Bing Zhang¹, Jing-Tao Huang^,2,5, Long Lin^,2,5, Yong-Hao Xu³, Hua-Long Tao⁴¹Yellow River Conservancy Technical Institute, Kaifeng 475001, China
²Cultivating Base for Key Laboratory of Environment-Friendly Inorganic Materials in Henan Province, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China
³School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454000, China
⁴Liaoning Key Materials Laboratory for Railway, School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, Liaoning Province, China

First author contact: ⁵ Authors to whom any correspondence should be addressed.
Received:2020-01-4Revised:2020-03-5Accepted:2020-03-10Online:2020-04-22


Abstract
First-principles calculations are performed to investigate the electronic structures and magnetic properties of (Fe, Co)-codoped 4H-SiC using the generalized gradient approximation plus Hubbard U method. We find that 4H-SiC doped with an isolated Fe atom and an isolated Co atom produces a total magnetic moment of 5.98 μ_B and 6.00 μ_B respectively. We estimate T_C of about 263.1 K for the (Fe, Co)-codoped 4H-SiC system. We study ferromagnetic and antiferromagnetic coupling in (Fe, Co)-codoped 4H-SiC. Ferromagnetic behavior is observed. The strong ferromagnetic couplings between local magnetic moments can be attributed to p–d hybridization between Fe, Co and neighboring C. However, the (Fe, Co, V_Si)-codoped 4H-SiC system shows antiferromagnetic coupling when an Si vacancy is introduced in the same 4H-SiC supercell. The results may be helpful for further study on transition metal-codoped systems.
Keywords： first principles;dilute magnetic semiconductors;electronic structures;magnetic properties;4H-SiC


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Bing Zhang, Jing-Tao Huang, Long Lin, Yong-Hao Xu, Hua-Long Tao. Mechanism of ferromagnetism in (Fe, Co)-codoped 4H-SiC from density functional theory. Communications in Theoretical Physics, 2020, 72(5): 055502- doi:10.1088/1572-9494/ab7ed2

1. Introduction

The search for dilute magnetic semiconductor (DMS) materials that show ferromagnetism (FM) at or above room temperature is important for modern spintronic devices [1–3]. Silicon carbide (SiC)-based DMS materials have attracted significant attention as possible candidates future high-power and high-frequency spintronic devices for demonstrating room-temperature FM [4–8] because of their unique optical, electronic and magnetic properties [9–11]. SiC is a wide-bandgap semiconductor material and there are more than 200 known polytypes, such as 2H-SiC, 4H-SiC, 6H-SiC, 3C-SiC, 15R and 21R, etc [12–16]. 4H-SiC is a wide-bandgap material and one of the important polytypes, with high breakdown field and high thermal conductivity, etc [17].

A series of transition metal (TM=Mn, Fe, Co, Cr, etc)-doped SiC samples have been investigated by several research groups [18–27]. Experimentally, Kim and Kim [28] fabricated Fe-doped SiC bulk ceramics by hot-pressing and researched their structure and magnetic properties. They found that Fe-doped SiC ceramics exhibited ferromagnetic behavior at room temperature. Song et al [29] synthesized single-phase (Al, Fe)-codoped SiC by solid-state reaction and investigated its structural and magnetic properties. The origin of magnetism should be ascribed to the introduced Fe atom. Song et al [30] investigated structural and magnetic properties of Co-doped 6H-SiC. They found that room-temperature ferromagnetism was established in Co-doped 6H-SiC. Kuryliszyn-Kudelsk et al [31] investigated structural and magnetic properties of Fe-doped SiC by the physical vapor transport method. Bakhit and Akbari [32] electrodeposited Ni-Co/SiC microcomposite and nanocomposite coatings using conventional and sediment codeposition techniques. Yang et al [33] researched Co- and Ni-based ohmic contacts to n-type 4H-SiC. Their results show that the resistivity of the Co-based metal contact is an order of magnitude lower than that of the Ni-based contact [34]. A number of first-principles calculations have been performed to investigate the electronic structures and magnetic properties of transition metal-doped 4H-SiC. Lin et al [35] calculated the electronic structures and magnetic properties of (Al, Fe)-codoped 4H-SiC from first principles. The results showed that room-temperature ferromagnetism can be observed. Los et al [36] studied electronic structures of Fe-doped 4H-SiC using an ab initio full-potential linearized augmented plane-wave technique. They found that the neighboring C atoms strongly affected the electronic structure of Fe atoms. Luo et al [37] investigated the electronic structures and magnetic properties of Fe- and Co-doped SiC monolayers from first principles and they observed magnetism in them.

In terms of experiments, Pan et al studied the ferromagnetism of ZnO doped with transition metals [38]. Until now, relatively very little attention has been paid to the investigation of magnetic coupling of 4H-SiC-based DMSs doped with two different TM atoms by using first principles with the generalized gradient approximation (GGA) functional and the GGA+U approximation. The mechanisms responsible for polarization and ordering in TM-doped SiC-based DMS materials are still far from clear. Therefore, it is important to study the magnetic properties of 4H-SiC-based DMSs doped with two different TMs. In this article, to correct for the GGA error, we report the results of first-principles calculations on the structural and magnetic properties of Fe- and Co-monodoped and (Fe, Co)-codoped 4H-SiC with the GGA+U approximation. The electron correlation effect is not negligibly small in 4H-SiC based DMSs and should be taken into account in calculations. Therefore, the Hubbard U values of U=4.0 eV and 3.0 eV are adopted on the Fe:3d and Co:3d states [39–41], respectively. The U values are in best agreement with other theoretical studies reported previously.

2. Model and computational method

Intrinsic 4H-SiC is of a wurtzite structure, which belongs to the P6₃mc space group [42]. The calculated lattice parameters are a=b=3.073 Å, c=10.053 Å, which are consistent with experiment [10]. We simulated TM-doped 4H-SiC using a 3 × 3 × 1 supercell consisting of a total of 72 atoms, as shown in figure 1. The Cambridge Serial Total Energy Package (CASTEP) [43] was used to optimize the structure of pure 4H-SiC and calculate its electronic structures and magnetic properties. Calculations were performed based on first-principles density functional theory (DFT) [44–46] with the GGA [47], and the exchange–correlation functional is treated by the Perdew–Burke–Ernzerhof (PBE) model [48]. When the energy as a function of the lattice strain is used to obtain the elastic constants of a single crystal, the calculations require a very high degree of precision because the energy differences involved are of the order of several meV. This circumstance requires the use of a fine k-point mesh and a large energy cut-off. Therefore, the convergence of the total energy with respect to both the k-point sampling and the energy cut-off has been tested as shown in figures 2 and 3, respectively. With a larger energy cut-off or more points (larger k), the changes in total energy of the system were less than 0.001 eV. As a result, the electronic wavefunctions were expanded using a plane-wave basis set with a cut-off energy of 400 eV. The Brillouin-zone sampling was performed with a 2×2×2 Mokhorst–Pack k-point grid mesh. The convergence in energy was set as 2×10⁻⁵ eV atom⁻¹; all the atomic positions were fully optimized until all components of the residual forces became lower than 0.05 eV Å⁻¹, the maximum displacement was less than 2×10⁻⁴ nm, and the maximum stress was lower than 0.1 GPa.

Figure 1.

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Figure 1.72-atom 3×3×1 supercell model of (Fe, Co)-codoped 4H-SiC, with colored spheres denoting Si (yellow) and C (gray) atoms. The Si atoms labeled 1–10 are the sites to be replaced by Fe and Cr atoms; V₁, V₂ and V₃ represent silicon vacancies in different layers.

Figure 2.

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Figure 2.Test for convergence of total energy with k-point grid mesh.

Figure 3.

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Figure 3.Test for convergence of total energy with cut-off energy.

3. Results and discussion

3.1. Fe-monodoped 4H-SiC

First, we investigate the magnetic properties of Fe-monodoped 4H-SiC. This was done by substituting a single Si atom with a single Fe atom in the supercell at site 5. This led to a 4H-Si₃₅FeC₃₆ supercell with an Fe doping concentration of 2.28 at%; see figure 1.

To understand the spin state of the Fe atom in 4H-SiC, we calculated the density of states (DOS) of Fe-doped 4H-SiC-based DMSs within the GGA+U. Figure 4(a) depicts the total DOS (TDOS) of Fe-doped 4H-SiC, and figures 4(b)–(d) depict the partial DOS (PDOS) of Fe and its nearest-neighboring Si and second-nearest-neighboring carbon (C), respectively. It can be seen from figure 4 that strong hybridization is observed near the Fermi level. The hybridization is stronger in the spin-up channel than in the spin-down channel for Fe-doped 4H-SiC. The electronic structure of the Fe atom was affected strongly by the neighboring C atom. The hybridization is strong between Fe:3d states and C:2p states near the Fermi level. Within the valence band, the Fe:3d, Si:3p and C:2p states are mainly present from −1 eV to −8 eV. Within the conduction band, most Fe:3d states are found from 0 eV to 3 eV, Si:3p states are mainly present from 2 eV to 5 eV, and C:2p states from 0 eV to 2 eV.

Figure 4.

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Figure 4.(a) Total density of states for intrinsic Fe-doped 4H-SiC; (b)–(d) partial density of states for Fe, Si and C, respectively. The Fermi level is set to 0 eV.

3.2. Co-monodoped 4H-SiC

Next, we considered Co-doped 4H-SiC with one Si atom substituted by a Co atom in the supercell 4H-Si₃₅CoC₃₆ at site 5, with a Co doping concentration of 2.28 at%. The calculated total magnetic moment is 6.00 μ_B for Co-doped 4H-SiC systems. The substitution of Co for Si produces a magnetic moment of 2.84 μ_B per Co dopant. The remaining magnetic moments are provided by the C atoms adjacent to the doped Co atom and the Si atoms next to it. To understand the origin of the magnetic moment, we calculated the TDOS and the PDOS of a Co-doped 4H-SiC-based DMS within the GGA+U. TDOS and PDOS for the Co dopant and its nearest-neighboring Si atom and the second-nearest-neighboring carbon (C) are depicted in figures 5(a)–(d). From figure 5(a) we can find that the substitution of Co for Si introduces spin-polarized impurity states into the bandgap near the Fermi level in the Co-doped 4H-SiC system. The Co:3d states significantly overlap with the C:2p states around the Fermi level. The majority-spin channel is completely filled, while the minority-spin channel is partially occupied near the Fermi level. Therefore, the Co-doped 4H-SiC system has a half-metallic character. The top of the valence band is primarily contributed by Co:3d states, Si:3p states and C:2p states. The bottom of the valence band is primarily contributed by Co:3d states, Si:3s and C:2p states. The bottom of the conduction band is mainly Co:3p in character.

Figure 5.

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Figure 5.(a) Total density of states for Co-doped 4H-SiC; (b)–(d) partial density of states for Co, Si and C, respectively. The Fermi level is set to 0 eV.

3.3. (Fe, Co)-codoped 4H-SiC

In order to analyze the origin of the ferromagnetic properties of (Fe, Co)-codoped 4H-SiC, we considered doped 4H-SiC with two Si atoms substituted by one Fe atom and one Co atom in the supercell 4H-Si₃₄FeCoC₃₆. This corresponds to a TM doping concentration of 5.56 at%. We considered 12 different configurations of (Fe, Co)-codoped 4H-SiC models as in the case of 4H-SiC doped with a single TM atom (TM=Fe or Co). The dopant Fe atom is fixed at site 0, and the dopant Co atom is located at 12 Si sites. These Co atom sites are labeled 1–12, forming 12 different structures: (0, 1), (0, 2), ..., (0, 12); see figure 1. The 12 different configurations each contain one Fe atom and one Co atom, which allows calculation of the total energies corresponding to parallel ferromagnetic (FM) and antiparallel antiferromagnetic (AFM) impurity ordering. In these configurations, we considered the FM and AFM states with the same or opposite spin directions, respectively. The FM stabilization energy difference ΔE_FM=E_FM−E_AFM between the FM and AFM states is calculated for each configuration. E_FM and E_AFM are the total energies for FM and AFM ordering, respectively. If ΔE_FM is negative (positive), the FM (AFM) configuration is stable. The calculated relative energy of each configuration is the energy of the low-energy state (FM or AFM) of the optimized model relative to the lowest optimized energy structure with the same element. The lattice parameters, Fe–Co distance of non-spin-polarization and spin-polarization, ΔE_FM, and the magnetic moments of total, Fe and Co atoms have been calculated. The results are summarized in table 1.


Table 1.
Table 1.Results of calculations of 12 configurations for (Fe, Co)-codoped 4H-SiC: lattice parameters, Fe–Co distance before (NSP) and after (SP) relaxation, magnetization energy (ΔE_FM) and the magnetic moment (M) of total, Fe and Co atoms.

Configuration				Fe–Co distance (Å)		ΔEFM		M (μB)		Coupling
(a, b)	a	b	c	(NSP)	(SP)	(meV)	Total	Fe	Co
(0, 1)	9.286	9.277	10.149	3.082	3.098	−117.7	5.98	3.24	2.90	FM
(0, 2)	9.288	9.293	10.154	5.338	5.363	143.2	−0.01	3.77	−2.99	AFM
(0, 3)	9.299	9.274	10.148	6.163	6.277	−101.0	5.98	3.24	2.92	FM
(0, 4)	9.287	9.289	10.146	8.153	8.228	13.7	−0.05	3.57	−2.90	AFM
(0, 5)	9.287	9.286	10.143	4.360	4.342	−77.6	5.96	2.55	3.04	FM
(0, 6)	9.297	9.299	10.154	5.339	5.386	247.6	0.03	3.76	−2.98	AFM
(0, 7)	9.287	9.288	10.157	6.892	6.891	449.1	0.03	3.76	−2.96	AFM
(0, 8)	9.292	9.290	10.132	8.155	8.256	−136.5	5.99	3.31	2.84	FM
(0, 9)	9.294	9.292	10.168	5.344	5.305	286.6	−0.05	3.79	−2.97	AFM
(0, 10)	9.299	9.294	10.143	6.169	6.209	166.1	0.00	3.59	−3.09	AFM
(0, 11)	9.282	9.292	10.168	6.896	6.951	57.3	0.00	3.70	−2.98	AFM
(0, 12)	9.300	9.288	10.149	8.185	8.220	169.7	0.01	3.63	−2.95	AFM

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Table 1 shows that the change in lattice parameters and Fe–Co distance before and after relaxation is very small. This shows that our calculation is reasonable and reliable. From table 1 we know that the configurations (0, 1), (0, 3), (0, 5) and (0, 8) are FM states that are more stable than AFM states. The other configurations are AFM states that are more stable than FM states. Double exchange and p–d exchange are two of the most common mechanisms of magnetic interaction, and they can occur simultaneously. It can be seen from table 1 that among the optimized distances, the distance configured by (0, 8) is the greatest. This is the reason why the (0, 8) configuration has the strongest ferromagnetism. Usually double exchange and p–d exchange will promote the ferromagnetic coupling of the system, which is also the result of the competing mechanisms of double exchange and p–d exchange when the magnetic atoms are far away. Among these configurations of FM states, (0, 8) has the largest magnitude of ΔE_FM, and the FM state is more stable by about 136.5 meV. In experiments, Sun et al [49] have studied the effect of temperature on the structure and magnetic properties of Co-doped SiC films, and they found that when the annealing temperature rose to 1200 °C, the doped Co atoms formed the compound CoSi completely, and the results on magnetism of the films revealed that all films exhibited intrinsic ferromagnetism at 300 K. To evaluate the FM magnetic coupling strength, T_C was roughly estimated by means of the mean-field approximation from the total energy difference ΔE_FM=E_FM−E_AFM, and calculated according to the equation [50–54](1)$\begin{eqnarray}{T}_{{\rm{C}}}=2{\rm{\Delta }}{E}_{{\rm{FM}}}/3{k}_{{\rm{B}}}x,\end{eqnarray}$where k_B is the Boltzmann constant and x is the number of doping atoms (x=2). Using equation (1), we estimated T_C of about 263.1 K for the (Fe, Co)-codoped 4H-SiC system. It can be expected that ferromagnetism can be obtained above room temperature for (Fe, Co)-codoped 4H-SiC-based DMSs. It can also be found from table 1 that the total magnetic moment is about 6.00 μ_B for all the FM state configurations, but close to zero for all the AFM state configurations. For the (0, 8) configuration, the total magnetic moment is 5.99 μ_B, and the magnetic moments of Fe and Co are 3.31 and 2.84 μ_B. As expected, the Fe and Co dopants are the main contributors to the total magnetic moment.

To further study the contribution of different atoms in the FM system for (Fe, Co)-codoped 4H-SiC, the TDOS and PDOS of the (0, 8) configuration in the FM state are calculated. Figure 6(a) shows the TDOS, and figures 6(b)–(e) show the PDOS of Fe, Co and nearest-neighboring Si and the second-nearest-neighboring C, respectively. We found that the pronounced spin-polarization consists mostly of the p states of the nearest-neighbor C atoms around the TM dopants. There is strong hybridization between Fe:3d, Co:3d and C:2p states near the Fermi level. To understand the origin of FM coupling in (Fe, Co)-codoped 4H-SiC, the spin density of the (0, 8) configuration is shown in figure 7 (iso-surface value=0.05 e Å⁻³). The distribution in figure 7 shows that polarized components are mainly located at Fe and Co atoms. The local structure surrounding the doped atoms plays a major role in the magnetic properties of (Fe, Co)-codoped 4H-SiC systems. The neighboring C atom between a doped Fe atom and a doped Co atom mediates the magnetic coupling.

Figure 6.

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Figure 6.(a) Total density of states for (Fe, Co)-codoped 4H-SiC. (b)–(e) Partial density of states for Fe, Co, Si and C, respectively. The Fermi level is set to 0 eV.

Figure 7.

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Figure 7.Spin density distribution for (Fe, Co)-codoped 4H-SiC in the (0, 8) configuration in FM coupling. The isovalue is set to 0.05 e Å⁻³.

3.4. (Fe, Co, V_Si)-codoped 4H-SiC

Understanding and controlling defect-induced magnetism in a semiconductor such as SiC opens up the possibility of producing spintronic devices based on classical semiconductor technologies [55]. In order to investigate the effect of a vacancy, we calculated the magnetic properties with an isolated Si vacancy (V_Si) at the different layers in the (0, 8) configuration, as shown in figure 1. Our results show that AFM states are more stable than FM states for three different doped configurations. The calculated energy differences between FM and AFM states are 362.7, 385.2 and 574.8 meV for the V₁-, V₂- and V₃-doped cases, respectively. Therefore, the results verify that the introduction of an Si vacancy cannot induce room-temperature ferromagnetism in the (Fe, Co)-codoped 4H-SiC system.

4. Conclusions

In summary, we carried out density functional calculations to study the electronic structures and magnetic properties of 4H-SiC codoped with Fe, Co and Si vacancies within the GGA+U method. The results show that long-range ferromagnetic coupling can be expected in the (Fe, Co)-codoped 4H-SiC system. The origin of ferromagnetism can be attributed to the p–d hybridization between Fe and Co impurities and the nearest-neighbor C atom around the TM dopants. The results of calculations show the introduction of an Si vacancy cannot induce room-temperature ferromagnetism in the (Fe, Co)-codoped 4H-SiC system. This work suggests that (Fe, Co)-codoped 4H-SiC has considerable potential for application in spintronic devices.

Acknowledgments

This work was supported by the Natural Science Foundation of Henan Province (182300410288), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (CXTD2017089), Science and Technology of Henan Province (182102210305), the Henan Postdoctoral Science Foundation (Lin’s), the Program for Innovative Research Team of Henan Polytechnic University (T2016-2), the Key Research Project for the Universities of Henan Province (19A140009) the Doctoral Foundation of Henan Polytechnic University (B2018-38), and the Open Project of Key Laboratory of Radio Frequency and Micro-Nano Electronics of Jiangsu Province (LRME201601). Computational resources have been provided by the Henan Polytechnic University high-performance grid computing platform.

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