Surface properties of the (001) surface of cubic BaMnO3: A density
functional theory study
N. Li, K. L. Yao, G. Y. Gao, L. Zhu, and Y. Y. Wu
Citation: J. Appl. Phys. 107, 123704 (2010); doi: 10.1063/1.3410797
View online: http://dx.doi.org/10.1063/1.3410797
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Published by the American Institute of Physics.
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JOURNAL OF APPLIED PHYSICS 107, 123704 共2010兲
Surface properties of the „001… surface of cubic BaMnO3: A density
functional theory study
N. Li,1,2,a兲 K. L. Yao,1,2,3 G. Y. Gao,2 L. Zhu,2 and Y. Y. Wu1,2
1
Pulsed High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074,
People’s Republic of China
2
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of
China
3
International Center of Materials Physics, Chinese Academy of Science, Shenyang110015, People’s
Republic of China
共Received 10 December 2009; accepted 27 March 2010; published online 16 June 2010兲
We have theoretically investigated surface properties of the 共001兲 surface in cubic barium
manganese 共BaMnO3兲 by the full-potential linear augmented plane wave methods within the local
spin-density approximation. We present and discuss the electronic properties of the 共001兲 surface of
cubic BaMnO3 with BaO- and MnO2-terminations. Surface structure, Mulliken effective atomic
charges, surface energies and stability, band structure, and partial density of states have been
obtained. For the BaO-terminated surface, we find that all layer atoms relax inward 共toward the
central layer兲, while for the MnO2-terminated surface all layer atoms relax outward 共toward the
vacuum兲. The largest relaxations emerge on the first-layer atoms on the two terminations. The
surface rumpling of the BaO-terminated is much larger than that of the MnO2-terminated surface.
Based on the results of the calculated surface energies and stability, we obtain that only the
BaO-terminated surface can exist in the 共001兲 surface of cubic BaMnO3. From the analysis of their
band structure, we can see that the BaO-terminated surface has obvious half-metallic character,
compared with the bulk materials and the MnO2-terminated surface. © 2010 American Institute of
Physics. 关doi:10.1063/1.3410797兴
I. INTRODUCTION
As is known, the thin films of ABO3 perovskite compounds have many important applications, such as multiferroicity, high-temperature superconductivity, colossal magnetoresistance, and heterostructures containing twodimensional 共2D兲 electron gases.1–5 In above mentioned
applications, surface and interface structure and properties
play important roles. Barium manganese 共BaMnO3兲 is a typical ABO3 perovskite material, thus detailed information on
BaMnO3 surface structures would be very helpful in understanding the structure and behavior of its interfaces with
other materials. However, to the best of our knowledge, there
has no theoretically investigation of BaMnO3 surfaces reported by now. We present a first principle study of the
BaMnO3 共001兲 surface structure using the density functional
theory 共DFT兲 with the full-potential linear augmented plane
wave 共FPLAPW兲 method.6 Recently, the surface structure of
SrTiO3 共Ref. 7兲 is reported, which is the most studied perovskite materials. The SrTiO3 共001兲 surface relaxation and
rumpling have been studied experimentally by means of several powerful techniques: low energy electron diffraction,8
reflective high energy electron diffraction,9 x-ray surface
scattering,10 and metastable impact electron spectroscopy.11
Both BaMnO3 and SrTiO3 crystals have the same cubic perovskite structure at ambient conditions and formal ionic
charges are also identical in the two crystals. So we expect
that surface properties of both crystals are similar as well.
a兲
Electronic mail: [email protected].
0021-8979/2010/107共12兲/123704/6/$30.00
In this work, we are the first time to study the cubic
BaMnO3 共001兲 surface properties, including relaxations of
atoms and rumpling of the surfaces, Mulliken effective
charges, band structures, density of states 共DOS兲, surface
energy, and stability by the first principles. Our motivation of
choosing cubic phase perovskite BaMnO3 has two reasons:
first, BaMnO3 remains in cubic paraelectric phase when the
temperature is cooled down to low temperature. This property make BaMnO3 a very good candidate used as a substrate
for thin film deposition.12,13 Second, recent calculations14,15
for CaMnO3 showed that ferroelectricity can be artificially
stabilized by increasing the lattice constants 共equivalent to
applying negative hydrostatic pressure兲 or with tensile strain,
so that the short-range repulsions are substantially reduced.
Since the Ba2+ ion has a larger radius than Ca2+, perovskitestructured BaMnO3 is analogous to CaMnO3 under negative
pressure. This chemical pressure approach was suggested in
Ref. 14, where the authors calculated an unstable zone-center
phonon mode in perovskite-structured SrMnO3 and
BaMnO3. From the results of our calculation, we find that
there is large inward displacement of the Ba atoms in the first
layer, and it results in the large surface rumpling of the BaOterminated surface. Moreover, the results of the grand thermodynamic potential shows that only BaO-terminated surface can exist in the 共001兲 surface structure of cubic
BaMnO3. The remainder of this article is structured as follows: first, we present the computational details of our calculations. Then, in Sec. III, we show the computational results and give some discussions. The summary is presented
in Sec. IV.
107, 123704-1
© 2010 American Institute of Physics
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123704-2
J. Appl. Phys. 107, 123704 共2010兲
Li et al.
II. COMPUTATIONAL METHOD
We used the CASTEP computer code16 to optimize the
lattice constants and calculate the Mulliken charge. The local
density approximation 共LDA兲 within the CA-PZ form17,18
was used with the Vanderbilt ultrasoft pseudopotentials.19
The structure was optimized with the Broyden–Fletcher–
Goldfarb–Shanno method,20 the forces on each ion were converged to less than 0.05 eV/Å and the displacements of the
atoms were less than 0.002 Å. The plane-wave energy cutoff
is 340 eV for all calculations and the Brillouin zone integration is performed by the Monkhorst–Pack scheme21 with Ba
共5s , 5p , 6s兲, Mn 共3d , 4s兲, and O 共2s , 2p兲 treated as valence.
The calculations used a 共8, 8, 1兲 Monkhorst–Pack mesh
which corresponds to eight k-points in the irreducible Brillouin zone. The result shows that these cutoff energies and
k-points are enough for this system. Before starting the surface calculations, we optimized the bulk structure of the cubic phase by the same method and the same computational
conditions 共the k-points mesh was 共8, 8, 1兲兲. Considering the
symmetry of cubic BaMnO3, we only take half of the surface
area as our calculating object: two symmetrical repeat-slab
surface models with BaO- and MnO2-terminations are used
for the calculations. The top view of the two types of surface
and the unit cell of the 共001兲 surface structure of BaMnO3
slab model are displayed in Fig. 1. The periodic boundary
condition was used in calculations with the repeated slab
model. For the BaO-terminated surface, the unit slab consists
of four BaO and three MnO2 layers, so that the slab is terminated with BaO layer on either surface. For the
MnO2-terminated slab, there are three BaO and four MnO2
layers in the unit slab, so we have a slab with MnO2 layers
terminated on both outmost surfaces. For both cases, the
slabs with a thickness of 43.087 Å are separated by a 15 Å
vacuum. During the surface structure optimization, we attempted top 3–5 layers for the relaxation, it is found the
differences both the Ba–O bond length 共the distance between
the surface and subsurface atoms兲 and the magnetic moments
of surface atoms are very small. Namely, the differences of
the Ba–O bond length are less than 0.002 Å, and the magnetic moment of surface atoms are less than 0.001 ␮B. So,
the relaxation of the top four layers for the two typical slabs
is adequate to study the surface properties.
The total energy calculation and the analysis of the electronic structure are all calculated by the FPLAPW method in
the WIEN2K package22 with the local spin-density approximation method.23 In this contribution, the self-consistent field
calculations are based on the following parameters: the values of the atomic sphere radii 共Rmt兲 were chosen as 2.5, 1.94,
and 1.72 a.u. for Ba, Mn, and O atoms, respectively. The
valence wave functions inside the spheres were expanded up
to Lmax = 10 while the charge density was Fourier expanded
up to Gmax = 14 in the muffin-tins. We adopted the same
Monkhorst–Pack mesh 共8, 8, 1兲 which corresponds to hundred k-points in the first Brillouin zone. The cut off parameter RmtKmax limiting the number of the plane waves is equal
to 8.6, where Kmax is the maximal value of the reciprocal
lattice vector used in the plane wave expansion, and Rmt is
the smallest atomic sphere radius in the surface cell. We
BaO-terminated surface
MnO2-terminated surface
(c) The top view the two types surface of BaMnO3 (001)surface
FIG. 1. 共Color online兲 Unit cell for the 共001兲 surface structure of cubic
BaMnO3: the green, red, and purple color spheres represent the Ba, O, and
Mn atoms, respectively. 共a兲 BaO-terminated surface, 共b兲 MnO2-terminated
surface, and 共c兲 the top view the two types surface of BaMnO3 共001兲surface.
adopt the plane-wave cut off energy is 340 eV, which is the
same to optimized parameter. The self-consistency is better
than 10−4 e / a.u.3 for the charge density and spin density,
and the stability is better than 10−5 Ry for the total energy
per formula unit.
III. RESULTS AND DISCUSSIONS
A. Surface relaxation and surface rumpling
In the surface structure calculations, atoms are allowed
to relax along the z-axis of the 共001兲 surface of cubic
BaMnO3 from its ideal structure. The obtained atomic displacements ␦z of the outmost four layers of the BaOterminated and MnO2-terminated surfaces are listed in Table
I. As shown in Table I, for the BaO-terminated surface, all
layer atoms move inward 共toward the central layer兲. For both
kinds of terminations the largest relaxation occurs on the first
layer atoms: for the BaO-terminated surface, the Ba atoms
move inward by 7.07% and the O atoms move inward by
5.69% compared with the bulk lattice constant, while for
the MnO2-terminated surface the Ba atoms move outward
共toward the vacuum兲 by 6.37% and the O atoms move outward by 7.40%. There is a remarkable character that the
metal atoms relax less than O atoms in all layers for
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123704-3
J. Appl. Phys. 107, 123704 共2010兲
Li et al.
TABLE I. Atomic displacement 共relative to ideal positions兲 of the top three
layers of BaO- and MnO2-terminated surfaces of BaMnO3. Units are percentages of theoretical lattice constant 共a0 = 3.89493 Å兲, and positive values
refer to displacements toward the surface.
TABLE II. Surface relaxation parameters 共in percent of theoretical lattice
constant a0 = 3.89493 Å兲 for BaO- and MnO2-terminated surfaces of
BaMnO3.
BaO-terminated surface
Layer
BaO-terminated
␦Z
MnO2-terminated
␦Z
1
Ba
O
Mn
O
Ba
O
Mn
O
⫺7.07
⫺5.69
⫺2.78
⫺4.20
⫺2.69
⫺2.56
⫺1.17
⫺1.16
Mn
O
Ba
O
Mn
O
Ba
O
6.37
7.40
6.05
5.39
2.34
3.63
1.81
2.11
2
3
4
MnO2-terminated surface. In distinguishing, for the BaOterminated surface, the metal atoms in the second layer relax
less than O atoms, but in the other layers, the case is opposite.
To describe the change in the surface structure after relaxation more clearly, surface rumpling parameter S and interlayer distance ⌬dij are introduced. The side view of BaOand MnO2-terminated BaMnO3 共001兲 surfaces with the definition of the surface rumpling S and the near-surface interlayer distance ⌬d12, ⌬d23, ⌬d34, and ⌬d45 are shown in Fig.
2. The magnitude of the surface rumpling parameter S measures the displacement of the first layer oxygen with respect
to the first layer metal atoms. The parameter ⌬d12 is defined
as the change in the interlayer distance measured from the
first layer metal atoms to the second layer metal atoms along
the z-direction. Similarly, ⌬d23, ⌬d34, and ⌬d45 definitions
are similar to ⌬d12, which is distance between the near layers. Structural parameters for the two types of surfaces of
BaMnO3 are presented in Table II. As in the Table II, the
rumpling of BaO-terminated surface is much greater than
that of MnO2-terminated surface. This is mainly because of
the much larger displacement of the surface layer Ba atom on
the BaO-termination than that of the surface layer Mn atom
on the MnO2-termination. The result suggests that the
BaMnO3 共001兲 surface could be rougher if it is terminated
with BaO rather than MnO2. The magnitude of ⌬d12 is negative for both kinds of terminations, which means that the
distance between the first layer and the second layer becomes
smaller by comparing with its bulk value. The absolute value
of ⌬d12 for MnO2-terminated surface is larger than that of
BaO-terminated surface, which suggests that the distance between the surface layer and the second layer is much more
S
1
d12
2
d23
3
4
(a)MnO2-terminated
S
3.16
Method
LDA PW
S
2.68
MnO2-terminated surface
䉭 d23
䉭 d12
⫺5.86
2.47
䉭 d34
⫺1.39
䉭 d45
0.62
䉭 d34
⫺2.11
䉭 d45
0.72
The effective static charges, which are obtained by the
Mulliken population analysis,24 are shown in the Table III.
As we can see, the Mulliken charges of the Ba and Mn ions
are much smaller than its ionic charges, which is due to the
plane waves and virtual atomic basis sets in the calculations.
Our calculated Mulliken charge of the Ba ions in the first
layer for the BaO-terminated surface is 0.79 e, which is
smaller than the corresponding value in the bulk. The Mulliken charge of the Mn ions in the first layer for the
MnO2-terminated surface is 1.02 e, and is similar to the bulk
system. This result means that the excess electronic charges
of dangling bonds on the BaO-terminated surface transfer to
the inner atom of the surface, which results to the fact of
interaction being changed between atoms and the total energy of the system be reduced.
TABLE III. Calculated Mulliken effective atomic charges 共in e兲 for the bulk,
the BaO- and MnO2-terminated surfaces of BaMnO3.
BaO-terminated
MnO2-terminated
Layer
Ion
Charges
共e兲
Ion
Charge
共e兲
1
Ba
O
Mn
O
Ba
O
Mn
O
Ba
Mn
O
0.79
⫺1.12
1.91
⫺1.01
1.66
⫺0.98
1.51
⫺1.01
1.55
1.42
⫺0.99
Mn
O
Ba
O
Mn
O
Ba
O
Ba
Mn
O
1.02
⫺0.68
1.54
⫺0.92
1.46
⫺1.00
1.56
⫺1.00
1.55
1.42
⫺0.99
2
Mn
2
O
3
4
FIG. 2. 共Color online兲 Side view of BaMnO3 共001兲 surface: 共a兲
MnO2-terminated surface and 共b兲 BaO-terminated surface, with the definitions of the surface rumpling S and the near-surface interplanar separation
d12, d23, and d34.
䉭 d23
1.54
B. Mulliken charge analysis
Ba
(b)BaO-terminated
䉭 d12
⫺2.67
reduced for MnO2-terminated surface. On the contrary,
the distance between the second layer and the third layer
expands for both terminations since parameter ⌬d23 is positive for both cases, and the expansion is larger for
MnO2-terminated surface than for BaO-terminated surface.
Furthermore, the lattice constant between the third and the
fourth layers are reduced, while the lattice constant between
the fourth and the fifth layers are expanded.
1
3
d34
Method
LDA PW
4
Bulk
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123704-4
J. Appl. Phys. 107, 123704 共2010兲
Li et al.
0.5
1
0.0
spin down
Energy(eV)
0.0
-1
1
0.0
Λ
Γ
∆
Ζ
Χ
Σ
Μ
Γ
wave vector
(a)
Central layer O 2p
2
0
2nd layer Mn 3d
-2
Central layer Mn 3d
0.5
1.5
0.0
spin down
1st layer Ba
-0.5
0.0
Energy(eV)
-0.0
0.0
3.0
0.0
-1.5
3rd layer Ba
15
-3.0
3.0
0
spin up
1.5
-15
0.0
Total
-6
-4
-2
0
2
4
6
E-EFermi(eV)
-1.5
FIG. 4. 共Color online兲 Total and projected DOS for BaO-terminated surface.
-3.0 R
Λ
∆
Γ
Ζ
Χ
Σ
Μ
Γ
wave vector
(b)
1
spin down
0
-1
1
spin up
0
-1
DOS(states/eV)
R
3rd layer O 2p
-0.5
0
-1
2nd layer O 2p
-0.5
0.5
spin up
Energy(eV)
1st layer O 2p
0.5
-0.5
0
R
Λ
Γ
∆
Χ
Ζ
Μ
Σ
Γ
wave vector
(c)
FIG. 3. 共Color online兲 Band structures of BaMnO3: 共a兲 BaO-terminated
surface, 共b兲 cubic bulk, and 共c兲 MnO2-terminated surface.
C. Band structure and DOS
The calculated band structures of BaO- and
MnO2-terminated relaxed surfaces along the typical 2D Brillouin zone direction ⌫ − ⌾ − ⌴ − ⌫, and band structure of bulk
BaMnO3 are also presented for comparison as shown in Figs.
3共a兲–3共c兲, respectively. From Fig. 3共a兲, the top valence band
is very flat for BaO-terminated surface, especially between ⌫
and ⌾ points, and for the majority spin, there is a typical
metallic band-configuration. However, for the minority spin,
the highest point of the occupied states and the lowest point
of the unoccupied states are all located at the ⌫-point, which
means there is a direct gap. In other word, the BaOterminated surface shows half-metallic properties. Compared
with the bulk system, which is shown in Fig. 3共b兲, there is a
tendency in the BaO-terminated surface for the band states of
O p around the Fermi level to extend upward, especially at
the ⌫-point. From this point of view, it can be deduced that
the surface state appears at the ⌫-point. Moreover, from Fig.
3共a兲, we can see that the upward shift in the conduction band
in the BaO-terminated surface is mainly attributed to the
states from the surface-layer O atoms. Thus, the surface
states appearing in the BaO-terminated surface are caused by
the O atoms in the surface layer. The band structure of
MnO2-terminated surfaces is shown in Fig. 3共c兲. As we can
see, both spin-majority and spin-minority conduction bands
cross the Fermi level, which displays typical metallic.
Figures 4 and 5 show the partial DOS for the BaO- and
MnO2-terminated surfaces, respectively. We find that the
O 2p electronic states make a great contribution to the valence band top. Moreover, the conduction band bottom is
dominating composed of Mn 3d and Ba 6s electronic states.
The electronic states of O 2p in the first layer move up more
obviously to the top of the valence band than O atoms in the
other layers. The first layer Ba 6s electronic states move to
the lower energy side. For the second layer, the partial DOS
of Mn 3d electronic states seems to be the same as that of
central layer Mn 3d electronic states. Therefore, the reduc-
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123704-5
J. Appl. Phys. 107, 123704 共2010兲
Li et al.
0.5
TABLE IV. Average surface energy 共in eV/ a20兲 for BaMnO3.
0.0
1st layer O 2p
-0.5
0.5
0.0
0.0
-0.5
0.0
Central layer O 2p
2
0
1st layer Mn 3d
2
0
3rd layer Mn 3d
-2
0.0
2nd layer Ba
0.5
0.0
Central layer Ba
-0.5
0
-15
Total
-6
-3
0
Erel共BaO兲
共eV兲
Erel共MnO2兲
共eV兲
Es共BaO兲
共eV兲
Es共MnO2兲
共eV兲
2.45
⫺1.92
⫺0.17
2.28
3.40
1 rel
unrel
Erel共I兲 = 关Eslab
共I兲 − Eslab
共I兲兴,
2
3rd layer O 2p
3
6
E-EFermi(eV)
FIG. 5. 共Color online兲 Total and projected DOS for MnO2-terminated
surface.
tion in the band gap of the BaO-terminated surface is mainly
originated from the first layer atoms, especially the Ba 6s
electronic states. So, the presence of this surface, especially
the surface of Ba and O atoms, changes the band electronic
structure.
D. Surface energy and surface stability
The surface energy 共Es兲 of BaMnO3 is defined as the
average surface energy of the two slabs25
1
Es = 关Eslab共BaO兲 + Eslab共MnO2兲 − 7Ebulk兴,
4
共1兲
where Eslab共BaO兲 and Eslab共MnO2兲 are the energies for relaxed BaO- and MnO2- terminated slabs, respectively, and
Ebulk is the bulk unit cell energy. The factor 1/4 is due to the
fact that four surfaces are created during the cleavage, and
the factor 7 is introduced because the two seven-layer slabs
represent seven bulk unit cells. Since surfaces with the two
terminations emerge simultaneously under cleavage, it is assumed that the relevant cleavage energy is the same for both
terminations
1 unrel
unrel
共BaO兲 + Eslab
共MnO2兲 − 7Ebulk兴,
Ecle = 关Eslab
4
共2兲
unrel
unrel
共BaO兲 and Eslab
共MnO2兲 are the energies for unwhere Eslab
relaxed BaO- and MnO2- terminated slabs, respectively. The
relaxation energy is defined as the energy change after relaxation
共3兲
rel
共I兲 is the slab energy after relaxation, and
where Eslab
index “I” in the parentheses stands for either BaO- or MnO2termination. Since both top and bottom surfaces of the slab
are relaxed, a factor 1/2 is introduced in Eq. 共3兲. The average
surface energy, the cleavage energy and the relaxation energy
of BaMnO3 are listed in Table IV. As is seen in this table, we
can easily know that the absolute value of the relaxation
energy of the MnO2-terminated surface is smaller than that
of the BaO-terminated one. The surface energy for BaOterminated structure is 2.28 eV, lower than the surface energy
共3.40 eV兲 for MnO2-terminated structure, which implies that
there would be more BaO-terminated surface on BaMnO3
共001兲 surface.
With the purpose of further exploring the surface stability of the two types of surfaces, we analyzed the grand thermodynamic potential F of the BaO- and MnO2-terminated
surfaces. The details of the computational method and conditions can be found in Ref. 26. The calculated F for
the surface structure of BaMnO3 is shown in Fig. 6. As in
the figure, the grand thermodynamic potential of the
MnO2-terminated surface is always larger than the BaOterminated one, which means that only the BaO-terminated
surface can exist in the 共001兲 surface structure of BaMnO3.
This is different from cubic BaTiO3 and SrTiO3. For
the 共001兲 surface of cubic BaTiO3, previous study using
the similar method has shown that the BaO- and
TiO2-terminated surface have comparable stability.27 Also,
the SrO-terminated surface is more stable than the TiO2terminated one in the 共001兲 surface of SrTiO3.
IV. SUMMARY AND CONCLUSIONS
In summary, from DFT calculations we find that the surface rumpling of BaO-terminated cubic BaMnO3 共001兲 surBaO-term inated
MnO 2 -term inated
1.4
1.3
F(eV)
DOS(states/eV)
BaMnO3
2nd layer O 2p
-0.5
0.5
Ecle
共eV兲
1.2
1.1
1.0
0.9
0.0
0.1
0.2
0.3
0.4
μ MnO (eV )
2
FIG. 6. Grand thermodynamic potential F as a function of the chemical
potential of ␮MnO2 for the two types of surfaces of BaMnO3.
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123704-6
face is larger than that of MnO2- terminated surface. Ba atom
has the largest relaxation for both kinds of surface termination. Therefore, the largest relaxation is on the outmost surface layer atom for BaO-termination. However, for the
MnO2-termination, the largest relaxation is not on the surface
layer Mn atom, but on the second layer Ba atom. Surface
energy calculations reveal that only the BaO-terminated surface can exist in the 共001兲 surface of cubic BaMnO3. The
band gap for MnO2-terminated surface is reduced more than
that for BaO-termination. The reduction in band gap of
MnO2-terminated surface with respect to the bulk is mainly
due to the upward intrusion of the upper valence band states
near the M point.
ACKNOWLEDGMENTS
This work was supported by the National 973 Project
共Grant No. 2006CB921605兲 and the National Natural Science Foundation of China under the Grant No. 10774051.
This work was also supported by the Hubei Province Natural
Science Foundation of China under the Grant No.
2008CDB002.
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