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The integrated spintronic functionalities of an individual high-spin state spin-crossover molecule between graphene nanoribbon electrodes
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 315201 (http://iopscience.iop.org/0957-4484/26/31/315201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 134.117.10.200 This content was downloaded on 20/07/2015 at 09:10
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Nanotechnology Nanotechnology 26 (2015) 315201 (6pp)
doi:10.1088/0957-4484/26/31/315201
The integrated spintronic functionalities of an individual high-spin state spin-crossover molecule between graphene nanoribbon electrodes L Zhu1, F Zou1, J H Gao1, Y S Fu1, G Y Gao1, H H Fu1, M H Wu1, J T Lü1 and K L Yao1,2 1
School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China 2 International Center of Materials Physics, Chinese Academy of Science, Shenyang 110015, People’s Republic of China E-mail: [email protected] Received 23 April 2015, revised 31 May 2015 Accepted for publication 12 June 2015 Published 16 July 2015 Abstract
The spin-polarized transport properties of a high-spin-state spin-crossover molecular junction with zigzag-edge graphene nanoribbon electrodes have been studied using density functional theory combined with the nonequilibrium Green’s-function formalism. The molecular junction presents integrated spintronic functionalities such as negative differential resistance behavior, spin filter and the spin rectifying effect, associated with the giant magnetoresistance effect by tuning the external magnetic field. Furthermore, the transport properties are almost unaffected by the electrode temperature. The microscopic mechanism of these functionalities is discussed. These results represent a step toward multifunctional molecular spintronic devices on the level of the individual spin-crossover molecule. Keywords: DFT, spin-crossover, giant magnetoresistance, spin filter, spin rectifying effect (Some figures may appear in colour only in the online journal) Introduction
very long; consequently, these kinds of systems are potential candidates for the applications of molecular switches, display, and memory devices [4–6]. Among the SCO molecular complexes, octahedral 3d6 iron (II) molecules are systems of particular interest [7, 8]. For these types of SCO compounds, the HS state, S = 2, has t 2 g 4eg 2 electron configuration. However, the traditional topics are mainly on the charge transport properties of the spincrossover molecule. It is confirmed that the HS state molecule has a closer state to the Fermi level than the LS state, so the HS state shows higher conductance than the LS state [9, 10]. But by adsorbing a HS state SCO molecule onto a suitable spin injector, a single-molecule device potentially in spatially dense, multifunctional memory applications could be achieved [10]. Motivated by this viewpoint, in the present work, using the nonequilibrium Green’s function (NEGF)
One of the challenges in the area of molecular spintronics is the search for an organic molecule with magnetism at room temperature. However, traditional molecular magnets have very low Curie temperature, that is far from the actual applications. Transition metal complexes that exhibit a temperature dependent crossover from a low-spin (LS) state to a high-spin (HS) state have attracted much research attention [1, 2]. In contrast to other magnetic molecular systems that present attractive physical properties at low temperatures, the spin crossover (SCO) materials can show bistability at the molecular level near room temperature, and it is possible to use the electronic field as an external stimulus for switching [3]. On the other hand, when exciting the molecule from the LS state to HS state, the lifetime of the metastable HS state is 0957-4484/15/315201+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
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Nanotechnology 26 (2015) 315201
formalism combined with the spin-polarized density functional theory (DFT), we study the spin-resolved electron transport properties of Fe(tzpy)2(NCS)2 (tzpy is 3-(2-pyridyl) [1,2,3]triazolo[1,5-a]pyridine) synthesized by Niel et al [11] to facilitate the contacts with two zigzag-edge graphene nanoribbon (ZGNR) electrodes. The ZGNR has an antiferromagnetic (AFM) ground state; however, the FM state can be obtained with the help of a transverse electrical field or an external magnetic field [12, 13]. On the other hand, by nanofabrication technology, it is possible to contact single molecules with a GNRs electrode [14]. Our results show multifunctional properties in this molecular device, such as perfect spin-filter efficiency, giant magnetoresistance, spinrectifying and negative differential resistance behaviors, which are almost unaffected by the electrode temperature. The mechanism for these features is also discussed.
configuration. The FM state 4-ZGNRs have metallic electronic properties, and the AFM sate has semiconductive properties, as displayed in figure 1(b). When the electrode is in the FM or AFM state, the transport property should be distinctly different. Here we have considered two different spin configurations of the electrode: FM state AP (the spin of the left and right electrode is antiparallel) spin configuration and AFM state. For the FM state P (the spin of the left and right electrode is parallel) spin configuration, when the bands of the left and right electrodes in the bias windows mismatch, and the electrons around the Fermi level are localized in the molecule, the currents for the FM state P spin configuration are oscillating and very small, so this spin configuration is not considered in the paper. Figures 2(a) and (b) present the spin-resolved I–V curves for the above two spin configurations, which clearly demonstrate several important features: (1) Spin-rectifying effect and spin filter efficiency (SFE). For the FM state AP spin configuration electrode, in the positive bias region, the current of the spin-down electron is obviously larger than that of the spin-up one and increases rapidly within the bias range from 0.25 to 0.95 V. Therefore, relatively good spin-filtering can be expected at positive bias. The observed spin-filtering effect defined as SFE = [IDown − IUp]/[ IDown + IUp] is nearly 100% in the above bias range; here, IDown and IUp stand for the spin-down and spin-up current, respectively, indicating perfect spin-filtering behavior. In the negative bias region, the spin-up and spindown current are both almost zero. These observations indicate that a significant spin filter effect and obvious spin rectifying effect can coexist in the proposed Fe(tzpy)2(NCS)2 molecular junction with a FM state ZGNRs electrode. From the inset in figure 2(a), one can see that the maximum recti-
Computational methods Our theoretical simulation is performed by using the ATOMISTIX TOOLKIT (ATK) [15], which combines the Keldysh nonequilibrium Green’s function (NEGF) formalism with density-functional theory (DFT). As the total current is spin polarized, the spin current Iσ was calculated using the non-equilibrium Green’s function approach that is based on the Landauer−Büttike formula [16] Iσ =
e h
∞
∫−∞ Tσ ( E , Vb ) ⎡⎣ fL ( E − μL ) − fR ( E − μR ) ⎤⎦ dE
(1)
Here σ = ↑ , ↓ are the spin indices, μ L,R are the chemical potential for left-electrode (LE) and right-electrode (RE), respectively. fL,R (E − μ L,R ) is Fermi–Dirac distribution function. The spin-dependent transmission coefficients is calculated from the Green functions Tσ (E , V ) = Tr (ΓR, σ GσR ΓL, σ GσA ), which depends on external bias voltage Vb, where ΓL,R, σ is the coupling matrix, and GσR/A is the retarded and advanced Green functions, respectively. For a given bias voltage Vb, [ μ L (Vb ), μR (Vb )] is referred to as the bias window, the electrochemical potential in the left/right electrode ( μ L (Vb ), μR (Vb )) is shifted to μ L (Vb ) = μ L (0) + eVb /2 and μR (Vb ) = μR (0) − eVb /2. Here μ L (0) = μR (0) = E F (Fermi level) is set to zero, so the bias window corresponds to the range [−Vb/2, +Vb/2] [17].
fication ratio (RR) RR =
I↓ pos I↓ neg
(I↓ pos and I↓ neg are the spin-
down polarized current at positive and negative bias, respectively) reaches a 103 order of magnitude. Such a large ratio is very desirable for practical applications. (2) Giant magnetoresistance (GMR) effect. The total current of the FM AP spin configuration is much bigger than that of the AFM at low bias, resulting in a high GMR effect. The magnetoresistance ratio (MR) of GMR defined by MR = [(IFM _ AP − IAFM ) /IAFM ]*100% shown in figure 2(c) is about a 1010 order of magnitude at zero bias, which is much bigger than those reported previously [19, 20]. In particular, in the bias range from −0.7 to −0.3 V and 0.4 to 0.7 V, the MR remains as high as 105 orders of magnitude. Here IFM _ AP and IAFM are the total current in the FM state AP spin configurations and the AFM state, respectively. (3) Negative differential resistance (NDR) effect. The current of the spindown electrons in the FM state AP spin configuration initially increases with the applied bias, when the bias goes higher than 0.65 V, the current drops dramatically, indicating the onset of the NDR effect [21]. The maximum current of the spin-down electrons is up to about 3.36 μA at the peak position (Vbias = 0.65 V), while the current reaches its minimum value (0.53 μA) at the valley site (Vbias = 0.9 V). The above results highlight that the Fe(tzpy)2(NCS)2 molecular
Results and discussion The designed molecular device is displayed in figure 1(a), The molecule is covalently bridged between two 4-ZGNR electrodes, where the number 4 is the number of zigzag carbon chains (ZCCs) along the direction perpendicular to the nanoribbon axis [18], The dangling bond of each edge carbon atom is passivated with a hydrogen atom. As the magnetization of the left and right ZGNR electrodes can be controlled by applying an external magnetic field, the magnetization of the device can be set to parallel (P) or antiparallel (AP) spin 2
L Zhu et al
Nanotechnology 26 (2015) 315201
Figure 1. (a) The model structure of the two-probe system. Purple, orange, blue, grey and white spheres represent iron, sulfur, nitrogen,
carbon and hydrogen atoms, respectively. (b) Spin-resolved band structure for the FM (left panel) and AFM (right panel) state 4-ZGNRs.
junction has multifunctional applications in molecular spintronic devices. To understand the nature of the above observed effects, we plot the spin-polarized zero-bias transmission spectra of the FM state AP spin configuration and the AFM state in figure 3. From figure 3(a) it is clear that the transmission spectra of the spin-up and spin-down electrons display remarkably different behavior around the Fermi level. At zero bias, for the spin-down electrons, one significant transmission peak is located at 0.3 eV, which is mainly contributed by the degenerate spin-down molecular orbital just above the lowest unoccupied molecular orbital (LUMO) (LUMO + 1 and LUMO + 2), which is delocalized over the whole molecular junction, as shown in figure 4(a). The Fe dxy orbital gives considerable contribution. From the projected density of states (PDOS) shown in figure 3(c), it can be found that these molecular orbitals (MOs) mainly come from the spin-down Fe(tzpy)2(NCS)2-electrode hybrid state originating from the coupling between the electrode and Fe’s d atomic orbitals along with the tzpy-ligands. Meanwhile, the transmission coefficient of the spin-up channel is quite small in the wide energy region from −1.0 to 1.0 eV. The distinct difference in transmission spectrum between the two spin channels can be evaluated with SFE. It turns out that the calculated SFE at zero bias is about 100%, indicating that conductance through the molecular junction is mainly governed by the spin-down channel. From figure 3(b), one can see that there is a large
transmission gap at the EF for both the spin-up and spin-down channels of AFM state at low bias, and the gap increases with an increase of bias. Thus the current is prohibited and almost zero at low bias. Just as the bias voltages reach above 0.7 V and below −0.7 V, there are resonance peaks appearing around the Fermi level, then the currents begin to increase rapidly at these biases. Therefore, large values of GMR between the FM state and the AFM state electrodes can be acquired at small biases. The mechanism of NDR can be indicated from bias dependent transmission (figure 3(a)). From figure 3(a), it is clear that the spin-down transmission curves gradually shift toward the low-energy side with applied bias voltage. As the forward bias voltage increases, the transmission peaks above the Fermi level continually approach the Fermi level and some T(E, Vb) enter into the transport window contributing to the integration of current. As a result, the spin-down current continuously increases and reaches its maximum value at Vbias = 0.65 V. When Vbias increases to 0.9 V, the feature of the spin-down transmission function changes dramatically, the transmission peak around the Fermi level is strongly suppressed and even disappears. As a result, in the bias window, the transmission coefficients of the spin-down electrons are very small. Thus, the current decreases, and the I−V valley appears. When Vbias continually increases, the current increases again since another transmission peak appears and enters into the bias window. 3
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Nanotechnology 26 (2015) 315201
Figure 3. (a), (b) The spin polarized transmission spectra for the FM
state AP spin configuration and the AFM state at different biases, respectively. (c) The projected density of states (PDOS) for the Fe (tzpy)2(NCS)2 molecule in the two-probe system at zero bias.
Figure 2. (a), (b) The spin-resolved I−V curves for the FM state AP
spin configuration and the AFM state, respectively. The inset of (a) shows the rectification ration (RR) as a function of the applied bias. (c) The magnetoresistance ratio (MR) as a function of the applied bias. For clarity, the inset is the MR at a smaller scale.
are both delocalized and contribute to the transport, then there is a large transport peak around the Fermi level, leading to the current reaching its maximum. However, at 0.9 V, the LUMO is localized and only HOMO contributes to the transport, leading to the dropping of the transport peak, so NDR appears. Also, the spin diode effect mainly comes from the mismatch of FMO with the energy level of the electrodes. When the positive bias is applied, the energy bands shift downward and upward for the LE and RE, respectively. There are four MOs (HOMO-1, HOMO, LUMO and LUMO + 1) within the bias window at 0.65 V for the spin-down state.
The NDR can be understood from the degree of delocalization of the frontier molecular orbitals (FMOs) displayed in figure 4(a), especially the highest occupied molecular orbital (HOMO) and LUMO, since they are close to the EF. Due to the coupling between molecule and electrodes [22], there is small misalignment between transmission peaks and the molecular projected self-consistent Hamiltonian (MPSH). From the MPSH displayed in figure 4(a), the following features can be found: at 0.65 V, the HOMO and LUMO orbitals 4
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Nanotechnology 26 (2015) 315201
Figure 4. (a) The spatial distribution of the MPSH for the spin-down electrons at different biases. (b), (c) The spin-down band structures of
the left/right electrode and transmission spectra for the FM state AP spin configuration at 0.65 and −0.65 V, respectively.
There is overlap between the HOMO and LUMO orbitals, which are delocalized and contribute to the transport. The energy subbands of LE and RE are also symmetric in the bias window from −0.325 to 0.325 eV, leading to a strong and broad transmission peak in the bias window and making the current reach its maximum. Although there are five MOs (HOMO − 2, HMO − 1, HOMO, LUMO and LUMO + 1) within the bias window at −0.65 V for the spin-down state. As shown in figure 4(a), the HOMO and HOMO-1 orbitals are more delocalized through the molecular junction, which is localized at −0.08 and −0.05 eV, respectively. However, at the energy region from −0.325 to 0.325 eV, which is just the bias window, the subbands of LE and RE are asymmetric, where the spin-down π-subband of LE overlaps with the spindown π*-subband of RE. As a result, there is no spin-down transmission peak within the bias window, the current is very small. Therefore, a spin diode effect is obtained. As we know, when the electrodes are contacted in a different way, current dissipation in the electrodes may lead to different temperatures. Motivated by this, we evaluated whether a spin-polarized thermopower current can affect the integrated spintronic functionalities of this molecular junction. For this purpose, we take a temperature drop ΔT = 10 and −10 K ( ΔT = TL − TR ) between electrodes, and calculate the spin-polarized current Iσ using equation (1) at different temperatures for the FM state AP spin configuration. At zero and very low bias, below a critical bias Vc ≈ k B ΔT , the current is very small, less than 0.01 nA in all of the considered temperature region, the conductance is fully polarized and almost unchanged with the temperature, which can be seen from transmission spectra (figure 5(a)) at different
temperatures of the left electrode at zero bias. When the bias increases, the current contributed from bias increases quickly, which is much larger than that contributed from temperature, then the current induced by temperature gradient can be neglected. Figure 5(b) displays the current as a function of left electrode temperature at 0.65 V for ΔT = ± 10 K. The results show that although the numerical value of the current is slightly affected by the thermal effects, the current polarization is almost unchanged. The change of SFE, GMR and NDR is also negligible, which shows that this molecular junction is a perfect spintronic device and is robust against the thermal effects.
Conclusions In summary, we have carried out first-principles calculation in combination with the NEGF approach to examine the spinpolarized transport of a spin-crossover molecule Fe (tzpy)2(NCS)2 with two 4-ZGNR electrodes. Perfect spinfilter efficiency with almost 100% spin polarization, giant magnetoresistance, spin-rectifying, and negative differential resistance behaviors can be obtained by tuning the external magnetic field. The NDR behavior with the FM state electrode mainly originates from the shifting of molecular orbitals with the energy level of the electrode. The spin diode effect mainly comes from the mismatch of FMO with the energy level of the electrodes. The different conductive properties of ZGNRs in the FM and AFM states lead to a giant magnetoresistance effect with large magnetoresistance ratio. The above results indicate that this spin-crossover molecule can be designed as multifunctional molecular spintronic devices, 5
L Zhu et al
Nanotechnology 26 (2015) 315201
11274130, 11274128, 11304107, 11474113 and 61371015, and by the Natural Science Foundation of Hubei Province no. 2014CFB236.
References [1] Matar S F, Guionneau P and Chastanet G 2015 Int. J. Mol. Sci. 16 4007 [2] Pronschinske A, Chen Y, Lewis G F, Shultz D A, Calzolari A, Nardelli M B and Dougherty D B 2013 Nano Lett. 13 1429 [3] Gopakumar T G, Matino F, Naggert H, Bannwarth A, Tuczek F and Berndt R 2012 Angew. Chem. Int. Ed. 51 6262 [4] Aravena D and Ruiz E 2012 J. Am. Chem. Soc. 134 777 [5] Baadji N, Piacenza M, Tugsuz T, Sala F D, Maruccio G and Sanvito S 2009 Nat. Mater. 8 813 [6] Chattopadhyaya M, Alam M M and Chakrabarti S 2013 RSC Adv. 3 19894 [7] Abhervé A, Clemente-León M, Coronado E, Gómez-García C J and López-Jordà M 2014 Dalton Trans. 43 9406 [8] Mondal A, Li Y, Chamoreau L, Seuleiman M, Rechignat L, Bousseksou A, Boillotd M and Lescouëzec R 2014 Chem. Commun. 50 2893 [9] Baadji N and Sanvito S 2012 Phys. Rev. Lett. 108 217201 [10] Miyamachi T et al 2012 Nat. Commun. 3 938 [11] Niel V, Gaspar A B, Muñoz M C, Abarca B, Ballesteros R and Real J A 2003 Inorg. Chem. 42 4782 [12] Son Y W, Cohen M L and Louie S G 2006 Nature 444 347 [13] Munoz-Rojas F, Fernandez-Rossier J and Palacios J J 2009 Phys. Rev. Lett. 102 136810 [14] Prins F, Barreiro A, Ruitenberg J W, Seldenthuis J S, Aliaga-Alcalde N, Vandersypen L M K and van der Zant H S J 2011 Nano Lett. 11 4607 [15] Brandbyge M, Mozos J L, Ordejón P, Taylor J and Stokbro K 2002 Phys. Rev. B 65 165401 [16] Wang B G, Wang J and Guo H 2001 J. Phys. Soc. Japan 70 2645 [17] Datta S, Tian W, Hong S, Reifenberger R, Henderson J I and Kubiak C P 1997 Phys. Rev. Lett. 79 2530 [18] Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 J. Phys. Soc. Japan 65 1920 [19] Yang Z, Zhang B L, Liu X G, Li X Y, Yang Y Z, Xiong S J and Xu B S 2014 Phys. Chem. Chem. Phys. 16 1902 [20] Zhao P, Wu Q H, Liu H Y, Liu D S and Chen G 2014 J. Mater. Chem. C 2 6648 [21] Chen J, Reed M A, Rawlett A M and Tour J M 1999 Science 286 1550 [22] Stokbro K, Taylor J and Brandbyge M 2003 J. Am. Chem. Soc. 125 3674
Figure 5. (a) The transmission spectra at different temperatures of the left electrode at zero bias for the FM state AP spin configuration when ΔT = 10 K. (b) The spin polarized current as a function of the left electrode temperature at 0.65 V for the FM state AP spin configuration when ΔT = ±10 K, respectively.
which can improve the integration density of molecular circuits in the near future. Moreover, the transport properties are robust against thermal effects.
Acknowledgments This work was supported by the National Natural Science Foundation of China under the grant nos. 11374111,
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The integrated spintronic functionalities of an individual high-spin state spin-crossover molecule between graphene nanoribbon electrodes
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 315201 (http://iopscience.iop.org/0957-4484/26/31/315201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 134.117.10.200 This content was downloaded on 20/07/2015 at 09:10
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 26 (2015) 315201 (6pp)
doi:10.1088/0957-4484/26/31/315201
The integrated spintronic functionalities of an individual high-spin state spin-crossover molecule between graphene nanoribbon electrodes L Zhu1, F Zou1, J H Gao1, Y S Fu1, G Y Gao1, H H Fu1, M H Wu1, J T Lü1 and K L Yao1,2 1
School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China 2 International Center of Materials Physics, Chinese Academy of Science, Shenyang 110015, People’s Republic of China E-mail: [email protected] Received 23 April 2015, revised 31 May 2015 Accepted for publication 12 June 2015 Published 16 July 2015 Abstract
The spin-polarized transport properties of a high-spin-state spin-crossover molecular junction with zigzag-edge graphene nanoribbon electrodes have been studied using density functional theory combined with the nonequilibrium Green’s-function formalism. The molecular junction presents integrated spintronic functionalities such as negative differential resistance behavior, spin filter and the spin rectifying effect, associated with the giant magnetoresistance effect by tuning the external magnetic field. Furthermore, the transport properties are almost unaffected by the electrode temperature. The microscopic mechanism of these functionalities is discussed. These results represent a step toward multifunctional molecular spintronic devices on the level of the individual spin-crossover molecule. Keywords: DFT, spin-crossover, giant magnetoresistance, spin filter, spin rectifying effect (Some figures may appear in colour only in the online journal) Introduction
very long; consequently, these kinds of systems are potential candidates for the applications of molecular switches, display, and memory devices [4–6]. Among the SCO molecular complexes, octahedral 3d6 iron (II) molecules are systems of particular interest [7, 8]. For these types of SCO compounds, the HS state, S = 2, has t 2 g 4eg 2 electron configuration. However, the traditional topics are mainly on the charge transport properties of the spincrossover molecule. It is confirmed that the HS state molecule has a closer state to the Fermi level than the LS state, so the HS state shows higher conductance than the LS state [9, 10]. But by adsorbing a HS state SCO molecule onto a suitable spin injector, a single-molecule device potentially in spatially dense, multifunctional memory applications could be achieved [10]. Motivated by this viewpoint, in the present work, using the nonequilibrium Green’s function (NEGF)
One of the challenges in the area of molecular spintronics is the search for an organic molecule with magnetism at room temperature. However, traditional molecular magnets have very low Curie temperature, that is far from the actual applications. Transition metal complexes that exhibit a temperature dependent crossover from a low-spin (LS) state to a high-spin (HS) state have attracted much research attention [1, 2]. In contrast to other magnetic molecular systems that present attractive physical properties at low temperatures, the spin crossover (SCO) materials can show bistability at the molecular level near room temperature, and it is possible to use the electronic field as an external stimulus for switching [3]. On the other hand, when exciting the molecule from the LS state to HS state, the lifetime of the metastable HS state is 0957-4484/15/315201+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
L Zhu et al
Nanotechnology 26 (2015) 315201
formalism combined with the spin-polarized density functional theory (DFT), we study the spin-resolved electron transport properties of Fe(tzpy)2(NCS)2 (tzpy is 3-(2-pyridyl) [1,2,3]triazolo[1,5-a]pyridine) synthesized by Niel et al [11] to facilitate the contacts with two zigzag-edge graphene nanoribbon (ZGNR) electrodes. The ZGNR has an antiferromagnetic (AFM) ground state; however, the FM state can be obtained with the help of a transverse electrical field or an external magnetic field [12, 13]. On the other hand, by nanofabrication technology, it is possible to contact single molecules with a GNRs electrode [14]. Our results show multifunctional properties in this molecular device, such as perfect spin-filter efficiency, giant magnetoresistance, spinrectifying and negative differential resistance behaviors, which are almost unaffected by the electrode temperature. The mechanism for these features is also discussed.
configuration. The FM state 4-ZGNRs have metallic electronic properties, and the AFM sate has semiconductive properties, as displayed in figure 1(b). When the electrode is in the FM or AFM state, the transport property should be distinctly different. Here we have considered two different spin configurations of the electrode: FM state AP (the spin of the left and right electrode is antiparallel) spin configuration and AFM state. For the FM state P (the spin of the left and right electrode is parallel) spin configuration, when the bands of the left and right electrodes in the bias windows mismatch, and the electrons around the Fermi level are localized in the molecule, the currents for the FM state P spin configuration are oscillating and very small, so this spin configuration is not considered in the paper. Figures 2(a) and (b) present the spin-resolved I–V curves for the above two spin configurations, which clearly demonstrate several important features: (1) Spin-rectifying effect and spin filter efficiency (SFE). For the FM state AP spin configuration electrode, in the positive bias region, the current of the spin-down electron is obviously larger than that of the spin-up one and increases rapidly within the bias range from 0.25 to 0.95 V. Therefore, relatively good spin-filtering can be expected at positive bias. The observed spin-filtering effect defined as SFE = [IDown − IUp]/[ IDown + IUp] is nearly 100% in the above bias range; here, IDown and IUp stand for the spin-down and spin-up current, respectively, indicating perfect spin-filtering behavior. In the negative bias region, the spin-up and spindown current are both almost zero. These observations indicate that a significant spin filter effect and obvious spin rectifying effect can coexist in the proposed Fe(tzpy)2(NCS)2 molecular junction with a FM state ZGNRs electrode. From the inset in figure 2(a), one can see that the maximum recti-
Computational methods Our theoretical simulation is performed by using the ATOMISTIX TOOLKIT (ATK) [15], which combines the Keldysh nonequilibrium Green’s function (NEGF) formalism with density-functional theory (DFT). As the total current is spin polarized, the spin current Iσ was calculated using the non-equilibrium Green’s function approach that is based on the Landauer−Büttike formula [16] Iσ =
e h
∞
∫−∞ Tσ ( E , Vb ) ⎡⎣ fL ( E − μL ) − fR ( E − μR ) ⎤⎦ dE
(1)
Here σ = ↑ , ↓ are the spin indices, μ L,R are the chemical potential for left-electrode (LE) and right-electrode (RE), respectively. fL,R (E − μ L,R ) is Fermi–Dirac distribution function. The spin-dependent transmission coefficients is calculated from the Green functions Tσ (E , V ) = Tr (ΓR, σ GσR ΓL, σ GσA ), which depends on external bias voltage Vb, where ΓL,R, σ is the coupling matrix, and GσR/A is the retarded and advanced Green functions, respectively. For a given bias voltage Vb, [ μ L (Vb ), μR (Vb )] is referred to as the bias window, the electrochemical potential in the left/right electrode ( μ L (Vb ), μR (Vb )) is shifted to μ L (Vb ) = μ L (0) + eVb /2 and μR (Vb ) = μR (0) − eVb /2. Here μ L (0) = μR (0) = E F (Fermi level) is set to zero, so the bias window corresponds to the range [−Vb/2, +Vb/2] [17].
fication ratio (RR) RR =
I↓ pos I↓ neg
(I↓ pos and I↓ neg are the spin-
down polarized current at positive and negative bias, respectively) reaches a 103 order of magnitude. Such a large ratio is very desirable for practical applications. (2) Giant magnetoresistance (GMR) effect. The total current of the FM AP spin configuration is much bigger than that of the AFM at low bias, resulting in a high GMR effect. The magnetoresistance ratio (MR) of GMR defined by MR = [(IFM _ AP − IAFM ) /IAFM ]*100% shown in figure 2(c) is about a 1010 order of magnitude at zero bias, which is much bigger than those reported previously [19, 20]. In particular, in the bias range from −0.7 to −0.3 V and 0.4 to 0.7 V, the MR remains as high as 105 orders of magnitude. Here IFM _ AP and IAFM are the total current in the FM state AP spin configurations and the AFM state, respectively. (3) Negative differential resistance (NDR) effect. The current of the spindown electrons in the FM state AP spin configuration initially increases with the applied bias, when the bias goes higher than 0.65 V, the current drops dramatically, indicating the onset of the NDR effect [21]. The maximum current of the spin-down electrons is up to about 3.36 μA at the peak position (Vbias = 0.65 V), while the current reaches its minimum value (0.53 μA) at the valley site (Vbias = 0.9 V). The above results highlight that the Fe(tzpy)2(NCS)2 molecular
Results and discussion The designed molecular device is displayed in figure 1(a), The molecule is covalently bridged between two 4-ZGNR electrodes, where the number 4 is the number of zigzag carbon chains (ZCCs) along the direction perpendicular to the nanoribbon axis [18], The dangling bond of each edge carbon atom is passivated with a hydrogen atom. As the magnetization of the left and right ZGNR electrodes can be controlled by applying an external magnetic field, the magnetization of the device can be set to parallel (P) or antiparallel (AP) spin 2
L Zhu et al
Nanotechnology 26 (2015) 315201
Figure 1. (a) The model structure of the two-probe system. Purple, orange, blue, grey and white spheres represent iron, sulfur, nitrogen,
carbon and hydrogen atoms, respectively. (b) Spin-resolved band structure for the FM (left panel) and AFM (right panel) state 4-ZGNRs.
junction has multifunctional applications in molecular spintronic devices. To understand the nature of the above observed effects, we plot the spin-polarized zero-bias transmission spectra of the FM state AP spin configuration and the AFM state in figure 3. From figure 3(a) it is clear that the transmission spectra of the spin-up and spin-down electrons display remarkably different behavior around the Fermi level. At zero bias, for the spin-down electrons, one significant transmission peak is located at 0.3 eV, which is mainly contributed by the degenerate spin-down molecular orbital just above the lowest unoccupied molecular orbital (LUMO) (LUMO + 1 and LUMO + 2), which is delocalized over the whole molecular junction, as shown in figure 4(a). The Fe dxy orbital gives considerable contribution. From the projected density of states (PDOS) shown in figure 3(c), it can be found that these molecular orbitals (MOs) mainly come from the spin-down Fe(tzpy)2(NCS)2-electrode hybrid state originating from the coupling between the electrode and Fe’s d atomic orbitals along with the tzpy-ligands. Meanwhile, the transmission coefficient of the spin-up channel is quite small in the wide energy region from −1.0 to 1.0 eV. The distinct difference in transmission spectrum between the two spin channels can be evaluated with SFE. It turns out that the calculated SFE at zero bias is about 100%, indicating that conductance through the molecular junction is mainly governed by the spin-down channel. From figure 3(b), one can see that there is a large
transmission gap at the EF for both the spin-up and spin-down channels of AFM state at low bias, and the gap increases with an increase of bias. Thus the current is prohibited and almost zero at low bias. Just as the bias voltages reach above 0.7 V and below −0.7 V, there are resonance peaks appearing around the Fermi level, then the currents begin to increase rapidly at these biases. Therefore, large values of GMR between the FM state and the AFM state electrodes can be acquired at small biases. The mechanism of NDR can be indicated from bias dependent transmission (figure 3(a)). From figure 3(a), it is clear that the spin-down transmission curves gradually shift toward the low-energy side with applied bias voltage. As the forward bias voltage increases, the transmission peaks above the Fermi level continually approach the Fermi level and some T(E, Vb) enter into the transport window contributing to the integration of current. As a result, the spin-down current continuously increases and reaches its maximum value at Vbias = 0.65 V. When Vbias increases to 0.9 V, the feature of the spin-down transmission function changes dramatically, the transmission peak around the Fermi level is strongly suppressed and even disappears. As a result, in the bias window, the transmission coefficients of the spin-down electrons are very small. Thus, the current decreases, and the I−V valley appears. When Vbias continually increases, the current increases again since another transmission peak appears and enters into the bias window. 3
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Nanotechnology 26 (2015) 315201
Figure 3. (a), (b) The spin polarized transmission spectra for the FM
state AP spin configuration and the AFM state at different biases, respectively. (c) The projected density of states (PDOS) for the Fe (tzpy)2(NCS)2 molecule in the two-probe system at zero bias.
Figure 2. (a), (b) The spin-resolved I−V curves for the FM state AP
spin configuration and the AFM state, respectively. The inset of (a) shows the rectification ration (RR) as a function of the applied bias. (c) The magnetoresistance ratio (MR) as a function of the applied bias. For clarity, the inset is the MR at a smaller scale.
are both delocalized and contribute to the transport, then there is a large transport peak around the Fermi level, leading to the current reaching its maximum. However, at 0.9 V, the LUMO is localized and only HOMO contributes to the transport, leading to the dropping of the transport peak, so NDR appears. Also, the spin diode effect mainly comes from the mismatch of FMO with the energy level of the electrodes. When the positive bias is applied, the energy bands shift downward and upward for the LE and RE, respectively. There are four MOs (HOMO-1, HOMO, LUMO and LUMO + 1) within the bias window at 0.65 V for the spin-down state.
The NDR can be understood from the degree of delocalization of the frontier molecular orbitals (FMOs) displayed in figure 4(a), especially the highest occupied molecular orbital (HOMO) and LUMO, since they are close to the EF. Due to the coupling between molecule and electrodes [22], there is small misalignment between transmission peaks and the molecular projected self-consistent Hamiltonian (MPSH). From the MPSH displayed in figure 4(a), the following features can be found: at 0.65 V, the HOMO and LUMO orbitals 4
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Nanotechnology 26 (2015) 315201
Figure 4. (a) The spatial distribution of the MPSH for the spin-down electrons at different biases. (b), (c) The spin-down band structures of
the left/right electrode and transmission spectra for the FM state AP spin configuration at 0.65 and −0.65 V, respectively.
There is overlap between the HOMO and LUMO orbitals, which are delocalized and contribute to the transport. The energy subbands of LE and RE are also symmetric in the bias window from −0.325 to 0.325 eV, leading to a strong and broad transmission peak in the bias window and making the current reach its maximum. Although there are five MOs (HOMO − 2, HMO − 1, HOMO, LUMO and LUMO + 1) within the bias window at −0.65 V for the spin-down state. As shown in figure 4(a), the HOMO and HOMO-1 orbitals are more delocalized through the molecular junction, which is localized at −0.08 and −0.05 eV, respectively. However, at the energy region from −0.325 to 0.325 eV, which is just the bias window, the subbands of LE and RE are asymmetric, where the spin-down π-subband of LE overlaps with the spindown π*-subband of RE. As a result, there is no spin-down transmission peak within the bias window, the current is very small. Therefore, a spin diode effect is obtained. As we know, when the electrodes are contacted in a different way, current dissipation in the electrodes may lead to different temperatures. Motivated by this, we evaluated whether a spin-polarized thermopower current can affect the integrated spintronic functionalities of this molecular junction. For this purpose, we take a temperature drop ΔT = 10 and −10 K ( ΔT = TL − TR ) between electrodes, and calculate the spin-polarized current Iσ using equation (1) at different temperatures for the FM state AP spin configuration. At zero and very low bias, below a critical bias Vc ≈ k B ΔT , the current is very small, less than 0.01 nA in all of the considered temperature region, the conductance is fully polarized and almost unchanged with the temperature, which can be seen from transmission spectra (figure 5(a)) at different
temperatures of the left electrode at zero bias. When the bias increases, the current contributed from bias increases quickly, which is much larger than that contributed from temperature, then the current induced by temperature gradient can be neglected. Figure 5(b) displays the current as a function of left electrode temperature at 0.65 V for ΔT = ± 10 K. The results show that although the numerical value of the current is slightly affected by the thermal effects, the current polarization is almost unchanged. The change of SFE, GMR and NDR is also negligible, which shows that this molecular junction is a perfect spintronic device and is robust against the thermal effects.
Conclusions In summary, we have carried out first-principles calculation in combination with the NEGF approach to examine the spinpolarized transport of a spin-crossover molecule Fe (tzpy)2(NCS)2 with two 4-ZGNR electrodes. Perfect spinfilter efficiency with almost 100% spin polarization, giant magnetoresistance, spin-rectifying, and negative differential resistance behaviors can be obtained by tuning the external magnetic field. The NDR behavior with the FM state electrode mainly originates from the shifting of molecular orbitals with the energy level of the electrode. The spin diode effect mainly comes from the mismatch of FMO with the energy level of the electrodes. The different conductive properties of ZGNRs in the FM and AFM states lead to a giant magnetoresistance effect with large magnetoresistance ratio. The above results indicate that this spin-crossover molecule can be designed as multifunctional molecular spintronic devices, 5
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Nanotechnology 26 (2015) 315201
11274130, 11274128, 11304107, 11474113 and 61371015, and by the Natural Science Foundation of Hubei Province no. 2014CFB236.
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Figure 5. (a) The transmission spectra at different temperatures of the left electrode at zero bias for the FM state AP spin configuration when ΔT = 10 K. (b) The spin polarized current as a function of the left electrode temperature at 0.65 V for the FM state AP spin configuration when ΔT = ±10 K, respectively.
which can improve the integration density of molecular circuits in the near future. Moreover, the transport properties are robust against thermal effects.
Acknowledgments This work was supported by the National Natural Science Foundation of China under the grant nos. 11374111,
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