Growth of metallic nanowires assisted with a tip. Study of their

physical properties.

BAUD StéphanieLaboratoire de Physique Moléculaire, UMR CNRS 6624,

Faculté des Sciences, la Bouloie,Université de Franche Comté, 25030 Besançon Cedex, France

Draft of the presentation

1st 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.

2nd 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.

3rd part: Properties of Co nanowires study of magnetic properties of an unsupported Co chain. study of magnetic properties of a supported Co chain.

1st 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.

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.

nEnUnTnE xc0

x

z

Flat platinum surfaces

(hkl) LDA GGA spd TB experiments

(111) 1.10 0.85 1.01 1.03

(100) 1.50 1.16 1.45

(110) 2.26 1.70 2.18

Electronic structures :

Surface energies :

Good agreement between TB and FLAPW for the LDOS and bandstructures results.

Narrowing of the band for the surface atoms.

)(2

)()()(

12

2112

nn

nEnnEnhklE hklhkl

S

))((21

)( bulkhklS nEnEhklE

or

(111)

(100)

(110)

(111)

(100)

(110)

(111) face

Values in eV/surface atom

Flat platinum surfaces

Surface relaxations :

(hkl) LDA spd TB

(111) 1.10 0.98

(100) 1.49 1.45

(110) 2.16 2.04

FLAPW spd TB FLAPW spd TB FLAPW spd TB

d12(%) +1.3 +1.8

+3.8 -1.9 -1.5

-0.5 -14.0 -15.8

-16.7

d23(%) +0.3 +0.4

+0.2 +0.3 +0.8

+0.4 +8.3 +9.6

+12.4

d34(%) +0.5 +0.7

-0.4 +0.9 +1.3

+0.04 -0.8 -1.1

-3.0

Pt(111) Pt(100) Pt(110)

1000

0

d

ddΔd ij

ij

Surface energies for relaxed surfaces :

Values in eV/surface atom

LDA

GGA

Flat platinum surfaces

It is shown both experimentally and theoretically that the Pt(110) as well as Au(110) faces present a (12) reconstruction.

Relaxation:

method d12 (%) d23 (%) d34(%) P2(Å) P4(Å) 3(Å)

FLAPW -18.8 +0.5 +1.7 0.04 0.07 0.28

spd TB -26.0 -3.7 -1.5 0.05 0.08 0.42

Experiments -20.8 -1.1 -1.1 0.05 0.05 0.17

FLAPW spd TB

Surface energy (11) in eV 4.36 4.17

4.36 4.10

Surface energy (12) in eV 4.23 3.93

4.16 3.63

Reconstruction energy (eV) -0.13 -0.24

-0.20 -0.47

Stepped surfaces : application of the EPP

From the surface energies determination of the effective pair potential:

sN

sssS VhklnhklE

1)()(

sN

sssstepstep VpnpE

1, )()(

With these quantities it is then possible to calculate the energies of isolated step using the formula:

Vi FLAPW spd TB

V1 0.410 0.441

V2 -0.017 -0.055

V3 -0.07 -0.012

Orientation Step energy FLAPW spd TB

p(111)(100) (A step) 2V1+ 4V3 0.792 0.832

p(111)(111) (B step) 2V1+ 4V3 0.792 0.832

p(100)(111) V1+ 2V2 0.376 0.330

p(100)(010) 2V1+ 2V2 0.786 0.771

p(110)(111) V2+ 2V3 -0.048 -0.080

, ( ) ( ) ( 1 ) ( )step s s sn p n p p f n with

Values in eV/step atom

Values in eV

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) facets5 k-points in the IDBZ (20 for the DOS calculations)kmax=3.8 a.u, rMT=2.3 a.u

LDOS on different atomic sitesfor the 6(111)(100) surface

(( 1) ) ( )step surf surfE E p f E

The step energy is given by:

Nature of the step step 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 similarnarrowing of the bands from bulk to surface and then to edge atoms

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 dij (%)

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 dij (%)

21 and 22 -3.29

16 and 22 -4.84

17 and 22 -1.65

Nature of the step step 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 inducesvalues in better agreement with experimental results: (111) faceted stepis now favored over (100) in ratio of about 0.88.

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

STM study of Pt vicinal surfaces

During the experiments images obtained for a constant chosen current I. According to the Tersoff theory :

( , )I r E

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 [EF-E; EF] or [EF;EF+E].

r

r

Integration over the range [EF; EF + 0.3 eV]

= 210-4

Integration over the range [EF -10 meV; EF]

= 210-6

We can not underline any enhancement of the local density of states near the step edge.

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.

2nd 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 surfaceP. Gambardella, M. Blanc, H. Brune,K. Kuhnke and K. Kern, PRB 61, 2254 (2000)

Maybe we could combine the 2 techniques.

The KMC growth model

deposition (F)

aggregation (Elat)

diffusionD

i(T,E

i)

Deposition

DiffusionAggregation

F

T

Ei

Ei and Elat 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)

Two ways of using the tip

We use the confinement of the vicinal surfaces.

Attractive mode(A)

Repulsive mode (R)

Parameters : Ed=100K Ea=1.5 Ed

= 0.125The singularities of the step are included in the model of the potential.

W=8

1 12

34

5 56

Without the tip

Attractive tip

Repulsive tipS. 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

Moving STM tip

Simulations runned with 3 temperatures.Parallel sweeping mode in a repulsive mode.

T= 10 K

STEP

1st row

T= 10 K T= 5 K

At 15K, adatoms can diffuse more easily on the surface and the step coating is not favoured.

T= 15 K

Moving STM tip

Simulations runned at 10K.4 different repulsive sweepings.

1 2 3 4 5

Sweepings in row 4

Perpendicularsweepings

The most efficient sweeping is the complete parallel crossing of the terrace.

Sweeping in row 3

Moving STM tip

T= 10K= 0.125 MLF=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.

After deposition

Sorting atoms with a tip T= 10K / Surface 100x100

A= B= 0.1 MLF=0.001 ML/sEa(AA)=Ea(BB)=3Ea(AB)=1.5 Ed

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

Sorting atoms with a tip

V3-4(A)=0.625 V3-4(B)Ea(AA)=Ea(BB)=3Ea(AB) =1.5 Ed

T= 5K

A= B= 0.125 MLF=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 RA - RB50 AA - RB

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.

3rd 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.

What’s 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.

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 IDBZa=2.81Åkmax=3.4 a.u, rMT=2.6 a.u

MS = 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.

Unsupported Co chain

Spin orbit Coupling :

SLrH SO

.)(

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.

L

•MS 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,

ML = 0.977 B

LMEEE

Unrelaxed supported Co chain

parameters:5 k-points in the IDBZ (40 for the bandstructure and the DOS)a=2.81Åkmax=3.2 a.u, rMT=2.2 a.u

Bandstructure:

Strong modifications compared to the unsupported chain due the presence of the substrate.

MS(Co) = 2.14 B

The presence of the substrate induces a decrease of the magnetic moment of the Co atom.

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(,)

ML (B) E (meV)

0 0 0.123 (0.756) -2.99 (-2.17)

/2 0 0.149 (0.756) -0.27 (-2.17)

/2 /2 0.124 (0.977) 0 (0)

Strong quenching of the orbital moments.

The easy axis is still along the chain direction.

Relaxed supported Co chain

Pti atom dCoPti(%)

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.

WM S

1

The bandwidth W decreases when the system is relaxed.

Relaxed supported Co chain

ML (B) E (meV)

0 0 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 /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)

Conclusion of the third part

Using the SOC term in the Hamiltonian, we were able to determine the orbital moment ML 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

MS = 2.33 B

E = E - E= -2.2 meV

ML 1 B

Spin quantization axis along the chain

Supported and relaxed Co chain

MS = 2.10 B

E = E - E= -2.3 meV

MLeasy = 0.1 B

Spin quantization axis along the (,) = (/2,0) direction.

Compare to experiments, we found that anisotropies are in good agreement (Eexp= 2 meV), whereas large discrepancies between experimental and theoretical orbital moments (MLexp= 0.68 B) are determined.

Collaborations •Xavier BoujuLPM UMR 6624, groupe NanoSciences CEMES Toulouse.

•Pietro Gambardella et Harald Brune

Laboratoire de nanostructures superficielles, EPF Lausanne, Switzerland.

•Thomas Michely and Carsten BusseRWTH Aachen, Germany.

•Peter Zeppenfeld

University of Linz, Austria.

•Stefan Blügel, Gustav Bihmayer and the PhD students of theory IIFF, Forschungszentrum Jülich, Germany.

•Daniel SpanjaardLPS Orsay•Marie-Catherine Desjonquères et Cyrille BarreteauCEA Saclay

And all the other people present today and during these last three years …..