Magnetoresistance through a single molecule
The use of single molecules to design electronic devices is an extremely challenging and fundamentally different approach to further downsizing electronic circuits. Two-terminal molecular devices such as diodes were first predicted Aviram1974 () and, more recently, measured experimentally Elbing2005 (). The addition of a gate then enabled the study of molecular transistors McEuen (); Delft (); Natelson05 (). In general terms, in order to increase data processing capabilities, one may not only consider the electron’s charge but also its spin Wolf2001 (); Zutic2004 (). This concept has been pioneered in giant magnetoresistance (GMR) junctions that consist of thin metallic films Baibich1988 (); Binasch1989 (). Spin transport across molecules, i. e. Molecular Spintronics remains, however, a challenging endeavor. As an important first step in this field, we have performed an experimental and theoretical study on spin transport across a molecular GMR junction consisting of two ferromagnetic electrodes bridged by a single hydrogen phthalocyanine (HPc) molecule. We observe that even though HPc in itself is nonmagnetic, incorporating it into a molecular junction can enhance the magnetoresistance by one order of magnitude to 52%.
Scanning Tunneling Microscopy (STM) has proven to be a powerful and versatile tool for studying electron transport properties of single molecules, be it by continually addressing individual molecules on a one by one level Joachim1995 (); Haiss2006 (); Neel2007 (); Takacs2008 (), or in an automated break junction protocol Venkataraman06 (); Wandlowski2007 (). In this work, we introduce spin-polarized STM (Sp-STM) to measure the magnetoresistance of single molecules, employing spin-polarized electrodes. Experiments were carried out in a home-built STM working in ultra high vacuum at 4 K Balashov2006 () on individual HPc molecules (CHN) sandwiched between Co-coated W tips and ferromagnetic Co nano-islands on Cu(111) single crystals.
In Fig. 1 we present the STM topography of the sample after depositing HPc molecules, that identify themselves by their four aromatic isoindole (BzPy) side groups Lippel1989 (); Takacs2008 (). We note that the Co nano-islands exhibit a spontaneous out-of-plane magnetization due to a strong surface anisotropy Pietzsch2004 (). By using Co-coated tips (10 monolayers) with an out-of-plane magnetization, we can use the Sp-STM technique’s sensitivity to the spin-polarized density of states Tersoff1985 () to determine the relative orientation (parallel:P or antiparallel:AP) of the magnetization of individual islands relative to that of the tip. Fig. 1b shows the differential conductance (d/d) curves measured atop two islands with P and AP alignments with respect to the tip. Particularly large differences in the spectra are found at -350 meV, which corresponds to the surface state of Co Diekhoener2003 (). This difference allows us to detect the local magnetization direction of Co islands by recording maps of the local differential conductance at this bias voltage (see Fig. 1a). The differential tunneling magnetoresistance (differential TMR), defined as the difference in conductance divided by the smaller conductance of the tunneling junction formed by the tip and sample, is strongly energy-dependent as depicted in Fig. 1c. We note here that the differential TMR for this Co/vacuum/Co junction is only 5 % at low bias voltage.
To contact single molecules, we positioned the STM-tip above the aromatic side groups of a HPc molecule, opened the feedback loop and decreased the tip-to-molecule distance ( 1 Å/s) while measuring the tunneling current. We thus obtain conductance-distance curves Joachim1995 (); Haiss2006 (); Neel2007 (). Since the observed conductances of phthalocyanine molecules are rather high Takacs2008 (), a small voltage (10 mV) has to be used to avoid the thermal disintegration of the molecules. We observe an exponential increase of the conductance that reflects the decreasing tunneling barrier width (see Fig. 2a). Below a certain tip-to-surface separation — typically 3-4 Å — the conductance abruptly increases, which indicates a sudden change of the junction geometry. Similar jumps have been seen, e. g., for alkanedithiol molecular wires Haiss2006 (). We have recently shown that, for phthalocyanine molecules, this corresponds to a lifting of the flat HPc molecule’s aromatic group as it contacts the tip Takacs2008 ().
The conductance after the molecular jump-to-contact depends only slightly on the distance and encompasses both the transport across the molecule and direct tunneling between the tip and the sample Haiss2006 () (see Fig. 2c). This conductance in molecular contact mode depends markedly on whether the underlying island is of P or AP type. In the particular measurement of Fig. 2a, we find and ) measured at 10 mV bias, where is the quantum of conductance. We may eliminate a sizeable proportion of the spin-dependent direct (tip-to-island) tunneling contribution to the conductance by subtracting the measured conductance before the jump from that after , i. e. .
To ensure identical tip conditions when quantitatively comparing P and AP conductances, measurements on two Co islands of P and AP type were performed in the same scan. This approach further eliminates magnetostriction of the two ferromagnetic electrodes. Each such measurement was in turn repeated several hundred times and the distribution of the P and AP conductances is depicted in Fig. 2d. The width of the conductance distribution – which underscores the noise of the conductance measurement and a variation in contact geometries – is relatively small when compared to previous work Haiss2006 (); the histogram of the measurements on nearly 800 P and AP junctions clearly reveals a difference in conductance between the P and AP junctions. Gaussian fits were used to determine the GMR from the measurement statistics. We find and . These values result in an optimistic GMR ratio of
Surprisingly, the GMR ratio obtained at V = 10 mV is one order of magnitude larger than the differential TMR found for direct tunneling between the tip and the Co surface.
To understand what causes this large value of GMR, we have performed transport calculations based on density functional theory (DFT) employing the nonequilibrium Green’s function (NEGF) formalism and the TURBOMOLE package arnold2007 (); details may be found in the Supplementary Information.
To find the atomic structure of the molecular junction, we first performed a geometry optimization for HPc on the Co(111) surface, represented by a cluster with 65 atoms. Our analysis suggests that HPc adsorbs preferentially in the bridge position onto Co(111) (see Fig. 3a), owing to a binding energy eV that is larger than that found in either the hollow site position ( eV) or the atop site position ( eV), consistent with earlier findings Iacovita2009 (); Heinrich2010 ().
We have calculated spin-polarized transport in the linear response at low bias voltage for the two junction geometries schematized in Fig. 3a,b) before (”flat”) and after (”contact”) the jump-to-contact. To establish the latter configuration, a free HPc molecule has been bent along the low energy vibrational eigenmode with frequency meV Takacs2008 (). Within the NEGF calculations, the magnetization direction (P or AP relative to the tip) of each Co-cluster is a control parameter. We have ascertained that, in our study, the electronic structure of the Co surface is properly reproduced with, in particular, an exchange splitting of the -states of 1.8 eV (see Supplementary Information). This leads to a magnetic moment (Co) per surface Co atom, in agreement with previously reported calculations ABagrets2007 ().
On a qualitative level, our transport calculations (see Fig. 3c) reproduce very well our experimental findings (see Fig. 2a). We confirm the exponentially increasing conductance in the tunneling regime, , for which the distance between the two electrodes is still large. The slope is independent of the relative alignment of electrode magnetizations and the computational value Å (i. e. the work function eV) is in agreement with experiment ( Å; eV).
Once contact between the tip and the molecule has been established, varies much more weakly with the contact distance just as observed in the experiment. It is, however, still sensitive to the relative orientation of the magnetization of the electrodes. We find that is always much lower than . For a quantitative comparison with experiment, we consider the GMR ratio at the distance for which the ratio matches the value found experimentally. We thus find that GMR % and is only weakly dependent on .
We now discuss the conduction mechanism from the substrate onto the molecule and across the molecular contact established between the tip and the aromatic group, and its impact on the large GMR measured. Pc molecules are characterized by an energetically isolated highest occupied molecular orbital (HOMO) and a nearly doubly degenerate lowest unoccupied molecular orbital (LUMO) Rosa2001 (). We note that the HOMO levels corresponding to the aromatic group hybridize only very weakly, with almost no amplitude on the bridging nitrogen (N). By contrast, the LUMO states are located on two out of the four aromatic groups, with a strong hybridization to all N atoms forming the inner macro-cycle (see Supplementary Information). Since the N bond to Co includes states at the Fermi energy Takacs2008 (), transport should occur via the quasi-degenerate LUMO level. We confirm this fact by examining in Fig. 3d) the transmission probability per spin direction at the Fermi energy across a junction of P type. We find that near is indeed weighted by a peak centered slightly above that underscores transmission through the LUMO level. As we discuss in the Supplementary Information, the larger density of Co minority states at results, through the N-Co bond, in a larger efficiency of LUMO hybridization, and thus of LUMO broadening, in the spin channel.
This difference in LUMO broadening for the two spin channels has a direct impact on the GMR measured across the molecular junction. Indeed, the conductance across a single level, here the LUMO, generically takes on the Breit-Wigner form Huisman2009 () , which considers the energy separation between the LUMO and , as well as the LUMO broadenings (inverse lifetimes) and due to hybridization to the substrate and tip, respectively. Each is in turn split into depending on the spin channel considered. Because transport is off-resonant, i.e. , we have while . Introducing the ratio we thus find
This simple formula implies two important rules of thumb for spin-polarized transport off-resonance across a molecule. First, the GMR is insensitive to the precise location of the resonance energy. Second, it is mainly indicative of the ratio of minority and majority molecular orbital broadenings due to hybridization. Relative to the small differential TMR ratio found between the Co substrate and tip, the larger GMR ratio measured experimentally can be explained theoretically by the above ratio . The imbalance within the two spin channels of the hybridization-induced level broadening to the molecular orbital responsible for transport promotes a high GMR across the molecule.
In conclusion, we have experimentally demonstrated a GMR of over 50 % in single molecule junctions that is much larger than the value of differential TMR found without the presence of molecules in the junction. Such a high value is caused by a strong hybridization of the molecular LUMO, responsible for transport, with minority states of the two metallic electrodes. Such a selective hybridization thus leads to a spin filtering effect that could be generic to all molecular junctions.
We express our gratitude to O. Hampe, J. Kortus, K. Fink, S. Boukari, Xi Chen, M. Alouani, R. Mattana, J. van Ruitenbeek and P. Seneor for useful communications and acknowledge support by the DFG (WU 349/3-1 and SPP1243), the Alexander von Humboldt foundation and the ANR (ANR-06-NANO-033-01).
The Cu(111) crystal was cleaned thanks to several cycles of Ar sputtering and annealing. The molecules were evaporated in situ from a Knutsen cell heated to 500 K. During the deposition process we keep the sample at 270 K to reduce thermal diffusion of the deposited molecules. d/d curves were measured on the bare islands with the lock-in technique.
DFT-based transport calculations were carried out with a homemade code building upon the NEGF formalism and the TURBOMOLE package arnold2007 (). Our implementation enables us to perform transport simulations with free boundary conditions, which for the present case have been extended to account for the spin-polarized electronic structure of the magnetic electrodes (for further details, see Supplementary Information). The gradient corrected approximation (GGA) DFT-energy has been amended by empirical corrections Grimme () to account for dispersive van der Waals interactions between the molecule and the surface.
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Magnetoresistance through a single molecule
Stefan Schmaus, Alexei Bagrets, Yasmine Nahas, Toyo K. Yamada
Annika Bork, Martin Bowen, Eric Beaurepaire, Ferdinand Evers, and Wulf Wulfhekel
1. Geometry optimization
We used the quantum chemistry package TURBOMOLE [Ref.1] to find the atomic structure of molecular junctions. We have performed standard geometry optimization for HPc on Cu(111) surface, represented by a cluster with 65 atoms. (The use of Co(111)-clusters for structure optimization is impaired by the very large number of energetically almost degenerate spin multiplets.) The gradient corrected approximation (GGA [Ref.2]) DFT-energy has been amended by empirical corrections [Ref.3] to account for dispersive van der Waals interactions between the molecule and the surface. Our analysis suggests, that HPc prefers the ”bridge” position (see the paper, Figure 3a) with binding energy eV, against the ”hollow” site position (binding energy eV) and ”atop” site position (binding energy eV), which is consistent with earlier findings [Refs.4,5].
2. Electronic structure and transport calculations through HPc
Density functional theory (DFT) based electronic structure and transport calculations through HPc molecular junctions have been performed within the non-equilibrium Green’s function (NEGF) approach as implemented in a homemade simulation code [Ref.6] interfaced to the quantum chemistry package TURBOMOLE [Ref.1].The atomic configuration of the ”extended molecule” used to simulate a bottle-neck of the molecular junction is shown in Suppl. Fig. 1a (”contact” regime): HPc is bound to the two Co(111) clusters with 51 and 19 atoms, representing the Co surface and the Co STM-tip, respectively. To establish this configuration a free HPc molecule has been bent along the low energy vibrational eigenmode with frequency meV. A similar atomic configuration, with HPc bound to the surface only, has been used for transport simulations in the tunneling regime (see the paper, Figure 3b). The generalized gradient approximation (GGA, BP86 functional [Ref.2]) and a contracted Gaussian-type split-valence basis set with polarization functions (SVP) [Ref.7] have been employed for calculations.
First, a closed-shell (nonmagnetic) solution for the ”extended molecule” comprising 2156 electrons has been found. To account for infinite reservoirs with spin-polarized electrons, the spin-dependent () local self-energies, have been ascribed to the outermost boundaries of the simulation cluster (dark gray atoms at Suppl. Fig. 1a). Here, a parameter eV accounts for exchange splitting of the bulk Co -states [Ref.8]. A freedom to choose a sign of independently for the ”surface” and ”STM-tip” clusters allows for two solutions: with parallel and antiparallel alignment of electrodes’ magnetizations. The non-equilibrium Green’s function formalism is employed to evaluate the charge- and spin-density matrices in the presence of open boundaries insuring a charge neutrality within the ”extended molecule”. The density matrices are given back to TURBOMOLE to find a modified set of Kohn-Sham orbitals, with a cycle to be repeated unless the self-consistent solution is reached. For the given value of the level broadening, ( eV in present calculations), the contribution to the real piece of the self-energy has been defined by imposing the condition of spurious charge accumulation to be absent at the cluster’s boundaries. Further details of the computational approach will be published elsewhere [Ref.9].
As an example, details of electronic structure for the molecular junction in the case of parallel alignment of magnetizations are presented in Suppl. Fig. 1c,d. The electronic states at the Co-surface are spin-polarized with exchange splitting eV (Suppl. Fig. 1d), giving rise to an average magnetic moment per a surface Co atom. Inspecting the local density of states (DOS) at HPc, Suppl. Fig. 1c, we observe the majority spin resonance above the Fermi level () to be identified with the quasi-degenerate LUMO, which has a significant weight on the nitrogen atoms (cf. Suppl. Fig. 1b). In contrast, no density is seen on nitrogens for the majority spin HOMO resonance positioned eV below that reflects the stucture of the HOMO (Suppl. Fig. 1b). Furthermore, the minority spin HPc LUMO level evolves into a broad peak due to a hybridization with the minority spin Co states, which density near significantly exceeds the ones for majority spin electrons. The asymmetry in the LUMO level broadenings, , gives rise to a magnetoresistance effect (see text of the paper for further details).
References (Supplementary Information)
[Ref.1] TURBOMOLE V5.10 by R. Ahlrichs et al. (www.turbomole.com)
[Ref.2] (a) Becke A. D. Phys. Rev. A 1988, 38, 3098; (b) Perdew J. P. Phys. Rev. B 1986, 33, 8822.
[Ref.3] Grimme, S. J. Comp. Chem. 2006, 27, 1787–1799.
[Ref.4] Iacovita, C.; Rastei, M.; Heinrich, B. W.; Brumme, T.; Kortus, J.; Limot, L. & Bucher, J. Phys. Rev. Lett. 2009, 101, 116602.
[Ref.5] Heinrich, B. W.; Iacovita, C.; Brumme, T.; Choi, D.-J.; Limot, L.; Rastei, M. V.; Kortus, J.; Hofer, W. A. & Bucher, J.-P. Selective bonding and apparent symmetry of single Cobalt-Phtahalocyanine molecules on a copper (111) surface. Preprint, 2010.
[Ref.6] Arnold, A.; Evers, F. & Weigend, F. J. Chem. Phys. 2007, 126, 174101.
[Ref.7] Schäfer, A.; Horn H. & Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571.
[Ref.8] Moruzzi, V.L.; Janak, J. F. & Williams, A. R. Calculated Electronic Properties of Metals (Pergamon Press, New York, 1978).
[Ref.9] Bagrets A. 2009, unpublished.