Tuning spin transport properties and molecular magnetoresistance through contact geometry Kanchan Ulman, Shobhana Narasimhan, and Anna Delin Citation: The Journal of Chemical Physics 140, 044716 (2014); doi: 10.1063/1.4862546 View online: http://dx.doi.org/10.1063/1.4862546 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Spin-dependent thermoelectronic transport of a single molecule magnet Mn(dmit)2 J. Chem. Phys. 140, 204707 (2014); 10.1063/1.4879056 Spintronic transport of a non-magnetic molecule between magnetic electrodes Appl. Phys. Lett. 103, 233115 (2013); 10.1063/1.4840176 Spin transport properties of single metallocene molecules attached to single-walled carbon nanotubes via nickel adatoms J. Chem. Phys. 134, 244704 (2011); 10.1063/1.3603446 Molecular spin valve and spin filter composed of single-molecule magnets Appl. Phys. Lett. 96, 082115 (2010); 10.1063/1.3319506 Spin-filtering effect in the transport through a single-molecule magnet Mn 12 bridged between metallic electrodes J. Appl. Phys. 105, 07E309 (2009); 10.1063/1.3072789
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THE JOURNAL OF CHEMICAL PHYSICS 140, 044716 (2014)
Tuning spin transport properties and molecular magnetoresistance through contact geometry Kanchan Ulman,1 Shobhana Narasimhan,1,2 and Anna Delin3 1
Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 2 Sheikh Saqr Laboratory, ICMS, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 3 Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology (KTH), SE-16440 Kista, Sweden; Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden; and SeRC (Swedish e-Science Research Center), KTH, SE-10044 Stockholm, Sweden
(Received 4 November 2013; accepted 1 January 2014; published online 31 January 2014) Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green’s function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its “closed” and “open” conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862546] I. INTRODUCTION
Since the miniaturization of conventional semiconductor technology will soon hit its physical limits, the field of molecular electronics has attracted considerable interest.1–7 Here, the electronic components will conceivably consist of single molecules; in addition, the use of the spin degree of freedom can lead to new types of functionalities.8, 9 The typical system studied in molecular electronics consists of a molecule placed between metal leads; for spintronics applications, it is of interest to consider the case where the metal is ferromagnetic.10–12 By studying such systems both experimentally and theoretically, it has been shown that, by a suitable choice of molecules and anchoring groups, it is possible to obtain a large biasdependent magnetoresistance (MR).9, 13 Large values of MR are desirable for applications such as information storage and recording. Molecule-metal interfaces14 and system geometry have been shown to play a vital role in determining the properties of systems relevant to molecule electronics. It has, for example, been shown that the charge transfer and ionization potential of organic thin films can be tuned by varying the orientation of the organic molecules.15, 16 It has also been shown that the symmetry of small molecules affects the accessible conformational fluctuations, and as a result the 0021-9606/2014/140(4)/044716/8/$30.00
measured conductance.7 An extreme example of the influence of molecular conformation on conductance is provided by photoswitching molecules such as dithienylethenes, diarylethenes, and their derivatives,17–25 where the breaking of a C–C bond switches the molecule reversibly between highly conducting and highly resistive conformations. In addition to varying molecular orientations and molecular conformations, another way of changing the system geometry is by varying the shape of the leads, or the way in which the molecule makes contact to the leads. Among the many open questions in the field of molecular spintronics is that of how best to connect molecular components with the outside world. There have been a few previous theoretical studies of how the transport properties of molecular systems are affected by the molecule-lead contact.26–30 In these studies, the authors found that the conductance depended on the contact geometry, by up to an order of magnitude. Break junction and Scanning Tunneling Microscopy (STM) experiments on molecular transport observed either conductance values distributed over a wide range, or peaks at a few values, which was attributed to the presence of a number of different molecule-lead atomic conformations when performing repeated experiments.4, 30, 31 However, none of these previous studies considered magnetic systems. In this work, we examine how the contact geometry affects the properties of spin molecular systems, in particular,
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the magnetoresistance. We show that this property is surprisingly easy to understand, and that the contact geometry plays a crucial role in determining the magnetoresistance. For our study, we choose a dithienylethene (DTE) molecule attached between nickel leads. DTE is a photoswitching molecule that can be reversibly switched between two stable conformations (“closed” and “open”) by shining ultraviolet or visible light (see Figure 1(a)). In the closed conformation, the molecule is a good conductor via resonant transport, while in the open conformation it is a poor conductor via a tunneling mechanism. For our purpose, using DTE is of interest because this permits us to investigate and compare these two different conduction regimes, while retaining the same molecule-lead anchoring configuration. Ni is a socalled strong ferromagnet, i.e., one spin channel in the d-band is completely filled; it has a high degree of spin polarization at the Fermi level EF , which makes it a good choice in order to study spin-polarized transport. DTE belongs to a class of photoswitching molecules that have recently been the focus of much experimental and theoretical investigation. It has been shown that the molecule can be reversibly switched between the highly conducting (closed) and poorly conducting (open) conformations by shining either visible or ultraviolet light.32, 33 This offers the possibility of using such molecules as optical switches. Crystals of some related molecules have even been shown to undergo significant changes in shape upon being exposed to light, and can therefore be used as photo-responsive actuators.34 Experiments on pyridine-terminated DTE molecules attached to gold leads showed that the conductance in the closed conformation was greater than in the open conformation, by at least a factor of 30.25 There have also been a number of theoretical studies of DTE and related molecules attached to Au leads; some of these did not perform a fully self-consistent treatment; however a recent study used methods similar to those utilized in the present work to investigate DTE connected to Au leads.35 The effect of changing the lead material has been examined by us in subsequent studies,36, 37 where we considered DTE attached to Ag and non-spin-polarized as well as spin-polarized Ni leads. While the transport properties were found to be similar for Au and Ag leads, differences were found in the case of Ni leads; these were attributed to the presence of d electrons involved in the transport. II. COMPUTATIONAL METHODS
We have used ab initio spin-polarized density functional theory38 (DFT) as implemented in the SIESTA code39 to calculate the electronic structure and optimized geometries. In these calculations, we have utilized norm conserving, nonlocal pseudopotentials.40 In SIESTA, the electronic wavefunctions are described using a numerical basis set, which is advantageous in reducing the computational time of the calculations due to the localized nature of the basis functions. The numerical basis used consists of a double ζ plus polarization orbital basis set for all the atoms in the molecule, while the atoms in the leads were treated at the level of single ζ orbitals for the d electrons and double ζ orbitals for the s electrons plus a p polarization orbital. The PBE41 form of the gen-
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eralized gradient approximation for the exchange-correlation functional was used. The spin-polarized electronic transport calculations presented here were performed with the SMEAGOL code9, 42, 43 that interfaces the non-equilibrium Green’s function (NEGF) scheme for transport44 with the DFT numerical implementation contained in SIESTA. A typical two terminal transport setup consists of the scattering centre (SC) connected to two semi-infinite metallic leads on the left (L) and the right (R). The metallic leads (L and R) are treated as reservoirs of electrons, each with a chemical potential (μL and μR ), and the effect of an applied bias voltage is to produce a rigid shift in the energy spectrum of the leads. The non-equilibrium Green’s function for the SC is given as G(E, V ) = [E + i0+ − H (V ) − L (E, V ) − R (E, V )]−1 , (1) where H (V ) is the Hamiltonian of the SC (which is a functional of the charge density), V is the applied potential (bias), E is the energy, and α (α = L, R) are the energy- and biasdependent self-energies of the leads. The self energies describe the interaction of the SC with the leads and are essential for establishing the appropriate open boundary conditions of the transport problem. The Green’s functions are calculated via a self-consistent procedure, which also accounts for the effect of the external bias potential on the charge density of the scattering centre. After the convergence of the self-consistent procedure, the transmission function T (E, V ) is calculated using the Landauer-Büttiker formula,45 T (E, V ) = Tr[L (E, V )G(E, V )R (E, V )G† (E, V )], (2) where α (E, V ) = i(α − α† ) is the broadening matrix for lead α. The transmission function is calculated for each spin channel and thus is labeled by a spin index σ . The transmission function of Eq. (2) is integrated over the bias window (EF − eV /2, EF + eV /2) to yield the spin-dependent current: e ∞ σ T (E, V )[f (E − μL ) − f (E − μR )]dE. I σ (V ) = h −∞ (3) In order to compute the magnetoresistance, we calculate the I-V characteristics for two different relative spin orientations of the leads: (i) parallel, and (ii) antiparallel to each other. We note that, recently, wavefunction-based methods have also been used to compute the molecular magnetoresistance.46, 47 III. RESULTS AND DISCUSSION
We study the DTE molecule in both its closed and open conformations, anchored to Ni leads that are either flat (in the Ni(100) geometry) or pointed. In the calculations on DTE anchored to flat leads, the Ni(100) surface was modeled by a slab consisting of five layers of Ni, with 3 × 3 atoms per layer, on each side of the molecule; periodic boundary conditions were used in the perpendicular direction. In the calculations
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FIG. 1. (a) The closed (left) and open (right) conformations of the DTE molecule. (b) Case A: The DTE molecule between flat Ni leads, attached to the hollow site. (c) Case B: DTE between sharp Ni leads. (d) Case C: DTE between flat Ni leads, attached to the atop sites. In (b), (c), and (d), only the closed conformation is depicted. Color code: C – yellow, S – red, H – green, Ni – gray.
on DTE anchored to leads with a pointed tip, a pyramidal Ni apex was placed over a Ni(100) surface (see Figure 1(c)). To explore the effect of the lead geometry on the MR, we perform calculations with two extreme lead geometries, one (Case A) consisting of the flat Ni(100) surface (see Figure 1(b)) and the other (Case B) where the tip of the lead consists of a single atom (see Figure 1(c)). In the flat case, the molecule binds to a hollow site on the Ni(100) surface, whereas in the tip case it binds to an atop site. To verify that changes in MR arise from differences in tip geometry rather than anchoring site, we also perform calculations on a third, intermediate, situation (Case C) where the DTE molecule is attached at the energetically unfavorable atop site on the flat Ni(100) surface (see Figure 1(d)). We consider both closed and open conformations of the DTE molecule in all these three cases. In order to calculate the MR, for each of these geometries, we need to consider two different relative spin orientations of the leads: (i) parallel (↑↑), and (ii) antiparallel (↑↓) to each other. We look at the contribution of the two spin channels to the current in each of the twelve situations thus obtained. The calculations are carried out at bias voltages varying from 0 V to 0.8 V. The geometry of the DTE molecule plays a crucial role in its photoswitching properties. The central sixfold carbon ring is connected on either side to fivefold rings composed of four carbon atoms and one sulfur atom (see Fig. 1(a)). Two more sulfur atoms protrude from these rings,
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which form the anchors that can bind to metal leads. When the molecule changes its conformation from the closed to the open form, one of the C–C bonds in the hexagon is broken, resulting in a change in electronic and transport properties. For example, the energies and charge densities of the frontier molecular orbitals, i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) look very different for the closed and open conformations of the isolated DTE molecule (see Figs. 2 and 3). Note, in particular, that in the closed conformation, the HOMO exhibits a significant charge density between alternate C atoms in the carbon backbone (atoms C1 –C8 ) that connects the two anchoring sulfur atoms S1 and S2 (see Fig. 3(a)). By contrast, for the open conformation, in the HOMO there is significant charge density primarily between alternate carbon atoms in the central carbon ring (see Fig. 3(c)). This already gives us a hint that resonant transport will be possible in the closed conformation but not in the open conformation. Note also that an examination of these figures gives some hints that when the transition between the two conformations occurs, the energy surface of the HOMO/LUMO of the closed conformation will cross over to the LUMO/HOMO of the open conformation, leading to the so-called “conical intersections.”48 When the molecule is connected to the leads, the energy levels both broaden and shift in energy. As an example, we show in Figs. 2(b) and 2(d) the densities of states when the
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FIG. 2. DOS for the (a) closed and (c) open conformations of the DTE molecule. Panels (b)/(d) depict the broadening and energy shift when the closed/open molecule is connected to the hollow site of the flat nickel leads in the ↑↑ (black) and ↑↓ (magenta) spin orientations of the leads.
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(a) Closed HOMO
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(b) Closed LUMO
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(e) FIG. 3. Molecular orbitals for the (a), (b) closed and (c), (d) open conformations of the DTE molecule corresponding to the HOMO and the LUMO, respectively. The charge density corresponding to an isosurface value of 0.005 e/bohr3 is shown in blue. Panel (e) shows, as an example, the charge-density distribution of the orbital responsible for the transport, taken in an energy window of EF ± 0.4 eV, for the closed conformation in the ↑↑ situation for Case B, i.e, when the closed conformation is attached to the sharp tip. The charge density corresponds to an isosurface value of 0.01 e/bohr3 . Color code: C – yellow, S – red, H – green, Ni – gray.
resulting in resonant transport. However, for the open conformation, the PDOS decays exponentially as one goes from the end to the middle of the C-backbone, leading to tunneling transport. Note that the y-axis scales in Figs. 4(a) and 4(b) are different. Our results for the transmission function T (E, V ) are presented in Figures SF1 and SF2 in the supplementary material.49 Figures 5 and 6 show our results for the current I (V ) for the closed and open conformations, respectively. Note that the current is smaller (by about two orders of magnitude) in the latter case, as expected.37 We also note that, in general, the spin polarization of the current becomes most pronounced for the ↑↓ situation, at higher values of V . Previous authors have shown that the conductance through an organic molecule is affected by the interface to
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molecule is connected to the hollow site of the flat Ni leads, in both ↑↑ (black) and ↑↓ spin orientations of the leads. For the closed conformation, the HOMO becomes a broad peak centered at around 0.5 eV below the Fermi level (EF ), while the LUMO becomes another broad peak at around 1.1 eV. The broadening of the HOMO and LUMO is less marked in the case of the open conformation, leading to fairly sharp peaks at around −1.5 eV and 1.2 eV, respectively. A number of previous studies have established that the DTE molecule is a good conductor via resonant transport, in the closed conformation, but becomes a poor conductor, via a tunneling mechanism, in the open conformation. In our case, evidence for this can be obtained by examining the projected density of states (PDOS) on the different atoms in the system. These results are shown in Fig. 4, again using as an example the case of attachment to the hollow site of flat leads, in the ↑↑ spin orientation. It is clearly evident that for the closed conformation, the PDOS in the neighborhood of the Fermi energy varies only slightly as one traverses the C-backbone,
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FIG. 4. Projected density of states over the different carbon atoms along the C-backbone for (a) closed conformation and (b) open conformation of the DTE molecule connected to the hollow site of the flat Ni leads at zero bias in the ↑↑ spin orientation. The PDOS is summed over both the spin channels. See Fig. 1(a) for the convention used to label the C-atoms.
FIG. 5. The I-V characteristics for the closed conformation of DTE between Ni leads. (a) and (b) denote the ↑↑ and ↑↓ situations for Case A, (c) and (d) denote the ↑↑ and ↑↓ situations for Case B, and (e) and (f) denote the ↑↑ and ↑↓ situations for Case C, respectively. The red, blue, and black dots indicate the up-spin, down-spin, and total currents, Iup , Idown , and Itot , respectively. The insets show the degree of spin polarization of the current, defined as (Iup − Idown )/(Itot ).
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Ulman, Narasimhan, and Delin
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Bias Voltage (V) FIG. 6. The I-V characteristics for the open conformation of DTE between Ni leads. (a) and (b) denote the ↑↑ and ↑↓ situations for Case A, (c) and (d) denote the ↑↑ and ↑↓ situations for Case B, and (e) and (f) denote the ↑↑ and ↑↓ situations for Case C, respectively. The red, blue, and black dots indicate the up-spin, down-spin, and total currents, respectively. The insets show the degree of spin polarization of the current.
the leads. For example, it has been shown theoretically that the zero-bias conductance for alkanethiols connected to gold leads is significantly impacted by the atomic arrangement of the leads; in this system, the transport is believed to be primarily due to a non-resonant tunneling process.27 It is interesting to see that in our case, the impact of the attachment to the leads is experienced to a different extent in the resonant transport regime (in the closed conformation of the DTE molecule) and the tunneling transport regime (in the open conformation). This can be seen by examining Iclosed /Iopen , the ratio of the currents in the two conformations. Our results for this ratio, in the various tip geometries and attachment sites, are plotted in Fig. 7. While this ratio is always greater than 1, as expected, we see that the value of this ratio varies considerably depending on the scenario with respect to the leads. When the attachment is to the hollow site on the flat leads, this ratio is quite large, between 80–90 for the ↑↑ spin orientation of the leads, and ∼70 for the ↑↓ orientation. However, when the attachment is to the sharp tip, this ratio drops markedly,
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where I↑↑ and I↑↓ are the currents when the molecule is placed between leads that are spin-polarized parallel or anti-parallel relative to each other, respectively. Our ab initio results for the MR, as a function of applied bias voltage, are shown by the dots and squares in Figure 8. In most cases, the MR is found to have a significant bias dependence. The most striking feature of these results is that in general, the MR is significantly higher, in Case B, where the contacts are made to the sharp tips, than in Case A, where the contacts are made to the flat surfaces. More precisely, the slope of the curve of MR vs. V is greater in Case B than in Case A, which leads to larger magnitudes of MR at most values of V . Interestingly, this is true for both the closed and open conformations of the molecule, i.e., in both resonant transport and tunneling conduction regimes. Upon comparing with the results obtained for Case C, where the contacts are made to atop sites on the flat surfaces, we can conclude that the enhancement in MR arises from the sharpened geometry of the leads, rather than from the change in anchoring sites. The other interesting feature of the graphs plotted in Figure 8 is that the MR becomes negative at higher values of bias. It has been noted by previous authors that this may be
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being 20–50 for ↑↑, and 10–20 for ↑↓. When we check what happens when the molecule is attached to the (energetically unfavorable) atop site on the flat leads, the ratio is again small, suggesting that this effect is primarily a result of the attachment site on the surface, rather than the lead geometry. From Figs. 5 and 6, we see that the currents when the molecule is in the closed conformation are approximately the same in Cases A, B, and C, whereas the currents in the open conformation rise significantly in Cases B and C (when the attachment is to an atop site) compared to Case A (when the attachment is to a hollow site). These results again underline the importance of the contact to the leads in determining transport properties; if one wants a high ratio between the “on” and “off” states of the molecule, it would appear to be best to make contact to the hollow sites on a flat lead. We are now in a position to compute the magnetoresistance, defined by I↑↑ I↑↑ − I↑↓ − 1 × 100, (4) × 100 = MR(%) = I↑↓ I↑↓
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Ulman, Narasimhan, and Delin
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expected to happen in general for molecules placed between ferromagnetic leads.50 However, these authors had speculated that this effect may not be observed for Ni leads because of the relatively small spin splitting in Ni (compared to, e.g., Fe); our results are contrary to this. We would now like to gain some insight into our results for the behavior of the MR. Upon examining how the PDOS for the various atoms in the system varies as a function of applied bias, we find that the most significant change occurs for the two sulfur atoms at the ends of the DTE molecule, which are anchored to the Ni leads. This suggests that it may be possible to formulate an explanation for the behavior of the MR of the entire system by focusing on the PDOS of the end sulfur atoms alone. We now proceed to do this. Our explanation for the behavior of the MR can be understood by looking at Figure 9. For purposes of demonstration, we present here only data for Case A, similar arguments hold for Cases B and C. In this figure, we have plotted the PDOS for the end sulfur atoms, S1 and S2 (shown in red and green, respectively). The graphs on the left-hand side show the PDOS for the ↑↑ orientation, while those on the righthand side show the PDOS for the ↑↓ orientation. We have shown how the PDOS changes, as a function of bias voltage, for the closed (panels (a)–(d)) and open (panels (e)–(h)) conformations. In order to facilitate interpretation, we have also shown a schematic model PDOS, with semi-circular densities of states, at the bottom (panels (i)–(l)), and we refer to this in giving our explanation. The PDOS over S1 and S2 is spinsplit due to coupling with the magnetic leads. At V = 0, in the ↑↑ situation, the PDOS over S1 and S2 is identical, as is shown schematically in Figure 9(i) (see also Figures 9(a) and 9(e)), whereas in the ↑↓ case they are spin-reversed, so that the PDOS is as shown in Figure 9(j) (see also Figures 9(b) and 9(f)). A large PDOS for both the ends, within the bias window, is favorable for better conductance, whereas a larger mismatch in the PDOS will reduce the conductance, since the introduction of a mismatch in the PDOS will inhibit resonant transport. Now, when a bias is applied, the PDOS for S1 shifts to higher energies, while that for S2 shifts to lower energies. For the ↑↑ situation, this leads to an increasing mismatch between the PDOS of the left and right contacts as the bias is increased; this situation is depicted schematically in Figure 9(k) (and with actual data in Figures 9(c) and 9(g)); while for the ↑↓ situation it leads to a better match in one of the spin channels, as is shown in Figure 9(l) (see also Figures 9(d) and 9(h)). This explains the increasing spin polarization at higher V in the ↑↓ situation, since the conductance, in the spin channel where the PDOS starts matching, increases. Thus, for example, we see from Figs. 9(a) and 9(c), that as the bias is increased, the conductance will decrease for the ↑↑ situation for the closed molecule, because we have gone from a situation where the PDOS of the left and right sulfur atoms (the red and green curves) overlapped, to one where there is almost no overlap between them, within the bias window. If we look instead at the ↑↓ situation (see Figs. 9(b) and 9(d)), we see that we go from a scenario where there is no overlap between the red and green curves, i.e., the PDOS of the left and right S atoms, and therefore low conductance, to one where we have almost total overlap, and a high PDOS, in
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0.5
1
E-EF(eV)
Open (j)
Majority Bias Voltage
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(l)
Cartoon FIG. 9. Understanding the bias dependence of the magnetoresistance through the behavior of the PDOS on the anchoring molecules: a molecule (depicted as a hexagon) is anchored to spin-polarized leads through two sulfur atoms S1 and S2 (colored red and green). The panels on the left show the situation when the leads are spin-polarized parallel to each other (↑↑), and the three on the right when they are polarized anti-parallel (↑↓). (a)–(d) show the PDOS for the closed conformation, Case A, and (e)–(h) show the PDOS for the open conformation, Case A; and (i)–(l) are schematic depictions of a cartoon of the general behavior of the PDOS, to aid understanding. The red and green curves correspond to the PDOS on S1 and S2 , respectively. The vertical dashed lines indicate the bias window.
the majority spin channel, within the bias window. This leads to both the greater spin polarization and the higher conductance. It also explains the negative MR at higher V , since at high bias voltages, I↑↓ becomes larger than I↑↑ . We now proceed to put our model on a more quantitative footing. We first calculate ρσSi (E, V = 0), the PDOS on the anchoring sulfur atom Si (i = 1, 2), at V = 0, from our
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ab initio DFT calculations. σ is a spin index that runs over “up” and “down.” Within our model, we assume that the only effect of a bias voltage V on the PDOS is to cause a rigid shift:
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ρσSi (E, V ) ≈ ρ˜σSi (E, V ) = ρσSi (E ± V /2, 0), where the + and − signs are for i = 1 and 2, respectively. It follows from our model, and Eq. (4), that the MR can then be estimated by
S1 S2 S1 S2 ρ˜up (E, V ) · ρ˜up (E, V ) + ρ˜down (E, V ) · ρ˜down (E, V ) dE − 1 × 100. MR(%) = S1 S2 S1 S2 ρ˜up (E, V ) · ρ˜down (E, V ) + ρ˜down (E, V ) · ρ˜up (E, V ) dE
The approximate values of MR, as estimated from Eq. (5), are plotted as the solid lines in Figure 8. Upon comparing with the more accurate results obtained from the self-consistent NEGF calculations, we see that the model performs remarkably well, given its very simple nature. In particular, it succeeds in capturing the main features of our more exact results, viz., (i) the larger value of MR for the sharp tip (Case B) than for the flat surface (Case A), and (ii) the transition from positive MR to negative MR as the bias is increased. This suggests that the MR is mainly governed by the electronic structure of the anchoring atoms as expressed by their projected DOS at zero bias, given the spin polarization in the contact material. In turn, since the electronic structure of the anchoring atoms is sensitively dependent on the contact geometry, our main conclusions follow. The enhancement in MR in the tip case can thus be traced back to the presence of peaks in the PDOS of S1 and S2 (see Figure SF3 in the supplementary material49 ), e.g., in the closed conformation, there is a peak at the Fermi energy in the up-spin PDOS of both S1 and S2 , in the ↑↑ situation in Case B, due to hybridization between the p states of sulfur and d states of nickel. IV. CONCLUSIONS
To summarize, we have carried out ab initio DFT and NEGF transport calculations on a system consisting of a DTE molecule placed between spin-polarized Ni leads. Our results underline the importance of the molecule-metal interface in determining the properties of molecular spintronic systems. Our findings show that precisely tailored transport properties will require atomic-scale precision in the contact geometry; however this is typically difficult to control experimentally. The magnitude of the magnetoresistance shows a significantly enhanced value, at most bias voltages, for the case where the molecule is anchored to a sharp metal tip rather than a flat metal surface. We also observe a transition from positive to negative magnetoresistance as the bias voltage is increased. In addition, we find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations also depends on the geometry of the leads. Our results are surprisingly simple to understand – our NEGF-level results for the behavior of magnetoresistance as a function of voltage can be reproduced not just qualitatively,
(5)
but also to a large extent quantitatively, by a simple model which requires as its input only the projected density of states on the anchoring atoms of the molecule, calculated at zero bias. Estimates using this model can be obtained at significantly lower computational cost than that required when invoking the full machinery of the bias-dependent NEGF calculation. Importantly, our model is seen to hold for both the resonant transport and tunneling conducting regimes.
ACKNOWLEDGMENTS
This work was sponsored by the Swedish Research Links program of the Swedish Research Council, the Royal Swedish Academy of Sciences (KVA), the Knut and Alice Wallenberg foundation (KAW), the CSIR, India, and the DST, Nanomission, India. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at High Performance Computing Center North (HPC2N). We thank Ivan Rungger for helpful suggestions. 1 A.
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THE JOURNAL OF CHEMICAL PHYSICS 140, 044716 (2014)
Tuning spin transport properties and molecular magnetoresistance through contact geometry Kanchan Ulman,1 Shobhana Narasimhan,1,2 and Anna Delin3 1
Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 2 Sheikh Saqr Laboratory, ICMS, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 3 Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology (KTH), SE-16440 Kista, Sweden; Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden; and SeRC (Swedish e-Science Research Center), KTH, SE-10044 Stockholm, Sweden
(Received 4 November 2013; accepted 1 January 2014; published online 31 January 2014) Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green’s function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its “closed” and “open” conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862546] I. INTRODUCTION
Since the miniaturization of conventional semiconductor technology will soon hit its physical limits, the field of molecular electronics has attracted considerable interest.1–7 Here, the electronic components will conceivably consist of single molecules; in addition, the use of the spin degree of freedom can lead to new types of functionalities.8, 9 The typical system studied in molecular electronics consists of a molecule placed between metal leads; for spintronics applications, it is of interest to consider the case where the metal is ferromagnetic.10–12 By studying such systems both experimentally and theoretically, it has been shown that, by a suitable choice of molecules and anchoring groups, it is possible to obtain a large biasdependent magnetoresistance (MR).9, 13 Large values of MR are desirable for applications such as information storage and recording. Molecule-metal interfaces14 and system geometry have been shown to play a vital role in determining the properties of systems relevant to molecule electronics. It has, for example, been shown that the charge transfer and ionization potential of organic thin films can be tuned by varying the orientation of the organic molecules.15, 16 It has also been shown that the symmetry of small molecules affects the accessible conformational fluctuations, and as a result the 0021-9606/2014/140(4)/044716/8/$30.00
measured conductance.7 An extreme example of the influence of molecular conformation on conductance is provided by photoswitching molecules such as dithienylethenes, diarylethenes, and their derivatives,17–25 where the breaking of a C–C bond switches the molecule reversibly between highly conducting and highly resistive conformations. In addition to varying molecular orientations and molecular conformations, another way of changing the system geometry is by varying the shape of the leads, or the way in which the molecule makes contact to the leads. Among the many open questions in the field of molecular spintronics is that of how best to connect molecular components with the outside world. There have been a few previous theoretical studies of how the transport properties of molecular systems are affected by the molecule-lead contact.26–30 In these studies, the authors found that the conductance depended on the contact geometry, by up to an order of magnitude. Break junction and Scanning Tunneling Microscopy (STM) experiments on molecular transport observed either conductance values distributed over a wide range, or peaks at a few values, which was attributed to the presence of a number of different molecule-lead atomic conformations when performing repeated experiments.4, 30, 31 However, none of these previous studies considered magnetic systems. In this work, we examine how the contact geometry affects the properties of spin molecular systems, in particular,
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the magnetoresistance. We show that this property is surprisingly easy to understand, and that the contact geometry plays a crucial role in determining the magnetoresistance. For our study, we choose a dithienylethene (DTE) molecule attached between nickel leads. DTE is a photoswitching molecule that can be reversibly switched between two stable conformations (“closed” and “open”) by shining ultraviolet or visible light (see Figure 1(a)). In the closed conformation, the molecule is a good conductor via resonant transport, while in the open conformation it is a poor conductor via a tunneling mechanism. For our purpose, using DTE is of interest because this permits us to investigate and compare these two different conduction regimes, while retaining the same molecule-lead anchoring configuration. Ni is a socalled strong ferromagnet, i.e., one spin channel in the d-band is completely filled; it has a high degree of spin polarization at the Fermi level EF , which makes it a good choice in order to study spin-polarized transport. DTE belongs to a class of photoswitching molecules that have recently been the focus of much experimental and theoretical investigation. It has been shown that the molecule can be reversibly switched between the highly conducting (closed) and poorly conducting (open) conformations by shining either visible or ultraviolet light.32, 33 This offers the possibility of using such molecules as optical switches. Crystals of some related molecules have even been shown to undergo significant changes in shape upon being exposed to light, and can therefore be used as photo-responsive actuators.34 Experiments on pyridine-terminated DTE molecules attached to gold leads showed that the conductance in the closed conformation was greater than in the open conformation, by at least a factor of 30.25 There have also been a number of theoretical studies of DTE and related molecules attached to Au leads; some of these did not perform a fully self-consistent treatment; however a recent study used methods similar to those utilized in the present work to investigate DTE connected to Au leads.35 The effect of changing the lead material has been examined by us in subsequent studies,36, 37 where we considered DTE attached to Ag and non-spin-polarized as well as spin-polarized Ni leads. While the transport properties were found to be similar for Au and Ag leads, differences were found in the case of Ni leads; these were attributed to the presence of d electrons involved in the transport. II. COMPUTATIONAL METHODS
We have used ab initio spin-polarized density functional theory38 (DFT) as implemented in the SIESTA code39 to calculate the electronic structure and optimized geometries. In these calculations, we have utilized norm conserving, nonlocal pseudopotentials.40 In SIESTA, the electronic wavefunctions are described using a numerical basis set, which is advantageous in reducing the computational time of the calculations due to the localized nature of the basis functions. The numerical basis used consists of a double ζ plus polarization orbital basis set for all the atoms in the molecule, while the atoms in the leads were treated at the level of single ζ orbitals for the d electrons and double ζ orbitals for the s electrons plus a p polarization orbital. The PBE41 form of the gen-
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eralized gradient approximation for the exchange-correlation functional was used. The spin-polarized electronic transport calculations presented here were performed with the SMEAGOL code9, 42, 43 that interfaces the non-equilibrium Green’s function (NEGF) scheme for transport44 with the DFT numerical implementation contained in SIESTA. A typical two terminal transport setup consists of the scattering centre (SC) connected to two semi-infinite metallic leads on the left (L) and the right (R). The metallic leads (L and R) are treated as reservoirs of electrons, each with a chemical potential (μL and μR ), and the effect of an applied bias voltage is to produce a rigid shift in the energy spectrum of the leads. The non-equilibrium Green’s function for the SC is given as G(E, V ) = [E + i0+ − H (V ) − L (E, V ) − R (E, V )]−1 , (1) where H (V ) is the Hamiltonian of the SC (which is a functional of the charge density), V is the applied potential (bias), E is the energy, and α (α = L, R) are the energy- and biasdependent self-energies of the leads. The self energies describe the interaction of the SC with the leads and are essential for establishing the appropriate open boundary conditions of the transport problem. The Green’s functions are calculated via a self-consistent procedure, which also accounts for the effect of the external bias potential on the charge density of the scattering centre. After the convergence of the self-consistent procedure, the transmission function T (E, V ) is calculated using the Landauer-Büttiker formula,45 T (E, V ) = Tr[L (E, V )G(E, V )R (E, V )G† (E, V )], (2) where α (E, V ) = i(α − α† ) is the broadening matrix for lead α. The transmission function is calculated for each spin channel and thus is labeled by a spin index σ . The transmission function of Eq. (2) is integrated over the bias window (EF − eV /2, EF + eV /2) to yield the spin-dependent current: e ∞ σ T (E, V )[f (E − μL ) − f (E − μR )]dE. I σ (V ) = h −∞ (3) In order to compute the magnetoresistance, we calculate the I-V characteristics for two different relative spin orientations of the leads: (i) parallel, and (ii) antiparallel to each other. We note that, recently, wavefunction-based methods have also been used to compute the molecular magnetoresistance.46, 47 III. RESULTS AND DISCUSSION
We study the DTE molecule in both its closed and open conformations, anchored to Ni leads that are either flat (in the Ni(100) geometry) or pointed. In the calculations on DTE anchored to flat leads, the Ni(100) surface was modeled by a slab consisting of five layers of Ni, with 3 × 3 atoms per layer, on each side of the molecule; periodic boundary conditions were used in the perpendicular direction. In the calculations
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Visible Light
C4 C2 C3
C1 UV Light
C9
S1
C5 C6
C10
C7 C8
S2
(a)
(b)
(c)
(d)
FIG. 1. (a) The closed (left) and open (right) conformations of the DTE molecule. (b) Case A: The DTE molecule between flat Ni leads, attached to the hollow site. (c) Case B: DTE between sharp Ni leads. (d) Case C: DTE between flat Ni leads, attached to the atop sites. In (b), (c), and (d), only the closed conformation is depicted. Color code: C – yellow, S – red, H – green, Ni – gray.
on DTE anchored to leads with a pointed tip, a pyramidal Ni apex was placed over a Ni(100) surface (see Figure 1(c)). To explore the effect of the lead geometry on the MR, we perform calculations with two extreme lead geometries, one (Case A) consisting of the flat Ni(100) surface (see Figure 1(b)) and the other (Case B) where the tip of the lead consists of a single atom (see Figure 1(c)). In the flat case, the molecule binds to a hollow site on the Ni(100) surface, whereas in the tip case it binds to an atop site. To verify that changes in MR arise from differences in tip geometry rather than anchoring site, we also perform calculations on a third, intermediate, situation (Case C) where the DTE molecule is attached at the energetically unfavorable atop site on the flat Ni(100) surface (see Figure 1(d)). We consider both closed and open conformations of the DTE molecule in all these three cases. In order to calculate the MR, for each of these geometries, we need to consider two different relative spin orientations of the leads: (i) parallel (↑↑), and (ii) antiparallel (↑↓) to each other. We look at the contribution of the two spin channels to the current in each of the twelve situations thus obtained. The calculations are carried out at bias voltages varying from 0 V to 0.8 V. The geometry of the DTE molecule plays a crucial role in its photoswitching properties. The central sixfold carbon ring is connected on either side to fivefold rings composed of four carbon atoms and one sulfur atom (see Fig. 1(a)). Two more sulfur atoms protrude from these rings,
(b)
-3
-2
(c)
DOS (arbitrary units)
DOS (arbitrary units)
(a)
which form the anchors that can bind to metal leads. When the molecule changes its conformation from the closed to the open form, one of the C–C bonds in the hexagon is broken, resulting in a change in electronic and transport properties. For example, the energies and charge densities of the frontier molecular orbitals, i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) look very different for the closed and open conformations of the isolated DTE molecule (see Figs. 2 and 3). Note, in particular, that in the closed conformation, the HOMO exhibits a significant charge density between alternate C atoms in the carbon backbone (atoms C1 –C8 ) that connects the two anchoring sulfur atoms S1 and S2 (see Fig. 3(a)). By contrast, for the open conformation, in the HOMO there is significant charge density primarily between alternate carbon atoms in the central carbon ring (see Fig. 3(c)). This already gives us a hint that resonant transport will be possible in the closed conformation but not in the open conformation. Note also that an examination of these figures gives some hints that when the transition between the two conformations occurs, the energy surface of the HOMO/LUMO of the closed conformation will cross over to the LUMO/HOMO of the open conformation, leading to the so-called “conical intersections.”48 When the molecule is connected to the leads, the energy levels both broaden and shift in energy. As an example, we show in Figs. 2(b) and 2(d) the densities of states when the
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FIG. 2. DOS for the (a) closed and (c) open conformations of the DTE molecule. Panels (b)/(d) depict the broadening and energy shift when the closed/open molecule is connected to the hollow site of the flat nickel leads in the ↑↑ (black) and ↑↓ (magenta) spin orientations of the leads.
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(a) Closed HOMO
J. Chem. Phys. 140, 044716 (2014)
(b) Closed LUMO
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(e) FIG. 3. Molecular orbitals for the (a), (b) closed and (c), (d) open conformations of the DTE molecule corresponding to the HOMO and the LUMO, respectively. The charge density corresponding to an isosurface value of 0.005 e/bohr3 is shown in blue. Panel (e) shows, as an example, the charge-density distribution of the orbital responsible for the transport, taken in an energy window of EF ± 0.4 eV, for the closed conformation in the ↑↑ situation for Case B, i.e, when the closed conformation is attached to the sharp tip. The charge density corresponds to an isosurface value of 0.01 e/bohr3 . Color code: C – yellow, S – red, H – green, Ni – gray.
resulting in resonant transport. However, for the open conformation, the PDOS decays exponentially as one goes from the end to the middle of the C-backbone, leading to tunneling transport. Note that the y-axis scales in Figs. 4(a) and 4(b) are different. Our results for the transmission function T (E, V ) are presented in Figures SF1 and SF2 in the supplementary material.49 Figures 5 and 6 show our results for the current I (V ) for the closed and open conformations, respectively. Note that the current is smaller (by about two orders of magnitude) in the latter case, as expected.37 We also note that, in general, the spin polarization of the current becomes most pronounced for the ↑↓ situation, at higher values of V . Previous authors have shown that the conductance through an organic molecule is affected by the interface to
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molecule is connected to the hollow site of the flat Ni leads, in both ↑↑ (black) and ↑↓ spin orientations of the leads. For the closed conformation, the HOMO becomes a broad peak centered at around 0.5 eV below the Fermi level (EF ), while the LUMO becomes another broad peak at around 1.1 eV. The broadening of the HOMO and LUMO is less marked in the case of the open conformation, leading to fairly sharp peaks at around −1.5 eV and 1.2 eV, respectively. A number of previous studies have established that the DTE molecule is a good conductor via resonant transport, in the closed conformation, but becomes a poor conductor, via a tunneling mechanism, in the open conformation. In our case, evidence for this can be obtained by examining the projected density of states (PDOS) on the different atoms in the system. These results are shown in Fig. 4, again using as an example the case of attachment to the hollow site of flat leads, in the ↑↑ spin orientation. It is clearly evident that for the closed conformation, the PDOS in the neighborhood of the Fermi energy varies only slightly as one traverses the C-backbone,
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FIG. 4. Projected density of states over the different carbon atoms along the C-backbone for (a) closed conformation and (b) open conformation of the DTE molecule connected to the hollow site of the flat Ni leads at zero bias in the ↑↑ spin orientation. The PDOS is summed over both the spin channels. See Fig. 1(a) for the convention used to label the C-atoms.
FIG. 5. The I-V characteristics for the closed conformation of DTE between Ni leads. (a) and (b) denote the ↑↑ and ↑↓ situations for Case A, (c) and (d) denote the ↑↑ and ↑↓ situations for Case B, and (e) and (f) denote the ↑↑ and ↑↓ situations for Case C, respectively. The red, blue, and black dots indicate the up-spin, down-spin, and total currents, Iup , Idown , and Itot , respectively. The insets show the degree of spin polarization of the current, defined as (Iup − Idown )/(Itot ).
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Ulman, Narasimhan, and Delin
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J. Chem. Phys. 140, 044716 (2014)
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Bias Voltage (V) FIG. 6. The I-V characteristics for the open conformation of DTE between Ni leads. (a) and (b) denote the ↑↑ and ↑↓ situations for Case A, (c) and (d) denote the ↑↑ and ↑↓ situations for Case B, and (e) and (f) denote the ↑↑ and ↑↓ situations for Case C, respectively. The red, blue, and black dots indicate the up-spin, down-spin, and total currents, respectively. The insets show the degree of spin polarization of the current.
the leads. For example, it has been shown theoretically that the zero-bias conductance for alkanethiols connected to gold leads is significantly impacted by the atomic arrangement of the leads; in this system, the transport is believed to be primarily due to a non-resonant tunneling process.27 It is interesting to see that in our case, the impact of the attachment to the leads is experienced to a different extent in the resonant transport regime (in the closed conformation of the DTE molecule) and the tunneling transport regime (in the open conformation). This can be seen by examining Iclosed /Iopen , the ratio of the currents in the two conformations. Our results for this ratio, in the various tip geometries and attachment sites, are plotted in Fig. 7. While this ratio is always greater than 1, as expected, we see that the value of this ratio varies considerably depending on the scenario with respect to the leads. When the attachment is to the hollow site on the flat leads, this ratio is quite large, between 80–90 for the ↑↑ spin orientation of the leads, and ∼70 for the ↑↓ orientation. However, when the attachment is to the sharp tip, this ratio drops markedly,
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where I↑↑ and I↑↓ are the currents when the molecule is placed between leads that are spin-polarized parallel or anti-parallel relative to each other, respectively. Our ab initio results for the MR, as a function of applied bias voltage, are shown by the dots and squares in Figure 8. In most cases, the MR is found to have a significant bias dependence. The most striking feature of these results is that in general, the MR is significantly higher, in Case B, where the contacts are made to the sharp tips, than in Case A, where the contacts are made to the flat surfaces. More precisely, the slope of the curve of MR vs. V is greater in Case B than in Case A, which leads to larger magnitudes of MR at most values of V . Interestingly, this is true for both the closed and open conformations of the molecule, i.e., in both resonant transport and tunneling conduction regimes. Upon comparing with the results obtained for Case C, where the contacts are made to atop sites on the flat surfaces, we can conclude that the enhancement in MR arises from the sharpened geometry of the leads, rather than from the change in anchoring sites. The other interesting feature of the graphs plotted in Figure 8 is that the MR becomes negative at higher values of bias. It has been noted by previous authors that this may be
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being 20–50 for ↑↑, and 10–20 for ↑↓. When we check what happens when the molecule is attached to the (energetically unfavorable) atop site on the flat leads, the ratio is again small, suggesting that this effect is primarily a result of the attachment site on the surface, rather than the lead geometry. From Figs. 5 and 6, we see that the currents when the molecule is in the closed conformation are approximately the same in Cases A, B, and C, whereas the currents in the open conformation rise significantly in Cases B and C (when the attachment is to an atop site) compared to Case A (when the attachment is to a hollow site). These results again underline the importance of the contact to the leads in determining transport properties; if one wants a high ratio between the “on” and “off” states of the molecule, it would appear to be best to make contact to the hollow sites on a flat lead. We are now in a position to compute the magnetoresistance, defined by I↑↑ I↑↑ − I↑↓ − 1 × 100, (4) × 100 = MR(%) = I↑↓ I↑↓
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Bias Voltage (V) FIG. 7. The ratio of the current for the closed and the open molecule Iclosed /Iopen for (a) ↑↑ and (b) ↑↓ situations, for Case A (black circles), Case B (red squares), and Case C (green triangles), respectively.
Closed Open Model
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Ulman, Narasimhan, and Delin
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expected to happen in general for molecules placed between ferromagnetic leads.50 However, these authors had speculated that this effect may not be observed for Ni leads because of the relatively small spin splitting in Ni (compared to, e.g., Fe); our results are contrary to this. We would now like to gain some insight into our results for the behavior of the MR. Upon examining how the PDOS for the various atoms in the system varies as a function of applied bias, we find that the most significant change occurs for the two sulfur atoms at the ends of the DTE molecule, which are anchored to the Ni leads. This suggests that it may be possible to formulate an explanation for the behavior of the MR of the entire system by focusing on the PDOS of the end sulfur atoms alone. We now proceed to do this. Our explanation for the behavior of the MR can be understood by looking at Figure 9. For purposes of demonstration, we present here only data for Case A, similar arguments hold for Cases B and C. In this figure, we have plotted the PDOS for the end sulfur atoms, S1 and S2 (shown in red and green, respectively). The graphs on the left-hand side show the PDOS for the ↑↑ orientation, while those on the righthand side show the PDOS for the ↑↓ orientation. We have shown how the PDOS changes, as a function of bias voltage, for the closed (panels (a)–(d)) and open (panels (e)–(h)) conformations. In order to facilitate interpretation, we have also shown a schematic model PDOS, with semi-circular densities of states, at the bottom (panels (i)–(l)), and we refer to this in giving our explanation. The PDOS over S1 and S2 is spinsplit due to coupling with the magnetic leads. At V = 0, in the ↑↑ situation, the PDOS over S1 and S2 is identical, as is shown schematically in Figure 9(i) (see also Figures 9(a) and 9(e)), whereas in the ↑↓ case they are spin-reversed, so that the PDOS is as shown in Figure 9(j) (see also Figures 9(b) and 9(f)). A large PDOS for both the ends, within the bias window, is favorable for better conductance, whereas a larger mismatch in the PDOS will reduce the conductance, since the introduction of a mismatch in the PDOS will inhibit resonant transport. Now, when a bias is applied, the PDOS for S1 shifts to higher energies, while that for S2 shifts to lower energies. For the ↑↑ situation, this leads to an increasing mismatch between the PDOS of the left and right contacts as the bias is increased; this situation is depicted schematically in Figure 9(k) (and with actual data in Figures 9(c) and 9(g)); while for the ↑↓ situation it leads to a better match in one of the spin channels, as is shown in Figure 9(l) (see also Figures 9(d) and 9(h)). This explains the increasing spin polarization at higher V in the ↑↓ situation, since the conductance, in the spin channel where the PDOS starts matching, increases. Thus, for example, we see from Figs. 9(a) and 9(c), that as the bias is increased, the conductance will decrease for the ↑↑ situation for the closed molecule, because we have gone from a situation where the PDOS of the left and right sulfur atoms (the red and green curves) overlapped, to one where there is almost no overlap between them, within the bias window. If we look instead at the ↑↓ situation (see Figs. 9(b) and 9(d)), we see that we go from a scenario where there is no overlap between the red and green curves, i.e., the PDOS of the left and right S atoms, and therefore low conductance, to one where we have almost total overlap, and a high PDOS, in
J. Chem. Phys. 140, 044716 (2014)
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Cartoon FIG. 9. Understanding the bias dependence of the magnetoresistance through the behavior of the PDOS on the anchoring molecules: a molecule (depicted as a hexagon) is anchored to spin-polarized leads through two sulfur atoms S1 and S2 (colored red and green). The panels on the left show the situation when the leads are spin-polarized parallel to each other (↑↑), and the three on the right when they are polarized anti-parallel (↑↓). (a)–(d) show the PDOS for the closed conformation, Case A, and (e)–(h) show the PDOS for the open conformation, Case A; and (i)–(l) are schematic depictions of a cartoon of the general behavior of the PDOS, to aid understanding. The red and green curves correspond to the PDOS on S1 and S2 , respectively. The vertical dashed lines indicate the bias window.
the majority spin channel, within the bias window. This leads to both the greater spin polarization and the higher conductance. It also explains the negative MR at higher V , since at high bias voltages, I↑↓ becomes larger than I↑↑ . We now proceed to put our model on a more quantitative footing. We first calculate ρσSi (E, V = 0), the PDOS on the anchoring sulfur atom Si (i = 1, 2), at V = 0, from our
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ab initio DFT calculations. σ is a spin index that runs over “up” and “down.” Within our model, we assume that the only effect of a bias voltage V on the PDOS is to cause a rigid shift:
J. Chem. Phys. 140, 044716 (2014)
ρσSi (E, V ) ≈ ρ˜σSi (E, V ) = ρσSi (E ± V /2, 0), where the + and − signs are for i = 1 and 2, respectively. It follows from our model, and Eq. (4), that the MR can then be estimated by
S1 S2 S1 S2 ρ˜up (E, V ) · ρ˜up (E, V ) + ρ˜down (E, V ) · ρ˜down (E, V ) dE − 1 × 100. MR(%) = S1 S2 S1 S2 ρ˜up (E, V ) · ρ˜down (E, V ) + ρ˜down (E, V ) · ρ˜up (E, V ) dE
The approximate values of MR, as estimated from Eq. (5), are plotted as the solid lines in Figure 8. Upon comparing with the more accurate results obtained from the self-consistent NEGF calculations, we see that the model performs remarkably well, given its very simple nature. In particular, it succeeds in capturing the main features of our more exact results, viz., (i) the larger value of MR for the sharp tip (Case B) than for the flat surface (Case A), and (ii) the transition from positive MR to negative MR as the bias is increased. This suggests that the MR is mainly governed by the electronic structure of the anchoring atoms as expressed by their projected DOS at zero bias, given the spin polarization in the contact material. In turn, since the electronic structure of the anchoring atoms is sensitively dependent on the contact geometry, our main conclusions follow. The enhancement in MR in the tip case can thus be traced back to the presence of peaks in the PDOS of S1 and S2 (see Figure SF3 in the supplementary material49 ), e.g., in the closed conformation, there is a peak at the Fermi energy in the up-spin PDOS of both S1 and S2 , in the ↑↑ situation in Case B, due to hybridization between the p states of sulfur and d states of nickel. IV. CONCLUSIONS
To summarize, we have carried out ab initio DFT and NEGF transport calculations on a system consisting of a DTE molecule placed between spin-polarized Ni leads. Our results underline the importance of the molecule-metal interface in determining the properties of molecular spintronic systems. Our findings show that precisely tailored transport properties will require atomic-scale precision in the contact geometry; however this is typically difficult to control experimentally. The magnitude of the magnetoresistance shows a significantly enhanced value, at most bias voltages, for the case where the molecule is anchored to a sharp metal tip rather than a flat metal surface. We also observe a transition from positive to negative magnetoresistance as the bias voltage is increased. In addition, we find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations also depends on the geometry of the leads. Our results are surprisingly simple to understand – our NEGF-level results for the behavior of magnetoresistance as a function of voltage can be reproduced not just qualitatively,
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but also to a large extent quantitatively, by a simple model which requires as its input only the projected density of states on the anchoring atoms of the molecule, calculated at zero bias. Estimates using this model can be obtained at significantly lower computational cost than that required when invoking the full machinery of the bias-dependent NEGF calculation. Importantly, our model is seen to hold for both the resonant transport and tunneling conducting regimes.
ACKNOWLEDGMENTS
This work was sponsored by the Swedish Research Links program of the Swedish Research Council, the Royal Swedish Academy of Sciences (KVA), the Knut and Alice Wallenberg foundation (KAW), the CSIR, India, and the DST, Nanomission, India. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at High Performance Computing Center North (HPC2N). We thank Ivan Rungger for helpful suggestions. 1 A.
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