Research Article  Open Access
Wang Chen, Ruijie Li, Yanhui Liu, "Effect of (0001) Strain on the Electronic and Magnetic Properties of the HalfMetallic Ferromagnet Fe_{2}Si", Advances in Materials Science and Engineering, vol. 2017, Article ID 1853159, 7 pages, 2017. https://doi.org/10.1155/2017/1853159
Effect of (0001) Strain on the Electronic and Magnetic Properties of the HalfMetallic Ferromagnet Fe_{2}Si
Abstract
The electronic and magnetic properties of the halfmetallic ferromagnet Fe_{2}Si under (0001) strain have been evaluated by the firstprinciples density functional theory method. The spinup band structure shows that bulk Fe_{2}Si has metallic character, whereas the spindown band structure shows that bulk Fe_{2}Si is an SL indirect band gap of 0.518 eV in the vicinity of Fermi surface. Indirecttodirect band gaps and an unstabletostable transition are observed in bulk Fe_{2}Si as strain is applied. In the range −11% to 11% (excluding zero strain), bulk Fe_{2}Si has stable halfmetallic ferromagnetism, the spin polarization at the Fermi surface is 100%, and the magnetic moment of the Fe_{2}Si unit cell is 4.0 μB. The density distribution shows that the spin states of bulk Fe_{2}Si mainly come from the Fe^{1}3d and Fe^{3}3d states, indicating that bulk Fe_{2}Si has spinpolarized ferromagnetism. The halfmetallic ferromagnetism of bulk Fe_{2}Si is mainly caused by d–d exchange and p–d hybridization, which are not sensitive to strain. It is very important to investigate the effect of changes in the lattice constant on the halfmetallic ferromagnetic properties of bulk Fe_{2}Si.
1. Introduction
Halfmetallic ferromagnets (HMFs) have attracted much attention because of their potential applications in spintronics [1]. Like a normal ferromagnet, HMFs have two different spin channels [2–4]. They have an energy gap in one spin direction at the Fermi level, whereas the other spin is strongly metallic, which results in complete spin polarization of the conduction electrons. Such materials generally have a high Curie temperature and close to 100% spin polarization [5, 6]. Therefore, halfmetallic ferromagnetic materials will undoubtedly be an ideal semiconductor spin electron injection source. This shows that halfmetallic ferromagnetic research is important and has application prospects. In addition, it will promote the rapid development of semiconductor spin electronics.
Bulk Fe_{2}Si has not been well investigated. Chen and Tan [7] used Xray diffraction (XRD) to study the structure of Fe_{2}Si thin films. They found that the film thickness is affected by the base material, and the magnetic, electric, and optical characteristics are affected by the film structure. The structure, lattice parameter, phonon spectrum, and reflectance spectrum of hexagonal Fe_{2}Si have been investigated by firstprinciples calculations [8]. The results show that Fe_{2}Si is a ferromagnetic material and it has a spinpolarized halfmetallike band structure. However, there have been no studies associating the magnetism and mechanical properties of Fe_{2}Si. Therefore, in the present work, the properties of bulk Fe_{2}Si under (0001) strain were calculated using planewave pseudopotential methods based on density functional theory (DFT), and the results were analyzed in detail.
2. Calculation Method
There are four Fe atoms and two Si atoms in the Fe_{2}Si unit cell. The fractional coordinates of the three nonequivalent Fe atoms are (0, 0, 0), (0, 0, 0.5), and (0.333, 0.667, 0.78). The fractional coordinate of the Si atoms is (0.333, 0.667, 0.28). Fe_{2}Si belongs to space group (number 164). The lattice parameters are and . The crystal plane angles are = = 90° and = 120°. The (0001) strain line changes with the lattice constant of the hexagonal Fe_{2}Si structure with strain ranging from −12% to 12%.
The calculations were performed with the planewave pseudopotential method implemented in the Cambridge sequential total energy package [9] to calculate the effect of (0001) strain on the electromagnetic mechanism of halfmetallic ferromagnet Fe_{2}Si. The generalized gradient approximation [10] with the revised approximation of the Perdew–Burke–Ernzerhof scheme was used for the exchange–correlation potential. All of the possible structures were optimized by the Broyden–Fletcher–Goldfarb–Shanno algorithm [11, 12]. Geometry optimization was performed to fully relax the structures until selfconsistent field (SCF) convergence per atom. The tolerance in the SCF calculation was 5.0 × 10^{−6} eV/atom. The ultrasoft pseudopotentials were expanded within a planewave basis set with 330 eV, and the iteration convergence accuracy was 5.0 × 10^{−7} eV. The energy of bulk Fe_{2}Si was calculated based on optimization of the structural system, with the minimum energy structure which was chosen as the stable structure. Sampling of the Brillouin zone (BZ) was performed with an 8 × 8 × 6 kpoint mesh according to the Monkhorst–Pack method [13].
3. Results and Discussion
3.1. Electronic Structure
3.1.1. Band Structure
Figure 1 shows the effect of (0001) strain on the band structure of bulk Fe_{2}Si near the Fermi energy. Figure 1(c) shows the band structure without strain. It shows that the band structure of spinup electrons has metallic character and the band structure of spindown electrons has semiconductor character. The valence band maximum is 0.164 eV at point S and the conduction band minimum is 0.682 eV at the BZ point L. Thus, Fe_{2}Si forms a band gap of 0.518 eV in the vicinity of Fermi surface (spindown). The halfmetallic gap [14] is determined by the minimum difference between the lowest energy of the spin conductive bands with respect to the Fermi level and the absolute value of the highest energy of the spin valence bands. Therefore, the halfmetallic gap of bulk Fe_{2}Si is 0.164 eV.
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Under (0001) plane strain, the lattice constant strain of bulk Fe_{2}Si changes its band structure, which leads to an energy change of the conduction band bottom and the valence band top. The valley near the bottom of the conduction band is divided into two groups of the degenerate valley, forming the conduction band edge and secondary conduction band edge. The energy shift of the valence band changes the light and heavy hole band into two groups of peaks, forming the valence band edge and the secondary valence band edge. The band gap of the strain is determined by the heavy cavities and degenerate valleys. Figures 1(a) and 1(b) show the band structure of bulk Fe_{2}Si under compressive strain, which changes to a direct band gap of 0.338 eV at point L (spindown). The strain reaches −12%; then bulk Fe_{2}Si becomes metallic. Figures 1(d)–1(f) show the band structure under tensile strain, which is the same as the band structure when applying compressive strain. This indicates that, under strain, bulk Fe_{2}Si is first a stable halfmetallic ferromagnet and then changes to metallic with increasing strain. In conclusion, the band structure of bulk Fe_{2}Si can be changed using compressive and tensile strain, verifying that strain is an effective way to control the band structure.
3.1.2. Density of States
Figure 2 shows the total density of states (TDOS) and partial density of states (PDOS) of bulk Fe_{2}Si under various strains. The plotted energy range is −6 to 5 eV, and lower lying semicore states are omitted for clarity. Only the density of states (DOS) distribution near the Fermi level determines the magnetic properties. Hence, we concentrate on the DOS in the vicinity of the Fermi level, which is set to zero. To investigate the effect of strain on the subelectron structure of the system, the Sis, Sip, Fes, and Fed PDOS were investigated under various strains. The configuration of the extranuclear electrons of Si is 3s^{2}3p^{2}, and the configuration of the extranuclear electrons of Fe is 3d^{6}4s^{2}. Figure 2 shows that the DOS near the Fermi level mainly comes from Fe3d spin states, and the contributions of Si3p spin states are small. There is large exchange splitting between the spinup and spindown bands of the Fe3d states, which leads to a large localized spin magnetic moment at the Fe atoms and results in polarization of the Fe3d bands away from the Fermi level. Hybridization of 3p states provided by Si atoms with 3d electrons determines the degree of occupation of the p–d orbitals. Therefore, the halfmetallic ferromagnetism of bulk Fe_{2}Si under various strains is mainly caused by d–d exchange and p–d hybridization.
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The spinup DOS is mainly distributed below the Fermi level. The spindown DOS has two main peaks, which are located on both sides of the Fermi level. The spinup and spindown TDOS distributions near the Fermi surface are asymmetric; that is, the number of electrons in the spinup and spindown is quite different, which is the main contribution to the magnetic properties. Figures 2(b), 2(d), and 2(e) show that the Fermi level is completely located in the band gap of the spindown energy band and the spin polarization of bulk Fe_{2}Si at the Fermi level is 100%, so the spin polarization of bulk Fe_{2}Si can be improved by strain.
3.2. Magnetic Properties
3.2.1. Magnetic Mechanism Analysis
The magnetic moments of all of the atoms in the Fe_{2}Si unit cell under various strains are given in Table 1. The total magnetic moment of the Fe_{2}Si unit cell under strains of −12%, −7%, 0%, 5%, 9%, and 12% are 9.29 μB, 4.01 μB, 3.54 μB, 4.00 μB, 4.00 μB, and 4.05 μB, respectively. This shows that bulk Fe_{2}Si has stable halfmetallic ferromagnetism under strain of −11% to 11% (excluding zero strain), which agrees well with Figures 1 and 2. If halfmetals are in the same applied magnetic field, larger magnetic moments possibly result in stronger spincorrelation scattering of conductive electrons, and the variation of the resistance is then larger. Therefore, bulk Fe_{2}Si under strain of −12% and 12% will have more magnetoresistance than under no strain. Table 1 shows that the magnetic moment of bulk Fe_{2}Si mainly comes from the Fe^{1}3d and Fe^{3}3d states.

In the range −11% to 11% (excluding zero strain), the total magnetic moment of bulk Fe_{2}Si is 4.0 μB and the spin polarization is 100% from the DOS map, indicating that the halfmetallic ferromagnetic properties of bulk Fe_{2}Si are not sensitive to strain. In practical application in an optional electronic device, a small change in the lattice constant may have a significant effect on the electron transport properties at the Fermi level [15]. Therefore, it is very important to investigate the effect of changes in the lattice constant on the halfmetallic ferromagnetic properties of bulk Fe_{2}Si.
3.2.2. Distribution of the Magnetic and Electric Charge
Figure 3 shows the spin density distributions of bulk Fe_{2}Si under various strains. The results show that the Fe atoms are surrounded by a high potential, whereas the Si atoms are surrounded by a low potential. The charge of Fe_{2}Si under various strains is mainly localized on the Fe atoms and there is little charge on the Si atoms, indicating that bulk Fe_{2}Si has spin polarization ferromagnetism, which is consistent with the results in Table 1. The charge cloud distribution of the Si atom is affected by the Fe atom, making the distribution along the (11 0) crystal face. Charge transfer of the atoms in the system under stress is because of Fe d–d exchange and Fed–Sip hybridization. In the range −11% to 11% (excluding zero strain), the charge density between atoms is relatively low. Figure 3 shows that the spin states of bulk Fe_{2}Si mainly come from the Fe^{1}3d and Fe^{3}3d states. Bulk Fe_{2}Si maintains its spin polarization ferromagnetism in the strain range.
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4. Conclusion
The effect of (0001) strain on the electronic structure and magnetic properties of bulk Fe_{2}Si has been investigated by the firstprinciple pseudopotential method based on DFT. The spinup band structure shows that bulk Fe_{2}Si has metallic character, whereas the spindown band structure shows that bulk Fe_{2}Si is an SL indirect band gap in the vicinity of Fermi surface. The halfmetallic gap of bulk Fe_{2}Si is 0.164 eV. Applying strain, bulk Fe_{2}Si is first a stable halfmetallic ferromagnet, and it then becomes metallic with further increasing strain. The DOS near the Fermi level mainly comes from Fe3d spin states, and the DOS of Fe mainly comes from the Fe^{1}3d and Fe^{3}3d states, which are the source of the ferromagnetic properties of bulk Fe_{2}Si. The magnetic moment and charge transfer of bulk Fe_{2}Si are mainly caused by Fe d–d exchange and Fed–Sip hybridization. In the strain range −11% to 11% (excluding zero strain), bulk Fe_{2}Si has stable halfmetallic ferromagnetism and the spin polarization at the Fermi level is 100%, indicating that the spin polarization and halfmetallic ferromagnetism of bulk Fe_{2}Si can be improved by strain.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was mainly supported by the Cultivated Project of Outstanding Young Teachers of Guangdong Province (no. YQ2015124). This support is greatly appreciated.
References
 H. Ohno, “Making nonmagnetic semiconductors ferromagnetic,” Science, vol. 281, no. 5379, pp. 951–956, 1998. View at: Publisher Site  Google Scholar
 W.H. Xie and B.G. Liu, “Halfmetallic ferromagnetlsm in ternary transltionmetal compounds based on ZnTe and CdTe semiconductors,” Journal of Applied Physics, vol. 96, no. 6, pp. 3559–3561, 2004. View at: Publisher Site  Google Scholar
 R. Y. Oeiras, F. M. AraújoMoreira, and E. Z. Da Silva, “Defectmediated halfmetal behavior in zigzag graphene nanoribbons,” Physical Review B  Condensed Matter and Materials Physics, vol. 80, no. 7, Article ID 073405, 2009. View at: Publisher Site  Google Scholar
 K. Hasegawa, M. Isobe, T. Yamauchi et al., “Discovery of ferromagnetichalfmetaltoinsulator transition in K2Cr8O16,” Physical Review Letters, vol. 103, no. 14, Article ID 146403, 2009. View at: Publisher Site  Google Scholar
 R. A. De Groot, F. M. Mueller, P. G. V. Engen, and K. H. J. Buschow, “New class of materials: Halfmetallic ferromagnets,” Physical Review Letters, vol. 50, no. 25, pp. 2024–2027, 1983. View at: Publisher Site  Google Scholar
 S. M. Watts, S. Wirth, S. Von Molnár, A. Barry, and J. M. D. Coey, “Evidence for twoband magnetotransport in halfmetallic chromium dioxide,” Physical Review B  Condensed Matter and Materials Physics, vol. 61, no. 14, pp. 9621–9628, 2000. View at: Publisher Site  Google Scholar
 Y. T. Chen and Y. C. Tan, “The optical, magnetic, and electrical characteristics of Fe_{2}Si thin films,” Journal of Alloys and Compounds, vol. 615, pp. 946–949, 2014. View at: Publisher Site  Google Scholar
 C. P. Tang, K. V. Tam, S. J. Xiong, J. Cao, and X. Zhang, “The structure and electronic properties of hexagonal Fe2Si,” AIP Advances, vol. 6, no. 6, Article ID 065317, 2016. View at: Publisher Site  Google Scholar
 M. D. Segall, P. J. D. Lindan, M. J. Probert et al., “Firstprinciples simulation: ideas, illustrations and the CASTEP code,” Journal of Physics Condensed Matter, vol. 14, no. 11, pp. 2717–2744, 2002. View at: Publisher Site  Google Scholar
 J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, no. 18, pp. 3865–3868, 1996. View at: Publisher Site  Google Scholar
 C. G. Broyden, “The convergence of a class of doublerank minimization algorithms. II. The new algorithm,” Journal of the Institute of Mathematics and Its Applications, vol. 6, pp. 222–231, 1970. View at: Publisher Site  Google Scholar  MathSciNet
 D. Goldfarb, “A family of variablemetric methods derived by variational means,” Mathematics of Computation, vol. 24, pp. 23–26, 1970. View at: Publisher Site  Google Scholar  MathSciNet
 H. J. Monkhorst and J. D. Pack, “Special points for Brillouinzone integrations,” Physical Review. B. Solid State, vol. 13, no. 12, pp. 5188–5192, 1976. View at: Publisher Site  Google Scholar  MathSciNet
 W. Xie, Y. Xu, B. Liu, and D. G. Pettifor, “Erratum: Halfmetallic ferromagnetism and structural stability of zincblende phases of the transitionmetal chalcogenides,” Physical Review Letters, vol. 91, no. 21, 2003. View at: Publisher Site  Google Scholar
 T. Block, M. J. Carey, B. A. Gurney, and O. Jepsen, “Bandstructure calculations of the halfmetallic ferromagnetism and structural stability of full and halfHeusler phases,” Physical Review B  Condensed Matter and Materials Physics, vol. 70, no. 20, Article ID 205114, pp. 1–205114, 2004. View at: Publisher Site  Google Scholar
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Copyright © 2017 Wang Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.