Letter pubs.acs.org/NanoLett
Symmetry-Derived Half-Metallicity in Atomic and Molecular Junctions Alexander Smogunov* and Yannick J. Dappe Service de Physique de l’Etat Condensé DSM/IRAMIS/SPEC (CNRS UMR 3680), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France ABSTRACT: Achieving highly spin-polarized electric currents in atomic-scale junctions is of great importance in the field of nanoelectronics and spintronics. Based on robust symmetry considerations, we propose a mechanism to block completely one of spin conduction channels for a broad class of atomic and molecular junctions bridging two ferromagnetic electrodes. This particular behavior is due to the wave function orthogonality between spin up s-like states in ferromagnetic electrode and available π channels in the junction. As a consequence, the system would ideally yield 100% spinpolarized current, with a junction acting thus as a ”half-metallic” conductor. Using ab initio electron transport calculations, we demonstrate this principle on two examples: (i) a short carbon chain and (ii) a π-conjugated molecule (polythiophene) connected either to model semi-infinite Ni wires or to realistic Ni(111) electrodes. It is also predicted that such atomic-scale junctions should lead to very high (ideally, infinite) magneto-resistance ratios since the electric current gets fully blocked if two electrodes have antiparallel magnetic alignment. KEYWORDS: Spin-polarized transport, molecular spintronics, spin-filtering, magnetoresistance, atomic nanocontacts
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chains of various species joining two Co electrodes has also revealed, in some cases, MR ratios as large as 50%. For molecular nanobridges, moderate values of MR, up to 60%, were recently reported11−13 and were attributed to spindependent hybridization of molecular orbitals with electrode states. Spin-polarized transport through benzenedithiol (BDT) molecules sandwiched between ferromagnetic electrodes was also studied in context of thermal transport14 and magnetic switches.15 The property of spin-filtering by either (nonmagnetic) atomic junctions or organic molecules, however, was found to depend strongly on the details of nanocontact geometry and electronic hybridization. In the present Letter we suggest a mechanism, based on robust (with respect to atomic geometry) symmetry considerations, which may lead to perfect spin-filtering and to huge (ideally, infinite) MR ratios. Our observation is that in ferromagnetic electrodes two spin channels possess, quite generally, very different electron populations at the Fermi energy, EF: for majority spin (spin up), only s-orbital states are available (all the d states are fully occupied), while for minority spin (spin down), both s and d states are present at EF. If metallic nanocontact is then formed between two ferromagnetic electrodes the current will be largely dominated by s electrons in both spin channels (and, generally, smaller contribution from spin down d channels), which makes it only partially spin-polarized as it is found, for example, in Ni
pin-polarized electron transport across a single organic molecule or an atomic junction connecting ferromagnetic electrodes is currently of great interest for possible applications in nanoelectronics and spintronics.1 Among important effects we can emphasize the spin-filtering, which measures the degree of spin-polarization of electronic conductance, (G↑ − G↓)/(G↑ + G↓), and related property of spin-injection if one of the electrodes is nonmagnetic. Another important property is the magneto-resistance, MR, which characterizes the change of the current with the relative orientation of the magnetization of the two ferromagnetic electrodes, MR = (GP − GAP)/GAP, where P and AP stand for parallel and antiparallel magnetization alignments, respectively. Suggesting and designing possible atomic-scale junctions producing as high as possible spinpolarization of the current and MR is one of the most important issues in the field. Recent study of electron transport through thick organic molecular layers grown on ferromagnetic substrates2 suggested the possibility for tunneling MR (TMR) to reach up to 300%. More than 100% MR values were predicted theoretically for Fe/fullerene/Fe magnetic junctions.3,4 At the single molecule level, large spin-polarizations of different organic molecules due to hybridization with magnetic substrates were reported.5−7 This can result in large TMR ratios as was shown, for example, for C60 molecules on Cr(001) terraces.7 For atomic nanocontacts, the values of giant MR (GMR) of about 70% were reported recently for Co/Au/Co metallic junctions8 as a result of strong perturbation of s-states at Au contact atoms, and very large spin-polarizations of the current were found in halfmetallic NiO monatomic junctions.9 Rather detailed analysis done by Bagrets and co-workers10 for short (3-atom long) © XXXX American Chemical Society
Received: March 16, 2015 Revised: April 13, 2015
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DOI: 10.1021/acs.nanolett.5b01004 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters nanocontacts.16,17 On the contrary, if such electrodes are joined by a junction having no s-symmetry states available at the Fermi level, the spin up electrons could be completely blocked. The electric current will be provided by the remaining (compatible with a junction) minority d-states resulting in 100% polarized current with the junction playing thus a role of half-metallic conductor. We illustrate our symmetry arguments on the example of two possible atomic-scale junctions: namely, short carbon chains or thiophene molecules bridging two ferromagnetic Ni electrodes (or semi-infinite Ni nanowires). Spin-polarized electronic structure calculations have been performed using ab initio density functional theory (DFT) plane-wave package Quantum-ESPRESSO (QE).18 The coherent electron transport was studied by means of the quantum transport code PWCOND,19 which is a part of the QE package. The ballistic conductance for each spin channel can be evaluated from the corresponding electron transmission function at the Fermi energy using the Landauer−Buttiker formula, G = G0T(EF), where G0 = e2/h is the conductance quantum per spin. We note that our wellestablished DFT approach to electron transport taking electron−electron interactions at the mean-field level should be sufficient since electron correlations are not expected to play an important role in the present case and should not affect significantly our main conclusions resulting from solid symmetry mismatch reasoning. Structural optimizations of considered junctions have been done using more fast DFT tight-binding molecular dynamics code FIREBALL,20 following a well established procedure.21 We start our discussion with a model case of semi-infinite monatomic Ni wires joined by a short (4-atom) carbon chain, as shown in Figure 1. Such carbon atomic chains of different lengths were recently obtained experimentally by retracting an STM tip from a graphitic material.22 In Figure 1a the band structure and the projected density of states (PDOS, shown for the spin down channel only, for simplicity) are presented for an infinite Ni wire. As stated above, for spin up polarization only one s-like band crosses the Fermi energy, while five more dchannels are available for transport for spin down electrons. Among the latter, the most attention should be paid to the 2fold degenerate dxz,yz band (with a negative dispersion), which will play an important role in the following. The carbon chain has a 2-fold degenerate px,y band at the Fermi energy for each spin channel, as it is shown in Figure 1b, which is orthogonal to the s-symmetry bands of Ni nanowire. Therefore, a carbon chain is expected to act as a perfect spin filter passing only the spin down electrons from dxz,yz Ni channels, the only ones having nonzero overlap with px,y states of C chain. These conclusions are illustrated in Figure 1c where transmission functions for parallel (P) and antiparallel (AP) magnetic alignments of Ni nanowires are presented. We note that in the parallel configuration, the spin up transmission is indeed essentially zero around the Fermi energy, while the spin down one shows a broad structure reaching a maximum value of 2 (one per each channel dxz,yz) close to EF. Therefore, we obtain G↓ ≈ 1.8G0 and G↑ = 0 for the P configuration. In the antiparallel configuration, the spin down d xz,yz electrons passing through the left Ni−C junction will be completely reflected at the right C−Ni junction since they are orthogonal to the only available s-symmetry channel at the Fermi level of the right Ni nanowire. Hence, the total conductance should be fully quenched in AP configuration, which is confirmed by our calculations (red curve in Figure 1c).
Figure 1. Model four-atom carbon chain junction. (a) Spin-polarized band structure of an infinite Ni nanowire (at equilibrium interatomic distance of d = 2 Å) and DOS projected onto s- and d-atomic orbitals (shown for simplicity only for spin down polarization). (b) Band structure and PDOS of C nanowire at d = 1.3 Å. At the Fermi level there are two degenerate px,y bands orthogonal to s-like channels of the Ni nanowire. (c) Transmission functions for parallel (P) and antiparallel (AP) magnetic orientations of two Ni nanowires. Up and down transmissions for P configurations are shown by solid and dashed black curves, respectively. In AP configuration, up and down transmissions are the same by symmetry and are shown in red.
Therefore, such kind of junctions provides not only perfect spin filtering but also an infinite magneto-resistance. We note that carbon chains are not unique and are chosen just as a possible example for such metallic junctions: for example, Al chains have also only px,y states at the EF in a broad range of interatomic spacings. As another example we considered a molecular bridge made of π-conjugated molecules such as the one shown in Figure 2 (polythiophene). Such junctions could be realized using an STM tip to controllably lift a single conjugated polymer chain from the substrate.23,24 The electron transport through such molecules should be mediated by HOMO and LUMO orbitals. For such molecules all electron states can be classified as even or odd with respect to the molecule XZ plane as it is presented in Figure 2a. The orbitals around the Fermi energy, including B
DOI: 10.1021/acs.nanolett.5b01004 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 2. Model molecular junction. (a) Molecular levels of the free molecule (polythiophene) classified as even/odd (shown in blue/red) with respect to the symmetry plane XZ. (b) Up (solid) and down (dashed) transmission functions for the parallel magnetic orientations of two Ni nanowires. The real-space distributions of right-moving scattering states at the Fermi energy are shown for spin up (in red) and spin down (in blue) polarizations. Spin up state is completely reflected, while spin down state is partially transmitted.
Figure 3. Carbon chain junction with realistic Ni electrodes. (a) Spindependent PDOS on dxz,yz orbitals of the Ni apex atom. (b) Spindependent total DOS at four-atom carbon chain. (c) Spin-resolved transmission function for the parallel magnetic configuration of two Ni electrodes.
HOMO and LUMO, are found all to be of odd symmetry originating mainly from py carbon atomic orbitals. By symmetry, these molecular states will only couple to the ones of spin down channels, namely, those of dyz symmetry. This is reflected in a finite spin down transmission around the Fermi energy (Figure 2b), while spin up electrons, as for the carbon chain, are completely reflected at the junction. From the transmissions at the Fermi level we can extract thus G↓ ≈ 0.65G0 and G↑ = 0. The squared wave functions of right-moving states for both spin channels at EF, shown in Figure 2b, validate our symmetry considerations: spin up channel (in red) is fully blocked at the junction, while spin down state (in blue) clearly has the shape of py-derived molecular orbital and is partially transmitted. We did not perform here calculations for AP magnetic configuration, but similarly to the carbon chain, we can deduce that also for molecular junction, the ideal infinite value is expected for the MR ratio. Having illustrated the main idea on simple model systems we pass now to more realistic nanocontact geometries by replacing semi-infinite Ni wires by fcc Ni(111) electrodes as it is shown in the upper panels of Figures 3 and 4. The same junctions are now attached to crystalline electrodes via 4-atom Ni pyramids on both sides. An important quantity to look at is the (spinpolarized) PDOS at the Ni apex atom since it provides the information on the possible nature of incoming conductance channels. For a C chain junction, the dxz,yz PDOS reported in Figure 3a, are of major importance, since only these states can match by symmetry to a couple of C chain px,y conduction channels available around the Fermi energy. These PDOS show, as for the previous cases, a strong spin-polarization, which is required for a good spin-filtering of the current: only spin down channel has a large dxz,yz PDOS appearing at E − EF
< 0.5 eV and originating from the corresponding 2-fold degenerate band of the infinite Ni wire (see Figure 1a). This results in a rather big G↓ ≈ 1G0, and a very tiny G↑ = 0.02. Moreover, the large spin down transmission around EF is accompanied by substantial spin down DOS on the C chain as it can be seen in Figure 3b. Overall, we find a good spin-filtering also for this realistic junction though it is not as good as for the model case with semi-infinite Ni nanowires (Figure 1) because of two main reasons: (i) G↓ is smaller due to stronger reflection of dxz,yz electrons at the nanocontact; (ii) G↑ is not exactly zero due to small but still finite spin up DOS of dxz,yz character at the Ni apex atom (Figure 3a). In the case of molecular junction, shown in Figure 4, the relevant PDOS of the Ni apex atom is the one of dyz-symmetry since only states with this orbital character will have nonzero overlap with molecular π orbitals. As above, the PDOS of interest shows a strong spin unbalance around the Fermi energy with a very tiny spin up component, which starts growing significantly only at E − EF < −0.75 eV. Contrary to the case of “metallic” carbon chain nanocontact (where the conductance is controlled by the number of bands of C chain at the Fermi level), electron transport across molecular junctions is usually interpreted in terms of tunneling through molecular orbitals. We therefore present in Figure 4b the DOS projected onto different free molecule orbitals (without Ni contacts and with two additional H atoms at the ends in order to passivate dangling bonds). One can see that the conductance is largely dominated by the HOMO orbital located at E − EF ≈ −0.1 eV. The width of HOMO (as well as of HOMO − 1) resonance, depending on hybridization strength with electrodes, is much C
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with a single Ni atom, in order to have our symmetry argument to work more efficiently. In the case of “flat” Ni electrodes (no apex atoms in Figures 3 and 4), out of three spin up Ni sorbitals, one can always make a combination having nonzero overlap with π states of the junction, which will reduce the overall spin-polarization of the current. The degree of spinpolarization is thus higher if electrodes are closer in structure to the 1D infinite nanowire. Such kind of contacts can be, in fact, achieved in break-junction experiments as has been recently reported by Yelin and co-workers25 where different molecules captured at the Pt contact were shown to facilitate the formation of longer 1D Pt chains. We emphasize, moreover, that it is not necessary to have symmetric “sharp” connections on both sides of the junction as shown in Figures 3 and 4: one “sharp” tip on either side should be enough to fully spinpolarize the electrical current, which would apply thus to the case of deposited molecules probed by a single atom sharp ferromagnetic STM tip.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was performed using HPC computation resources from GENCI-[TGCC] (Grant No. 2015097416).
Figure 4. Molecular junction with realistic Ni electrodes. (a) Spindependent PDOS on dyz orbital of the Ni apex atom. The same PDOS but for the semi-infinite Ni nanowire is shown on the inset. (b) Spinresolved DOS projected onto different molecular orbitals of the free molecule. Solid and dashed lines correspond to spin up and spin down polarizations, respectively. (c) Spin-resolved transmission function for the parallel magnetic configuration.
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REFERENCES
(1) Rocha, A. R.; Garcia-Suarez, V. M.; Bailey, S. W.; Lambert, C. J.; Ferrer, J.; Sanvito, S. Nat. Mater. 2005, 4, 335−339. (2) Barraud, C.; Seneor, P.; Mattana, R.; Fusil, S.; Bouzehouane, K.; Deranlot, C.; Graziosi, P.; Hueso, L.; Bergenti, I.; Dediu, V. Nat. Phys. 2010, 6, 615−620. ́ (3) Ç akır, D.; Otlvaro, D. M.; Brocks, G. Phys. Rev. B 2014, 89, 115407. ́ (4) Ç akır, D.; Otlvaro, D. M.; Brocks, G. Phys. Rev. B 2014, 90, 245404. (5) Caffrey, N. M.; Ferriani, P.; Marocchi, S.; Heinze, S. Phys. Rev. B 2013, 88, 155403. (6) Atodiresei, N.; Brede, J.; Lazić, P.; Caciuc, V.; Hoffmann, G.; Wiesendanger, R.; Blügel, S. Phys. Rev. Lett. 2010, 105, 066601. (7) Kawahara, S. L.; Lagoute, J.; Repain, V.; Chacon, C.; Girard, Y.; Rousset, S.; Smogunov, A.; Barreteau, C. Nano Lett. 2012, 12, 4558− 4563. PMID: 22827486 (8) Sivkov, I. N.; Brovko, O. O.; Bazhanov, D. I.; Stepanyuk, V. S. Phys. Rev. B 2014, 89, 075436. (9) Jacob, D.; Fernández-Rossier, J.; Palacios, J. J. Phys. Rev. B 2006, 74, 081402. (10) Bagrets, A.; Papanikolaou, N.; Mertig, I. Phys. Rev. B 2004, 70, 064410. (11) Schmaus, S.; Bagrets, A.; Nahas, Y.; Yamada, T. K.; Bork, A.; Bowen, M.; Beaurepaire, E.; Evers, F.; Wulfhekel, W. Nat. Nanotechnol. 2011, 6, 185−189. (12) Bagrets, A.; Schmaus, S.; Jaafar, A.; Kramczynski, D.; Yamada, T. K.; Alouani, M.; Wulfhekel, W.; Evers, F. Nano Lett. 2012, 12, 5131− 5136. (13) Tao, L.; Liang, S.; Liu, D.; Han, X. J. Appl. Phys. 2013, 114, 213906. (14) Lee, M. H.; Dunietz, B. D. Phys. Rev. B 2013, 88, 045421. (15) Pati, R.; Senapati, L.; Ajayan, P. M.; Nayak, S. K. Phys. Rev. B 2003, 68, 100407. (16) Jacob, D.; Fernández-Rossier, J.; Palacios, J. J. Phys. Rev. B 2005, 71, 220403.
larger for spin down channel due to much higher electrode dyz DOS, as discussed above. As a consequence we find G↓ = 0.19G0 and G↑ = 0.02G0, which results, however, in more moderate spin-polarization of the current with respect to other cases. This result goes in line with recent study on spindependent hybridization of molecular orbitals found in ferromagnet/molecule/ferromagnet junctions.11 We note also that the sharp peak observed in T↓ at about E − EF = 0.3 eV can be attributed to rapidly varying electrode DOS at the dyz band onset, as can be seen in Figure 4a. This behavior is opposite to the one-dimensional case of semi-infinite Ni wires where dyz DOS at the contact Ni atom is a rather smooth function, as shown on the inset of Figure 4a, resulting in a more regular transmission curve as seen in Figure 2b. In summary, we propose a symmetry argument allowing to fully block majority spin conductance channel at the ferromagnet/junction interface, which should work for a rather broad class of atomic and π-conjugated molecular junctions. This feature relies on an orbital symmetry orthogonality of slike spin up channel of the ferromagnetic electrode and of π symmetry channels available at the Fermi energy in a junction. That should result in a perfect spin-polarization of the current and huge (ideally, infinite) MR ratios. Our predictions are confirmed by ab initio calculations: for ideal Ni electrodes, simulated by semi-infinite Ni nanowires, the perfect 100% spinpolarizations are predicted, while more moderate (but still very high) values are found with crystalline Ni(111) electrodes. Note that it is important to have “sharp” Ni electrodes, ending D
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Nano Letters (17) Smogunov, A.; Dal Corso, A.; Tosatti, E. Phys. Rev. B 2006, 73, 075418. (18) Giannozzi, P.; et al. J. Phys.: Condens. Matter 2009, 21, 395502. (19) Smogunov, A.; Dal Corso, A.; Tosatti, E. Phys. Rev. B 2004, 70, 045417. (20) Lewis, J. P.; Jelínek, P.; Ortega, J.; Demkov, A. A.; Trabada, D. G.; Haycock, B.; Wang, H.; Adams, G.; Tomfohr, J. K.; Abad, E. Phys. Status Solidi B 2011, 248, 1989−2007. (21) Schull, G.; Dappe, Y. J.; González, C.; Bulou, H.; Berndt, R. Nano Lett. 2011, 11, 3142−3146. (22) la Torre, A.; Botello-Mendez, A.; Baaziz, W.; Charlier, J.-C.; Banhart, F. Nat. Commun. 2015, 6, 6636. (23) Lafferentz, L.; Ample, F.; Yu, H.; Hecht, S.; Joachim, C.; Grill, L. Science 2009, 323, 1193−1197. (24) Reecht, G.; Scheurer, F.; Speisser, V.; Dappe, Y. J.; Mathevet, F.; Schull, G. Phys. Rev. Lett. 2014, 112, 047403. (25) Yelin, T.; Vardimon, R.; Kuritz, N.; Korytár, R.; Bagrets, A.; Evers, F.; Kronik, L.; Tal, O. Nano Lett. 2013, 13, 1956−1961.
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