Effect of strain on the electronic and magnetic properties of an Fe-doped WSe₂ monolayer

Abstract

We investigate the electronic and magnetic properties of an Fe-doped single-layer WSe₂ sheet with strain from −10% to 10% using first-principles methods based on density functional theory. In our calculation, an Fe-doped WSe₂ monolayer is a magnetic semiconductor without strain. With the tensile strain increasing, its magnetic moment increases slightly, and the system shows a half-metal feature from 4% to 9% and transforms to a metal at 10% strain. The largest half-metallic gap is 0.183 eV at 4% tensile strain. However, with compressive strain increasing, its magnetic moment decreases slightly and disappears from −5% to −10%, and the system transforms from half-metallic to metallic. Fe-doped WSe₂ can endure strain from −4% to 10%. Our studies predict Fe-doped WSe₂ monolayers under strain to be candidates for dilute magnetic semiconductors. Moreover, the formation energy calculations also indicate that it is energy favorable and relatively easier to incorporate Fe atom into the WSe₂ monolayer under Se-rich experimental conditions.

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1. Introduction

Since an easy fabrication method called “micromechanical cleavage” was introduced by Novoselov and Geim, research of two-dimensional (2D) materials has become a hot topic. There is no doubt that graphene is the most widely studied 2D material because of its unique and fascinating electronic properties.¹ However, the gapless feature of pristine graphene limits its applications on microelectronic devices.² On the other hand, research has shown that the transition-metal dichalcogenides (TMDC) have a wide variety of interesting physical properties such as semiconducting, metallic, superconducting, and magnetic behavior.³ These compounds show profound anisotropy in the physical properties arising from the formation of MX₂ layers with covalent bonding within the layers and weak van der Waals bonding between the layers.⁴ Layered semiconductor TMDs have been proven to be important candidates for use as an absorber layer in low cost thin film solar cells.⁵ This is due to their relatively small band gap (1–2 eV) and large absorption coefficient.⁶ Semiconducting TMDCs such as MoS₂ and WSe₂ have been established themselves as strong candidates for future electronic and optoelectronic applications.^7–14 Previous experiments have proved that when Fe, Co, Gd, Fe₃O₄ and Fe₄N doped monolayer MoS₂ respectively, it shows magnetic.^15–18 The magnetic moment of 1.93, 1.45, 3.18, 2.08 and 2.21 μ_B are obtained in Fe-X₆ doped MoS₂ for X = S, C, N, O and F, respectively.¹⁹ Among the family of TMDC semiconductors, WSe₂ is probably the most interesting material for potential applications. It is expected to possess the largest spin-splitting at the K/K′ point among all the MX₂ semiconductors,²⁰ which makes WSe₂ an ideal platform for studying spin and valley dependent properties as well as for spintronic applications.^21,22 Electrochemical devices based on WSe₂ have been reported to possess conversion efficiencies up to 17%.²³ Developing effective method to manipulate electronic structures, magnetic states of two-dimensional (2D) materials is vital to realize its application in nanoscale devices. Introducing transition metal (TM) in 2D system is an effective route to modulate its magnetic and electronic properties. Previous works have revealed that TM doping not only profoundly influences the electronic structures of 2D materials, but also promotes magnetic properties of the system.^24–34 However, the systematical study of the electronic and magnetic characteristics in Fe-doped WSe₂ monolayer with strain so far is still limited.

In present study, we perform first-principles calculations to explore the electronic and magnetic properties of Fe-doped monolayer WSe₂. Furthermore, the effect of strain on electronic structure and magnetic properties of Fe-doped WSe₂ is thoroughly studied. We find that Fe dopant can induce the magnetic moment about 1.902 μ_B. The magnetic moment of Fe-doped WSe₂ monolayer is sensitive with strain. These finding starts a new route to facilitate the design of spintronic devices.

2. Theoretical models and methods

The structures of monolayer WSe₂ are hexagonal lattices. In each unit cell, the W atom is bonded to six neighboring Se atoms to form a triangular prism. As shown in Fig. 1. Meanwhile, Fe atom substituted to W atom in WSe₂ monolayer for 6.25% (one Fe atom, 15 W atoms and 32 Se atoms). The adjacent layers of WSe₂ are held together by weak van der Waals force which makes it easy to gain WSe₂ monolayer by using the method of mechanical exfoliation.

Fig. 1 The schematic of Fe-doped WSe₂ (a) top view and (b) side view. The green and grey balls represent Se and W atoms, respectively. d₁, d₂ and d₃ represent the distance between the Fe and it's three nearest Se, respectively.

Our calculations were performed within first-principles density functional theory (DFT) using the projector augmented wave (PAW) method³⁵ was used within the Vienna ab initio simulation package (VASP).³⁶ Electron exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) parametrization.³⁷ In all calculations, an energy cutoff of 500 eV for the plane-wave expansion of the wavefunctions was used. In order to check the convergence of the results with supercell size, the supercell of size 4 × 4 × 1 of the WSe₂ primitive cell was used with a separation of 15 Å between two layers. The atomic positions were relaxed using a 9 × 9 × 1 K-points, all the structures are fully relaxed to minimize the total energy of the systems until a precision of 10⁻⁵ is reached. Both the atomic positions and cell parameters are optimized until the residual forces fall below 0.01 eV Å⁻¹.

3. Results and discussion

In our work, we perform GGA calculations to investigate the influence of strain effect on the electronic and magnetic properties of Fe-doped WSe₂. The average bond length d_Se–Fe (defined as d_Se–Fe = (d₁ + d₂ + d₃)/3, where d₁, d₂ and d₃ represent the bond lengths between the Fe atom and the three nearest neighbor (NN) Se atoms, respectively, as shown in Fig. 1) are shown in Fig. 2. The d_W–Fe was calculated in the same way. It is obvious that the d_W–Fe changes more quickly than d_Se–Fe with increasing strain.

Fig. 2 The average distance between Fe and its three nearest Se, Fe–Se (black line). The average distance between Fe and its nearest W, Fe–W (red line). The average distance between W and the nearest Se, W–Se (blue line).

In the following, we present our calculation results on the effect of equibiaxial strain on the magnetic properties of Fe-doped WSe₂. At the zero strain, we observed spin polarization in Fe-doped WSe₂ and the magnetic moment is 1.902 μ_B. With the tensile strain increase to 10%, the magnetic moment enhanced to 2.117 μ_B slightly. Combining with bond length between the atoms, we can found that the increasing strain induces the change of the structure symmetry and the redistribution of intra-atomic d states, which changes the magnetic moments. When we applied compressive strain on Fe-doped WSe₂, the magnetic moment are 1.863 μ_B (−2% strain) and 1.814 μ_B (−4% strain), respectively. Then its magnetism vanishes at −5% strain. It suggests that the excessive compressive strain changes WSe₂ monolayer intrinsic properties and is meaningless. Through this analysis, we find that the strain plays an important role in electronic and magnetic properties for Fe-doped WSe₂ monolayer. The results indicate that the Fe-doped WSe₂ 2D nanostructures can endure the strain from −4% to 10%. It is similar to ref. 38–40.

The band structures with and without strain are shown in Fig. 3. As we can see from the band structures without strain, the spin-up and spin-down band structures are not symmetric and show that the Fe-doped WSe₂ is a magnetic semiconductor. The impurity states within the band gap are mainly from the Fe atom, whereas the contribution from the WSe₂ can be neglected. While at 4% tensile strain, the band crossing at the Fermi level occurs with little dispersion in spin-up band structure, in spin-down band structure, there is a 0.183 eV half-metallic band gap. The half-metallic (HM) gap is an important parameter to determine application in spintronic devices, which is defined as a minimum of E_c and E_v, where E_c is the bottom energy of the minority-spin conduction band with respect to the Fermi level and E_v is the absolute value of the top energy of the minority-spin valence band, also with respect to the Fermi level. The calculated band structures show Fe-doped WSe₂ has a half-metallic feature at 4% tensile strain. With the increase of tensile strain, it keeps half-metallic feature from 4% to 9% (see Table 1). According to this rule, the half-metallic gap is about 0.183, 0.166, 0.161, 0.176 eV, respectively, for strain = 4%, 6%, 8%, 9%. Then at 10% strain, both spin-up and spin-down band structure crossing at the Fermi level occur with little dispersion. It means that the Fe-doped WSe₂ turn into metal at 10% tensile strain. When we apply the compressive strain on Fe-doped WSe₂, we can see that it has half-metallic feature at −2% strain and then turns into magnetic metal at −4%. The system turns into the non-magnetic metal material from −5% to −10%. The system shows metal feature under larger compressive strain. Compared with tensile strain, the compressive strain is more effective on the electronic and magnetic properties of Fe-doped WSe₂.

Fig. 3 Spin-polarized band structures of Fe-doped WSe₂ monolayer structures with strain 0%, 4%, 10%, −4%, and −10%, respectively. The red and black lines represent the spin-up and spin-down components, respectively. Where the Fermi level is indicated by the black imaginary line.

Table 1 The half-metallic gap ΔE_HM-gap, magnetic moment, and the formation energy in different experimental conditions E_form in Fe-doped WSe₂

Strain (%)		−10	−8	−6	−5	−4	−2	0	2	4	6	8	9	10
ΔEHM-gap (eV)		—	—	—	—	—	0.149	—	—	0.183	0.166	0.161	0.176	—
Eform (eV)	W-rich	20.825	13.966	8.957	7.653	5.527	3.444	2.349	2.563	3.584	5.453	8.693	10.267	11.422
	Se-rich	19.129	12.269	7.261	5.957	3.831	1.748	0.653	0.867	1.888	3.759	6.397	8.571	9.726
Magnetic moment (μB)		0	0	0	0	1.814	1.863	1.902	1.941	2.001	2.035	2.072	2.089	2.117

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In order to further understand the electronic characteristics in the Fe-doped WSe₂ monolayer, the total density of states (TDOS) and the partial density of states (PDOS) for Fe-doped WSe₂ monolayer with different stain are shown in Fig. 4 and 5, respectively. It is obvious that the polarized charges mainly arise from the localized 3d electrons of Fe atom, a little from the localized 5d electrons of the W atom and hardly from the localized 4p electrons of the Se atom near the Fermi level in Fig. 4. Fig. 5 further confirms that the Fe-doped WSe₂ is magnetic semiconductor at 0% strain and turn into half-metal at 4% tensile strain. It keeps half-metal feature until applied 10% tensile strain and shows metal properties at 10% tensile strain. Under compressive strain, it has half-metallic feature at −2% and then becomes metal at −4%. From −5% to −10% strain, the spin-up and spin-down of DOS are symmetric and the magnetism disappears. The system turns into the non-magnetic metal material. These results indicate that the strain can change the electronic occupied of Fe-doped WSe₂, which are analyzed to explain the strong strain effect on the electronic and magnetic properties.

Fig. 4 Total density of stats (TDOS) and partial density of states (PDOS) of Fe-doped WSe₂ monolayer with 0% strain.

Fig. 5 Total density of stats (TDOS) of Fe-doped WSe₂ monolayer with different strain.

The spin density of the Fe-doped monolayer WSe₂ with different strain is shown in Fig. 6 can help us understand more deeply. It is noted that without strain, the neighboring Se atoms are antiferromagnetically coupled to the Fe atom and four nearest neighboring W atoms bonded to the Fe atom display ferromagnetic. At the 2% tensile strain, the neighboring Se atoms are antiferromagnetically coupled to the Fe atom, the p character of the spin-polarized orbitals of the Se atoms is clearly visible. Two atoms of six neighboring W atoms couple antiferromagnetically to the Fe atom, the rest bonded to the Fe atom display ferromagnetic. The d character of the spin-polarized orbitals of the W atoms is clearly visible. With the increasing of tensile strain, the antiferromagnetically of the two W atoms transform into ferromagnetic. The hybridization between the Fe 3d and the Se 4p or W 5d states enhance slowly and reach largest at 10% tensile strain. At the −2% compressive strain, the neighboring Se atoms are antiferromagnetically coupled to the Fe atom and the nearest neighboring W atoms bonded to the Fe atom display ferromagnetic. When the compressive strain reach −4%, both the neighboring Se atoms and the nearest neighboring W atoms bonded to the Fe atom display ferromagnetic mostly.

Fig. 6 Spin density for a single Fe dopant atom in WSe₂ monolayer when the strain is 0%, 2%, 4%, 6%, 8%, 10%, −2% and −4%. Yellow and cyan isosurfaces represent positive and negative spin densities (±0.001 e Å⁻³).

To probe the stability of the Fe-doped WSe₂ monolayer, the formation energy E_form can be calculated according to the following formula.^41–45

E_form = E_(doped) − E_(pure) + n(μ_W − μ_Fe)

where E_(doped) and E_(pure) are the total energies of the WSe₂ monolayer with and without the Fe dopants. μ_W and μ_Fe are the chemical potential for W host and dopant atoms, respectively, which depends on the material growth conditions and satisfies the boundary conditions. n is the number of W atoms replaced by Fe dopants. We use the energy per atom of Fe metal as μ_Fe. μ_W is defined within a range of values corresponding to W-rich or Se-rich growth conditions. For a W-rich condition, μ_W is taken as the energy of a W atom within its stable fcc lattice, while for a Se-rich condition, μ_W is determined from the difference in energy between a diatomic S₂ molecule and one formula unit of stoichiometric 2D WSe₂.⁴⁶ We can see from Table 1 that for the Fe-doped WSe₂, the formation energy is lower under S-rich conditions, which indicates that it is energy favorable and relatively easier to incorporate Fe atom into WSe₂ under Se-rich experimental conditions.

4. Conclusion

In our work, we investigated the electronic and magnetic properties of Fe-doped WSe₂ monolayer using the first-principles methods based on density functional theory. The compressive strain is more effective on electronic and magnetic properties in Fe-doped WSe₂ monolayer than the tensile strain. Within the scope of the strain we applied, the largest magnetic moment is 2.117 μ_B at the 10% tensile strain and the minimum magnetic moment is 1.814 μ_B at the −4% compressive strain. The system undergoes a change from semiconductor to half-metal then to metal under strain. Further analysis show that strain changes the redistribution of charges and enhances the coupling between the 3d orbital of Fe atom, 5d orbital of W atom and 4p orbital of Se atom. Moreover, the formation energy calculations also indicate that it is energy favorable and relatively easier to incorporate Fe atom into the WSe₂ monolayer under Se-rich experimental conditions. These results suggest that Fe-doped WSe₂ monolayer might have important potential application in spintronic devices.

Acknowledgements

This work is supported by a Grant from the National Natural Science Foundation of China (NSFC) under the Grant No. 11504092 and U1304518, National Undergraduate Training Programs for Innovation and Entrepreneurship (No. 201510476043), Science and technology research key project of education department of Henan province (No. 14A140012), and High Performance Computing Center of Henan Normal University.

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