Z. Phys. D 40, 250–253 (1997) ZEITSCHRIFTFUR PHYSIK Dc© Springer-Verlag 1997

Optical response of cesium coated C60

S. Frank, N. Malinowski?, F. Tast, M. Heinebrodt, I.M.L. Billas, T.P. Martin

Max-Planck-Institut fur Festkorperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany

Received: 5 July 1996 / Final version: 25 September 1996

Abstract. Photoabsorption spectra are reported for Cs+n and

C60Csn+ clusters for n=40, 60, 120 and 310. The spectra

were obtained by heating the mass selected clusters in abeam by means of photoabsorption until they evaporatedmetal atoms. The resulting mass loss was observed in a time-of-flight mass spectometer. The plasmon-like resonance inpure Cs clusters shifts to lower energies with decreasingcluster size. The collective electronic excitations in clusterscontaining C60 are split in energy as would be expected forfullerene molecules coated with layers of metal.

PACS: 36.40.+d; 73.20.Mf; 71.45.Gm

Introduction

Alkali metal coated C60 clusters have been shown to possesstwo properties characteristic of pure alkali metal clusters.Those containing an even number of electrons are resistentto evaporation, i.e. have an increased stability. The elec-trons in these clusters are organized into a shell structurewhich can be described by quasi-free electrons moving ina spherically symmetric potential [1, 2]. Coated C60 mightdemonstrate also the third property so often associated withpure metal clusters: collective excitations of the electrons.If so, this would allow us to study plasmon-like modes in asystem which might be described as hollow, spherical shellsof metal.

In this paper we report the absorption spectra of sizeselected Cs+n and C60Csn

+ clusters. The clusters are heatedin the drift tube of a time-of-flight (TOF) mass spectome-ter with laser light of variable wavelength. The hot clustersevaporate cesium atoms resulting in a mass loss that is eas-ily detected. The probability of mass loss can be related tothe cross section for the absorption of light.

? Permanent address:Central Laboratory of Photoprocesses, BulgarianAcademy of Sciences, BG-1040 Sofia, Bulgaria

He

Ovens

Oven-Chamber(ca. 1 Torr He) Nozzle

Pump

Skimmers

Ion-Optics

AccelerationVoltage

Reflectron

Detector

DepletionLaser

IonizationLaser

Pump

Time-of-FlightMass Spectrometer

lq.

N2

Fig. 1. The experimental set-up of the optical absorption measurements.The thick line with arrows indicates the flight path of the clusters.Circleswith a crossshow the interaction regions of the clusters with the ionizationlaser and the depletion laser

Experimental

It is possible to coat the outside of a fullerene moleculewith cesium atoms in the following way. Two ovens, oneoven for C60 and a second for cesium metal, are mountedin a cluster condensation cell containing 1 mbar of He gascooled to a temperature of 100 K [3]. The vapors mix abovethe ovens and the mixture cools by collisions with the Hegas. By changing the temperatures of the two ovens, it ispossible to control the amount of metal that condenses ontothe C60 molecule. The metal coated C60 clusters are entrainedin the flowing He gas, pass through a series of skimmersand enter a high vacuum chamber where they are ionizedwith a light pulse originating from a XeCl or a KrF excimerlaser. This laser pulse is strong enough not only to ionize theclusters but also to heat the clusters to a temperature at whichthey evaporate cesium atoms during the laser pulse. Theionized clusters are extracted at right angles into a TOF massspectrometer which contains a window in the drift tube. Asclusters of a predetermined mass are passing underneath this

251

window a second laser pulse is triggered. Since the clusterswere “preheated” with the ionizing laser, the absorption ofone or two photons from the second laser is sufficient tocause further mass loss. The geometry of the set-up is shownin Fig. 1. In this sketch, the interaction regions of the laserswith the cluster beam are marked with crossed circles.

The idea of the experiment is to measure the probabilityof mass loss as a function of the wavelength of the heatinglaser. The tunable laser is a Nd:YAG pumped Optical Para-metric Oscillator (OPO) that covers the wavelength rangefrom 400 to 1600 nm. As the wavelength is scanned the lightintensity is kept constant using a liquid crystal based vari-able attenuator. The high mass resolution of the TOF massspectrometer with reflectron makes it possible to distinguishbetween immediate evaporation caused by the ionizing laserfrom subsequent evaporation caused by the heating laser.

Results and discussion

The temperatures of the two ovens can be adjusted so thatthe clusters contain one and only one C60 molecule and hun-dreds of cesium atoms. Very few pure cesium clusters areproduced, presumably because cesium does not easily self-nucleate. A seed is needed on which the cesium can con-dense. In our case that seed is C60. Electronic shell struc-ture is not expected to influence the probability of ionizationsince the energy of the photons used is far above threshold.Although shell structure does affect the probability of frag-mentation, no electronic shell closings are expected in themass range illustrated in this paper [4]. Since cesium is al-most certainly molten after heating with the ionizing laser,the mass spectrum would not be expected to show structuralmagic numbers either. For these reasons the mass spectrumbefore depletion in the drift tube has a smooth envelope,Fig. 2a. If the heating laser is triggered as clusters having anaverage composition C60Cs92 are passing the window of thedrift tube, these clusters will lose mass, and a “hole” willbe burned into the mass spectrum, Fig. 2b. Since clustersof a given mass are not so tightly bunched in space at thislocation in the drift tube, packets of clusters with similarmasses are irradiated. The mass resolution, m/∆m, of theheating pulse is only 100 compared with the mass resolu-tion of 20000 for the TOF. For this reason the “hole” israther broad. The two mass spectra in Fig. 2 were collectedsimultaneously, by alternately heating every second packetof ions. This allows the two spectra to be substracted fromone another without concern for drifting signal strength. Theresulting difference spectrum is shown in Fig. 2c. Here it isapparent that the clusters destroyed reappear at a lower mass.

Optical absorption cross sections can be extracted fromthese measurements in the following way. First, differencespectra similar to those in Fig. 2 are obtained for vari-ous OPO intensities at a fixed wavelength. The probabil-ity for the evaporation of at least one atom is calculated aspev = (c0 − c)/c0. Here, c0 denotes the counts of a peakwithout depletion laser firing, c denotes the counts with de-pletion. pev is plotted vs. the OPO intensity in Fig. 3 forthe cluster C60Cs60

+. Note that pev includes only the addi-tional evaporation induced by the OPO while evaporationprocesses induced by the ionization laser cancel out in the

0

400

800C60Csn

+

0

400

800C60Csn

+ (b) with depletion

8000 10000 12000 14000-200

-150

-100

-50

0

50

Mass [amu]

(c) Difference (b)-(a)

n=92

Cou

nts

(a) without depletion

Gaussian smooth applied

Fig. 2a–c.Mass spectra of C60Csn+ clusters.a without depletion laser,bwith depletion laser (λ=700 nm),c difference between the spectra

hν = 1.77 eV

Max. Depletion: 93 %nphot: 1.872

1.0

0.8

0.6

0.4

0.2

0.00 2 4 6 8 10 12

C60Cs60+

Energy-Density [µJ/mm2]

Eva

pora

tion-

Pro

babi

lity

Fig. 3. The probability of evaporating at least one atom from C60Cs60+ vs.

the fluence of the OPO. The fit is an integrated poisson-distribution with afitted maximum of 0.93. One result of the fit is the need of 1.872 photonsin average to stimulate evaporation on the time-scale of our experiment

normalization with c0. The dependence of pev on the laser in-tensity is given by pev = dmax·pabs(nphot, σ ·ρphot). Here, dmaxdenotes the maximum depletion at the high intensity limit,σ the cross-section,ρphot the photon density, and nphot theaverage number of photons needed to induce evaporation.pabs(k,m) is the probability for absorbing at least k photonsif m photons are absorbed in average and is given by the

252

0

10

20

30

40

hν [eV]

Cs20+

1.0 1.5 2.00

20

40

60 Cs310+

0

10

20Cs120

+

0

5

10

15 Cs40+

0

5

10

15

20 Cs60+

Mie-Value

1.8 eV

cros

s-se

ctio

n [a

.u.]

Fig. 4. Photoabsorption cross-sections for Cs+n clusters. The experimental

results (dots) are fitted with a lorentzian peak (solid line). The dotted linemarks the position of the size independent surface plasmon according toMie’s classical theory

0.0 0.1 0.2 0.3 0.4 0.51.5

1.6

1.7

1.8

Res

onan

ce-E

nerg

y [e

V]

Csn+

n=20

40

60120

310

classical Mie-Resonance

n-1/3

Fig. 5. The resonance frequency of Cs+n clusters vs. 1/3

√n. Thedotted line

marks the Mie-plasmon, thesolid line is just a guide to the eye

poisson distribution. The three parameters dmax, σ, and nphotcan be fitted to the experimental data as shown in Fig. 3.

Using the results of this fit, a second experiment is per-formed, where the wavelength of the depletion laser is variedand its intensity is kept constant. Since the fitted values forthe maximum depletion and the energy needed to induceevaporation do not depend on the wavelength, it is possi-ble to use the fit results to calculate the optical absorptioncross-section from pev. By means of this method, optical

absorption cross-sections have been measured for Cs+n for

n=20, 40, 60, 120, and 310. The results are plotted in Fig. 4.The dots represent the experimental data, the solid lines arefits with a single peak lorentzian function. The dotted line inFig. 4 marks the position of the surface-plasmon accordingto the classical Mie-theory [5]. According to this theory, thefrequency of the surface-plasmonωs is given by the condi-tion ε1(ωs) = −2 for spherical clusters in vacuum, whereε1denotes the real part of the complex dielectric function. Thecomplex dielectric function of cesium is measured in [6].

For decreasing numbers of atoms, the clusters show anincreasing red-shift of the observed resonance relative to theclassical Mie-value. Only the resonance of Cs+

20, which isin good agreement with [7], does not follow this behaviourexhibiting a higher resonance energy than Cs+

40 and Cs+60.The peak-energies of the resonances are plotted vs. 1/3

√n in

Fig. 5. The dependence of the resonance on 1/3√n is pre-

dicted to be linear by extending the classical theory with aspill-out parameter as suggested in [8]. This parameter con-siders a decrease of the effective electron density due to thespill-out of the electron-cloud over the geometric border ofthe cluster. In our experiment the clusters follow roughly thissimple prediction down to Cs+

40. The fitted length-scale of thespill-out is in the order of half the Wigner-Seitz-radius. Sim-ilar results are reported for potassium in [9] and for sodiumin [10]. The high peak energy of Cs+

20 is in good qualitativeagreement with the observations of Reiners et al. for sodium[10] but cannot be explained with a simple model.

The main subject of this work, the optical absorptioncross-section of cesium coated C60 is displayed in Fig. 6.The values are fitted with a double peak lorentzian (solidlines) and compared to the fits of the pure cesium resultsof Fig. 4 (dotted lines). The main feature of the C60Csn

+

absorption spectra is a double peak structure consisting of ared-shifted and a blue-shifted peak relative to the resonanceof cesium clusters of comparable size. For increasing cesiumcoverage, the height of the red-shifted peak increases rela-tive to the blue-shifted peak approaching the pure cesiumpeak. The latter observation suggests the identification ofthe red-shifted peak with the surface plasmon on the outersurface of the cluster. With decreasing coverage, the pertur-bation of the plasmon due to the C60-center increases. Onepossible interpretation for the blue-shifted peak is a secondplasma-oscillation at the cesium-C60 interface. Lambin et al.[11] and Ostlin et al. [12] suggest a second plasmon modefor C60 treating it classically as a hollow jellium. For thissecond mode, the so called void mode, a blue-shift relativeto the Mie-plasmon and a decrease of height for increas-ing thickness is predicted. This fundamental behaviour of ahollow metallic sphere could be a qualitative explanation ofthe observed double peak structure. But the position of theobserved blue-shifted peak is much closer to the surface-plasmon than is predicted for the void mode by this clas-sical model. For hollow cesium, the void mode should ap-pear between 2.5 and 3 eV depending on the thickness ofthe layer. But measurements of C60Cs20

+ and C60Cs500+ in a

wavelength-range between 2 and 2.8 eV do not show any ad-ditional structures. Recently, several theoretical approachesto the optical response of metal coated C60 have been pre-sented [13–16]. Rubio et al. treat the problem of up to 93sodium atoms coating C60 by means of a two-shell jellium-

253

0

5

10

C60Cs43+

0

5

10

15

20

C60Cs63+

0

5

10C60Cs92

+

0

5

10

15

20

1.0 1.5 2.0 2.50

25

50

75

C60Cs310+

Cs40+

Cs60+

C60Cs120+

Cs120+

Cs310+

hν [eV]

cros

s-se

ctio

n [a

.u.]

Fig. 6. Photoabsorption cross-sections for C60Csn+ clusters. The experi-mental results (dots) are fitted with a double lorentzian peak (solid line).The dashed linesshow thefitted curvesfrom Fig. 4 normed arbitrarily

on-jellium model in [13] based on [17]. The results of thesecalculations do not show the classically expected void modepeak, although the charge density is located at both inter-faces, sodium-C60 and sodium-vacuum, up to C60Na93

+. Onthe other hand, the calculations do show a double-peak finestructure similar to our observations. For this reason, onehas to consider the possibility that the observed double peakstructure is a non-classical fine structure. Several reasons forthe nonexistence of the void mode are suggested in [17].

Conclusion

Photoabsorption measurements were performed on pure ce-sium and cesium coated C60 clusters. Pure cesium clustersshow reasonable agreement with classical theories similarto other alkali metals. Cesium covered C60 clusters show aclear double peak structure consisting of a red-shifted and ablue-shifted peak relative to the pure cesium resonance. Twopeaks merge together with increasing thickness of the ce-sium layer approaching the pure cesium peak. The interpre-tation of the peaks as two surface plasmons at the interfacescesium-C60 and cesium-vacuum can explain the qualitativebehaviour but fails quantitatively. Different interpretationscannot be excluded.

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