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Spin-filtering, negative differential resistance, and giant magnetoresistance in (2 × 1) reconstructed zigzag MoS2 nanoribbons
Physica B: Physics of Condensed Matter 528 (2018) 9–13
Contents lists available at ScienceDirect
Physica B: Physics of Condensed Matter journal homepage: www.elsevier.com/locate/physb
Spin-filtering, negative differential resistance, and giant magnetoresistance in (2 1) reconstructed zigzag MoS2 nanoribbons Y.Z. Lv a, P. Zhao a, *, D.S. Liu b, c a b c
School of Physics and Technology, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China Department of Physics, Jining University, Jining 273155, China
A R T I C L E I N F O
A B S T R A C T
Keywords: MoS2 nanoribbon Spin-polarized transport Spin-filtering Negative differential resistance Magnetoresistance
Based on density functional theory combined with nonequilibrium Green's function method, we have investigated the spin-polarized transport properties of the (2 1) reconstructed zigzag MoS2 nanoribbon (ZMoS2NR)-based devices. The results show that these devices can exhibit multiple high-performance spin-dependent transport properties by modulating the applied magnetic field, including spin-filtering, negative differential resistance and giant magnetoresistance effects. These effects are explained by the spin band structures around the Fermi level, as well as their symmetries. Moreover, all effects are robust regardless of the nanoribbon width. These findings suggest the (2 1) reconstructed ZMoS2NRs have great potential in the field of spintronics.
1. Introduction Two-dimensional (2D) molybdenum disulfide (MoS2) nanosheets with one or few layers have recently attracted considerable interest in the fields of electronics, optoelectronics, spintronics, etc., due to their excellent electronic, optical and magnetic properties [1–3]. Especially, monolayer MoS2, a sandwich structure with two hexagonal layers of S atoms outside and a hexagonal layer of Mo atoms in the middle, has been considered as a highly competitive candidate for field-effect transistors (FETs) with high on/off ratio exceeding 108 because of its sizable direct band gap ~ 1.8 eV [4,5]. For many novel applications, the onedimensional (1D) MoS2 nanoribbons also draw much attention since their electronic properties can be different from and thus complementary to their monolayer counterpart. Similar to graphene nanoribbon, two typical kinds of MoS2 nanoribbons can be distinguished according to the different edge types: armchair and zigzag MoS2 nanoribbons (AMoS2NRs and ZMoS2NRs) [6,7]. AMoS2NRs are nonmagnetic semiconductors and the band gaps gradually converge to a constant value of ~0.56 eV as the nanoribbon width increases [6,7]. In contrast, ZMoS2NRs are magnetic with sizable magnetic moments on edge atoms, irrespective of the nanoribbon width [6,7]. However, the dangling bonds along the edge lead these nanoribbons to be energetically unfavorable. In general, edge reconstruction is an efficient way to eliminate dangling bonds [8–10]. Very recently, Cui et al. revealed a (2 1) reconstructed ZMoS2NRs with the stoichiometric ratio of Mo/S ¼ 1:2
[11]. The (2 1) reconstruction along the Mo edge is via place exchange or self-passivation mechanism, with substantial inward displacements of all the first-row Mo atoms and corresponding outward displacements of half of the second-row S atoms. The (2 1) reconstruction along the S edge is much milder than that at the Mo edge, characterized by slight local place readjustments of the edge atoms. It has been recently demonstrated that this edge self-passivation mechanism can be exploited for controlled fabrication of properly tailored transition metal dichalcogenide nanoribbons under nonequilibrium growth conditions [12]. For the practical applications of these nanoribbons, it is important to further explore their bias-transport properties. Here, we investigate the spin-polarized transport properties of the (2 1) reconstructed ZMoS2NR-based devices with the help of external magnetic field. Our first-principles transport calculations show that those devices can present multiple high-performance spin-dependent transport properties, including spin-filtering, negative differential resistance (NDR), and giant magnetoresistance (GMR) effects. 2. Model and formalism Fig. 1(a) shows the designed (2 1) reconstructed 6-ZMoS2NR-based device, where the prefix 6 indicates the number of zigzag chains across the width of original unreconstructed ZMoS2NR (W ¼ 6). The device is divided into three regions: a left electrode (LE), a central scattering region (CSR), and a right electrode (RE). Each electrode is modeled by one
* Corresponding author. E-mail address: [email protected] (P. Zhao). https://doi.org/10.1016/j.physb.2017.10.099 Received 11 September 2017; Received in revised form 15 October 2017; Accepted 22 October 2017 Available online 23 October 2017 0921-4526/© 2017 Elsevier B.V. All rights reserved.
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Physica B: Physics of Condensed Matter 528 (2018) 9–13
Tσ within the energy region [-eV/2, eV/2], which is referred to as the bias window. 3. Numerical results and discussion We first calculate the energy of the (2 1) reconstructed 6-ZMoS2NR unit cell at antiferromagnetic (AFM), ferromagnetic (FM) and nonmagnetic (NM) states. The energy difference between AFM and FM states is 0.08 meV, while that between AFM and NM states is 68.65 meV. These energy differences indicate that the AFM state is the ground state and the AFM and FM states can transform easily each other, while the NM state is quite unstable compared to those spin-polarized states. As the magnetization of LE/RE can be controlled by applying external magnetic fields [20], two distinct magnetic configurations (MCs) are considered: parallel (P) and antiparallel (AP) MCs with magnetic fields at two electrodes pointing in the same (þy, þy) and opposite (þy, -y) directions, respectively. Fig. 1(b) shows the spin density (difference between spin-up and spin-down electron density) for the P and AP MCs under zero bias, where the pink and cyan colors indicate the spin-up and spin-down components, respectively. It is evident that, for the bottom edge, the spin density distributes on the edge S atoms and the Mo-trimers (mainly on the sub-edge Mo atoms). For the top edge, the spin density mainly distributes on the edge Mo atoms. Moreover, in contrast to the case of P MC, the spins on the top and bottom edges change from up to down going from left to right in the AP MC. Fig. 2 shows the spin-resolved current-voltage (I-V) curves for the P and AP MCs in the bias range from 0 to 0.2 V in steps of 0.02 V. Three interesting features can be obtained from these I-V curves: (1) Spinfiltering effect. For the P MC, the spin-down current (Idn) is strongly suppressed in the whole bias range, while there is obvious spin-up current (Iup) through the device. This means the (2 1) reconstructed 6ZMoS2NR-based device in the P MC exhibits good spin-filtering effect. The spin-filtering efficiency (SFE) can be used to evaluate this effect, which is defined as
Fig. 1. (a) Schematic view of the (2 1) reconstructed 6-ZMoS2NR-based device. The cyan and yellow balls represent molybdenum and sulfur atoms, respectively. The device is divided into three regions: a left electrode (LE), a central scattering region (CSR), and a right electrode (RE). z is the transport direction. Labels P and AP represent the magnetic configurations (MCs) of two electrodes. (b) The spin density for the P and AP magnetic configurations (MCs) under zero bias, where the pink and cyan colors indicate the spin-up and spin-down components, respectively, and the isosurface level is taken as 0.02 jej/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(2 1) reconstructed ZMoS2NR unit cell. The CSR contains three repeated (2 1) reconstructed ZMoS2NR unit cells along the transport direction (z). A 20 Å vacuum slab is adopted to eliminate interactions between two neighboring nanoribbons. Geometric optimization is performed for the (2 1) reconstructed ZMoS2NR unit cell using the quasiNewton method until the force on each atom reaches the tolerance limit of 0.001 eV/Å. The geometric optimization and subsequent spin-polarized transport calculations are both carried out by the Atomistix Toolkit (ATK) program package [13–16], which is based on the nonequilibrium Green's function (NEGF) combined with the density functional theory (DFT). In this work, the spin-dependent generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof is adopted as the exchange-correlation function [17]. It has been shown that the effect of spin-orbit coupling (SOC) on the spin bands around the Fermil level is negligible [11]. Therefore, the SOC is not considered in our work. The core electrons are described by the Troullier-Martins norm-conserving pseudopotentials [18] and a double-ξ plus polarization (DZP) basis set is adopted for the valence electron wave function. A mesh-cutoff energy of 150 (350) Ry and a Monkhorst-Pack k-point of 1 1 100 (1 1 21) are chosen for transport (optimization) calculations. The spin-resolved currents through the device are calculated by the Landauer-Büttiker formula [19],
i e Iσ ¼ ∫ Tσ ðE; Vb Þ½fL ðE μL Þ fR ðE μR Þ dE h
SFE ¼ [(Iup-Idn)/(Iup þ Idn)] 100%
(2)
Fig. 3(a) presents the SFE as a function of the applied bias Vb. Clearly, the SFE is near 100% when the bias is less than 0.18 V, indicating the high-efficiency spin-filtering behavior in the P MC. (2) NDR effect. The NDR effect is characterized by an increase followed by a decease in current with the increase in applied bias, which is the basis for many device applications including high-frequency oscillators, analog-todigital converters, and logic gates [21–23]. As shown in Fig. 2, the Iup
(1)
where, e and h are the electron charge and Planck's constant, respectively. σ ¼ up (spin-up) or dn (spin-down). Tσ ðE; Vb Þ ¼ Tr½Γ L GRσ Γ R GAσ is the spin-resolved transmission function for electrons with energy E under R=A
bias Vb. Here, Gσ is the spin-resolved retarded/advanced Green functions of CSR, Γ L=R is the coupling matrix between CSR and LE/RE. fL/R and μL/R ¼ EF eVb/2 are the Fermi-Dirac distribution function and electrochemical potential of LE/RE, respectively. EF is the equilibrium Fermi level of LE/RE, which has been set to energy origin in our calculations. Clearly, the spin-resolved current is determined by the integral of
Fig. 2. Calculated spin-resolved I-V curves for the P and AP MCs. 10
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Physica B: Physics of Condensed Matter 528 (2018) 9–13
two electrodes switches between P and AP MCs. To evaluate this effect quantitatively, we define the magnetoresistance ratio (MR) as MR ¼ [(IP-IAP)/IAP] 100%
(3)
Fig. 3(c) presents the MR as a function of the applied bias Vb. It is clear that the MR is higher than 105% when the bias is less than 0.18 V and the maximum MR reaches up to 1.41 106% at 0.12 V. The spin-filtering and magnetoresistance effects are very interesting physical phenomena in the field of electronics, and can be set as perfect spin-filters and spin-valves [34–36]. So we can draw the conclusion that the (2 1) reconstructed 6-ZMoS2NR-based device can present multiple high-performance spindependent transport properties. According to equation (1), the current is obtained by the integral of transmission function within the bias window. Then in order to elucidate the above three interesting effects, as shown in Fig. 4, we focus on the spin-resolved transmission spectra as a function of the electron energy E and bias Vb for P and AP MCs. Fig. 4(a) and (b) correspond to the spin-up and spin-down transmission spectra of P MC, while Fig. 4(c) and (d) correspond to the spin-up and spin-down transmission spectra of AP MC, respectively. The two red dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. For the P MC, the zero bias spin-up transmission spectrum exhibits a strong transmission band (TB) around the EF (Fig. 4(a)). Although the width and height of this TB decrease gradually as the bias increases, there is always considerable transmission within the bias window when the bias is less than 0.18 V. In contrast, the zero bias spin-down transmission spectrum exhibits a narrow transmission peak just above the EF (Fig. 4(b)), which quenches to zero rapidly as the bias increases. Since there is no any spin-down transmission peak inside the bias window, the Idown is strongly blocked, resulting in the perfect spin-filtering effect. Meantime, when the overall shrink in TB suppresses any gain resulting from a wider bias window, the Iup begins to decrease and thus the NDR effect occurs. For the AP MC, both the zero bias spin-up and spin-down transmission spectrum exhibit a large transmission gap of 0.5 eV
Fig. 3. (a) and (b) Calculated spin-filtering efficiency (SFE), differential conductance (dI/ dV) as a function of bias for the P MC. (c) Calculated magnetoresistance ratio (MR) as a function of bias.
in the P MC increases rapidly at first, and then begins to drop quickly when the bias exceeds 0.08 V, indicating a low-bias NDR occurs at 0.08 V. This observed low-bias NDR behavior can be further validated by the variation of differential conductance (dI/dV) vs. Vb. As shown in Fig. 3(b), the dI/dV is negative between 0.08 and 0.2 V. Moreover, since the Iup is almost quenched to zero after 0.18 V, a giant current peak-to-valley ratio (PVR ¼ (Ipeak/Ivalley) 100%, where Ipeak/Ivalley is the peak/valley currents of Iup, respectively) up to 2.34 106% is obtained. Although NDR behaviors have been realized in many nanoscale systems, they typically take place at relatively high biases and their PVRs are very small [24–28]. Thus, the giant low-bias NDR in the (2 1) reconstructed 6-ZMoS2NR device is desirable from the point view of power consumption [29–33]. (3) GMR effect. As shown in Fig. 2, both the Iup and Idn in the AP MC are completely blocked in the whole bias range. As a result, the total current (sum of Iup and Idn) in the P MC (IP) is much larger than that in the AP MC (IAP). Then one can expect a GMR effect when the spin magnetization of
Fig. 4. (a) and (b) Calculated spin-up, spin-down transmission spectra as a function of the electron energy E and bias Vb for the P MC. (c) and (d) Calculated spin-up, spin-down transmission spectra as a function of the electron energy E and bias Vb for the AP MC. The energy origin is the Fermi level EF. The two red dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. 11
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Fig. 5. Calculated spin-resolved band structures of left electrode (left panel) and right electrode (right panel), and the spin-resolved transmission spectra (middle panel) at different biases. (a), (b) and (c) correspond to the case of P MC at 0, 0.08 and 0.2 V, respectively. (d) Corresponds to the case of AP MC at zero bias, respectively. The energy origin is the Fermi level EF. The two blue dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
around the EF (Fig. 4(c) and (d)), which is also extended as the bias increases. Since there is no any transmission within the bias window, both the Iup and Idn cannot pass through the device in the AP MC. Then the high-performance GMR effect can be obtained when the P and AP MCs transform each other. To further clarify the different transmission phenomena, we analyze the spin-resolved band structures of two electrodes at different biases. Fig. 5 (a), (b) and (c) correspond to the case of P MC at 0, 0.08 (Ipeak), and 0.2 V (Ivalley), respectively, and Fig. 5(d) corresponds to the case of AP MC at 0 V. The two blue dotted lines indicate the electrochemical potential of two electrodes. As shown in Fig. 5(a), for the P MC, the bands in LE (left panel) have the same structures as those in RE (right panel) at 0 V. There is a spin-down band I just above the EF, while there is a spin-up band II in the energy range from 0.26 to 0.24 eV. Fig. 6 (a) and (b) plot the Bloch wave function for bands I and II at the Γ point, respectively. As one can see, the spin-down band I is mainly dominated by dxy orbitals of the subedge Mo atoms and 3p orbital of the outmost S atoms at the bottom edge, while the spin-up band II is mainly formed by d2y orbitals of the sub-edge Mo atoms at the top edge. As shown in Fig. 5(a), at zero bias, the perfect matching between spin-up band II in LE and that in RE gives rise to the strong spin-up TB around the EF (middle panel). As the bias increases, the bands in LE shift downwards, while those in RE shift upwards. As shown in Fig. 5(b), at 0.08 V, the overlapping between spin-up band II in LE and that in RE is reduced significantly compared to that at zero bias due to the shift in the opposite direction of bands in two electrodes. When the bias exceed 0.18 V, the overlapping between spin-up band II in LE and that in RE is completely quenched to zero (Fig. 5(c)). In this process, the width and height of the spin-up TB around the EF decrease all the way down to zero as the bias increases (>0.18 V). As a result, the Iup in the P MC increases at first and then decrease as the bias increases, and the NDR effect
Fig. 6. (a) and (b) Calculated Bloch wave function for spin-down band I and spin-up II at the Γ point, respectively. The isosurface level is taken as 0.2/(Å3⋅eV).
occurs. Meantime, as shown in Fig. 5(b) and (c), there is no any overlapping of spin-down band I between two electrodes at finite bias, and thus the Idn in the P MC cannot flow through the device. Therefore, a near 100% spin-filtering is realized in the P MC. As shown in Fig. 5(d), for the AP MC, the spin-up and spin-down band structures in RE are exchanged compared to those in LE. In the energy region [0.015 eV, 0.035 eV], the spin-down band I (spin-up band II) in LE overlaps with the spin-down band II (spin-up band I) in RE. However, this overlapping can not contribute any spin-down and spin-up transmission. This point can be 12
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around the EF nearly remain unchanged, which guarantees the robustness of three spin-dependent effects. 4. Summary In summary, we have investigated the spin-polarized transport properties of the (2 1) reconstructed ZMoS2NR-based devices by using the first-principles DFT þ NEGF method. Our results show that these devices can exhibit multiple high-performance spin-dependent transport properties, including spin-filtering, NDR and GMR effects, by tuning the applied magnetic field on two electrodes. All three effects can be attributed to the matching and mismatching of spin bands around the Fermi level, as well as their symmetries. Moreover, all three effects are robust regardless of the nanoribbon width. These findings suggest the (2 1) reconstructed ZMoS2NRs are potential candidates for developing the high-performance multifunctional spintronic devices. Fig. 7. (a) and (b) Calculated bias-dependent spin-filtering efficiency (SFE), differential conductance (dI/dV) of the (2 1) reconstructed ZMoS2NR-based devices with nanoribbon width W ¼ 6, 7 and 8 for the P MC, respectively. (c) Calculated bias-dependent magnetoresistance ratio (MR) of the (2 1) reconstructed ZMoS2NR-based devices with width W ¼ 6, 7 and 8.
Acknowledgements This work is supported by the Natural Science Foundation of Shandong Province of China (No. ZR2016AM11).
understood by the symmetry of two bands. As shown in Fig. 6 (a) and (b), the symmetry of two bands is completely opposite, namely, the bands I and II have odd and even parities under the xz midplane mirror operation, respectively, leading to the transmission be forbidden from LE to RE [37,38], and the blocking of Iup and Idn in the AP MC. As a result, the GMR effect can be obtained when the spin magnetization of two electrodes switches between P and AP MCs. At last, we study the effects of nanoribbon width on these spindependent transport properties. As shown in Fig. 7(a)-(c), we plot the SFE, dI/dV and MR as a function of the applied bias Vb for the (2 1) reconstructed ZMoS2NR-based devices with width W ¼ 6,7 and 8, respectively. As one can see, all the SFEs are near 100% when the bias is less than 0.18 V (Fig. 7(a)), the dI/dVs are negative between 0.08 and 0.2 V (Fig. 7(b)), and the MRs are greater than 105 before 0.18 V (Fig. 7(c)). This means the spin-filtering, NDR and GMR effects in the (2 1) reconstructed ZMoS2NR-based devices are robust regardless of the nanoribbon width W. As discussed above, all three effects are originated from the matching and mismatching of spin bands I/II around the EF. As shown in Fig. 8, when the width is changed, the spin bands I/II
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Fig. 8. (a), (b) and (c) Calculated spin-resolved band structures of the (2 1) reconstructed ZMoS2NRs with nanoribbon width W ¼ 6, 7 and 8 in the AFM ground state, respectively. The black solid line and red dashed line denote the spin-up and spin-down, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 13
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Physica B: Physics of Condensed Matter journal homepage: www.elsevier.com/locate/physb
Spin-filtering, negative differential resistance, and giant magnetoresistance in (2 1) reconstructed zigzag MoS2 nanoribbons Y.Z. Lv a, P. Zhao a, *, D.S. Liu b, c a b c
School of Physics and Technology, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China Department of Physics, Jining University, Jining 273155, China
A R T I C L E I N F O
A B S T R A C T
Keywords: MoS2 nanoribbon Spin-polarized transport Spin-filtering Negative differential resistance Magnetoresistance
Based on density functional theory combined with nonequilibrium Green's function method, we have investigated the spin-polarized transport properties of the (2 1) reconstructed zigzag MoS2 nanoribbon (ZMoS2NR)-based devices. The results show that these devices can exhibit multiple high-performance spin-dependent transport properties by modulating the applied magnetic field, including spin-filtering, negative differential resistance and giant magnetoresistance effects. These effects are explained by the spin band structures around the Fermi level, as well as their symmetries. Moreover, all effects are robust regardless of the nanoribbon width. These findings suggest the (2 1) reconstructed ZMoS2NRs have great potential in the field of spintronics.
1. Introduction Two-dimensional (2D) molybdenum disulfide (MoS2) nanosheets with one or few layers have recently attracted considerable interest in the fields of electronics, optoelectronics, spintronics, etc., due to their excellent electronic, optical and magnetic properties [1–3]. Especially, monolayer MoS2, a sandwich structure with two hexagonal layers of S atoms outside and a hexagonal layer of Mo atoms in the middle, has been considered as a highly competitive candidate for field-effect transistors (FETs) with high on/off ratio exceeding 108 because of its sizable direct band gap ~ 1.8 eV [4,5]. For many novel applications, the onedimensional (1D) MoS2 nanoribbons also draw much attention since their electronic properties can be different from and thus complementary to their monolayer counterpart. Similar to graphene nanoribbon, two typical kinds of MoS2 nanoribbons can be distinguished according to the different edge types: armchair and zigzag MoS2 nanoribbons (AMoS2NRs and ZMoS2NRs) [6,7]. AMoS2NRs are nonmagnetic semiconductors and the band gaps gradually converge to a constant value of ~0.56 eV as the nanoribbon width increases [6,7]. In contrast, ZMoS2NRs are magnetic with sizable magnetic moments on edge atoms, irrespective of the nanoribbon width [6,7]. However, the dangling bonds along the edge lead these nanoribbons to be energetically unfavorable. In general, edge reconstruction is an efficient way to eliminate dangling bonds [8–10]. Very recently, Cui et al. revealed a (2 1) reconstructed ZMoS2NRs with the stoichiometric ratio of Mo/S ¼ 1:2
[11]. The (2 1) reconstruction along the Mo edge is via place exchange or self-passivation mechanism, with substantial inward displacements of all the first-row Mo atoms and corresponding outward displacements of half of the second-row S atoms. The (2 1) reconstruction along the S edge is much milder than that at the Mo edge, characterized by slight local place readjustments of the edge atoms. It has been recently demonstrated that this edge self-passivation mechanism can be exploited for controlled fabrication of properly tailored transition metal dichalcogenide nanoribbons under nonequilibrium growth conditions [12]. For the practical applications of these nanoribbons, it is important to further explore their bias-transport properties. Here, we investigate the spin-polarized transport properties of the (2 1) reconstructed ZMoS2NR-based devices with the help of external magnetic field. Our first-principles transport calculations show that those devices can present multiple high-performance spin-dependent transport properties, including spin-filtering, negative differential resistance (NDR), and giant magnetoresistance (GMR) effects. 2. Model and formalism Fig. 1(a) shows the designed (2 1) reconstructed 6-ZMoS2NR-based device, where the prefix 6 indicates the number of zigzag chains across the width of original unreconstructed ZMoS2NR (W ¼ 6). The device is divided into three regions: a left electrode (LE), a central scattering region (CSR), and a right electrode (RE). Each electrode is modeled by one
* Corresponding author. E-mail address: [email protected] (P. Zhao). https://doi.org/10.1016/j.physb.2017.10.099 Received 11 September 2017; Received in revised form 15 October 2017; Accepted 22 October 2017 Available online 23 October 2017 0921-4526/© 2017 Elsevier B.V. All rights reserved.
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Tσ within the energy region [-eV/2, eV/2], which is referred to as the bias window. 3. Numerical results and discussion We first calculate the energy of the (2 1) reconstructed 6-ZMoS2NR unit cell at antiferromagnetic (AFM), ferromagnetic (FM) and nonmagnetic (NM) states. The energy difference between AFM and FM states is 0.08 meV, while that between AFM and NM states is 68.65 meV. These energy differences indicate that the AFM state is the ground state and the AFM and FM states can transform easily each other, while the NM state is quite unstable compared to those spin-polarized states. As the magnetization of LE/RE can be controlled by applying external magnetic fields [20], two distinct magnetic configurations (MCs) are considered: parallel (P) and antiparallel (AP) MCs with magnetic fields at two electrodes pointing in the same (þy, þy) and opposite (þy, -y) directions, respectively. Fig. 1(b) shows the spin density (difference between spin-up and spin-down electron density) for the P and AP MCs under zero bias, where the pink and cyan colors indicate the spin-up and spin-down components, respectively. It is evident that, for the bottom edge, the spin density distributes on the edge S atoms and the Mo-trimers (mainly on the sub-edge Mo atoms). For the top edge, the spin density mainly distributes on the edge Mo atoms. Moreover, in contrast to the case of P MC, the spins on the top and bottom edges change from up to down going from left to right in the AP MC. Fig. 2 shows the spin-resolved current-voltage (I-V) curves for the P and AP MCs in the bias range from 0 to 0.2 V in steps of 0.02 V. Three interesting features can be obtained from these I-V curves: (1) Spinfiltering effect. For the P MC, the spin-down current (Idn) is strongly suppressed in the whole bias range, while there is obvious spin-up current (Iup) through the device. This means the (2 1) reconstructed 6ZMoS2NR-based device in the P MC exhibits good spin-filtering effect. The spin-filtering efficiency (SFE) can be used to evaluate this effect, which is defined as
Fig. 1. (a) Schematic view of the (2 1) reconstructed 6-ZMoS2NR-based device. The cyan and yellow balls represent molybdenum and sulfur atoms, respectively. The device is divided into three regions: a left electrode (LE), a central scattering region (CSR), and a right electrode (RE). z is the transport direction. Labels P and AP represent the magnetic configurations (MCs) of two electrodes. (b) The spin density for the P and AP magnetic configurations (MCs) under zero bias, where the pink and cyan colors indicate the spin-up and spin-down components, respectively, and the isosurface level is taken as 0.02 jej/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(2 1) reconstructed ZMoS2NR unit cell. The CSR contains three repeated (2 1) reconstructed ZMoS2NR unit cells along the transport direction (z). A 20 Å vacuum slab is adopted to eliminate interactions between two neighboring nanoribbons. Geometric optimization is performed for the (2 1) reconstructed ZMoS2NR unit cell using the quasiNewton method until the force on each atom reaches the tolerance limit of 0.001 eV/Å. The geometric optimization and subsequent spin-polarized transport calculations are both carried out by the Atomistix Toolkit (ATK) program package [13–16], which is based on the nonequilibrium Green's function (NEGF) combined with the density functional theory (DFT). In this work, the spin-dependent generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof is adopted as the exchange-correlation function [17]. It has been shown that the effect of spin-orbit coupling (SOC) on the spin bands around the Fermil level is negligible [11]. Therefore, the SOC is not considered in our work. The core electrons are described by the Troullier-Martins norm-conserving pseudopotentials [18] and a double-ξ plus polarization (DZP) basis set is adopted for the valence electron wave function. A mesh-cutoff energy of 150 (350) Ry and a Monkhorst-Pack k-point of 1 1 100 (1 1 21) are chosen for transport (optimization) calculations. The spin-resolved currents through the device are calculated by the Landauer-Büttiker formula [19],
i e Iσ ¼ ∫ Tσ ðE; Vb Þ½fL ðE μL Þ fR ðE μR Þ dE h
SFE ¼ [(Iup-Idn)/(Iup þ Idn)] 100%
(2)
Fig. 3(a) presents the SFE as a function of the applied bias Vb. Clearly, the SFE is near 100% when the bias is less than 0.18 V, indicating the high-efficiency spin-filtering behavior in the P MC. (2) NDR effect. The NDR effect is characterized by an increase followed by a decease in current with the increase in applied bias, which is the basis for many device applications including high-frequency oscillators, analog-todigital converters, and logic gates [21–23]. As shown in Fig. 2, the Iup
(1)
where, e and h are the electron charge and Planck's constant, respectively. σ ¼ up (spin-up) or dn (spin-down). Tσ ðE; Vb Þ ¼ Tr½Γ L GRσ Γ R GAσ is the spin-resolved transmission function for electrons with energy E under R=A
bias Vb. Here, Gσ is the spin-resolved retarded/advanced Green functions of CSR, Γ L=R is the coupling matrix between CSR and LE/RE. fL/R and μL/R ¼ EF eVb/2 are the Fermi-Dirac distribution function and electrochemical potential of LE/RE, respectively. EF is the equilibrium Fermi level of LE/RE, which has been set to energy origin in our calculations. Clearly, the spin-resolved current is determined by the integral of
Fig. 2. Calculated spin-resolved I-V curves for the P and AP MCs. 10
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two electrodes switches between P and AP MCs. To evaluate this effect quantitatively, we define the magnetoresistance ratio (MR) as MR ¼ [(IP-IAP)/IAP] 100%
(3)
Fig. 3(c) presents the MR as a function of the applied bias Vb. It is clear that the MR is higher than 105% when the bias is less than 0.18 V and the maximum MR reaches up to 1.41 106% at 0.12 V. The spin-filtering and magnetoresistance effects are very interesting physical phenomena in the field of electronics, and can be set as perfect spin-filters and spin-valves [34–36]. So we can draw the conclusion that the (2 1) reconstructed 6-ZMoS2NR-based device can present multiple high-performance spindependent transport properties. According to equation (1), the current is obtained by the integral of transmission function within the bias window. Then in order to elucidate the above three interesting effects, as shown in Fig. 4, we focus on the spin-resolved transmission spectra as a function of the electron energy E and bias Vb for P and AP MCs. Fig. 4(a) and (b) correspond to the spin-up and spin-down transmission spectra of P MC, while Fig. 4(c) and (d) correspond to the spin-up and spin-down transmission spectra of AP MC, respectively. The two red dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. For the P MC, the zero bias spin-up transmission spectrum exhibits a strong transmission band (TB) around the EF (Fig. 4(a)). Although the width and height of this TB decrease gradually as the bias increases, there is always considerable transmission within the bias window when the bias is less than 0.18 V. In contrast, the zero bias spin-down transmission spectrum exhibits a narrow transmission peak just above the EF (Fig. 4(b)), which quenches to zero rapidly as the bias increases. Since there is no any spin-down transmission peak inside the bias window, the Idown is strongly blocked, resulting in the perfect spin-filtering effect. Meantime, when the overall shrink in TB suppresses any gain resulting from a wider bias window, the Iup begins to decrease and thus the NDR effect occurs. For the AP MC, both the zero bias spin-up and spin-down transmission spectrum exhibit a large transmission gap of 0.5 eV
Fig. 3. (a) and (b) Calculated spin-filtering efficiency (SFE), differential conductance (dI/ dV) as a function of bias for the P MC. (c) Calculated magnetoresistance ratio (MR) as a function of bias.
in the P MC increases rapidly at first, and then begins to drop quickly when the bias exceeds 0.08 V, indicating a low-bias NDR occurs at 0.08 V. This observed low-bias NDR behavior can be further validated by the variation of differential conductance (dI/dV) vs. Vb. As shown in Fig. 3(b), the dI/dV is negative between 0.08 and 0.2 V. Moreover, since the Iup is almost quenched to zero after 0.18 V, a giant current peak-to-valley ratio (PVR ¼ (Ipeak/Ivalley) 100%, where Ipeak/Ivalley is the peak/valley currents of Iup, respectively) up to 2.34 106% is obtained. Although NDR behaviors have been realized in many nanoscale systems, they typically take place at relatively high biases and their PVRs are very small [24–28]. Thus, the giant low-bias NDR in the (2 1) reconstructed 6-ZMoS2NR device is desirable from the point view of power consumption [29–33]. (3) GMR effect. As shown in Fig. 2, both the Iup and Idn in the AP MC are completely blocked in the whole bias range. As a result, the total current (sum of Iup and Idn) in the P MC (IP) is much larger than that in the AP MC (IAP). Then one can expect a GMR effect when the spin magnetization of
Fig. 4. (a) and (b) Calculated spin-up, spin-down transmission spectra as a function of the electron energy E and bias Vb for the P MC. (c) and (d) Calculated spin-up, spin-down transmission spectra as a function of the electron energy E and bias Vb for the AP MC. The energy origin is the Fermi level EF. The two red dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. 11
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Fig. 5. Calculated spin-resolved band structures of left electrode (left panel) and right electrode (right panel), and the spin-resolved transmission spectra (middle panel) at different biases. (a), (b) and (c) correspond to the case of P MC at 0, 0.08 and 0.2 V, respectively. (d) Corresponds to the case of AP MC at zero bias, respectively. The energy origin is the Fermi level EF. The two blue dotted lines indicate the electrochemical potential of two electrodes, and thus the region between them is the bias window. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
around the EF (Fig. 4(c) and (d)), which is also extended as the bias increases. Since there is no any transmission within the bias window, both the Iup and Idn cannot pass through the device in the AP MC. Then the high-performance GMR effect can be obtained when the P and AP MCs transform each other. To further clarify the different transmission phenomena, we analyze the spin-resolved band structures of two electrodes at different biases. Fig. 5 (a), (b) and (c) correspond to the case of P MC at 0, 0.08 (Ipeak), and 0.2 V (Ivalley), respectively, and Fig. 5(d) corresponds to the case of AP MC at 0 V. The two blue dotted lines indicate the electrochemical potential of two electrodes. As shown in Fig. 5(a), for the P MC, the bands in LE (left panel) have the same structures as those in RE (right panel) at 0 V. There is a spin-down band I just above the EF, while there is a spin-up band II in the energy range from 0.26 to 0.24 eV. Fig. 6 (a) and (b) plot the Bloch wave function for bands I and II at the Γ point, respectively. As one can see, the spin-down band I is mainly dominated by dxy orbitals of the subedge Mo atoms and 3p orbital of the outmost S atoms at the bottom edge, while the spin-up band II is mainly formed by d2y orbitals of the sub-edge Mo atoms at the top edge. As shown in Fig. 5(a), at zero bias, the perfect matching between spin-up band II in LE and that in RE gives rise to the strong spin-up TB around the EF (middle panel). As the bias increases, the bands in LE shift downwards, while those in RE shift upwards. As shown in Fig. 5(b), at 0.08 V, the overlapping between spin-up band II in LE and that in RE is reduced significantly compared to that at zero bias due to the shift in the opposite direction of bands in two electrodes. When the bias exceed 0.18 V, the overlapping between spin-up band II in LE and that in RE is completely quenched to zero (Fig. 5(c)). In this process, the width and height of the spin-up TB around the EF decrease all the way down to zero as the bias increases (>0.18 V). As a result, the Iup in the P MC increases at first and then decrease as the bias increases, and the NDR effect
Fig. 6. (a) and (b) Calculated Bloch wave function for spin-down band I and spin-up II at the Γ point, respectively. The isosurface level is taken as 0.2/(Å3⋅eV).
occurs. Meantime, as shown in Fig. 5(b) and (c), there is no any overlapping of spin-down band I between two electrodes at finite bias, and thus the Idn in the P MC cannot flow through the device. Therefore, a near 100% spin-filtering is realized in the P MC. As shown in Fig. 5(d), for the AP MC, the spin-up and spin-down band structures in RE are exchanged compared to those in LE. In the energy region [0.015 eV, 0.035 eV], the spin-down band I (spin-up band II) in LE overlaps with the spin-down band II (spin-up band I) in RE. However, this overlapping can not contribute any spin-down and spin-up transmission. This point can be 12
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around the EF nearly remain unchanged, which guarantees the robustness of three spin-dependent effects. 4. Summary In summary, we have investigated the spin-polarized transport properties of the (2 1) reconstructed ZMoS2NR-based devices by using the first-principles DFT þ NEGF method. Our results show that these devices can exhibit multiple high-performance spin-dependent transport properties, including spin-filtering, NDR and GMR effects, by tuning the applied magnetic field on two electrodes. All three effects can be attributed to the matching and mismatching of spin bands around the Fermi level, as well as their symmetries. Moreover, all three effects are robust regardless of the nanoribbon width. These findings suggest the (2 1) reconstructed ZMoS2NRs are potential candidates for developing the high-performance multifunctional spintronic devices. Fig. 7. (a) and (b) Calculated bias-dependent spin-filtering efficiency (SFE), differential conductance (dI/dV) of the (2 1) reconstructed ZMoS2NR-based devices with nanoribbon width W ¼ 6, 7 and 8 for the P MC, respectively. (c) Calculated bias-dependent magnetoresistance ratio (MR) of the (2 1) reconstructed ZMoS2NR-based devices with width W ¼ 6, 7 and 8.
Acknowledgements This work is supported by the Natural Science Foundation of Shandong Province of China (No. ZR2016AM11).
understood by the symmetry of two bands. As shown in Fig. 6 (a) and (b), the symmetry of two bands is completely opposite, namely, the bands I and II have odd and even parities under the xz midplane mirror operation, respectively, leading to the transmission be forbidden from LE to RE [37,38], and the blocking of Iup and Idn in the AP MC. As a result, the GMR effect can be obtained when the spin magnetization of two electrodes switches between P and AP MCs. At last, we study the effects of nanoribbon width on these spindependent transport properties. As shown in Fig. 7(a)-(c), we plot the SFE, dI/dV and MR as a function of the applied bias Vb for the (2 1) reconstructed ZMoS2NR-based devices with width W ¼ 6,7 and 8, respectively. As one can see, all the SFEs are near 100% when the bias is less than 0.18 V (Fig. 7(a)), the dI/dVs are negative between 0.08 and 0.2 V (Fig. 7(b)), and the MRs are greater than 105 before 0.18 V (Fig. 7(c)). This means the spin-filtering, NDR and GMR effects in the (2 1) reconstructed ZMoS2NR-based devices are robust regardless of the nanoribbon width W. As discussed above, all three effects are originated from the matching and mismatching of spin bands I/II around the EF. As shown in Fig. 8, when the width is changed, the spin bands I/II
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Fig. 8. (a), (b) and (c) Calculated spin-resolved band structures of the (2 1) reconstructed ZMoS2NRs with nanoribbon width W ¼ 6, 7 and 8 in the AFM ground state, respectively. The black solid line and red dashed line denote the spin-up and spin-down, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 13
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