Room-Temperature Ferromagnetism in Two-Dimensional Fe2Si

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Room-Temperature Ferromagnetism in 2D Fe2Si Nanosheet with Enhanced Spin-Polarization Ratio Yingjie Sun, Zhiwen Zhuo, Xiaojun Wu, and Jinlong Yang Nano Lett., Just Accepted Manuscript • Publication Date (Web): 25 Apr 2017 Downloaded from http://pubs.acs.org on April 25, 2017

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Room-Temperature Ferromagnetism in 2D Fe2Si Nanosheet with Enhanced Spin-Polarization Ratio Yingjie Sun,#,† Zhiwen Zhuo,#,† Xiaojun Wu,*,†,‡,§ and Jinlong Yang ‡, § †

CAS Key Laboratory of Materials for Energy Conversion, School of Chemistry and Materials

Sciences, and CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, China. ‡

Hefei National Laboratory for Physical Science at the Microscale, University of Science and

Technology of China, Hefei, Anhui 230026, China. §

Synergetic Innovation Center of Quantum Information & Quantum Physics, University of

Science and Technology of China, Hefei, Anhui 230026, China KEYWORDS. First-principles calculations, two-dimensional Fe2Si, ferromagnetism

ABSTRACT. Searching experimental feasible two-dimensional (2D) ferromagnetic crystals with large spin-polarization ratio, high Curie temperature and large magnetic anisotropic energy is one key to develop next-generation spintronic nano-devices. Here, 2D Fe2Si nanosheet, one counterpart of Hapkeite mineral discovered in meteorite, with novel magnetism is proposed on the basis of first-principles calculations. 2D Fe2Si crystal has a slightly buckled triangular lattice

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with planar hexacoordinated Si and Fe atoms. The spin-polarized calculations with hybrid HSE06 function method indicate that 2D Fe2Si is a ferromagnetic half metal at its ground state with 100% spin-polarization ratio at Fermi energy level. The phonon spectrum calculation and ab-initio molecular dynamic simulation shows that 2D Fe2Si crystal has a high thermodynamic stability and its 2D lattice can be retained at the temperature up to 1200K. Monte Carlo simulations based on the Ising model predict a Curie temperature over 780 K in 2D Fe2Si crystal, which can be further tuned by applying a biaxial strain. Moreover, 2D structure and strong inplane Fe-Fe interaction endow Fe2Si nanosheet sizable magnetocrystalline anisotropy energy with the magnitude of at least two orders larger than those of Fe, Co and Ni bulks. These novel magnetic properties render the 2D Fe2Si crystal a very promising material for developing practical spintronic nano-devices

INTRODUCTION Spintronics, which uses the spin of electrons for information storage, transportation and processing, has attracted intensive interests from both science and industry in the past decades.1 In tradition, ferromagnetic crystals with large spin-polarization ratio, high Curie temperature, and large magnetocrystalline anisotropic energy (MAE) are fundamental to build practical spintronic devices that could work at room temperature2-6. To realize this concept at nanoscale, it is one key issue to develop low-dimensional ferromagnetic crystals that possess the above qualities. However, searching experimentally feasible low-dimensional ferromagnetic materials still remains a big challenge for the low yield, small domains and rich boundaries/defects of prepared samples, or the difficulty in obtaining crystalline structures.7-9


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Since the discovery of graphene, intensive research efforts have been devoted to develop spintronics based on two-dimensional (2D) crystals. 10-14 Graphene have attracted many interests for its gate tunable spin transport,15 long spin diffusion lengths of about 4 micros at room temperature.16 However, significant magnetism is rarely observed in experiment due to the delocalization of s and p orbitals in carbon materials. Alternatively, 2D inorganic graphene-like crystals, such as transition metal dichalcogenides17-19, oxides20,22, nitrides23,24, carbide25-27, halide28-29, silicide30-33, and complex ternary compounds34-39, present great opportunities in spintronics applications for the possible existence of d orbital itinerant magnetism transition metal atoms and coupling between them. Here, we propose a new 2D Fe2Si nanosheet, one counterpart of Fe2Si alloy, with roomtemperature ferromagnetism, enhanced spin-polarization ratio and sizeable MAE, suitable for spintronics application in the nanoscale. Fe2Si, also named as hapkeite mineral, is one unique member of Fe-Si alloys, which have many technologically important compounds with excellent soft magnetic properties, e.g. Fe3Si, Fe2Si, Fe5Si3, FeSi, β-FeSi2, and α-FeSi2.40-48 Fe2Si is the compound has to be formed under the space weathering condition on airless or meteorite impacts. Therefore, it was predicted that this compound should exist on the lunar surface, and was indeed found in a lunar meteorite named as Dhofar 280 in 2003.49 Experimentally, single phase Fe2Si alloy can be obtained by a rapid quenching technique.50 With novel high-saturation magnettization, low coercivity, high permeability, low magnetostrictive coefficient, low magnetocrystalline anisotropy, and possible half-metallic like band structure, Fe2Si has great potential applications in high-power transformers, microwaves, motors, and high-frequency applications etc. 51,52


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Based on first-principles calculations and ab-initio molecular dynamic (AIMD) simulation, we show that graphene-like 2D Fe2Si is a ferromagnetic crystal with high structural stability up to the temperature of 1200 K. The Curie temperature estimated with Monte Carlo simulation based on Ising model reaches 590 K, which can be further enhanced by applying biaxial strain. In particular, 2D Fe2Si crystal is half metal with 100% spin polarization ration at Fermi energy and its MAE is two orders higher than those of Fe, Co, and Ni, enabling 2D Fe2Si crystal a very promising candidate for spintronics at nanoscale.

COMPUTATIONAL METHODS Our first-principles calculations are performed on the basis of density functional theory (DFT) by using Vienna ab initio Simulation Package (VASP).53 Projector augmented-wave (PAW) pseudopotential54 is used to account electron–ion interactions. The exchange and correlation terms are described using general gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) functional.55 Test calculations with PBEsol functional present similar results as those of PBE functional. To deal with the strong-correlated effect on d-orbital electrons of Fe, the screened hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional56,57 is also used. A vacuum separation larger than 15 Å along the z direction is employed in order to avoid interactions between two Fe2Si images in nearest-neighbor unit cell. A cutoff energy of 500 eV is used to expand the wave functions in plane waves. Both the lattice constant and positions of all atoms are relaxed until the force is less than 10-2 eV/Å. The convergence criterion of the total energy is 10−5eV. A Γ-centered Monkhorst-Pack scheme58 with k-point mesh of 15 × 15 × 1 is used. The phonon dispersion spectrum is calculated with finite displacement method method59 on 4×4×1 supercell with 48 atoms by using PHONOPY package.60 The AIMD simulation61with a


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canonical ensemble is performed by using the algorithm of Nóse and the temperature of the system is maintained at 300, 600, 900, 1200, or 1500 K, respectively. The time step is 1.0 fs and the total simulation time is 10.0 ps.

RESULTS AND DISCUSSION 2D Fe2Si sheet can be obtained by extracted one stoichiometric layer from hexagonal Fe2Si crystal, as illustrated in Figure 1. The hexagonal Fe2Si crystal has layered structure with P3-M1 symmetric group (Group 146), composing uneven graphene-like honeycomb sublattice of FeSi intercalated with hexagonal sublattice of Fe atoms, as shown in Figure 1a and 1b. The optimized lattice constants with PBE calculations are a=b=3.93 Å, and c=4.84 Å, agreeing well with previous theoretical results.48,52 However, these values are significantly different from experimental values of a=b=4.05 Å , and c=5.09 Å.48 Note that GGA fails to correctly describe the structural and electronic properties of the strong-correlated system, such as underestimation of the lattice constants, local magnetic moments and band gaps, which can be improved by using HSE06 method.62 The optimized lattice constants of Fe2Si bulk with HSE06 method are a=b=4.07 and c=5.11 Å, agreeing well with experimental values.52 The spinpolarized electronic band structures of Fe2Si calculated with PBE method exhibit half-metalliclike property, as shown in Figure S1 (see Supporting Information), which is consistent with previous theoretical study at the same calculation level.52 Considering the strong-correlated effect, however, the electronic band structure calculated with the screened HSE06 hybrid function indicates that the hexagonal Fe2Si is a ferromagnetic metal, as shown in Figure 1c. Based on the calculated density of states (DOS) projected on atomic orbitals in Figure 1c, the magnetism is mainly contributed by d orbital of Fe atoms, and the local magnetic moments are


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2.92, 2.35, and 2.27 µB for Fe atoms in two hexagonal sublattices and honeycomb sublattice in the unit cell by using HSE06 method, respectively. These values are significantly larger than those obtained with PBE method (2.57, 0.10, and 0.70 µB).52 Note that The spin polarization ratio is defined as δ=|ρ↑-ρ↓|/(ρ↑+ρ↓), where ρ↑ and ρ↓ are the absolute values of DOS at the Fermi energy level for spin-up and down channels, respectively. The calculated spin-polarization ratio is about 19.5% at the Fermi energy level by using HSE06 method.

Figure 1. (a) and (b) are the top and side views of the optimized structure of hexagonal Fe2Si bulk, respectively. (c) The spin-polarized band structures and density of states of hexagonal Fe2Si bulk calculated with HSE06 functional. (d) The top and side views of the optimized structure of 2D Fe2Si crystal. The DOS of major and minor spin polarized channel are labelled with black up and down arrows, respectively. The fermi energy level is set as zero. Γ (0.0, 0.0, 0.0), A (0.0, 0.0, 1/2), H (-1/3, 2/3, 1/2), K (-1/3, 2/3, 0.0), M (0.0, 1/2, 0.0), L (0, 1/2, 1/2) refer to the high-symmetric k-points in the first Brillouin zone.


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Extracting one stoichiometric layer from hexagonal Fe2Si bulk, the optimized structure of 2D Fe2Si crystal is displayed in Figure 1d. Distinctly different from the structure of stoichiometric layer in bulk, 2D Fe2Si crystal has a slightly buckled structure with same symmetry group at its bulk counterpart (P3-M1). Quasi-planar hexa-coordinated Fe and Si atoms are packed in a triangular lattice where each Si atom is surrounded by six neighboring Fe atoms and Fe atoms form a graphene-like sublattice, sharing the similar structure as those of metal carbide and silides.63-66 Using HSE06 method, the optimized lattice constants increase to a=b=4.24 Å, where the Fe-Si and Fe-Fe bond lengths are 2.46 and 2.51 Å. Note that the optimized lattice constants are a=b=3.97 Å, and the Fe-Si and Fe-Fe bond lengths are 2.33 and 2.43 Å, respectively by using PBE method, which are significantly different from HSE06 method due to the strong-correlated effect of d electrons in system. Test calculations with PBE+U method with U=3.5 eV present similar results as HSE06 method, as summarized in Table S1. The thickness of 2D Fe2Si is about 0.56 Å at HSE06 calculation levels. To ascertain the structural stability of 2D Fe2Si crystal, the cohesive energy is calculated with the definition of Ecoh = (ESi + 2×EFe – EFe2Si)/3, where ESi, EFe, and EFe2Si are the total energies of Si, Fe atom, and 2D Fe2Si unitcell, respectively. The calculated cohesive energy is 4.10 eV per atom. This value is smaller than that of graphene (7.85 eV/atom), but is significantly larger than those of silicene (3.98 eV/atom), germane (3.26 eV/atom),65 and planar hexa-coordinated Cu2Si (3.46 eV/atom)64 and Cu2Ge (3.17 eV/atom)66, respectively, implying the possible stability of 2D Fe2Si crystal. The thermodynamic stability of 2D Fe2Si is evaluated with phonon spectrum calculation and AIMD simulation. Figure 2a displays the calculated phonon dispersion of 2D Fe2Si crystal without any presence of imaginary-vibration mode. This indicates that 2D Fe2Si crystal with


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buckled structure is dynamically stable. Test calculation is performed on 2D Fe2Si crystal with perfect planar structure and significant imaginary-vibration mode can be found. The AIMD simulation is further performed on 2D Fe2Si at the temperatures of 300, 600, 900, 1200, and 1500 K. Figure 2b to 2d display the snapshot of structures at 10.0 ps at the temperatures of 900, 1200, and 1500 K, respectively. And, the final structures of 300 and 600K are provided in Figure S2. It is clear that 2D Fe2Si retains its structures at the temperature up to 1200 K, and the structure is partially destroyed at the temperature of 1500 K in the simulating period, indicating that the structure of 2D Fe2Si sheet is thermally stable at high temperature at least up to 1200 K.

Figure 2. (a) The calculated phonon spectrum of 2D Fe2Si crystal. (b) to (d) are the structural snapshots of 2D Fe2Si crystal at time of 10 ps during AIMD simulation under the temperatures of 900, 1200, and 1500 K, respectively. Γ (0.0, 0.0, 0.0), M (0.0, 1/2, 0.0), K (−1/3, 2/3, 0.0) refer to the high-symmetric k-points in the first Brillouin zone. In the following, the electronic properties of 2D Fe2Si crystal are investigated. Two magnetic orders, i.e. ferromagnetic (FM) and antiferromagnetic (AFM) coupling orders, are considered to


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determine the magnetic ground state of 2D Fe2Si. Our calculations show that 2D Fe2Si has a FM ground state. The AFM and FM energy difference is 0.41 eV per cell. Figure 3a displays the calculated electronic band structures and DOS of 2D Fe2Si crystal at FM ground state by using HSE06 method. 2D Fe2Si crystal is half metal with 100% spin-polarization ratio at the Fermi energy level, which is over 5 times larger than that of hexagonal Fe2Si bulk (19.5%) at the HSE06 calculation level. The enhanced spin-polarization ratio endows 2D Fe2Si crystal great advantages in spintronics application at nanoscale.

Figure 3. (a) The band structures, total and partial DOS projected on atomic orbitals of 2D Fe2Si crystal are calculated by using HSE06 method. The fermi energy level is set to zero. “up” and “down” arrows denote the spin-up and down polarization, respectively. (b) The deformation charge density distribution with the isosurface value of 0.007 a.u. The yellow and green denote the charge density increase and decrease, respectively. (c) The spin charge density distribution with the isosurface value of 0.03 a.u. (d) The simulated magnetic moment (M) and specific heat (Cv) with respect to temperature for 2D Fe2Si crystal.


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The major magnetism in 2D Fe2Si crystal is contributed by Fe atoms, as illustrated by the spin charge density distribution in Figure 3c. The local magnetic moment on Fe atom is about 3.03 µB, which is larger than that in its bulk. The partial DOS projected on atomic orbitals indicate that the spin-polarization at the Fermi energy level is mainly contributed by dxz and dyz orbitals of Fe atoms. To further understand this novel magnetism behavior, crystal field theory is used to analysis the electronic occupation of d orbital in 2D Fe2Si crystal. Note that Fe atoms are hexcoordinated, the energies of five d orbitals in Fe atom are splitted into a(d2), e1(dxz, dyz), and e2(dxy, dx2-y2), as schemed in the insert of Figure 3a. A freestanding Fe atom has a valence electronic configuration of 3d64s2. The deformation charge density, shown in Figure 3b, and Bader charge analysis result indicate that each Fe atom losses about 0.28 electron to Si atom. Consequently, Fe atom is approximately +1 charged, and the left seven electrons occupy a, e1, and e2 orbitals with a and e1 orbital half-filled in a high spin state, resulting enhanced local magnetic moment of 3.07 µB and spin-polarization ratio. Table 1. Magnetic anisotropy energies in µeV/Fe and the easy axis (EA) for 2D Fe2Si crystal are summarized. E(100)-E(001) E(010)-E(001) E(110)-E(001) E(111)-E(001) EA 560

574

550

325

(001)

MAE is an important parameter of magnetic materials to determine the low-temperature magnetic orientation with respect to the lattice structure, which is directly related to the thermal stability of magnetic data storage. Large values of MAE per atom imply the possibility to reduce the grain size per bit of information. Note that reduced dimensionality and symmetry would significantly enhance the MAE value of material, a sizeable MAE is expected in 2D Fe2Si crystal


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when comparing with its bulk counterpart. In addition, spin-orbital coupling (SOC) calculations are performed on 2D Fe2Si crystal to obtain the relative stability along three magnetization directions in plane, i.e. (100), (010), and (111) direction, and two directions out of plane, i.e. (001) and (111) directions, as summarized in Table 1. The easy axis (EA) of 2D Fe2Si is along the out-of-plane (001) direction. The calculated MAEs for (100), (010), (110), and (111) directions are 0.560, 0.574, 0.550, and 0.325 meV per Fe atom based on PBE calculation level, respectively, which are about one to two orders larger than those of cubic Fe (1.4 µeV per atom), Co( 65 µeV per atom), and Ni (2.7 µeV per atom).67,68 Moreover, the magnitudes are comparable to those of Fe, Co monolayer deposited on Rh(111) and Pt(111) substrates (0.08 to 0.37 meV per metal atom).69 The MAE values are also calculated with HSE06 method, which is more expensive in computation. The MAE values with HSE06 method are smaller than that obtained with PBE method, which are 172, 198, 331 and 225µeV per Fe atom for (100), (010), (110) and (111) directions, respectively. The large MAE values make 2D Fe2Si suitable for magneto electronics applications. To develop a practical spintronics working at ambient environment, the Curie temperature (TC) of materials should be comparable to or above the room temperature. Since the easy axis of 2D Fe2Si is out-of-plane (001) direction and the calculated MAE is comparable to previous reported 2D CrXTe3,70 which behaviors as a 2D Ising-like ferromagnet,71 the Kosterlize-Thouless transition is unlikely to take place in Fe2Si sheet.71 Here, Monte Carlo (MC) simulation based on Ising model is used to estimate the TC of 2D Fe2Si crystal with FM state, which has been used to predict TC of 2D magnetic crystal in previous simulation.6, 37, 70 The Hamiltonian of Ising model is defined as H = − ∑

(1)


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, where Jij is the nearest-neighboring exchange parameter and M=3.0 is the spin magnetic moment on Fe atom. Using the energy difference between AFM and FM ground states based on HSE06 method, the estimated exchange parameter J is about 7.7 meV. To obtain Tc, we calculate the specific heat Cv at first after the system reaches equilibrium at a given temperature. A supercell of 60 × 60 × 1 with periodic boundary condition is used in MC simulation. In the simulations, the spins on all magnetic sites flip randomly. The Tc is obtained by locating the peak position in Cv(T) plot. From the simulated Cv(T) curve in Figure 3d, the Curie temperature of 2D Fe2Si is estimated to be 780 K. Based on PBE results of energy difference between AFM an FM states, the exchange parameter J is about 8.5 meV and the estimated TC reaches 860 K. It should be pointed out that the MAE in 2D Fe2Si is large but not infinite as assumed in Ising model. As a result, the calculated temperature with Ising model is likely overestimated. Generally, to fabricate 2D crystal based electronics, a high in-plane stiffness is required to avoid the curling and obtain free-standing membranes. Here, 2D Young’s modulus is calculated to estimate the in-plane stiffness of 2D Fe2Si. -The calculated in-plane Young’s modulus is 71 Nm-1, which is about 24% of in-plane Young’s modulus of graphene (295 Nm-1). Note this value is larger than that of silicene (61 Nm-1), germanene (42 Nm-1), and comparable to those of Cu2X and Ni2X (X=Si, and Ge) sheet (60 to 93 Nm-1).64-66 Then, the gravity induced out-of-plane deformation can be estimated by the equation of

h/L ≈ (ρgL/ )

(2)

, where ρ = 1.7 ×10-6 kg/m2 is the density of 2D Fe2Si crystal, and L is the size the nanosheet. Taking L≈100 µm, we obtain h/L≈2.84×10-4, comparable to that of graphene.73 Therefore, it is possible that 2D Fe2Si crystal keeps free-standing planar structure by withstanding its weight.


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Figure 4. (a) and (c) are the band structures and total DOS of 2D Fe2Si crystal under the biaxial strain of -3% and 3% by using HSE06 method, respectively. The Fermi energy level is set to zero. (b) and (d) are the simulated magnetic moment (M) and specific heat (Cv) with respect to temperature for 2D Fe2Si crystal under the biaxial strain of -3% and 3%, respectively. At last, the strain effect on the electronic and magnetic properties of 2D Fe2Si crystal is considered. Figure 4 displays the calculated band structures and DOS of 2D Fe2Si crystal under biaxial strain of -3% and 3%. Other results are displayed in Figure S3 (see Supporting Information). The biaxial deformation within the range from -3% to 3% won’t change the FM half metallicity of 2D Fe2Si crystal. Meanwhile, the energy difference between AFM and FM states varies from 0.501 eV to 0.289 eV, as summarized in Table S2. Consequently, the Curie temperature is enhanced to 820 K when the biaxial strain is -3%, but decreases to 680 K when the biaxial strain reaches 3%. Such behavior change with the biaxial strain can be understood with the structural deformation of 2D Fe2Si crystal. As summarized in Table S1, when the biaxial strain changes from -3% to 3%, the Fe-Si and Fe-Fe bond lengths increases


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monotonously from 2.39 to 2.53 and 2.44 to 2.57 Å, respectively, which result the couple interaction between neighbor Fe atoms. Experimentally, it is still a big challenge to obtain 2D Fe2Si nanosheet directly by exfoliating Fe2Si bulk. Note that Fe2Si ultrathin films have been obtained in experiment,51 and Fe2Si ultrathin film containing one stoichiometric layer spontaneously transforms into 2D Fe2Si nanosheet, it is possible to obtain 2D Fe2Si sheet by reducing the thickness of Fe2Si ultrathin film to the atomic scale, which has been used to obtain graphene-like ZnO nanosheet.74 Alternatively, it is still possible to obtain 2D Fe2Si nanosheet by using atomic layer deposition (ALD) and molecular beam epitaxy (MBE) techniques, which have been used to prepare 2D inorganic materials, such as transition metal disulfides, on selected substrates.75-77

CONCLUSIONS In summary, we presented a new 2D Fe2Si crystal with room-temperature ferromagnetism and enhanced spin-polarized ratio by using first-principles calculations. 2D Fe2Si crystal can be looked as a stoichiometric layer of its bulk counterpart. Distinctly different from Fe2Si bulk, quasi-planar hexa-coordinated Si and Fe atoms are packed in a slightly buckled triangular lattice in 2D Fe2Si crystal. Each Si atom is surrounded by six neighboring Fe atoms, and Fe atoms form a graphene-like structure. Both phonon spectrum calculation and AIMD simulation indicate that 2D Fe2Si crystal has a high thermodynamic stability, and can retain its lattice structure at the temperature up to 1200 K. Spin-polarized calculations with hybrid HSE06 function show that 2D Fe2Si crystal is FM half metal, and the spin-polarization ratio is over 5 times larger than that of its bulk counterpart. 2D Fe2Si crystal possesses both high Curie temperature of about 780 K, and


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a sizeable MAE, which is one to two orders larger than those of Co, Fe, and Ni bulk. These novel magnetic properties provide great opportunities for spintronics and electronics devices.

ASSOCIATED CONTENT Supporting Information. Supporting Information Available: The spin-polarized band structures of hexagonal Fe2Si calculated with PBE functional; the structural snapshots of 2D Fe2Si crystal of AIMD simulation under the temperatures of 300 and 600 K, respectively; the band structures of 2D Fe2Si crystal under a biaxial strain; the bond length, local magnetic moment, and AFM-FM energy differences of deformed 2D Fe2Si crystal by applying biaxial strain. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * [email protected] Author Contributions #

These authors contributed equally.

Notes The authors declare no competing financial interest. ACKNOWLEDGMENT


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This work is supported by the NSFC (21573204, 21421063, 51172223), MOST (2016YFA0200602), Strategic Priority Research Program of CAS (XDB01020300), the Fundamental Research Funds for the Central Universities (WK2060140014), National Key Basic Research Program (2012CB922001), National Program for Support of Top-notch Young Professional, External Cooperation Program of BIC CAS (211134KYSB20130017), and by USTCSCC, SCCAS, Tianjin, and Shanghai Supercomputer Centers

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Room-Temperature Ferromagnetism in Two-Dimensional Fe2Si

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