Spin-Resolved Transport Properties of a Pyridine-Linked Single

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Spin-Resolved Transport Properties of a Pyridine-Linked Single Molecule Embedded Between ZGNR Electrodes Xiaobo Li, Liemao Cao, Hui-Li Li, Haiqing Wan, and Guanghui Zhou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10880 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016

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The Journal of Physical Chemistry

Spin-Resolved Transport Properties of a Pyridine-Linked Single Molecule Embedded between ZGNR Electrodes Xiaobo Li,1 Liemao Cao,1 Hui-Li Li,2 Haiqing Wan,3 and Guanghui Zhou1 1

Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications of Hunan, Hunan Normal University, Changsha 410081, China 2 School of Computer Science, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004, China and 3 Department of Science, Nanchang Teachers College, Nanchang 330029, China ABSTRACT: We study the spin-dependent electron transport through a junction consisting of a single pyridine-linked (PDL) molecule sandwiched between two zigzag-edged graphene nanoribbon (ZGNR) electrodes modulated by an external magnetic field, where a 4,4’-bipyridine, 4,4’-vinylenedipyridine and 4,4’ethylenedipyridine molecules are considered, respectively. By using ab initio calculations based on the densityfunctional theory combined with nonequilibrium Green’s function formalism, it is shown that the spin-charge transport can be modulated by performing different magnetic configuration in the ZGNR electrodes. Specifically, we demonstrate that the proposed PDL molecular junctions exhibit several interesting effects, including (dual) spin-filtering, rectifying, negative differential resistance (NDR) and magnetoresistance. For the junction consisting of a 4,4’-bipyridine molecule with proper magnetic configuration in the two ZGNRs, it is interesting to note that a perfect spin polarization with filtering efficiency up to 100% can be found, the maximum value of rectification ratio can reach up to 104 , and the peak to valley ratio of NDR reach up to 328, respectively. Furthermore, the magnetoresistance ratio for this junction can also go up to 106 %. Besides, the physical mechanisms for those phenomenons are revealed. The mechanisms are revealed and analyzed by the connection of these effects to the evolution of the frontier molecular orbital, the spin-resolved transmission spectrum associated with the local density of states around the Fermi level at zero bias, and the molecular projected self-consistent Hamiltonian. INTRODUCTION

Organic molecular junction is going to become a promising candidate for the future application of spintronics devices due to its unique property. Recently, relevant experimental1−5 and theoretical6−26 works have been frequently reported on this issue. It is known that many particular effects can be observed in molecular junction devices, such as electronic switching,1 Kondo effect,3 spin crossover,7 rectifying,6,10−14 dual spinfiltering,15−18 spin-valve,19,20 negative differential resistance (NDR),21−24 magnetoresistance effect,25,26 and so on. However, to accurately reveal the corresponding mechanisms of overall complexes is still a big challenge, and the interpretation is dependent on many factors, such as overall crystal structure, spin configuration, positions of the terminal atoms on metal electrode surfaces, distance between the electrodes, etc.6,15,24,26 Especially, it is fundamentally important to choose suitable organic ligands with certain features, such as flexibility, appropriate angles and versatile binding modes. Among the existing organic molecular candidates, the pyridine-linked (PDL) molecules have become the popular building block for molecular spintronic devices due to their interesting electrical properties and functions.28−33 In recent years, the pyridine molecules and similar molecules consisting of vinyl or ethyl between two phenyl rings have attracted enormous research attentions.12,13,23,27 Since Fujita et al.28 have early applied a 4,4’-bipyridine molecule in preparation of two-dimensional square network material, a lot of research works have been continuously reported on single PDL molecule junctions.29−33 For example, Kamenetska et al.32 have experimentally and theoretically studied the properties of PDL molecules bridged between two gold electrodes. Their result indicates that all PDL molecules exhibit the bistable

conductance signatures by elongating and compressing the gold point contacts in a solution of molecules. Very recently, Adak et al.33 have also observed the impact of electrode band structure on transport through the junction by measuring the conductance of a PDL molecule between Ag and Au electrodes, respectively. However, the transport properties depend on the positions of the molecular terminal atoms on metal electrode surfaces. In other words, the electronic coupling in metal-organic interfaces do not follow simple rules but are rather the consequence of subtle local interactions.33 As the electrode of a molecular junction, nevertheless, the planarstructured graphene may overcome this difficulty.10,13−22 It is known that carbon as an all-purpose chemical element has three possible hybridization states (sp, sp2 and sp3 ) of its atomic orbitals. Comparing with the structures of sp or sp3 states, the structure of sp2 state displays a series of unique molecular electronic or spintronic transport properties. Since graphene and graphene nanoribbon (GNR) were fabricated, as the electrodes in molecular electronic devices for spin injection34 and spin-resolved transport, they have been triggered a massive interest.13.22 Further, carbon atoms are fundamentally important for creating functional organic electronic devices, and they have been directly carved out experimentally from a graphene.35,36 Nevertheless, graphene materials show ferromagnetism (FM) due to the existence of various defects or topological structures,37,38 and the application of a transverse electrical field39 or a magnetic field40 can also make the FM state more stable. Other experiments have also demonstrated that the spin-polarized antiferromagnetic (AFM) state and FM state would become unstable with respect to the spin-unpolarized state at finite temperature41 or in the existence of a ballistic current through a GNR.42 Obviously, it is necessary to consider various magnetic configu-

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rations of zigzag GNRs (ZGNRs) in order to simulate the experimentally detectable transport behaviors at a suitable bias voltage. Even though there have been some previous studies on the spin-charge transport for molecular bridges linking ZGNRs,10,14,17,18,21,25,40 there still lack of studies on the transport properties for a PDL molecule between two ZGNR electrodes. Motivated by the recent successful fabrication and measurement of single organic molecule sandwiched between graphene electrodes,43 in the present work we investigate the spin-resolved charge transport properties for a two probe molecular junction, where a PDL type molecule is sandwiched between two ZGNRs.17,19 Using the approach of the fully self-consistent ab initio density-functional theory (DFT) combing with the nonequilibrium Green’s function (NEGF), our result firstly predicts that there exist spin-filtering effect in the proposed model devices with parallel (P) spin configuration, and dual spin-filtering effect with antiparallel (AP) spin configuration, respectively. The spin filtering efficiency (SFE) reaches up to 100%, and the corresponding mechanism is revealed by analyzing the evolution of the frontier molecular orbitals (FMOs) and spin-resolved transmission spectrum associated with local density of states (LDOS) around the Fermi level E F at zero bias. Secondly, our study also shows the reason of formation for rectifying behavior though the analysis of the molecular projected self-consistent Hamiltonian (MPSH) eigenvalues and the spin-dependent transmission with AP configuration under various corresponding negative and positive biases. For the junction consisting of a 4,4’-bipyridine molecule, interestingly, the rectification ratio (RR) and the NDR effect with peak to valley ratio (PVR) can reach up to 104 and 328, respectively. The discussion on RR and PVR is followed by analyzing the spin-dependent transmission associated with spin-resolved LDOS around E F for the junction under external bias. Moreover, the magnetoresistance ratio (MR) can reach up to 106 % for the junction consisting of a 4,4’-bipyridine molecule, and 104 % for the junctions consisting of other PDL molecules. The corresponding mechanism on the transmission spectrum is proposed for the phenomena. The results indicate that our two-dimensional organic molecular devices are promising candidates for the future application of graphene-based spintronic devices. This paper is organized as follows: In Sec. II, we give the device model description and the calculational method. In Sec. III, we present our results and the discussion on the corresponding mechanisms, and we finally point out our concluding remarks in Sec. IV.

MODEL AND METHOD

The proposed model device, as shown in Figure 1, is a junction consisting of a PDL molecular wire with a π − σ − π architecture sandwiched between two symmetric semiinfinite ZGNR electrodes, where 4,4’-bipyridine (BPD), 4,4’vinylenedipyridine (VPD) and 4,4’-ethylenedipyridine (EPD) molecular wires are considered, respectively. A number of work has demonstrated that dual spin-filtering effect can only

Figure 1: Schematic view of the three PDL spintronic model devices, where model devices M1 , M2 and M3 are BPD, VPD and EPD molecules between two ZGNR electrode leads, respectively. The shaded areas indicate the leads (with two repeated carbon unit cells along the transport z direction) which are modulated by an external magnetic field along the +y or -y direction, and the red/green arrow indicates the spin-up/down direction in the leads.

take place in ZGNRs with an even number of zigzag carbon chains.15 We have tested our model devices with 4- or 8-ZGNR, and the result reveals that the magnetic transport property is almost the same. So we adopt 4-ZGNR as the electrode here. The examined molecular junction can be divided into three parts: left lead, scattering region, and right lead. All edge carbon atoms are saturated with hydrogen atoms. More specifically, the molecule is directly tied up to ZGNR electrodes with a five-membered ring.19 This structure has a perfect atomic interface leading to small contact resistance. For convenience, the scattering region including BPD molecule in the top panel of Figure 1 is called device M1 , and those including VPD and EPD molecules in the middle and bottom panels of Figure 1 are called devices M2 and M3 , respectively. The transport direction is along the z axis, and the two leads of ZGNR electrodes are modulated by attaching ferromagnets or applying external magnetic field along the y axis, within which results in a magnetization ML/R in the left/right electrode. The difference in the electrostatic potentials between electrode yields to a bias voltage Vb = µL -µR which generates a current through the junction. Moreover, the spin orientation in the two electrodes controlled by magnetic field can be set to be parallel (P) or antiparallel (AP) configuration.21,25 There is only a small energy difference (about 5meV) between the two cases, which indicates that energy barrier does not exist in our molecular device according to the previous work.26 Neverthe-


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Figure 2: The calculated spin-resolved I-V curves for the model devices with different molecules and spin configurations in ZGNR leads, where (a/b) for BPD molecular model M1 , (c/d) for VPD molecular device M2 and (e/f) for EPD molecular device M3 with P/AP configuration, respectively. For clarity, the I↓AP for M1 under low bias (-1,-0.2V) is natively plotted in inset of 2(b), and the spin-resolved I-V curves under low bias (-1,1V) for M3 with P and AP configurations are plotted in insets of 2(e) and (f), respectively.

less, the magnetic exchange interactions in a ZGNR between the spin states at two edges favor AFM configurations. In the presence of a suitable magnetic modulation, but a ZGNR with FM edge states could be more stable.37 However, FM-ZGNRs are metallic and AFM ones are semiconducting.25 This evidence confirms the suitability of our model device under certain range of biases. The structure was optimized before calculation. Further, the geometric optimization of structures and the quantum transport calculations for the model junctions have been carried out by using the first-principles method based on the fully self-consistent ab initio density-functional theory (DFT) combing with the nonequilibrium Green’s function (NEGF).7,44 According to the optimization, the bond distance of the carbon and nitrogen atoms is about 1.43 Å, which is close to the length of a C-N single bond. Thus, it indicates that the covalent bond type of C-N is a σ-bond.20 The detailed process has been realized as follows. We use normconserving pseudopotentials and the local spin density approximation for exchange-correlation potential. The k-point sampling of 1×1×100 Monkhorst-Pack grid in Brillouin zone, the cutoff energy is 150 Ry, and the single-zeta polarized basis are used for all elements including carbon, hydrogen and nitrogen atoms.17,20 Further, the convergence criterion for Hamiltonian and the electron density are 10−5 eV in total energy. And at least 15 Å is used to avoid the spurious interaction between periodic images.45,46 Furthermore, the geometries are optimized until all residual forces on each atom are smaller than 0.05eVÅ−1 . The spin-dependent current is calculated by using the Landauer-Büttiker formula7,15,16,44 Z µR Iσ (V) = (e/h) T σ (E, V)[ fL (E − µL ) − fR (E − µR )]dE, µL

where σ =↑/↓ denotes the electron spin-up/down, fL/R (E) = 1/[1 + e(E−µL/R )/KB T ] is the Fermi-Dirac distribution function

in the left/right electrode, and µL/R (V) = µL/R ± eV/2 is the electrochemical potential in terms of the common Fermi energy (E F ) under external bias. Therefore, the spin-dependent transmission probability as a function of energy E and bias V is defined T σ (E, V) = Tr[ΓL (E, V)Gσ (E, V)ΓR (E, V)G†σ (E, V)], where Gσ (E, V) is the Green function of central scattering region with complex conjecture G†σ (E, V), and ΓL/R is coupling matrix of central region with the left/right electrode. RESULTS AND DISCUSSIONS

The calculated spin-resolved current-voltage (I-V) curves within bias voltage from -2 to 2 V for the proposed model devices M1 -M3 with P and AP spin configurations between ZGNR electrodes, respectively, are shown in Figure 2. For clarity, the (red)/(blue) full up/down-triangle solid/dashed line is severally for the current with up/down-spin and P configuration (I↑P /I↓P ), whereas the (orange)/(olive) empty up/downtriangle solid/dashed line for the current with up/down-spin and AP configuration (I↑AP /I↓AP ). Firstly, we can see that all the currents for model devices M1 and M2 shown in Figures 2(a)-2(d) are one order of magnitude larger than those for M3 [see Figures 2(e) and 2(f)]. However, as shown in the insets of Figures 2(e) and 2(f), device M3 still owns a similar I-V behavior to those for M1 and M2 under lower bias range (-1, 1 V). This is because that the py channel of carbonous PDL molecular chain overlaps with the delocalized big π-orbital of ZGNRs, which contributes to the charge transport. When the overlap of the carbonous BPD and VPD molecular py channel and the phenyl ring’s π-orbital reaches a maximum value for M1 and M2 , py channel is fully open and π-electrons can easily flow through the phenyl rings. While the overlap reaches



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Figure 3: The calculated spin filtering efficiency as a function of bias voltage (upper panels) for model devices (a) M1 , (b) M2 and (c) M3 with P and AP spin configurations, where the left and right insets show the eigenstate spatial distribution of LUMOs and the corresponding MPSH eigenvalues with P spin configuration at zero bias around E F , respectively. The spin-resolved rectification ratio as a function of bias (lower panels) for model devices (d) M1 , (e) M2 and (f) M3 with AP configuration.

a small value for M3 consisting of EPD molecular, py channel is localized and π-electrons can hardly flow through phenyl rings. Therefore, the current in our proposed device is negligibly small for M3 shown in Figures 2(e) and 2(f). Moreover, the recent research on the current-voltage measurements of these PDL junctions indicates that the coupling of PDL molecules between metal electrodes does not impact the the charge transport of the systems.33 But it is an essential influence on the coupling of a EPD molecule with nonplanar structure between planar ZGNR electrodes,13 which also results in a small current for device M3 . In the following, the definite additional distinct features obtained from Figure 2 are summarized. (1) As shown in Figures 2(a) and 2(c), the I↑P for devices M1 and M2 within bias (-2, 2 V) is comparatively large, while I↓P is almost zero. This difference in transport between spin-up and -down electrons displays an interesting spin-filtering effect.15 In contrast to P spin configuration, as shown in Figures 2(b) and 2(d), I↑AP /I↓AP for M1 and M2 under negative/positive bias is quite large, otherwise it is very small. This implies that the devices with AP configuration may be preformed as a dual spin filter or dual spin diode.16 The similar I-V behavior appears in M3 under lower bias range (-1, 1 V) [see the insets of Figures 2(e) and 2(f)]. (2) The I↑AP of devices M1 and M2 under negative bias are

obviously larger than that under positive bias, and vise versa for I↓AP [see Figures 2(b) and 2(d)], which may imply a perfect rectifying effect.17 The similar I-V behavior occurs for device M3 under lower bias range (-1, 1 V) [the inset of Figure 2(f)]. Meanwhile, the asymmetric degree in the shape of I − V curve for M1 /M2 as shown in Figure 2(b)/2(d) is more obvious than that for M3 [Figure 2(f)]. (3) Furthermore, within the bias voltage range all model devices exhibit visible asymmetric pulse-like semiconducting I − V behavior as shown in Figures 2(a)-2(f), in which each curve shows several peaks. Particularly, the I↓AP of M1 around bias -0.6 V [see the inset in Figure 2(b)] is much larger than that around -0.7 V, which yields an obvious NDR effect with a PVR up to 328. Meanwhile, the I↓AP of M3 around bias -0.3 V [the inset in Figure 2(f)] is larger than that around -0.6 V, which also shows obvious NDR behavior. (4) Moreover, all the model devices exhibit an obvious magnetoresistance effect.25 For instance, I↑ prefer to flow from the devices with P configuration to the one with AP configuration under positive bias. This means that the intensive magnetoresistance transport of I↑ from P to AP configuration can be realized in the PDL molecular devices under positive bias. Nevertheless, the weaker magnetoresistance transport for I↑ under negative bias and I↓ under whole bias are ignored here.


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Figure 4: The spin-resolved transmission spectra as a function of energy for model devices (a) M1 , (b) M2 and (c) M3 at zero bias with P and AP configurations, where the insets show the distribution of the corresponding LDOS around E F .

The above mentioned interesting effects imply that in principal the high-speed and multi-valued integration density of organic molecular circuits can be realized in our proposed devices.1 Next, the followed Figures 3-7 then demonstrate the corresponding physical and chemical explanations in several aspects for the exhibited effects in the model devices. Firstly, in Figure 3 we present the spin-filtering efficiency (SFE), defined as SFE(%)=[(I↑ − I↓ )/(I↑ + I↓ )] × 100, for our proposed model devices. As shown in Figure 3(a), the SFE for device M1 under bias range (-2, 2 V) with P spin configuration [the (olive) diamond solid line] is nearly 100%, which implies a perfect spin-filtering effect. In contrast, the SFE for M1 with AP configuration [the (green) pentacle dashed line] is much different from that with P configuration, the SFE remains 100% under negative bias range (-1.8, 0 V) and yet it reverses to -100% under positive bias range (0, 1.8 V). Hence, a dual spin-filtering effect can be realized for M1 with AP configuration under a wide bias range. Further, the SFE for M2 with P [the (red) diamond solid line in Figure 3(b)] and AP [the (magenta) pentacle dashed line] configurations is similar to that for M1 . However, as shown in Figure 3(c), the value of SFE for M3 with P [the (blue) diamond solid line] and AP [the (cyan) pentacle dashed line] configurations within the same bias range shows a rapid oscillation, but its average is something like those for the former two devices. On the

other hand, to quantify the π (the highest occupied molecular orbitals-HOMOs) or π∗ (the lowest unoccupied molecular orbitals-LUMOs) contribution to the conductance, we analogize the charge transport from each molecular eigenstates in the planes of the pyridine rings. As is known, the distribution of the MPSH states can illustrate the coupling strength between the central molecule and electrodes, in general the more delocalized MPSH distribution of FMOs in the central region, the more easily the FMOs transport electrons.17 Moreover, the conductance is dominated by the LUMOs for PDL molecular devices, as has been verified experimentally and theoretically by other authors.32,33 Therefore, the spatial distributions of LUMOs with the associated MPSH eigenvalues for M1 -M3 at zero bias with P configuration are displayed correspondingly as insets in Figures 3(a)-3(c). The distributions of FMOs for three devices with P configuration have large difference between spin-up and -down orientations. The LUMO tracks an entirely evolution in spin-up at energy E=0.03, 0.05 and 0.13 eV as shown by the left insets, but it tracks partly evolution in spin-down at energy E=0.02, 0.03 and 0.01 eV as shown by the right insets of Figures 3(a)-3(c), respectively. This implies that I↑ can easily flow through the devices with P configuration but I↓ is rarely passed. Therefore, we can receive prefect spin-filtering spintronic devices by change the spin configuration in the ZGNR electrodes. It is clear that the distribution of LUMOs plays a key role in determining the spin-filtering effect for the devices. In order to fully evaluate the rectifying effect, the rectification ratio defined11 as RR(V) = |I(−V)|/I(V) [I(V)/|I(−V)|] for spin-up (down) current, where ∓V (±V) named forward (reverse) bias, is presented in Figures 3(d)-3(f) for M1 -M3 , respectively. As shown in Figure 3(d), with the increase of bias the RR of device M1 increases up to 104 order of magnitude at bias 0.5 V in I↑AP [the (olive) empty up-triangle solid line] and at bias 0.4 V in I↓AP [the (green) empty down-triangle dashed line], then they tend to decrease under higher biases. Whereas for M2 [the (red) empty up-triangle solid line] and M3 [the (blue) empty up-triangle solid line] in I↑AP , the peak of the RR exhibits a small value at low bias 0.3 V and rapidly decreases under higher biases, and the peak of RR in I↓AP move to bias 0.4 V for M2 [the (magenta) empty down-triangle dashed line] and 0.6 V for M3 [the (cyan) empty down-triangle dashed line]. Further, the maximum value of RR for I↑AP can reach 1.07×104 for M1 at bias ∓0.5 V, 296 for M2 at ∓0.3 V and 187 for M3 at ∓0.3 V. Besides, the rectifying behavior for I↓AP is something different, the rectifying direction of I↓AP is obviously reversed relative to I↑AP with the maximum value of RR reaching 9.6×103 for M1 at bias ±0.4 V, 141 for M2 at ±0.4 V and 103 for M3 at ±0.6 V, respectively. Further, to clearly illustrate the formation of spin-filtering effect, in Figure 4 we present the spin-resolved transmission probability T (E) at zero bias for the model devices (the color and type of lines correspond to Figure 2), where the insets show the LDOS around E F (set to be zero) of the ZGNR electrodes. First, we note that the T for M1 -M3 is nearly zero within E E F , but it is nonzero with different pattern within E & E F among the devices in different spin orientations and



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channels for spin-up electrons to principate in transport but no transport channel provided for spin-down electrons for M1 with P configuration. In consequence an obvious spin-filtering appears in M1 as shown in Figure 2(a). Similarly, as shown by the upper insets of Figure 4(b)/(c) for M2 /M3 , the spatial distribution of LDOS is the same as the ones in the upper insets of Figure 4(a), so the spin-filtering effect arises in Figure 2(c)/2(e). Meanwhile, in the lower insets of Figures 4(a)-4(c), the electronic cloud in spin-up and -down directions partly located similarly in the scattering region, which means the molecules provide similar channels for charge transport. This is because both the spin-up and -down transmission channels are opened in AP configuration, therefore, we can see dual spin-filtering effect shown in Figures 2(b), 2(d) and 2(f). The analysis gives an inside view of our observed results which suggest that the conducting property of dual spin-filtering effect can be reached by changing the spin orientation.

Figure 5: The spin-resolved MPSH eigenvalues evolution as a function of bias (the left column) and the spin-resolved transmission spectra as a function of energy (the right column) for model devices (a-d) M1 , (e-h) M2 and (i-l) M3 with AP configuration, respectively, where in the left column the middle region between two (blue) dashed crossing lines is the bias window, and in the right column the range between the dashed (black) vertical lines is the corresponding bias window.

spin configurations. The T ↑P for three devices shows a broad and strong peak at E F , but the T ↓P is nearly zero, which implies that the spin-up electrons can easily flow through the device while the spin-down ones are completely blocked at E F . However, the T ↑AP and T ↓AP are almost spin-independent for all devices and the peaks move to the higher energy region, which means that the spin-up and -down electrons commonly principate in the charge transport. This is because that the transmission channels in both spin-up and -down directions are partly opened in the case of AP configuration. Secondly, as shown by the LDOS for device M1 with P configuration at zero bias [see the upper insets of Figure 4(a)], the π-orbital amplitude [the (red) electronic cloud] distributes in the whole BPD molecule in the upper left inset, whereas there is almost not (green) electronic cloud located in the scattering region in the upper right inset. This indicates the molecule provides

The RR for the proposed devices presented in Figure 3 is quite comparable to that of a typical solid-state rectifier. It is known that the molecular orbital has a key influence on the transmission spectrum, and only the molecular orbital in the bias window can contribute to the transmission.11 Moreover, the resonant transport channel moves toward (away from) the bias window under the forward (reverse) bias, which results in rectifying. Therefore, this mechanism seems to hold true for our model devices. Here, the resonance channel under finite bias on the left column is made from the FMOs consisting of LUMO+1, LUMO, HOMO and HOMO+1. We can see from Figure 5(a) for M1 that the LUMO plays a major role on the resonant transport since there is a corresponding transmission peak around E F and the integral area of transmission coefficient in the bias window [the (olive) solid area] in Figure 5(b), and the LUMO [the (olive)/(green) circle corresponding to the solid/dashed area] enters into/moves away from the bias window at -/+0.6V serving as a conducting channel, which yields that the I↑AP at -0.6 V is larger than I↑AP at 0.6 V as shown in Figure 2(b). What is more, the LUMO+1 plays a mainly role in the resonant transport for M2 resulting in rectifying, and in Figure 5(e) the LUMO+1 [the (red)/(magenta) circle] moves toward/away from the bias window under the forward (∓) bias corresponding to the (red)/(magenta) transmission peak and integral area at bias -/+0.3 V shown in Figure 5(f). The spin-up current for M3 has the same transport mechanism as plotted with the (blue)/(cyan) circle line for MPSH eigenvalues in Figure 5(i), corresponding to T around E F and the solid/dashed integral area at bias ∓0.3 V shown in Figure 5(j). These are the reason why the forward rectifying phenomenon arises. On the other hand, the I↓AP for M1 -M3 , in contrast, has a reverse (±) rectifying transport mechanism as displayed in Figures 5(c) and 5(d) for M1 , 5(g) and 5(h) for M2 , and 5(k) and 5(l) for M3 , respectively. One can see that the transmission peak around E F and the integral area in the bias window under positive bias is larger than that under negative one corresponding to I↓AP at bias ±0.4 V for M1 , ±0.4 V for M2 and ±0.6 V for M3 , respectively. Moreover, the HOMO+1 and HOMO approach to E F for M1 and M3 under positive bias shown in Figures 6(c) and 6(k), while it moves far away from E F when a negative bias is applied. This asym-


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Figure 7: (a) The spin-up magnetoresistance ratio as a function of bias for model devices M1 -M3 . (b-d) The spin-resolved transmission spectra for model devices M1 -M3 under certain bias with P and AP configurations, respectively, where the range between two (black) dashed vertical lines indicates the corresponding bias window.

Figure 6: The spin-down transmission spectra for model devices (a, b) M1 and (c, d) M3 in AP configuration under certain bias, where the insets show the LDOS around E F and the range between two (black) dashed vertical lines indicates the corresponding bias window.

metric shift of the HOMO also contributes to a large current under positive bias, which results in a rectification. Whereas for M2 the LUMO+1 and LUMO approach to E F under positive bias shown in Figure 6(g) contributing to large current under positive bias. Similarly, it can be demonstrated by the transmission coefficient and the corresponding integral area in Figures 5(d) for M1 , 5(h) for M2 and 5(l) for M3 , respectively. Therefore, we can see the forward and reverse rectifications here. This outstanding rectifying effect makes the device a possibility for achieving an ideal spin diode. Next, we discuss the NDR effect originating from the FMOs for our model devices. For instance, the eigenvalue of HOMO and HOMO+1 in spin-down direction for M1 with AP configuration at bias -0.6 V are 0.08 and 0.23 eV in the bias window as shown in Figure 5(c), but they obviously increase up to 0.13 and 0.28 eV when a -0.7 V is applied. The HOMO and HOMO+1 at bias -0.6 V is very close to E F . However, as the bias reaches to -0.7 V, the HOMO and HOMO+1 move away from E F . Therefore, the HOMOs play a major role in charge transport, which results in a great change of current here. Moreover, the HOMO-LUMO gap in spin-down direction for M3 with AP configuration at bias -0.3 V is smaller than that at -0.6 V as shown in Figure 5(k), and the eigenvalue of HOMO+1 at bias -0.3 V is very close to E F in the bias window. However, as the bias reaches to -0.6 V, the HOMO-LUMO gap obviously increases and the HOMO+1 moves away from E F . This induces a large decrease of the

current, which leads to NDR. As we know, the FMOs serve as conducting channel for charge transport in a device under different biases, which produces a pulse-like I − V curve, and in consequence, the obvious NDR effect is then induced. However, we are unable to judge various NDR completely according to Figure 5 only. To obtain a further intuitive picture, we plot the spin transmission spectrum and LDOS for M1 and M3 under various biases in Figure 6, where the current is determined by the integral area under the T (E) for the device.21 In Figure 6(a) for M1 , we find that there is a large (olive) shadowed integral area within bias window at bias -0.6 V, which leads to a current peak corresponding to the inset of Figure 2(b). However, as the window becomes larger at bias -0.7 V, the transmission and the total (green) shadowed area are smaller, which produces a current valley. Meanwhile, the π-orbital amplitude of LDOS distributes in the whole atomic chain of BPD molecule as shown in the inset of Figure 6(a), whereas there is less electron (green) cloud located in the inset of Figure 6(b). This means that the conduction orbital is suppressed at certain bias voltage, which yields the formation of current peak and valley.22 Similarly, as seen in T ↓AP of Figures 6(c) and 6(d) for for M3 , with the increase of bias from -0.3 to -0.6 V the (blue) shadowed integral area at bias -0.3 V within the bias window is widened, however, the effective (cyan) shadowed at bias -0.6 V is narrowed. As a result, the transmission within the window is decreased. Clearly, the π-orbital electron density cloud uniformly distributes in the whole atomic chain of EPD molecule shown in the inset of Figure 6(c), but partly distributes in the inset of Figure 6(d). In consequence, it results in the formation of the current peak (at bias -0.3 V) and valley (at bias -0.6 V). Hence, we can gain an obvious NDR effect in device M3 . Nevertheless, the PVRs are very large but not steady [see Figure 3(f)], which needs to be improved further. Finally, we discuss the magnetoresistance effect by ana-



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lyzing the characteristic of the MR for our proposed model devices. The MR can be obtained from the I-V curves using the definition20 MR(%)=[(RAP -RP )/RP ]×100, where RP and RAP are the resistances of the junction with P and AP spin configurations, respectively. Note that when the bias is zero, the MR is defined as26,40 MR(%)=[(T ↑AP +T ↓AP )−1 (T ↑P +T ↓P )−1 ]/(T ↑P +T ↓P )−1 ×100; while with non-zero bias MR(%)=[(I P -I AP )/I AP ]×100 in Figure 7(a). By calculation, the MR under external bias reaches the maximum value of 1.04×106 % for M1 , 4.57×104 % for M2 and 3×104 % for M3 , respectively. To reveal the mechanism of magnetoresistance effect in the proposed model devices, we explore the origin of the maximum MR through the bias-dependent T at bias 0.5 V for M1 , 0.3 V for M2 and 0.1 V for M3 , as shown in Figures 7(b)-7(d), respectively. The unusual MR originates from the unique symmetry of the band structure in ZGNRs. Compared with the selective transmission in conventional devices derived only from spin matching, the additional orbital symmetry matching in the nanoribbons allows further selective transmission, leading to the striking enhancement in MR.25 In Figure 7(b)-7(d), the (olive, red, blue)/(green, magenta, cyan) solid/dashed line represents T ↑P /T ↑AP for the three devices. Therefore, when the electrode is set in P spin configuration, the current is larger than that in AP spin configuration. In the other words, the MR effect depends on the charge of magnetic set to two electrodes. As one can see, if there is always high transmission peak in the bias window, it contributes a large current according to the Landauer-Büttiker formula. For example, the T ↑P [the (olive) solid line] around E F is much higher than the (green) dashed one at bias 0.5 V as shown in Figure 7(b), in consequence the (olive) integral area is larger than the green one, and the magnetoresistance effect appears. Meanwhile, as given in Figure 7(c)/(d), at bias 0.3/0.1 V there is always a high and visible T ↑P peak around E F (solid lines) and a large shadowed integral area for M2 /M3 in the corresponding bias window, whereas a blurry T ↑AP peak (dashed line) and a small shadowed integral area corresponding to a weak current, which leads to a giant MR. As a result, the IV characteristics in Figure 2 also show a strong MR effect, whose origin can be traced to a change in the shape of the spinresolved transmission peaks shown in Figures 7(b)-7(d). The magnetoresistance effect is great of interest due to future wide application prospect, which has aroused many theoretical25,40 and experimental works47,48 . CONCLUSIONS

In conclusion, we have studied the spin-resolved charge transport properties for the junctions of a PDL molecule embedded between two ZGNR electrodes. The ZGNRs are modulated by an external magnetic field, and that BPD, VPD and EPD molecules are considered, respectively. By calculations based on the DFT combined with NEGF formalism, we have demonstrated that the spin-charge transport can be modulated by performing different magnetic configuration in the ZGNR electrodes. In particular, the BPD molecular junction can act as a single spin-conductor in proper spin con-

figuration of ZGNRs. The interesting spin-filtering is observed within the P configuration, and dual spin-filtering is also found in the AP configuration. The obvious NDR effect is also found in the proposed model devices. Furthermore, the rectifying effect and magnetoresistance effect can be observed in the junctions by modulating the external magnetic field. Therefore, a multi-functional molecular device is realized. The corresponding mechanisms of the above interesting phenomena originate from the evolution of the frontier molecular orbitals, the molecular projected self-consistent Hamiltonian eigenvalues, spin-resolved transmission spectrum, local density of states, etc. In short, the proposed organic molecular devices can serve as a perfect spin-filter, spin-diode, spinswitching, and so on.

AUTHOR INFORMATION

E-mail:[email protected]

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant No. 11274108) and Hunan Provincial Innovation Foundation for Postgraduate (Grant No. CX2015B124).

REFERENCES

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Spin-Resolved Transport Properties of a Pyridine-Linked Single

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