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Giant magnetoresistance in zigzag MoS2 nanoribbons Li Peng,ab Kailun Yao,*a Ruqian Wu,c Shuling Wang,a Sicong Zhu,a Yun Ni,a Fengxia Zu,a Zuli Liua and Bin Guob Using first principles calculations based on density functional theory, we investigated the transport properties of zigzag MoS2 nanoribbons with parallel and antiparallel spin configurations. The results show that the parallel configuration has conventional metallic properties while the antiparallel configuration presents semiconductor properties. Consequently, the conduction calculations predict that the zigzag MoS2 nanoribbons exhibit the giant magnetoresistance effect with a value over four orders of magnitude at room
Received 26th October 2014, Accepted 6th March 2015
temperature by altering the configuration from the parallel to the antiparallel spin junction. By analyzing the
DOI: 10.1039/c4cp04892j
Fermi level between spin up and spin down is a key factor to generate this large magnetoresistance. Our
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results indicate that the giant magnetoresistance effect in the zigzag MoS2 nanoribbons remains robust to the change in the ribbon widths and lengths.
spin-resolved band structures of zigzag MoS2 nanoribbons, we clarify that the orbital mismatching near the
Introduction Many excellent electronic, magnetic and optical properties of low-dimensional molybdenum disulfide (MoS2) have triggered extensive studies in recent years for the development of nextgeneration nanoelectronic and optoelectronic components, such as logic circuits, nonvolatile memory cells, small-signal amplifiers, and phototransistors.1–15 Unlike single-atom-thick graphene, monolayer MoS2 has a sandwich structure with two hexagonal layers of S atoms outside and a hexagonal layer of Mo atoms in the middle. The strong intralayer ionic–covalent forces between the S and Mo atoms and the weak interlayer van der Waals forces make it feasible to fabricate high quality monolayer MoS2 using the exfoliation method.16–20 MoS2 nanoribbons with either armchair or zigzag edges (AMoS2NRs or ZMoS2NRs) can be constructed by cutting the MoS2 monolayer. Theoretical calculations show that the structural, electronic and magnetic properties of MoS2 nanoribbons strongly depend on the edge structures.21–24 AMoS2NRs are typically nonmagnetic semiconductors and their band gaps oscillate with the increase of the nanoribbon width and gradually converge to a constant value of 0.56 eV.21 Fully hydrogenated AMoS2NRs also retain the semiconducting feature with larger band gaps than the pristine naroribbons.23,24 Interestingly, Ouyang et al. demonstrated that
a
School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China b School of Science, Wuhan University of Technology, Wuhan 430063, China c Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA. E-mail: [email protected]
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AMoS2NRs may display antiferromagnetic or ferromagnetic semiconducting properties with partially hydrogenated edges.25 By contrast, ZMoS2NRs are ferromagnetic with sizeable magnetic moments on edge atoms, as predicted by theory22–24,26 and also confirmed by experiment.27,28 The magnetic moments and the spin density of the ZMoS2NRs can be controlled by the degree of edge-hydrogenation.23,24 Manipulations of magnetic and electronic properties of AMoS2NRs and ZMoS2NRs by using other external factors such as strains and electric fields have also been reported.25,29,30 For the applications in nanodevices, it is important to further explore the transport properties of MoS2 nanoribbons under a finite bias, which has not been done thus far. In this work we explore bias-transport properties of ZMoS2NRs based on first principles calculations. Two different magnetic configurations are studied. One is the ZMoS2NRs with a parallel (P) spin junction, the other has an antiparallel (AP) spin junction. Our results show that the P spin configuration exhibits a metallic feature with a nearly linear I–V curve, while the AP spin configuration has a large resistance in a wide range of bias. The difference between the resistances of these two magnetic states is over four orders of magnitude, exhibiting the giant magnetoresistance (GMR) effect at room temperature. Although the GMR effect in zigzag graphene nanoribbons has also been predicted,31–33 it was demonstrated that the GMR effect may not exist in graphene nanoribbons with odd N (N denotes the number of zigzag lines across the ribbon width).31–34 Here, we show that the GMR effect in ZMoS2NRs is robust to the change in widths and thus it is much easier to design MoS2-based spintronic devices than graphene.
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Models and methods We use N-ZMoS2NR to denote a zigzag MoS2 ribbon with width N. Experimentally, single layer ZMoS2NRs with uniform widths down to 1 nm (N = 4) have been synthesized in carbon nanotubes in which their diameters determine the widths of the ZMoS2NRs.35 Fig. 1 shows the schematic configuration of the device based on the 5-ZMoS2NR, the two edges are terminated with Mo and S atoms, respectively. In our calculations, we focused on bare ZMoS2NRs without hydrogen (H) passivation. Although H-passivated ZMoS2NRs are more stable,36 bare ZMoS2NRs may also be obtained by heating treatments.37 Moreover, H-passivated ZMoS2NRs may lose above-mentioned interesting properties according to our calculations. To investigate transport properties, the ZMoS2NR is designed to be a two-probe device including a left electrode, a central scattering region (the device region) and a right electrode. Each electrode is a semi-infinite ZMoS2NR consisting of periodically repeated electrode supercells along the transport direction. Due to the periodic boundary conditions in the X and Y directions (defined in Fig. 1), the electrode supercells are sufficiently large in these directions to ensure the vacuum layers between two ZMoS2NRs to be 20 Å. Another integral parameter L, which denotes the number of unit cells in the scattering region, is used to describe the length of the ZMoS2NR. The calculations of the electronic transport properties of the two-probe systems are performed using the Atomistix Toolkit software package, which is based on the non-equilibrium Green’s function method combined with the density functional theory.38,39 The self-consistent calculations are controlled by the total energy tolerance of 105 Ry. The core electrons are described by norm-conserving pseudopotentials and the generalized gradient approximation (GGA) in the form of Perdew–Burke–Ernzerhof (PBE)40 is used as the exchange–correlation function. A double-zeta with polarization (DZP) basis set is adopted for electron wave function. In order to balance the computational time and accuracy, a mesh-cut off energy of 150 Ry and a Monkhorst–Pack k-point grid of 1 1 100 are
Fig. 1 Schematic of the 5-ZMoS2NR model device: blue and yellow balls stand for Mo and S atoms, respectively. The width and length of the ZMoS2NR are denoted by integers N and L, respectively. The left and right electrodes are described by the electrode supercells with three periodically repeated ZMoS2NR unit cells, which are denoted by the light blue shade. } and # denote the directions of the local magnetic field.
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chosen for the calculations. The electronic temperature is set to 300 K. Geometry optimizations are carried out for the ZMoS2NR unit cells using the quasi-Newton method until the absolute values of atomic forces converge to 0.03 eV Å1. The k-points of 1 1 100 are proved to be sufficient to optimize geometry and calculate band structures of the unit cells. The spin-resolved currents are calculated from the Landauer formula,41 ð e 1 Is ðVb Þ ¼ Ts ðE; Vb Þ½ fL ðE; Vb Þ fR ðE; Vb ÞdE; (1) h þ1 where s = a, b (a and b: spin up and spin-down, respectively), Ts(E,Vb) is the spin-transmission coefficient for electrons with energy E under bias voltage Vb, fL/R(E,Vb) is the equilibrium Fermi distribution for the left/right electrode. Effectively, the difference of fL(E,Vb) and fR(E,Vb) is well-defined in an energy window corresponding to the applied bias around the average Fermi level. Not only GGA23,24,29,42 but also local density approximation (LDA)30,43–45 has always been used to predict the properties of low-dimensional MoS2. We also calculate the electronic structures and transport properties of the ZMoS2NR by LDA. The results show that the transport spectra of the AP and P configurations at zero bias obtained by LDA are very similar to those obtained by GGA, with a 0.17 eV narrower zero transmission gap (ZTG) in the AP configuration. It is well known that the use of LDA and GGA leads to essential underestimate of the band gap for semiconductors, which results in the underestimate of the ZTG in the AP configuration. So we show only the results corresponding to GGA, which give the lower estimation error.
Results and discussion We first present the numerical results of the 5-ZMoS2NR with L = 6. Energies of the 5-ZMoS2NR unit cell at antiferromagnetic (AFM), ferromagnetic (FM) and nonmagnetic states are calculated. The energy differences are DE1 = EAFM EFM = 1.06 meV and DE2 = EAFM ENM = 141.0 meV. These differences imply that the AFM state is the ground state of 5-ZMoS2NR. The large value of DE2 indicates that the NM state of the nanoribbon is rather unstable. The small value of DE1 resulting from the weak spin coupling between the two edges reveals that the AFM and FM states of the 5-ZMoS2NR can transform easily each other.25,36 In our calculations, the two different magnetic configurations, AP and P spin junctions, of the ZMoS2NRs are operated by converging from different initial spin-polarization. Fig. 2(a) and (b) show the self-consistently determined spin densities at zero bias for the AP and P configurations of the 5-ZMoS2NR, respectively. Considerable magnetic moments originate from the edge Mo atoms and edge S atoms, which agree well with previous study.35 The AP configuration consists of AFM coupling between the zigzag edges and antiparallel spin junction at the central scattering region. The P configuration shows the AFM state in the whole system. Although, the energy difference between the two configurations is EAP EP = 1.489 eV, indicating that the P configuration is more energetically favored to the AP configuration, the coupling of the two configurations
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Fig. 2 The isosurfaces of spin density (rr = ra rb) for the 5-ZMoS2NR device with the AP (a) and P (b) spin configurations, where the red and blue colours stand for positive and negative signs. The rectangles indicate the left and right electrodes.
can be controlled by changing the directions of local magnetic fields as shown in Fig. 1.33 In Fig. 3, the bias-dependent transmission spectra of the P and AP configurations of 5-ZMoS2NR are shown. In the P case, both the a and b transmission spectra exhibit perfect transmission channels around the Fermi level (EF). The P-a transmission curves fluctuate near the coefficient value of 2. The maximum peak around EF corresponds to the equilibrium conductance of 5G0. With the increase of the bias, the width and height of the transmission peak gradually decrease. For the P-b transmission, the spectra display wide transmission plateaus with corresponding conductance value of G0. However, in the AP case, the degenerated spectra of the two spins at zero bias display large ZTG of 0.39 eV around EF. As the bias increases, the ZTG of the a spin is extended, but the ZTG of the b spin is narrowed. These behaviors that the perfect transmission channels in the P configuration and the wide ZTG in the AP configuration around EF indicate the GMR effect in the ZMoS2NRs. We find the ZTG of the AP configuration and the GMR effect in the ZMoS2NR can be understood by examining the band
Fig. 3 Transmission spectra of the 5-ZMoS2NR with the parallel (P) and antiparallel (AP) spin configurations at various bias voltages. The a and b denote spin-up and spin-down, respectively.
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structures of the left and right electrodes of the device. In Fig. 4, we show the spin-polarized band structures of the 5-ZMoS2NR, which are calculated from the unit cell of 5-ZMoS2NR with AFM coupling between the edges. Some bands crossing the EF indicate the metallic nature of the 5-ZMoS2NR, which coincides with previous studies.21,22 The electronic orbitals at the G and X points of the bands near the EF are plotted in the panels beside the band structures for further understanding the mechanism of the transmission. In the P configuration, the bands of the two electrodes have the identical structures at zero bias, and these constructive matchings open up perfect transmission channels. In the a spin three bands labeled B, C and D cross the EF (especially, the B band crosses the EF twice), and in the b spin only the F band crosses the EF. Such a system is exactly corresponding to the high ballistic conductance 4G0 at EF for the a spin (see P-a in Fig. 3) and conductance G0 for the b spin (see P-b in Fig. 3) in the P configuration at zero bias. Electronic orbitals show that the edge and sub-edge Mo-4d and S-3p orbitals contribute for the a spin conductance channels (see (b–d) in Fig. 4) and the orbital hybridized by Mo-4d and S-3p provides the b spin electron a conductance channel (see (f) in Fig. 4). In the AP configuration, the band structures of the a spin and b spin are exchanged for the two electrodes. Since the ground state of the AP configuration is spin degenerated, here we only discuss the a spin transmission. To improve clarity, the transmission spectrum of the AP configuration at zero bias is also arranged and shown in Fig. 4. As can be seen from the electronic orbital in the panels, in the b-spin, band F originates from the s* antibonding orbital that comes from the hybridization of Mo-dz2 and S-px distributed throughout the nanoribbon. But with the distribution extending to the middle of the ribbon, the electronic orbital gradually reduces. While in the a-spin the electron distributions of the three bands (B, C and D) near the EF are entirely different from that of band F. Both the bands B and C are formed by 4d orbitals of the Mo atoms in the edge and sub-edge of the nanoribbon. Clearly, band B is dominated by Mo-dxy, whereas band C is mainly dominated by dy2 of the edge Mo and dx2 of the sub-edge Mo. As for band D, it is formed by the nearly pure S-p orbitals located at the S-dominated edge. The orbital mismatching near the EF between the a and b spins
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Fig. 4 Band structures of the a spin (left panel) and the b spin (right panel) of the 5-ZMoS2NR in the AFM state, accompanied by the a spin transmission spectrum of the AP configuration of the 5-ZMoS2NR at zero bias. The blue shade denotes the energy range of the orbital mismatching between the a and b spins. The energy bands crossing the Fermi level are identified with red lines. The electronic orbitals (wavefunctions) of the labeled energy bands calculated for the G or X points are shown in the panels beside the band structures. The different colors in the orbitals mean positive and negative values of wavefunctions.
lead to the transmission be forbidden from the left to right electrodes and form the ZTG in the AP configuration. We notice that transmission plateaus near 1G0 appear on both sides of the ZTG as shown in Fig. 4. By comparing the electronic orbitals, the transmission plateau below the ZTG originates from the orbital matching between bands A and F, which have practically the same electronic distribution in the Mo-dominated edge of the ribbon. The matching orbitals provide electrons with a single conductance channel from left to right electrodes. Similarly, the spin-splitting bands E of the a and b spins account for the transmission channel of 1G0 above the ZTG. It can be seen that the ZTG is well consistent with the energy range of the orbital mismatching between a and b spins as denoted by the blue shade, which confirms the above conclusions. Fig. 5(a) shows the I–V relationship for the P and AP configurations of the 5-ZMoS2NR. The currents are the sum of the a and b currents, which are calculated from eqn (1). In the P configuration, the current increases quickly and shows
metallic behavior due to the wide transmission channels around EF. We notice that the P current increases with a slight decreasing growth ratio, that is because the transmission peak value of the a spin around EF gradually reduces with the increasing bias as shown in Fig. 3. In contrast, the current in the AP configuration is blocked, corresponding to the suppressed transmission near the EF in the AP transmission spectra. The GMR efficiency is characterized by the definition of magnetoresistance MR = (RAP RP)/RP, where RP and RAP are the resistances obtained from the I–V curves of the P and AP configurations, respectively.32,33 In Fig. 5(b), we plot the MR as a function of bias for the ZMoS2NRs with different widths N at 300 K. Strikingly, the MR of the 5-ZMoS2NRs at the small bias of 0.02 V has an ultrahigh value of 9 104%. The MR curve decreases with the increasing bias, which mainly arises from the increasing growth of the leakage current in the AP configuration as shown in the inset of Fig. 5(a). With the width change, the varying tendencies of the MR with respect to bias are similar. Especially, different from the GMR effect in graphene-based
Fig. 5 (a) I–V curves of the P configuration and the AP configuration of the 5-ZMoS2NR. The upper inset shows the zoom-in leakage current in the AP configuration. (b) MR values as a function of bias for different N-ZMoS2NRs.
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5-ZMoS2NRs and the value of the MR increases with the increase of the ribbon length. Our results indicate that the longer AP configurations with larger resistances account for the MR increase. Obviously, the longer the scattering region is, the more difficult the leakage current flows through the device and the larger resistance of the AP configuration is.
Conclusions
Fig. 6 Band structures of the a spin (left panel) and the b spin (right panel) of the 18-ZMoS2NR in the AFM state. The energy ranges of the orbital mismatching between the a and b spins are denoted by blue shades.
devices,32,33 the GMR effect in the ZMoS2NR remains robust regardless of the parity of the width N. As discussed above, this behavior originates from the transmission derived only from the spin orbitals matching near the EF, and that all these spin orbitals are edge states, which are independent of the width of the nanoribbon. So when the width changes, these spin orbitals maintain their characters and continue to determine the transmission behavior of the ZMoS2NR. In order to further prove the conclusion, the spin-polarized band structures of the ZMoS2NRs with N = 18 are also calculated as shown in Fig. 6. Comparisons show that the bands of the 18-ZMoS2NRs have almost the same structures near the EF as that of the 5-ZMoS2NR. The increase of the width changes the band structure below 0.3 eV, which has no effect on the overlap energy range of the spin orbital mismatching in the 18-ZMoS2NR, shown by the blue shade in Fig. 6. Thus the GMR effect is still expectable in the 18-ZMoS2NR. The effect of ZMoS2NR length on the GMR is also investigated. We compute the currents of the P and AP configurations of the 5-ZMoS2NR with L = 8 and 10 and then calculate resistances and the MR. As shown in Fig. 7, the GMR effect keeps in the longer
Fig. 7 MR values as a function of bias for the 5-ZMoS2NR with different lengths.
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In conclusion, we investigate the transport properties of the P and AP configurations of the ultranarrow ZMoS2NRs. In the AP configuration, a ZTG is open near the EF, and the ZMoS2NRs show semiconductor properties. But in the P configuration, transmission channels are widely open and the ZMoS2NRs show metallic nature. The conduction properties predict that the ZMoS2NRs exhibit the GMR effect with a value over four orders of magnitude at room temperature by altering the configuration from parallel to antiparallel spin junction. These remarkable values are attributed to the spin splits near the Fermi level in the ZMoS2NR, which lead to the spin orbital mismatching between the two electrodes in the AP configuration. Moreover, the GMR effect in the ZMoS2NRs remains robust to the change of the ribbon width and length. These results may open up a new way to explore spintronics based on MoS2 nanoribbons.
Acknowledgements The authors would like to acknowledge the support from the National Natural Science Foundation of China under Grant No. 11274130, 11274127 and 11205119.
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Giant magnetoresistance in zigzag MoS2 nanoribbons Li Peng,ab Kailun Yao,*a Ruqian Wu,c Shuling Wang,a Sicong Zhu,a Yun Ni,a Fengxia Zu,a Zuli Liua and Bin Guob Using first principles calculations based on density functional theory, we investigated the transport properties of zigzag MoS2 nanoribbons with parallel and antiparallel spin configurations. The results show that the parallel configuration has conventional metallic properties while the antiparallel configuration presents semiconductor properties. Consequently, the conduction calculations predict that the zigzag MoS2 nanoribbons exhibit the giant magnetoresistance effect with a value over four orders of magnitude at room
Received 26th October 2014, Accepted 6th March 2015
temperature by altering the configuration from the parallel to the antiparallel spin junction. By analyzing the
DOI: 10.1039/c4cp04892j
Fermi level between spin up and spin down is a key factor to generate this large magnetoresistance. Our
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results indicate that the giant magnetoresistance effect in the zigzag MoS2 nanoribbons remains robust to the change in the ribbon widths and lengths.
spin-resolved band structures of zigzag MoS2 nanoribbons, we clarify that the orbital mismatching near the
Introduction Many excellent electronic, magnetic and optical properties of low-dimensional molybdenum disulfide (MoS2) have triggered extensive studies in recent years for the development of nextgeneration nanoelectronic and optoelectronic components, such as logic circuits, nonvolatile memory cells, small-signal amplifiers, and phototransistors.1–15 Unlike single-atom-thick graphene, monolayer MoS2 has a sandwich structure with two hexagonal layers of S atoms outside and a hexagonal layer of Mo atoms in the middle. The strong intralayer ionic–covalent forces between the S and Mo atoms and the weak interlayer van der Waals forces make it feasible to fabricate high quality monolayer MoS2 using the exfoliation method.16–20 MoS2 nanoribbons with either armchair or zigzag edges (AMoS2NRs or ZMoS2NRs) can be constructed by cutting the MoS2 monolayer. Theoretical calculations show that the structural, electronic and magnetic properties of MoS2 nanoribbons strongly depend on the edge structures.21–24 AMoS2NRs are typically nonmagnetic semiconductors and their band gaps oscillate with the increase of the nanoribbon width and gradually converge to a constant value of 0.56 eV.21 Fully hydrogenated AMoS2NRs also retain the semiconducting feature with larger band gaps than the pristine naroribbons.23,24 Interestingly, Ouyang et al. demonstrated that
a
School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China b School of Science, Wuhan University of Technology, Wuhan 430063, China c Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA. E-mail: [email protected]
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AMoS2NRs may display antiferromagnetic or ferromagnetic semiconducting properties with partially hydrogenated edges.25 By contrast, ZMoS2NRs are ferromagnetic with sizeable magnetic moments on edge atoms, as predicted by theory22–24,26 and also confirmed by experiment.27,28 The magnetic moments and the spin density of the ZMoS2NRs can be controlled by the degree of edge-hydrogenation.23,24 Manipulations of magnetic and electronic properties of AMoS2NRs and ZMoS2NRs by using other external factors such as strains and electric fields have also been reported.25,29,30 For the applications in nanodevices, it is important to further explore the transport properties of MoS2 nanoribbons under a finite bias, which has not been done thus far. In this work we explore bias-transport properties of ZMoS2NRs based on first principles calculations. Two different magnetic configurations are studied. One is the ZMoS2NRs with a parallel (P) spin junction, the other has an antiparallel (AP) spin junction. Our results show that the P spin configuration exhibits a metallic feature with a nearly linear I–V curve, while the AP spin configuration has a large resistance in a wide range of bias. The difference between the resistances of these two magnetic states is over four orders of magnitude, exhibiting the giant magnetoresistance (GMR) effect at room temperature. Although the GMR effect in zigzag graphene nanoribbons has also been predicted,31–33 it was demonstrated that the GMR effect may not exist in graphene nanoribbons with odd N (N denotes the number of zigzag lines across the ribbon width).31–34 Here, we show that the GMR effect in ZMoS2NRs is robust to the change in widths and thus it is much easier to design MoS2-based spintronic devices than graphene.
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Models and methods We use N-ZMoS2NR to denote a zigzag MoS2 ribbon with width N. Experimentally, single layer ZMoS2NRs with uniform widths down to 1 nm (N = 4) have been synthesized in carbon nanotubes in which their diameters determine the widths of the ZMoS2NRs.35 Fig. 1 shows the schematic configuration of the device based on the 5-ZMoS2NR, the two edges are terminated with Mo and S atoms, respectively. In our calculations, we focused on bare ZMoS2NRs without hydrogen (H) passivation. Although H-passivated ZMoS2NRs are more stable,36 bare ZMoS2NRs may also be obtained by heating treatments.37 Moreover, H-passivated ZMoS2NRs may lose above-mentioned interesting properties according to our calculations. To investigate transport properties, the ZMoS2NR is designed to be a two-probe device including a left electrode, a central scattering region (the device region) and a right electrode. Each electrode is a semi-infinite ZMoS2NR consisting of periodically repeated electrode supercells along the transport direction. Due to the periodic boundary conditions in the X and Y directions (defined in Fig. 1), the electrode supercells are sufficiently large in these directions to ensure the vacuum layers between two ZMoS2NRs to be 20 Å. Another integral parameter L, which denotes the number of unit cells in the scattering region, is used to describe the length of the ZMoS2NR. The calculations of the electronic transport properties of the two-probe systems are performed using the Atomistix Toolkit software package, which is based on the non-equilibrium Green’s function method combined with the density functional theory.38,39 The self-consistent calculations are controlled by the total energy tolerance of 105 Ry. The core electrons are described by norm-conserving pseudopotentials and the generalized gradient approximation (GGA) in the form of Perdew–Burke–Ernzerhof (PBE)40 is used as the exchange–correlation function. A double-zeta with polarization (DZP) basis set is adopted for electron wave function. In order to balance the computational time and accuracy, a mesh-cut off energy of 150 Ry and a Monkhorst–Pack k-point grid of 1 1 100 are
Fig. 1 Schematic of the 5-ZMoS2NR model device: blue and yellow balls stand for Mo and S atoms, respectively. The width and length of the ZMoS2NR are denoted by integers N and L, respectively. The left and right electrodes are described by the electrode supercells with three periodically repeated ZMoS2NR unit cells, which are denoted by the light blue shade. } and # denote the directions of the local magnetic field.
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chosen for the calculations. The electronic temperature is set to 300 K. Geometry optimizations are carried out for the ZMoS2NR unit cells using the quasi-Newton method until the absolute values of atomic forces converge to 0.03 eV Å1. The k-points of 1 1 100 are proved to be sufficient to optimize geometry and calculate band structures of the unit cells. The spin-resolved currents are calculated from the Landauer formula,41 ð e 1 Is ðVb Þ ¼ Ts ðE; Vb Þ½ fL ðE; Vb Þ fR ðE; Vb ÞdE; (1) h þ1 where s = a, b (a and b: spin up and spin-down, respectively), Ts(E,Vb) is the spin-transmission coefficient for electrons with energy E under bias voltage Vb, fL/R(E,Vb) is the equilibrium Fermi distribution for the left/right electrode. Effectively, the difference of fL(E,Vb) and fR(E,Vb) is well-defined in an energy window corresponding to the applied bias around the average Fermi level. Not only GGA23,24,29,42 but also local density approximation (LDA)30,43–45 has always been used to predict the properties of low-dimensional MoS2. We also calculate the electronic structures and transport properties of the ZMoS2NR by LDA. The results show that the transport spectra of the AP and P configurations at zero bias obtained by LDA are very similar to those obtained by GGA, with a 0.17 eV narrower zero transmission gap (ZTG) in the AP configuration. It is well known that the use of LDA and GGA leads to essential underestimate of the band gap for semiconductors, which results in the underestimate of the ZTG in the AP configuration. So we show only the results corresponding to GGA, which give the lower estimation error.
Results and discussion We first present the numerical results of the 5-ZMoS2NR with L = 6. Energies of the 5-ZMoS2NR unit cell at antiferromagnetic (AFM), ferromagnetic (FM) and nonmagnetic states are calculated. The energy differences are DE1 = EAFM EFM = 1.06 meV and DE2 = EAFM ENM = 141.0 meV. These differences imply that the AFM state is the ground state of 5-ZMoS2NR. The large value of DE2 indicates that the NM state of the nanoribbon is rather unstable. The small value of DE1 resulting from the weak spin coupling between the two edges reveals that the AFM and FM states of the 5-ZMoS2NR can transform easily each other.25,36 In our calculations, the two different magnetic configurations, AP and P spin junctions, of the ZMoS2NRs are operated by converging from different initial spin-polarization. Fig. 2(a) and (b) show the self-consistently determined spin densities at zero bias for the AP and P configurations of the 5-ZMoS2NR, respectively. Considerable magnetic moments originate from the edge Mo atoms and edge S atoms, which agree well with previous study.35 The AP configuration consists of AFM coupling between the zigzag edges and antiparallel spin junction at the central scattering region. The P configuration shows the AFM state in the whole system. Although, the energy difference between the two configurations is EAP EP = 1.489 eV, indicating that the P configuration is more energetically favored to the AP configuration, the coupling of the two configurations
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Fig. 2 The isosurfaces of spin density (rr = ra rb) for the 5-ZMoS2NR device with the AP (a) and P (b) spin configurations, where the red and blue colours stand for positive and negative signs. The rectangles indicate the left and right electrodes.
can be controlled by changing the directions of local magnetic fields as shown in Fig. 1.33 In Fig. 3, the bias-dependent transmission spectra of the P and AP configurations of 5-ZMoS2NR are shown. In the P case, both the a and b transmission spectra exhibit perfect transmission channels around the Fermi level (EF). The P-a transmission curves fluctuate near the coefficient value of 2. The maximum peak around EF corresponds to the equilibrium conductance of 5G0. With the increase of the bias, the width and height of the transmission peak gradually decrease. For the P-b transmission, the spectra display wide transmission plateaus with corresponding conductance value of G0. However, in the AP case, the degenerated spectra of the two spins at zero bias display large ZTG of 0.39 eV around EF. As the bias increases, the ZTG of the a spin is extended, but the ZTG of the b spin is narrowed. These behaviors that the perfect transmission channels in the P configuration and the wide ZTG in the AP configuration around EF indicate the GMR effect in the ZMoS2NRs. We find the ZTG of the AP configuration and the GMR effect in the ZMoS2NR can be understood by examining the band
Fig. 3 Transmission spectra of the 5-ZMoS2NR with the parallel (P) and antiparallel (AP) spin configurations at various bias voltages. The a and b denote spin-up and spin-down, respectively.
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structures of the left and right electrodes of the device. In Fig. 4, we show the spin-polarized band structures of the 5-ZMoS2NR, which are calculated from the unit cell of 5-ZMoS2NR with AFM coupling between the edges. Some bands crossing the EF indicate the metallic nature of the 5-ZMoS2NR, which coincides with previous studies.21,22 The electronic orbitals at the G and X points of the bands near the EF are plotted in the panels beside the band structures for further understanding the mechanism of the transmission. In the P configuration, the bands of the two electrodes have the identical structures at zero bias, and these constructive matchings open up perfect transmission channels. In the a spin three bands labeled B, C and D cross the EF (especially, the B band crosses the EF twice), and in the b spin only the F band crosses the EF. Such a system is exactly corresponding to the high ballistic conductance 4G0 at EF for the a spin (see P-a in Fig. 3) and conductance G0 for the b spin (see P-b in Fig. 3) in the P configuration at zero bias. Electronic orbitals show that the edge and sub-edge Mo-4d and S-3p orbitals contribute for the a spin conductance channels (see (b–d) in Fig. 4) and the orbital hybridized by Mo-4d and S-3p provides the b spin electron a conductance channel (see (f) in Fig. 4). In the AP configuration, the band structures of the a spin and b spin are exchanged for the two electrodes. Since the ground state of the AP configuration is spin degenerated, here we only discuss the a spin transmission. To improve clarity, the transmission spectrum of the AP configuration at zero bias is also arranged and shown in Fig. 4. As can be seen from the electronic orbital in the panels, in the b-spin, band F originates from the s* antibonding orbital that comes from the hybridization of Mo-dz2 and S-px distributed throughout the nanoribbon. But with the distribution extending to the middle of the ribbon, the electronic orbital gradually reduces. While in the a-spin the electron distributions of the three bands (B, C and D) near the EF are entirely different from that of band F. Both the bands B and C are formed by 4d orbitals of the Mo atoms in the edge and sub-edge of the nanoribbon. Clearly, band B is dominated by Mo-dxy, whereas band C is mainly dominated by dy2 of the edge Mo and dx2 of the sub-edge Mo. As for band D, it is formed by the nearly pure S-p orbitals located at the S-dominated edge. The orbital mismatching near the EF between the a and b spins
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Fig. 4 Band structures of the a spin (left panel) and the b spin (right panel) of the 5-ZMoS2NR in the AFM state, accompanied by the a spin transmission spectrum of the AP configuration of the 5-ZMoS2NR at zero bias. The blue shade denotes the energy range of the orbital mismatching between the a and b spins. The energy bands crossing the Fermi level are identified with red lines. The electronic orbitals (wavefunctions) of the labeled energy bands calculated for the G or X points are shown in the panels beside the band structures. The different colors in the orbitals mean positive and negative values of wavefunctions.
lead to the transmission be forbidden from the left to right electrodes and form the ZTG in the AP configuration. We notice that transmission plateaus near 1G0 appear on both sides of the ZTG as shown in Fig. 4. By comparing the electronic orbitals, the transmission plateau below the ZTG originates from the orbital matching between bands A and F, which have practically the same electronic distribution in the Mo-dominated edge of the ribbon. The matching orbitals provide electrons with a single conductance channel from left to right electrodes. Similarly, the spin-splitting bands E of the a and b spins account for the transmission channel of 1G0 above the ZTG. It can be seen that the ZTG is well consistent with the energy range of the orbital mismatching between a and b spins as denoted by the blue shade, which confirms the above conclusions. Fig. 5(a) shows the I–V relationship for the P and AP configurations of the 5-ZMoS2NR. The currents are the sum of the a and b currents, which are calculated from eqn (1). In the P configuration, the current increases quickly and shows
metallic behavior due to the wide transmission channels around EF. We notice that the P current increases with a slight decreasing growth ratio, that is because the transmission peak value of the a spin around EF gradually reduces with the increasing bias as shown in Fig. 3. In contrast, the current in the AP configuration is blocked, corresponding to the suppressed transmission near the EF in the AP transmission spectra. The GMR efficiency is characterized by the definition of magnetoresistance MR = (RAP RP)/RP, where RP and RAP are the resistances obtained from the I–V curves of the P and AP configurations, respectively.32,33 In Fig. 5(b), we plot the MR as a function of bias for the ZMoS2NRs with different widths N at 300 K. Strikingly, the MR of the 5-ZMoS2NRs at the small bias of 0.02 V has an ultrahigh value of 9 104%. The MR curve decreases with the increasing bias, which mainly arises from the increasing growth of the leakage current in the AP configuration as shown in the inset of Fig. 5(a). With the width change, the varying tendencies of the MR with respect to bias are similar. Especially, different from the GMR effect in graphene-based
Fig. 5 (a) I–V curves of the P configuration and the AP configuration of the 5-ZMoS2NR. The upper inset shows the zoom-in leakage current in the AP configuration. (b) MR values as a function of bias for different N-ZMoS2NRs.
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5-ZMoS2NRs and the value of the MR increases with the increase of the ribbon length. Our results indicate that the longer AP configurations with larger resistances account for the MR increase. Obviously, the longer the scattering region is, the more difficult the leakage current flows through the device and the larger resistance of the AP configuration is.
Conclusions
Fig. 6 Band structures of the a spin (left panel) and the b spin (right panel) of the 18-ZMoS2NR in the AFM state. The energy ranges of the orbital mismatching between the a and b spins are denoted by blue shades.
devices,32,33 the GMR effect in the ZMoS2NR remains robust regardless of the parity of the width N. As discussed above, this behavior originates from the transmission derived only from the spin orbitals matching near the EF, and that all these spin orbitals are edge states, which are independent of the width of the nanoribbon. So when the width changes, these spin orbitals maintain their characters and continue to determine the transmission behavior of the ZMoS2NR. In order to further prove the conclusion, the spin-polarized band structures of the ZMoS2NRs with N = 18 are also calculated as shown in Fig. 6. Comparisons show that the bands of the 18-ZMoS2NRs have almost the same structures near the EF as that of the 5-ZMoS2NR. The increase of the width changes the band structure below 0.3 eV, which has no effect on the overlap energy range of the spin orbital mismatching in the 18-ZMoS2NR, shown by the blue shade in Fig. 6. Thus the GMR effect is still expectable in the 18-ZMoS2NR. The effect of ZMoS2NR length on the GMR is also investigated. We compute the currents of the P and AP configurations of the 5-ZMoS2NR with L = 8 and 10 and then calculate resistances and the MR. As shown in Fig. 7, the GMR effect keeps in the longer
Fig. 7 MR values as a function of bias for the 5-ZMoS2NR with different lengths.
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In conclusion, we investigate the transport properties of the P and AP configurations of the ultranarrow ZMoS2NRs. In the AP configuration, a ZTG is open near the EF, and the ZMoS2NRs show semiconductor properties. But in the P configuration, transmission channels are widely open and the ZMoS2NRs show metallic nature. The conduction properties predict that the ZMoS2NRs exhibit the GMR effect with a value over four orders of magnitude at room temperature by altering the configuration from parallel to antiparallel spin junction. These remarkable values are attributed to the spin splits near the Fermi level in the ZMoS2NR, which lead to the spin orbital mismatching between the two electrodes in the AP configuration. Moreover, the GMR effect in the ZMoS2NRs remains robust to the change of the ribbon width and length. These results may open up a new way to explore spintronics based on MoS2 nanoribbons.
Acknowledgements The authors would like to acknowledge the support from the National Natural Science Foundation of China under Grant No. 11274130, 11274127 and 11205119.
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