We have investigated Pd nanowires theoretically, and found that, unlike
either metallic or free atomic Pd, they exhibit Hund's rule magnetism. In long,
monoatomic wires, we find a spin moment of 0.7 Bohr magnetons per atom, whereas
for short, monoatomic wires between bulk leads, the predicted moment is about
0.3 Bohr magnetons per wire atom. In contrast, a coaxial (6,1) wire was found
to be nonmagnetic. The origin of the wire magnetism is analyzed.Comment: 6 pages, including 4 figure

A. Delin

E. Tosatti

J. M. Wills

J. P. Perdew

N. Zabala

R. Weht

R. E. Peierls

English

arXiv

Crossref

Magnetism in Atomic-Size Palladium Contacts and Nanowires

We have investigated Pd nanowires theoretically, and found that, unlike either metallic or free atomic Pd, they exhibit Hund’s rule magnetism. In long, monostrand nanowires, we find a spin moment of 0:7B per atom, whereas for short, monostrand nanowires between bulk leads, the predicted moment is about 0:3B per nanowire atom. In contrast, a coaxial (6,1) nanowire was found to be nonmagnetic. The origin of the nanowire magnetism is analyzed

Delin, A

Tosatti, E

Weht, R

Sissa Digital Library

P H Y S I C A L R E V I E W L E T T E R S week ending6 FEBRUARY 2004VOLUME 92, NUMBER 5Magnetism in Atomic-Size Palladium Contacts and NanowiresA. DelinAbdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34100 Trieste, ItalyE. TosattiAbdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34100 Trieste, ItalyInternational School for Advanced Studies (SISSA), via Beirut 2-4, 34014 Trieste, ItalyINFM DEMOCRITOS National Simulation Center, via Beirut 2-4, 34014 Trieste, ItalyR. WehtDepartamento de Fı́sica, Comisión Nacional de Energı́a Atómica (CNEA), Avenida General Paz y Constituyentes,1650 San Martı́n, Argentina(Received 30 July 2003; published 2 February 2004)057201-1We have investigated Pd nanowires theoretically, and found that, unlike either metallic or free atomicPd, they exhibit Hund’s rule magnetism. In long, monostrand nanowires, we find a spin moment of0:7B per atom, whereas for short, monostrand nanowires between bulk leads, the predicted moment isabout 0:3B per nanowire atom. In contrast, a coaxial (6,1) nanowire was found to be nonmagnetic. Theorigin of the nanowire magnetism is analyzed.DOI: 10.1103/PhysRevLett.92.057201 PACS numbers: 75.75.+a, 71.70.Ej, 73.63.NmFIG. 1 (color online). Schematical drawing of the nanowiregeometries addressed in this Letter. From left to right: (6,1)coaxial nanowire; monostrand nanowire; short monostrandshould be considered instead of those of the energy, since nanowire between bulk leads.Magnetism at the nanoscale is an exciting emergingresearch field, of both basic and applied relevance. For afuture spin-based technology working in the quantum-mechanical regime, an understanding of nanomagneticphenomena will be crucial; yet, relatively little is cur-rently understood about how magnetism arises and how itaffects the properties of metals at the nanoscale.Systems of special interest are nanowires and atomic-sized nanocontacts. The low dimensionality of such sys-tems causes specific physical phenomena to appear, forexample quantized ballistic conductance [1] and helicalnanowire geometries [2,3]. These phenomena interplaywith the possible presence of magnetism in the nano-system, especially of a genuine Hund’s rule magneticorder parameter. Here, we report theoretical studies ofemerging magnetism in Pd nanowires in various geome-tries (see Fig. 1). Monostrand nanowires of Pd, i.e., nano-wires consisting of a single straight line of atoms, haverecently been observed by Rodrigues et al. [4]. We findmagnetic moments as high as 0:7B per atom for infi-nitely long, straight, monostrand nanowires. Even short,three-atom Pd nanowire chains between bulklike leadsare predicted to possess a magnetic moment around0:3B per nanowire atom, while the bulk leads remainnonmagnetic. In contrast, thicker coaxial (6,1) nanowiresare predicted to be nonmagnetic.We have assumed that the ultimately thin wires arestraight, with equidistant atoms. For monatomic wires notattached to leads, one could imagine more complicatedwire geometries, such as zigzag configurations, or Peierlsdistortions [5] leading to dimerization, trimerization, ormultimerization. However, when suspended betweenleads, local minima or saddle points of the string tension0031-9007=04=92(5)=057201(4)$22.50 they alone will in quasiequilibrium correspond to long-lived, or ‘‘magic’’ nanowires [3]. In Au, the zigzag de-formations do not survive the string tension, and the samewould happen, if they existed, in Pd. Thus, we concludethat zigzag distortions do not exist in the systems ad-dressed here. With regards to Peierls dimerization, tri-merization, or multimerization distortions, they shouldlead to insulating nanowires.Of course, thermal fluctuations, very large in a nano-system, will generally act to destroy static magnetic orderin the absence of an external field. There are nonethelesstwo different fluctuation regimes: slow and fast. Slowfluctuations transform a nanomagnet to a superparamag-netic state, where magnetization fluctuates on a long timescale between equivalent magnetic valleys, separated,e.g., by anisotropy-induced energy barriers. If the barriers2004 The American Physical Society 057201-12.2 2.4 2.6 2.8 3 3.2 3.4 3.6bond length (Å)00.20.40.60.8magnetic moment (µ B)SR + SOSRPdFIG. 2. Magnetic moment per atom as a function of bondlength for a long, monostrand Pd nanowire. The vertical linepoints out the equilibrium bond length. (SR SO calculation including spin-orbit coupling and scalar relativisticterms; SR  calculation including scalar relativistic terms butnot spin-orbit coupling).P H Y S I C A L R E V I E W L E T T E R S week ending6 FEBRUARY 2004VOLUME 92, NUMBER 5are sufficiently large, the nanosystem spends most ofthe time in a single magnetic valley, and will for manypractical purposes behave as magnetic. We may underthese circumstances be allowed to neglect fluctua-tions altogether, and to approximate (as we will dohere) the calculated properties of the superparamagneticnanosystem with those of a statically magnetized one.Experimentally, evidence of one-dimensional (1D) super-paramagnetism with fluctuations sufficiently slow on thetime scale of the probe has been reported in Co atomicchains deposited at Cu surface steps [6]. At the oppositeextreme —a situation reached, for example, at high tem-peratures—the energy barriers are so readily overcomethat the magnetic state is totally washed away by fastfluctuations, leading to a conventional paramagneticstate. A complete description of this high entropy stateis beyond scope, but a conventional T  0 nonmagnetic,singlet solution of the Kohn-Sham electronic structureequations can be used in its place, at least as a crudeapproximation.The present density functional calculations [7] wereperformed with an all-electron full-potential linearmuffin-tin orbital (FP-LMTO) basis set [8] togetherwith a generalized gradient approximation (GGA) [9] tothe exchange-correlation functional. A simpler local den-sity functional [10] was also tested, giving results verysimilar to the GGA. As a double check, some of thecalculations were repeated using the linear augmentedplane-wave code WIEN2K [11]. None of these calculationsassume any shape approximation of the potential or wavefunctions. We performed both scalar-relativistic calcula-tions, and calculations including the spin-orbit couplingas well as the scalar-relativistic terms. In the calcula-tions involving the spin-orbit interaction, the spin axiswas chosen to be aligned along the nanowire direction.The calculations were performed with inherentlythree-dimensional codes. Thus, the infinitely long,straight, isolated monostrand nanowires, as well as the(6,1) coaxial nanowires, were simulated by regular arraysof well spaced nanowires. The short nanowire consistedof three atoms in a straight line attached to thick planarslabs of close-packed bulk Pd. The bond length in theshort nanowire was chosen to be 2:7 A, as suggested bytransmission electron microscope images of Pd mono-strand nanowires [4], and corresponds to a somewhatstretched nanowire. Convergence of the magnetic momentwas checked with respect to k-point mesh density, Fouriermesh density, tail energies, nanowire-nanowire vacuumdistance, and bulk thickness. In the calculations, spin-orbit coupling was seen to have only a minor effect on theresults, in contrast to the situation for 5d metals [12].Figure 2 shows the magnetic moment per atom for the(infinitely) long Pd monostrand nanowire, as a function ofthe bond length along the nanowire. The total magneticmoment rapidly reaches 0:7B at a bond length around2:3 A, and retains this magnetic moment over a long057201-2region. The steep rise at the onset of magnetism is almostentirely due to 4d polarization, which reaches a maxi-mum of 0:5B already at 2:6 A and then decreasesmonotonically. At 3:5 A, the magnetic moment dis-appears completely, where the straight nanowire under-goes a metal-insulator transition, with the opening of ads gap, foreshadowing that of the noninteracting atoms.Experimental data [4], as well as a negative curvature ofenergy versus length for spacings above 2:9 A suggest,however, that the nanowire has already broken due toexcessive string tension well before large bond lengthsin themselves provoke a metal-insulator transition.For the long monostrand nanowire, the energy gain peratom due to spin polarization is around 12 meV (spin-orbit coupling included) at 2:56 A, which is the bondlength minimizing the total energy. For comparison, wemention that in bulk Ni the corresponding energy gain isaround 40 meV, indicating that the Pd nanowire magne-tism might actually exist not only at ultralow tempera-tures. Antiferromagnetic Pd monostrand nanowireconfigurations were also tested, and found to be energeti-cally unstable compared to the ferromagnetic configura-tion. Our result differs from that of Bahn et al. [13] whofound no magnetism in pseudopotential calculations forPd monostrand nanowires. It seems possible that thedisagreement could arise in this very borderline casedue to the different methods used, in which case we wouldtend to trust our all-electron approach better.Why does the Pd monostrand nanowire magnetize? Inthe bulk, and also at surfaces, the Pd 4d band is slightlytoo wide to sustain spin polarization. In the atom, on theother hand, Pd forms a singlet with a completely filled 4dshell. Thus, the limiting cases are all nonmagnetic and thestrong Hund’s rule magnetism in the nanowire appears057201-2P H Y S I C A L R E V I E W L E T T E R S week ending6 FEBRUARY 2004VOLUME 92, NUMBER 5rather unexpected. However, the borderline case of Pdmagnetism is demonstrated by the fact that certain clus-ters are predicted to have a magnetic ground state [14].From the atomic perspective, as the distance between Pdatoms decreases, the increased interatomic hybridizationcauses the 4d band to become partially unfilled due tod ! s transfer, and thus symmetry breaking through spinpolarization becomes possible. Hund’s rules make it rea-sonable to assume that spin polarization will also beenergetically favorable. From the bulk perspective, thereduction of the number of nearest neighbors in the nano-wire compared to the bulk causes a narrowing of the 4dband, and the bandwidth may become sufficiently smallthat the gain in exchange energy due to spin polarizationis larger than the increase in kinetic energy. Thus, usingthis 4d band-narrowing argument, we can rationalize theexistence of a magnetic state in the nanowire.However, we have reason to believe that this ex-planation of the large magnetic moment in long Pdmonostrand nanowires is too simple, and that 4d bandnarrowing is not the only mechanism at work, but thatthe one-dimensionality of the system is crucial. Wewill illustrate this point by analyzing the band structureof the long Pd monostrand nanowires in some detail.Figure 3 shows the band structure of the Pd monostrandnanowire for several different bond lengths, as it goesfrom insulator, to ferromagnet, to paramagnet, for de-creasing bond length. There are six orbitals to consider,-2-1012energy (eV)-2-1012 3.6 Å 2.8 Å 2.6 Å 2.4 ÅΓ A2.2 ÅFIG. 3. Scalar-relativistic Pd monostrand nanowire bandstructures, along the nanowire direction. The Fermi energy isat zero. The upper panels show the ferromagnetic calculation,and the lower panels the nonmagnetic calculation.057201-3two s dz2 orbitals, two dxz; dyz orbitals, and twodxy; dx2y2 orbitals, as illustrated in Fig. 4. The twos dz2 orbitals give rise to the two bands with highestdispersion. Of these, the band with mostly s character hasan electron band edge close to the Fermi level at , andthe d character dominated one has a hole band edge closeto the Fermi level at the zone boundary A. Next, we havethe two dxz; dyz orbitals, which are degenerate and havea band edge close to the Fermi level at . Finally, thetwo dxy; dx2y2 orbitals form a flat band situated between0.5 and 1 eV below the Fermi level.The dxy; dx2y2 band lies far below the Fermi levelwith both spins completely occupied, and gives no con-tribution to magnetism. The spin moment is related to thes dz2 and dxz; dyz bands, which have a high dispersion,and display one-dimensional band edges close to theFermi level at  and A. In the magnetic regime, i.e.,from 2:3 A to 3:5 A, these three band edges all are nearlydegenerate in energy and close to the Fermi level. Thisaccidental feature of the long Pd monostrand nanowireband structure dramatically increases the density ofstates, with divergent Van Hove singularities close tothe Fermi level. A spin splitting of these band edgescan thus lower the total electron band energy, somewhatanalogous to a band Jahn Teller, or a Peierls instabilityeffect. Interestingly, for bond lengths of 2:8 A or more,even the s-dominated band edge at  is spin split aroundthe Fermi level.The fact that the Stoner stability criterion against mag-netism is necessarily violated leading to a magnetizednanowire when a band edge approaches to the Fermi levelis universal. It was pointed out earlier by Zabala et al. [15]-202energy (eV)Γ Akz-202Γ Akzs dz2(dxz, dyz) (dxy, dx2-y2)FIG. 4. Character-resolved scalar-relativistic band structurealong the nanowire direction, for a nonmagnetic Pd nanowirewith a bond length of 2:6 A. The Fermi energy is at zero.057201-3P H Y S I C A L R E V I E W L E T T E R S week ending6 FEBRUARY 2004VOLUME 92, NUMBER 5and demonstrated in explicit calculations for aluminumnanowires [16,17]. However, for a simple sp metal, suchas Al, the ensuing 1D magnetism implies rather smallmoments supported by a very weak exchange interaction.Consequently, those moments will readily be washedaway by fluctuations. In the Pd case, the situation isdifferent. Here, we expect a robust superparamagneticstate for temperatures not too high, transformable to agenuine magnetic state under an external field. The 1Dsingularities — in scattering terms the relevant bandedge singularities correspond to standing waves, here ofs dz2 and dxz; dyz electrons and holes — provide heremerely a mechanism to trigger awake a strong Hund’s rulemagnetic moment, based on the strong exchange interac-tion of the d electrons.If the Pd monostrand nanowire magnetism is mainlytriggered by a 1D scattering phenomenon, it should dis-appear or at least become much smaller when the numberof nearest neighbors becomes large. To test this assertion,we, as already mentioned, also performed calculations fora two-layer coaxial (6,1) nanowire. As expected, it wasfound to be nonmagnetic, supporting the view that themagnetism in the Pd monostrand nanowire is, to a largeextent, a 1D phenomenon. This 1D magnetism in Pdproves nevertheless to be remarkably robust, as it surviveseven down to three-atom chains suspended between non-magnetic leads.The magnetic moment in the short-nanowire sus-pended between bulk Pd leads is substantially smallerthan the moment of the long monostrand nanowire mo-ment; 0:3B per nanowire atom compared to 0:7B.Because of the high complexity of the band structurefor the short nanowire (not shown), it is not possible tosingle out individual band edges as responsible for trig-gering the Hund’s rule magnetism in the short-nanowirecase. However, we find that the bulk leads affect theelectronic structure in the short nanowire resulting in awider 4d band than in the long nanowire, which in turnreduces the magnitude of the magnetic moment.In summary, we predict that ultimately thin Pdnanowires, both short and long, exhibit a spin-polarizedground state. The resulting superparamagnetic state of thenanowire should show up in the ballistic conductance inthe form of a strong and unusual magnetic field andtemperature dependence as well as spin polarization ofthe current through the nanowire. Rodrigues et al. [4]recently measured the charge conductance of Pd nano-contacts and found features in the conductance histogramabove as well as below one conductance quantum G0 2e2=h. The existence of features below G0 is intriguingsince it seems to suggest that the s-dominated band cross-ing the Fermi level is spin split around the Fermi level, asituation our calculations do predict for a stretched wirewith bond length of 2:8 A or larger. Another speculativeexplanation of the low conductance could entail some057201-4kind of spin reversal amid the nanowire [18]. More theorywork will be needed to address their data, explicitlyincluding such elements as tip form, spin structures,impurities [19], and temperature as well as their effectson the system’s conductance. We are currently working toaddress some of these issues.A. D. acknowledges financial support from theEuropean Commission through Contract No. HPMF-CT-2000-00827, STINT (The Swedish Foundation forInternational Cooperation in Research and HigherEducation), and NFR (Naturvetenskapliga forskingsrå-det). Work at SISSA was also sponsored through TMRFULPROP, MUIR (COFIN and FIRB RBAU01LX5H),and by INFM/F. J. M.Wills is acknowledged for letting ususe his FP-LMTO code.We are also grateful to D. Ugarte forsharing with us the results of Ref. [4] prior to publication.[1] B. J. van Wees et al., Phys. Rev. Lett. 60, 848 (1988).[2] Y. Kondo and K. Takayanagi, Science 289, 606 (2000).[3] E. Tosatti et al., Science 291, 288 (2001).[4] V. Rodrigues, J. Bettini, P C. Silva, and D. Ugarte, Phys.Rev. Lett. 91, 096801 (2003).[5] R. E. Peierls, Quantum Theory of Solids (OxfordUniversity Press, London, 1955).[6] P. Gambardella et al., Nature (London) 416, 301 (2002).[7] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964);W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).[8] J. M. Wills, O. Eriksson, M. Alouani, and O L. Price, inElectronic Structure and Physical Properties of Solids,edited by H. Dreyssé (Springer-Verlag, Berlin, 2000).[9] J. P. Perdew, in Electronic Structure of Solids 1991,edited by P. Ziesche and H. Eschrig (Akademie Verlag,Berlin, 1991).[10] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566(1980); J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048(1981).[11] P. Blaha, K. Schwarz, and J. Luitz, computer code WIEN97(Vienna University of Technology, Vienna, 1997).[12] A. Delin and E. Tosatti, Phys. Rev. B 68, 144434 (2003);A. Delin and E. Tosatti (to be published).[13] S. R. Bahn and K.W. Jacobsen, Phys. Rev. Lett. 87,266101 (2001).[14] M. Moseler, H. Hakkinen, R. N. Barnett, andU. Landman, Phys. Rev. Lett. 86, 2545 (2001).[15] N. Zabala, M. J. Puska, and R. M. Nieminen, Phys. Rev.Lett. 80, 3336 (1998); 82, 3000 (1999).[16] A. Ayuela, H. Raebiger, M. J. Puska, and R. M. Nieminen,Phys. Rev. B 66, 35417 (2002).[17] T. Ono, H. Yamasaki, Y. Egami, and K. Hirose,Nanotechnology 14, 299 (2003).[18] A. Smogunov, A. Dal Corso, and E. Tosatti, Surf. Sci. 507,609 (2002); A. Smogunov, A. Dal Corso, and E. Tosatti,Surf. Sci. 532, 549 (2003).[19] C. Untiedt, D. M. T. Dekker, D. Djukic, and J. M.van Ruitenbeek, cond-mat/0309622.057201-4

Magnetism in atomic-size palladium contacts and nanowires

Palladium (Pd) nanowires, that exhibit Hund's rule magnetism are investigated. A spin moment of 0.7μB per atom is found in long, monostrand nanowires. The predicted moment is about 0.3μB per nanowire atom for short, monostrand nanowires between bulk leads. Results show that a coaxial (6,1) nanowire was nonmagnetic in nature.</p

Magnetism in Atomic-Sized Palladium Contacts and Nanowires

Abstract

Similar works

Full text

Available Versions

Crossref

Sissa Digital Library

Swepub

SISSA Digital Library