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Ferromagnetism in Cu-doped silicon carbide
Solid State Communications 152 (2012) 752–756
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Ferromagnetism in Cu-doped silicon carbide Cuilian Zhao, Congmian Zhen ∗ , Yuanzheng Li, Li Ma, Chengfu Pan, Denglu Hou Institute of Physics, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, PR China
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Article history: Received 9 November 2011 Received in revised form 4 January 2012 Accepted 2 February 2012 by P. Chaddah Available online 6 February 2012 Keywords: B. Cu-doped B. First-principles calculation D. Ferromagnetism D. SiC
abstract Cu doped silicon carbide is shown to be ferromagnetic based on experiment results and first-principles calculations. The magnetization value of the Cu doped silicon carbide decreased as the Cu concentration increased. When the films were annealed at 800 °C, the ferromagnetic signal was increased. Reduction of the C vacancy concentration will introduce a large total moment in the system. Theoretically, compared with the case of one Cu atom replacing one Si atom, increasing the Cu doping, changing the Cu atom location or including carbon vacancies in the calculations for the system all make the ferromagnetic moment decrease. One Cu atom replacing one Si atom with the addition of one C vacancy makes the energy band gap of the system disappear. Our investigations suggest that the ferromagnetism arises from the hybridization between Cu 3d orbital and C 2p orbital. Ferromagnetic moment is influenced by a symmetry-lowering distortion of the surrounding lattice by the Cu dopant. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Silicon carbide (SiC) is a well known wide-band-gap semiconductor that exists in more than 200 different polytypes. In particular, cubic SiC (3C-SiC) has many superior physical properties, such as a high melting point, high thermal conductivity, high electric breakdown field and high saturation electron drift velocity [1–3]. In addition, it is compatible with the planar growth processes of Si. SiC semiconductor devices are expected to replace traditional semiconductors in areas such as high-power and high-frequency devices. With respect to ferromagnetism, high Curie temperature (Tc ) ferromagnetism has been predicted for zinc-blended semiconductors consisting of transition metal impurities using Zener model [4,5]. Under this model, ferromagnetism is arising due to interaction between carriers and localized spins. The model also shows a tendency for an increase in the Curie temperature for dilute magnetic semiconductors (DMSs) as the semiconductor band gap increases. According to the trends and the underlying physics established by the theory, SiC is a promising material in spintronics. Transition metals (TMs), such as Fe, Mn, Co, Cr and Ni, as common impurities in SiC, have been extensively studied [6–11], and the observed room temperature ferromagnetism (RTFM) has been found to arise from magnetic secondary phases or precipitates of the magnetic dopants. Unfortunately, the TM dopants destroy the excellent characteristics of SiC itself. Recently, to avoid these problems related to magnetic precipitates, many researchers have begun to study semiconductors and oxides with
∗
Corresponding author. Tel.: +86 311 80787328. E-mail address: [email protected] (C. Zhen).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2012.02.001
nonmagnetic dopant elements, and RTFM has been demonstrated in C-, N- and Cu-doped ZnO [12–18], N-doped In2 O3 [19] and Cudoped SnO2 [20]. Song et al. [21] have reported the observation of glassy ferromagnetism (FM) in Al-doped 4H-SiC. However, despite considerable theoretical and experimental effort, the origin of the observed ferromagnetism is still under debate, and the basic mechanism responsible for RTFM in these materials has yet to be established. If one wishes to enhance the magnetic interactions and to improve the physical properties in these materials, it is essential to understand the mechanism of such phenomena. To date, little effort has been focused on the magnetism of Cudoped SiC film. In this letter, we report experimental results and first principles calculations to study the electronic structures and magnetic properties of the Cu-doped SiC system. We also discuss the origin of the ferromagnetism. 2. Experimental details The Cu-doped SiC films were prepared on Si (111) substrates using a magnetron sputtering method. Cu target and SiC target were alternately sputtered. By controlling the sputtering time of the Cu target, Cu-doped SiC films with different Cu concentrations were produced. Prior to deposition, the Si substrates were dipped in 10 at.% hydrofluoric acid to remove the surface native oxides, then rinsed with de-ionized water, dried with N2 , and immediately placed into the sputtering chamber. The chamber was evacuated to 2 × 10−4 Pa. The sputtering pressure was maintained at 2 Pa by introducing argon. High-temperature thermal annealing was adopted to crystallize the films. The thermal annealing was carried out under vacuum conditions for 10 min.
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Fig. 1. (a) XRD spectra of the as-deposited 3 at.% Cu doped SiC film and that annealed at 800 °C. (b) Room-temperature magnetization curves for the as-deposited 3 at.% Cu-doped SiC film, and for the 1.5 and 3 at.% Cu-doped SiC film annealed at 800 °C.
Fig. 2. Cu doped SiC 2 × 2 × 2 supercells. (a) Cu–SiC–Si. (b) 2Cu–SiC–Si. (c) Cu–SiC–Si–Vc. (d) Cu–SiC–C.
3. Results and discussion 3.1. Structure and magnetic properties The crystalline structure of the films was investigated using X-ray diffraction (XRD) on an ‘‘X’Perd Pro’’-type diffractometer. The magnetic properties of the films were measured using a Physical Properties Measurement System (PPMS-9) with the applied magnetic field parallel to the film plane. The XRD spectra of the 3 at.% Cu doped SiC films are shown in Fig. 1(a). No obvious peaks were observed except for the Si substrate signals located around 55° in the as-deposited films, which shows that the films were amorphous. When the thermal annealing temperature reached 800 °C, the crystallization of the Cu doped SiC films was improved and the SiC (111) diffusion peak appeared. Fig. 1(b) shows the room-temperature magnetization curves for the as-deposited 3 at.% Cu-doped SiC film, and for the 1.5 and 3 at.% Cu-doped SiC film annealed at 800 °C. It can
be seen from the curves that as the annealing temperature was raised 800 °C, the saturation magnetization was found to increase. The saturation magnetization of the annealed films increased further if we decrease the Cu concentration from 3 to 1.5 at.%. Cu concentration and degree of crystallization in the film play crucial roles in tuning the ferromagnetism of the Cu doped SiC films. 3.2. Model structures and numerical method To understand the origin of the observed ferromagnetism, the numerical calculations have been performed by considering four 2 × 2 × 2 SiC supercells (shown in Fig. 2). The four configurations of the Cu-doped SiC superlattice are based on the experiment: Fig. 2(a) randomly replacing one Si atom in the supercell by one Cu atom (Cu–SiC–Si), which corresponds to a doping concentration of 1.56 at.%; Fig. 2(b) replacing two Si atoms by two Cu atoms (2Cu–SiC–Si), which corresponds to a doping concentration of 3.13 at.%; Fig. 2(c) randomly replacing one Si atom with one
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Fig. 3. TDOSs and PDOSs for the Cu doped SiC supercells. (a) Cu–SiC–Si. (b) 2Cu–SiC–Si. (c) Cu–SiC–Si–Vc. (d) Cu–SiC–C. The Fermi energy is taken to be the zero of energy. Dotted curves represent spin down and solid curves represent spin up.
Cu atom and leaving one C vacancy (Cu–SiC–Si–Vc); Fig. 2(d) randomly replacing one C atom by one Cu atom (Cu–SiC–C). First-principles calculations based on density functional theory (DFT) were performed using the Cambridge Serial Total Energy Package (CASTEP) code [22] to investigate the properties of the Cu doped SiC supercells. The exchange–correlation functional was treated using the generalized gradient approximation [23] (GGA) employing the Perdew–Burke–Enzerh (PBE) functional form. The numerical integration of the Brillouin zone was performed using a 6 × 6 × 6 Monkhorst–Pack k-point sampling, the cutoff energy was assumed to be 300 eV for the plane wave basis. The valenceelectron configurations for the Si and C atoms were chosen as 3s2 3p2 and 2s2 2p2 , respectively. Considering 3s and 3p states of the transition metals in the basis sets having little influence on the magnetism of a system containing transition metals, therefore, we neglected 3s and 3p of Cu atom in our calculations. The valenceelectron configuration for the Cu atom was chosen as 3d10 4s1 . In the optimization process, the energy change, as well as the maximum tolerances for the force, stress, and displacement were set at 0.2 × 10−4 eV/atom, 0.5 × 10−1 eV/Å, 0.1 GPa, and 0.2 × 10−2 Å, respectively.
3.3. Electronic structure and ferromagnetism Fig. 3 depicts the total density of states (TDOSs) and partial DOSs (PDOSs) for the Cu doped SiC systems. The Fermi energy is taken to be the zero of energy. For the cases show in Fig. 3(a), (b) and (c), the Fermi energy level (EF ) enters the valence band, and all three cases (Cu–SiC–Si, 2Cu–SiC–Si and Cu–SiC–Si–Vc) show p-type doping. The Cu–SiC–C system, (Fig. 3(d)) on the other hand, shows n-type doping. Placing the doped Cu atom in different locations therefore resulted in different doping types. In the cases of Cu–SiC–Si, Cu–SiC–Si–Vc and Cu–SiC–C (Fig. 3(a), (c) and (d)), the systems show ferromagnetism while the 2Cu–SiC–Si system in which two Si atoms were replaced by two Cu atoms does not show ferromagnetism. As can be seen from Fig. 3(a), the uppermost valence band of the Cu–SiC–Si system consists mainly of C 2p states and Cu 3d states, and the lowest conduction band of the Cu–SiC–Si system is dominated by the 3p states of the Si atoms. The hybridization between the Cu dopant and its neighboring host atoms results in the splitting of the energy levels near EF , which shifts the majority spin states downward and the minority spin states upward to lower the total energy of the system. Due to
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Fig. 4. Spin-density of the Cu–SiC–Si.
the splitting of the energy levels near EF , the system possesses a magnetic moment of 2.86 µB , with the magnetic moments being mainly contributed by the C 2p orbital (about 2.24 µB ). The Si 3p orbital and Cu 3d orbital also contribute small parts, −0.18 µB and 0.68 µB , respectively. Therefore, the magnetic moment in the Cu–SiC–Si system is mainly due to the delocalized 2p orbital of the C atoms bonded with the Cu atom. The spin density of the Cu–SiC–Si system is shown in Fig. 4. Valence electrons in p states have much larger spatial extensions which could promote longrange exchange coupling interactions. Interaction between the Cu atom and the nearest-neighbor C atoms is through ferromagnetic coupling, while the interaction between the Cu atom and the second-neighbor Si atoms is through antiferromagnetic coupling. We have made an estimation of Tc from the classical Heisenberg model in mean-field approximation, which can be written as kB TC = 21E /3x [24,25]. Here kB is the Boltzmann constant, and x is the doping concentration of Cu dopants (x = 1.56% for the Cu–SiC–Si system). The energy difference (1E) between antiferromagnetic and ferromagnetic orderings was 666 meV, using as an indicator of the magnetic stability. We can therefore obtain Tc value of 330 K for the Cu–SiC–Si system, indicating that the Cu–SiC–Si system is ferromagnetic with the Curie temperature higher than room temperature. To understand further the influence of the doped Cu atom on the SiC system, we also considered two Cu atoms doped into the SiC system corresponding to a doping concentration of 3.13 at.%. The calculated TDOS is shown in Fig. 3(b). The results indicate that the net magnetic moment of the 2Cu–SiC–Si system is zero. As the Cu concentration increases, the ferromagnetism of the SiC
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system decreases, which is consistent with our experiments. It is proposed that antiferromagnetic interaction between those copper atoms is increased as the copper concentration increases [17]. The distributions of the electrons of the Cu atoms and their nearestneighbor C atoms in the Cu–SiC–Si and 2Cu–SiC–Si systems are different. The charge densities of the Cu–SiC–Si and 2Cu–SiC–Si systems are shown in Fig. 5. It is thought that when Cu atom is doped into the system, additional carriers are introduced into the system. Interaction between the Cu 3d electrons and the nearest-neighbor C 2p electrons is increased, which results in the spin polarization of C 2p electrons. The exchange interactions between unpaired electron spins arising from C 2p states are antiferromagnetic in 2Cu–SiC–Si systems. Experimentally, films such as those studied here are usually formed in a sputtering process, in which the sputtering rate of the Si atoms is much higher than that of the C atoms. Consequently, C vacancies are easily formed in Cu-doped SiC films. We therefore considered a case in which one C vacancy existed in the system and one Si atom was replaced by a Cu atom (Cu–SiC–Si–Vc). The system exhibited ferromagnetism with a total magnetic moment of 1 µB . This is smaller than in the case of Cu–SiC–Si system with no C vacancy as has been discussed above (Fig. 3(a)). In addition, an interesting observation from Fig. 3(c) for the system with a vacancy is that the Cu dopant and the C vacancy make the energy levels continuous in the band-gap of SiC. The energy band gap thus disappears completely. It is thought that C vacancies in SiC structures give rise to a symmetry-lowering distortion of the surrounding lattice [26]. Thermal annealing will reduce the C vacancy concentration and introduces a large total moment in the system. The researchers found that the Si site is more favorable compared to the C site for Cu atom substitution. Although a Cu atom replacing a C atom requires more energy, this case exists in experiment. Fig. 3(d) shows the calculated TDOS and PDOSs for the n-type doping in the Cu–SiC–C system. The calculated total magnetic moment of the Cu–SiC–C system is 1µB (∼0.34 µB from Cu atom itself, ∼0.4 µB from its first-neighbor Si atoms, and ∼0.3 µB from its second nearest-neighbor C atoms). The difference between the Cu atom in the Si atom location and the Cu atom in the C atom location is that in the Cu–SiC–C system not only is there a ferromagnetic coupling between the Cu atom and its first-neighbor Si atoms, but there is also ferromagnetic coupling between the Cu atom and its second-neighbor C atoms. It can be seen that the Si 2p states overlap slightly with those of the Cu 3d states near the Fermi level, suggesting a weak interaction between them. The existence of spin-polarized electrons is related to a change in the SiC structure. It is well known that the radius of the Cu atom is much larger than that of the C atom. When a Cu atom replaces a C atom in the Cu–SiC–C system, the crystal lattice surrounding the Cu
Fig. 5. Charge density of (a) the Cu–SiC–Si. (b) 2Cu–SiC–Si.
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atom undergoes significant changes, making the Si 2p states near the EF non-local. This in turn causes the interaction between the Cu 3d, Si 3p and C 3p orbitals to be in the form of a ferromagnetic coupling. 4. Conclusion Based on experiment results and the first-principles calculations, SiC doped by Cu element was confirmed to be ferromagnetic. If the Cu concentration is decreased or the degree of crystallization is improved, the ferromagnetism signal in Cu doped silicon carbide is always found to increase. The calculated highest ferromagnetic moment was about 2.86 µB for the configuration of one Cu atom at a Si site with no C vacancy. We propose the ferromagnetism of Cu-doped SiC is related to both the hybridization between Cu 3d orbital and C 2p orbital and symmetry-lowering distortions. Acknowledgments This work was supported by National Science Foundation of China (10804026), Natural Science Foundation of Hebei Province (E2010000429) and Foundation of Hebei Educational Committee (2006123). References [1] N. Achtziger, W. Witthuhn, Phys. Rev. B 57 (1998) 12181–12196. [2] A. Markwitz, S. Johnson, M. Rudolphi, Appl. Phys. Lett. 89 (2006) 153122–153124. [3] A. Qteish, Volker Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6534–6542. [4] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019–1022.
[5] P.W. Anderson, H. Hasegawa, Phys. Rev. 100 (1955) 675–681. [6] N. Theodoropoulou, A.F. Hebard, S.N.G. Chu, M.E. Overberg, C.R. Abernathy, S.J. Pearton, R.G. Wilson, J.M. Zavada, Electrochem. Solid-State Lett. 4 (2001) G119–G121. [7] J. Baur, M. Kunzer, J. Schneider, Phys. Status Solidi (A) 162 (1997) 153–172. [8] C.G. Jin, X.M. Wu, L.J. Zhuge, Z.D. Sha, B. Hong, J. Phys. D: Appl. Phys. 41 (2008) 035005–035008. [9] S.B. Ma, Y.P. Sun, B.C. Zhao, P. Tong, X.B. Zhu, W.H. Song, Physica B 394 (2007) 122–126. [10] K. Kudelska, R. Diduszko, E. Tymicki, W. Dobrowolski, K. Grasza, Phys. Status Solidi (B) 244 (2007) 1743–1746. [11] H. Zhao, Q.W. Chen, J. Magn. Magn. Mater. 313 (2007) 111–114. [12] H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, J.Y. Lin, Y.P. Feng, J. Ding, L.H. Van, J.H. Yin, Phys. Rev. Lett. 99 (2007) 127201–127204. [13] C.F. Yu, T.J. Lin, S.J. Sun, H. Chou, J. Phys. D: Appl. Phys. 40 (2007) 6497–6500. [14] H. Peng, H.J. Xiang, S.H. Wei, S.S. Li, J.B. Xia, J. Li, Phys. Rev. Lett. 102 (2009) 017201–017204. [15] H. Pan, Y.P. Feng, Q.Y. Wu, Z.G. Huang, J. Lin, Phys. Rev. B 77 (2008) 125211–125214. [16] L. Shen, R.Q. Wu, H. Pan, G.W. Peng, M. Yang, Z.D. Sha, Y.P. Feng, Phys. Rev. B 78 (2008) 073306–073309. [17] D.B. Buchholz, R.P.H. Chang, J.H. Song, J.B. Ketterson, Appl. Phys. Lett. 87 (2005) 082504–082506. [18] A. Tiwari, M. Snure, D. Kumar, J.T. Abiade, Appl. Phys. Lett. 92 (2008) 062509–062511. [19] L.X. Guan, J.G. Tao, C.H.A. Huan, J.L. Kuo, L. Wang, Appl. Phys. Lett. 95 (2009) 012509–012511. [20] L.J. Li, K. Yu, Z. Tang, Z.Q. Zhu, Q. Wan, J. Appl. Phys. 107 (2010) 014303–014307. [21] B. Song, H.Q. Bao, H. Li, M. Lei, T.H. Peng, J.K. Jian, J. Liu, W.Y. Wang, W.J. Wang, X.L. Chen, J. Am. Chem. Soc. 131 (2009) 1376–1377. [22] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717–2743. [23] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [24] K. Sato, P.H. Dederichs, H. Katayama-Yoshida, Europhys. Lett. 61 (2003) 403–408. [25] W. Jia, P.D. Han, M. Chi, S.H. Dang, B.S. Xu, J. Appl. Phys. 101 (2007) 113918–113921. [26] A. Zywietz, J. Furthmüller, F. Bechstedt, Phys. Status Solidi (B) 210 (1998) 13–29.
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Ferromagnetism in Cu-doped silicon carbide Cuilian Zhao, Congmian Zhen ∗ , Yuanzheng Li, Li Ma, Chengfu Pan, Denglu Hou Institute of Physics, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, PR China
article
info
Article history: Received 9 November 2011 Received in revised form 4 January 2012 Accepted 2 February 2012 by P. Chaddah Available online 6 February 2012 Keywords: B. Cu-doped B. First-principles calculation D. Ferromagnetism D. SiC
abstract Cu doped silicon carbide is shown to be ferromagnetic based on experiment results and first-principles calculations. The magnetization value of the Cu doped silicon carbide decreased as the Cu concentration increased. When the films were annealed at 800 °C, the ferromagnetic signal was increased. Reduction of the C vacancy concentration will introduce a large total moment in the system. Theoretically, compared with the case of one Cu atom replacing one Si atom, increasing the Cu doping, changing the Cu atom location or including carbon vacancies in the calculations for the system all make the ferromagnetic moment decrease. One Cu atom replacing one Si atom with the addition of one C vacancy makes the energy band gap of the system disappear. Our investigations suggest that the ferromagnetism arises from the hybridization between Cu 3d orbital and C 2p orbital. Ferromagnetic moment is influenced by a symmetry-lowering distortion of the surrounding lattice by the Cu dopant. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Silicon carbide (SiC) is a well known wide-band-gap semiconductor that exists in more than 200 different polytypes. In particular, cubic SiC (3C-SiC) has many superior physical properties, such as a high melting point, high thermal conductivity, high electric breakdown field and high saturation electron drift velocity [1–3]. In addition, it is compatible with the planar growth processes of Si. SiC semiconductor devices are expected to replace traditional semiconductors in areas such as high-power and high-frequency devices. With respect to ferromagnetism, high Curie temperature (Tc ) ferromagnetism has been predicted for zinc-blended semiconductors consisting of transition metal impurities using Zener model [4,5]. Under this model, ferromagnetism is arising due to interaction between carriers and localized spins. The model also shows a tendency for an increase in the Curie temperature for dilute magnetic semiconductors (DMSs) as the semiconductor band gap increases. According to the trends and the underlying physics established by the theory, SiC is a promising material in spintronics. Transition metals (TMs), such as Fe, Mn, Co, Cr and Ni, as common impurities in SiC, have been extensively studied [6–11], and the observed room temperature ferromagnetism (RTFM) has been found to arise from magnetic secondary phases or precipitates of the magnetic dopants. Unfortunately, the TM dopants destroy the excellent characteristics of SiC itself. Recently, to avoid these problems related to magnetic precipitates, many researchers have begun to study semiconductors and oxides with
∗
Corresponding author. Tel.: +86 311 80787328. E-mail address: [email protected] (C. Zhen).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2012.02.001
nonmagnetic dopant elements, and RTFM has been demonstrated in C-, N- and Cu-doped ZnO [12–18], N-doped In2 O3 [19] and Cudoped SnO2 [20]. Song et al. [21] have reported the observation of glassy ferromagnetism (FM) in Al-doped 4H-SiC. However, despite considerable theoretical and experimental effort, the origin of the observed ferromagnetism is still under debate, and the basic mechanism responsible for RTFM in these materials has yet to be established. If one wishes to enhance the magnetic interactions and to improve the physical properties in these materials, it is essential to understand the mechanism of such phenomena. To date, little effort has been focused on the magnetism of Cudoped SiC film. In this letter, we report experimental results and first principles calculations to study the electronic structures and magnetic properties of the Cu-doped SiC system. We also discuss the origin of the ferromagnetism. 2. Experimental details The Cu-doped SiC films were prepared on Si (111) substrates using a magnetron sputtering method. Cu target and SiC target were alternately sputtered. By controlling the sputtering time of the Cu target, Cu-doped SiC films with different Cu concentrations were produced. Prior to deposition, the Si substrates were dipped in 10 at.% hydrofluoric acid to remove the surface native oxides, then rinsed with de-ionized water, dried with N2 , and immediately placed into the sputtering chamber. The chamber was evacuated to 2 × 10−4 Pa. The sputtering pressure was maintained at 2 Pa by introducing argon. High-temperature thermal annealing was adopted to crystallize the films. The thermal annealing was carried out under vacuum conditions for 10 min.
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Fig. 1. (a) XRD spectra of the as-deposited 3 at.% Cu doped SiC film and that annealed at 800 °C. (b) Room-temperature magnetization curves for the as-deposited 3 at.% Cu-doped SiC film, and for the 1.5 and 3 at.% Cu-doped SiC film annealed at 800 °C.
Fig. 2. Cu doped SiC 2 × 2 × 2 supercells. (a) Cu–SiC–Si. (b) 2Cu–SiC–Si. (c) Cu–SiC–Si–Vc. (d) Cu–SiC–C.
3. Results and discussion 3.1. Structure and magnetic properties The crystalline structure of the films was investigated using X-ray diffraction (XRD) on an ‘‘X’Perd Pro’’-type diffractometer. The magnetic properties of the films were measured using a Physical Properties Measurement System (PPMS-9) with the applied magnetic field parallel to the film plane. The XRD spectra of the 3 at.% Cu doped SiC films are shown in Fig. 1(a). No obvious peaks were observed except for the Si substrate signals located around 55° in the as-deposited films, which shows that the films were amorphous. When the thermal annealing temperature reached 800 °C, the crystallization of the Cu doped SiC films was improved and the SiC (111) diffusion peak appeared. Fig. 1(b) shows the room-temperature magnetization curves for the as-deposited 3 at.% Cu-doped SiC film, and for the 1.5 and 3 at.% Cu-doped SiC film annealed at 800 °C. It can
be seen from the curves that as the annealing temperature was raised 800 °C, the saturation magnetization was found to increase. The saturation magnetization of the annealed films increased further if we decrease the Cu concentration from 3 to 1.5 at.%. Cu concentration and degree of crystallization in the film play crucial roles in tuning the ferromagnetism of the Cu doped SiC films. 3.2. Model structures and numerical method To understand the origin of the observed ferromagnetism, the numerical calculations have been performed by considering four 2 × 2 × 2 SiC supercells (shown in Fig. 2). The four configurations of the Cu-doped SiC superlattice are based on the experiment: Fig. 2(a) randomly replacing one Si atom in the supercell by one Cu atom (Cu–SiC–Si), which corresponds to a doping concentration of 1.56 at.%; Fig. 2(b) replacing two Si atoms by two Cu atoms (2Cu–SiC–Si), which corresponds to a doping concentration of 3.13 at.%; Fig. 2(c) randomly replacing one Si atom with one
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Fig. 3. TDOSs and PDOSs for the Cu doped SiC supercells. (a) Cu–SiC–Si. (b) 2Cu–SiC–Si. (c) Cu–SiC–Si–Vc. (d) Cu–SiC–C. The Fermi energy is taken to be the zero of energy. Dotted curves represent spin down and solid curves represent spin up.
Cu atom and leaving one C vacancy (Cu–SiC–Si–Vc); Fig. 2(d) randomly replacing one C atom by one Cu atom (Cu–SiC–C). First-principles calculations based on density functional theory (DFT) were performed using the Cambridge Serial Total Energy Package (CASTEP) code [22] to investigate the properties of the Cu doped SiC supercells. The exchange–correlation functional was treated using the generalized gradient approximation [23] (GGA) employing the Perdew–Burke–Enzerh (PBE) functional form. The numerical integration of the Brillouin zone was performed using a 6 × 6 × 6 Monkhorst–Pack k-point sampling, the cutoff energy was assumed to be 300 eV for the plane wave basis. The valenceelectron configurations for the Si and C atoms were chosen as 3s2 3p2 and 2s2 2p2 , respectively. Considering 3s and 3p states of the transition metals in the basis sets having little influence on the magnetism of a system containing transition metals, therefore, we neglected 3s and 3p of Cu atom in our calculations. The valenceelectron configuration for the Cu atom was chosen as 3d10 4s1 . In the optimization process, the energy change, as well as the maximum tolerances for the force, stress, and displacement were set at 0.2 × 10−4 eV/atom, 0.5 × 10−1 eV/Å, 0.1 GPa, and 0.2 × 10−2 Å, respectively.
3.3. Electronic structure and ferromagnetism Fig. 3 depicts the total density of states (TDOSs) and partial DOSs (PDOSs) for the Cu doped SiC systems. The Fermi energy is taken to be the zero of energy. For the cases show in Fig. 3(a), (b) and (c), the Fermi energy level (EF ) enters the valence band, and all three cases (Cu–SiC–Si, 2Cu–SiC–Si and Cu–SiC–Si–Vc) show p-type doping. The Cu–SiC–C system, (Fig. 3(d)) on the other hand, shows n-type doping. Placing the doped Cu atom in different locations therefore resulted in different doping types. In the cases of Cu–SiC–Si, Cu–SiC–Si–Vc and Cu–SiC–C (Fig. 3(a), (c) and (d)), the systems show ferromagnetism while the 2Cu–SiC–Si system in which two Si atoms were replaced by two Cu atoms does not show ferromagnetism. As can be seen from Fig. 3(a), the uppermost valence band of the Cu–SiC–Si system consists mainly of C 2p states and Cu 3d states, and the lowest conduction band of the Cu–SiC–Si system is dominated by the 3p states of the Si atoms. The hybridization between the Cu dopant and its neighboring host atoms results in the splitting of the energy levels near EF , which shifts the majority spin states downward and the minority spin states upward to lower the total energy of the system. Due to
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Fig. 4. Spin-density of the Cu–SiC–Si.
the splitting of the energy levels near EF , the system possesses a magnetic moment of 2.86 µB , with the magnetic moments being mainly contributed by the C 2p orbital (about 2.24 µB ). The Si 3p orbital and Cu 3d orbital also contribute small parts, −0.18 µB and 0.68 µB , respectively. Therefore, the magnetic moment in the Cu–SiC–Si system is mainly due to the delocalized 2p orbital of the C atoms bonded with the Cu atom. The spin density of the Cu–SiC–Si system is shown in Fig. 4. Valence electrons in p states have much larger spatial extensions which could promote longrange exchange coupling interactions. Interaction between the Cu atom and the nearest-neighbor C atoms is through ferromagnetic coupling, while the interaction between the Cu atom and the second-neighbor Si atoms is through antiferromagnetic coupling. We have made an estimation of Tc from the classical Heisenberg model in mean-field approximation, which can be written as kB TC = 21E /3x [24,25]. Here kB is the Boltzmann constant, and x is the doping concentration of Cu dopants (x = 1.56% for the Cu–SiC–Si system). The energy difference (1E) between antiferromagnetic and ferromagnetic orderings was 666 meV, using as an indicator of the magnetic stability. We can therefore obtain Tc value of 330 K for the Cu–SiC–Si system, indicating that the Cu–SiC–Si system is ferromagnetic with the Curie temperature higher than room temperature. To understand further the influence of the doped Cu atom on the SiC system, we also considered two Cu atoms doped into the SiC system corresponding to a doping concentration of 3.13 at.%. The calculated TDOS is shown in Fig. 3(b). The results indicate that the net magnetic moment of the 2Cu–SiC–Si system is zero. As the Cu concentration increases, the ferromagnetism of the SiC
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system decreases, which is consistent with our experiments. It is proposed that antiferromagnetic interaction between those copper atoms is increased as the copper concentration increases [17]. The distributions of the electrons of the Cu atoms and their nearestneighbor C atoms in the Cu–SiC–Si and 2Cu–SiC–Si systems are different. The charge densities of the Cu–SiC–Si and 2Cu–SiC–Si systems are shown in Fig. 5. It is thought that when Cu atom is doped into the system, additional carriers are introduced into the system. Interaction between the Cu 3d electrons and the nearest-neighbor C 2p electrons is increased, which results in the spin polarization of C 2p electrons. The exchange interactions between unpaired electron spins arising from C 2p states are antiferromagnetic in 2Cu–SiC–Si systems. Experimentally, films such as those studied here are usually formed in a sputtering process, in which the sputtering rate of the Si atoms is much higher than that of the C atoms. Consequently, C vacancies are easily formed in Cu-doped SiC films. We therefore considered a case in which one C vacancy existed in the system and one Si atom was replaced by a Cu atom (Cu–SiC–Si–Vc). The system exhibited ferromagnetism with a total magnetic moment of 1 µB . This is smaller than in the case of Cu–SiC–Si system with no C vacancy as has been discussed above (Fig. 3(a)). In addition, an interesting observation from Fig. 3(c) for the system with a vacancy is that the Cu dopant and the C vacancy make the energy levels continuous in the band-gap of SiC. The energy band gap thus disappears completely. It is thought that C vacancies in SiC structures give rise to a symmetry-lowering distortion of the surrounding lattice [26]. Thermal annealing will reduce the C vacancy concentration and introduces a large total moment in the system. The researchers found that the Si site is more favorable compared to the C site for Cu atom substitution. Although a Cu atom replacing a C atom requires more energy, this case exists in experiment. Fig. 3(d) shows the calculated TDOS and PDOSs for the n-type doping in the Cu–SiC–C system. The calculated total magnetic moment of the Cu–SiC–C system is 1µB (∼0.34 µB from Cu atom itself, ∼0.4 µB from its first-neighbor Si atoms, and ∼0.3 µB from its second nearest-neighbor C atoms). The difference between the Cu atom in the Si atom location and the Cu atom in the C atom location is that in the Cu–SiC–C system not only is there a ferromagnetic coupling between the Cu atom and its first-neighbor Si atoms, but there is also ferromagnetic coupling between the Cu atom and its second-neighbor C atoms. It can be seen that the Si 2p states overlap slightly with those of the Cu 3d states near the Fermi level, suggesting a weak interaction between them. The existence of spin-polarized electrons is related to a change in the SiC structure. It is well known that the radius of the Cu atom is much larger than that of the C atom. When a Cu atom replaces a C atom in the Cu–SiC–C system, the crystal lattice surrounding the Cu
Fig. 5. Charge density of (a) the Cu–SiC–Si. (b) 2Cu–SiC–Si.
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atom undergoes significant changes, making the Si 2p states near the EF non-local. This in turn causes the interaction between the Cu 3d, Si 3p and C 3p orbitals to be in the form of a ferromagnetic coupling. 4. Conclusion Based on experiment results and the first-principles calculations, SiC doped by Cu element was confirmed to be ferromagnetic. If the Cu concentration is decreased or the degree of crystallization is improved, the ferromagnetism signal in Cu doped silicon carbide is always found to increase. The calculated highest ferromagnetic moment was about 2.86 µB for the configuration of one Cu atom at a Si site with no C vacancy. We propose the ferromagnetism of Cu-doped SiC is related to both the hybridization between Cu 3d orbital and C 2p orbital and symmetry-lowering distortions. Acknowledgments This work was supported by National Science Foundation of China (10804026), Natural Science Foundation of Hebei Province (E2010000429) and Foundation of Hebei Educational Committee (2006123). References [1] N. Achtziger, W. Witthuhn, Phys. Rev. B 57 (1998) 12181–12196. [2] A. Markwitz, S. Johnson, M. Rudolphi, Appl. Phys. Lett. 89 (2006) 153122–153124. [3] A. Qteish, Volker Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6534–6542. [4] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019–1022.
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