Explanation of ferromagnetism origin in C-doped ZnO by first principle calculations

Explanation of ferromagnetism origin in C-doped ZnO by fi rst principle calculations

A. El Amiri ^a,n , H. Lassri ^b , E.K. Hlil ^c , M. Abid ^a

Q1

a

Laboratoire de Physique Fondamentale et Appliquée (LPFA), Faculté des Sciences Ain Chock, Université Hassan II, B.P. 5366 Mâarif, Casablanca, Morocco

b

Laboratoire de Physique des Matériaux, Micro-électronique, Automatique et Thermique (LPMMAT). Faculté des Sciences Ain Chock, Université Hassan II, B.P. 5366 Mâarif, Casablanca, Morocco

c

Institut Néel, CNRS et Université Joseph Fourier, BP 166, 38042 Grenoble, France

a r t i c l e i n f o

Article history:

Received 20 December 2012 Received in revised form 30 September 2013

Keywords:

C-doped ZnO

Diluted magnetic semiconductors DOS

a b s t r a c t

By ab-initio calculations, we systematically study possible source of ferromagnetism C-doped ZnO compound. The electronic structure and magnetic properties of C-doped ZnO with/without ZnO host and C defects were investigated using the Korringa–Kohn–Rostoker (KKR) method combined with coherent potential approximation (CPA). We show that Zn vacancy and presence of C defects (substitutional, interstitial or combination of both) induce the ferromagnetism in C-doped ZnO. From density of state (DOS) analysis, we show that p–p interaction between C atoms and/or C and O atoms is the mechanism of ferromagnetic coupling in C-doped ZnO.

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1. Introduction

Diluted magnetic semiconductor (DMS) is a compound obtained by doping a non-magnetic semiconductor with transition metal (TM) elements [1]. DMS is the most promising material for novel spintronic devices because the charge and spin of the carriers can be simultaneously controlled. In particular ZnO based systems have attracted considerable attention due to its abun- dance and environment friendly nature and also due to its both wide band gap 3.3 eV and high exciton binding energy (60 meV) [1]. Moreover, ZnO doped with 3d transition metal (TM) elements has been studied widely since the model calculation by Dietl et al.

predicted the possibility of ferromagnetism in ZnO with a small amount of Mn as an impurity [2]. However, TM doping often suffers from the problems related to precipitates or secondary phase formation undesirable for practical applications. A possible way to avoid the problem related to magnetic precipitates is to dope semiconductors with nonmagnetic elements instead of TM, which is referred as sp or d

⁰

magnetism since the magnetism is not induced by the localized unpaired electrons in d or f states of TM or rare-earth metals. Moreover, the magnetic properties arising from non-magnetic elements doped ZnO are different from TM-doped ZnO [3]. First, p orbital of non-magnetic elements are usually full in ionic state. Therefore, they do not have unpaired

spins. Second, the interaction between spin and orbit is weak for p states compared to the d states of TM. Third, valence electrons in p states are delocalized, and have much larger spatial extension, which may produce a long-range exchange coupling interactions.

Recently, ferromagnetism in C and N-doped ZnO has been inves- tigated [3 – 8]. Zhou et al. reported that they observed room temperature (RT) ferromagnetism in C-doped ZnO thin fi lms [4].

The experiments clearly showed that the ferromagnetism could be achieved by different preparation methods. Herng et al. [5] also observed RT ferromagnetism in p-type C-doped ZnO thin fi lms.

Pan et al. [6] observed ferromagnetism in n-type C-doped ZnO thin fi lms. The magnitude of the saturation magnetic moment (MM) varies: 1.5 – 3.0 μ

B

/C atom in PLD samples. Zhou et al., 0.54 μ

B

/C atom in ion implantation samples [4] and 1.35 μ

B

in samples prepared by the ion beam method [5]. Also several theoretical works in C-doped ZnO have been performed. Sharma1 and Singh have investigate by spin-polarized density functional theory (DFT) ferromagnetism into in C-doped (ZnO)

n

clusters; n ¼ 1 – 12, 16 [8].

They found that the interstitial C defects in ZnO clusters induce small magnetic moments, the combination of substitutional and interstitial C defects in ZnO clusters leads to magnetic moments of 0.0 – 2.0 μ

B

/C. They also reported that the coexistence of vacancy defects and substitutional C defects gives magnetic moments of greater than 2.0 μ

B

/C. Working on Carbone-doped thin fi lms, Shi and Yuan showed that such fi lms have FM ground state for majority con fi gurations [9]. They also found wide values for C magnetic moment (0 – 1.52 μ

B

). This wide range of C magnetic moments (MMs) shows that the origin of FM in C-doped is still not 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

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Journal of Magnetism and Magnetic Materials

http://dx.doi.org/10.1016/j.jmmm.2014.08.068

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n

Corresponding author.

E-mail address:

aelamiri@casablanca.ma

(A. El Amiri).

Please cite this article as: A. El Amiri, et al., Journal of Magnetism and Magnetic Materials (2014), http://dx.doi.org/10.1016/j.

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Journal of Magnetism and Magnetic Materials∎(∎∎∎∎)∎∎∎–∎∎∎

fully understood. From experimental side, this wide range of C MMs is attributed to the different growth conditions and prepara- tion methods of C-doped samples which induce defects in ZnO host and consequently in fl uence the chemical environment of C atoms. From theoretical side, the majority of authors adopts the supercell approach for construing ZnO cells and consequently imagines many con fi gurations. Considering this approach, the confusion arises from unclear magnetic interaction in different possible geometry con fi gurations. In this work, we attempt to give some insights into possible source of ferromagnetism in C-doped ZnO. Therefore, we performed on ZnO bulk the fi rst-principles spin-density functional calculations, using the Korringa – Kohn – Rostoker method (KKR) combined with the coherent potential approximation (CPA). The KKK-CPA method is one of the most ef fi cient band structure calculation methods for treating disorder systems like DMS.

2. Electronic and magnetic structure calculations

Electronic structure calculations were performed using the Korringa – Kohn – Rostoker (KKR) method within the density func- tional theory [10]. To solve the DFT one-particle equations we use multiple-scattering theory, i.e. the KKR Green's function (KKR-GF) method for the dilute impurity limit and the KKR coherent- potential approximation (KKR-CPA) for concentrated alloys with the KKR-CPA code MACHIKANEYAMA2002v08 package produced by Akai of Osaka University [11]. The Morruzi, Janack, Willaims (mjw) parameterization of exchange-correlation energy functional was used [12]. The form of the crystal potential is approximated by a muf fi n-tin potential, and the wave functions in the respective muf fi n-tin spheres were expanded in real harmonics up to l ¼ 2, where l is the quantum angular momentum number de fi ned at each site. Spin polarization, relativistic effect and spin – orbit interaction were taken into account. We use higher K-points up to 450 in the irreducible part of the fi rst Brillouin zone. To ensure high accuracy in our performed computations, the convergence criterion was chosen to be the total energy and set at 10

⁶

Ry. ZnO crystallize in the hexagonal wurtzite (space group P

6

3mc) and zinc blende phases (space group F43Mm). The normal phase of ZnO shows a wurtzite structure, which consist of hexagonal Zn and O planes stacking alternatively along the c axis. In this structure, the unit cell contains two Zn atoms placed at (2/3, 1/3, 0) and (1/3, 2/3, 1/2) and two O atoms placed at (2/3, 1/3, 3/8) and (1/3, 2/3, 1/3). In the original cell, the O sites are randomly occupied by C atoms with appropriate occupancies. Each Zn atom is surrounded by four O atoms at the corners of a tetrahedral and vice-versa. This structure is derived from hexagonal-close-packed array of anions.

We assume that the C-doping do not affect much more the experimental lattice constants (a ¼ 3.25 Å, c ¼ 5.21 Å) for ZnO [13]. We use internal coordinate for the ZnO wurzite structure u ¼ 0.345.

3. Results and discussion

First, we discuss the stability of C doped ZnO, we calculate corresponding formation energy which is expressed as

E

f

¼ E

t

E

ref

mE

C

þ mE

O

where E

tot

, E

ref

, E

C

and E

O

and are the energy of doped ZnO, pure ZnO, an isolated carbon atom, and O atom in the oxygen molecule and a Zn atom in bulk Zn respectively [14]. The integer m is the number of C which substitute O. The formation energy of ZnC

6.25

O

93.75

is calculated to be 2.03 eV. The moderate formation energy indicates that the ZnC

0.0625

O

0.9375

system can be easily

realized experimentally. In order to understand the experimen- tally observed sample dependence of C magnetic moments in ZnO systems, we aim to carry out systematic studies for the ZnC

0.0625

O

0.9375

compound using the KKR-CPA method. We have investigated different types of C substitution (at O sites C

O

, Zn sites C

Zn

and interstitial C

I

) and host defects (Zn (V

Zn

) and O (V

O

) vacancies). We found that ZnC

_O0.0625

O

_0.9375

compounds with C

_Zn

and V

O

are non-magnetic. In contrast to other theoretical works, we also found that ZnC

0.0625

O

0.9375

with carbone at O sites ( C

O

) is non-magnetic with total and C magnetic moments (MMs) equal to 0. However, ZnC

0.0625

O

0.9375

system is found to be magnetic when carbone atoms are placed into interstitial sites (C

I

) [15] or the ZnO host matrix contains Zn vacancies (V

Zn

). We performed calcula- tions of magnetic moments on ZnC

O0.0625

O

0.9375

(C at O sites), Zn

0.9

V

Zn0.1

C

0.0625

O

0.9375

(10% of Zn vacancies)

,

ZnC

I0.0625

O

0.9375

(C at interstitial sites) and ZnC

O0.3125

C

I0.3125

O

0.9375

(50% of C

O

and 50% of C

I

). The results are reported in Table 1. We found that the total and the local magnetic moments are zero for ZnC

0.0625

O

0.9375

. Shi and Yuan [9] have adopted the model of supercell and have shown that from 10 con fi gurations there are four are non- magnetic with the total and local C MMs are 0 which con fi rms our results by using the KKR-CPA for which no supercell is needed.

We assume random distribution of atoms which is much closer to the reality. The lack of magnetic moments can be explained by the fact that the carbon atoms have a clustering tendency. These form via sp

³

hybrid orbitals covalent bonds between them or with Zn atoms lead to paired valence electrons. In Fig. 1a, the total DOS for ZnC

O0.0625

O

0.9375

is plotted. It gives evidence that this compound exhibits metallic character. Moreover, symmetry of minority and majority spin at Fermi level con fi rms non magnetic behavior. Also, from calculations of partial DOS displayed in Fig. 2a we note that the 2p-C orbitals exhibit symmetry at the Fermi level con fi rming that carbon do not carry a magnetic moment. It is well known that the valence-electron con fi guration of the carbon is 1s

²

2p

²

, there- fore single carbon atom should have a magnetic moment. This proves that the substituted carbon atoms C

_O

are in bonds with Zn atoms or tend to form clusters. Pham et al. reported that C

O

has a tendency to form C

2

complexes inside the ZnO [16]. For Zn

_0.9

V

_Zn0.1

C

_0.0625

O

_0.9375

system we found that the total, the local C and O MMs are 0.23, 0.90 and 0.015 μ

B

respectively, whereas the magnetic moments of Zn and Zn vacancy are very weak (see Table 1). Trying to better understand this we performed the total and partial DOS calculations. In Fig. 2b, we note that at Fermi Level almost 100% spin polarized of DOS exhibiting a half-metallic character of Zn

0.9

V

Zn0.1

C

0.0625

O

0.9375

system. On other hand, the partial DOS of Zinc, Oxygen and Carbon are computed and plotted in Fig. 2b. By comparing with Fig. 1a, we note:

i) In the presence of cations vacancies the minority spin of C-2p states cross the Fermi level and become unoccupied while the majority spin states are partially occupied and dissymmetry between the minority and majority states at Fermi level takes place pointing out to that the atom carbon has a magnetic moment.

ii) The 2p-O states are more shifted towards the Fermi level.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Table 1

Magnetic moments on atoms, interstitial and vacancies in ZnC

0.0625

O

0.9375

, Zn

0.9

V

Zn0.1

C

0.0625

O

0.9375

, ZnC

I0.0625

O

0.9375

and ZnC

O0.3125

C

I0.3125

O

0.9375

.

MMs (μ

B

) M

T

M

CO

M

CI

M

O

M

Zn

M

Vzn

ZnC

O0.0625

O

0.9375

0 0

–

0 0 0

Zn

0.9

V

Zn0.1

C

O0.0625

O

0.9375

0.22 0.90

–

0.01 0.007 0.001

ZnC

I0.0625

O

0.9375

0.24

–

0.93 0.03 0.008

–

ZnC

O0.3125

C

I0.3125

O

0.9375

0.02

0.05

0.23

[8]

0.003 0

–

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These two facts can be explained by broken bonds of anions near cations vacancies. Moreover, as seen in Fig. 2b we note a high degree of overlap pointing out to the hybridization between C-2p and 2p-O orbitals around the Fermi level. This probable 2p-C – 2p-O interaction generates a ferromagnetic coupling inducing a total magnetic moment that we found equal to 0.23 μ

B

. For ZnC

I0.0625

O

0.9375

system, the total, the local C and O MMs are 0.24, 0.93 and 0.01 μ

B

respectively. In order to explain such values, we have reported the total and partial DOS in Figs. 1 and 2c respectively. The total DOS shows a metallic character of system.

By comparing the partial DOS with that in Fig. 2a, we note that the majority spin-density of 2p-C moves to lower energies and becomes fully occupied whereas those of minority spin moves to the highs energies. Moreover, since we cannot see a net overlap between 2p-C and 2p-O states, this dissymmetry between the

majority and minority spin-densities of 2p-C is attributed to p-p interaction between C atoms. The value of C MM 0.93 μ

B

) is much smaller than predicted (2 μ

B

) which indicates that the p – p interaction is antiferromagnetic. The last case we study a combi- nation of both substitutional and interstitial carbon doped ZnO via ZnC

O0.03125

C

I0.03125

O

0.9375

system. We found (see Table 1) that C

I

and C

O

MMs are 0.23 μ

B

and 0.05 μ

B

respectively. The total moment is 0.02. The negative sign of C

O

atom indicates its antiferrmagnetic coupling with its neighboring atoms. The total moment is 0.02 μ

B

. This case therefore shows us that the smaller C MMs experimentally observed are attributed to the nouniform distribution of C ions, rendering a large number of them magne- tically noactive [4]. Finally we investigate the dependence of C MM with carbone concentrations. It is shown that C MM increases with lower concentrations (x o 10%) and decreases for higher ones 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

-8 -6 -4 -2 0 2 4

-60 -40 -20 0 20 40 60

EF

Energy (eV)

DOS

3d_Zn 2p_O 2p_C

-8 -6 -4 -2 0 2 4

-60 -40 -20 0 20 40 60

DOS

Energy (eV)

3d_Zn 2p_O 2p_C 10xV_Zn

E_F

-8 -6 -4 -2 0 2 4 6

-60 -40 -20 0 20 40 60

EF

Energy (eV)

DOS

3d-Zn 2p_O 2p_C

Fig. 1.

Partial DOS of 3d-Zn, 2p-C, 2p-O and V

Zn

of (a) ZnC

O0.0625

O

0.9375

. (b) Zn

0.9

V

Zn0.1

C

0.0625

O

0.9375

and (c) ZnC

I0.0625

O

0.9375

.

-9 -6 -3 0 3 6

-120 -80 -40 0 40 80 120

Energy (eV)

Tot a l D O S

ZnC

O6.25

O

93.75

-9 -6 -3 0 3 6

-150 -100 -50 0 50 100 150

Energy (eV)

Tot a l D O S

Zn₉₀V_Zn10C_6.25O_93.75

-9 -6 -3 0 3 6

-120 -80 -40 0 40 80 120

Energy (eV)

Tot al D O S

ZnC

_I6.25

O

_93.75

Fig. 2.

Total DOS of (a) ZnC

O0.0625

O

0.9375

(b) Zn

0.9

V

Zn0.1

C

0.0625

O

0.9375

and (c) ZnC

I0.0625

O

0.9375

.

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(x 4 10%) (see Table 2). The reached value is 1 μ

B

. In this work we have adopted a CPA approximation which assumes a random distribution of carbone atoms in ZnO host. We therefore think that is the reason that we found smaller values of C MM ( o 1 μ

B

) than predicted theoretically. However, our calculations method explains well the origin of smaller values of C MMs observed in experiments.

4. Conclusion

In summary, the electronic structure and magnetic properties of C-doped in ZnO have been studied by the fi rst-principle calculations. Our results show that C-doped ZnO exhibits ferro- magnetism only when ZnO contains Zn vacancies or C atoms are logged in interstitial sites. The smaller values of calculated C MMs than those reported in the literature are due to the CPA approximation which assumes a random distribution of C atoms.

However, our results give insights into origin of small values of C MMs observed in experiments. From our DOS calculations we can explain ferromagnetism in terms of p – p interaction between C atoms and/or between Carbone and Oxygen atoms.

References

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[4] S.Q. Zhou, Q.Y. Xu, K. Potzger, Appl. Phys. Lett. 93 (2008) 232507.

[5] T.S. Herng, S.P. Lau, L. Wang, B.C. Zhao, S.F. Yu, M. Tanemura, A. Akaike T.S. Teng, Appl. Phys. Lett. 95 (2009) 012505.

[6] H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, Phys. Rev. Lett. 99 (2007) 127201.

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[9] L. Shi, H. Yuan, J. Magn. Magn.Mater. 323 (2011) 857–863.

[10] H. Akai, J. Phys. Condens. Matter 1 (1989) 8045.

[11] H. Akai, MACHIKANEYAMA2002v08, Department of Physics, Graduate School of Science, Osaka University, Japan.

[12] V.L. Moruzzi, J.F. Janak, A.R. Williams, Calculated Properties of Metals, Pergamon Press, New York, 1978.

[13] E.H. Kisi, M.M. Elcombe, Acta Crystallogr. 45 (1989) 1867.

[14] X.Y. Cui, J.E. Medvedeva, B. Delley, A.J. Freeman, C. Stanpfl, Phys. Rev. Lett. 95 (2005) 256404.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Table 2

Total and C

O

magnetic moments in Zn

0.9

V

Zn0.1

C

Ox

O

1x

systems.

x (%) M

T

(μ

B

) M

CO

(μ

B

)

5 0.16 0.87

6.25 0.22 0.89

10 0.43 0.99

15 0.39 0.58

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