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Ab initio calculations of magnetic properties of Ag-doped GaN
Computational Materials Science 55 (2012) 171–174
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Ab initio calculations of magnetic properties of Ag-doped GaN Alvaro González-García, William López-Pérez, Rafael González-Hernández ⇑ Grupo de Investigación en Fı´sica Aplicada, Departamento de Fı´sica, Universidad del Norte, Barranquilla, Colombia
a r t i c l e
i n f o
Article history: Received 30 August 2011 Received in revised form 2 December 2011 Accepted 5 December 2011 Available online 12 January 2012 Keywords: Spin-density functionals Dilute magnetic semiconductor Magnetic ordering Density functional theory GaN
a b s t r a c t We performed first-principles spin-polarized calculations to study the magnetic properties and electronic structure of AgxGa1xN (x = 0.0556, 0.0625, and 0.125) using density functional theory (DFT) within a plane-wave ultrasoft pseudopotential scheme. We found a stable ferromagnetic state in Ag-doped GaN with a total magnetization of 1.81 lB per supercell, indicating that Ag is ferromagnetically ordered in GaN. These results imply that the ferromagnetic ground state originates from the hybridized Ag (4d) –N (2p)–Ga (3d)–N (2p) chain formed through p–d coupling. This study shows that 4d transition metals, such as, silver may also be used as ferromagnetic dopants in semiconductors. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction At high Curie temperatures and room-temperature, ferromagnetism has been predicted to occur in GaN-doped with transition metal elements, which, can theoretically lead to semiconductor-based spintronic applications [1–3]. Compared to conventional semiconductors, spintronic devices have considerably more functionality when using both the electrical charge and the spin of the electrons. In recent years, the literature has included reports of ferromagnetism at room temperature in various dilute magnetic semiconductors (DMSs) [4]. Nevertheless, the introduction of transition metal atoms into III–V semiconductor host materials has been difficult, particularly because of solubility issues. Normally, magnetic dopants present these disadvantages, which have been observed in Mn doped GaN [5,6]. To address these difficulties, studies have shown that ferromagnetism exists in DMSs with 3d non-magnetic dopants [7–9] and a few DMSs with 4d non-magnetic dopants. Of these, the structural and optical properties of Ag and Cd impurities in ZnO have been theoretically considered thus far [10,11]. This scarcity is most likely due to 4d metals not being ferromagnetic in their natural phases. However, it has previously been shown that the substitutional Pd impurities in GaN are ferromagnetically ordered [12]. This is ascribed to the similarity between the symmetry of the environment of Pd in GaN and the hexagonal phase of Pd, which has previously been shown to be ferromagnetic [13]. However, no experimental or theoretical studies of the magnetic properties and electronic structure of Ag-doped GaN have been conducted
⇑ Corresponding author. Tel.: +57 5 3509509x3425; fax: +57 5 3598852. E-mail address: [email protected] (R. González-Hernández). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.12.009
in the crystallization wurtzite phase. Therefore, in this paper we have studied the electronic structure and possible ferromagnetic orderings in AgxGa1xN (x = 0.0556, 0.0625, and 0.125) using first principles pseudopotential calculations.
2. Computational methods The total energy and electronic structure calculations were performed using the first principle pseudopotential method within the spin density functional theory. We used atomic ultrasoft pseudopotentials [14] and the generalized gradient approximation (GGA) described by Perdew et al. [15] for the exchange and correlation potentials. The calculations were performed using the Quantum-ESPRESSO package [16]. The electron wave functions were expanded in plane waves up to a cutoff energy of 30 Ry, and a C centered 6 6 4 k mesh was used to sample the irreducible Brillouin zone in the special Monkhorst–Pack scheme [17]. The Methfessel-Paxton smearing technique was adopted with a smearing width of 0.02 Ry [18]. These parameters ensure a convergence better than 0.01 meV for the total energy. It has been observed experimentally that manganese impurities can substitute for gallium atoms in GaN semiconductors [19]. Based on the similarity between the electronegativities and the atomic radii of silver and manganese, we expect Ag to substitute for Ga in GaN compounds. Thus, to investigate the magnetic properties of AgxGa1xN with x = 0.0625, we have calculated the electronic structure of Ag-doped GaN using a 32-atom 2a 2a 2c supercell, which was constructed based on a conventional GaN wurtzite unit cell with the common lattice parameters a and c. A Ga atom in the supercell was replaced by an Ag atom to represent
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a concentration of 6.25%. We have also examined the ferromagnetic and antiferromagnetic interactions between the Ag atoms. For this purpose, 32-atom 2a 2a 2c supercells were constructed, each of which contained two substitutional Ag atoms with the largest possible separation of 6.21 Å in the supercells, thus establishing a concentration of 12.5%. We calculated the total energies of the supercells with two spin-polarized Ag atoms coupled in the ferromagnetic and antiferromagnetic states. To confirm the results, we repeated the calculations using a 72-atom 3a 3a 2c supercell with two substitutional Ag atoms separated by a distance of 7.72 Å. This final structure corresponds to a concentration of 5.56% silver atoms. The atomic positions were optimized until the maximum force was smaller than 2 meV/Å.
3. Results and discussion The pure GaN structure of the 2a 2a 2c wurtzite supercell was optimized. The calculated lattice constant a and the obtained c/a ratio (3.218 Å and 1.629, respectively), are slightly larger than the experimental values: a = 3.190 Å and c/a = 1.627 [20,21]. These results confirm that the GGA approach tends to overestimate the lattice constant values. However, the calculated internal parameter (u = 0.377 c) slightly underestimates the experimental value (u = 0.382c) [21]. When one Ga atom in the 2a 2a 2c supercell is substituted by an Ag atom, the lattice parameters in the Ag0.0625Ga0.9375N compound increase lightly. The lattice constant a increases by 0.024 Å, while the c/a ratio increases by 0.006 after structural optimization due to the difference in atomic radii of the Ag and Ga atoms. For Ag0.0625Ga0.9375N, the calculated total energy of the spinpolarized state is 65 meV lower than that of the non-spin-polarized state. Spin polarization results in a magnetic moment of 1.81 lB per supercell that contains one Ag atom, this magnetic moment is slightly higher than that of Pd-doped GaN (1.3 lB) [12]. In this magnetic semiconductor, we observe a different behavior than that has been previously reported for a magnetic moment contribution [12]. We found that the nitrogen neighbors in the basal plane of the AgN4 tetrahedron are the main contributors to the magnetic moment, with a localized magnetic moment of 0.42 lB per atom. The nitrogen neighbor bound to the Ag dopant along the z axis (at the top of the AgN4 tetrahedron), contributes 0.33 lB to the magnetic moment. The Ag dopant atom contributes less (0.32 lB per atom) to the magnetic moment. The results show more magnetic polarization in the N atoms than in the Ag impurity. For the second and third nearest neighbors of silver (Ga and N respectively), we found total magnetizations of 0.024 lB and 0.082 lB per supercell, respectively. Therefore, the hybridization between Ag and the neighboring N atoms leads to the formation of an Ag (4d)–N (2p)–Ga (3d)–N (2p) coupling chain, which induces strong indirect FM coupling in AgxGa1 xN with x = 0.0625. In addition, we observed local deformation around the Ag atoms after the relaxation of the atomic positions. A 0.200 Å increase in the bond length between the nitrogen atom at the top of the AgN4 tetrahedron and the Ag dopant was observed with respect to the ideal value (1.998 Å). A similar 0.205 Å increase in the bond lengths between the Ag dopant and the remaining nitrogen neighbors at the AgN4 tetrahedron was obtained with respect to the ideal values (1.982 Å). The total magnetic moment (1.81 lB per supercell) is mainly distributed on the Ag and the surrounding N atoms. This result is reasonable for the following physical reasons. The valence electron configurations of Ag and Ga are 4d105s1 and 3d104s24p1, respectively. If Ga+3 is replaced by Ag, the configuration of Ag+3 is 4d8. Therefore, we expect a total magnetic moment of no more than 2.0 lB, which is what appeared to have occurred. Moreover, be-
cause GaN is covalently bound, one should expect that the moments of the N and Ag atoms have the same order, which is the case. To study the stable configuration for Ag substitution in GaN bulk, we calculated the formation energy for AgxGa1xN (x = 0.0556, 0.0625 and 0.125). The formation energy (Ef) can be defined as:
Ef ¼ E½Agx Ga1x N E½GaN gAg E½Ag þ gGa E½Ga where gAg and gGa are the numbers of Ag added and Ga removed to the GaN semiconductor host, respectively. E[AgxGa1xN], E[GaN], E[Ag] and E[Ga] are the total energies of the supercell with Ag impurity, pure GaN without impurity, Ag atom and Ga atom, respectively. The results of the calculated formation energies for AgxGa1xN (x = 5.56%, 6.25% and 12.5%) are listed in Table 1. It clearly shows that FM phase is the most stable for all x concentrations. Furthermore, the calculated formation energies are lower than those of Li-doping in GaN [22] and higher than those of Ag-doping in ZnO [23]. In Table 1, we also present the total energy difference (DE = EAFM EFM), ground state (GS) and total magnetization for ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic configurations (NM) of AgxGa1xN (x = 5.56%, 6.25% and 12.5%). The structure containing two Ag atoms, at a concentration of 12.5%, shows a stable ferromagnetic state with a total energy of 38 meV per dopant atom lower than the antiferromagnetic state. The calculated total energy of the ferromagnetic (antiferromagnetic) state is 87.5 meV (49.5 meV) per dopant atom lower than that of the non-spin-polarized state. Next, we performed the total energy calculation using a 72-atom 3a 3a 2c supercell with two Ag atoms separated by a distance of 7.72 Å, thus establishing a concentration of 5.56%. Again, we found a stable ferromagnetic state. In this case, the energy difference between the ferromagnetic and the antiferromagnetic states was considerably reduced to 10.4 meV per dopant atom in the supercell. From this result, we infer that, the interaction between the doping atoms decreases with distance in a similar manner for both FM and AFM ordering. Direct derivation of the Curie temperature would be difficult with these energy differences. Nevertheless, Ye et al. [24] predicted room temperature ferromagnetism in CuxZn1xO (x = 12.5%) with a corresponding energy difference of 42 meV. In addition, room temperature ferromagnetism in ZnO doped with 7% Cu has been observed experimentally [25]. Therefore, room temperature ferromagnetism may also be expected in GaN doped with 7% Ag. GaN is a direct semiconductor with an experimental gap of 3.5 eV, and our results show a direct band-gap of 1.8 eV in the C position (see Fig. 1a). It is well known that the exchange–correlation energy of PBE underestimates the energy gap in the semiconductor [26]. In order to confirm the results of electronic structure calculations of Ag0.0625Ga0.9375N within GGA approximation, we have also taken into account the correlations effect of the 4d-Ag orbitals within the GGA + U method [27], where the U parameter used in the calculation is 3.5 eV [28]. We have found that the ferromagnetic configuration is also the ground state. The
Table 1 Calculated formation energies (Ef in eV), total magnetization (MMT in lB), total energy difference (DE = EAFM EFM in meV) and ground state (GS) for ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic configurations (NM) of AgxGa1xN (x = 5.56%, 6.25% and 12.5%). x (%)
5.56 6.25 12.5
FM
AFM
NM
Ef
MMT
Ef
MMT
Ef
DE
GS
5.53 5.47 5.43
2.09 1.81 1.96
5.55 5.48 5.46
0.00 0.00 0.00
5.64 5.54 5.51
10.4 1.80 38.0
FM FM FM
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(a)
(b)
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(c)
Fig. 1. (a) The band structure of the GaN semiconductor in the 2a 2a 2c supercell. The calculated (b) majority-spin and (c) minority-spin band structures in GGA + U scheme for Ag0.0625Ga0.9375N. The dashed line indicates the Fermi energy level, which is carried to zero.
electronic structure of Ag0.0625Ga0.9375N was calculated with optimized structural parameters and relaxed atomic positions. The spin-polarized band structures of Ag0.0625Ga0.9375N in the 2a 2a 2c wurtzite supercell are shown in Fig. 1b and c, for the majority and the minority spin, respectively. In these figures, the Fermi energy level is adopted as the zero energy level. In Fig. 1b, the majority spin retains a semiconducting character with an energy gap larger than 1.1 eV and an insignificant amount of states belonging to the impurity band in the Fermi level. In Fig. 1c, the energy gap around the Fermi energy level does not exits for the minority spin. The minority spin orientation of Ag0.0625Ga0.9375N presents a metallic character with some unfilled and dispersed bands above the Fermi level. Thus, it behaves as if it contains delocalized holes in the host semiconductor introduced by Ag dopant. The high polarization of the conduction carriers is confirmed by the ferromagnetic coupling of the dopant atoms and the significant presence of conduction carriers in the minority spin channel. The strong polarization of the states that is responsible for conduction in Ag-doped GaN is necessary for spintronic applications. Both the majority and the minority spin states retain a band gap, which indicates that Ag-doped GaN still maintains the natural semiconducting character of GaN. Spin splitting between the majority and the minority spin orientations near the Fermi level indicates that the Ag dopant can be magnetically ordered in the GaN host semiconductor. To further study the atomic contribution to ferromagnetism in the magnetic semiconductor, we have calculated the total and partial density of states in Ag0.0625Ga0.9375N, as shown in Fig. 2. In the majority spin polarization, the total density of states presents a region that is approximately below the Fermi level, which is mainly due to 2p-N electrons. A smaller contribution is also provided by the 4d-Ag states. A similar states contribution below the Fermi energy level is presented by the total density of states in the minority spin orientation. In the majority spin polarization, the partial density of states belonging to the 2p-N orbitals show a strong peak very near and below the Fermi level, which indicates localized states in that region. This peak overlaps with another shorter peak that corresponds to the 4d orbitals of the Ag dopant. In the partial density of states of the minority spin, the 2p-N, 4d-Ag and 3d-Ga orbitals clearly contribute to the unoccupied states above the Fermi level, and all of these show similarly shaped curves in the same energy window. This reveals considerable atomic hybridization between
Fig. 2. Calculated total and partial density of states for Ag0.0625Ga0.9375N in GGA + U method: (a) The total density of states of Ag0.0625Ga0.9375N wurtzite, the partial density of the states corresponding to (b) Ag, and the contributions from the N neighbors (c) at the top and (d) in the basal plane at the AgN4 tetrahedron. The contributions of the (e) second and (f) third nearest neighbors of silver (second NN and third NN, respectively) are shown. The dashed line indicates the Fermi energy level, which is carried to zero. The positive (negative) values of the states correspond to the majority (minority) spin components.
the 4d orbitals of the dopant atom and the 2p states of its four nearest neighboring nitrogen atoms. Thus, this causes magnetization in each neighboring nitrogen atoms of the silver atom, which is what appeared to have happened. In turn, the second-nearest gallium is coupled to the third-nearest nitrogen. Therefore, the hybridized Ag (4d)–N (2p)–Ga (3d)–N (2p) chain mechanism is responsible for the FM coupling in Ag0.0625Ga0.9375N via p d-like coupling.
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that the ferromagnetic spin configuration of the Ag-ions is more energetically favorable than the antiferromagnetic state. The Ag (4d)–N (2p)–Ga (3d)–N (2p) chain mechanism formed through the p–d interaction is responsible for the ferromagnetic characteristics of Ag0.0625Ga0.9375N. When the Ga atoms are substituted by Ag atoms in GaN semiconductor, the Ag spin polarization magnetizes the p states of the neighboring nitrogens via the p–d mechanism. The neighboring nitrogens are spin polarized, and they are ferromagnetically coupled to the Ag. Thus, the second-nearest Ga cations are coupled to the third-nearest N anions. The Ag in GaN is ferromagnetically ordered with conduction holes in the band structure of the minority spin component. The electronic structure of Ag-doped GaN is sensitive to the spin orientation, which is related to the state contribution around the Fermi energy level. Our results suggest that production of GaN-based dilute magnetic can be done by doping the semiconductor with silver. Thus, Ag-doped GaN is an important candidate for designing new functional devices for spintronic applications. Acknowledgements The calculations reported in this paper were performed using the computing facilities at the HIPERLAB-cluster of Universidad del Norte. The research published in this paper is supported by DIDI-Universidad del Norte, Barranquilla, Colombia. Fig. 3. Contour plot of the difference between the majority and minority spin charge–density distributions in the ferromagnetic state of the Ag0.0625Ga0.9375N compound. The N (top) atom is the higher nitrogen atom within the AgN4 tetrahedron. The magnetic polarization of the second and third neighboring atoms of the silver are also shown. The contours are drawn on a logarithmic scale. The red region indicates an increase in the majority-spin density. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The charge–density difference between the majority and minority spin electron density distributions in the ferromagnetic state for Ag0.0625Ga0.9375N is shown in Fig. 3. This reflects the polarization of the N atoms induced by Ag, and the magnetic polarization of the second and third neighboring atoms of the silver, which are induced by the top N atom of the AgN4 tetrahedron. These different spin charge–density distributions show an increase (red region) in the majority-spin density within the AgN4 tetrahedron, which indicates that the magnetic moments are mainly localized around the Ag and N tetrahedron atoms. We also observe magnetic polarization in the second (Ga) and third (N) neighboring atoms of the silver, confirming that the ferromagnetic coupling between the Ag impurity atom and its four surrounding N atoms may help to extend the ferromagnetic interaction to the more distant atoms through the chain mechanism. The hybridization between Ag, and its neighboring host atoms leads to the formation of an Ag (4d)–N (2p)–Ga (3d)– N (2p) coupling chain, which induces a strong indirect FM state in Ag0.0625Ga0.9375N. This type of p–d interaction chain enhances the magnetic properties of Ag0.0625Ga0.9375N and establishes its ferromagnetic character. These results are consistent with previous studies on Pd-doped ZnO, in which the Pd (4d)–O (2p)–Zn (3d)–O (2p)–Pd (4d) chain mechanism formed through p–d interaction is responsible for FM coupling [29]. 4. Conclusions In conclusion, we have studied the electronic structure of Agdoped GaN using spin density functional calculations. We found
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Contents lists available at SciVerse ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Ab initio calculations of magnetic properties of Ag-doped GaN Alvaro González-García, William López-Pérez, Rafael González-Hernández ⇑ Grupo de Investigación en Fı´sica Aplicada, Departamento de Fı´sica, Universidad del Norte, Barranquilla, Colombia
a r t i c l e
i n f o
Article history: Received 30 August 2011 Received in revised form 2 December 2011 Accepted 5 December 2011 Available online 12 January 2012 Keywords: Spin-density functionals Dilute magnetic semiconductor Magnetic ordering Density functional theory GaN
a b s t r a c t We performed first-principles spin-polarized calculations to study the magnetic properties and electronic structure of AgxGa1xN (x = 0.0556, 0.0625, and 0.125) using density functional theory (DFT) within a plane-wave ultrasoft pseudopotential scheme. We found a stable ferromagnetic state in Ag-doped GaN with a total magnetization of 1.81 lB per supercell, indicating that Ag is ferromagnetically ordered in GaN. These results imply that the ferromagnetic ground state originates from the hybridized Ag (4d) –N (2p)–Ga (3d)–N (2p) chain formed through p–d coupling. This study shows that 4d transition metals, such as, silver may also be used as ferromagnetic dopants in semiconductors. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction At high Curie temperatures and room-temperature, ferromagnetism has been predicted to occur in GaN-doped with transition metal elements, which, can theoretically lead to semiconductor-based spintronic applications [1–3]. Compared to conventional semiconductors, spintronic devices have considerably more functionality when using both the electrical charge and the spin of the electrons. In recent years, the literature has included reports of ferromagnetism at room temperature in various dilute magnetic semiconductors (DMSs) [4]. Nevertheless, the introduction of transition metal atoms into III–V semiconductor host materials has been difficult, particularly because of solubility issues. Normally, magnetic dopants present these disadvantages, which have been observed in Mn doped GaN [5,6]. To address these difficulties, studies have shown that ferromagnetism exists in DMSs with 3d non-magnetic dopants [7–9] and a few DMSs with 4d non-magnetic dopants. Of these, the structural and optical properties of Ag and Cd impurities in ZnO have been theoretically considered thus far [10,11]. This scarcity is most likely due to 4d metals not being ferromagnetic in their natural phases. However, it has previously been shown that the substitutional Pd impurities in GaN are ferromagnetically ordered [12]. This is ascribed to the similarity between the symmetry of the environment of Pd in GaN and the hexagonal phase of Pd, which has previously been shown to be ferromagnetic [13]. However, no experimental or theoretical studies of the magnetic properties and electronic structure of Ag-doped GaN have been conducted
⇑ Corresponding author. Tel.: +57 5 3509509x3425; fax: +57 5 3598852. E-mail address: [email protected] (R. González-Hernández). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.12.009
in the crystallization wurtzite phase. Therefore, in this paper we have studied the electronic structure and possible ferromagnetic orderings in AgxGa1xN (x = 0.0556, 0.0625, and 0.125) using first principles pseudopotential calculations.
2. Computational methods The total energy and electronic structure calculations were performed using the first principle pseudopotential method within the spin density functional theory. We used atomic ultrasoft pseudopotentials [14] and the generalized gradient approximation (GGA) described by Perdew et al. [15] for the exchange and correlation potentials. The calculations were performed using the Quantum-ESPRESSO package [16]. The electron wave functions were expanded in plane waves up to a cutoff energy of 30 Ry, and a C centered 6 6 4 k mesh was used to sample the irreducible Brillouin zone in the special Monkhorst–Pack scheme [17]. The Methfessel-Paxton smearing technique was adopted with a smearing width of 0.02 Ry [18]. These parameters ensure a convergence better than 0.01 meV for the total energy. It has been observed experimentally that manganese impurities can substitute for gallium atoms in GaN semiconductors [19]. Based on the similarity between the electronegativities and the atomic radii of silver and manganese, we expect Ag to substitute for Ga in GaN compounds. Thus, to investigate the magnetic properties of AgxGa1xN with x = 0.0625, we have calculated the electronic structure of Ag-doped GaN using a 32-atom 2a 2a 2c supercell, which was constructed based on a conventional GaN wurtzite unit cell with the common lattice parameters a and c. A Ga atom in the supercell was replaced by an Ag atom to represent
172
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a concentration of 6.25%. We have also examined the ferromagnetic and antiferromagnetic interactions between the Ag atoms. For this purpose, 32-atom 2a 2a 2c supercells were constructed, each of which contained two substitutional Ag atoms with the largest possible separation of 6.21 Å in the supercells, thus establishing a concentration of 12.5%. We calculated the total energies of the supercells with two spin-polarized Ag atoms coupled in the ferromagnetic and antiferromagnetic states. To confirm the results, we repeated the calculations using a 72-atom 3a 3a 2c supercell with two substitutional Ag atoms separated by a distance of 7.72 Å. This final structure corresponds to a concentration of 5.56% silver atoms. The atomic positions were optimized until the maximum force was smaller than 2 meV/Å.
3. Results and discussion The pure GaN structure of the 2a 2a 2c wurtzite supercell was optimized. The calculated lattice constant a and the obtained c/a ratio (3.218 Å and 1.629, respectively), are slightly larger than the experimental values: a = 3.190 Å and c/a = 1.627 [20,21]. These results confirm that the GGA approach tends to overestimate the lattice constant values. However, the calculated internal parameter (u = 0.377 c) slightly underestimates the experimental value (u = 0.382c) [21]. When one Ga atom in the 2a 2a 2c supercell is substituted by an Ag atom, the lattice parameters in the Ag0.0625Ga0.9375N compound increase lightly. The lattice constant a increases by 0.024 Å, while the c/a ratio increases by 0.006 after structural optimization due to the difference in atomic radii of the Ag and Ga atoms. For Ag0.0625Ga0.9375N, the calculated total energy of the spinpolarized state is 65 meV lower than that of the non-spin-polarized state. Spin polarization results in a magnetic moment of 1.81 lB per supercell that contains one Ag atom, this magnetic moment is slightly higher than that of Pd-doped GaN (1.3 lB) [12]. In this magnetic semiconductor, we observe a different behavior than that has been previously reported for a magnetic moment contribution [12]. We found that the nitrogen neighbors in the basal plane of the AgN4 tetrahedron are the main contributors to the magnetic moment, with a localized magnetic moment of 0.42 lB per atom. The nitrogen neighbor bound to the Ag dopant along the z axis (at the top of the AgN4 tetrahedron), contributes 0.33 lB to the magnetic moment. The Ag dopant atom contributes less (0.32 lB per atom) to the magnetic moment. The results show more magnetic polarization in the N atoms than in the Ag impurity. For the second and third nearest neighbors of silver (Ga and N respectively), we found total magnetizations of 0.024 lB and 0.082 lB per supercell, respectively. Therefore, the hybridization between Ag and the neighboring N atoms leads to the formation of an Ag (4d)–N (2p)–Ga (3d)–N (2p) coupling chain, which induces strong indirect FM coupling in AgxGa1 xN with x = 0.0625. In addition, we observed local deformation around the Ag atoms after the relaxation of the atomic positions. A 0.200 Å increase in the bond length between the nitrogen atom at the top of the AgN4 tetrahedron and the Ag dopant was observed with respect to the ideal value (1.998 Å). A similar 0.205 Å increase in the bond lengths between the Ag dopant and the remaining nitrogen neighbors at the AgN4 tetrahedron was obtained with respect to the ideal values (1.982 Å). The total magnetic moment (1.81 lB per supercell) is mainly distributed on the Ag and the surrounding N atoms. This result is reasonable for the following physical reasons. The valence electron configurations of Ag and Ga are 4d105s1 and 3d104s24p1, respectively. If Ga+3 is replaced by Ag, the configuration of Ag+3 is 4d8. Therefore, we expect a total magnetic moment of no more than 2.0 lB, which is what appeared to have occurred. Moreover, be-
cause GaN is covalently bound, one should expect that the moments of the N and Ag atoms have the same order, which is the case. To study the stable configuration for Ag substitution in GaN bulk, we calculated the formation energy for AgxGa1xN (x = 0.0556, 0.0625 and 0.125). The formation energy (Ef) can be defined as:
Ef ¼ E½Agx Ga1x N E½GaN gAg E½Ag þ gGa E½Ga where gAg and gGa are the numbers of Ag added and Ga removed to the GaN semiconductor host, respectively. E[AgxGa1xN], E[GaN], E[Ag] and E[Ga] are the total energies of the supercell with Ag impurity, pure GaN without impurity, Ag atom and Ga atom, respectively. The results of the calculated formation energies for AgxGa1xN (x = 5.56%, 6.25% and 12.5%) are listed in Table 1. It clearly shows that FM phase is the most stable for all x concentrations. Furthermore, the calculated formation energies are lower than those of Li-doping in GaN [22] and higher than those of Ag-doping in ZnO [23]. In Table 1, we also present the total energy difference (DE = EAFM EFM), ground state (GS) and total magnetization for ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic configurations (NM) of AgxGa1xN (x = 5.56%, 6.25% and 12.5%). The structure containing two Ag atoms, at a concentration of 12.5%, shows a stable ferromagnetic state with a total energy of 38 meV per dopant atom lower than the antiferromagnetic state. The calculated total energy of the ferromagnetic (antiferromagnetic) state is 87.5 meV (49.5 meV) per dopant atom lower than that of the non-spin-polarized state. Next, we performed the total energy calculation using a 72-atom 3a 3a 2c supercell with two Ag atoms separated by a distance of 7.72 Å, thus establishing a concentration of 5.56%. Again, we found a stable ferromagnetic state. In this case, the energy difference between the ferromagnetic and the antiferromagnetic states was considerably reduced to 10.4 meV per dopant atom in the supercell. From this result, we infer that, the interaction between the doping atoms decreases with distance in a similar manner for both FM and AFM ordering. Direct derivation of the Curie temperature would be difficult with these energy differences. Nevertheless, Ye et al. [24] predicted room temperature ferromagnetism in CuxZn1xO (x = 12.5%) with a corresponding energy difference of 42 meV. In addition, room temperature ferromagnetism in ZnO doped with 7% Cu has been observed experimentally [25]. Therefore, room temperature ferromagnetism may also be expected in GaN doped with 7% Ag. GaN is a direct semiconductor with an experimental gap of 3.5 eV, and our results show a direct band-gap of 1.8 eV in the C position (see Fig. 1a). It is well known that the exchange–correlation energy of PBE underestimates the energy gap in the semiconductor [26]. In order to confirm the results of electronic structure calculations of Ag0.0625Ga0.9375N within GGA approximation, we have also taken into account the correlations effect of the 4d-Ag orbitals within the GGA + U method [27], where the U parameter used in the calculation is 3.5 eV [28]. We have found that the ferromagnetic configuration is also the ground state. The
Table 1 Calculated formation energies (Ef in eV), total magnetization (MMT in lB), total energy difference (DE = EAFM EFM in meV) and ground state (GS) for ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic configurations (NM) of AgxGa1xN (x = 5.56%, 6.25% and 12.5%). x (%)
5.56 6.25 12.5
FM
AFM
NM
Ef
MMT
Ef
MMT
Ef
DE
GS
5.53 5.47 5.43
2.09 1.81 1.96
5.55 5.48 5.46
0.00 0.00 0.00
5.64 5.54 5.51
10.4 1.80 38.0
FM FM FM
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(a)
(b)
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(c)
Fig. 1. (a) The band structure of the GaN semiconductor in the 2a 2a 2c supercell. The calculated (b) majority-spin and (c) minority-spin band structures in GGA + U scheme for Ag0.0625Ga0.9375N. The dashed line indicates the Fermi energy level, which is carried to zero.
electronic structure of Ag0.0625Ga0.9375N was calculated with optimized structural parameters and relaxed atomic positions. The spin-polarized band structures of Ag0.0625Ga0.9375N in the 2a 2a 2c wurtzite supercell are shown in Fig. 1b and c, for the majority and the minority spin, respectively. In these figures, the Fermi energy level is adopted as the zero energy level. In Fig. 1b, the majority spin retains a semiconducting character with an energy gap larger than 1.1 eV and an insignificant amount of states belonging to the impurity band in the Fermi level. In Fig. 1c, the energy gap around the Fermi energy level does not exits for the minority spin. The minority spin orientation of Ag0.0625Ga0.9375N presents a metallic character with some unfilled and dispersed bands above the Fermi level. Thus, it behaves as if it contains delocalized holes in the host semiconductor introduced by Ag dopant. The high polarization of the conduction carriers is confirmed by the ferromagnetic coupling of the dopant atoms and the significant presence of conduction carriers in the minority spin channel. The strong polarization of the states that is responsible for conduction in Ag-doped GaN is necessary for spintronic applications. Both the majority and the minority spin states retain a band gap, which indicates that Ag-doped GaN still maintains the natural semiconducting character of GaN. Spin splitting between the majority and the minority spin orientations near the Fermi level indicates that the Ag dopant can be magnetically ordered in the GaN host semiconductor. To further study the atomic contribution to ferromagnetism in the magnetic semiconductor, we have calculated the total and partial density of states in Ag0.0625Ga0.9375N, as shown in Fig. 2. In the majority spin polarization, the total density of states presents a region that is approximately below the Fermi level, which is mainly due to 2p-N electrons. A smaller contribution is also provided by the 4d-Ag states. A similar states contribution below the Fermi energy level is presented by the total density of states in the minority spin orientation. In the majority spin polarization, the partial density of states belonging to the 2p-N orbitals show a strong peak very near and below the Fermi level, which indicates localized states in that region. This peak overlaps with another shorter peak that corresponds to the 4d orbitals of the Ag dopant. In the partial density of states of the minority spin, the 2p-N, 4d-Ag and 3d-Ga orbitals clearly contribute to the unoccupied states above the Fermi level, and all of these show similarly shaped curves in the same energy window. This reveals considerable atomic hybridization between
Fig. 2. Calculated total and partial density of states for Ag0.0625Ga0.9375N in GGA + U method: (a) The total density of states of Ag0.0625Ga0.9375N wurtzite, the partial density of the states corresponding to (b) Ag, and the contributions from the N neighbors (c) at the top and (d) in the basal plane at the AgN4 tetrahedron. The contributions of the (e) second and (f) third nearest neighbors of silver (second NN and third NN, respectively) are shown. The dashed line indicates the Fermi energy level, which is carried to zero. The positive (negative) values of the states correspond to the majority (minority) spin components.
the 4d orbitals of the dopant atom and the 2p states of its four nearest neighboring nitrogen atoms. Thus, this causes magnetization in each neighboring nitrogen atoms of the silver atom, which is what appeared to have happened. In turn, the second-nearest gallium is coupled to the third-nearest nitrogen. Therefore, the hybridized Ag (4d)–N (2p)–Ga (3d)–N (2p) chain mechanism is responsible for the FM coupling in Ag0.0625Ga0.9375N via p d-like coupling.
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that the ferromagnetic spin configuration of the Ag-ions is more energetically favorable than the antiferromagnetic state. The Ag (4d)–N (2p)–Ga (3d)–N (2p) chain mechanism formed through the p–d interaction is responsible for the ferromagnetic characteristics of Ag0.0625Ga0.9375N. When the Ga atoms are substituted by Ag atoms in GaN semiconductor, the Ag spin polarization magnetizes the p states of the neighboring nitrogens via the p–d mechanism. The neighboring nitrogens are spin polarized, and they are ferromagnetically coupled to the Ag. Thus, the second-nearest Ga cations are coupled to the third-nearest N anions. The Ag in GaN is ferromagnetically ordered with conduction holes in the band structure of the minority spin component. The electronic structure of Ag-doped GaN is sensitive to the spin orientation, which is related to the state contribution around the Fermi energy level. Our results suggest that production of GaN-based dilute magnetic can be done by doping the semiconductor with silver. Thus, Ag-doped GaN is an important candidate for designing new functional devices for spintronic applications. Acknowledgements The calculations reported in this paper were performed using the computing facilities at the HIPERLAB-cluster of Universidad del Norte. The research published in this paper is supported by DIDI-Universidad del Norte, Barranquilla, Colombia. Fig. 3. Contour plot of the difference between the majority and minority spin charge–density distributions in the ferromagnetic state of the Ag0.0625Ga0.9375N compound. The N (top) atom is the higher nitrogen atom within the AgN4 tetrahedron. The magnetic polarization of the second and third neighboring atoms of the silver are also shown. The contours are drawn on a logarithmic scale. The red region indicates an increase in the majority-spin density. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The charge–density difference between the majority and minority spin electron density distributions in the ferromagnetic state for Ag0.0625Ga0.9375N is shown in Fig. 3. This reflects the polarization of the N atoms induced by Ag, and the magnetic polarization of the second and third neighboring atoms of the silver, which are induced by the top N atom of the AgN4 tetrahedron. These different spin charge–density distributions show an increase (red region) in the majority-spin density within the AgN4 tetrahedron, which indicates that the magnetic moments are mainly localized around the Ag and N tetrahedron atoms. We also observe magnetic polarization in the second (Ga) and third (N) neighboring atoms of the silver, confirming that the ferromagnetic coupling between the Ag impurity atom and its four surrounding N atoms may help to extend the ferromagnetic interaction to the more distant atoms through the chain mechanism. The hybridization between Ag, and its neighboring host atoms leads to the formation of an Ag (4d)–N (2p)–Ga (3d)– N (2p) coupling chain, which induces a strong indirect FM state in Ag0.0625Ga0.9375N. This type of p–d interaction chain enhances the magnetic properties of Ag0.0625Ga0.9375N and establishes its ferromagnetic character. These results are consistent with previous studies on Pd-doped ZnO, in which the Pd (4d)–O (2p)–Zn (3d)–O (2p)–Pd (4d) chain mechanism formed through p–d interaction is responsible for FM coupling [29]. 4. Conclusions In conclusion, we have studied the electronic structure of Agdoped GaN using spin density functional calculations. We found
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