Highly conductive and complete spin filtering of nickel atomic contacts in a nitrogen atmosphere
HHighly conductive and complete spin filtering of nickel atomic contacts in a nitrogen atmosphere
Dongzhe Li ∗ Department of Physics, University of Konstanz, 78457 Konstanz, Germany (Dated: May 30, 2019)Generating efficient and highly spin-polarized currents through nanoscale junctions is essential in the fieldof nanoelectronics and spintronics. In this paper, using ab initio electron transport calculations, we predicthighly conductive and perfect spin filtering of nickel atomic contacts in a nitrogen environment, where a singleN molecule sits in parallel (energetically most favorable) between two nickel electrodes. Such a particularperformance is due to the wave function orthogonality between majority spin s -like states of ferromagneticelectrodes and the lowest unoccupied molecular orbital of the N molecule, and thus, majority spin electronsare completely blocked at the interface. For the minority spin, on the contrary, two almost saturated conductingchannels were formed due to the effective coupling between d zx,zy of the Ni atom and p x,y of the N atom,resulting in large conductance of about 1 G ( = 2 e /h ). As a consequence, a single N molecule acts as ahighly conductive and half-metallic conductor. On the other hand, the CO and NO incorporated molecularjunctions exhibit rather low conductance with a partially spin-polarized current. PACS numbers:
I. Introduction
A crucial issue remaining in the development of molecu-lar spintronics is the manipulation of charge transport andin particular its degree of spin polarization (SP), which can bedefined as SP = ( G ↓ − G ↑ ) / ( G ↑ + G ↓ ) × , where G ↑ and G ↓ are spin up (majority) and spin down (minority) conduc-tance, respectively. Recently, it was shown that tunable SPthrough a single molecule can be obtained by a mechanicalstrain , anchoring groups , the spin-dependent quantum inter-ference effect etc. Unexpected large magneto-resistive ratioswere observed in gas-stabilized platinum nanocontacts . Con-trol and manipulation of spin filtering in atomic and molecularjunctions in order to suggest and design possible molecular-based devices with large SP and high conductance are one ofthe most important issues in this field.In ferromagnetic nanocontacts, quite generally, the electri-cal current is dominated by weakly polarized s orbitals forboth spin channels, with a smaller contribution from par-tially polarized minority spin d orbitals, leading to limitedspin-polarized current in the related nanodevices. . For in-stance, the SP was found to be about only 33% in Ni atomiccontacts .In molecular junctions, unlike metallic contacts, the trans-port between two electrodes is often mediated by a weaklycoupled molecule. In particular, the molecular orbitals are ex-pected to preserve their own symmetry and localized nature,and thus, they can be expected to exhibit properties that cannotbe observed in the pure atomic contacts or even the moleculeitself. For example, M. Kiguchi et al demonstrated that theelectronic conductance of the Pt/benzene/Pt molecular junc-tion is close to that of a metal nanocontact although free ben-zene is actually an insulator. Large SP was obtained at variousspinterfaces due to spin-dependent hybridization of molecularorbitals with magnetic substrate states .Currently, charge transport of metal atomic contacts inthe presence of a gas such as H , O , CO or N has at-tracted a lot of interest. In the case of cobalt and palla-dium nanocontacts, while atomic chains were not formed for clean metals, the atomic chains can be formed in the pres-ence of hydrogen . High conductance as large as 1 G was observed in a single-molecule Pt/H /Pt bridge . Here, G = 2 e /h is the conductance quantum. Additionally,high spin polarization in Ni/O/Ni atomic conductors was pre-dicted by first-principles calculations and confirmed lateron by shot noise measurements . Moreover, it was shownthat N atmosphere greatly helps to stabilize the formationof longer Cu atomic wires, confirmed by both ab initio calculations and mechanically controllable break junction(MCBJ) measurement . Using the MCBJ technique, thePt/N /Pt junction was formed where the N molecule lies par-allel to current, leading to a conductance of 1 G which is closeto the metal atomic contact .We recently suggested a mechanism , based on robustsymmetry considerations (with respect to the atomic geome-try), which can lead to the upper limit of spin polarization (SP= 100%) in π -conjugated molecular junctions. Due to symme-try match/mismatch between molecular orbitals (involved incharge transport) and ferromagnetic leads, the electron trans-port is carried only through minority spin-states while the s -channels for both spins are fully reflected at the molecule-metal interface. Here, by ab initio transport calculations,we predict highly conductive and perfect spin filtering of Ninanocontacts in a nitrogen atmosphere based on similar orbitalsymmetry argument. From total energy calculations withindensity functional theory (DFT), we identified a “parallel”configuration (i.e., single N is placed between two Ni atoms)which is energetically most stable. Interestingly, the major-ity spin channel is completely blocked due to wavefunctionorthogonality between s -states of Ni and the lowest unoccu-pied molecular orbital (LUMO) of the N molecule, resultingin 100% spin-polarized current with the junction thus playingthe role of a half-metallic conductor. For the minority spinchannel, on the contrary, the conductance of the single N molecular junction is found to be as large as 1 G ( = 2 e /h )due to effective orbital matching between d ↓ zx,zy and LUMOof the N molecule, leading to a conductance is close to thepure Ni atomic contacts. a r X i v : . [ c ond - m a t . m e s - h a ll ] M a y -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6050100150200 HOMO LUMO (x2)total p x + p y Energy (eV) P DO S ( a . u . ) Free N -3 -2 -1 0 1 20123 T r a n s m i ss i on E - E F (eV) P: upP: downAP: up/down (b)(a) Up Down y z
FIG. 1: Model molecular junction: a single N molecule is sand-wiched between two semi-infinite Ni monoatomic chains. (a) Den-sity of states (DOS) of the N molecule in gas phase, note that theHOMO is mainly from the p z orbital and the two-fold degenerateLUMO is from p x and p y orbitals which are orthogonal to s -likechannels of the Ni nanowire. (b) Spin-polarized transmission func-tions for parallel (P) and anti-parallel (AP) spin configurations. Thespin up state is completely blocked while the spin down state is par-tially transmitted, resulting in perfect spin filtering (SP = 100%) andinfinite magneto-resistance. Transmission eigenchannel scatteringstates at the Fermi energy are shown for spin up (in blue) and spindown (in red) channels. II. Method
Molecular junctions were described in a supercell contain-ing a single N molecule and two four-atom Ni pyramids at-tached to Ni(111) slabs containing six and six atomic layerson the left and right sides. A 4 × XY plane (16 atoms per layer). The atomic relaxation wascarried out using plane waves Q UANTUM E SPRESSO (QE)package within DFT framework at the PBE level . Thesame computational parameters as in Ref. 26 were used.Then, ab initio spin-polarized electronic transport proper-ties were evaluated using the T RANSIESTA code whichemploys a non-equilibrium Green’s function (NEGF) formal-ism combined with DFT. We used Troullier-Martins norm- conserving pseudopotentials , PBE functional and an energycutoff for the real-space mesh of 250 Ry. A double ζ plus po-larization (DZP) basis set with an energy shift of 50 meV wasused, which resulted, as we have checked, in a good agree-ment with QE results (see Fig. 5 in Appendix A). A 6 × × k -point mesh was found to be enough to obtain well con-verged transmission functions.In the linear response regime, the total conductance ( G ) ofmagnetic systems is given by the Landauer-B¨uttiker formula, G = ( 12 ) G (cid:88) σ T σ ( E F ) , (1)where G = 2 e /h is the conductance quantum ( e beingthe electron charge and h Plank’s constant) and T σ ( E F ) isthe transmission function for spin σ = ↑ , ↓ at the Fermi en-ergy. The spin-dependent conductance is then defined as G σ = ( ) G T σ ( E F ) , such that G = G ↑ + G ↓ . Note that allthe conductance values presented in this paper for both non-magnetic and magnetic systems are in units of G = 2 e /h for the convenience of comparison.Spin-resolved transmission function is evaluated using theNEGF formalism: T σ ( E ) = Tr[Γ L,σ ( E ) G rσ ( E )Γ R,σ ( E ) G aσ ( E )] , (2)where G r,aσ are the retarded and advanced Green’s functionsof the scattering region (molecule plus some parts of left andright electrodes), G r/aσ = [( E ± iη ) S − H Cσ − Σ r/aL,σ − Σ r/aR,σ ] − (3)where η is an infinitesimal positive number, S is the overlapmatrix, H Cσ is the Hamiltonian matrix for the scattering re-gion and Σ r/aL/R,σ are retarded or advanced self-energies due toleft/right electrodes. Coupling matrices Γ L/R,σ are evaluatedfrom the imaginary parts of the corresponding self-energies as Γ L/R,σ = i (Σ rL/R,σ − Σ aL/R,σ ) . III. Results and discussionA. Model system: Ni chain/N junctions First we consider a simple model system in which oneN molecule sandwiched in the “parallel” configuration (withrespect to the transport direction) by two semi-infinite Nimonoatomic wires. In gas phase, as plotted in Fig. 1(a), wefound that the highest occupied molecular orbital (HOMO) ismainly from p z orbital ( (cid:104) p z | s (cid:105) (cid:54) = 0 ) while the two-fold de-generate LUMO originates from p x,y (plotted in red) atomicorbitals which have zero overlap with s -states of Ni. As de-scribed in Ref. 25, for the Ni monoatomic chain, only one s band crosses E F for spin up while five more d bands areavailable for spin down. We plot in Fig. 1(b) transmission
14 15 16 17 1800.511.522.5 14 15 16 17 1800.250.50.751 updown14 15 16 17 18020406080100 I II III IV V T o t a l e n e r gy ( e V ) C ondu c t a n ce ( G = e / h ) S p i n po l a r i za ti on ( % ) distance d z (Å) (b)(a)(c) II IIIIV VI y z
FIG. 2: Realistic molecular junction: N molecular junctions withfcc-Ni(111) crystalline electrodes. (a) Total energy variation as afunction of the stretch distance d z which is defined as the distancebetween the (111) surfaces; note that the lowest energy point is set aszero. Spin-dependent conductance (b) and the spin polarization (c)as a function of d z . Five representative molecular junction geome-tries of the different stages of the evolution of the junction during thestretching process are presented in the top panel. functions for parallel (P) and antiparallel (AP) magnetic align-ments of Ni chains. Interestingly, T ( E ) is dominated by theLUMO level and the effect of HOMO on transport is negligi-ble due to the large band gap ( > molecule.In the case of the P configuration, near E F , the spin uptransmission is essentially zero, while the spin down oneshows a broad structure with the maximum transmission co-efficient going up to about 2. The physical reason can be explained by orbital symmetry argument. Since the LUMOoriginates from p x,y orbitals which are orthogonal to the s -symmetry bands of the Ni nanowire, the spin up electron (plot-ted in blue) is completely blocked at the Ni-N interface. Onthe other hand, for the spin down (plotted in red) case elec-trons from only d zx,zy (starting at about E F +0 . eV with neg-ative band dispersion) Ni channels are transmitted due to goodorbital matching with p x,y orbitals. This also can be clearlyseen from the transmission eigenchannel scattering states atthe E F , shown in Fig. 1(b). As a result, we obtain G ↑ =0.00 G ( = 2 e /h ) and G ↓ = 0.75 G for the P configuration,here, a single N molecule plays the role of a perfect spin fil-tering component.In the AP configuration, the emergence of almost perfecthalf-metallicity leads to a complete suppression of the cur-rent. This is due to the fact that the transmitted d ↓ zx,zy elec-trons from the left Ni − N interface are then blocked at the rightNi − N interface. Therefore, such junctions provide not onlyperfect spin filtering but also an infinite magneto-resistance(MR), which is defined as the change in electrical conductancebetween P and AP magnetic orientations of two ferromagneticelectrodes.
B. Realistic system: Ni(111)/N junctions Encouraged by the favorable results from the model sys-tem, we constructed more realistic junctions with fcc-Ni(111)electrodes for detailed analysis.To simulate the realistic experimental situations in MCBJ,we gradually stretch the junction up to the breaking point,starting from the N molecule which is in a upright bridgeconfiguration (the bottom N atom is symmetrically bonded totwo Ni apex atoms), shown in Fig. 2 of geometry I. In thestretching process, by increasing the electrode separation d z ,we optimize the junction geometry by fixing three and threebottom layers on the left and right sides at every step untilthe junction breaks, then calculate the corresponding conduc-tance trace. The five representative geometries depicted ontop of Fig. 2 are examples of the stable configurations ob-tained from this procedure. We note that the junctions createdtheoretically in the work are the idea model systems, whichcould be studied in MCBJ experiments.Our ab initio geometry optimization has shown that uponincreasing the stretching distance of d z the N configurationwith Ni electrodes changes dramatically. Electronic and trans-port properties are summarized in Fig. 2, where we showthe total energy (relative to the lowest energy configurationof d z = 15 . ˚A), the spin-dependent conductance [evaluatedby Eq. 1 in the unit of G = 2 e /h ] and the SP as a functionof the electrode displacement of d z .Interestingly, the calculated conductance exhibits highlystrain-dependent behavior for both spin channels. In gen-eral, the conductance with respect to d z can be distinguishedwith five different regimes as described in the following. Forthe first three configurations (first elastic stage), the con-ductance for both spins decreases monotonically. This caneasily be understood by the fact that the N molecule in -4 -3 -2 -1 0 1 2 3 400.5 P DO S ( a . u . l ) Ni apex d zx ( d zy ) E - E F (eV) -4 -3 -2 -1 0 1 2 3 4012-4 -3 -2 -1 0 1 2 3 400.5 T r a n s m i ss i on P DO S ( a . u . ) LUMO N - p x ( p y )updown zy (a)(b)(c) ApexApex
FIG. 3: Electronic and transport properties in theNi(111)/N /Ni(111) junction for the lowest energy configura-tion (see configuration IV in Fig. 2). (a) Spin-polarized transmissionspectra for the parallel spin configuration of two Ni electrodes.(b) Spin-dependent PDOS on both nitride atoms of p x,y orbitals.(c) Spin-dependent PDOS on d zx,zy orbitals of the Ni apex atom.Note that spin up and down channels are plotted in blue and red,respectively. the upright configuration remains stable but the hybridiza-tion strength between Ni apex atoms with the molecule de-creases due to increasing d z . As a result, the conductance de-creases from 0.23 G /0.90 G to 0.14 G /0.65 G for the spinup/down channel. As the lead-lead distance is increased be-tween 14.6 ˚A and 15.2 ˚A the molecule begins to tilt awayfrom the direction y (second elastic stage), and the conduc-tance for both spins further decreases leading to the low con-ductance plateaus of about 0.05 G and 0.37 G for spin upand down, respectively. As the contact is stretched further(15.3 ˚A < d z < z (geometry III) until forming the lowest energy configuration (geometry IV)where the molecule is placed between Ni electrodes in par-allel with almost the same x and y coordinates as Ni apexatoms. These results are similar to those reported previouslyfor Pt/N /Pt and Ag/CO/Ag nanojunctions. Importantly,the spin down conductance is dramatically increased up toabout 1 G . On the contrary, the conductance for spin downslightly decreases, resulting in a highly polarized spin cur-rent (SP > < d z < G is observed for spin down while the spin upconductance is completely quenched showing almost 100%spin-polarized current. When d z is larger than 17.6 ˚A (fifthelastic stage) the Ni − N bond breaks causing an abrupt decayof T ( E F ) almost to zero for both spin channels. Note thatduring the stretching evolution the N intra-molecular bondsdo not change significantly. For more detailed spin-dependenttransmission functions for five representative configurations,see Appendix B.Let us now focus on the lowest energy configuration (seegeometry IV in Fig. 2) where the N molecule sits in parallelbetween Ni electrodes. We plot in Fig. 3(a) the spin-resolvedenergy dependent transmission function, where the energy ismeasured with respect to the Fermi energy. Interestingly, a re-markable difference of T ( E ) curves for the two spin channelswas observed. In the vicinity of E F , for spin down electrons,we found a significant and broad transmission peak locatedbetween − . eV and . eV with respect to E F showing itsmaximum at E F . In contrast, the transmission coefficient inthe spin-up channel is strongly suppressed near E F .To get more insights on the T ( E ) curve, we plot in Fig.3b-c the projected density of states (PDOS) on p x,y of N molecule and d zx,zy of the Ni apex atom, which are of majorimportance based on the symmetry argument discussed beforein the model system. As seen in Fig. 3(b), the charge transportis dominated by LUMO located at about 1.6 eV above E F , re-sulting in a broad resonance peak in the corresponding T ( E ) .The large broadening of LUMO indicates strong hybridizationbetween N- p x,y and Ni- d zx,zy due to almost perfect orbitalmatching. Moreover, near E F , the PDOS of N- p x,y is largelydominated by spin down states. The induced spin moment onN was found to be about -0.14 µ B (“antiferromagnetic” cou-pling). An important quantity to look at is the PDOS at theNi apex atom since it provides the information on the possi-ble nature of incoming conductance channels (see Fig. 3c).Clearly, the PDOS of the Ni apex atom is dominated by theminority spin states near E F as expected in 3 d ferromagneticelectrodes. As a consequence, the electron transport is almostdominated by minority spin electrons; we find G ↑ = 0 . G and G ↓ = 0 . G , for spin up and down channels, respec-tively. Moreover, an orbital eigenchannel analysis reveals thatthe transport is mainly due to two efficient (almost saturatedconductance of about 0.50 G for each channel) transmittingminority-spin channels composed of Ni- d zx,zy and N- p x,y or-bitals. As a result, a single N molecule acts as a highly con-ductive ( G total ≈ G ) and an almost 100% spin-polarizedconductor. Note that we also double-checked the conductancecalculations by using the P WCOND code based on scatter-ing theory within plane-wave basis sets as implemented in theQE package. The calculated conductance is found to be about0.03 G and 0.79 G which is in good general agreement withT RANSIESTA results (see Appendix A for more details). -4 -3 -2 -1 0 1 2 3 400.511.522.53-4 -3 -2 -1 0 1 2 3 400.511.522.53 T r a n s m i ss i on E - E F (eV)updown T r a n s m i ss i on (a)(b) CONO
FIG. 4: Spin-dependent transmission functions for Ni/CO/Ni (a) andNi/NO/Ni (b) junctions where the molecules sit in parallel betweentwo electrodes.
We note that the work presented here has much betterperformance in terms of conductance and SP compared tothe previously reported magnetic metal atomic junctions withvarious absorbed molecules. For example, the Ni junctionbridged by a H molecule has a conductance of approximately . G ∼ . G and is almost not spin-polarized (SP =0.2%), as confirmed by both theory and experiment . Alarge conductance of 1 G is reported by MCBJ experimentin Co/H /Co , but the electrical current is only partiallyspin-polarized. In addition, a smaller conductance of about0.5 G is found in Ni/CO/Ni in the break junction experi-ment. Moreover, in the case of Fe/O /Fe, rather low conduc-tance and SP of about 0.13 G and 50% are found . Veryrecently, R. Vardimon et al indicated up to 100% spin-polarized currents in the Ni/O/Ni atomic junction with mea-sured conductance of about . G ∼ . G C. Realistic system: Ni(111)/CO and Ni(111)/NO junctions
Motivated by promising results with the N molecule, wealso investigated the transport properties of Ni atomic con-tacts in the presence of CO and NO molecules in the parallelconfiguration (also fully relaxed). These molecules are cho-sen because they have electronic properties in gas phase verysimilar to those of N , namely, LUMO is the linear combina-tion of p x,y atomic orbitals while HOMO is from p z and s or- bitals. These molecular junctions have been created with var-ious metals by MCBJ or via scanning tunneling microscope(STM) with functionalized tips . Note that the Ni − COcontact spin polarizes and the major current is carried by theminority spin channel (red line), while the majority spin chan-nel (blue line) only has a minor contribution at the Fermi level,shown in Fig. 4(a). Clearly, the coupling between d zx,zy ofapex Ni atoms and p x,y of CO molecule determines the trans-mission. The calculated conductance is about 0.32 G with SPof about 75% which is in general agreement with a previouslyreported experimental result for the Ni/CO/Ni junction . Inthe case of the NO molecule (see Fig. 4b), the LUMO posi-tion is about 1.0 eV closer to E F compared to the CO and N molecules. On the contrary, the broadening of the LUMO issmaller in the NO than in the other two molecules. For spindown, two peaks at about 0.25 eV and 0.75 eV just above E F originate from the spin-split hybridized d -states of Ni apexatoms. The calculated conductance was found to be about0.13 G and 0.23 G for majority and minority spins, respec-tively, resulting in a rather small SP of about 28%.Finally, let us discuss the generality of symmetry argumentsand accuracy issues. The symmetry reasoning presented herein principle work for a rather broad class of atomic and molec-ular junctions, where no s -like channels are available in themolecular spin-valve set-up. They could be realized by MCBJor STM measurements, for instance, atomic chains such ascarbon sandwiched by magnetic electrodes , π -conjugatedmolecular spin valves such as polythiophene and the atomicscale contacts in the presence of gas molecules such as N . Inthis work, we base our theoretical prediction on the NEGF-DFT technique which is widely recognized as a robust ap-proach, providing an understanding of the behavior on a goodqualitative basis at a reasonable computational cost, as seen,for example, in Ref. 11,24 for nanoscale junctions. However,from quantitative point of view, standard DFT could underes-timate the HOMO-LUMO gap and overestimate the conduc-tance. GW self-energy has been recognized as a good ap-proximation to describe accurately the energy level alignmentat the molecule-metal interface but much more computation-ally demanding. The DFT error is in general systematic, thusconductance ratios are usually in good agreement with exper-iment, for instance the rectification ratios predicted by NEGF-DFT were found to be reliable . So we believe that the spinfiltering ratios predicted in this work are reliable as well. Insummary, the DFT-error introduced here plays a role (for theoverestimation of conductance values) in a quantitative basisbut should not affect significantly our main conclusions result-ing from robust symmetry mismatch arguments. IV. Conclusions
To conclude, using a combination of density functional the-ory and non-equilibrium Green’s function method, we predicthighly conductive and perfect spin filtering of nickel mag-netic point contacts in a nitrogen atmosphere. For Ni/N /Ninanocontacts we identified that an energetically stable con-figuration is the N molecule providing a parallel configura- -4 -3 -2 -1 0 1 2 3 400.5-4 -3 -2 -1 0 1 2 3 400.5 P DO S ( a . u . ) E - E F (eV) SiestaQuantum Espresso up N - p x, y N - p x, y down FIG. 5: Comparison between localized atomic-orbital basis S
IESTA and plane-wave basis QE results. Calculated spin-dependent PDOSon nitride p x,y by S IESTA (top) and QE (bottom). The transmissioncoefficient at E F evaluated by T RANSISESTA and P
WCOND werealso shown. A good general agreement was found between two dif-ferent codes. tion (with respect to the current flow) between two Ni apexatoms. The N junction shows a high conductance of about1 G ( = 2 e /h ), which is comparable to that of correspond-ing pure Ni atomic contacts. More importantly, the major-ity spin conductance is almost quenched near E F due to thesymmetry mismatch between s -states of the Ni and p x,y ofthe N molecule. In contrast, for the minority spin, two al-most saturated conducting channels originate from the effec-tive coupling between p x,y -symmetry of the N molecule and d zx,zy -symmetry of the Ni apex atoms due to the symmetry.However, if the N is replaced by CO or NO, the conduc-tance, as well as the SP, is reduced due to less pronouncedspin-split hybridized molecular states near E F . We hope thatour theoretical prediction may inspire further experimental ex-plorations (i.e. measurements of shot noise) to reach the upperlimit of spin polarization with large conductance in magneticmetal nanocontacts with various absorbed molecules. Acknowledgments : D.L. wants to thank S. Lamowski forhelpful comments. D.L. was supported by the Alexander vonHumboldt Foundation through a Fellowship for PostdoctoralResearchers.
Appendix A: Comparison between
SIESTA and QE results
In order to check the reliability of the DZP basis sets used inthis work, we compared the electronic and transport propertiesin the Ni/N /Ni junction (geometry IV presented in Fig. 3) us-ing the SIESTA and QUANTUM ESPRESSO (QE) packages. Within the plane-wave basis sets, ab initio transport proper-ties were evaluated using the PWCOND code , which is part ofthe QE package. Separate calculations were performed for theleads (complex band structure) and scattering regions, whichwere combined using the wave-function matching technique.In Fig. 5 we plot the spin-resolved PDOS on p x,y of Natoms using S ISESTA (top) and QE (bottom). Good gen-eral agreement was found in terms of energy level alignment,namely, LUMO is located about 1.6 eV above E F and thePDOS at E F is largely dominated by minority spin. Theinduced spin moment was found to be about -0.14 µ B and -0.12 µ B for S ISESTA and QE, respectively. The conductancecalculated by
PWCOND was about 0.03 G and 0.79 G for spinup and down which is slightly smaller than the correspondingT RANSISESTA results. -4 -3 -2 -1 0 1 2 3 40123 -4 -3 -2 -1 0 1 2 3 40123-4 -3 -2 -1 0 1 2 3 40123 -4 -3 -2 -1 0 1 2 3 40123-4 -3 -2 -1 0 1 2 3 40123
I IIIVIIIV T r a n s m i ss i on E - E F (eV) updown FIG. 6: Spin-dependent transmission functions of five representa-tive relaxed geometries with different elongation distances presentedin Fig. 2. Blue and red lines denote spin up and down channels,respectively.
Appendix B: Spin-dependent
T(E) for five representativegeometries
We display in Fig. 6 the spin-polarized transmission spec-tra for stretched Ni/N /Ni junctions for five representative ge-ometries at equilibrium as presented in Fig. 3. During thestretching process, the positions and structures of the trans-mission peaks are nearly invariant but the magnitudes arechanged dramatically near E F when the junction is stretched.In the case of configuration I, the non-negligible spin up trans-mission coefficient of about 0.45 is from the partially transmit-ted s -channel of direct Ni − Ni contact. Note that a significantreduction of spin up transmission is observed when the junc-tion is elongated to configuration IV. In contrast, for the spindown channel, the conductance was decreased first and thenincreases up to about 1 G (geometry IV). From configurationI to II, the decreases conductance is related to the breakingof the direct Ni − Ni bond at the nanocontact. 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