Based on first-principles calculations, we demonstrate that magnetism impedes
the formation of long chains in break junctions. We find a distinct softening
of the binding energy of atomic chains due to the creation of magnetic moments
that crucially reduces the probability of successful chain formation. Thereby,
we are able to explain the long standing puzzle why most of the
transition-metals do not assemble as long chains in break junctions and provide
thus an indirect evidence that in general suspended atomic chains in
transition-metal break junctions are magnetic.Comment: 5 pages, 3 figure

Blügel, Stefan

Heinze, Stefan

Mokrousov, Yuriy

Thiess, Alexander

English

arXiv

Thiess, A.

Mokrousov, Y.

Heinze, S.

Blügel, S.

Juelich Shared Electronic Resources

Magnetically hindered chain formation in transition metal break junctions

Based on first-principles calculations, we demonstrate that magnetism impedes the formation of long chains in break junctions. We find a distinct softening of the binding energy of atomic chains due to the creation of magnetic moments that crucially reduces the probability of successful chain formation. Thereby, we are able to explain the long standing puzzle why most of the transition metals do not assemble as long chains in break junctions and thus provide indirect evidence that in general suspended atomic chains in transition-metal break junctions are magnetic

Magnetically Hindered Chain Formation in Transition-Metal Break JunctionsA. Thiess,1,* Y. Mokrousov,1 S. Heinze,2 and S. Blu¨gel11Institut fu¨r Festko¨rperforschung and Institute for Advanced Simulation, Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany2Institut fu¨r Theoretische Physik und Astrophysik, Christian-Albrechts-Universita¨t zu Kiel, D-24098 Kiel, Germany(Received 30 June 2009; published 16 November 2009)Based on first-principles calculations, we demonstrate that magnetism impedes the formation of longchains in break junctions. We find a distinct softening of the binding energy of atomic chains due to thecreation of magnetic moments that crucially reduces the probability of successful chain formation.Thereby, we are able to explain the long standing puzzle why most of the transition metals do not assembleas long chains in break junctions and thus provide indirect evidence that in general suspended atomicchains in transition-metal break junctions are magnetic.DOI: 10.1103/PhysRevLett.103.217201 PACS numbers: 75.75.+a, 73.63.RtOne-dimensional systems, realized experimentally assuspended monatomic chains in break junctions (BJs),have altered our conceptional view on atomic scale junc-tions. For example, because of their enhanced tendency tomagnetism they bear high potential in the field of spin-tronics by combining the possibility to probe, control [1,2],and switch the magnetic state by spin-polarized electricalcurrents. Recent first-principles calculations support theseexpectations and report on sizable magnetic moments [3–7] and giant magnetocrystalline anisotropy energies [4,5,7]in suspended and free-standing transition-metal (TM)monowires (MWs). While the formation of long atomicchains of selected TMs and conductance quantization havebeen experimentally demonstrated [8–10], any conclusiveevidence of magnetism in chains is still missing.This lack of evidence seems even more surprising asmeasurements on chains deposited on surfaces show uni-vocal signatures of local magnetic moments [11,12].Measuring the magnetoresistance in BJs would serve as aproof for magnetism in atomic-sized contacts. In materials,where long MWs can be successfully suspended as re-ported for Ir and Pt [9,13,14], the leads are nonmagnetic,which prevents the pinning tip-magnetization and thus theanalysis via magnetoresistivity measurements. On theother hand, so far it has not been shown that breakingcontacts of magnetic 3d-TMs results in one-dimensionalstructures beyond point contacts.An alternative approach to prove that monatomicchains are magnetic is the search for half-integer conduc-tance originating from 100% spin-polarized conductancechannels. Although Rodrigues et al. [15] reported on sucha half-integer conductance for Co, Ni and Pt BJs, it wasshown both experimentally [16] and theoretically [17] thatnot only magnetic ordering but, e.g., also the adsorption ofH2 can lead to similar values of conductance. In otherwords, the presence of half-integer conductance is not aunique attribute of full spin-polarization and thus cannotserve as a proof of it.Because of these uncertainties, in this Letter we take anew path to address the emergence of magnetism in BJs.We base our study on the most fundamental and easiestaccessible experimental quantity: the probability for suc-cessful chain formation of a given material itself. The trendarising from numerous BJ experiments is that monatomicchain formation is most probable for late 5d TMs as well asAg and Au [10,13,14,18]. To analyze the role of magne-tism for the chain formation in BJs of 3d, 4d, and 5d TMswe apply a recently developed material-specific theoreticalmodel [19] for the formation of long monatomic chainswhich operates in terms of parameters extracted fromab initio calculations. By explicitly including and ex-cluding magnetic exchange interactions, we prove thatmagnetism significantly suppresses the chain formationdue to a substantial reduction of the chain hardness ex-pressed in terms of the maximally sustainable break force.Comparing our results to experimental findings, we areable to provide an indirect evidence that chains in BJsare indeed magnetic.We will briefly recall the model which allows us toinvestigate the formation probability of suspended mona-tomic chains under tension in BJs [19] before applying it toboth magnetic and nonmagnetic chains. In this model,chain formation succeeds if the criteria for stability andproducibility are met. The criterion for stability addressesthe rupture of the chain via breaking of the bond betweentwo neighboring chain atoms. The criterion for produci-bility is concerned with the chain elongation that is com-posed of two processes: At first one atom has to beextracted out of the lead into the chain. This transfer leadsto a reduction of the coordination of this particular atomand consequently additional external energy is required,which we account for by the difference ELead ¼ EMW ELead of the energy of cohesion for an atom in the lead,ELead, and in the chain, EMW, both at equilibrium distance.This energy can be stored mechanically and is released inthe second process of relaxing all chain’s bonds to asmaller interatomic distance after an additional atom hasjoined the chain. These competing contributions to the totalenergy of the system determine whether it is energeticallyfavorable to grow the chain by one atom or not. In order toPRL 103, 217201 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending20 NOVEMBER 20090031-9007=09=103(21)=217201(4) 217201-1  2009 The American Physical Societyapply both criteria only two quantities have to be known:the binding energy EðdÞ of a MW atom as a function ofinteratomic distance d and the cohesive energy differenceELead. We will show that both parameters depend on theformation of magnetic moments.In order to determine these parameters we carried outspin-polarized and non-spin-polarized ab initio calcula-tions in the generalized gradient approximation [20] tothe density functional theory for selected 3d, 4d, and 5dTMs, employing the full-potential linearized augmentedplane-wave method for one-dimensional (1D) systems[21], as implemented in the FLEUR code [22]. We usedthe bulk version of this code to calculate the cohesionenergy [23]. Here we considered in all cases the truemagnetic (3d) or nonmagnetic (4d, 5d) bulk ground stateas the reference configuration. For calculations of the bareMWs in all cases we considered the non- (NM), ferro-(FM) and antiferromagnetic (AFM) order and includedbasis functions with plane waves up to kmax ¼ 4:4 a:u:1and used 64 k points in one-half of the 1D Brillouin zone.We calculated all 3d MWs in the scalar-relativistic ap-proach, while spin-orbit coupling was added for all 4d’sand 5d’s.The calculated spin moments MðdÞ and the bindingenergy EðdÞ are shown in Fig. 1 for Fe and W MWs asexamples. Both chains exhibit sizable magnetic momentsand the binding energies for the nonmagnetic (NM) andmagnetic (M) case differ substantially. This is true, inparticular, for large distances, where the energy differ-ence EspðdÞ ¼ ENMðdÞ  EMðdÞ approaches the spin-polarization energy Espð1Þ of an isolated atom. A closerlook reveals, that this overall tendency to magnetism in 1Dchains results in finite magnetic moments even in 5d-TMsalready at the NM equilibrium distance dNM0 or upon smallstretching leading to a magnetic expansion of, e.g., dM0 dNM0 ¼ 0:2 a:u: for W [Fig. 1(a)] and being more pro-nounced, e.g., for Fe [Fig. 1(b)], in agreement withRefs. [5,25]. Overall, the binding potential energies of Mand NM chains differ not only by spin-polarization energyand a constant shift in d0, but also their slopes are cruciallydifferent [Figs. 1(a) and 1(b)].In order to analyze the binding energy quantitatively, wefit a Morse potentialE ðdÞ ¼ Eð1Þð1 eðdd0ÞÞ2 (1)to the discrete set of calculated energy points [Figs. 1(a)and 1(b)] for the different magnetic states. Besides theequilibrium distance d0, the Morse potential can be char-acterized by the following two physically transparent pa-rameters: the inflection point d^ ¼ d0 þ ln 2= and thebreak force F0 ¼ Eð1Þ=2, which is the maximal slopeFðd^Þ of the potential. Together withELead we evaluate fora given close-packed surface [Fig. 2(a)], these four quan-tities constitute a minimal basis for a realistic descriptionof the chain formation process, providing us with an accu-rate and continuous representation of the binding energycurve.As we see from Fig. 2, magnetism has a very differentimpact on these four quantities: The cohesion energy dif-ference ELead [Fig. 2(a)] of 4d and 5d TMs remainsalmost unchanged for magnetic and nonmagnetic chains,as these elements are nonmagnetic at surfaces and developonly small magnetic moments at d0. For 3d TMs thesituation is different: in the wire the magnetic momentsat d0 are already close to the saturated values and largerthan for atoms at surfaces, which leads to a sizable gain inspin-polarization energy and thereby to a considerablereduction of ELead [26]. The position of d^ with respectto d0 [Fig. 2(b)], a quantity crucial for the stability of thewires, reveals only minor changes of less than 5% betweencalculations with and without spin polarization. The cru-cial impact of magnetism is the softening of the bindingenergy curve, which leads to a significant reduction of thebreak force F0 for all considered 3d, 4d (not shown) and 5dTMs [Fig. 2(c)]. For example, the break forces with andwithout spin-polarization forW differ by a factor of 2. Bothat the beginning and the end of the 5d series, this ratioreduces according to smaller maximal magnetic momentsand is equal to one for the nonmagnetic noble metal Au.The break force F0 not only represents the maximal forceapplicable to a chain, but also serves as a measure for themaximal amount of mechanical energy which can begained upon relaxation of its bonds. In any case, highvalues of F0 favor successful chain creation in BJ experi-ments. Thus, as the appearance of magnetism cruciallyreduces F0, we can conclude that the formation of localmagnetic moments suppresses chain formation.FIG. 1 (color online). Calculated MW energy EðdÞ (circles) asa function of interatomic distance d (throughout the Letter givenin a:u: ¼ 0:0529 nm) for both nonmagnetic (NM) (black) andmagnetic (M) state (green or gray) are shown for (a) Fe and(b) W. The Morse fit (lines) provides a universal fit to thesepoints well below the required accuracy of about 100 meV forchemical bonding and can be characterized by the equilibriuminteratomic distance d0 and the inflection point d^. EðdÞ and themagnetic moments M in (c) and (d) correspond to the FM andAFM ground state for Fe and W, respectively.PRL 103, 217201 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending20 NOVEMBER 2009217201-2In order to capture the origin of the magnetically in-duced reduction of F0, we relate the magnetic quantities tothe nonmagnetic ones. In the first approximation, the in-fluence of the magnetization on the binding energy poten-tial EspðdÞ ¼ ENMðdÞ  EMðdÞ can be attributed to theHund-type intra-atomic exchange interaction 12 IM2ðdÞ be-tween mostly d electrons but also s electrons on the atomicsites and the interatomic Heisenberg JðdÞ ~MiðdÞ ~Miþ1ðdÞexchange contributions between the atomic spins. Thebinding energy, EMð1Þ, prefactor in Eq. (1), then readsEMð1Þ ¼ ENMð1Þ  Espð1Þ þ Espðd0Þ, where Espð1Þ ¼12 IM2ð1Þ is purely given by intra-atomic exchange of afree atom and Espðd0Þ ¼ ENMðdNM0 Þ  EMðdM0 Þ is the en-ergy difference of the NM and M states at the correspond-ing equilibrium distance. Taking as an example 5d TMs wecan safely assume even for W, exhibiting the largest equi-librium magnetic moment of MðdM0 Þ  1B through theseries, that the impact of magnetism on the equilibriumproperties of the chains is small and set for simplicity dM0 ¼dNM0 and Espðd0Þ¼0. As is apparent from Fig. 2(b), it isalso reasonable to assume that M ¼ NM, in which casethe magnetic break force simplifies toFM0 ¼M2EMð1Þ ¼ FNM0 NM2IdM2ð1Þ: (2)For 5d TM chains we estimated FM0 according to Eq. (2)using ab initio values of the nonmagnetic break force FNM0 ,magnetic moments at d ¼ 6:5 a:u: and the atomic ex-change integrals between d electrons, Id, from Ref. [27],and plotted it in comparison to the magnetic break forceFIG. 3 (color online). Phase diagrams for Fe, Ru, and W-BJswith (a), (c), (e) and without (b), (d), (f) spin polarization of thechain atoms. Plots indicate regions of stability (S, gray), pro-ducibility (P, light gray), separated by a white region or over-lapping in the SP region (in green or dark gray). The startingpoint along the x axis is d0 and the assumed surface orientationsof the leads are indicated. The input parameters for W are givenin Figs. 2(a)–2(c) and for Fe and Ru in [26]. (g) provides aschematic summary of our results. Shown is the chain formationprobability, proportional to the size of SP regions, versus chainlength, proportional to the highest N for which an SP regionexists, with (green boxes) and without spin polarization (graycircles) in relation to the experimental findings (bold red)[10,13,14,16,18,29] in all cases in arbitrary units relative toAu. Arrows indicate (exemplified for Fe, Ru, and W) the con-sequence on the chain formation caused by switching off thefinite magnetization in the chain.FIG. 2 (color online). (a) Cohesion energy difference ELead,(b) difference d^ d0 ¼ ln2= and (c) break force F0 for non-magnetic (marked as NM, black squares) and magnetic (markedas FM or AFM, green circles) 5d-TM chains. Broken line in(c) stands for the break force FM0 calculated according to Eq. (2).As indicated by the gray shaded area, W and Re MWs reveal anAFM ground state at all interatomic distances, while the rest ofthe chains are FM. With orange squares in (c) the break force forthe FM W and Re MWs is shown for comparison.PRL 103, 217201 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending20 NOVEMBER 2009217201-3determined from ab initio in Fig. 2(c). Good qualitativeagreement between the two break force curves underlinesthat the intra-atomic exchange I is the major origin of themagnetically driven reduction of F0, while the interatomicexchange plays only a minor role. This conclusion isfurther verified by the observation that changing the mag-netic order from AFM to FM in W and Re MWs resultsonly in a small change of F0 [see Fig. 2(c)].We now turn back to the analysis of our ab initio results.With the knowledge of all key quantities entering thecriteria for stability and producibility we can further ana-lyze both criteria in the phase space of the number of atomsN and interatomic distance d presented in Fig. 3. Each ofthe criteria leads to a distinct region where it is fulfilled andaccordingly the chain is stable (S) or producible (P).Ideally for a successful chain elongation event to happen,both regions (S) and (P) have to overlap (SP).Comparison of the phase diagrams for different TMs,shown for Fe, Ru, and W in Fig. 3, underlines, that theformation of local magnetic moments strongly suppressesthe probability of chain formation for 3d, 4d, and 5delements. If we ignore the formation of magnetism amongthe 3d-, 4d-, and 5d-TM series Cr, Mn, Fe, Ru, Rh, Ag, Re,Os, Ir, Pt, and Au exhibit extensive SP regions [Figs. 3(b)and 3(d)] indicating successful chain formation for theseelements. Even for W [Fig. 3(f)] with bcc(110) electrodesneglecting magnetism results in touching S and P regions,indicating chain formation for more open lead structures.Allowing for the formation of local spin moments thepicture changes completely: SP regions emerge exclu-sively for Ru [Fig. 3(c)], Ag, Ir, Pt, and Au while for allother elements the S and P regions are clearly separatedand no chain formation occurs [Figs. 3(a) and 3(e) and in[19] ]. While for Pd and Pt chains the influence of magne-tism is small due to relatively small moments enteringEq. (2), the SP regions of Ru [Fig. 3(c)] and Ir are consid-erably less extended for magnetic chains than for non-magnetic ones, underlining the suppression of chainformation by magnetism.While our predictions based on the assumption thatchains in BJs are magnetic match and explain the experi-mental findings for successful Ag, Ir, Pt, and Au chainformation, the results of the model for nonmagnetic sus-pended chains contradict the experimental observations atseveral crucial points [Fig. 3(g)]. First, nanocontacts of3d-TMs such as Fe are reported to form only point contactswith no tendency to form longer chains [16]. Second, alsoBJ experiments using Was tip material result only in pointcontacts [28], moreover, W tips are widely used in STMand AFM experiments due to their structural rigidity pre-venting substrate-induced reformations [29]. Third, non-magnetic Ir chains would become as long as those of Pt,and almost as long as those of Au, in direct disagreementwith experiments which report significant decrease ofchain formation probability and length when going fromAu to Ir [10,13,14,18]. These clear contradictions to exist-ing experimental evidence lead us to the conclusion thatonly when chains in BJs are magnetic, the experimentallyobserved trends can be reproduced and explained through-out the 3d, 4d, and 5d transition- and noble-metal series.Therefore, by reductio ad contradictum, comparing theo-retical predictions with experimental findings, we providea convincing evidence that TM chains in BJs are magnetic.We thank J.M. van Ruitenbeek for fruitful discussions.S. H. thanks the Stifterverband fu¨r die DeutscheWissenschaft for financial support.*a.thiess@fz-juelich.de[1] P. Lucignano et al., Nature Mater. 8, 563 (2009).[2] M. R. Calvo et al., Nature (London) 458, 1150 (2009).[3] A. Delin and E. Tosatti, Phys. Rev. B 68, 144434 (2003).[4] Y. Mokrousov et al., Phys. Rev. Lett. 96, 147201 (2006).[5] J. C. Tung and G.Y. Guo, Phys. Rev. B 76, 094413 (2007).[6] J. Ferna´ndez-Rossier et al., Phys. Rev. B 72, 224418(2005).[7] A. Smogunov, A. Dal Corso, and E. Tosatti, Phys. Rev. B78, 014423 (2008).[8] A. I. Yanson et al., Nature (London) 395, 783 (1998).[9] R. H.M. Smit et al., Phys. Rev. Lett. 87, 266102 (2001).[10] T. Kizuka, Phys. Rev. B 77, 155401 (2008).[11] P. Gambardella et al., Nature (London) 416, 301 (2002).[12] C. F. Hirjibehedin, C. P. Lutz, and A. J. Heinrich, Science312, 1021 (2006).[13] M. Ryu and T. Kizuka, Jpn. J. Appl. Phys. 45, 8952(2006).[14] T. Shiota et al., Phys. Rev. B 77, 125411 (2008).[15] V. Rodrigues et al., Phys. Rev. Lett. 91, 096801 (2003).[16] C. Untiedt et al., Phys. Rev. B 69, 081401(R) (2004).[17] V.M. Garcı´a-Sua´rez et al., Phys. Rev. B 72, 045437(2005).[18] W.H.A. Thijssen et al., Phys. Rev. Lett. 96, 026806(2006).[19] A. Thiess et al., Nano Lett. 8, 2144 (2008).[20] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996).[21] Y. Mokrousov, G. Bihlmayer, and S. Blu¨gel, Phys. Rev. B72, 045402 (2005).[22] http://www.flapw.de.[23] We calculate Esurf by substracting the surface energy ofthe corresponding element from Ref. [24] from the calcu-lated energy difference Ebulk between a bulk atom and aMW atom at d0.[24] H. L. Skriver and N.M. Rosengaard, Phys. Rev. B 46,7157 (1992).[25] D. Spisˇa´k and J. Hafner, Phys. Rev. B 67, 214416 (2003).[26] See EPAPS Document No. E-PRLTAO-103-034947 forthe set of parameters obtained for Fe and Ru chains. Formore information on EPAPS, see http://www.aip.org/pubservs/epaps.html.[27] M. S. S. Brooks and B. Johansson, J. Phys. F 13, L197(1983).[28] A. Halbritter et al., Phys. Rev. B 68, 035417 (2003).[29] U. Landman et al., Science 248, 454 (1990).PRL 103, 217201 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending20 NOVEMBER 2009217201-4

Magnetically hindered chain formation in transition-metal break junctions

Abstract

Similar works

Full text

Available Versions

Juelich Shared Electronic Resources

Juelich Shared Electronic Resources

Crossref