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Physica B 405 (2010) 1447–1451
Contents lists available at ScienceDirect
Physica B
journal homepage: www.elsevier.com/locate/physb
First principles calculations of Co-doped zinc-blende ZnO
magnetic semiconductor
J. Zhang a,, K.L. Yao a,b, Z.L. Liu a, G.Y. Gao a
a
b
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
International Center of Materials Physics, Chinese Academy of Science, Shenyang110015, China
a r t i c l e in fo
abstract
Article history:
Received 22 November 2008
Received in revised form
25 September 2009
Accepted 10 November 2009
We have investigated the electronic structure of Co-doped zinc-blende ZnO using first principles full
potential linearized augmented plane-wave (FP-LAPW) method. The relative stability of the ground
state, the density of states and the electronic band structure are examined. The results reveal that the
antiferromagnetism (AFM) state is the ground state and the ferromagnetism (FM) state is the
metastable one. The obtained electronic structure reveal that the Co-doped zinc-blende ZnO exhibits
metallic with LDA while a semiconductor within the LDA +U scheme in the AFM ground state. The
magnetic moments mainly arise from the Co atom with a little contribution from the nearestneighboring O atoms due to the hybridization between the Co 3d states and the nearest-neighboring O
2p states.
& 2009 Elsevier B.V. All rights reserved.
Keywords:
Electronic structure
First-principles
Diluted magnetic semiconductor
1. Introduction
Recently, diluted magnetic semiconductors (DMS) have been
studied extensively in both theory and experiment, because of
their potential usage of both charge and spin of freedom of
carriers in the electronic devise, namely, the spintronics [1,2]. A
chief goal of current research is to find DMS with Curie
temperature as high as possible for the spintronic applications.
There have been trials based on two types of DMS families: II–VI,
such as Mn-doped ZnSe and CdTe [3], and III–V, such as Mn-doped
GaAs [4]. However, they have Tc about 110 K or less. The higher
Curie temperature TC reported in (Ga, Mn) As grown by molecular
beam epitaxy (MBE), however, is about 170 K, which sets TC
higher than room temperature as the major challenge for GaAsbased DMS. In the past few years, room temperature ferromagnetism have been observed in Mn-doped ZnSnAs2 [5], Ni-doped
wurtzite ZnO [6], Cu-doped wurtzite ZnO [7] and Co-doped
anatase TiO2 [8].
As wide band gap semiconductors, ZnO and GaN have attracted
much attention in searching for high Tc ferromagnetic DMS materials
since Dietl et al. [9] predicted that ZnO- and GaN-based DMSs could
exhibit ferromagnetism above room temperature when doped
sufficient carriers and magnetic atoms. This work motivated intensive
studies on the structural and physical properties of ZnO and GaN.
Studies on electronic structure and magnetism of wurtzite ZnO-doped
by transition metals (TM) such as Mn, Fe, Ni, Co, V and Cr have also
been widely performed [10–15]. We know that ZnO have three
Corresponding author. Tel.: + 86 27 87556265; fax: + 86 27 87544525.
E-mail address: [email protected] (J. Zhang).
0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2009.11.001
different crystal structures: the normal low-pressure phase hexagonal
wurtzite (B4) structure, the rocksalt (NaCl or B1) structure and the
cubic zinc-blende (B3) structure [16–18]. Generally speaking, many
studies of TM-doped ZnO have been concentrated on the wurtzite
structure, and room ferromagnetic semiconductor or half-metal
ferromagnetism have been predicted or synthesized, however, the
electronic structure of the TM-doped zinc-blende ZnO are not widely
studied both in theory and experiment.
In this paper, the purpose of our work is to study the electronic
structure and magnetism of Co-doped zinc-blende ZnO by means
of first principles full potential linearized augmented plane-wave
(FP-LAPW) method based on density functional theory (DFT). This
paper is organized as follows. In Section 2, we describe the
theoretical background and computational method. In Section 3,
we show the computational results and discussion. The summary
of our calculations is presented in Section 4.
2. Method of calculation
First principles calculation based on the density functional
theory (DFT) is one of the most powerful tools to study the
ground-state property of materials. In this paper, we use the
WIEN2 K [19] package, it is based on the FP-LAPW+ local orbital
(lo) method, one among the most accurate schemes for band
structure calculations, which allows inclusion of local orbits in
basis, improving upon linearization and making possible a
consistent treatment of semi-core and valence in one energy
window.
The electronic structure and magnetic studies on Co-doped
zinc-blende ZnO are based on the Zn1 xCoxO (x = 0.125).
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According to the Ref. [16], the zinc-blende ZnO has a cubic crystal
system (space group F-43M, a =b= c =4.60 Å, and a = b = g =901). The
doping of x= 0.125 (Zn1 xCoxO) is based on the 1 2 2 supercell
containing sixteen ZnO (Fig. 1), where the two nearest-neighboring or next nearest-neighboring Zn atoms are replaced by two
Co atoms. We investigate the electronic structure and magnetic
coupling via the density of states (DOS) and the electronic band
structure. These results will help us to further understand the
origin of magnetism in the Zn1 xCoxO. In our calculations, the
radii of atom spheres are 2.0, 1.97, 1.77 a.u. for Zn, Co and O
atoms, respectively. The cutoff parameter RMTKMAX is taken as 7.0,
where RMT is the smallest radius of atoms and KMAX is the
maximum value of the reciprocal lattice vectors used in the plane
wave expansion. In our calculation, the LDA+U as well as LDA
[20,21] method are used to treat exchange and correlation, we
choose the 3d–3d Coulomb interaction U on Co sites with an
effective value of Hubbard parameter Ueff =U J [11]. For the
Brillouin zone integration, we used 200 k-points in the first
Brillouin. The self-consistent calculations are considered to be
converge only when the integrate charge difference per formula
R
unit, jrn rn1 jdr, between input charge density ½rn1 and
output ½rn is less than 0.0001.
3. Results and discussion
To examine the energetic between the FM, AFM and NM (nonmagnetism) electronic spin configurations of the Co ions, we have
performed the energy calculation for zinc-blende Zn1 xCoxO
(x= 0.125). In this case, there are two Co ions in the Zn14Co2O16,
which is based 1 2 2 supercell of zinc-blende ZnO for two
possible different configurations: the nearest-neighboring Zn (1)
and Zn (2) atoms (represented by C-1 configuration) and the next
nearest-neighboring Zn (1) and Zn (3) atoms (represented by C-2
configuration) are replaced by two Co atoms. Based on above two
different configurations, we carry out both geometric optimization and atomic relaxation to find the equilibrium configuration.
For the C-1 and C-2 configurations, the optimized length of the
nearest Zn–O bond is 2.034 and 2.061 Å, respectively. The
calculated lattice constants of the two different configurations
are listed in Table 1.
In FM, AFM and NM phase with LDA, we considered parallel,
antiparallel and none spin for the two Co atoms. The LDA energy
calculations (Table 2) show that the AFM state both in C-1 and C-2
configurations are energetically more favorable than its FM state,
so the AFM state should be the ground state, the FM state is the
metastable state for Zn14Co2O16. Moreover, in the AFM ground
state we find that the total energy of C-1 configuration is lower
than that of C-2 configuration. Therefore, we mainly give the
results of the electronic structure calculations in C-1 configuration. In the LDA+ U calculations, we choose the different Ueff
(from 3 to 6 eV) to find the appropriate value. By comparing the
total energies and magnetic moments with different Ueff, it is
found that above 3 eV these values have no difference, so in our
LDA+ U calculation we use Ueff = 3 eV as the computational value in
this paper. Then, we perform the electronic structure calculations
for zinc-blende Zn1 xCoxO (x =0.125) in the FM and AFM
configurations.
First, we present the total DOS of Zn1 xCoxO (x = 0.125) in the
FM metastable state in Fig. 2 by using LDA and LDA+ U schemes,
respectively. The highest-occupied energy band in the valence
bond (VB), i.e., Ef, is marked by the dotted line. From Fig. 2(a), the
total DOS of spin-up electrons shows an insulator characteristic,
while spin-down electrons shows semiconducting behavior with
about 1 eV energy gap. In the vicinity of the Fermi level, and the
total DOS distribution of the spin-up and spin-down electrons is
obviously split, hence the spin arrangement is dominated by the
exchange interaction. Moreover, the total magnetic moments of
Zn14Co2O16 are 6.0366mB, so the FM phase has semiconducting
electronic structure. Then, we take account of the Coulomb
correlation interaction of Co 3d electrons within the LDA+ U
method to calculate the band structure in the FM state, with
parameter U= 3.0 eV and J= 0. With LDA+ U scheme, the total DOS
also shows a semiconducting characteristic in the FM state.
Comparing the DOS with LDA and LDA+ U in Fig. 2(a) and (b), we
can see clearly that the energy levels and peaks of DOS have a
tendency shifting: the conduction band energy levels and peaks of
DOS shift to higher positions and the valence band energy levels
and peaks of DOS shift to lower positions, so the calculated energy
gap arises from about 1.0 eV to nearly 2.0 eV due to the influence
of the Coulomb repulsion interaction.
Table 1
The calculated lattice constants of the Zn14Co2O16 supercell in C-1 and C-2
configurations.
Lattice constants (Å)
a
b
C
C-1
C-2
4.6920
4.7731
9.8109
9.7806
9.7870
9.6085
In C-1 and C-2 configurations, the two nearest-neighboring and near nearestneighboring Zn atoms are replaced by Co atoms, respectively.
Table 2
The total energy for two different configurations of Zn14Co2O16 supercell.
Fig. 1. The 1 2 2 supercell of zinc-blende ZnO. The large and small balls
represent Zn and O atoms, respectively.
Configurations
ENM (Ry)
EFM (Ry)
EAFM (Ry)
C-1
C-2
58273.4692
58273.4335
58274.0992
58274.0638
58274.1419
58274.1065
ENM, EFM and EAFM represent the total energy in the NM, FM and AFM states,
respectively.
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60
LDA
40
20
DOS (states/eV)
0
-20
-40
-60
50
LDA+U
25
0
-25
-50
-4
-6
-2
0
2
4
Energy (eV)
Fig. 2. The spin-dependent total DOS of Zn14Co2O16 in FM state within LDA and LDA + U, respectively. The Fermi levels are located at 0 eV.
6
LDA
Co t2g
3
DOS (states/eV)
0
-3
-6
10
LDA
Co eg
5
0
-5
-10
-15
-6
-4
-2
0
2
4
Energy (eV)
4
Co t2g
LDA+U
2
0
DOS (states/eV)
-2
-4
-6
4
LDA+U
Co eg
2
0
-2
-4
-6
-8
-6
-4
-2
0
2
4
Energy (eV)
Fig. 3. The spin-dependent partial DOS of Co 3d electrons in FM state: (a) LDA and (b) LDA+ U. The Fermi levels are located at 0 eV.
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moments of Zn14Co2O16 in FM state are 6.0366 and 2.4747mB,
6.0044 and 2.5690mB within LDA and LDA+ U schemes, respectively. It is obviously that total magnetic moment mainly comes
from the Co atom, i.e., the spin-polarization occurs at the Co site,
and the results reveal that the nearest-neighboring O can be
polarized to 0.0764 and 0.0518mB within LDA and LDA+U, respectively, due to the hybridization between the Co 3d states and the
nearest-neighboring O 2p states.
In the AFM ground state, there are two different configurations
of C1 and C2. According to the above results of energy calculations, it is found that the total energy of C-1 configuration is
lower than that in C-2 configuration. In order to consider the
influence of the doping position of Co in zinc-blende ZnO, we have
carried out the calculations of electronic structure of the two
different configurations in the AFM state. However, there is no
obviously difference between the two AFM configurations. Hence,
we only give the results of AFM state in C-1 configuration. The
total and Co 3d DOS in the AFM states in LDA is shown in Fig. 4(a),
The following discussion mainly focuses on the partial DOS of
Co2 + (3d7) electrons in the FM state, which is presented in Fig. 3.
Both in the LDA and LDA+U schemes, the splitting of the exchange
and crystal field leads to the asymmetry of the DOS of spin-up
and spin-down electrons. There exists some similar character that
Co2 + 3d orbital are split into double eg (dz2 and dx2 y2) states with
lower energy and triple t2g (dxy, dxz and dyz) states with higher
energy by the crystal field in tetrahedral symmetry. This is similar
to what was found for Co-doped wurtzite ZnO [11]. These results
reveal that exchange splitting is larger than the crystal field,
resulting in the nearly full-filled eg states and the half-filled t2g
spin-down states. In the Fig. 3(a) with LDA, the top of the valence
band (VB) is near the Fermi level; however in Fig. 3(b) with
LDA+U, the top of the VB and the peak of eg spin-down states
are depressed by 0.7 eV. The Fermi level locates at the conduction band minimum between eg spin-down and t2g spin-down
minority states, it reveals the semiconducting character and no
half-metal [22–26] nature. The total and per Co ion spin magnetic
60
total
LDA
40
20
0
DOS (states/eV)
-20
-40
-60
12
Co 3d
LDA
6
0
-6
-12
-8
-6
-4
-2
Energy (eV)
0
2
4
2
4
90
total
LDA+U
60
30
0
DOS (states/eV)
-30
-60
-90
12
Co 3d
LDA+U
8
4
0
-4
-8
-12
-8
-6
-4
-2
Energy (eV)
0
Fig. 4. The spin-dependent total DOS and partial DOS of Co 3d electrons in AFM state: (a) LDA and (b) LDA +U. The Fermi levels are located at 0 eV.
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from which we can find finite DOS values in the vicinity of the
Fermi level. As spin-up and spin-down DOS are all cut the Fermi
level, the AFM configuration exhibits metallic character in the LDA
band calculation. In the vicinity of the Fermi level, it is found that
the total DOS mainly arises from the Co 3d electrons and the
partial O 2p electrons due to the hybridization between the Co 3d
and nearest-neighboring O 2p states.
To the best of our knowledge, the success of LDA shows that
this treatment is actually sufficient for many materials, both for
calculating ground state energies and band structures, implying
that electronic correlations are rather weak in these materials.
But, there are other important materials where LDA fails, such as
transition metal oxides or heavy Fermions systems, so application
of the LDA band in these strongly correlated materials usually
leads to a serve underestimation of the band gap and in some case
predicts metallic behavior for systems that are known to be
insulators or semiconductors [27,28]. In order to further investigate the influence of effective on-site Coulomb interaction
between the Co 3d electrons in the AFM state, we also perform
the electronic structure calculations based on LDA+U scheme. The
total and partial DOS are presented in Fig. 4(b). In the AFM state,
comparing the DOSs of LDA+ U with that of LDA, we find that
there is obviously difference. The total DOS in LDA+ U shows a
semiconducting characteristic with the energy gap of near 1.2 eV
due to the Co 3d Coulomb exchange interaction. Considering the
shortcoming of the LDA approximation which leads to underestimate the band gap of the transition metal oxides, the band
structure of LDA+U scheme is in good agreement with the
experimental results.
In the AFM ground state with LDA and LDA+ U schemes, the
Zn1 xCoxO (x = 0.125) system shows a transition from a metal
state to semiconductor. The similar phenomenon of metal/
insulator transition also was found on FexMn1 xSi [29] and
(V1 xCrx)2O3 [30]. By investigating to the partial DOS Co and O
atoms, the distribution of their electron clouds occur an obviously
overlap. The strong hybridization between Co 3d and O 2p orbitals
play an important role on the magnetic order. In Zn1 xCoxO
(x= 0.125) system, the Zn2 + has a completely filled 3d shell,
however the substitutional impurities Co2 + provide no charge
carries. In order to determine the exchange coupling of the two
localized magnetic Co2 + ions with a local spin Si, we adopt the
Heisenberg Hamiltonian for a localized pair of spins given by
H= 2JSiSj. The Co2 + (3d7) has a pin S= 3/2. The energy difference
between the FM and AFM arrangements can be used to calculate
the exchange coupling parameters J. From Table 2, it is found that
the total energies In AFM state are lower than that in FM state,
hence the exchange coupling coefficient is negative in the ground
state. In addition, the absolute values of total magnetic moments
of Zn14Co2O16 are 5.89 and 5.91 with LDA and LDA+ U schemes in
its AFM state, respectively.
4. Conclusions
In conclusion, we have investigated the electronic structure
and the magnetic properties of Co-doped zinc-blende ZnO using
the first principles FP-LAPW method within LDA and LDA+U
schemes. The energy calculations show that the AFM state is more
energetically favorable than its FM state. In the FM state within
1451
LDA+U, the energy gap becomes larger than which within LDA,
we find there exists large exchange splitting and crystal field
splitting in the Co 3d orbital. In the AFM ground state, the
obtained electronic structure reveals that the Zn0.875Co0.125O
system exhibits metallic character with LDA. However, the result
of LDA+ U shows that this system is a semiconductor. As the
results of LDA do not correctly take into account the localized
character of the transitional metal Co atoms, the LDA+ U
predictions should be in good agreement with the experimental
results. In the AFM ground state with LDA and LDA+ U schemes,
the interesting metal/semiconductor phase transition mainly
attributes to Co 3d strong Coulomb repulsion interaction.
Acknowledgments
The authors would like to acknowledge the support from the
National 973 Project (no. 2006CB921605) and Major Project of the
National Natural Science Foundation of China (no. 20490210).
This work was also supported by the National Natural Science
Foundation of China (nos. 10574048, 10574047 and 10774051).
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