Mechanical, Electrical, and Magnetic Properties of Ni Nanocontacts
M. R. Calvo, M. J. Caturla, D. Jacob, C. Untiedt, J. J. Palacios
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J un Mechanical, Electrical, and Magnetic Properties of Ni Nanocontacts
M. R. Calvo, M. J. Caturla, D. Jacob, Carlos Untiedt, and J. J. Palacios Departamento de Fisica Aplicada, Facultad de Ciencias,Universidad de Alicante, San Vicente del Raspeig, E-03790 Alicante, Spain
The dynamic deformation upon stretching of Ni nanowires as those formed with mechanicallycontrollable break junctions or with a scanning tunneling microscope is studied both experimentallyand theoretically. Molecular dynamics simulations of the breaking process are performed. In addi-tion, and in order to compare with experiments, we also compute the transport properties in thelast stages before failure using the first-principles implementation of Landauer ′ s formalism includedin our transport package ALACANT. I. INTRODUCTION
In a foreseeable future, the functionality of elec-tronic devices will rely on the conduction properties ofmolecules or nanoscopic regions comprised of a surpris-ingly small number of atoms. Over the past 10 years, var-ious experimental groups have developed different tech-niques to connect two large metallic electrodes by justan atom or a chain of atoms . These systems receivenames such as atomic-size contacts or nanocontacts. Al-though they are not expected to be of any practical tech-nological application in the near future, these systems arean excellent test bed to learn about electrical transportat the atomic scale.While a large amount of experimental and theoreticalwork has been reported for many metals, a deep theoret-ical understanding is still lacking in the case of magneticnanocontacts, which exhibit a very rich and complexbehavior . Modeling their mechanical, electrical, andmagnetic properties with accuracy is a challenge fromwhich we expect to learn important lessons on our waytoward reliable theoretical descriptions of more sophis-ticated systems of relevance in present and future spin-based devices. We present here a comparison betweentheoretical results of the mechanical, magnetic, and con-duction properties of Ni nanocontacts, and experimentscarried out in our laboratory. II. SCANNING TUNNELING MICROSCOPEHISTOGRAMS
For the experiments, we used a high-stability scanningtunneling microscope (STM) at low temperatures (4.2K)and under cryogenic vacuum conditions. For both tipand sample, we used Ni wire 99.99+% pure. The wire wascleaned by sonication in an acetone bath and scratched toremove contamination attached to the surface. The con-ductance properties of the contacts formed in betweentip and sample were measured in a typical two-probeconfiguration. A constant bias voltage (typically 10-100mV) was applied between tip and sample, and the cur-rent was measured using a homemade current amplifier inthe range of tens of microammeters. We recorded tracesof conductance as a function of the relative tip-sample
FIG. 1: Experimental conductance histogram for Ni nanocon-tacs recorded at a bias voltage of 100 mV and a temperatureof 4.2K where two low-conductance peaks are clearly visible. distance as the two electrodes were brought together andseparated. In every trace, we made a deep tip-sample in-dentation in order to prevent the repetition of the sameatomistic configurations and to assure the clearness of thecontacts. Afterward, the traces were collected to build aconductance histogram such as the one shown in Fig. 1.Histograms, similar to the aforementioned, for the firststages of conduction in Ni nanocontacts have been stud-ied before . There a broad peak around 1.6 G , where G = 2 e /h is the quantum of conductance, has been re-ported as the first peak after vacuum tunneling. Thispeak is attributed to the cases in which the contact con-sists of a single atom. On the other hand, for values ofconductance below the one-atom peak, we can notice alarge amount of data coming from tunneling. This effectis stronger in Ni than in other metals, such as Au, sincefor Ni, some of the traces show a smooth transition fromtunneling to contact without a jump .Here, we have studied in detail the lowest conductancepeak after tunneling and noticed that, indeed, it is not asingle broad peak, but the superposition of two at around1.2 G and 1.5 G . The position of these peaks slightlychanges for different contacts, and this may be the rea-son why they have not always been clearly resolved. Wehave performed separated conductance histograms from FIG. 2: Inset: experimental breaking histograms recorded at4.2K at different bias voltages. The peak above 1 G can beresolved as two different peaks, marked as lower conductancepeak (LC) and higher conductance peak (HC). The figureshows the dependence of the position of the two peaks withthe applied bias voltage averaged over different experimentalrealizations. the traces for the cases of either forming or breaking thecontacts. There we find a different ratio in the height ofthe peaks, being in the case of breaking traces the peakat 1.2 G , in general, higher than the one at 1.5 G andvice versa in the case of making the contacts. Finally, wenotice a dependence of the position of the peaks with thebias voltage with a variation of even 0.3 G in a voltagerange of 300 mV, as shown in Fig. 2.To the best of our knowledge, the described featureshave not been previously reported for any material. Nor-mally, the peaks in the conductance histograms do notchange as a function of the bias voltage , and are equalfor the cases of breaking or forming the contacts. In or-der to understand our observations, one should first try toidentify all the possible atomic configurations that couldlead to a conductance in between 1 G and 2 G in Ninanocontacts, and next look for the reasons that makethe value of conductance to be so dependent on the biasvoltage. In the following discussion, we will address thefirst question. III. MECHANICAL PROPERTIES
The dynamic deformation of Ni nanowires uponstretching until failure has been studied using molec-ular dynamics with empirical potentials. This type ofmodeling has provided significant information about theatomic scale processes occurring during deformation ofnanowires . In this particular work, we focus on thelast stages before failure of Ni nanocontacts. The inter-atomic potential for Ni developed by Mishin et al. wasused in these calculations. This potential has been fit-ted to reproduce the stacking fault energy of Ni. In all FIG. 3: Minimum cross section as a function of elongationalong the [1 0 0] direction for a case with 2645 atoms. Insertshows configurations at different stages of the deformation. calculations, deformation is achieved by displacing theouter two layers of atoms on each side of the simulationbox a fixed distance every 1000 simulation steps, simi-lar to what is done by other authors . Two differentdeformation velocities were used, 1 and 10 m/s .The dependence of different parameters on the defor-mation and, in particular, on the last stages before fail-ure has been studied. On one hand, we have comparedthe deformation of different system sizes, between 77 and2645 atoms, with initial cross sections between 1.5 and3.5 a , where a is the lattice parameter, a =3.52 ˚A ,for the case where tension is applied along the [1 0 0] di-rection. The dependence with crystallographic directionhas also been studied for systems with similar number ofatoms (between 610 and 658) and for directions [1 0 0],[1 1 1], [1 1 0], and [1 1 2]. All these calculations wereperformed at a fixed temperature of 4.2K by rescalingthe velocities of all atoms. Finally, the dependence withtemperature was also studied for the particular case ofdeformation along the [1 0 0] direction and a cross sec-tion of 2 a .The minimum cross section perpendicular to the ap-plied tension is computed every 1000 steps following themethod developed by Bratkovsky et al. . This methodallows us to compare the results of deformation alongdifferent crystallographic directions. Fig. 3 shows theminimum cross section as a function of elongation ob-tained for one particular case with 2645 atoms and de-formation along the [1 0 0] direction. The insets showseveral configurations during the deformation: the ini-tial configuration, an intermediate configuration that isparticularly stable, and the final configuration, which, inthis case, consists of a single atom, a monomer, connect-ing the two sides of the nanowire. The mechanisms fordeformation at this scale have been studied in detail byother authors . Consistent with their work, we observethe sliding of planes during deformation (such as in theintermediate inset in Fig. 3) that results in a narrowing FIG. 4: Histogram of minimum cross sections from 100 independent simulations for crystallographic directions. (a) [1 0 0] and[1 1 2]. (b) [1 1 1] and [1 1 0].FIG. 5: Histogram of minimum cross sections from 25 inde-pendent simulations and four different temperatures. [1 0 0]crystallographic direction. of the wire. This results in preferential configurations,reflected in the plateaus observed in Fig. 3.The dependence of the deformation on the stretchingdirection has been studied for [1 0 0], [1 1 1], [1 1 0],and [1 1 2] directions. Static calculations to obtain theenergy to fracture along these different directions showthat the [1 1 2] direction has the lowest energy per unitsurface, followed by the [1 0 0], [1 1 0], and [1 1 1] direc-tions. However, this behavior could be different duringdynamic deformation. For each direction, calculationswere repeated 100 times in order to gain some statis-tics and obtain a histogram of cross sections. Fig. 4shows the histograms obtained for all crystallographicdirections with clear peaks at particular cross sections.These preferential cross sections do not depend on thesystem size. Histograms obtained from smaller systemsresult in peaks located at exactly the same positions. Itis interesting to point out that the first four peaks ap-pear in all cases. These correspond to the smallest crosssections, consisting of less than three atoms across.These first peaks are also very stable with temperature. Fig. 5 shows the histograms obtained for four differenttemperatures, 4.2K as before and 300K, 610K, and 770K.These histograms were obtained from 25 independent cal-culations and for the [1 0 0] direction. Notice that from4.2K to room temperature, there is a strong reduction inthe first peak. Therefore, the contact breaks very rapidlyat high temperatures. On the contrary, structures withcross sections of two or three atoms seem to be very sta-ble with temperature. For wider structures, there is nota clear peak at high temperature as in the case of 4.2K,which seems to point to very different types of structurespossible when temperature increases. The dependencewith temperature of these structures has been studiedpreviously by other authors .In what follows, we focus on the final stage before fail-ure of these nanocontacts. Two structures have beenidentified: a monomer, where a single atom acts as abridge between the two contacts, and a dimer,where twoatoms aligned forming a bridge between the two sides ofthe wire. These two configurations are shown in the in-sets of Fig. 6, (a) being the monomer and (b) the dimer.In order to identify the dimer, we have calculated thetotal number of neighbors for each atom and the numberof neighbors to the left of the atom position and to theright along the z-direction. In this manner, it is easy toidentify a dimer since it will consist of two neighboringatoms each one with only one neighbor on one side, oneatom to the left, the second one to the right. From all thecases computed including all crystallographic directions(4 0 0), a total of 82% form a dimer before failure, whileonly 18% break from the monomer. In the cases studiedin detail, the monomer is formed before the dimer, but, ina few cases, the contact breaks before forming the dimer. IV. TRANSPORT PROPERTIES
We have finally computed the transport properties ofthe two possible types of configurations, i.e., a monomerand a dimer, before failure. The basics to calculatethe zero-bias, zero-temperature conductance, G , in a FIG. 6: (Left panel) Transmission for both spin species as afunction of energy for the monomer configuration (shown inthe inset) before failure. (Right panel) The same, but for adimer configuration before failure. metallic nanocontact are contained in Landauer ′ s formal-ism, where G is proportional to the quantum mechanicaltransmission probability of the electrons at the Fermi en-ergy, E F G = e h [ T ↑ ( E F ) + T ↓ ( E F )] (1)In this expression, the contributions from spin up (ma-jority) and spin down (minority) channels have been ex-plicitly separated, while the contribution from all theorbital channels has been condensed in T . For sim-plicity, we assume no spin mixing due to either spin-orbit scattering or noncollinear magnetic structures atthe bridge. The detailed electronic and magnetic struc-ture of the nanocontact is important, and, in order toachieve a quantitative level of agreement with experi-ments, one has to rely on first-principles or ab initiocalculations. These calculations are performed with ourcode ALACANT . The details of the calculationhave been presented in previous publications .Essentially, one computes the self-consistent Kohn-Sham Hamiltonian for the narrowest part of the nanocontact,replacing the rest of atoms by a self-energy calculatedbased on a parametrized Bethe lattice.Using as input data two representative atomic configu-rations, as those shown in Fig. 6, the transmission spec-trum of these two structures has been calculated at thelocal spin density approximation (LSDA) level, and closeattention has been paid to the choice of basis set for thecentral part of the nanocontact. As expected for Ni, ma-jority conduction is smooth as a function of energy due tothe s -like nature of this channel, while minority conduc-tion is strongly fluctuating close to the Fermi energy dueto the d -like character of this channel . Interestingly,the average value of the conductance around the Fermilevel for both the examples lies somewhere in the vicinityof 1.6(2 e /h ), which agrees fairly well with the value ofthe highest conductance peak in the histogram (see Fig.1). Remarkably, this value can only be obtained with anLSDA Kohn-Sham potential. The use of generalized gra-dient corrected functionals or hybrid functionals reducesstrongly the conductance for minority electrons, leavingno possible explanation for the high-conductance peak.As far as the origin of the low-conductance peak, onecould possibly attribute it to the presence of a domainwall at the narrowest section. Domain walls have a smallbut sizeable effect on the conductance of Ni nanocontacs,reducing it by an amount that agrees in magnitude withthe conductance of the lowest peak. More experimentaland theoretical work is, however, needed in this directionbefore this hypothesis can be confirmed. Acknowledgments
This work was supported in part by the Min-istry of Education and Science (MEC) of Spain un-der Grant MAT2007-65487, Grant FIS2004-02356, andGrant CONSOLIDER CSD2007-00010 and in part bythe Generalitat Valenciana under Grant ACOMP06/138.The works of M. J. Caturla and C. Untiedt were sup-ported by the Spanish McyT. F. under a Ram´on y Cajalgrant. C. J. Muller, J. M. van Ruitenbeek, and L. J. de Jongh,Phys. Rev. Lett. , 140 (1992). N. Agra¨ıt, J. G. Rodrigo, and S. Vieira, Phys. Rev. B ,12345 (1993). N. Agra¨ıt, A. Levy-Yeyati, and J. M. van Ruitenbeek,Physics Reports , 81 (2003). M. Viret, S. Berger, M. Gabureac, F. Ott, D. Olligs, I. Pe-tej, J. F. Gregg, C. Fermon, G. Francinet, and G. L. Goff,Phys. Rev. B , 220401 (2002). C. Untiedt, D. M. T. Dekker, D. Djukic, and J. M. vanRuitenbeek, Phys. Rev. B , 081401 (2004). C. Sirvent, J. G. Rodrigo, S. Vieira, L. Jurczyszyn, N. Mingo, and F. Flores, Phys. Rev. B , 16086 (1996). C. Untiedt, M. J. Caturla, M. R. Calvo, J. J. Palacios,R. C. Segers, and J. M. van Ruitenbeek, Physical ReviewLetters , 206801 (pages 4) (2007). U. Landman, W. D. Luedtke, N. A. Burnham, and R. J.Colton, Science , 454 (1990). T. N. Todorov and A. P. Sutton, Phys. Rev. Lett. , 2138(1993). Y. Mishin, D. Farkas, M. J. Mehl, and D. A. Papaconstan-topoulos, Phys. Rev. B , 3393 (1999). M. R. Sørensen, M. Brandbyge, and K. W. Jacobsen, Phys.Rev. B , 3283 (1998). A. M. Bratkovsky, A. P. Sutton, and T. N. Todorov, Phys.Rev. B , 5036 (1995). A. Hasmy, E. Medina, and P. A. Serena, Phys. Rev. Lett. , 5574 (2001). J. J. Palacios, A. J. P´erez-Jim´enez, E. Louis, and J. A.Verg´es, Phys. Rev. B , 115411 (2001). J. J. Palacios, A. J. P´erez-Jim´enez, E. Louis, E. SanFabi´an,and J. A. Verg´es, Phys. Rev. B , 035322 (2002). E. Louis, J. A. Verg´es, J. J. Palacios, A. J. P´erez-Jim´enez,and E. SanFabi´an, Phys. Rev. B , 155321 (2003). URL . D. Jacob, J. Fern´andez-Rossier, and J. J. Palacios, Phys-ical Review B (Condensed Matter and Materials Physics)71