plane formed by non-hydrogenated C atoms in Figure 3a, calculated for all four structures in Figure 3. The H
atoms are presented by small blue spheres. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
much as 6.36 eV per unit cell more favorable than the structure in
Figure 3c. These results clearly demonstrate the tendency of graphone to decompose to other, thermodynamically more stable
forms of hydrogenated graphene.
The binding energies of all H adsorption configurations considered in the present study are compared in Figure 4. The set of studied structures includes the H monomer, three dimers (O, P, M), the
two trimer structures in Figure 1b, as well as graphone and related
structures in Figure 3. The plot clearly demonstrates the tendency
of H adatoms to form structures with small g values, i.e. minimal
possible total magnetic moments. This could be rationalized taking
into account the finding that magnetism in hydrogenated graphene
is induced due to a non-zero value of g. According to theory [13,38]
g counts the number of so-called mid-gap states in graphene
[39–42]. These are non-bonding states, positioned in vicinity of
the Fermi level and give rise to magnetism. The total energy of H
configurations on graphene decrease when the number of midgap states decreases, reaching the minimum for g equal to 0 or 1,
i.e. for adsorption structures with small magnetic moment.
In addition to being thermodynamically unfavorable, all H structures with high g values are kinetically unstable. Since the calculated
barrier for H atom hopping to the neighboring C site are very similar
for all configurations in Figs. 1 and 2 we will estimate the life-time of
structures with high magnetic moments considering graphone as an
example. Using an Arrhenius rate expression and assuming an H
attempt frequency of 1013 Hz, the estimated rate of H diffusion in
the graphone structure at room temperature is 16 s1. Hence,
our DFT calculations show that at room temperature graphone is
unstable against H diffusion as depicted in Figure 2. The same conclusion can be applied to the H dimer and trimer structures with
large values of the g parameter. At a temperature of 300 K graphone
would transform to some more stable structures of semi-hydrogenated graphene within few micro-seconds. Only at temperatures below 100 K will graphone be stable over several years, which is
required for applications in electronic devices.
Now we illuminate the process of quenching of the magnetism
upon diffusion of H atoms from one sublattice to the another. The
effect of H diffusion on the spin density of semi-hydrogenated
graphene is presented in Figure 5. Graphone (Figure 5a) is a ferromagnet, as reported in Ref. [21], the structure in Figure 5b shows
local quenching of the magnetism due to diffusion of the first H
atom in the super cell. The sequential diffusion of more H atoms
further diminish the local magnetic moments on C atoms
(Figure 5c), which finally leads to full suppression of magnetism
in the system (Figure 5d). The structure in Figure 5d is by
0.76 eV per H atom more stable than graphone (Figure 5a), but is
probably only one of several favorable nonmagnetic configurations
of semi-hydrogenated graphene.
4. Conclusions
In conclusion, we have demonstrated the tendency of H adsorbates to evenly adsorb on the C sites of both graphene sublattices
in order to minimize the number of energetically unfavorable midgap states. We identified low energy barrier pathways for H diffusion that would lead to fast transformations of small H clusters
with high magnetic moments to configurations with smaller
spin-polarization. Non-zero total magnetic moments are likely to
occur only in H clusters with an odd number of adsorbates. We
show that at room temperature diffusion of H adatoms is a very
efficient mechanism for fast decomposition of graphone into thermodynamically more favorable forms of semi-hydrogenated
graphene, which are non-magnetic.
Acknowledgments
This work has been supported by the Serbian Ministry of
Education and Science under Grant No. 171033 and by the Danish
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Ž. Šljivančanin et al. / Chemical Physics Letters 541 (2012) 70–74
Research Councils. The calculations were performed at the Danish
Center for Scientific Computing.
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