Strain and SpinâOrbital Coupling Effects on Electronic Structures and

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Strain and Spin-orbital Coupling Effects on Electronic Structures and Magnetism of Semi-Hydrogenated Stanene Wenqi Xiong, Congxin Xia, Tian-Xing Wang, Yuting Peng, and Yu Jia J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00537 • Publication Date (Web): 04 May 2016 Downloaded from http://pubs.acs.org on May 10, 2016

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The Journal of Physical Chemistry

Strain and Spin-Orbital Coupling Effects on Electronic Structures and Magnetism of Semi-Hydrogenated Stanene Wenqi Xiong,a Congxin Xia,*,a Tianxing Wang,a Yuting Peng,b Yu Jiac a

Department of Physics, Henan Normal University, Xinxiang, Henan 453007, China

b c

Department of Physics, University of Texas at Arlington, Texas 76019, USA

School of Physics and Engineering, Zhengzhou University, Zhengzhou 450052,China

ABSTRACT The

magnetic

configurations

and

electronic

properties

of

semi-hydrogenated (SH) stanene nanosheets are studied by means of using first-principle calculations, considering spin-orbital coupling (SOC) and strain effects. The results show that the SH stanene possesses the ferromagnetic ground states with magnetic moments of 1µB and high Curie temperature under different strains. Moreover, the SOC effects increase remarkably the gap values of pristine stanene while reduce that of SH stanene. Interestingly, the semiconductor-metal transition occurs when only about 2% strain is applied to the SH stanene considering the SOC effects. These studies indicate that the SH stanene nanosheets may be potential in the applications of spin-electronics.

1. INTRODUCTION Recently, two-dimensional (2D) tin monolayer called as stanene has been attaching much attention.1-3 Compared to the other group IV

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elements-based 2D materials, such as graphene, silicene and germanene, theoretical predictions have shown that the stable 2D stanene monolayer possess the larger buckled altitude (0.85Å) and gap value.4 In particular, more recently, the 2D stanene has been grown successfully on the Bi2Te3(111) substrates.5 For the studies of stanene monolayer, other research groups have also carried out the related work. Wang et al. studied the strain effects on the band gap and found the energy gap was closed when some strain is applied on stanene.6 Lado et al. studied the interplay of ferromagnetic orders and spin-orbit interactions at zigzag edges of stanene systems.7 In addition, Cai et al’s studies show that stanene has a remarkable band gap value (72 meV) considering spin-orbital coupling (SOC) effects.8 Also, theoretical studies further testified the 2D tin films were quantum spin Hall (QSH) insulators with sizable bulk gaps of 0.3 eV, sufficiently large for practical applications at room temperature.9 Moreover, some studies reported the stable epitaxial growth of stanene on substrate and render stanene feasible use as a topological insulator.10 These studies indicate that the new 2D stanene-based nanomaterials have a promising applications in the nanoelectronic devices. As is well known, magnetism plays an important role in the low-dimensional quantum information and spintronics devices.11-14 Therefore, inducing and manipulating magnetism have been attracting 2


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intensive attention and keeping an open question in the studies of 2D materials by various ways, such as vacancy defect,15,16 adatom,17-19 substitutional doping20-22 and strain.23,24 Among these ways of tuning the electronic and magnetic properties, the hydrogenation has been proved as a novel method to get unexpected properties, such as opening band gaps and introducing the magnetism into nanosheets.25-29 For instance, fully hydrogenated graphene has been predicted theoretically to be a semiconductor with a direct band gap of 3.5 eV,30 while the semi-hydrogenated

(SH)

graphene

become

a

ferromagnetic

semiconductor with the band gap of 0.46 eV.31 In particular, Elias et al. successfully synthesized a crystal by exposing graphene to a hydrogen plasma environment.32 Surprising with the behaviors of hydrogenated graphene, the researchers further theoretically predicted the electronic structures and magnetic properties of silicene and germanene. The fully hydrogenated and SH silicene are also predicted to be semiconductor with the band gap of 2.2 eV and ferromagnetic semiconductor with the band gap of 1.7 eV,33,34 respectively. Moreover, the hydrogen atoms are adsorbed on two sides and one side of germanene sheet to form stable 2D fully hydrogenated and SH germanene.34,35 For the studies of hydrogenated stanene nanosheets, previous results showed that the fully hydrogenated stanene nanosheets were the nonmagnetic semiconductor and the non-trivial 2D topological insulators 3



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phases.36 However, the characteristics of electronic structures and magnetism of SH stanene nanosheets are still unknown. Therefore, in this article, we calculate the crystal structures and electronic properties of SH stanene with external strain by using the first-principle calculations. Our results show that compared with graphene, silicene and germanene, the stable SH stanene has ferromagnetic (FM) ground states and high Curie temperature. Moreover, the stain can tune effectively the band structures of the SH stanene nanosheets.

2. THEORETICAL METHODS In this work, spin-polarized density functional calculations are carried out with the Vienna ab initio simulation package (VASP).37,38 The exchange–correlation functional is treated by the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhofer (PBE) parameterization.39 The projected augmented wave potential is also employed to describe the electron-ion potential.40 Pseudopotentials with 1s1 and 4d105s25p2 are considered as valence electron configurations for H and Sn atoms, respectively. For the Brillouin Zone (BZ) integration, a 11×11×1 grid for k-point sampling for the geometry optimization of unit cells and an energy cut-off of 300 eV are consistently used in our calculations.41 In addition, to avoid the interactions between periodic images of the slabs, a vacuum space of at least 20 Å is included in the 4


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unit cell to eliminate the coupling between neighboring cells. The SOC effects are included in the self-consistent calculations of electronic structure. All atomic positions are fully relaxed using the conjugated gradient method until the Hellmann-Feynman force on each atom is less than 0.01 eV/Å. Moreover, the convergence for energy is chosen as 10-5 eV between two steps. Since the PBE calculations usually underestimate the band gap of semiconductors, we also use the hybrid functional Heyd-Scuseria-Ernzerhof (HSE06) as implemented into VASP to correct the band gap values.42 To examine the stability of SH stanene with different strains and the possibility of experimental fabrication, the formation energy of SH stanene has been calculated as38 E f = Etot (Stanene + H ) − Etot (Stanene ) − E ( H )

(1)

where Etot (Stanene + H ) and Etot (Stanene) are the total energies of the SH stanene under different strain strength and unit cell of stanene, respectively. E (H ) is the energy of the H atom.

3. RESULTS AND DISCUSSIONS 3.1 The Electronic Properties of Pristine Stanene We start briefly our calculations on the structural parameters and electronic characteristics of the 2D pristine stanene monolayer. The

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optimized crystal is a honeycomb structure with a low-buckled geometry, which indicates that the stanene prefer sp3 orbital unlike the case of graphene. Moreover, the unit cell of stanene monolayer has a lattice constant of a = 4.674Å, the bond length of nearest Sn atoms d = 2.831Å, and the buckled height ∆ = 0.85Å,4 respectively, which are in excellent agreement with the previous reports. As Figure 1 illustrates, the stanene shows the semiconducting properties with a small direct gap and the Dirac point at K points due to the valence bands (π) and conduction band (π*) crossing linearly the Fermi level. In particular, Figure 1a further shows that when the SOC effects are considered, the large direct band gap (73 meV) can be obtained, which indicates that the SOC effects are more pronounced in stanene than that in graphene, silicene, and germanene systems.4

Figure 1. (a) The band structures of pristine stanene without (black lines) and with (red lines) SOC effects. The inset of (a) shows a zoomed figure near the K point. The Fermi level is indicated by the dashed line. (b) The optimized top and side views of the SH stanene structures. The a, dSn-H, dSn-Sn and ∆ denote the lattice constant, bond lengths Sn-H, bond lengths Sn-Sn and buckled height, respectively. 6


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3.2 The Electronic Properties of SH Stanene To investigate the electronic properties of SH stanene, only one side of stanene is hydrogenated while keeping the other side unhydrogenated. After the total energy optimization, the optimized SH stanene keeps a buckled structure with the lattice constant, the bond length dSn-Sn, the dSn-H and buckled height ∆ of 4.761 Å, 2.888Å, 1.76Å, and 0.89Å, respectively, as shown in Figure 1b. Moreover, the calculated formation energy of SH stanene is negative value of -2.035 eV per unit cell, which indicates that SH stanene possesses stable structure. Now we turn to study the electronic structures of SH stanene. Moreover, in order to study how the SOC interaction affects the electronic properties of SH stanene, in Figure 2, we have calculated the band structures of SH stanene with and without the SOC effects. Numerical results show that when the SOC effects are considered, the valence band maximum (VBM) and conduction band minimum (CBM) locate at Г points, which indicates that the SH stanene possess the characteristics of direct band gap. Moreover, Figure 2a also shows that the direct gap value is 0.26 eV, which is larger than that of stanene nanosheets. In the following, in order to further clarify underlying physics mechanism and understand the influences of SOC on electronic structures, in Figures 2b and 2c, we also calculate the band structures and electronic density of states (DOS) of SH stanene without the SOC effects. 7



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Numerical results show that for PBE calculations, the majority spin and minority spin channels behave semiconducting and metallic characters, respectively, which indicates that the SH stanene has half-metallic characteristics. To correct the band gap value of the SH stanene, we further calculate the band structures of SH stanene by HSE06 method. Interesting, we can see from Figure 2a that the SH stanene is the direct-gap semiconductor with the band gap of 0.39 eV. Moreover, Figure 2a also shows that unlike the behaviors of pristine stanene cell with π and π* bands linearly crossed at K points of BZ, the SH stanene presents that the π bands are removed by the hydrogen atoms. Moreover, the VBM and CBM shift to the Г points of BZ where the σ bands become the highest occupied state. In addition, Figure 2b shows that the projected density of states (PDOS) of SH stanene are asymmetric between majority spin and minority spin channels due to the presence of magnetism. The lowest unoccupied states are mainly attributed to Sn s and 5pz orbitals; while the highest occupied states consist of 5px and 5py orbitals of Sn atoms. When the hydrogenated Sn atoms lie on one side of the stanene, the Sn atoms are covalently bonded with H atoms forming sp3 hybridization, and the 5p orbitals of unhydrogenated Sn atoms remain unpaired. In conclusion, our results indicate that the gap value of SH stanene is decreased in the presence of SOC effects, while the gap value of pristine stanene is

8


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increased remarkably. Therefore, the SOC effects are also obvious on electronic structures of SH stanene.

Figure 2. (a) The band structures of SH stanene obtained without the SOC effects by PBE (black lines) and HSE06 (red lines). The left and right panels represent majority spin and minority spin bands, respectively. (b) PDOS obtained by HSE06. (c) The band structure of SH stanene with the SOC effects. The Fermi level is set to zero energy. The Fermi level is set as zero energy.

3.3 The Strain Effects on Electronic Structures of the SH Stanene In order to simulate the strain effects on the electronic structures of SH stanene, the in-plane biaxial strain is applied to the SH stanene which is defined as

ε=

a − a0 × 100% , a0

where a and a0 are the lattice constants of

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stanene with and without strain, respectively. In the article, we consider the external tension from -5% to 8%. The formation energy as a function of biaxial strain is plotted in Figure 3a. It can be seen that the function of formation energy is a parabola curve and the case of ε=0% represents the most stable structure, as expected. In addition, we can see from Figure 3a that for all considered strain cases, the formation energies are negative, which indicates that all the SH stanene cases are stable under the presence of different strains.

Figure 3. (a) The formation energy of SH stanene as a function of strain. (b) The bond lengths of Sn-Sn, Sn-H and buckled height ∆ of SH stanene as a function of strain, respectively.

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In the following, we discuss the structural parameters of SH stanene via the control of external strain. Figure 3b shows the variations of Sn-Sn bond length dSn-Sn, the Sn-H bond length dSn-H and buckled height ∆ as the strain from -5% to 8%, respectively. We can see that when the strain is applied to SH stanene from compress to tensile, the Sn-Sn bond length and the Sn-H bond length increase. Moreover, the bond length dSn-Sn is larger than that of pristine cell when the strain is larger than -4%. In contrast to the variation of bond length dSn-Sn, the buckled height ∆ decreases as the strain from -5% to 8% and is smaller than that in pristine cell for ε> 2%. Thus, when we stretch the plane of stanene, the interaction between Sn 5pz orbital and the hybridization Sn-Sn bonds are weakened. In addition, Figure 3b also shows that the Sn-H bond length is insensitive to the variation of strain. The reason is that the bond length for hydrogenated Sn atom and hydrogen atom only change 0.012 Å for various strain strength. Now we turn to discuss the magnetism of SH stanene. Our calculations clearly show that the spin-polarized states emerge in the SH stanene under different strains. Thus, the magnetic configurations FM coupling and antiferromagnetic (AFM) coupling are further examined by using a 2×2×1 supercell. Moreover, according to the equation ∆E = E AFM − E FM , we calculate the energy difference between FM and AFM states as a function

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of strain, where E FM and E AFM are the total energies of FM and AFM states, respectively. The related results are shown in Figure 4a. It can be seen clearly that EFM is always lower than that of the EAFM for various strain, so the SH stanene has the characteristics of FM ground states, which behaves the same magnetic characteristics with SH graphene, silicene, and germanene.31,34 In addition, the results also show that the magnetism of SH stanene is insensitive to the strain and still possess the magnetic moment of about 1µB.43

Figure 4. (a) The variations of total energy difference between FM and AFM states and Curie temperature Tc as a function of strain ɛ for SH stanene. The spin densities and bader charge analysis of SH stanene in the cases of (b) ε= 0% and (c) 7%.

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In order to understand the magnetism of SH stanene in the presence of strain, in Figure 4b and 4c, we plot the spin densities of SH stanene in the cases of ε= 0 % and 7% as examples. It can be clearly seen that for both cases, the spin density of SH stanene distribute mainly around the unhydrogenated Sn atom, which indicates that the magnetic moments mainly originates from unhydrogenated Sn atom. Moreover, our calculations about magnetic moments show that for zero (7%) strain, the H atom, hydrogenated Sn atom, and unhydrogenated Sn atom contribute the magnetic moments of 0.1 (0.08)µB, 0.18 (0.21)µB, and 0.72 (0.71)µB, respectively, which indicate the magnetic moments are mainly attributed to unhydrogenated Sn atom with unsaturated dangling bonds. Therefore the results are same as above consequence from spin densities. To understand the reason that the magnetic moments are unchanged with various strains, the bader charge is shown in Figure 4b and 4c. Numerical results show that the H atom gains 0.304 electrons in the case of without strain, while the hydrogenated Sn atom and unhydrogenated Sn atom lose 0.262 electrons and 0.042 electrons, respectively. However, comparing with the case of SH stanene without strain, at the tensile strain of 7%, the H atom and unhydrogenated Sn atom lose 0.008 electrons and 0.017 electrons, while hydrogenated Sn atom gains 0.025 electrons. Therefore, this sable phenomenon of magnetic moments can be explained

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that the charge transfer between different atoms in the SH stanene is extremely insensitive to the magnitude of various strains. In addition, since the high Curie temperature Tc is necessary for a stable FM state, we have estimated the Curie temperature Tc by using mean-field theory and the Heisenberg model with the formula of γkBTc 2 = EAFM − EFM ,

34,44

where γ and kB are the coordinated number of the

system and Boltzmann constant. As shown in Figure 4a, the Curie temperature Tc of SH stanene for strain ε is always larger than that in the SH silicene nanosheets (121.6 K).34

Figure 5. The band gap values of SH stanene obtained from HSE without (blue solid line) and with (red solid line) SOC effects as the functions of strain. The green region denotes the band gap values difference between without and with SOC effects.

In Figure 5, the evolution of the band gap values as a function of external strain are given. It is clearly shown that the SH stanene exhibits

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the modulation of its band gap by strain, and the similar behaviors with and without SOC effects. In the case of tensile strain, the band gaps decrease linearly with increasing the strain. Especially, the band gap values reach to zero only when ε= 2% with SOC effects and ε= 4% without SOC effects, respectively. In the range of -5%

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