Ab initio calculation of Zn0.8Mn0.2O1−yNy

ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 320 (2008) 2760– 2765

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Ab initio calculation of Zn0.8Mn0.2O1yNy O. Mounkachi a, A. Benyoussef a,1, A. El Kenz a,, E.H. Saidi b,1, E.K. Hlil c a b c

´ des Sciences, B.P. 1014, Rabat, Morocco Laboratoire de Magne´tisme et de Physique des Hautes Energies, De´partement de Physique, Faculte ´ des Sciences, B.P. 1014, Rabat, Morocco Laboratoire de Physique des Hautes Energies, De´partement de Physique, Faculte Laboratoire de Cristallographie, C.N.R.S, B.P. 166, 38042 Grenoble Cedex, France

a r t i c l e in f o

a b s t r a c t

Article history: Received 21 March 2008 Received in revised form 17 May 2008 Available online 22 June 2008

Based on first-principles spin-density functional calculations, using the Korringa–Kohn–Rostoker method (KKR) combined with the coherent potential approximation (CPA), we investigated the magnetic and half-metallic properties of Mn-doped p-type ZnO and the mechanism which control these properties. Mn-doped ZnO is anti-ferromagnetic spin-glass state, but it becomes half-metallic ferromagnetic upon holes doping. The electronic structure, total magnetic moment of Zn0.8Mn0.2O1yNy and magnetic moments of Mn and N in Zn0.8Mn0.2O1yNy are calculated for different holes (y) concentrations. In this paper we address the origin of half-metallic and ferromagnetic properties as controlled and oriented by the nature of hybridization of the Mn (3d) state and host p(N) states. The band structure has been used to explain the strong ferromagnetism observed in Zn0.8Mn0.2O0.1N0.9. We applied magnetic fields to Mn and we calculated the spin magnetic moments of Mn and N. We show that the spin alignments of Mn atoms and the interlocking N atoms can be shown as Mn(m)–N(k)–Mn(m), indicating that ferromagnetism is mediated through the RKKY or double exchange interaction between the carriers and Mn atoms. We show that for weak holes concentrations the ferromagnetism is due to the double exchange interaction, and for higher holes concentrations the RKKY exchange interaction, mediated by mobile holes, strongly oscillates with distance. Finally, we propose a damped or undamped RKKY interaction model to describe the exchange coupling constants Jij between the local moments Mni and Mnj. & 2008 Elsevier B.V. All rights reserved.

Keywords: ZnO Ab initio calculation Band structure model DMS Magnetic property Carrier mediated ferromagnetism RKKY

1. Introduction Recently, ZnO attracted much attention because of its low cost, abundance and being environmentally friendly. Besides, ZnO has a band gap energy of 3.3 eV at 300 K and a large exaction binding energy of 60 meV. So it is one of the most promising substances for optoelectronics. As was shown by Fukumura et al. [1] solubility of Mn was incorporated into the ZnO matrix is relatively high (xp0.35) by pulsed laser deposition (PLD). In this particular work up to 35% Mn in ZnO without affecting much the crystallographic quality of the diluted magnetic semiconductors (DMSs), whereas about 5% is tolerable for III–V-based hosts. Moreover, Joseph et al. [2] prepared successfully p-type ZnO thin films by using the co-doping method. Indeed, this result could be confirmed if the hole mediated ferromagnetism is the dominant mechanism, attainment of p-type ZnO could pave the way for a promising potential of Mn-doped ZnO. Therefore, it is worth

 Corresponding author.

E-mail address: [email protected] (A. El Kenz). Member of the Hassan II Academy of Sciences and Technology.

1

0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.06.023

investigating the carrier-induced ferromagnetism in the ZnObased DMSs. The various experimental and theoretical investigations of the magnetic order in Zn1xMnxO give contradictory results. However, some groups have reported ferromagnetism in (Zn, Mn)O systems [3], while others observed anti-ferromagnetic or spin-glass behavior [4]. The very latest experimental study finds no evidence for magnetic order, down to T ¼ 2 K [5]. These conflicting results also exist concerning the distribution of Mn in ZnO. In the experimental results of Cheng et al. [6] we are aware of that Mn is distributed homogeneously. Yet Jin et al. [7] report clustering of Mn atoms. ZnO-based DMSs have been described within the framework of the coherent potential approximation (CPA), to take disorder into account [8]. Owing to this treatment, it is possible to simulate the random distribution of the TM (transition metal) impurities in ab initio manner. There are two directions of the magnetic moment along the quantization axis, i.e. up and down directions; consequently, there are two self-consistent solutions for the electronic structure of the ZnO-based DMS. One is the ferromagnetic (FM) state in which all of the magnetic moments are parallel with each other. This is written as (Zn1x, TMup x )O, where x is the TM concentration. The other is the spin-glass state

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TM moments and delocalized holes carriers. ZnO is n-type doped with free electrons in the conduction band or p-type with free holes carriers in the valance band. The stabilization of ferromagnetism will be more efficient when the carriers are holes instead of electrons. Gopal and Spaldin [10] performed a systematic study of the magnetic behavior of TM-doped ZnO for a range of TM ions and defects: Zn vacancies, octahedral Zn interstitials, TM interstitials and Li interstitials. They study the possible p-type dopants, Cu and Li with TM in ZnO. Their main result is the absence, in general, of a tendency for pairs of TM ions substituted for Zn to order ferromagnetically; in most cases AFM ordering is more favorable. FM ordering of TM ions is not induced by the addition of substitutional Cu impurities or by oxygen vacancies. Incorporation of interstitial or substitutional Li is favorable for ferromagnetism, as are Zn vacancies. Maouche et al. [11] reported a theoretical study of (Zn, Mn)O system co-doped with N, and show that this co-doping can change the ground state from anti-ferromagnetic to FM.

in which the magnetic moments are pointed randomly at each other. Therefore, the system has no magnetization. This is down written as (Zn1x, TMup x=2 , TMx=2 )O. Comparing the total energy of the FM state with that of the spin-glass state, DE ¼ TE (spin-glass state)TE (ferromagnetic state) it is possible to judge which state is more stable. Sato and Katayama-Yoshida [8] had carried out the Korringa–Kohn–Rostoker coherent-potential approximation (KKR-CPA) calculations in randomly substituted 3d TM impurities in ZnO and found FM state to be stable for half-filled or more than half-filled impurities such as V, Cr, Fe, Co and Ni, while a spinglass like state is found to be stable for ZnO containing 5% of Mn impurities. Mn impurities are introduced randomly into cation sites of the ZnO semiconductor. This disordered substitution in DMS is well described by the KKR-CPA method. With respect to previous theoretical studies, Zn1xMnxO is not FM without additional carriers. In order to stabilize the FM phase, it is necessary to insert carriers into the system. According to the Zener model approach by Dietel et al. [9] ferromagnetism in DMS originates from the RKKY-like interaction between the localized

Ef 120 100 80

Density of states

60

Up Spin

40 20 0 -20 -40 -60

Down Spin

-80 -100 -120 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Energy relative to the Fermi energy (Ry)

0.4

0.5

0.6

0.7

Ef 120 100 80

Up spin

Density of states

60 40 20

t+CFR

e+CFR

t+DBH

0 -20 -40

t-DBH

-60 -80

Down spin

-100 -120 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 Energy relative to the Fermi energy (Ry)

0.5

0.6

0.7

Fig. 1. Density of state: total, d and p states projected density of state (DOS) of Mn, N-doped and co-doped ZnO, Zn1xMnxO1yNy: (a) x ¼ 0.2 and y ¼ 0, (b) x ¼ 0.2 and y ¼ 0.1, (c) x ¼ 0.2 and y ¼ 0.2 and (d) x ¼ 0.2 and y ¼ 0.25. Black, green and red solid lines correspond to total, d-Mn and p-N projected DOS, respectively.

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Ef 120 100 80

Density of states

60

Up spin

40 20 0 -20 -40 -60

Down spin

-80 -100 -120 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Energy relative to the Fermi energy (Ry)

0.4

0.5

0.6

0.7

0.4

0.5

0.6

0.7

Ef 120 100 80

Density of states

60

Up spin

40 20 0 -20 -40 -60

Down spin

-80 -100 -120 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Energy relative to the Fermi energy (Ry) Fig. 1. (Continued)

In this paper, the magnetism of Zn0.8Mn0.2O1yNy is investigated. Based on the first principles calculations, a materials design of new FM ZnO-based DMS is proposed. Our calculations are based on KKR-CPA method within the density functional theory (DFT). We present a band structure model to explain mechanism interaction between p-levels of the anion and d-levels of TM. We show that this mechanism can explain the magnetic coupling and half-metallic properties in Zn0.8Mn0.2O1yNy. We show that the spin alignments of the Mn atoms and the interlocking N atoms can be shown as Mn(m)–N(k)–Mn(m). This study attempts to guide a design rule for a candidate material concerning about practical application of Zn1xMnxO1yNy. Finally, we consider a damped or undamped RKKY interaction model to describe the exchange coupling constants Jij between the local moments Mni and Mnj, depending on the N concentration. The most relevant feature of DMS, which attracted considerable interest, is the coexistence and interaction of two different subsystems: delocalized conduction (s- or p-type) and localized (d- or f-type) band electron of

magnetic ions. That we see for our system Zn0.8Mn0.2O0.9N0.1; so it is the most probable candidate for DMS applications.

2. Calculation methods and structural optimization of ZnO Within the present work we used the KKR-CPA method [12], with the parameterization of Vosko ,Wilk and Nusair (VWN) [13]. The VWN functional predicts a band gap of E3 eV for bulk ZnO, close to the experimental value of 3.3 eV. Mn impurities are introduced randomly into cation sites of the ZnO semiconductor. To solve the DFT one-particle equations we use multiplescattering 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. Gopal and Spaldin [10] show, with energy differences between the near and far configurations of substitutional TM ions, that for Mn the energy difference is negligible, while it is favorable for the

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MACHIKANEYAMA2002v08 package produced by Akai of Osaka University [14]. In ZnO crystal, each atom of zinc is surrounded by four cations of oxygen at the corners of a tetrahedron and vice versa. This tetrahedral coordination is typical of sp3 covalent bonding but do not forget that these materials also have a substantial ionic character. This crystalline structure is known as wurtzite structure and has a hexagonal unit cell with two lattice parameters, a ¼ 3.27 A˚ and c ¼ 5.26 A˚, which were measured for

other TM ions to cluster together; so the CPA approximation is available for Mn substitution. The form of the crystal potential is approximated by a muffin-tin potential, and the wave functions in the respective muffin-tin spheres were expanded in real harmonics up to l ¼ 2, where l is the angular momentum quantum number defined at each site. We use higher K-points up to 456 in the irreducible part of the first Brillouin zone. In the present calculations, we used the KKR-CPA code

0.00

3.8 3.6

moment of N (uB)

Moment on Mn (uB)

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3.4 3.2 3.0

-0.02 -0.04 -0.06 -0.08 -0.10 -0.12

2.8

0.05 0.10 0.15 0.20 0.25 0.30 holes concentrations

0.00 0.05 0.10 0.15 0.20 0.25 0.30 holes concentrations

total moment uB

1.8 1.7

Double exchange

1.6 damped RKKY 1.5 1.4 1.3

undamped RKKY 0.00

0.05

0.10 0.15 0.20 holes concentrations

0.25

0.30

Fig. 2. Total and local magnetic moment of Zn0.8Mn0.2OyN1y: the calculated total (c) and atom projected magnetic moment of Mn (a), N-doped in ZnO (b) for different Nconcentrations.

3.62 0.00 moment of N (uB)

moment of Mn (uB)

3.60 3.58 3.56 3.54

-0.02 -0.04 -0.06 -0.08

3.52 -0.10 3.50 0.00 0.01 0.02 0.03 0.04 0.05 magnetic field (T)

0.00 0.01 0.02 0.03 0.04 0.05 magnetic field (T)

Fig. 3. Mn(m)–N(k)–Mn(m) configuration: (a) magnetic moment of Mn versus magnetic field H and (b) magnetic moment of N versus magnetic field H for Zn0.8Mn0.2O0.9N0.1.

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(Zn, Mn)O by Fukumura et al. [15]. The internal coordinate u for the wurzite structure was not determined, we used the value for pure ZnO, i.e. u ¼ 0.345.

3. Results and discussion Our model is derived from the coupling level repulsion between the magnetic ion’s d-state and the host element’s p-state, Mn atoms introduce d levels in the band gap of semiconductor. The splitting of the five-time degenerate atomic minority-spin 3d level into the e and t subgroups is caused by the influence of the crystal environment. For Zn0.8Mn0.2O0.9N0.1 The occupied majority d bands are in the host valance band maximum (VBM), which contains mostly anions p states of N, The unoccupied minority d bands is above the conduction band maximum (CBM), Fig. 1b. The dangling bond hybrid (DBH) states are shown on the right hand side, the crystal field (CF) and exchange split Mn d levels are shown on the left hand side of Fig. 4. The introduced d orbitals will interact with the host p states of N, Figs. 1(b–d), forming hybrid p–d orbitals. This hybridization occurs because the Mn d states in a tetrahedral CF into t and e states. The levels generated after hybridization are shown in the central panel Fig. 4. The p–d exchange for Zn0.8Mn0.2O1yNy is believed to result from the less 5 than half-field d shell of Mn ions (d ¼ e2þ t3þ e0 t0 ) and from particular delocalization of occupied t+ orbital (above the top of the valence band) [16]. The ed (CFR) state is very localized, whereas the td (DBH) after hybridization state is less localized due to the coupling with the host p states. The p–d exchange plays the key role in the ion–ion FM d–d exchange [17]. Fermi level locate on majority t states and half-metallic character was predicted. The new character of p–d exchange for Zn0.8Mn0.2O1yNy is of crucial importance for understanding the mechanism of this interaction in DMS. To seek the origin of FM in our systems we concentrate on the results of DOS corresponding to the Zn0.8Mn0.2O1yNy. This is accomplished through a study of local magnetic moment as function of magnetic field, Figs. 3(a and b), and holes concentrations, Figs. 2(a and b). To reveal the relations between electronic structure and effective exchange interactions in a magnetic system is one of the important tasks of the theory of magnetism.

Mn atom

Mn in Td

CBM t-2(d)

We begin with the DOS of Zn0.8Mn0.2O in which the unoccupied minority d bands is above the CBM, Fig. 1a. The Fermi energy lies in a region of vanishing electron density. This is due to the fact that the isovalent Mn2+ ions do not introduce any carrier, The states near the Fermi energy are dominated by Mn2+ valency ground state configuration and are in agreement with experimental observation [18]. These impurity states show a large exchange splitting, leading to the high-spin configuration of d electrons. The exchange splitting (E4 eV) is consistently larger than the crystal-field splitting (E0.8 eV) and our results agree with earlier LSDA+U calculations [10,19]. The Mn impurities proved the localized moment, but without acceptor co-doping, there are no carriers to mediate the long range FM interaction. We p-dope Zn0.8Mn0.2O by substituting O atoms with N, and here we see that the Fermi energy passes through the spin-up density of states and causes a delocalization of Mn d-electrons. We find that the global energy minimum is now obtained in the Mn3+state because the 3d state of Mn is partially filled. As was stated earlier, theory predicts ferromagnetism to occur in Mn-doped ZnO, only if additional holes carriers are introduced [9,10,20,21]. According to the band structure calculations, due to the holes states, the majority spin-band is only partially filled. So with p-doped there are carriers to mediate the long range FM interaction. There are no contributions to the DOS from the spin-down band. The system thus behaves as a half-metallic system. We can distinctly overlap between Mn 3d and N 2p states in the spin-up bands, which leads to significant DOS at the Fermi energy and hence to the halfmetallic character of N co-doped Zn0.8Mn0.2O system. With the results represented in Figs. 3(a and b), we can conclude that Mn and N atoms prefer to exist as nearest neighbors in ZnO, while doping Mn atoms introduces local magnetic moments, the magnetic moment of Mn polarizes the spins at the neighboring N sites anti-ferromagnetically. Ferromagnetism is mediated through the p–d exchange (double exchange or RKKY interactions) interaction between carriers and Mn atoms, and half-metallic character was predicted. So this material can be used for DMS applications. In Zn0.8Mn0.2O1yNy holes are itinerant in keeping with their d-character due to the large hybridization of the N-p states with the Mn-3d states. For small holes concentration, this kinetic energy is lowered (Fig. 1b) so efficiently that the FM state is

Mn-on-N t-CFR

3d e-(d)

N(P) e-CFR t+DBH 0

Ef t+2(d)

t+CFR t+2(p)

3d

VBM

t-DBH

e+(d)

e+CFR

Fig. 4. Band structure model of magnetic coupling in Zn0.8Mn0.2O0.9N0.1.

0 t-2(p)

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stabilized by the double exchange mechanism or damped d–d RKKY exchange mechanism. For higher holes concentration, Fig. 1c, the doped holes go with the Mn-3d states into VBM at Ef level, holes are more itinerant and so its kinetic energy is higher. So FM state is stabilized by the undamped RKKY d–d exchange mechanism. For still higher holes concentration y40.2, Fig. 1d, RKKY exchange strongly oscillates with distance. We can show that we have this behavior in Zn0.8Mn0.2O1yNy. For this reason we calculate the total moment of this system for various holes concentrations, see Figs. 2(a–c). We find that for weak holes concentrations the moment does not vary too much. So, the anti-ferromagnetic interaction between Mn and N which supports the FM Mn–Mn interaction in Zn0.8Mn0.2O1yNy is a short range interaction (damped RKKY interaction), while for large holes concentrations the total moment changes strongly. This shows that the FM interaction between the spins does not remain local but has long range characters (undamped RKKY interaction).

4. Conclusion The results of our investigations on the magnetism in Zn0.8Mn0.2O1yNy DMS were presented by the first principles calculations for several holes concentrations for controlling the magnetism in Zn0.8Mn0.2O1yNy. We show that without additional holes doping, the Fermi level separates a completely filled majority-spin band from a completely empty minority-spin band resulting in a spin-glass state and we show that the co-doping by nitrogen atoms can change the ground state from no-metallic anti-ferromagnetic to half-metallic ferromagnetic. The total magnetic moment and magnetic moments of Mn and N in Zn0.8Mn0.2O1yNy are calculated for different holes concentrations and the band structure model of Zn0.8Mn0.2O0.9N0.1 has been used to explain the strong ferromagnetism observed and the mechanism that stabilizes the ferromagnetic state is proposed. We applied a magnetic field to Mn and calculated the spin magnetic

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moment of Mn and N; we show that the spin alignments of the Mn atoms and the interlocking N atoms can be show as Mn(m)–N(k)–Mn(m). Sato and Katayama-Yoshida [8] have explained the ferromagnetic ordering observed in Zn1xMnxO1yNy by double exchange. In this paper we show that this is true only for small holes concentrations, while for large holes concentrations the RKKY interaction is dominant. In conclusion, we have shown that by co-doping N and Mn, it is possible to make ZnO into a dilute magnetic semiconductor. References [1] T. Fukumura, Z. Jin, A. Ohtomo, H. Koinuma, M. Kawasaki, Appl. Phys. Lett. 78 (2001) 958. [2] M. Joseph, H. Tabata, T. Kawai, Jpn. J. Appl. Phys. 38 (1999) L1205. [3] P. Sharma, A. Gupta, K.V. Rao, F.J. Owens, R. Sharma, R. Ahuja, J.M.O. Guillen, B. Johansson, G.A. Gehring, Nat. Mater. 2 (2003) 673. [4] A. Tiwari, C. Jin, A. Kvit, D. Kumar, J.F. Muth, J. Narayan, Solid State Commun. 121 (2002) 371. [5] G. Lawes, A.P. Ramirez, A.S. Risbud, R. Seshadri, cond-mat/0403196. [6] X.M. Cheng, C.L. Chien, J. Appl. Phys. 93 (2003) 7876. [7] Z. Jin, Y.-Z. Yoo, T. Sekiguchi, T. Chikyow, H. Ofuchi, H. Fujioka, M. Oshima, H. Koinuma, Appl. Phys. Lett. 83 (2003) 39. [8] K. Sato, H. Katayama-Yoshida, Jpn. J. Appl. Phys. 40 (2001) L485. [9] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [10] P. Gopal, N.A. Spaldin, Issue Series Title: Phys. Rev. 74 (2006) 094418. [11] D. Maouche, P. Ruterana, L. Louail, Phys. Lett. A 365 (2007) 231. [12] H. Akai, J. Phys. Condens. Matter 1 (1989) 8045. [13] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [14] H. Akai, MACHIKANEYAMA2002v08, Department of Physics, Graduate School of Science, Osaka University, Japan ([email protected]). [15] T. Fukumura, Z. Jin, A. Ohtomo, H. Koinuma, M. Kawasaki, Appl. Phys. Lett. 75 (1999) 3366. [16] A. Twardowski, in: H. Heinrich, J.B. Mullin (Eds.), Proceedings of the International Workshop on Diluted Magnetic Semiconductors, Linz, 1994, Trans Tech Publications, 1995, p. 599. [17] A. Twardowski, Phys. Scr. T39 (1991) 124. [18] P.B. Dorain, Phys. Rev. 112 (1985) 1058. [19] T. Chanier, M. Sargolzaei, I. Opahle, R. Hayn, K. Koepernik, Phys. Rev. B 73 (2006) 134418. [20] M.S. Park, B.I. Min, Phys. Rev. B 68 (2003) 224436. [21] S.J. Han, J.W. Song, C.H. Yang, C.H. Park, J.H. Park, Y.H. Jeong, K.W. Rhite, Appl. Phys. Lett. 81 (2002) 4212.