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Ferromagnetism in Carbon-Doped Zinc Oxide Systems B. J. Nagare,*,† Sajeev Chacko,‡ and D. G. Kanhere*,‡ Department of Physics, UniVersity of Mumbai, Santacruz (East), Mumbai 400 098, India, and Department of Physics and Center for Modeling and Simulation, UniVersity of Pune, Ganeshkhind, Pune 411 007, India ReceiVed: NoVember 6, 2009; ReVised Manuscript ReceiVed: January 15, 2010
We report spin-polarized density functional calculations of ferromagnetic properties for a series of ZnO clusters and ZnO solid containing one or two substitutional carbon impurities. We analyze the eigenvalue spectra, spin densities, molecular orbitals, and induced magnetic moments for ZnC, Zn2C, Zn2OC, carbon-substituted ZnnOn (n ) 3-10, 12) clusters and the bulk ZnO. The results show that the doping induces magnetic moment of ∼2 µB in all the cases. All systems with two carbon impurities show ferromagnetic interaction, except when carbon atoms share the same zinc atom as the nearest neighbor. This ferromagnetic interaction is predominantly mediated via π-bonds in the ring structures and through π- and σ-bonds in the three-dimensional structure. The calculations also show that the interaction is significantly enhanced in the solid, bringing out the role of dimensionality of the Zn-O network connecting two carbon atoms. Introduction Dilute magnetic semiconductors are a focus of much attention due to their potential application as spintronic materials. These materials, apart from having a desirable band gap, can exhibit room temperature ferromagnetism upon doping by suitable impurities. Several oxides (e.g., TiO2, SnO2, In2O3, HfO2, and the more popular ZnO) have been investigated and have been found to exhibit ferromagnetism when doped with transition metal impurities.1–5 Among these, ZnO is preferred because of its many attractive features. It is transparent to visible light (band gap of 3.37 eV), is suitable for applications using shortwavelength light, and has a large exciton binding energy and a low lasing threshold. There are a number of theoretical and experimental studies reported on ZnO that yield a variety of data on their magnetic behavior. The data has raised many issues and, at times, controversies. The density functional calculations show that doping of Cu produces a half-metallic ferromagnet.6 This prediction has been verified experimentally.7 Co doping has generated much controversy about the origin of magnetism. Cobalt-doped ZnO is reported to have a high Curie temperature (TC) of up to 700 K. A robust ferromagnetic state has been predicted at the oxygen surface, even in the absence of magnetic atoms.8,9 If Mn or Co is doped in insulating and metallic ZnO films, ferromagnetic behavior is observed whenever the carrier density is not intermediate.10–12 Recently, nonmagnetic impurities have been shown to induce ferromagnetic behavior.13 Vacancy-induced magnetism in ZnO thin films and nanowires have been reported on the basis of density functional investigations.14 In fact, defects of several types, such as a vacancy at the zinc site, oxygen surface, interstitial edges in nanoribbons,15 etc., have been found to induce magnetic interactions. The carbon-doped ZnO has been shown to exhibit ferromagnetic behavior with a Curie temperature around room temperature.16 The experi* To whom correspondence should be addressed. E-mail: (B.J.N.)
[email protected]; (D.G.K.)
[email protected]. † University of Mumbai. ‡ University of Pune.
ment has been performed with two levels of doping, 1% and 2.5%. The spin density functional theory (SDFT) results show that the magnetism is due to the Zn-C system. The magnetic moment per carbon atom decreases slightly for the higher concentration from 2-3 to 1.5-2.5 µB. The room temperature ferromagnetism has also been observed in C-implanted ZnO thin films by Zhou et al.17 However, they report a smaller value of magnetic moment of ∼0. 54 µB per carbon ion. They attributed this reduction to the nonuniform distribution of C ions, rendering a large number of them magnetically nonactive. The room temperature ferromagnetism in C-doped ZnO film has also been reported by Yi. et al.,18 with a magnetic moment of ∼1.8 µB per carbon atom. Interestingly, they found that N-codoping above a certain concentration enhances the magnetic moment by ∼85%. It may be mentioned that the present work is within the framework of density functional formalism at the level of GGA. It is well-known that GGA underestimates the bandgap by a substantial amount.19 The question of the validity of DFT in describing the magnetic interactions in ZnO-based systems is a matter of serious debate. In the context of Co-doped ZnO, Walsh et al.9 have analyzed the nature of single particle states (ed and t2d) in cobalt and their placement with respect to the bandgap. They argued that the stability of the ferromagnetic or antiferromagnetic state is crucially dependent on the competition between direct exchange and superexchange energy as well as their placement with respect to the bandgap, as mentioned above. Their calculations based on GGA, DFT + U, and hybrid functionals failed to give a correct description. However, their view that the DFT employing a hybrid functional and self-interaction correction (SIC) failed to reproduce correct intra-d splitting has been questioned by Sanvito and Pemmaraju.20 The intra-d band gap calculated by these authors with SIC (1.9 eV) is quite close to the experimental reported value (1.1-1.65 eV).21 The question of d0 magnetism has been addressed by Droghetti et al.22 They also bring out the fact that the local spin density approximation leads to excessive delocalization of spinpolarized holes. They advocate a simple self-interaction cor-
10.1021/jp910594m 2010 American Chemical Society Published on Web 02/02/2010
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Figure 1. Optimized ground state geometries of C-doped (ZnO)n (n ) 1-5) clusters. The binding energy per atom (BE) in electronvolts is also shown. The oxygen atoms are red, and substituted carbon is marked by C. The second and third column shows structures with single and double i i carbon substitution, respectively. The binding energy, which is defined as BE ) Σi Eatom - Etot, where, Eatom and Etot are the total energies of an isolated atom and the cluster, respectively.
rection (SIC) scheme. The SIC weaken the magnetic coupling between the magnetic impurities and correct the overestimation of the exchange energy (EJ) within DFT. A similar conclusion has also been drawn by Moirea et al.19 within the context of magnetic coupling in NiO. With this background, it is interesting to note that the DFT calculation of Pan et al. supports the experimental observation, at least qualitatively. In the recent work on a d0 semiconductor, Peng et al. have reported the analysis of C-doped ZnO based on DFT within GGA. They report a ferromagnetic ground state with a magnetic moment
of ∼2 µB on carbon sites.23 Clearly, the SIC inherent in all the present day functionals is biased toward the metallicity. The above discussion indicates that a judicious application of SDFT in combination with available experimental data is a useful tool to gain some insight into the physical phenomena. As noted earlier, there are several unclear issues: the origin of the magnetic moment on the carbon site, the role of zinc and oxygen, the nature of the long-range interaction between the two carbon sites, and the role of the oxygen-zinc network connecting the two sites. To gain some insight into some of
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Figure 2. Optimized ground state geometries of C-doped (ZnO)n (n ) 6-8, 12) clusters. The binding energy per atom in electronvolts is also shown. The oxygen atoms are red, and substituted carbon is marked by C. The second and third column shows structures with single and double carbon substitution, respectively.
these issues, we have carried out systematic density functional investigations on a series of systems, beginning with the ZnC molecule. We have investigated the evolution of magnetic moments and magnetic interaction in ZnC, Zn2C, Zn2OC, Zn2C2, and then in a series of clusters, ZnnOn (n ) 3-12), with a single and double carbon substitution. Finally, we examine ZnO solid with a large unit cell containing 72 atoms. We bring out the role of exchange splitting in the carbon atom, the role of hybridization of carbon p orbitals with zinc, the role of the oxygen-zinc network, and the dimensionality in stabilizing magnetic interactions.
Computational Method The calculations have been performed using SDFT with ultrasoft pseudopotential and plane wave basis.24,25 We have used two different codes: namely, CASTEP25 and VASP.26,27 In all the cases, we have used generalized gradient approximation (GGA) given by Perdew-Burke-Ernzerhof.28 For clusters, we have used supercells having lengths of ∼15-30 Å. The energy cutoff for the plane wave basis was 300 eV. The structures were considered to be converged when the force on each ion was less than ∼0.05 eV/Å, with a maximum
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TABLE 1: The Magnetic Moment (µM) in µB, Exchange Energy EJ (energy difference between ferromagnetic and antiferromagnetic state) in meV, and the Nature of the Magnetic Ground State for All the Systems Investigated Magnetic Moment µM host systems
singly doped
C ZnO Zn2O Zn2O2 Zn3O3 Zn4O4 Zn5O5 Zn6O6 Zn7O7 Zn7O71 Zn8O8 Zn9O9 Zn10O10 Zn12O12 ZnO solid2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
doubly doped
EJ (meV)
0 0 4 4 4 4
-26.4 -3.3 -2.5 -1.1
4 4 4 4 4
-0.9 -46.3 -26.3 -85.3 -89.3
nature of ground state
geometry
AFM AFM FM FM FM FM AFM FM FM FM FM FM
linear triangle rhombous cap-triangle square ring ring ring ring two connected rings 3D 3D 3D wurtzite
Results and Discussions
Figure 3. The eigenvalue spectra for some clusters. In each of the cases, the left column is for R electrons and the right column is for β electrons. The unoccupied levels are shown by dotted lines. The number near the level shows degeneracy.32
displacement of ∼0.002 Å and a convergence in the total energy of about 2 × 10-6 eV/atom. In all the cases, the geometries of all the lowest-energy structures are in good agreement with the results of Matxain et al.29 To study the magnetic properties of C-doped (ZnO)n clusters, carbon atoms were doped substitutionally at various O sites. The C-doped clusters were also optimized with the same set of parameters as used for the (ZnO)n clusters. We have verified the accuracy of our model on the ZnO molecule and ZnO solid. We find a bond length of 1.736 Å and a binding energy of 1.79 eV for the ZnO molecule. The previous studies30 report a bond length between 1.71 and 1.75 Å. We also calculate the binding energy of the ZnO solid in the wurtzite structure. The calculated binding energy of 7.23 eV per ZnO unit agrees well with the experimental binding energy of 7.52 eV per ZnO, as reported by Jaffe et al.31 To understand the basic mechanism of ferromagnetism, we have performed the calculations on series of clusters; namely, ZnC, Zn2C, (ZnO)n, and the substitutionally doped ZnnOn-mCm clusters with n ) 2-10, 12 and m ) 1-2, as well as on the ZnO solid. In each of the cases, we substitute either one or two carbon atoms at the O-sites. In the next section, we present and discuss our results.
It is most fruitful to examine the electronic structure and systematics of magnetic properties of some important motifs in the zinc oxide solid. When the carbon atom is substitutionally doped at the O site in the bulk zinc oxide, it has a zinc atom as the first nearest neighbor and an oxygen atom as the second nearest neighbor. Therefore, we begin by examining the magnetism and the electronic structure of ZnC, Zn2C, Zn2OC, and Zn2C2 clusters. We have also calculated the electronic structure and the magnetic properties of ring structures of the ZnnOn cluster (n ) 3-8) and Zn9O9-Zn12O12, which form threedimensional structures. The results are also presented for bulk zinc oxide by using a large unit cell with 72 atoms. The optimized ground state geometries of these ZnO systems are shown in Figures 1 and 2. It can also be seen that the substitutional doping by carbon atoms has a small effect on the geometries of the hosts, with exception of Zn2O. In Table 1, we summarize the results of all the carbon-doped clusters. The table shows the magnetic moments per site, and the exchange energy, EJ, is calculated as EFM - EAFM (wherever appropriate), where EFM and EAFM are the total energies of the ferromagnetic and antiferromagnetic states, respectively, the nature of the magnetic ground state and the nature of the ground state geometries of C-doped clusters. A number of features can be discerned from the table: (1) A majority of doubly doped (ZnO)n clusters turn out to be ferromagnetic with a magnetic moment of ∼2 µB per carbon atom. (2) Whenever the same zinc atom is the nearest neigbhor to both the carbon atoms, the ground state is antiferromagnetic. This is the case for Zn2C2 and Zn3OC2. (3) It turns out that ∼80-90% magnetic moment is localized on carbon sites with a small but significant induced magnetic moment on the oxygen and zinc sites (see Figure 5 and the discussion). This is true for all the singly and doubly substituted clusters, irrespective of the placement of the carbon atoms. (4) A remarkable observation is that the exchange energy (EJ) is sensitive to the dimensionality of the clusters and is highest for three-dimensional clusters. Thus, the number of paths connecting two carbon atoms via the zinc-oxygen network is a significant factor favoring the ferromagnetic coupling. In a sense, this also brings out the role of oxygen in establishing the ferromagnetic interaction. We elaborate on this point in the discussion below. To elucidate the origin of magnetism, we examine the eigenvalue spectra (Figure 3) and the nature of molecular orbitals for ZnC, Zn2C, Zn2OC, and Zn2C2 along with the molecular
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Figure 4. Isovalued surfaces of molecular orbitals for R and β electrons. The position of substituted carbon is marked by C. The last column shows the spin density for ZnC, Zn2C, Zn2OC, and Zn2C2. It may be noted that the sign of the spin density on one of the carbons is negative, indicating the antiferromagnetic state.
orbitals of atomic Zn, O, and C, which are shown in Figure 4. We use the nomenclature alpha HOMO and beta HOMO to denote the highest occupied molecular orbitals for up spin and down spin, respectively. In Figure 3, we show the eigenvalue spectra for up-spin (left part) and down-spin (right part) electrons. The relevant molecular orbitals are shown in Figure 4 as isovalued surfaces. We also show the induced magnetic moments on all the sites in Figure 5 for some of the relevant systems. We will discuss the spectra, molecular orbitals, and site distribution of the magnetic moments together. Let us note that the exchange splitting for the carbon atom between spinup and spin-down electron is ∼2.49 eV.27 The magnetic moment is due to two up-spin occupied orbitals, consistent with the Hund’s rule. This brings the eigenvalues of atomic carbon p and zinc 4s quite close to each other for up states, while the down-spin eigenvalue of carbon p is placed significantly higher. The formation of the spectra across the series reveals that the action is in the s-p complex formed by carbon p and zinc 4s
orbitals, and the splitting of the up and down “bands” persists for all the systems, leading to the formation of the magnetic moment around carbon. ZnC carries a magnetic moment of ∼2 µB on the carbon site. Because of the linear nature of ZnC, only one of the p orbitals is capable of hybridizing with the s orbitals on Zn. As a consequence, triply degenerate p states (for both spins) split into two states as a single, nondegenerate one and doubly degenerate one, retaining the exchange splitting between up and down. The corresponding molecular orbitals are shown in Figure 4. The lowest state in the complex for both the spins is of similar nature and shows significant hybridization and delocalization. The magnetic moment is due to the doubly degenerate pure p states localized on the carbon atom. The Mulliken population analysis shows effective charge transfer from Zn to C on the order of ∼1.7 electrons. Thus, ignoring the splitting between up-down eigenvalues, a simple picture emerges. The charge transfer from zinc makes one of the p orbitals on the carbon
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Figure 5. Spin moments (Bohr magneton, µB) at the atomic sites depicted in C-doped clusters. The position of substituted carbon is marked as C.
Figure 6. Isovalued surfaces of molecular orbitals for R and β electrons in C-doped Zn7O7 clusters. The oxygen atoms are red, and the position of the substituted carbon is marked by C.
doubly occupied. The delocalization caused by hybridization with the 4s reduces the Coulomb repulsion. Next, we turn to Zn2C.33 Since in ZnC, two spin-down orbitals on the carbon are still unoccupied, one would naively expect Zn2C to be nonmagnetic. Interestingly, Zn2C also shows a magnetic moment of ∼2 µB, mainly localized around the carbon atom. The hybridization of one of the p orbitals with two zinc 4s orbitals splits the spectrum of up and down electrons, forming bonding and antibonding orbitals, the splitting being much less in the case of down electrons. As a consequence, four up and two down orbitals are occupied. Once again, by examining the molecular orbitals (Figure 4), we arrived at a simple description; namely, that there are two doubly occupied orbitals (HOMO and HOMO-3) which are delocalized (2p-4s hybridized). The HOMO-3 orbitals for alpha and beta electrons are the same (not shown in Figure 4). The magnetic moment arises out of two carbon-based p orbitals (HOMO-1 and HOMO-2 for up electrons). As a consequence of the hybridization, a small but significant magnetic moment is induced on both zinc atoms. Next, we examine a typical motif Zn2OC, which brings in the role of oxygen. With the introduction of oxygen, there is a
competition between oxygen and carbon for charge transfer from zinc. The occupied molecular orbitals show an interesting pattern. Evidently, relevant orbitals leading to magnetic interactions are HOMO and HOMO-1. The HOMO shows π bond formation between the carbon and oxygen (HOMO perpendicular to the plane), whereas HOMO-1 shows the σ bond. There are three down orbitals nearly compensating the charge in the three up orbitals. It can be seen that a significant magnetic moment (∼0.42 µB) is induced on the oxygen sites, clearly because of HOMO and HOMO-1. The existence of π and σ bonds establishes the coupling between carbon and oxygen and is a crucial element in the formation of long-range magnetic interactions, even in the extended systems. The ground state of symmetric cluster Zn2C2 is antiferromagnetic. There is a charge transfer of one electron to carbon atoms from each of the zinc atoms. As a consequence, the zinc-zinc distance increases by ∼0.2 Å. As can be seen from Figure 4, it is HOMO-2 that is responsible for antiferromagnetic coupling. This is an analog of the superexchange mechanism. It may be noted that a similar observation can be made for Zn3OC2 as well as for all the ring clusters when carbon atoms
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Figure 7. Isovalued surfaces of molecular orbitals for R and β electrons in C-doped Zn12O12 clusters. The isosurface of the spin density at the site is also shown. The position of the substituted carbon is marked by C.
Figure 8. Isovalued surfaces of molecular orbitals in C-doped zinc oxide solid for R electrons at the top of the valence band. The position of substituted carbon is marked as C.
are placed on both sides of the zinc atom. We recall that the experiment indicates a saturation of magnetic moment per carbon atom around 5% substitution. The spin density for ZnC, Zn2C, Zn2OC, and Zn2C2 are shown in column 4. The localized nature and the induced magnetic moment on the carbon are clearly seen. Now, we turn our attention to ring structures Zn5O5-Zn7O7. We discuss the typical case of Zn7O5C2 showing the ferromagnetic behavior. The relevant molecular orbitals are shown in Figure 6. In this case, two carbon atoms are separated by a chain of zinc-oxygen-zinc (see Figure 5). It can be seen from alpha HOMO and alpha HOMO-1 that there is a π bond formation among three p orbitals centered on two carbon atoms and one oxygen atom. A similar bonding is also seen in alpha HOMO-2 and alpha HOMO-3, as well as in the beta orbitals (figure is not shown). These are the orbitals that are responsible for the ferromagnetic interaction between the carbon atoms mediated via oxygen. Zn12O10C2 is a three-dimensional structure. As pointed out earlier, when the structure changes to a three-dimensional one, there is a significant change in the connectivity of two carbon atoms via zinc and oxygen. The ground state structure for this system is shown in Figure 2. The induced magnetic moments are shown in Figure 5. It can be seen that the induced magnetic moments on the two nearest-neighbor oxygen sites are substantial, ∼0.180 µB. Other oxygen sites connecting them also have notable magnetic moments. The relevant molecular orbitals (alpha HOMO-1 and alpha HOMO-2) and the spin density are shown in Figure 7. Clearly, the picture described in the earlier
cases continues in the present case. The induced spin density shows the magnetic moment on carbon and oxygen sites. These HOMOs show interaction between two carbon atoms mediated via oxygen. Thus, in these cases, once again, the magnetic interaction between the carbon atoms is mediated via p orbitals (π bond). The most significant point is that the interaction is strengthened by the availability of multiple sites connecting two carbon atoms. In this case, the C-C distance is ∼5.410 Å. We expect a similar picture to be valid in the ZnO solid. We have considered a large unit cell with 72 atoms containing two carbon atoms separated by 7.6 Å. Our results for the density of states and magnetic moments are consistent with the report of Pan et al.16 We find that the spin-up bands are fully occupied, whereas the spin-down bands are partially filled, resulting in a magnetic moment of ∼2 µB per carbon atom. We show the relevant molecular orbitals near the top of the valence band for up electrons. It can be noted from Figure 8 that the two carbon atoms are separated by a zinc oxide plane. The molecular orbitals depict two different ways in which the interaction is mediated. In the case of alpha-1, the carbon (in the top plane) induces magnetic moments on oxygen sites within the plane, which then couples to the oxygen in the bottom plane, as seen in Figure 8. Such a role of mediating oxygen has been also noted by Henrik et al34 for the case of NO2 absorption on a BaO surface. In the case of orbitals marked as alpha-2, the carbon induces the magnetic moments in the plane, below and above which couples the carbon site in the bottom plane. These figures clearly bring out the role of the three-dimensional oxygen network in providing the multiple paths between two carbon
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atoms. The resulting spin density is positive and is mainly around carbon sites (figure is not shown). The induced magnetic moments on the oxygen sites are clearly seen. It is of some interest to examine the effect of n-type of doping on the ferromagnetism. We have carried out the calculation on ZnO solid containing 72 atoms with two carbon atoms having two excess electrons. The charge neutrality is maintained by compensating a uniform background. The result indicates that although the ground state is still ferromagnetic, the exchange energy (EJ) reduced by a factor of 2 (from 89 to 44 meV). Since DFT overestimates the EJ considerably, the electron doping is likely to kill ferromagnetism in the systems. This result is consistent with the results of Peng et al.23 Summary and Concluding Remarks We have carried out spin-polarized electronic structure calculations on a series of (ZnO)n and substitutionally doped ZnnOn-mCm clusters with n ) 1-10, 12 and m ) 1-2 as well as for zinc oxide solid with a view to elucidate the origin of the magnetism in the carbon-doped zinc oxide. Our calculations reveal the crucial role played by oxygen in mediating the ferromagnetic interaction. A detailed study of molecular orbitals shows that the interaction is mediated via π as well as σ bonds (especially in the three-dimensional solid) formed out of p electrons of carbon and oxygen. Our calculations also bring out the role played by the hybridization of zinc 4s with carbon 2p and oxygen 2p orbitals. We expect the antiferromagnetic coupling if carbon atoms get substituted on sites adjacent to zinc, leading to saturation of the magnetic moment with increasing carbon content. The results clearly bring out the role of multiple connectivity (between two carbon atoms) of the Zn-O network. Acknowledgment. We are grateful to Accelrys Inc. for providing us a demonstration version of CASTEP. It is a pleasure to acknowledge CDAC, India for providing us the highperformance computing facility. A number of helpful discussion with Balchandra Pujari and Vaibhav Kaware are acknowledged. References and Notes (1) Coey, J. M. D.; Venkatesh, M.; Fitzgereald, C. B. Nat. Mater. 2005, 4, 173. (2) Hong, N. H.; Sakai, J.; Poirot, N.; Ruyter, A. Appl. Phys. Lett. 2005, 86, 242505. (3) He, J.; Xu, S.; Yoo, Y. K.; Xue, Q.; Lee, H. C.; Cheng, S.; Xiang, X.; Dionne, G.; Takeuchi, I. Appl. Phys. Lett. 2005, 86, 052503. (4) Hong, N. H.; Sakai, J.; Prellier, W.; Hassini, G. F. A. Phys. ReV. B 2005, 72, 045336. (5) Venkatesh, M.; Fitzgerald, C. B.; Lunney, J. G.; Coey, J. M. D. Phys. ReV. Lett. 2004, 93, 177206. (6) Lin-Hui, Y.; Freeman, A. J.; Delley, B. Phys. ReV. B 2006, 73, 033203.
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