Controllable photoenhanced spin- and valley-polarized transport in ferromagnetic MoS2 junction

Journal Pre-proofs Research articles Controllable photoenhanced spin- and valley-polarized transport in ferromag‐ netic MoS2 junction Yaser Hajati, Zahra Amini, Mohammad Sabaeian PII: DOI: Reference:

S0304-8853(19)34034-X https://doi.org/10.1016/j.jmmm.2020.166580 MAGMA 166580

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Journal of Magnetism and Magnetic Materials

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27 November 2019 21 January 2020 6 February 2020

Please cite this article as: Y. Hajati, Z. Amini, M. Sabaeian, Controllable photoenhanced spin- and valleypolarized transport in ferromagnetic MoS2 junction, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166580

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Controllable photoenhanced spin- and valley-polarized transport in ferromagnetic MoS2 junction Yaser Hajatia,b*, Zahra Aminia, Mohammad Sabaeiana,b aDepartment

of Physics, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran for Research on Laser and Plasma, Shahid Chamran University of Ahvaz, Ahvaz, Iran *Corresponding author: [email protected] bCenter

Abstract We propose fully valley- and spin-polarized currents in a normal/ferromagnetic/normal MoS2 junction by applying a circularly polarized light in the off-resonance regime in the ferromagnetic (FM) region. It is found that the circularly polarized light and exchange field remove the valley and spin degeneracies of the conduction band edges, respectively. In this situation, by choosing appropriate values for gate voltage, the Fermi level intersects with one valley form one spin channel leading to the fully valley- and spin-polarized currents through the proposed junction. Interestingly, the sign of both valley and spin polarizations can be easily switched from -100% to 100% by varying the intensity of the circularly polarized light and gate voltage. The full valley- and spin-polarized currents provide desirable routines to construct spin/valley filter for MoS2 based devices. Keywords: spin, valley, polarization, circularly polarized light, MoS2

1. Introduction Investigation of spin and valley degree of freedom in two-dimensional (2D) materials is essential for realizing new quantum technologies [1-4]. Recently, transition metal dichalchogenides have attracted great attention due to their superior applications in spin-valley related physics applicable in nanoelectronics devices [5-12]. A monolayer MoS2 is a direct gap semiconductor with band gap of 1.9 eV. The conduction and valence band edges of the MoS2 consist of two degenerate valleys (K and K') located at the corners of the hexagonal Brillouin Zone, similar to graphene[13]. It is found that MoS2 has very high career mobility and high thermal stability [14]. The monolayer MoS2 has strong spin-orbit coupling which originates from the d-orbital of the heavy metal atoms [10,15]. Absence of inversion symmetry in monolayer MoS2 gives rise to valley-dependent optical transition selective rules [16]. Inversion symmetry breaking with strong spin-orbit coupling leads to coupling the spin and valley locking relation, where the spin splitting of the valence bands is opposite at two valleys due to the time reversal symmetry [2,14,17,18]. Recently, Li et al found that the valley and spin transport can be electrically tuned by a gate voltage in a normal/ferromagnetic/normal (NFN) MoS2 junction [19]. They have shown that fully spin- and valley-polarized currents can be achieved in the proposed junction due to the spin-valley coupling of valence edge band together with the exchange field. The group of Yuan et al have studied the resonance tunneling effect with large incident angles through single 1

electronic barrier in NFN MoS2 junction [20]. They have found that the spin and valley dependent line-type resonances appear in the transmission and conductance spectra leading to fully spin and valley polarizations in the proposed junction [20]. In these studies the fully valley- and spin-polarized currents are due to the spin-valley coupling of the valence-band edges together with the exchange field. Vasilopoulos et al have studied the transport properties of monolayer MoS2 in the presence of a perpendicular magnetic field [21]. They found that the spin splitting in the conduction band significantly enhances in the presence of the magnetic field, B. Majidi et al have shown that the spin- and valley-polarized currents can be inverted by reversing the direction of the exchange field in the ferromagnetic region (FM) in the NFN MoS2 junction [22]. The transport properties of ferromagnetic/insulator/normal/ferromagnetic (FINF) have been studied by Lu et al [23]. They have found that N region could behave as a quantum well, leading to the formation of spin-polarized quantum well state, which greatly affects the negative valley polarization and negative magnetoresistance. MoS2 due to its intrinsic direct band gap at visible and near-infrared wavelengths accompanied by atomic thin thickness has sparked significant interest in integrated semiconductor optoelectronic devices and optical manipulations [9,11,24]. Its optical properties are of particular interest in relation to valleytronics and possible device applications. In this regard, both valley polarization and valley coherence can be obtained by optical pumping with circularly and linearly polarized light [10, 25-27]. It is experimentally demonstrated that, in MoS2 monolayer the photoluminescence (PL) has the same helicity of circularly polarized component as the excitation laser, a signature of the optically pumped valley polarization. Therefore, by optically pumping a MoS2 with circularly polarized light and analyzing the subsequent photoluminescence for right and left helicity, one could measure the polarization of the light [26,27]. It is found that by using circularly polarized light in the off-resonance regime, it is possible to tune the band gap of MoS2 at the K and K' valleys, which leads to fully valley transport in monolayer MoS2 [28]. In fact, the off-resonance light can produce the topological phase transitions in two-dimensional materials such as graphene, silicene, and other topological insulators [29-31, 32-36]. In this paper, we propose fully spin- and valley-polarized currents through the NFN MoS2 junction in the presence of circularly polarized light in the off-resonance regime in the ferromagnetic region. By tuning the intensity of circularly polarized light, the band gap in one valley decreases, while it enhances in the other valley. However, the exchange field removes the spin degeneracy of conduction band edges. Hence, in the presence of circularly offresonance light in the ferromagnetic region, the fully spin- and valley-polarized currents can be obtained through the proposed junction due to the spin-valley coupling of the conduction band edges. In fact, in this situation, by choosing appropriate values for gate voltage, the Fermi level intersects with one valley form one spin channel in the conduction band which is different from the fully valley- and spin-polarized conductances due to the spin-valley coupling of valence-band edges together with the exchange field in the Ref. [19]. Note also that, the sign of the valley and spin polarizations can be easily switched from -100% to 100% in this device by varying the intensity of the circularly polarized light and gate voltage. Hence, circularly

2

polarized light is an effective and sensitive knob for controlling valley polarization which is very important for realistic applications. 2. Theoretical model and formalism Here, we systematically investigate the ballistic electron transport in a NFN MoS2 junction with an electrostatic gate and off-resonance circularly polarized light placed in the FM region (Fig. 1). The low-energy effective Hamiltonian of a normal/ferromagnetic/normal MoS2 junction, which occurs in the vicinity of the Dirac points (K and K') is given by [10,37] H = ℏυf(kxτzσx + kyσy) +Δσz + (λτzsz ― λτzszσz) +U.

(1)

m

Here, vf = 5.3 × 105 s represents the Fermi velocity in MoS2 and sz = +1( ― 1) denotes the electron spin-up (spin-down). τz = +1( ― 1) corresponds to the K (K') valley point and σx,y,z represents the Pauli matrix in sublattice space. λ = 37.5 meV is the spin splitting at the valence band top caused by the intrinsic spin-orbit coupling. Δ = 833 meV is the mass term that breaks the inversion symmetry and h is the exchange splitting induced by the ferromagnetic stripe. U is the electrostatic gate voltage applied through the ferromagnetic stripe. The circularly polarized light is described by an electromagnetic potential as [28] (2) A(t) = ( ± AsinΩt,AcosΩt), where Ω is the frequency of light and plus (minus) sign corresponds to the right (left) circular ∂A(t) polarization and A=E0/ Ω with E0 being the amplitude of the electric field E(t)= ∂t . Based on ℏvf

the Floquet theory [29,38] and off-resonance [29,39] regime ℏΩ ≫ tj (tj = a is the hopping 0 parameter between two nearest neighbors with a0 being the lattice constant), the effect of time dependence electromagnetic potential from the light is reduced to a static effective Hamiltonian, which is defined through the time evolution operator over one period. In this regime, the light does not directly excite the electrons and instead effectively modifies the electron band structure through virtual photon absorption/emission process [40]. With the limit of eAvfΩ ≪ 1, the static effective Hamiltonian is particularly simple around the Dirac points and it has the form of τz∆Ωσz, where τz 1 (-1) denotes K (K′. Hence, the Hamiltonian (1) in the presence of off-resonance light can be written as (3) H = ℏυf(kxτzσx + kyσy) +Δσz + τz∆Ωσz + (λτzsz ― λτzszσz) +U, 2 3 3 where ∆Ω = (eℏAvf ) ℏ Ω is the effective energy term describing the effects of the circularly polarized light, which essentially renormalizes the mass of the Dirac fermions. According to Eq. (3), the energy dispersion in the ferromagnetic (FM) region is given by 2 (4) E ± = U + (τzsz ― szh) ± (∆ ― τzszλ + τzΔΩ)2 + (ℏυk′) , 2

where k′2 = (τzk′x) ± (ky)2, ± labels the occupied and empty bands, respectively. In the normal region, the eigenvalue can be acquired by setting U=h=ΔΩ=0 and k2 = (τzkx)2 ± (ky)2. The wave functions for an electron ballistically transports from the left to the right of this junction has the following plane wave solutions in each region: ΨI = eikyy{

1 ℏvfk ― ik x rτzsz ―ℏvfk + ―ik x e x + e x, Eq Ep Eq Ep

(

)

(

)

3

{ (

ΨII = eikyy aτzsz

ΨIII =

tτzsz Ep

)

(

) }

ℏvfk′― ik′xx ―ℏvfk′+ ―ik′xx e + b e , τ s z z Eq Eq

(ℏvEk )e f ― q

i(kxx + kyy)

,

(5)

with k ± = τzkx ± iky ،k′± = τzk′x ± iky ،Eq = E ± ―∆ ,Ep = ((ℏvfk)2 + E2q)

12

, where rτzsz,

aτzsz, bτzsz, tτzsz are the valley- and spin-resolved coefficients. kx (k′x) and ky (k′y) are the perpendicular and parallel wave vector components of electron in normal (ferromagnetic) region with (k′ = k = (E ± ― τzszλ)2 ― (∆ ― τzszλ)2 ℏυf (E ± + hsz ― U ― τzszλ)2 ― (∆ ― τzszλ + τzΔΩ)2 ℏvf), respectively. Because of the translational invariance in the y-direction, all transverse wave vectors (ky) during the scattering process are conserved. Using the condition of continuity of wave function at the boundaries (boundary conditions), the amplitude the spin- and valley-dependent transmission coefficient (tτzsz) can be calculated by ψI(x = 0) = ψFII(x = 0)

,

ψII(x = L) = ψIII(x = L).

(6)

Then, the transmission probability is evaluated according to the formula Tτzsz = |tτzsz|2. The normalized conductance for a particular spin in a perpendicular valley at zero temperature is evaluated according to standard Landauer-Buttiker formalism as [41] 1 π2

(7)

Gτzsz = 2∫ ―π 2Tτzszcosθdθ,

where θ is the incident angle with respect to the x-direction. The spin-resolved and valleyresolved conductance can be introduced as G↑(↓) = (GK↑(↓) + GK′↑(↓)) 2 and GK(K′) = (GK(K′)↑ + GK(K′)↓) 2, respectively. The valley and spin polarizations can be written as PV = (GK + GK′) (GK ― GK′) Ps = (G↑ + G↓) (G↑ ― G↓).

(8)

3. Result and discussion Figs. 2(a) to (c) display the spin transmission probability for the K and K′ valleys as a function of gate voltage U for different values of ΔΩ . As can be easily seen in Fig. 2(a), in the absence of U and ΔΩ , the spin-up electrons have a large contribution to the transmission of the junction. By increasing U for both spin channels (up and down) there are gap regions where electrons cannot pass through the junction. A part of these gap regions 0.33 eV ≪ U ≪ 1.59 eV is common for both spin channels. It is worth mentioning that only for a specific interval of U, the electrons pass through the junction, which leads to spin energy gap. The spin energy gap for spin-up (spin-down) electrons is presented in the gate voltage region 0 ≪ U ≪ 1.59 eV (0.33 eV ≪ U ≪ 1.92 eV). Therefore, the junction in these regions is completely spinpolarized and it can be used as a spin filter. In fact, this phenomenon arises from the exchange 4

field in the ferromagnetic region, which results in a spin splitting of the valence band edges for both the K and K′valleys [19]. By applying circularly polarized light ∆Ω = 0.4Δ in Fig. 2(b), electrons from both spin channels can contribute to the transport when U=0. In this case, the transmission gap region becomes shorter for both spin channels. Note that, for ΔΩ = 0.8Δ, there is no longer a common gap region for the electrons from both spin channels, as shown in Fig. 2(c). In this case, for the gate voltage range 0.99 eV ≪ U ≪ 1.4 eV (0.66 eV ≪ U ≪ 0.92 eV ) only spin-up (spin-down) electrons can contribute to the transport, indicating a complete spin polarization at these voltages (Fig. 2(c)). Therefore, by applying a circularly polarized light, the full spin polarization region can be easily adjusted and controlled. In Fig. 3(a), the valley transmission probability is plotted in U for different values of ΔΩ . It is seen that the electron from K′ valley can contribute to the transport in a small range of U, which results in a valley polarization in this range. For ΔΩ = 0.4Δ in Fig. 3(b), the transmission gap (valley gap) for the K (K′) valley increases (decreases) significantly. Consequently, the junction is valley polarized for a certain interval of U, as shown by the green dashed region in Fig. 3(b). As demonstrated in Fig. 3(c) for ΔΩ = 0.8Δ, the valley gap for the K valley noticeably increases ( ― 0.49 eV ≪ U ≪ 2.49 eV) but for the K′ valley there will be no longer gap, so the junction is valley polarized in these regions. Therefore, it can be easily concluded that ΔΩ is a very useful tool to create a fully valley polarized current. In Fig. 4, the valley polarization (Pv) and spin polarization (Ps) are plotted as a function of U for different values of ΔΩ . It can be observed from Fig. 4(a) that in the absence of ΔΩ (ΔΩ = 0) both full spin- and valley-polarized currents can be achieved at the some gate voltage regions but rather small transmission at these gate voltages (as seen in Fig. 3(b)) makes it impossible for detection. Therefore, it is not very useful for practical applications. By applying ΔΩ = 0.4Δ in Fig. 4(b), the fully spin- and valleypolarizations can be obtained in the shaded regions. In this case, according to Figs. 2(b) and 3(b), the regions with simultaneous spin- and valley- polarizations have relatively large transmissions which are very important for practical applications. It should be noted that in the case of valley polarization, since the transmission is only through the K′ valley, the valley polarization is ―1 but the spin polarization changes from +1 to ―1 by changing U. When polarization is +1 ( ―1), only spin-up (spin-down) electrons contribute to the transmission. For example, when Pv = Ps = ― 1, the output current consists of spin-down electrons from K′ valley. Therefore, the valley and spin filter can be achieved simultaneously in this device. As demonstrated in Fig. 4(c), by increasing circularly polarized light for ΔΩ = 0.8Δ, the valley polarization region increases substantially, however, in the case of spin polarization the region becomes smaller and eventually disappears for ΔΩ = Δ in Fig. 4(d). At ΔΩ = Δ, according to Eq. (4) the energy gap for K valley is (2∆ ― szλ)2, however the energy gap for K' valley is (szλ)2. In this case, the energy gap of K' valley is very small and it does not depend on the spin index. Therefore, only electrons with spin-up and spin-down bands from the K' valley contribute to the transport. Now, the junction is valley polarized (at a wide range of U) but it is not spin polarized. In this situation, the Fermi level simultaneously intersects with the spinup and spin-down bands from the K' valley. Consequently, the transport all originates from both spin bands, and the spin polarized transmission shows oscillatory behavior, as shown in Fig. 4(d). To understand how the transport properties of the junction change with U and ΔΩ , the band structure diagrams in Fig. 5 can be very useful. In this figure, the left (right) column corresponds to the energy bands of the K (K′) valley. By applying the gate voltage U = 0.3Δ and in the absence of ΔΩ , we can see in Figs. 5(a) and 5(b) that the exchange field h lifts the spin degeneracy of the conduction band edges, therefore the Fermi level only crosses the spinup electrons, indicating complete spin polarization. Figs. 5(c) and 5(d) show that by applying a right circularly polarized light (∆Ω=0.6∆), in the absence of gate voltage (U=0), the Fermi 5

level crosses only the K′ valley electrons from both spin channels leading to eliminating the valley degeneracy. In fact, by applying a circularly polarized light, the gap for the K valley increases, however the gap for the K′ valley decreases. As a result, a valley gap is created and the junction becomes completely valley polarized. In Figs. 5(e) and 5(f), by applying the right circular polarized light (ΔΩ = 0.6Δ) in the presence of gate voltage (U = 0.8Δ), it is seen that the energy bands move in such a way that the Fermi level crosses only the spin-down electrons from the K′ valley. Thus, only the spin-down electrons from the K′ valley contributes to the transport indicating the simultaneous fully spin- and valley-polarizations (Pv = Ps = ― 1). In fact, circularly polarized light and exchange field in the FM region lifts the valley and spin degeneracies in the conduction band edges, respectively. Thus, by applying both the ΔΩ and h, the junction acts as a simultaneous spin and valley filter. In fact, despite Li [19] the exchange field in the FM region causes the spin splitting of the edges of the valence band results in the spin- and valley-polarizations simultaneously, but in our structure, applying a circularly polarized light combined with the exchange field in the FM region leads to fully spin- and valley-polarizations simultaneously in the conduction band edges. In Figs. 5(e) and 5(h), h is set to zero to show the effect of the exchange field in the ferromagnetic region on the spin polarization. It is seen that in the absence of h, the spin polarization of the conduction band edges removes. In Figs. 5(i) and 5(j), the effect of left circularly polarized light (ΔΩ = ― 0.6Δ) on the band structure is investigated. As can be seen in this figure, by applying a left circularly polarized light, the gap valley K (K′) decreases (increases) and for U = 0.8Δ, the Fermi level only crosses the spin-up electrons from the K′ valley, so the junction is spin- and valleypolarized. So far, it has been found that U and ΔΩ are two important parameters for achieving the complete spin- and valley- polarizations. Therefore, in Fig. 6 the contour plot of the valley transmission for K and K' valleys is plotted in terms of U and ΔΩ . In these figures, the transmission regions are well represented in terms of two parameters U and ΔΩ . For K valley in Fig. 6(a), for both right and left circularly polarized lights the transmission curves oscillate and reach a maximum in the dark red regions. At any given U, the transmission range for the left circular polarized light is much greater than the right one. Also, as the right circularly polarized light intensity increases from 0 to 1 eV, the transmission gap increases but with increasing the intensity of the left circularly polarized light, the transmission gap first decreases and then disappears. Subsequently, as the intensity of the left circularly polarized light increases, the gap region increases, too. For the K' valley in Fig. 6(b), this is almost the opposite, and at higher values of U more transmission for the right circularly polarized light is seen. By comparing Figs. 6(a) and 6(b), one can conclude that in regions of U and ΔΩ where the cones of these two shapes do not overlap, we have a valley polarization. In Figs. 7(a) and 7(b), the contour plot of spin transmissions for spin-up and spin-down electrons from both valleys are plotted in U and ΔΩ , respectively. In both figures, the left (right) cone represents the transmission of electrons through the K (K′) valley. As can be seen in this figure, for both right and left circularly polarized lights we have the transmission in many regions of U and ΔΩ . Note that when two cones overlap, the transmission noticeably increases (the dark red regions) because in these cases we have the transmission from both valleys in each spin channel. In green regions, as only one valley contributes to the transport, the intensity of transmission reduces. By comparing Figs. 7(a) and 7(b) one can conclude that in regions of U and ΔΩ where the cones of these two shapes do not overlap, a spin polarization occurs. Also, by comparing Figs. 6 and 7 we can conclude that at a certain range of U and ΔΩ where the cones of these two shapes do not overlap, we have simultaneous spin- and valley-polarizations. After studying the transmission coefficient, as the conductance is a physical quantity and can be measurable in the laboratory, we plot the valley conductance curves as a function of ΔΩ for different values 6

of U in Fig. 8. As can be seen in this figure, in the absence of the gate voltage (U = 0) and at the small values of ΔΩ in the range ―0.33 eV ≪ ΔΩ ≪ 0.33 eV, electrons from both valleys contribute to the conductance (the green shaded region in Fig. 8(a)). As a result, the total conductance increases in these regions, but by increasing the intensity of the right and left polarized lights, only electrons from one valley contribute to the conduction, as shown in Fig. 8(a). With increasing U for U = 0.2Δ, for ΔΩ ranging ―0.16 eV ≪ ΔΩ ≪ 0.16 eV the valley conductance from both valleys decreases, as shown by the green shaded region in Fig. 8(b). By applying U = 0.4Δ in Fig. 8(c), the junction becomes completely valley polarized (except ΔΩ = 0), and the electrons from both valleys do not contribute to the conductance at any range of ΔΩ simultaneously. By applying the right (left) polarized light, the electrons from K′(K) valley contribute to the conductance. Therefore, the right (left) polarized light gives a valley polarization ―1( + 1). With increasing the gate voltage for U = 0.8Δ, there is no conductance at the small values of ΔΩ , but with increasing ΔΩ only in certain regions the electrons from specific valley contribute to the conductance, as shown in Fig. 8(d). In this case the junction is valley-polarized. The results obtained here are validated for ΔΩ = 0.6Δ in Figs. 5(e) and 5(f), and for ΔΩ = ― 0.6Δ in Figs. 5(i) and 5(j). It should be noted that one of the most important results of the present study is that by applying circularly polarized light at a given U, the valley polarization can be easily reversed from +1 to ―1. In Fig. 9, the spin conductance is plotted as a function U for different values of ΔΩ . As shown in Fig. 9(a), at U = ΔΩ = 0 only the spin-up electrons strongly contribute to the conductance indicating a perfect spin polarization. By increasing ΔΩ the electrons from both spin channels and each valley contribute to the conductance. By applying the gate voltage for U = 0.2Δ and U = 0.4Δ in Figs. 9(b) and 9(c), respectively, it can be seen that at small values of ΔΩ we have a spin gap for spin-down electrons and the size of this gap increases with U. Therefore, only spin-up electrons contribute to the conductance, which results in spin polarization +1. Also, by comparing Figs. 9(b) and 9(c), it can be seen that at ΔΩ = 0 the conductance for spin-up electrons is 2 and zero, respectively. As U increases for U = 0.8Δ, we can see in Fig. 9(d) that at certain regions of ΔΩ , the junction is fully spin polarized (+1) for both the right and left circularly light. According to this figure, spin-up electrons are generally more involved in the conductance. Therefore, it can be easily concluded that U and ΔΩ are two important factors in controlling and tuning the transport properties of the junction and by choosing appropriate values for them the junction will be spin- and valley-polarized. Finally, we emphasize that the similarity of our work with NFN WSe2 junction is that the band gap of the K and K′ valleys are oppositely tuned by off-resonance light leading to filtering K′ (K) valley-dependent transmission by the right (left), ∆Ω > 0 (∆Ω < 0) circularly polarized light [28,42,43]. However, there are two main differences between MoS2 and WSe2 junction: 1- The spin-orbit coupling in WSe2 is three times more than MoS2 leading to the spin polarization even without ferromagnetic exchange field [42]. 2- The valley Zeeman field in WSe2 leads to valley polarization [28,43].

4. Summary In this paper, we proposed the fully spin- and valley-polarized currents through a NFN MoS2 junction in the presence of circularly polarized light in the off-resonance regime in the ferromagnetic region. By tuning the intensity of circularly polarized light (ΔΩ ), the 7

band gap in one valley decreases, while it is enhanced in the other valley. However, the exchange field removes the spin degeneracy of conduction band edges. Hence, in the presence of circularly polarized light in the ferromagnetic region the fully spin- and valleypolarized currents can be obtained through the proposed junction due to the spin-valley coupling of the conduction band edges. In fact, in this situation, by choosing appropriate values for gate voltage, the Fermi level intersects with one valley form one spin channel in the conduction band. Note also that, the sign of the valley and spin polarizations can be easily switched from -100% to 100% by varying the intensity of the circularly polarized light and gate voltage. For example, for U=0.4Δ, the junction is totally valley polarized and the valley polarization for left (right) polarized light is +100% (-100%), hence circularly polarized light is a useful tool for controlling valley polarization which is very important for realistic applications. This work has revealed the potential of MoS2 for future spinvalleytronics devices.

Acknowledgement The research leading to these results has received funding from Shahid Chamran University of Ahvaz under grant agreement no. SCU.SP98.100.

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Figure captions

Fig 1. Schematic of a NFN MoS2 junction, in which the ferromagnetic region is exposed to a circularly polarized light. Fig 2. Spin transmission probability as a function of gate voltage U with different ∆Ω. (a) ∆Ω = 0, (b) ∆Ω = 0.4∆, and (c) ∆Ω = 0.8∆. Blue (sz=1) and red (sz=-1) curves correspond to spin up and spin down channels. The other parameters are h=0.2∆, E=1.2∆, θ = 0, and L=7nm. Fig 3. Valley transmission probability as a function of gate voltage U with different ∆Ω. (a) ∆Ω = 0, (b) ∆Ω = 0.4∆, and (c) ∆Ω = 0.8∆. Blue and red curves correspond to K′ and K valleys. The other parameters are the same as Fig. 2. Fig 4. Spin polarization (Ps) and valley polarization (Pv) as a function of gate voltage U with different ∆Ω. (a) ∆Ω = 0, (b) ∆Ω = 0.4∆, (c) ∆Ω = 0.8∆ , and (d) ∆Ω = ∆. The other parameters are the same as Fig. 2. Fig 5. Band structure at K and K′ valleys in ferromagnetic MoS2. The left (right) panel correspond to the K (K′) valley. The horizontal lines denotes the Fermi energy E=1.2∆. Here, h=0.2∆ (except in Figs. 5(g) and 5(h)) and the other parameters are the same as Fig. 2. Fig 6. Contour plot of valley transmission probability as a function of gate voltage U and ∆Ω for K (a) and K' (b) valleys. The other parameters are the same as Fig. 2. Fig 7. Contour plot of spin transmission probability as a function of gate voltage U and ∆Ω for spin up (a) and spin down (b) channels. The other parameters are the same as Fig. 2. Fig 8. Valley conductance as a function of ∆Ω with different U. (a) U = 0, (b) U = 0.2∆, (c) U = 0.4∆ and (d) U = 0.8∆. The other parameters are the same as Fig. 2. Fig 9. Spin conductance as a function of ∆Ω with different U. (a) U = 0, (b) U = 0.2∆, (c) U = 0.4∆ and (d) U = 0.8∆. The other parameters are the same as Fig. 2.

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Figure 1

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Figure 2

(a)

(b)

(c)

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Figure 3

(a)

(b)

(c)

13

Figure 4

(a)

(b)

(c)

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(d)

Figure 5 (a)

U=0.3∆, ∆𝛀 = 𝟎

(b)

U=0.3∆, ∆𝛀 = 𝟎

(c)

U=0, ∆𝛀=0.6∆

(d)

U=0, ∆𝛀=0.6∆

(e)

U=0.8∆, ∆𝛀=0.6∆

(f)

U=0.8∆, ∆𝛀=0.6∆

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(g)

U=0.8∆, ∆𝛀=0.6∆,h=0

(i)

U=0.8∆, ∆𝛀=-0.6∆

(h)

U=0.8∆, ∆𝛀=0.6∆,h=0

(j)

U=0.8∆, ∆𝛀=-0.6∆

Figure 6

(a)

K valley

∆Ω(eV)

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(b) valley𝐊′

∆Ω(eV)

Figure 7

(a) Spin-up

∆Ω(eV) 17

(b) Spin-down

∆Ω(eV)

Figure 8

(a)

∆Ω(eV)

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(b)

∆Ω(eV) (c)

∆Ω(eV) (d)

∆Ω(eV) Figure 9

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(a)

∆Ω(eV) (b)

∆Ω(eV) (c)

∆Ω(eV) (d)

∆Ω(eV)

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1- Fully spin- and valley-polarized currents in a NFN MoS2 junction can be achieved simultaneously. 2- Circularly polarized light and exchange field remove the valley and spin degeneracies of the conduction band edges, respectively. 3- Sign of both the valley and spin polarizations can be easily switched from -100% to 100% by varying the circularly polarized light and gate voltage.

Conflict of Interest and Authorship Conformation Form

Title: Controllable photoenhanced spin- and valley-polarized transport in ferromagnetic MoS2 junction

Please check the following as appropriate:

o

All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.

o

This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.

Author’s name Y. Hajati (Corresponding author) Z. Amini M. Sabaeian

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