| Краткое содержание: | Much attention has long been devoted
to finding macroscopic
magnetic ordering phenomena
in organic materials. Experimentally, ferromagnetism
has been discovered in pure
carbon systems, such as carbon foam,
graphite, oxidized C60, and polymerized
rhombohedral C60,18 which has stimulated
renewed interests in their fundamental importance
and potential applications in hightechnology
(e.g., spintronics). Much theoretical
work has been done to study
magnetism in nanographites,917 C60 polymers,
18 and all-carbon nanostructures.1922
However, the microscopic origin of ferromagnetism
remains controversial.
The recent proton irradiation experiments
in graphite25 have shown the importance
of hydrogen in inducing the magnetization
instead of magnetic impurities.
Disorder induced by He ion irradiation
does not produce such a large magnetic
moment as obtained with protons.23 Theoretically,
the possible magnetism arising
from the adsorption of hydrogen atom on
graphite has been studied.16,17 It can be easily
speculated that hydrogen can trigger
the sp2sp3 transformation, promoting the
magnetic ordering in other carbon structures,
especially carbon nanotubes with a
surface of positive curvature.
Herein, we focus on the electronic and
magnetic properties of single-walled carbon
nanotubes (SWNTs) with hydrogen atoms
adsorbed on their surfaces. Our results
show that hydrogenated carbon nanotubes
are on the verge of magnetism instability,
and the combination of charge transfer and
carbon network distortion drives flat-band
ferromagnetism. To our knowledge, this is
the first comprehensive ab initio study on
the physical origin of flat-band ferromagnetism
in the real carbon nanotube materials.
Moreover, the applied strain and exte
al
electric field are found to have a strong
influence on the flat-band spin-splitting, resulting
in the variation of spin-relevant
physical properties.
RESULTS AND DISCUSSION
Instead of the simple sp2 bonds in
graphite, the bonds in carbon nanotubes
are of sp2sp3 character due to the tube’s
curvature effect, making the hybridization
of , *, , and * orbitals quite larger, especially
for small-diameter tubes. Thus the
magnetic properties of hydrogenated
SWNTs are more complicated than that of
hydrogenated graphite, with a large dependence
on the radii, the chiralities, and hydrogen
concentration. Here, two types of
linear hydrogen concentration A and B are
shown in Figure 1. There is one hydrogen
atom per tube period in the higher concentration
A and one hydrogen atom per every
two tube periods in the lower concentration
B. The higher H concentration leads
to a larger structure deformation, as can be
seen in Figure 1. Stable CH bond length is
1.1 Å, typical of covalent bonding (cf. 1.09
Å in methane). Recently, the cooperative
alignment of the absorbed atoms has been
observed in graphene experimentally.24
*Address correspondence to
xp.yang@fkf.mpg.de,
wugaxp@gmail.com.
Received for review January 20, 2009
and accepted June 17, 2009.
10.1021/nn900379y CCC: $40.75
© XXXX American Chemical Society
ABSTRACT We investigate the electronic and magnetic properties of hydrogenated carbon nanotubes using
ab initio spin-polarized calculations within both the local density approximation (LDA) and the generalized
gradient approximation (GGA). We find that the combination of charge transfer and carbon network distortion
makes the spin-polarized flat-band appear in the tube’s energy gap. Various spin-dependent ground state
properties are predicted with the changes of the radii, the chiralities of the tubes, and the concentration of
hydrogen. It is found that strain or exte
al electric field can effectively modulate the flat-band spin-splitting
and even induce an insulatormetal transition.
KEYWORDS: hydrogenated carbon nanotube · density functional calculation · spinpolarized
electronic structure · strain effect · electric field effect
ARTICLE
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In the case of carbon nanotubes, the absorption of hydrogen
on the tube wall is easier than that on graphene
due to the curvature effect.25 Moreover, the adatoms’
cooperative alignment can be enhanced by high curvature
regions of nanotube25 that can result from pressure,
26 compression transverse to its axis,25,27 or
tubesubstrate interaction.28
Now, let us study electronic structures of hydrogenated
SWNTs, taking the zigzag (8,0), (9,0), armchair
(5,5) and (10,10) tubes as examples. Figure 2 presents
their ground state band structures obtained by using
spin-polarized LDA (left panels) and GGA (PBE exchange
correlation functional) (right panels). In spinunpolarized
LDA and GGA paramagnetic (PM) band
structures (not shown here completely), a common feature
is that a hydrogen atom induces a half-filled flatband
in the tube’s energy gap around F due to the odd
electrons in compounds, as seen in the LDA PM ground
state band structure of (5,5)-B in Figure 2. Apparently,
flat-band causes an extremely high density of states
around F, and if the Coulomb interaction between itinerant
electrons in the band is introduced, magnetic instability
would occur. It has been shown that flat-band
leads to ferromagnetism for certain models.29 In hydrogenated
SWNTs, the spinspin interaction plays a similar
role as the Coulomb one and lifts the spin degeneracy
of the flat band. As a result, the flat-band’s spinsplitting
magnitude and the energy position relative to
F determine the ground state properties of system. As
we can see in the right panels of Figure 2, the spinsplitting
magnitude has increased after introducing
the generalized gradient correction in the exchange
correlation functional, compared to the LDA without
correction (left panels), which makes the ferromagnetic
(FM) state become more favorable in energy. The adsorption
of the hydrogen atom is found to hardly affect
the gaps of zigzag (8,0) and (9,0) tubes,30,31 while a
large tube’s energy gap is opened in the metallic armchair
(5,5) and (10,10) tubes. In the LDA results, (8,0)-A,B,
(5,5)-A, and (10,10)-A exhibit FM semiconducting characteristics,
whereas (9,0)-A,B and (10,10)-B are FM metals.
(5,5)-B has a PM metallic ground state under LDA.
However, the enhanced spin-splitting in GGA makes
(9,0)-A,B and (10,10)-B present a FM semiconducting
behavior, not metallic one under LDA. Furthermore, a
FM metallic state is produced for (5,5)-B, not the PM metallic
one obtained by LDA.
In order to investigate the physical origin of flatband
ferromagnetism, we plot the spin-up density of
the full-occupied GGA flat-band of (9,0)-B (black band,
see Figure 2) in Figure 3. A sp3-like hybridization is induced
on the carbon atom attached to the hydrogen
atom, leading to whole carbon network distortion, accompanied
by charge transfer from hydrogen to the
bonded carbon atom (0.352 and 0.334 electron for LDA
and GGA (PBE), respectively). Magnetism is strong itinerant
in both circumferential and tube axial directions,
arising from the hybridization of H s orbital with tube
orbitals. Magnetic moments per unit cell are 0.63 and
0.96 B in LDA and GGA, respectively.
Figure 1. Schematic geometrical structures of hydrogenated
zigzag (top panels) and armchair (bottom panels) tubes in the
higher hydrogen concentration A with one hydrogen per tube
period, or the lower hydrogen concentration B with one hydrogen
per every two tube periods. Blue (gray) balls represent
the hydrogen (carbon) atoms.
Figure 2. Spin-polarized LDA (left panels) and GGA (right panels) ground state band structures of hydrogenated zigzag (8,0) and (9,0),
and armchair (5,5) and (10,10) tubes in the two different systems A (top panels) and B (bottom panels). Insets show the band structures
around F in an enlarged energy scale. The Fermi level is set at zero. Spin-up and spin-down channels are represented by black and cyan,
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Obviously, this s hybridization is relevant to
structure distortion and affects the flat-band spinsplitting
magnitude. To get such an insight, we carried
out both LDA and GGA calculations on the undistorted
(9,0)-B structure with only the location of the hydrogen
atom relaxed. Charge transfer still exists, and the band
structures plotted in Figure 3c clearly show a disappearance
of the flat-band spin-splitting and also magnetism.
Weak magnetic moment 0.2 B per unit cell appears
even if on-site Coulomb repulsion, U 3.0 eV,32
is considered in the LDAU calculation. These results
indicate that only charge transfer is not sufficient to induce
a large magnetic moment; therefore, structure distortion
is indispensable. As a result, we can anticipate
that the applied strain could tune the physical properties
of hydrogenated SWNTs by affecting the spinsplitting
of flat-band. We applied a 4% stretch or compression
strain along the tube axis, then the atomic
positions were optimized again. Corresponding ground
state electronic structures are given in Figure 3d,e. As
expected, strain does have an important effect on the
magnetic ground state properties. The 4% axial stretch
strain causes the length of CC bonds, beneath the H
atom, to further stretch and deviate from the regular
value of 1.42 Å, which enlarges the energy gap, as
shown in Figure 3d. Even a metalinsulator transition
is found in LDA band structure, accompanied by an increase
in the magnetic moment to 0.96 B (normally
0.63 B). Under 4% axial compression strain, the compound
presents the metallic or semiconducting characteristics
similar to those without strain in both LDA
and GGA, but the magnetic moment in LDA is reduced
to 0.53 B. Under both axial strains, the transferred
charge remains 0.350.36 electrons in LDA and
0.330.34 electrons in GGA, proving that carbon network
distortion plays a very
important role in the flat-band
spin-splitting. Of course, flatband
and magnetism would
also disappear if we remove
the hydrogen atom from the
distorted SWNTs, indicating
the necessity of hydrogen in
inducing the ferromagnetic
ordering, which is similar to
the role of so-called “carbon
radicals” in magnetic allcarbon
structures.12,13
Figure 4 summarizes structure
information and ground
state properties of hydrogenated
zigzag (n,0) (n 612)
and armchair (n,n) (n 511)
tubes in both A and B cases
(see Figure 1). Generally
speaking, magnetic moment
per unit cell has increased
Figure 3. The 0.003 Å3 magnetization density isosurfaces for the fulloccupied
spin-up GGA flat-band in (9,0)-B: (a) top view and (b) front view.
Spin-polarized LDA and GGA ground state band structures for (9,0)-B: (c)
with only the location of hydrogen atom relaxed, (d) under the 4% axial
stretch strain, (e) under the 4% axial compression strain.
Figure 4. From the top down, the evolution of magnetic moment per unit cell and energy difference
(EPM EFM) per unit cell vs the tube index n. Left panels are from spin-polarized LDA, and right panels
are from spin-polarized GGA (PBE).
ARTICLE
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gradually with the change of tube index n (top panels)
and approaches a saturation value in both LDA and
GGA results. In the (n,0)-A case, the magnetic moment
curve presents oscillation behavior (especially in LDA)
that might be relevant to periodic change of the band
gap in zigzag-type tubes. The higher concentration
A-type compounds have a magnetic moment larger
than that of the lower concentration B-type compounds,
especially in smaller diameter tubes. In the bottom
panels of Figure 4, the curves of energy difference
(EPM EFM) between FM and PM states per unit cell versus
tube index n present a similar trend as found in
the curves of magnetic moment versus n. Introducing
of the generalized gradient correction enhances the
spin-splitting, as discussed for Figure 2, which leads that
the FM state becomes more favorable in GGA than in
LDA, evidenced by the energy difference EPM EFM. This
reveals that magnetic properties of hydrogenated
carbon nanotubes are affected by the structure characteristic
of the SWNTs and the concentration of
hydrogen.
Finally, we also investigate the effect of transverse
electric fields in the Y direction of cross section (see Figure
3a). Absorption of a H atom makes the SWNT become
a polar organic compound. Here, the polar CH
bond is just along the Y direction.
It can be anticipated
that charge redistribution
driven by an exte
al electric
field could occur, which
would induce a subtle
change of electronic structure.
Both LDA and GGA
simulations on (10,10)-A reveal
the spin-dependent effect
of applied exte
al electric
fields with a magnitude
of 0.10.4 V/Å, illustrated in
Figure 5. Compared with Figure
2, the applied field
gradually decreases the gap
between spin-up and spindown
flat-band at 0.1 and 0.2
V/Å, finally closes it, and directly
drives an insulator
metal transition at 0.3 V/Å in
LDA and 0.4 V/Å in GGA. This
effect is different from the
case of graphene nanoribbons,911 where the band
gap closure takes place only for one spin channel. The
fantastic “beating” behavior of spin-polarized flat-band
under the exte
al electric field can be used for designing
quantum switches. |
