Ab Initio Study of Ferromagnetism Induced by Electronic Hole

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Ab Initio Study of Ferromagnetism Induced by Electronic Hole Localization in Al-Doped #-SiO

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Fei Mao, Cong-Zhang Gao, Feng Wang, Chao Zhang, and Feng-Shou Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06680 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 26, 2017

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The Journal of Physical Chemistry

Ab Initio Study of Ferromagnetism Induced by Electronic Hole Localization in Al-doped 𝛼-SiO2 Fei Mao,∗,† Cong-Zhang Gao,‡ Feng Wang,¶ Chao Zhang,§ and Feng-Shou Zhang∥ School of Nuclear Science and Technology, University of South China, Hengyang 421001, China, Data Center for High Energy Density Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China, School of Physics, Beijing Institute of Technology, Beijing 100081, China, School of Materials Science and Engineering, Anhui University of Science & Technology, Huainan 232001, China , and The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China E-mail: [email protected]

∗

To whom correspondence should be addressed School of Nuclear Science and Technology, University of South China, Hengyang 421001, China ‡ Data Center for High Energy Density Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China ¶ School of Physics, Beijing Institute of Technology, Beijing 100081, China § School of Materials Science and Engineering, Anhui University of Science & Technology, Huainan 232001, China ∥ The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China †

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Abstract We study the lattice and electronic structure of substitutional Al in 𝛼-SiO2 based on ab initio density functional method. For various charge states and doping concentrations of Al ions, our results show that the strongly localized O 2p derived hole states are created in the energy gap with local magnetic moments, which are predicted to behave a ferromagnetic order due to the strong interaction between the electronic holes and the distorted lattice. Our ab initio calculations clarify for the first time that the paramagnetism observed in Al-doped 𝛼-SiO2 originates from p-p ferromagnetic coupling, and the role of Al dopants is to mediate the short-range ferromagnetic coupling between the O ions on which the electronic holes are localized. Our results present an improved scientific understanding of the experimentally observed paramagnetism in Al-doped 𝛼-SiO2 , and paves the way towards the realization of high-temperature ferromagnetism in Al-doped 𝛼-SiO2 in the future experiments.

INTRODUCTION Dilute ferromagnetic oxide systems have received great scientific attention because of their potential ferromagnetic behaviour at room temperature which can be utilized for facilitating the injection, switching, and amplification of spin-polarized current in spintronic devices. 1 The ferromagnetism produced by magnetic 3d transition-metal (TM) doping is considered as an effective method to introduce extrinsic magnetic behaviours in dilute magnetic semiconductors (DMSs), such as Mn-doped GaAs, 2 Al-doped ZnO 3 and Fe-doped SiC. 4 Apart from cation substitutions, it is also predicted that doping with 2p light anions in oxides can result in ferromagnetism, such as C- or N-doped ZnO, 5,6 and C-doped SnO2 . 7 In these situations, it is found that the electronic holes are formed in the 2p band of the doped systems, which is proposed to mediate the long-range ferromagnetism by the p-p coupling between

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the dopants. 5,8 These ferromagnetic materials of which the magnetism is not introduced by the partially filled d orbitals are often referred as d0 magnetism. 9 Silicon dioxide (SiO2 ) plays an important role in the oxide-semiconductor based microelectronic industry due to its excellent optical and electrical performance. 10 It is found that the electronic and magnetic properties of 𝛼-SiO2 can be greatly influenced by the impurities, 11–14 which might bring degradation to the performance and reliability of SiO2 -based electronic devices. The most prominent Al impurity center in 𝛼-SiO2 is [AlO4 ]0 , which is one of the well-studied states in much previous literatures both experimentally 15–17 and theoretically. 18–20 As an Al atom has one less valence electron than a Si atom, the [AlO4 ]0 center intrinsically introduce an electronic hole in 𝛼-SiO2 energy band. As a consequence, the [AlO4 ]0 center is observed to display paramagnetic behaviours at room temperature. 15 Nevertheless, to our best knowledge, the mechanism of the observed paramagnetic behaviour of Al-doped 𝛼-SiO2 has rarely been analyzed explicitly both in experiments and calculations. Motivated by this fact, we systematically studied in this paper the magnetic properties of Al dopant center in 𝛼-SiO2 . The influences of the impurity charge states and the doping concentrations of Al impurities on the magnetism were analyzed and compared in detail. We clarify for the first time that the paramagnetism observed in Al-doped 𝛼-SiO2 arises from p-p coupling, and Al dopants mediate the short-range ferromagnetic coupling between the O ions on which the electronic holes are localized. Although density functional theory (DFT) as the most widely used ab initio approach has awarded great success in studying the electronic properties of point defects in solids, the modelling of localized hole states in doped oxides can still be challenging. It was confirmed that the failure of the approximate DFT exchange-correlation (XC) functionals, such as local density approximation (LDA) and generalized gradient approximation (GGA), for describing the localization of the electronic hole is caused by the incomplete self-interaction cancellation. In this sense, the quality of XC functionals in DFT directly determines the behaviours of hole state in doped materials. When the self-interaction effects are mostly counteracted, 3



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the hole localization with an elongated bond in Al-doped silica can be described correctly. Recently, the atomic and electronic structure of Al-doped 𝛼-SiO2 are studied by the selfinteraction corrected (SIC) Perdew-Zunger functional, the highly localized electronic hole on a single O atom is reproduced. 21 Similar results are also displayed by the spin unrestricted Hartree-Fock (UHF) calculation 22 in which the self-interaction is exactly canceled out. In an attempt to account for the locality of hole states, elaborate XC functionals have been employed and tested in doped oxides, which already found similar characters of hole states revealed by UHF calculations. Pacchioni et al. 14 studied the electronic structure of [AlO4 ]0 based on the B3LYP hybrid-DFT method which includes 20 % exact exchange (EXX), and the results showed a delocalized hole spatially spreading over two of the four neighbor O ions. However, To et al. 18 based on BB1K functional, with a large amount (42 %) EXX included, obtained the hole localization on an isolated O ion. The exact fraction of required EXX can be obtained from the macroscopic electronic dielectric constant (𝜖∞ ) of 𝛼-SiO2 based on ab initio method, which is referred to as “sc-PBE0𝛼𝜖∞ ”. 20 These previous DFT studies demonstrated that a significant fraction of EXX is necessarily required to yield the actual hole localization. Instead of using more advanced XC functionals, the other affordable attempt is to add a sufficiently large orbital dependent 𝑈 term within DFT+𝑈 method, which correctly describes the hole localization by accounting for the on-site electronelectron interaction. By applying the 𝑈 term to O 2p states for the defective oxide system, 19 the calculated electronic structure and geometry distortion are found to agree well with the experimental results. The structure of the paper is as follows. In the following section we briefly introduce the theoretical framework and the computational details of this work. In the Results and Discussion section, we present and discuss the results in three parts. In the first one, the distorted atomic geometry and the formation energy of Al dopant center with various charge states are studied systematically. In the second part, we analyze the electronic structure and clarify the physics of the magnetism of Al-doped 𝛼-SiO2 . In the third one, we focus on the 4


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doping concentration effects on the magnetism of Al-doped 𝛼-SiO2 . Conclusions are drawn in the final section.

COMPUTATIONAL METHODS In this study, spin-polarized total-energy and band-structure calculations are performed by employing DFT-based first principles method. Whereas a correct description of the band gap and the strongly localized O 2p derived hole states are critically important for oxidesemiconductors upon substitutional doping of the cation with a metal ion which has one less electron, the DFT+𝑈 scheme is adopted to study Al-doped 𝛼-SiO2 . The 𝑈 is optimal at 7 eV applied to the O 2p orbital of 𝛼-SiO2 , 12,19 which is carefully tested against the band gap. We simulate Al-doped 𝛼-SiO2 by using a 2×2×2 supercell containing 72 atoms. Our calculations are based on plane-wave basis sets and norm-conserving pseudopotentials. The interactions between the ionic cores and valence electrons are represented by TroullierMartins (TM) pseudopotentials, and the parametrization proposed by Perdew, Burke, and Ernzerhof (PBE) 23 is used for the XC functional. The plane-wave basis sets are defined by an energy cutoff of 70 Ry, and a 2×2×2 Monkhorst-Pack k-points mesh is used to sample the Brillouin zone of the unit cell. The cell parameters and the atomic positions of all structures are optimized until all components of the residual forces are less than 0.01 eV/˚ A, and the convergence tolerance for the self-consistent energy is set to 1.0×10−8 eV. In the present case, the calculated band gap for 𝛼-SiO2 with GGA+𝑈 is 8.57 eV, which agrees well with the experimental values 7-9 eV. The calculated lattice constants (a = 4.977 ˚ A, c = 5.476 ˚ A) for bulk 𝛼-SiO2 are again in a nice agreement with the experiment data (a = 4.914 ˚ A, c = 5.405 ˚ A). The positively charged states are simulated by removing electrons from the 𝛼-SiO2 supercell and a compensating jellium background is thus introduced to maintain charge neutrality in the periodic calculations. Our calculations are carried out by the ab initio simulation codes QUANTUM ESPRESSO. 24

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In order to study the relative stability of the charge states of the dopants, we have calculated the formation energies of Al dopant with various charge states. The formation energy is the energy required for the creation of the defect in a crystal. Within a supercell model, the formation energy of a defect X in the charged state q is calculated as 𝐸 𝑓 𝑜𝑟 (𝑋 𝑞 ) = 𝐸𝑡𝑜𝑡 (𝑋 𝑞 ) − 𝐸𝑡𝑜𝑡 [𝑏𝑢𝑙𝑘] −

∑

𝑛𝛼 𝜇𝛼 + 𝑞[𝜖𝑣 + 𝜖𝐹 + △𝑉 (𝑋 𝑞 )],

(1)

𝛼

where 𝐸𝑡𝑜𝑡 (𝑋 𝑞 ) and 𝐸𝑡𝑜𝑡 [𝑏𝑢𝑙𝑘] are the total energies of the supercell with and without the defect, respectively. 𝜇𝛼 is the chemical potential of the atomic species 𝛼 and 𝑛𝛼 is the number of atomic species 𝛼 added (𝑛𝛼 > 0) or removed (𝑛𝛼 < 0) from the pristine compound. 𝜖𝑣 is the valence band maximum (VBM) as calculated in the bulk supercell (defect free), and 𝜖𝐹 is the Fermi energy (the electron reservoir energy), which is customarily given referenced to the VBM in the bulk. Since the formation of dopants is related to the experimental growth or annealing environments, we consider both Si-rich and O-rich conditions, in which 𝜇𝑆𝑖 = 𝜇𝑆𝑖[𝑏𝑢𝑙𝑘] and 𝜇𝑂 = 𝜇𝑂[𝑂2 ] , respectively. In either of the considered conditions, the chemical potential of the other species is determined according to the thermodynamic equilibrium condition in SiO2 : 𝐸𝑡𝑜𝑡 [𝑆𝑖𝑂2 ]= 𝜇𝑆𝑖[𝑏𝑢𝑙𝑘] +2𝜇𝑂[𝑂2 ] +Δ𝐻(𝑆𝑖𝑂2 ), where Δ𝐻(𝑆𝑖𝑂2 ) is the formation enthalpy of SiO2 , which is negative for a stable compound. Our calculated value for Δ𝐻(𝑆𝑖𝑂2 ) is -9.56 eV (exp. -9.47 eV; Ref. 25 ). For charge defects, Δ𝑉 (𝑋 𝑞 ) is the alignment of the averaged electrostatic potential in the bulk and in the impurity-containing supercell. 26

RESULTS AND DISCUSSION Atomic structure distortion A single cation substitution in 𝛼-SiO2 is modeled by replacing a silicon atom by an aluminum atom in the supercell. This corresponds to a doping concentration of 4.17 at. %. The structural distortion and spin density of Al impurity doped with various charge states are 6


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displayed in Figure 1. As can be seen, the Al dopants bring in the hole localization and geometry distortion of the AlO4 tetrahedron. Table 1 compiles the calculated length and elongation of the 4 Al-O bonds. Apparently, Figure 1a presents an electronic hole of p state character that is almost localized on No. 1 O, and meanwhile a distorted geometry for the corresponding Al-O bond is substantially increased to 1.940 ˚ A, which is in accord with the theoretical study. 18 Compared to the other three bonds, the elongated bond length is increased by 15.9 %, which agrees fairly well with the electron paramagnetic resonance (EPR) measurements. 15 This result shows clearly that the hole localization manifests itself in the form of a small polaron, a localized charge carrier together with a lattice distortion. According to the electron hole state formation mechanism of acceptors, it is expected to introduce more electronic holes by the higher charge states of Al dopant, as seen in Figure 1bd. In the case of the singly charged Al dopant (see Figure 1b), one more localized electronic hole is yielded. The two holes are localized on two symmetrical O ions (Nos. 2 and 4 O) with equivalently elongated Al-O bonds, which agrees well with the EPR measurements 16 that showed the aluminum center can introduce two holes localized on two of the four oxygen neighbors, respectively. Similar localized electronic hole pair has also been identified in Mgdoped wurtzite GaN 27 using the hybrid functional based DFT calculations, which in turn confirms that the present DFT+𝑈 strategy is robust and reliable to describe the systems characterized by the strongly localized electronic holes. The result provides a clear theoretical evidence for experimentally observed double-hole generated by Al center in 𝛼-SiO2 . 16 For Al2+ Si , as shown in Figure 1c, besides a pair of electron holes are distributed on Nos. 2 and 4 ions of the AlO4 center which results in the corresponding Al-O bonds are equally elongated, a third electron hole is produced on No. 5 O ion of the adjacent SiO4 tetrahedron. The bond length between No. 5 O ion and the central Si ion of that SiO4 tetrahedron is elongated to 1.789 ˚ A, which is increased by 15.4 % compared to the remaining three Si-O bonds. For Al3+ Si dopant, as shown in Figure 1d, there are four electron hole states produced around the Al dopant. It can be seen from Table 1 that, the elongation of the Al-O bond 7



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length decreases as the number of the electron hole increasing. This is expected because the polaron interaction energy is distributed among the elongated bonds. Moreover, the fourth hole state is emerged on No. 5 ion as shown in Figure 1d, which is far away from the AlO4 center, indicating a strong repulsion between the electronic holes. The formation energies of Al dopants in 𝛼-SiO2 with considered charged states are calculated. Figure 2 shows only the lowest formation energies of the most stable charge states of Al dopants as a function of the Fermi energy. As seen in Figure 2, when the 𝜖𝐹 is pinned at the VBM, the 𝐸 𝑓 𝑜𝑟 for Al3+ Si is the lowest among the considered charged states, indicating the greater possibility for Al3+ Si dopant formation in the 𝑝-type doping condition. When the 𝜖𝐹 shifts up towards the conduction band minimum (CBM), the 𝐸 𝑓 𝑜𝑟 for Al0Si becomes the lowest, suggesting the greater possibility for neutral AlSi dopant creation in the 𝑛-type 𝛼-SiO2 . The calculated 𝐸 𝑓 𝑜𝑟 for Al0Si is 3.77 eV (cal. 3.65 eV; Ref. 12 ) and 1.38 eV (cal. 1.72 eV; Ref. 12 ) under Si-rich and O-rich conditions, respectively. As a general trend, the 𝐸 𝑓 𝑜𝑟 obtained under O-rich condition is smaller than that under Si-rich condition.

Electronic structure and the magnetism Figure 3a displays the density of states (DOS) of Al0Si center, and it can be observed that an unoccupied state with down spin is localized in the band gap. A detailed analysis of the projected DOS (PDOS) of 2p state of the O ion (see Figure 3b) with a hole localization finds an unoccupied state with down spin localized at the same energy scale as that in DOS, which induces a magnetic moment of 1.0 𝜇𝐵 with up spin that agrees well with our magnetization calculations. This indicates that the unoccupied state in DOS derives from the 2p state of the O ion, supporting the fact that the Al0Si introduces a single electronic hole in the valence band. In contrast, we find the scenario is completely different in the standard GGA calculations (no augmented 𝑈 term), in which the electronic hole is distributed uniformly over the four O neighbors of Al dopant. 21 As can be seen from Figure 3b that, the O 2p states overlap with those of the Al 2p except in the energy gap, suggesting a strong interaction between 8


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them. It should be noted that we have also calculated the spin density and the electronic structure of the Al0Si center with smaller 𝑈 values, and found that the hole localization and the hole state can be well described when the 𝑈 ≥ 4 eV. The offset from the VBM to the hole state is increased with the increasing of the 𝑈 values, which is in accordance with the previous results. 19 After analyzing the total energy, we find that Al0Si center favors a spin-polarized state and its total energy is 59.24 meV lower than that of the nonspin-polarized state obtained from standard DFT method. However, in GGA+𝑈 calculations, due to the strong interaction between the localized hole and the distorted lattice, the polarization energy increases to 1.5 eV which illustrates that the bound hole polaron is extremely energetically favorable. Because the Al1+ Si complex introduces two highly localized electronic holes in the system, resulting the final magnetization of the optimized Al1+ Si system yields 2 𝜇𝐵 with up spin, which is also convinced by the DOS analysis. To further investigate the magnetism induced by electronic hole localization, we made 3+ respective analysis for Al2+ Si and AlSi dopants. In the former case (see Figure 1c), three

electronic holes are formed around the Al2+ Si center. It is found that these local spin magnetic moments are aligned in parallel, they are thus ferromagnetic (FM) coupled, which agrees well with the total magnetization (TM) of 3 𝜇𝐵 . Figure 4a shows the DOS of Al2+ Si doped 𝛼-SiO2 . There are two unoccupied states with different amplitudes introduced by the electronic holes localized in the band gap. To understand this structure, we rely on the PDOS analysis for the spin-polarized p states of O ions (Nos. 2, 4 and 5) trapped with holes, see Figure 4b. The p state of No. 5 O contributes to the unoccupied state with lower energy in the gap. Meanwhile, the other unoccupied one with relatively higher energy is dominated by the p states of Nos. 2 and 4 O. The equivalent sites of Nos. 2 and 4 O ions with respect to the Al impurity result in the p states with the same energy, which leads to a superposition state suggesting a strong p-p exchange coupling between the O ions. This coupling between the highly localized 2p states with the same spin is demonstrated by the band-coupling mode, 9



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which is responsible for the stabilization of the ferromagnetism of C-doped ZnO. 8 This also explains the fact that the peak height of the superposition state is approximately two times as large as that of the lower energy state. We conclude that the p-p coupling interaction between the holes plays a key role for the FM alignments of the magnetic moments on O ions. For the Al3+ Si complex (see Figure 1d), the local spin magnetic moments are not completely FM coupled. The local magnetic moment located on No. 3 O ion is down spin, but the other three magnetic moments are up spin. This is because in the Al3+ Si complex, there are three hole states distributed around the Al dopant, which results in the hole wave function of No. 3 O is overlapped with those of Nos. 1 and 2 O at the same energy scale, causing a hole carrier transfer from the up-spin state to the down-spin state, thus reducing the local magnetic moment and exchange splitting, which is displayed by the DOS of Al3+ Si complex, as shown in Figure 5. The reduced exchange splitting stabilizes the antiferromagnetic (AFM) ground state. 8 Further calculations show that when the p state of No. 3 O ion is AFM coupled with those of Nos. 1, 2 and 5 O ions is more energetically favourable by 1.655 eV than that when the local magnetic moments are all aligned up. So, the saturation magnetization is 3 𝜇𝐵 per Al-dopant, this agrees with the studies 5,8 that revealed the hole-induced ferromagnetism has a maximum at a critical hole concentration.

Doping concentration effects In order to investigate the stability of the FM and AFM alignments between the magnetic moments produced by different Al dopants, a pair of Al ions are incorporated into the same supercell depending on the distance between the substitutional sites, nearest-neighboring (NN, the distance between the two Al dopants is 3.33 ˚ A) and second-nearest-neighboring (SNN, the corresponding distance is 5.20 ˚ A). Note that both cases correspond to a doping concentration of 8.34 at. %. The DOS results of 2 Al ions doped in the NN configuration are shown in Figure 6, it can be seen from the figure that the total magnetization of 2 𝜇𝐵 10


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are contributed by the spin magnetic moments of the two O ions on which the holes are localized, respectively. Figure 7 shows p-p coupling between the oxygen and aluminum ions in the NN configuration. Again, the unoccupied states are spin down in the band gap, and we find that the Al 2p states overlap exactly with those of Nos. 1 and 2 O ions at the same energy scale. This indicates that the spin magnetic moments on both O ions tend to align parallel to those of the cation impurities under the p-p interaction. Consequently, the Al dopants are considered to mediate the FM coupling between the O ions, and this p-p interaction results in the alignment of the magnetic moments on the O ions. It should be noted that this mechanism is different from the conventional double exchange for the FM coupling, in which it is the anions that mediate the FM coupling between the cation ions. 28 The isosurface of the spin density and the DOS of 2 Al substituted in the SNN sites are provided in the Supporting Information (see Figures S1 and S2). It can be seen from Figure 7 that the contributions of the Al dopants to the PDOS are very small, which means that the p-p exchange interaction between O ions and Al dopants is not so strong. In either of NN or SNN atomic configuration, the two electronic holes are localized around just one of the two Al ions, implying that the FM coupling interaction between the holes is weak and in short range, which is consistent with the PDOS results presented in Figure 7. This short-range FM interaction accounts for the paramagnetism of Al-doped 𝛼-SiO2 . Finally, we have compared the total energies when the doped system is in the AFM and FM order, respectively. Our studies show that the magnetic moments contributed by the O ions favor FM coupling in both NN and SNN atomic configurations. Table 2 collects the magnetic energy (defined as the total energy difference between the AFM and FM states) for two Al ions doped in the system with both atomic configurations. In the case of NN atomic configuration, the energy of the FM state is 846 meV and 77.3 meV lower than that of the corresponding AFM state obtained from DFT+𝑈 and DFT studies, respectively. The large magnetic energies suggest a high Curie temperature for this local ferromagnetism. 11



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In the case of SNN cases, the DFT+𝑈 results show that the magnetic energy is 5.6 meV, while it is 80.4 meV predicted by the DFT calculations. As the separation between the Al dopants increases, the magnetic interactions drop off rapidly in the DFT+𝑈 calculations. This means that the FM coupling only holds when the Al dopants are clustered. We have compared the total energy of the FM ground state of NN and SNN configurations, and find out that the NN configuration is more energetically favourable by 1 eV, which suggests that the Al dopants tends to be clustered. However, in the DFT description, the two holes are distributed over eight O ions surrounding the Al dopants (see Figure S3). There are enough holes to mediate the FM coupling between the spin magnetic moments, therefore the ferromagnetic solution is over stabilized by the DFT calculations, which do not correctly describe the hole localization. Further calculations using the 162-atom 3×3×2 supercell where the distance between two Al dopants is 7.42 ˚ A show that the magnetic moments disappear, the doping concentration is 3.7 at. % in this situation. The results show that the magnetic interaction between the local magnetic moments displays a very short-ranged characteristic, decaying very quickly with distance. This tendency is in a nice agreement with the experimental observed paramagnetic behaviour of Al-doped 𝛼-quartz. By contrast, due to the absence of small polaron formation, this difference in magnetic energy between the NN and SNN atomic configurations is much smaller in the DFT studies.

CONCLUSIONS In conclusion, we have studied the lattice distortion and electronic structure of Al-doped 𝛼SiO2 based on ab initio density functional method. With a DFT+𝑈 approach, we obtained a description of the local atomic distortion of the substitutional Al impurity in 𝛼-SiO2 which is quite consistent with the EPR measurement. Our studies reveal that the 2p electrons of dopants and hosts contribute to the ferromagnetism in Al-doped 𝛼-SiO2 . The magnetic

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moments are mainly contributed by the anions, which are induced by the strongly localized electronic hole states. In both NN and SNN configurations, the magnetic moments of the two O ions with holes localized favor FM coupling, this suggests the presence of a sizable short-range FM order in the paramagnetic states of Al-doped 𝛼-SiO2 . Our studies show that the ferromagnetism in Al-doped 𝛼-SiO2 can be achieved through p-p coupling interaction between the anion ions, and it is the Al dopants that mediate the short-range exchange coupling interactions. The high-temperature FM order is predicted at the high doping concentration due to the strong polaron interaction. In the present studies, only the influences of Al dopants (and the charge states) on the magnetic properties of 𝛼-SiO2 are considered. However, the magnetism of the real 𝛼-SiO2 system can be affected by the intrinsic defects, such as O vacancies (donors, can compensate the electron holes induced by Al dopants), which should be considered as to comprehensively evaluate the magnetic properties of real 𝛼-SiO2 system. Our studies do not exclude the contributions of other mechanisms. Our results present an improved scientific understanding the experimentally observed paramagnetism in Al-doped 𝛼-SiO2 , and provide an experimentally viable method for achieving the high-temperature ferromagnetism in Aldoped 𝛼-SiO2 .

Acknowledgement This work is supported by the National Natural Science Foundation of China under Grant Nos. 11505092, 11774030 and 11505003, and the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ3266). One of the authors (C.-Z.G.) is grateful for the financial support from the China Postdoctoral Science Foundation (Grant No. 2017M610819). This work is also partially supported by the PhD Start-up Foundation of University of South China (USC) under Project No. 2014XQD06, the Innovation Group of Nuclear and Particle Physics in USC, and the construct program of the key discipline in hunan province.

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Supporting Information Available The isosurface of the spin density for 2 Al substituted in the SNN sites of 𝛼-SiO2 obtained from standard DFT and DFT+𝑈 calculations, respectively. The DOS of 2 Al substituted in the SNN sites obtained from DFT+𝑈 calculation. This material is available free of charge via the Internet at http://pubs.acs.org/.

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(19) Nolan, M.; Watson, G. W. Hole Localization in Al Doped Silica: A DFT+𝑈 Description. J. Chem. Phys. 2006, 125, 144701. (20) Gerosa, M.; Valentin, C. D.; Bottani, C. E.; Onida, G.; Pacchioni, G. Communication: Hole Localization in Al-Doped Quartz SiO2 within Ab Initio Hybrid-Functional DFT. J. Chem. Phys. 2015, 143, 111103. ¨ Jónsson, H. Calculations of Al Dopant in 𝛼-Quartz (21) Gudmundsdóttir, H.; Jónsson, E. O.; Using a Variational Implementation of the Perdew-Zunger Self-interaction Correction. New J. Phys. 2015, 17, 083006. (22) Lægsgaard, J.; Stokbro, K. Hole Trapping at Al Impurities in Silica: A Challenge for Density Functional Theories. Phys. Rev. Lett. 2001, 86, 2834-2837. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (24) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, 395502. (25) Lide, D. R. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, Florida, 2004. (26) Lany, S.; Zunger, A. Accurate Prediction of Defect Properties in Density Functional Supercell Calculations. Modelling Simul. Mater. Sci. Eng. 2009, 17, 084002. (27) Lyons, J. L.; Janotti, A.; Van de Walle, C. G. Shallow versus Deep Nature of Mg Acceptors in Nitride Semiconductors. Phys. Rev. Lett. 2012, 108, 156403. (28) Zener, C. Interaction between the 𝑑-Shells in the Transition Metals. II. Ferromagnetic Compounds of Manganese with Perovskite Structure. Phys. Rev. 1951, 82, 403-405. 16


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Table 1: The Al-O bond lengths (𝑑, in ˚ A) and the elongation of the elongated Al-O bonds around the Al dopants in various charge states. The results are obtained from DFU+𝑈 calculations. Charge states Al0Si Al+ Si Al2+ Si Al3+ Si

𝑑1 1.940 1.645 1.641 1.797

𝑑2 1.674 1.853 1.834 1.840

17

𝑑3 1.674 1.645 1.669 1.812

𝑑4 Elongation 1.683 15.9% 1.853 12.6% 1.840 12.1% 1.633 11.0%



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Table 2: DFT+𝑈 calculation results for the magnetic energy (meV) of 2 Al ions substituted in 𝛼-SiO2 with NN and SNN atomic configurations, respectively. The corresponding results obtained from DFT calculations are also presented for comparison. Configurations Methods NN DFT+𝑈 DFT SNN DFT+𝑈 DFT

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Magnetic energy 846 77.3 5.6 80.4


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Figure Captions Figure 1 Local structures and spin density distributions of Al dopant with various charge states in 𝛼-SiO2 . The localization of the electron hole on the oxygen neighbors is illustrated by the spin-density isosurface. (a) Neutral charge state Al0Si . (b) Singly positively charged 2+ 3+ state Al+ Si . (c) Doubly positively charged state AlSi . (d) Triply positively charged state AlSi .

The elements are labeled in (a). Gray and blue isosurfaces correspond to up- and down-spin densities, respectively. Figure 2 Calculated formation energies of Al dopants in 𝛼-SiO2 as a function of Fermi energy. Only the lowest formation energy is shown for varying Fermi energy. Si-rich (solid line) and O-rich (dashed line) conditions are both assumed in the studies, respectively. Figure 3 (a) Spin resolved total DOS and (b) PDOS plots of the 2p states of oxygen ion (solid line) with hole localization and the Al ion (dotted line) in neutrally charged Al-doped 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent up- and down-spin densities, respectively. Figure 4 (a) Spin resolved total DOS and (b) spin down PDOS plots of the oxygen ions [No. 2, 4 and 5 O in Figure 1c] with hole localization in Al2+ Si . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines in (a) represent up- and down-spin states, respectively. Figure 5 Spin resolved total DOS of Al3+ Si doped in 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent upand down-spin states, respectively. Figure 6 (a) Spin resolved total DOS and [(b) and (c)] PDOS plots of oxygen ions with hole localization of 2 Al ions doped in the NN sites of 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent upand down-spin states, respectively. See the inset of Figure 7. Figure 7 The spin down PDOS plots of p bands of oxygen and aluminum ions when 2 Al ions are doped in the NN sites of 𝛼-SiO2 . The inset shows the lattice structure and spin 19



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density distribution of the corresponding configuration. The position of the Fermi level is shifted to 0 eV.

20


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Figure 1: Local structures and spin density distributions of Al dopant with various charge states in 𝛼-SiO2 . The localization of the electron hole on the oxygen neighbors is illustrated by the spin-density isosurface. (a) Neutral charge state Al0Si . (b) Singly positively charged 2+ 3+ state Al+ Si . (c) Doubly positively charged state AlSi . (d) Triply positively charged state AlSi . The elements are labeled in (a). Gray and blue isosurfaces correspond to up- and down-spin densities, respectively.

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Formation energy (eV)


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Si-rich

4

0

Al

0

O-rich

Si

3+

Al

Si

-4

0

1

2

3

4

5

6

Fermi energy (eV)

Figure 2: Calculated formation energies of Al dopants in 𝛼-SiO2 as a function of Fermi energy. Only the lowest formation energy is shown for varying Fermi energy. Si-rich (solid line) and O-rich (dashed line) conditions are both assumed in the studies, respectively.

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20

up-spin

10

DOS (states/eV)

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0 -10 -20

(a)

0.6 0.0

-0.6 -1.2

down-spin

(b)

-12

-8

-4

0

4

8

12

Energy (eV)

Figure 3: (a) Spin resolved total DOS and (b) PDOS plots of the 2p states of oxygen ion (solid line) with hole localization and the Al ion (dotted line) in neutrally charged Al-doped 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent up- and down-spin densities, respectively.

23



up-spin

20 10 DOS (states/eV)

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0 -10 -20

(a)

0.0

-0.4 -0.8

2O_p 4O_p

-1.2 -1.6

5O_p

(b)

-12

down-spin

-8

-4

0

4

8

12

Energy (eV)

Figure 4: (a) Spin resolved total DOS and (b) spin down PDOS plots of the oxygen ions [No. 2, 4 and 5 O in Figure 1c] with hole localization in Al2+ Si . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines in (a) represent up- and down-spin states, respectively.

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30 DOS (states/eV)

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up-spin

20 10 0 -10 -20 -30

down-spin

-10

-5

0

5

10

Energy (eV)

Figure 5: Spin resolved total DOS of Al3+ Si doped in 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent upand down-spin states, respectively.

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(a)

up-spin

1

20

DOS (states/eV)

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0 -1 -2

10

-3 -4

0

1O_p

(b)

1

2O_p

0

-10

-1 -2

-20

-3 -4

-12

-8

-4

0

4

8

down-spin

(c)

12 -12

-8

-4

0

4

8

12

Energy (eV)

Figure 6: (a) Spin resolved total DOS and [(b) and (c)] PDOS plots of oxygen ions with hole localization of 2 Al ions doped in the NN sites of 𝛼-SiO2 . The vertical dashed line indicates the position of the Fermi level (E𝐹 =0 eV). The black and red lines represent upand down-spin states, respectively. See the inset of 6.

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2

1O_p 2O_p

1 PDOS (states/eV)

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1Al_p 10 2Al_p 10

0 -1 -2 -3 -4 -10

-5

0

5

10

Energy (eV)

Figure 7: The spin down PDOS plots of p bands of oxygen and aluminum ions when 2 Al ions are doped in the NN sites of 𝛼-SiO2 . The inset shows the lattice structure and spin density distribution of the corresponding configuration. The position of the Fermi level is shifted to 0 eV.

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Graphical TOC Entry

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Ab Initio Study of Ferromagnetism Induced by Electronic Hole

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