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Growth of metallic nanowires assisted with a tip. Study of their physical properties. BAUD Stéphanie Laboratoire de Physique Moléculaire, UMR CNRS 6624, Faculté des Sciences, la Bouloie, Université de Franche Comté, 25030 Besançon Cedex, France

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Draft of the presentation 1 st part: Study of platinum surfaces method of calculation (FLAPW). surface energies, electronic structures and relaxation of platinum surfaces. step energies and step relaxations. determination of STM pictures. 2 nd part: Elaboration of nanowires presentation of the KMC code. growth of nanowires with a repulsive or attractive moving STM tip. sorting of atoms with a moving STM tip. 3 rd part: Properties of Co nanowires study of magnetic properties of an unsupported Co chain. study of magnetic properties of a supported Co chain.

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1 st part : Study of platinum surfaces Why platinum ? The platinum surfaces, like the gold surfaces are used by experimentalists as templates for the growth of different adatoms showing interesting properties such as Ag, Co, Ni, Fe … Previous KMC studies done in the lab used the platinum surfaces as a substrate. In this case, the potentials and energies were described using a semi empirical potential. The platinum surfaces are well known and described. They constitute a model system in order to investigate a new method of calculation such as the FLAPW one.

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The FLAPW method Electronic structure calculations : use of the DFT as implemented in the FLEUR code[1]. This code is based on a FLAPW (Full-potential Linearized Augmented Planewave) method. DFT : the total energy is the sum of three contributions : The exchange correlation term accounts for all the many body effects. There are two main approximations for this potential : LDA and GGA. [1] http://www.flapw.de/ (I) Muffin-tin region : electronic wavefunction developped as a linear combination of spherical waves. (II) Interstitial region : electronic wavefunction developped as a linear combination plane waves. (III) Vacuum : exponantial decay of the electronic wavefunctions. x z

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Flat platinum surfaces (hkl)LDAGGAspd TBexperiments (111)1.100.851.011.03 (100)1.501.161.45 (110)2.261.702.18 Electronic structures : Surface energies : Good agreement between TB and FLAPW for the LDOS and bandstructures results. Narrowing of the band for the surface atoms. or (111) (100) (110) (111) (100) (110) (111) face Values in eV/surface atom

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Flat platinum surfaces Surface relaxations : (hkl)LDAspd TB (111)1.100.98 (100)1.491.45 (110)2.162.04 FLAPWspd TBFLAPWspd TBFLAPWspd TB d 12 (%) +1.3 +1.8 +3.8 -1.9 -1.5 -0.5 -14.0 -15.8 -16.7 d 23 (%) +0.3 +0.4 +0.2 +0.3 +0.8 +0.4 +8.3 +9.6 +12.4 d 34 (%) +0.5 +0.7 -0.4 +0.9 +1.3 +0.04 -0.8 -1.1 -3.0 Pt(111)Pt(100)Pt(110) Surface energies for relaxed surfaces : Values in eV/surface atom LDA GGA

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Flat platinum surfaces It is shown both experimentally and theoretically that the Pt(110) as well as Au(110) faces present a (1 2) reconstruction. Relaxation: method d 12 (%) d 23 (%) d 34 (%) P2(Å)P2(Å)P4(Å)P4(Å) 3 (Å) FLAPW-18.8+0.5+1.70.040.070.28 spd TB-26.0-3.7-1.50.050.080.42 Experiments-20.8-1.1 0.05 0.17 FLAPWspd TB Surface energy (1 1) in eV 4.36 4.17 4.36 4.10 Surface energy (1 2) in eV 4.23 3.93 4.16 3.63 Reconstruction energy (eV) -0.13 -0.24 -0.20 -0.47

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Stepped surfaces : application of the EPP From the surface energies determination of the effective pair potential: With these quantities it is then possible to calculate the energies of isolated step using the formula: ViVi FLAPWspd TB V1V1 0.4100.441 V2V2 -0.017-0.055 V3V3 -0.07-0.012 OrientationStep energyFLAPWspd TB p(111) (100) (A step) 2V 1 + 4V 3 0.7920.832 p(111) (111) (B step) 2V 1 + 4V 3 0.7920.832 p(100) (111) V 1 + 2V 2 0.3760.330 p(100) (010) 2V 1 + 2V 2 0.7860.771 p(110) (111) V 2 + 2V 3 -0.048-0.080 with Values in eV/step atom Values in eV

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Stepped surfaces : full calculations We now consider two specific steps and perform full ab initio calculations on these systems. parameters: p=6; step with (100) and (111) facets 5 k-points in the IDBZ (20 for the DOS calculations) k max =3.8 a.u, r MT =2.3 a.u LDOS on different atomic sites for the 6(111) (100) surface The step energy is given by: Nature of the stepstep energy (eV/atom) 6(111) (100) (A step) 0.546 6(111) (111) (B step) 0.583 (100) faceted step is favored over (111) in ratio of about 0.94 Density of states: FLAPW results and TB results are similar narrowing of the bands from bulk to surface and then to edge atoms

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Stepped surfaces : full calculations Each system is relaxed until the forces on the atoms belonging to the external layers are lower than 2 meV/a.u atoms i and j d ij (%) 17 and 25-3.09 18 and 25-3.04 19 and 25-0.12 12 and 24-3.29 13 and 24+1.50 23 and 24-2.92 atoms i and j d ij (%) 21 and 22-3.29 16 and 22-4.84 17 and 22-1.65 Nature of the stepstep energy (eV/atom) 6(111) (100) (A step) 0.275 (0.546) 6(111) (111) (B step) 0.241 (0.583) The relaxation strongly modifies the step formation energies and induces values in better agreement with experimental results: (111) faceted step is now favored over (100) in ratio of about 0.88.

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STM study of Pt vicinal surfaces Basic requirement for self-organized patterns like regular wires by step decoration is a good template. The Pt(997) surface is frequently used by the experimentalists STM z/ x image of the clean Pt(997) surface. I = 1.0 nA, V = 0.6 V. 3D close up of the Pt steps. I = 2.7 nA, V = 10 mV. Top view of the STM image and corresponding linescan. Courtesy given by the EPFL team

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STM study of Pt vicinal surfaces During the experiments images obtained for a constant chosen current I. According to the Tersoff theory : In order to compare with experimental results, we evaluate the local density of states (,E) at different positions and then integrate it over an energy range [E F - E; E F ] or [E F ;E F + E]. Integration over the range [E F ; E F + 0.3 eV] = 2 10 -4 Integration over the range [E F -10 meV; E F ] = 2 10 -6 We can not underline any enhancement of the local density of states near the step edge.

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Conclusion of the first part We used the FLEUR code in order to characterize theoretically a substrate which is often use during the experiments: the platinum. We have calculated surface energies, electronic structures, step energies and relaxations with a good accuracy. The results were in good agreement with other theoretical results, as well as experimental results. In particular, most of our results showed agreement with spd TB results. We have calculated theoretical STM pictures of the Pt stepped surface and in particular, we could underline that from a theoretical point of view, no enhancement of the LDOS could be evidenced near the step edge. The strength of the code in the field of STM picture was reinforced by the study of the stacking of Ir on the Ir(111) surface. The calculations conducted on this system have corroborated and enlightened the experimental findings.

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2 nd part : Elaboration of nanowires Two main ways to create nano-objects : Self-organized growth STM manipulations Advantage : large number of objects. Drawback : broad size distribution. Advantage : very good distribution. Drawback : low number of objects. Ag nanowires on Pt(997) vicinal surface P. Gambardella, M. Blanc, H. Brune, K. Kuhnke and K. Kern, PRB 61, 2254 (2000) Maybe we could combine the 2 techniques.

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The KMC growth model deposition (F) aggregation (E lat ) diffusion D i (T, E i ) Deposition Diffusion Aggregation F T E i E i and E lat calculated with Surface geometry Semi empirical potentials DFT Defects taken into account Only 3 parameters F, T and Comparison with experiments F. Picaud, C. Ramseyer, C. Girardet and P. Jensen, PRB 61, 16154 (2000) Simulate MBE growth experiments through different RANDOM microscopic processes Tip motion : fixed or mobile Tip height (z) : repulsive or attractive mode Tip location (x,y) (x,y,z)

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Two ways of using the tip We use the confinement of the vicinal surfaces. Attractive mode(A) Repulsive mode (R) Parameters : E d =100K E a =1.5 E d = 0.125 The singularities of the step are included in the model of the potential. W=8 11 2 3 4 55 6 Without the tip Attractive tip Repulsive tip S. Baud et al. (Surf. Sci. 532-535, 531 (2003)) Use of a moving STM tip No interest in a peculiar system but inspired by real systems Build a simple model, capture the salient features of the growth

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Moving STM tip Simulations runned with 3 temperatures. Parallel sweeping mode in a repulsive mode. T= 10 K STEP 1 st row T= 10 KT= 5 K At 15K, adatoms can diffuse more easily on the surface and the step coating is not favoured. T= 15 K

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Moving STM tip Simulations runned at 10K. 4 different repulsive sweepings. 12345 Sweepings in row 4 Perpendicular sweepings The most efficient sweeping is the complete parallel crossing of the terrace. Sweeping in row 3

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Moving STM tip T= 10K = 0.125 ML F=1 ML/s In repulsive mode : increase by 50 % of the first row density In attractive mode : increase by 5% of the first row density Comparison of the repulsive and attractive modes.

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After deposition Sorting atoms with a tip T= 10K / Surface 100x100 A = B = 0.1 ML F=0.001 ML/s E a (AA)=E a (BB)=3E a (AB)=1.5 E d Kinetic state The tip : creates a local order pulls the system in its thermodynamic equilibrium state Thermodynamic equilibrium state After 50 sweepings Jump with T or with the tip

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Sorting atoms with a tip V 3-4 (A)=0.625 V 3-4 (B) E a (AA)=E a (BB)=3E a (AB) =1.5 E d T= 5K A = B = 0.125 ML F=0.1 ML/s Sorting between terrace sites and step sites. The confinement may not be favorable to the formation of two distinct lines A-B or B-A. 50 R A - R B 50 A A - R B

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Conclusion of the second part The tip as a fixed or a mobile defect can be used: to build monoatomic nanowires to measure the diffusion coefficient Perspectives: Regarding the sorting of different species, there is still some work to be done. For example, real physical systems like coadsorption of Ag and Co on Pt could be investigated in order to compare with the experimental results.

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3 rd part : Properties of Co nanowires d-bandfilling of the Co atom An isolated Co atom has a magnetic moment of 3 B. Experimentally, the magnetic moment of the bulk Co is determined to be equal to 1.6 B. Whats happening in between ? Experimentalists use the Pt(997) surfaces to grow nanowires of different species like Ag, Ni or Co. This pictures shows Co chains adosrbed on this substrate.

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Unsupported Co chain In a spherical environment, the five d-orbitals have the same energy single d-band. In the case considered here: Splitting of the d-band due to cylindrical symetry parameters: 40 k-points in the IDBZ a=2.81Å k max =3.4 a.u, r MT =2.6 a.u M S = 2.33 B s band g g g This value is larger than the one corresponding to the bulk system (1.65 B ) or an adsorbed Co monolayer (2.066 B ), but it is lower than the value of 3 B corresponding to the isolated Co atom.

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Unsupported Co chain Spin orbit Coupling : is the orbital moment. It characterizes the motion of the electrons around the core. This is a tiny quantity but very important in many applications. M S is independant of the spin quantization axis and equals 2.33 B For a free standing chain the easy axis is along the chain. In this case, M L = 0.977 B

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Unrelaxed supported Co chain parameters: 5 k-points in the IDBZ (40 for the bandstructure and the DOS) a=2.81Å k max =3.2 a.u, r MT =2.2 a.u Bandstructure: Strong modifications compared to the unsupported chain due the presence of the substrate. M S (Co) = 2.14 B The presence of the substrate induces a decrease of the magnetic moment of the Co atom.

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Unrelaxed supported Co chain Distribution of the magnetic moments: The presence of the cobalt atoms induces magnetic moments on the neighbouring Pt atoms. Namely the atoms forming the step edges. Variations of the orbital moments and of the anisotropy energies: We have considered 3 different couples of angles (, ) and defined the anisotropy E as: E - E (, ) M L ( B ) E (meV) 000.123 (0.756)-2.99 (-2.17) /2 00.149 (0.756)-0.27 (-2.17) /2 0.124 (0.977)0 (0) Strong quenching of the orbital moments. The easy axis is still along the chain direction.

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Relaxed supported Co chain Pt i atom d CoPti (%) 21-7.26 16-13.20 17-7.42 The relaxation of the Co atom is quite large with respect to the surface atoms. Effect of the relaxation on the magnetic moments: Compared to the unrelaxed case: Decrease of the Co magnetic moment and increase of the Pt magnetic moments. The bandwidth W decreases when the system is relaxed.

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Relaxed supported Co chain M L ( B ) E (meV) 00 0.089 (0.123) 0.097 -3.53 (-2.99) -2.28 /2 0 0.091 (0.149) 0.100 +0.82 (-0.27) +0.72 /2 0.058 (0.124) 0.060 0 (0) 0 Effect of the relaxation on the orbitals moments: We consider two types of calculation. Either full calculations done with 5 k-points in the IDBZ, or calculations done with the force theorem and using 20 k-points in the IDBZ. Now, the easy axis is not any more along the Co chain. Among the three directions investigated here the favoured one corresponds to the couple of angles (, ) = ( /2,0). E is still defined as: E - E (, ) Full calculations (5 k-points) Without relaxation (5 k-points) Force theorem (20 k-points)

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Conclusion of the third part Using the SOC term in the Hamiltonian, we were able to determine the orbital moment M L and the orientation of the easy axis with respect to the chain direction. The main result is that the presence of the substrate quenches the values of the Co orbital moment and the relaxation induces a change in the spin quantization axis. Unsupported Co chain M S = 2.33 B E = E - E = -2.2 meV M L 1 B Spin quantization axis along the chain Supported and relaxed Co chain M S = 2.10 B E = E - E = -2.3 meV M Leasy = 0.1 B Spin quantization axis along the (, ) = ( /2,0) direction. Compare to experiments, we found that anisotropies are in good agreement ( E exp = 2 meV), whereas large discrepancies between experimental and theoretical orbital moments (M Lexp = 0.68 B ) are determined.

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Collaborations Xavier Bouju LPM UMR 6624, groupe NanoSciences CEMES Toulouse. Pietro Gambardella et Harald Brune Laboratoire de nanostructures superficielles, EPF Lausanne, Switzerland. Thomas Michely and Carsten Busse RWTH Aachen, Germany. Peter Zeppenfeld University of Linz, Austria. Stefan Blügel, Gustav Bihmayer and the PhD students of theory I IFF, Forschungszentrum Jülich, Germany. Daniel Spanjaard LPS Orsay Marie-Catherine Desjonquères et Cyrille Barreteau CEA Saclay And all the other people present today and during these last three years …..

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