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Electronic and magnetic properties of C-doped Mg3N2: A density functional theory study
Solid State Communications 150 (2010) 2223–2226
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Electronic and magnetic properties of C-doped Mg3 N2 : A density functional theory study C.W. Niu, Kesong Yang, Yingbo Lv, Wei Wei, Ying Dai ∗ , Baibiao Huang School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China
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Article history: Received 12 July 2010 Accepted 28 September 2010 by Y.E. Lozovik Available online 12 October 2010 Keywords: B. C-doped Mg3 N2 D. Electronic properties D. Magnetic properties E. Density functional theory
abstract Based on density functional theory, we investigate the electronic and spin-polarized properties of C-doped Mg3 N2 with C at two nonequivalent N sites. Results of our calculations reveal that the electronic properties are sensitive to the doping sites while the magnetic moment is not. The substitution of C by N favors a spin-polarized state with a total magnetic moment of 1.0 µB per C, which is equal to the number of holes in the system. Our magnetic coupling calculations also indicate that substantial ferromagnetism is possible in the C-doped Mg3 N2 . © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Diluted magnetic semiconductors (DMS) that combine functions of semiconductors and magnetic materials, have attracted much interest in recent years because of their promising applications in spintronics. Most of the previous studies have focused on 3d transition metal (TM) doped DMS, such as TM doped GaN [1–3] and ZnO [4–7]. More recently, the so-called d0 magnetism [8] which is not caused by partially filled d or f shells is observed in lots of C-doped semiconductors such as C-doped ZnO [9,10], CdS [11], TiO2 [12], and MgO [13]. These studies show that the replacement of anions with C atoms leads to spontaneous spin polarization, and the p–p coupling interaction could induce ferromagnetism [9]. In recent years, the research of nitrides has become one of the most important subjects because of their potential applications. For example, GaN is widely used for light-emitting diodes, high-power and high-frequency devices and blue optoelectronics [14,15]; AlN for laser diodes and optoelectronic devices [16,17]. The d0 magnetism of doped and undoped GaN and AlN have also been studied systematically [18–21] and Mg3 N2 may serve as a potential semiconducting material and an optoelectronic lightemitting device because it is a direct energy gap semiconductor (2.8 eV) [22]. Different from the GaN and AlN mentioned above, Mg3 N2 has two nonequivalent N ions [labeled as N(1) and N(2)]. As a result, it
∗ Corresponding author. Tel.: +86 531 88377035x8317; fax: +86 531 88377035x8317. E-mail address: [email protected] (Y. Dai). 0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.09.039
is assumed that the C-doped Mg3 N2 with C at different N sites may show different electronic and magnetic characteristics. However, to the best of our knowledge, there has been no report on the magnetic properties of C-doped Mg3 N2 . In the present work, we investigate the electronic and magnetic properties and explore the possible ferromagnetism of C-doped Mg3 N2 on the basis of the first-principles calculations. Two of the possible C dopant sites with C replacing N(1) and N(2) are considered. It is found that the two kinds of different doped structures show different electronic structure characteristics despite the same spin moment, and a substantial ferromagnetic coupling is possible in this material. 2. Computational details Magnesium nitride, Mg3 N2 , has an antibixbyite structure and belongs to the space group of Ia3 (206) [23,24]. In this paper, a unit cell of Mg3 N2 composed of 80 atoms with lattice parameters a = 9.9726 Å [24] is used. Various structures of carbon-doped Mg3 N2 with C atoms at N sites are constructed using the 80-atom unit cell (see Fig. 1(a)). The calculations based on first-principles spinpolarized density functional theory (DFT) are performed using the projector augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP) [25,26]. The generalized gradient approximation (GGA) parameterized by Perdew–Wang 91 (PW91) is used for the exchange–correlation functional [27]. The cutoff energy is 400 eV for the plane-wave basis and Γ -centered 2 × 2 × 2 k-points for the Brillouin zone. Good convergence is obtained with these parameters. The structures are fully relaxed until the residual forces on each atom are smaller than 0.025 eV/Å, and the convergence threshold for self-consistent field energy is set at 10−6 eV.
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Table 1 Lattice parameter a, band gap and N–Mg distances of bulk Mg3 N2 after structural relaxation. Available theoretical results are included for comparison.
Present calc. Ref. [28]
a (Å)
Band gap (eV)
Distance (Å) N(1)–Mg1
N(1)–Mg2
N(1)–Mg3
N(2)–Mg
9.9726 9.977
1.522 1.59
2.088 2.086
2.165 2.165
2.186 2.187
2.147 2.147
Fig. 1. (Color online) (a) 80-atom unit cell of Mg3 N2 employed to define C-doped Mg3 N2 structure. The positions of N substituted by C are denoted by 0–7. (b) and (c) show the partial geometrical structures of two nonequivalent N sites. The green, blue and gray balls represent Mg, N(1) and N(2) atoms, respectively.
Fig. 2. (Color online) (a) Plots of TDOS and PDOS of C 2p, N 2p and Mg 2p states for single C-doped Mg3 N2 unit cell with C at N (1) sites, (b) PDOS plot for C 2px , C 2py , and C 2pz states. The Fermi level is indicated by the dashed line at 0 eV.
3. Results and discussion The pure 80-atom Mg3 N2 unit cell is composed of 48 Mg atoms and 32 N atoms. According to the Wyckoff notation, there are 24 N atoms [N(1)] occupying the d sites and 8 N atoms [N(2)] occupying the b sites. In contrast to the N atoms, all Mg atoms are equivalent and occupy the e sites. First of all, we perform the spin-polarization DFT calculations for pure Mg3 N2 using this 80-atom unit cell. The calculated results illustrate that pure Mg3 N2 is nonmagnetic. The other calculated parameters are listed in comparison with available theoretical data [28] in Table 1 and the relaxed local geometrical structures of two nonequivalent N sites are shown in Fig. 1(b) and (c). Each N(1) has six Mg neighbors with three different N–Mg bond lengths while N(2) is coordinated by six Mg atoms with the same N–Mg distance. Every equivalent Mg atom is coordinated with three N(1) and one N(2). The calculated results are in good agreement with Ref. [28] (see Table 1). The calculated band gap is smaller than the experimental value (1.522 vs. 2.8 eV), which is a shortcoming of DFT calculations, and has no influence on the magnetic state. Then we examine the electronic structure and magnetism of a single C substitution, which is modeled by replacing one N atom with one C atom corresponding to a 1.25 at.% C concentration in doped Mg3 N2 . The total density of states (TDOS) and partial DOS (PDOS) for the single C-doped Mg3 N2 at N(1) and N(2) sites are presented in Fig. 2(a) and Fig. 3(a), respectively. For an insight into the magnetism in C-doped Mg3 N2 , the PDOS for C 2px , 2py and 2pz are also plotted in Fig. 2(b) and Fig. 3(b). Both of them are spin polarized, and produce a magnetic moment of 1.0 µB per carbon which is equal to the number of holes in the system. It shows that C substitution for N introduces spin-polarized impurity states near and above the top of the valence band. Fermi level is pinned in the impurity states and the system is of p-type conductive character. It can be easily understood that the substitution of C for N means that an C4− (p2) ion replaces an N3− (p3) ion, since each C atom requires one more electron from the Mg3 N2 lattice than does each
Fig. 3. (Color online) (a) Plots of TDOS and PDOS of C 2p, N 2p and Mg 2p states for single C-doped Mg3 N2 unit cell with C at N (2) sites, (b) PDOS plot for C 2px , C 2py , and C 2pz states. The Fermi level is indicated by the dashed line at 0 eV. The inset shows the DOS of the localized gap states near the Fermi level.
N atom, which leads to the Fermi level located at the top of the valence band. It can be also seen that the C 2p states near the Fermi level overlap significantly with the Mg 2p states and N 2p states, suggesting a strong hybridization between them, which results in the splitting of the energy level and spin polarization near the Fermi level [9,29]. In addition, the calculated result indicates that the spin-polarized state is more stable than the nonspin-polarized state by about 139 meV for N(1) and 81 meV for N(2), indicating that the ground state of C-doped Mg3 N2 should be magnetic. From the calculated TDOS of C-doped Mg3 N2 with C at N(1) site, it is found that spin-up states are fully occupied while the spin-down states are partially filled and lead to an obvious spin polarization, shown in Fig. 2(a). Further PDOS of C 2px , C 2py , and C 2pz states show that the electronic structure of C 2pz states are quite different from C 2px and C 2py states (see Fig. 2(b)). The spin-up state is fully occupied but the spin-down state is completely empty for C 2pz states while C 2px and 2py states are not. Similarly, from TDOS and PDOS of C-doped Mg3 N2 with C at N
C.W. Niu et al. / Solid State Communications 150 (2010) 2223–2226
Fig. 4. (Color online) Local geometrical structures of a single C-doped Mg3 N2 at N(1) sites (a) and N(2) sites (b). The labeled N atoms have the shortest C–N distance and the numbers are the distance between C atom and neighbor Mg or N atoms after structural relaxation.
(2) site, it can be found that spin-up states are fully occupied while the spin-down states straddle the Fermi level. Furthermore, PDOS indicates that the C 2px , 2py and 2pz states have the same electronic structure, which is different from that of C-doped Mg3 N2 with C at N(1) site. The different electronic characteristics may result from the optimized local geometrical structures displayed in Fig. 4(a) and (b). Although the substitutional C atom coordinated by six Mg atoms forms a distorted octahedron in both of the structures, C (1) has six Mg neighbors of different C–Mg distances ranging from 2.136 to 2.228 Å, while C (2) is coordinated by six Mg with the same bond length of 2.193 Å. This means that the symmetry of the former structure is lower than that of the later structure, which leads to the different splitting behaviors of C 2p orbitals as well as the different gap state distribution characteristics. Comparing Fig. 4 with Fig. 1(b) and (c), one can find that C–Mg bond is longer than the N–Mg bond. This is because the electronegativity of carbon (2.55) is much smaller than that of nitrogen (3.04) and leads to the outward relaxation of Mg [30]. The magnetic moment is mainly contributed by the carbon 2p orbital [0.348 µB from C atom, 0.280 µB from the first shell Mg atoms, 0.148 µB from the second shell N atoms for N(1); 0.324 µB from C atom, 0.282 µB from the first shell Mg atoms, 0.212 µB from the second shell N atoms for N(2)]. This is consistent with the results of ZnO [9,29], TiO2 [12], CdS [11] and In2 O3 [31]. Fig. 5(a) displays the spin density distribution for single C-doped Mg3 N2 at N(2) sites. It indicates that the magnetic moment is mainly localized at the C atom and extends a little to the six second-nearest-neighboring N atoms. Despite that, contributions of C and N atoms to magnetic moment are different (0.348 vs. 0.324 µB , 0.148 vs. 0.212 µB ) from N(1) to N(2). This can also be explained by the optimized local geometrical structures (see Fig. 4(a) and (b)). For C substituted at the N(1) site, the shortest C–N distance is 3.341 Å, and there are four N atoms at the same distance from the dopant C atoms. However, the shortest C–N distance is 3.339 Å and the number of N atoms which have the shortest C–N distance is six for C substitute at N(2) site. The smaller C–N distance and the greater number of N atoms lead to the increase of contributions of N atoms to magnetic moment and the decrease of contributions of C atom from N(1) to N(2). In order to examine the magnetic coupling between C atoms in C-doped Mg3 N2 , ten uniquely different structures of two-C-atomdoped Mg3 N2 are considered, which are modeled by replacing two N atoms with two C atoms and these correspond to a doping concentration of 2.5 at.%. The replaced N atoms have been marked with numbers 0–7 in Fig. 1(a). As can be seen from Fig. 1(a), the eight N(2) atoms are placed at the vertex of the cubic structure. We select four of the eight and label 0, 3, 6, 7. The other four N atoms which are labeled with 1, 2, 4, 5 are at the surface of the cubic structure and belong to N(1). The ten structures are obtained by substituting two C atoms for two N atoms at (0, 1), (0, 2), (0, 3),
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Fig. 5. (Color online) Spin density distribution for C-doped Mg3 N2 . (a) Single C atom doped at N(2) site, (b) two-C-atom-doped Mg3 N2 of (0, 6) configuration in FM ordering. Table 2 Values of the C–C distance before and after structural relaxation, relative energy ∆E, magnetization energy Emag , and magnetic moment on each C atom calculated for the (i, j) configuration of the two-C-atom-doped Mg3 N2 , where ∆E = E (i, j)–E (0, 1), and E (i, j) is the energy of the stable state for each (i, j) configuration.
(i, j) (0, 1) (1, 2) (0, 2) (1, 4) (0, 3) (2, 4) (0, 4) (0, 5) (0, 6) (0, 7)
C–C (Å)
∆E (meV)
Before
After
3.317 3.331 3.748 3.761 4.986 5.024 5.989 6.238 7.052 8.637
3.284 3.275 3.737 3.725 4.986 5.022 5.979 6.239 7.052 8.637
0 24 173 206 279 337 279 291 154 308
Emag (meV)
35 16 94 67 18 5 21 4 122 31
µB /N i
j
0.369 0.420 0.342 0.409 0.347 0.346 0.311 0.344 0.360 0.329
0.430 0.421 0.407 0.367 0.347 0.346 0.378 0.350 0.360 0.329
(0, 4), (0, 5), (0, 6), (0, 7), (1, 2), (1, 5), and (2,4) with different C–C distances from about 3 to 8 Å, respectively. From now on, these structures are referred to as the (i, j) structures for convenience. For each (i, j) structure, the total energies for both ferromagnetic (FM) and antiferromagnetic (AFM) ordering are calculated. The magnetization energy, Emag = EAFM − EFM , (EAFM and EFM are the total energies for AFM and FM ordering, respectively), is used to indicate the relative stability of the FM or AFM ordering and is listed in Table 2. The C–C distance before and after structure relaxation, relative energy ∆E and magnetic moment for the stable state are also listed in Table 2. The results indicate that the geometric structure changes slightly for the geometry relaxation. However, it deserves to be specially noted that the configurations of (0, 3), (0, 6) and (0, 7), where i and j belong to N(2), the C–C distance is equivalent before and after structural relaxation. This is determined by their symmetric geometrical structure. The FM coupling is the stable state for all of these configurations independent of the C–C distance. This is different from TiO2 [12,32,33], and In2 O3 [31] doped with 2p light elements, in which either FM or AFM is the stable state for different configurations. Therefore, it may be more effective to obtain d0 ferromagnetism in Mg3 N2 than TiO2 and In2 O3 . Among all configurations, the (0, 1) has the lowest total energy and relative energy ∆E becomes larger with increasing C–C distance. The exceptional cases are the (2, 4) and (0, 6) configurations. For the (2, 4) configuration, it has the largest relative energy ∆E but magnetization energy Emag is small, which means that stable ferromagnetic coupling is hard in this configuration. The situation of (0, 6) is reverse, for which Emag is the largest one (122 meV) but ∆E is relatively small in all of the configurations, namely the obvious ferromagnetism in C-doped Mg3 N2 is preferred as the C–C distance is about 7 Å.
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The FM ordering spin density distribution for two-C-atom-doped Mg3 N2 of (0, 6) configuration is plotted in Fig. 5(b), in which it displays that the magnetic orbitals of the two C dopants could be mediated by the magnetic orbitals of second-nearest N ions, and the p–p coupling interaction may be responsible for the strong ferromagnetic coupling. For the configurations of (0, 1), (0, 2), (0, 4) and (0, 5), where i belongs to N(1) and j belongs to N(2), the magnetic moment on each C atom is different (i < j) for all of the four configurations. This is in good agreement with our above discussion about single C-doped Mg3 N2 in different N sites.
[4] [5] [6] [7] [8] [9] [10]
4. Conclusions In summary, first-principles DFT calculations are carried out to study the electronic and spin-polarized properties of C-doped Mg3 N2 with C at two nonequivalent N sites. Results of the calculations indicate that the two doped structures show different electronic characteristics though the same magnetic moment of 1.0 µB per C is obtained, which means that the electronic properties are sensitive to the doping sites while the magnetic moment is not. The discrepancy of electronic properties mainly results from the different local structures with different types of symmetry. The long-range ferromagnetic interaction is found in C-doped Mg3 N2 system. Acknowledgements This work is supported by the National Basic Research Program of China (973 program, Grant No. 2007CB613302), National Natural Science Foundation of China under Grant No. 10774091 and 20973102, Natural Science Foundation of Shandong Province under Grant No. Y2007A18. References [1] Q. Wang, Q. Sun, P. Jena, Phys. Rev. Lett. 95 (2005) 167202. [2] S. Dhar, L. Perez, O. Brandt, A. Trampert, K.H. Ploog, J. Keller, B. Beschoten, Phys. Rev. B 72 (2005) 245203. [3] (a) S. Dhara, B. Sundaravel, K.G.M. Nair, R. Kesavamoorthy, M.C. Valsakumar, T.V.C. Rao, L.C. Chen, K.H. Chen, Appl. Phys. Lett. 88 (2006) 173110;
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Electronic and magnetic properties of C-doped Mg3 N2 : A density functional theory study C.W. Niu, Kesong Yang, Yingbo Lv, Wei Wei, Ying Dai ∗ , Baibiao Huang School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China
article
info
Article history: Received 12 July 2010 Accepted 28 September 2010 by Y.E. Lozovik Available online 12 October 2010 Keywords: B. C-doped Mg3 N2 D. Electronic properties D. Magnetic properties E. Density functional theory
abstract Based on density functional theory, we investigate the electronic and spin-polarized properties of C-doped Mg3 N2 with C at two nonequivalent N sites. Results of our calculations reveal that the electronic properties are sensitive to the doping sites while the magnetic moment is not. The substitution of C by N favors a spin-polarized state with a total magnetic moment of 1.0 µB per C, which is equal to the number of holes in the system. Our magnetic coupling calculations also indicate that substantial ferromagnetism is possible in the C-doped Mg3 N2 . © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Diluted magnetic semiconductors (DMS) that combine functions of semiconductors and magnetic materials, have attracted much interest in recent years because of their promising applications in spintronics. Most of the previous studies have focused on 3d transition metal (TM) doped DMS, such as TM doped GaN [1–3] and ZnO [4–7]. More recently, the so-called d0 magnetism [8] which is not caused by partially filled d or f shells is observed in lots of C-doped semiconductors such as C-doped ZnO [9,10], CdS [11], TiO2 [12], and MgO [13]. These studies show that the replacement of anions with C atoms leads to spontaneous spin polarization, and the p–p coupling interaction could induce ferromagnetism [9]. In recent years, the research of nitrides has become one of the most important subjects because of their potential applications. For example, GaN is widely used for light-emitting diodes, high-power and high-frequency devices and blue optoelectronics [14,15]; AlN for laser diodes and optoelectronic devices [16,17]. The d0 magnetism of doped and undoped GaN and AlN have also been studied systematically [18–21] and Mg3 N2 may serve as a potential semiconducting material and an optoelectronic lightemitting device because it is a direct energy gap semiconductor (2.8 eV) [22]. Different from the GaN and AlN mentioned above, Mg3 N2 has two nonequivalent N ions [labeled as N(1) and N(2)]. As a result, it
∗ Corresponding author. Tel.: +86 531 88377035x8317; fax: +86 531 88377035x8317. E-mail address: [email protected] (Y. Dai). 0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.09.039
is assumed that the C-doped Mg3 N2 with C at different N sites may show different electronic and magnetic characteristics. However, to the best of our knowledge, there has been no report on the magnetic properties of C-doped Mg3 N2 . In the present work, we investigate the electronic and magnetic properties and explore the possible ferromagnetism of C-doped Mg3 N2 on the basis of the first-principles calculations. Two of the possible C dopant sites with C replacing N(1) and N(2) are considered. It is found that the two kinds of different doped structures show different electronic structure characteristics despite the same spin moment, and a substantial ferromagnetic coupling is possible in this material. 2. Computational details Magnesium nitride, Mg3 N2 , has an antibixbyite structure and belongs to the space group of Ia3 (206) [23,24]. In this paper, a unit cell of Mg3 N2 composed of 80 atoms with lattice parameters a = 9.9726 Å [24] is used. Various structures of carbon-doped Mg3 N2 with C atoms at N sites are constructed using the 80-atom unit cell (see Fig. 1(a)). The calculations based on first-principles spinpolarized density functional theory (DFT) are performed using the projector augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP) [25,26]. The generalized gradient approximation (GGA) parameterized by Perdew–Wang 91 (PW91) is used for the exchange–correlation functional [27]. The cutoff energy is 400 eV for the plane-wave basis and Γ -centered 2 × 2 × 2 k-points for the Brillouin zone. Good convergence is obtained with these parameters. The structures are fully relaxed until the residual forces on each atom are smaller than 0.025 eV/Å, and the convergence threshold for self-consistent field energy is set at 10−6 eV.
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C.W. Niu et al. / Solid State Communications 150 (2010) 2223–2226
Table 1 Lattice parameter a, band gap and N–Mg distances of bulk Mg3 N2 after structural relaxation. Available theoretical results are included for comparison.
Present calc. Ref. [28]
a (Å)
Band gap (eV)
Distance (Å) N(1)–Mg1
N(1)–Mg2
N(1)–Mg3
N(2)–Mg
9.9726 9.977
1.522 1.59
2.088 2.086
2.165 2.165
2.186 2.187
2.147 2.147
Fig. 1. (Color online) (a) 80-atom unit cell of Mg3 N2 employed to define C-doped Mg3 N2 structure. The positions of N substituted by C are denoted by 0–7. (b) and (c) show the partial geometrical structures of two nonequivalent N sites. The green, blue and gray balls represent Mg, N(1) and N(2) atoms, respectively.
Fig. 2. (Color online) (a) Plots of TDOS and PDOS of C 2p, N 2p and Mg 2p states for single C-doped Mg3 N2 unit cell with C at N (1) sites, (b) PDOS plot for C 2px , C 2py , and C 2pz states. The Fermi level is indicated by the dashed line at 0 eV.
3. Results and discussion The pure 80-atom Mg3 N2 unit cell is composed of 48 Mg atoms and 32 N atoms. According to the Wyckoff notation, there are 24 N atoms [N(1)] occupying the d sites and 8 N atoms [N(2)] occupying the b sites. In contrast to the N atoms, all Mg atoms are equivalent and occupy the e sites. First of all, we perform the spin-polarization DFT calculations for pure Mg3 N2 using this 80-atom unit cell. The calculated results illustrate that pure Mg3 N2 is nonmagnetic. The other calculated parameters are listed in comparison with available theoretical data [28] in Table 1 and the relaxed local geometrical structures of two nonequivalent N sites are shown in Fig. 1(b) and (c). Each N(1) has six Mg neighbors with three different N–Mg bond lengths while N(2) is coordinated by six Mg atoms with the same N–Mg distance. Every equivalent Mg atom is coordinated with three N(1) and one N(2). The calculated results are in good agreement with Ref. [28] (see Table 1). The calculated band gap is smaller than the experimental value (1.522 vs. 2.8 eV), which is a shortcoming of DFT calculations, and has no influence on the magnetic state. Then we examine the electronic structure and magnetism of a single C substitution, which is modeled by replacing one N atom with one C atom corresponding to a 1.25 at.% C concentration in doped Mg3 N2 . The total density of states (TDOS) and partial DOS (PDOS) for the single C-doped Mg3 N2 at N(1) and N(2) sites are presented in Fig. 2(a) and Fig. 3(a), respectively. For an insight into the magnetism in C-doped Mg3 N2 , the PDOS for C 2px , 2py and 2pz are also plotted in Fig. 2(b) and Fig. 3(b). Both of them are spin polarized, and produce a magnetic moment of 1.0 µB per carbon which is equal to the number of holes in the system. It shows that C substitution for N introduces spin-polarized impurity states near and above the top of the valence band. Fermi level is pinned in the impurity states and the system is of p-type conductive character. It can be easily understood that the substitution of C for N means that an C4− (p2) ion replaces an N3− (p3) ion, since each C atom requires one more electron from the Mg3 N2 lattice than does each
Fig. 3. (Color online) (a) Plots of TDOS and PDOS of C 2p, N 2p and Mg 2p states for single C-doped Mg3 N2 unit cell with C at N (2) sites, (b) PDOS plot for C 2px , C 2py , and C 2pz states. The Fermi level is indicated by the dashed line at 0 eV. The inset shows the DOS of the localized gap states near the Fermi level.
N atom, which leads to the Fermi level located at the top of the valence band. It can be also seen that the C 2p states near the Fermi level overlap significantly with the Mg 2p states and N 2p states, suggesting a strong hybridization between them, which results in the splitting of the energy level and spin polarization near the Fermi level [9,29]. In addition, the calculated result indicates that the spin-polarized state is more stable than the nonspin-polarized state by about 139 meV for N(1) and 81 meV for N(2), indicating that the ground state of C-doped Mg3 N2 should be magnetic. From the calculated TDOS of C-doped Mg3 N2 with C at N(1) site, it is found that spin-up states are fully occupied while the spin-down states are partially filled and lead to an obvious spin polarization, shown in Fig. 2(a). Further PDOS of C 2px , C 2py , and C 2pz states show that the electronic structure of C 2pz states are quite different from C 2px and C 2py states (see Fig. 2(b)). The spin-up state is fully occupied but the spin-down state is completely empty for C 2pz states while C 2px and 2py states are not. Similarly, from TDOS and PDOS of C-doped Mg3 N2 with C at N
C.W. Niu et al. / Solid State Communications 150 (2010) 2223–2226
Fig. 4. (Color online) Local geometrical structures of a single C-doped Mg3 N2 at N(1) sites (a) and N(2) sites (b). The labeled N atoms have the shortest C–N distance and the numbers are the distance between C atom and neighbor Mg or N atoms after structural relaxation.
(2) site, it can be found that spin-up states are fully occupied while the spin-down states straddle the Fermi level. Furthermore, PDOS indicates that the C 2px , 2py and 2pz states have the same electronic structure, which is different from that of C-doped Mg3 N2 with C at N(1) site. The different electronic characteristics may result from the optimized local geometrical structures displayed in Fig. 4(a) and (b). Although the substitutional C atom coordinated by six Mg atoms forms a distorted octahedron in both of the structures, C (1) has six Mg neighbors of different C–Mg distances ranging from 2.136 to 2.228 Å, while C (2) is coordinated by six Mg with the same bond length of 2.193 Å. This means that the symmetry of the former structure is lower than that of the later structure, which leads to the different splitting behaviors of C 2p orbitals as well as the different gap state distribution characteristics. Comparing Fig. 4 with Fig. 1(b) and (c), one can find that C–Mg bond is longer than the N–Mg bond. This is because the electronegativity of carbon (2.55) is much smaller than that of nitrogen (3.04) and leads to the outward relaxation of Mg [30]. The magnetic moment is mainly contributed by the carbon 2p orbital [0.348 µB from C atom, 0.280 µB from the first shell Mg atoms, 0.148 µB from the second shell N atoms for N(1); 0.324 µB from C atom, 0.282 µB from the first shell Mg atoms, 0.212 µB from the second shell N atoms for N(2)]. This is consistent with the results of ZnO [9,29], TiO2 [12], CdS [11] and In2 O3 [31]. Fig. 5(a) displays the spin density distribution for single C-doped Mg3 N2 at N(2) sites. It indicates that the magnetic moment is mainly localized at the C atom and extends a little to the six second-nearest-neighboring N atoms. Despite that, contributions of C and N atoms to magnetic moment are different (0.348 vs. 0.324 µB , 0.148 vs. 0.212 µB ) from N(1) to N(2). This can also be explained by the optimized local geometrical structures (see Fig. 4(a) and (b)). For C substituted at the N(1) site, the shortest C–N distance is 3.341 Å, and there are four N atoms at the same distance from the dopant C atoms. However, the shortest C–N distance is 3.339 Å and the number of N atoms which have the shortest C–N distance is six for C substitute at N(2) site. The smaller C–N distance and the greater number of N atoms lead to the increase of contributions of N atoms to magnetic moment and the decrease of contributions of C atom from N(1) to N(2). In order to examine the magnetic coupling between C atoms in C-doped Mg3 N2 , ten uniquely different structures of two-C-atomdoped Mg3 N2 are considered, which are modeled by replacing two N atoms with two C atoms and these correspond to a doping concentration of 2.5 at.%. The replaced N atoms have been marked with numbers 0–7 in Fig. 1(a). As can be seen from Fig. 1(a), the eight N(2) atoms are placed at the vertex of the cubic structure. We select four of the eight and label 0, 3, 6, 7. The other four N atoms which are labeled with 1, 2, 4, 5 are at the surface of the cubic structure and belong to N(1). The ten structures are obtained by substituting two C atoms for two N atoms at (0, 1), (0, 2), (0, 3),
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Fig. 5. (Color online) Spin density distribution for C-doped Mg3 N2 . (a) Single C atom doped at N(2) site, (b) two-C-atom-doped Mg3 N2 of (0, 6) configuration in FM ordering. Table 2 Values of the C–C distance before and after structural relaxation, relative energy ∆E, magnetization energy Emag , and magnetic moment on each C atom calculated for the (i, j) configuration of the two-C-atom-doped Mg3 N2 , where ∆E = E (i, j)–E (0, 1), and E (i, j) is the energy of the stable state for each (i, j) configuration.
(i, j) (0, 1) (1, 2) (0, 2) (1, 4) (0, 3) (2, 4) (0, 4) (0, 5) (0, 6) (0, 7)
C–C (Å)
∆E (meV)
Before
After
3.317 3.331 3.748 3.761 4.986 5.024 5.989 6.238 7.052 8.637
3.284 3.275 3.737 3.725 4.986 5.022 5.979 6.239 7.052 8.637
0 24 173 206 279 337 279 291 154 308
Emag (meV)
35 16 94 67 18 5 21 4 122 31
µB /N i
j
0.369 0.420 0.342 0.409 0.347 0.346 0.311 0.344 0.360 0.329
0.430 0.421 0.407 0.367 0.347 0.346 0.378 0.350 0.360 0.329
(0, 4), (0, 5), (0, 6), (0, 7), (1, 2), (1, 5), and (2,4) with different C–C distances from about 3 to 8 Å, respectively. From now on, these structures are referred to as the (i, j) structures for convenience. For each (i, j) structure, the total energies for both ferromagnetic (FM) and antiferromagnetic (AFM) ordering are calculated. The magnetization energy, Emag = EAFM − EFM , (EAFM and EFM are the total energies for AFM and FM ordering, respectively), is used to indicate the relative stability of the FM or AFM ordering and is listed in Table 2. The C–C distance before and after structure relaxation, relative energy ∆E and magnetic moment for the stable state are also listed in Table 2. The results indicate that the geometric structure changes slightly for the geometry relaxation. However, it deserves to be specially noted that the configurations of (0, 3), (0, 6) and (0, 7), where i and j belong to N(2), the C–C distance is equivalent before and after structural relaxation. This is determined by their symmetric geometrical structure. The FM coupling is the stable state for all of these configurations independent of the C–C distance. This is different from TiO2 [12,32,33], and In2 O3 [31] doped with 2p light elements, in which either FM or AFM is the stable state for different configurations. Therefore, it may be more effective to obtain d0 ferromagnetism in Mg3 N2 than TiO2 and In2 O3 . Among all configurations, the (0, 1) has the lowest total energy and relative energy ∆E becomes larger with increasing C–C distance. The exceptional cases are the (2, 4) and (0, 6) configurations. For the (2, 4) configuration, it has the largest relative energy ∆E but magnetization energy Emag is small, which means that stable ferromagnetic coupling is hard in this configuration. The situation of (0, 6) is reverse, for which Emag is the largest one (122 meV) but ∆E is relatively small in all of the configurations, namely the obvious ferromagnetism in C-doped Mg3 N2 is preferred as the C–C distance is about 7 Å.
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The FM ordering spin density distribution for two-C-atom-doped Mg3 N2 of (0, 6) configuration is plotted in Fig. 5(b), in which it displays that the magnetic orbitals of the two C dopants could be mediated by the magnetic orbitals of second-nearest N ions, and the p–p coupling interaction may be responsible for the strong ferromagnetic coupling. For the configurations of (0, 1), (0, 2), (0, 4) and (0, 5), where i belongs to N(1) and j belongs to N(2), the magnetic moment on each C atom is different (i < j) for all of the four configurations. This is in good agreement with our above discussion about single C-doped Mg3 N2 in different N sites.
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4. Conclusions In summary, first-principles DFT calculations are carried out to study the electronic and spin-polarized properties of C-doped Mg3 N2 with C at two nonequivalent N sites. Results of the calculations indicate that the two doped structures show different electronic characteristics though the same magnetic moment of 1.0 µB per C is obtained, which means that the electronic properties are sensitive to the doping sites while the magnetic moment is not. The discrepancy of electronic properties mainly results from the different local structures with different types of symmetry. The long-range ferromagnetic interaction is found in C-doped Mg3 N2 system. Acknowledgements This work is supported by the National Basic Research Program of China (973 program, Grant No. 2007CB613302), National Natural Science Foundation of China under Grant No. 10774091 and 20973102, Natural Science Foundation of Shandong Province under Grant No. Y2007A18. References [1] Q. Wang, Q. Sun, P. Jena, Phys. Rev. Lett. 95 (2005) 167202. [2] S. Dhar, L. Perez, O. Brandt, A. Trampert, K.H. Ploog, J. Keller, B. Beschoten, Phys. Rev. B 72 (2005) 245203. [3] (a) S. Dhara, B. Sundaravel, K.G.M. Nair, R. Kesavamoorthy, M.C. Valsakumar, T.V.C. Rao, L.C. Chen, K.H. Chen, Appl. Phys. Lett. 88 (2006) 173110;
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