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EPJ manuscript No. (will be inserted by the editor) Stability of two-component alkali clusters formed on helium 9 nanodroplets 0 0 2 G. Droppelmann1, M. Mudrich2, C.P. Schulz3, and F. Stienkemeier2 n a 1 Fakultät fu¨r Physik,Universität Bielefeld, 33615 Bielefeld, Germany J 2 Physikalisches Institut,Universität Freiburg, 79104 Freiburg, Germany 6 3 Max-Born-Institut,Berlin, Germany 1 Received: date/ Revised version: date ] s u Abstract. Thestabilityoftwo-componentclustersconsistingoflight(NaorK)andheavy(RborCs)alkali l c atomsformedonheliumnanodropletsisstudiedbyfemtosecondlaserionizationincombinationwithmass - spectrometry.Characteristicstabilitypatternsreflectingelectronshell-closuresareobservedindependence m ofthetotal numberofatomscontainedinthemixedclusters.Fasterdecayofthestabilityofmixedclusters t compared to the purelight ones as a function of size indicates a destabilizing effect of heavy alkali atoms a . on light alkali clusters, presumably dueto second orderspin-orbit interaction. s c PACS. PACS-key discribing text of that key – PACS-key discribing text of that key i s y h 1 Introduction to be much more loosely bound than their metallic coun- p [ terparts [5], and the same behavior may be expected for the heavier alkali species. 1 Metal clusters have proven to be particularly well suited v test objects for studying the transition from molecular While most atomic species reside inside the helium 8 quantum dynamics to solid state physics [1,2,3,4]. Clus- droplets due to the attractive interaction with the he- 4 tersformedofmonovalentalkalimetalshavebeenstudied lium surroundings,alkaliatoms andmolecules are weakly 4 in great detail both experimentally as well as theoreti- bound to the droplet surface in bubble states. This weak 2 cally[1,2,3,5,6,7].Inthesesimplemetalclusterstheelec- binding energy of the order of 10K leads to the fact that . 1 tronic structure is dominated by the number of valence out of all clusters formed on the droplet surface prefer- 0 electrons whereas the ionic cores are of secondary impor- entially the weakly bound ones remain attached to the 9 tance. The electrons are delocalized, and the electronic droplets[11].Thisleadstoanenrichmentofweaklybound 0 system exhibits a shell structure that is closely related to high-spindiatomicandtriatomicmoleculesofuptoafac- v: the well-known nuclear shell structure. The simple model tor 104 [12,13]. Xi of the free-electron gas inside a spherical potential well The formation of high-spin alkali clusters using the of the dimension of the cluster (Jellium model) applies helium nanodroplet technique has been reported by our r a particularly well to alkali clusters [2,3,6,7]. group[10]. In this previous experiment we observedchar- Important information on the electronic structure of acteristicdifferencesintheabundancespectraoflightand metal clusters has been gained from simple cluster abun- heavyalkaliclusters.Whilealkaliclustersofsizesupto25 dancespectra,reflectingthestabilitywithrespecttofrag- atomswereseeninthecaseofsodium(Na)andpotassium mentation: Clusters in which the number of valence elec- (K), cluster sizes exceeding 5 and 3 atoms are strongly tronsmatchesthesphericalshell-closingnumbersarepro- suppressedinthe caseofrubidium(Rb) andcesium(Cs), duced more abundantly. In addition, odd-even alterna- respectively. This behavior has been interpreted in terms tions reflectthe enhancedstability ofpairedelectroncon- of the reduced stability of high-spin states of Rb and Cs figurations [8,2]. These shell effects have also been ob- clusterswithrespecttodepolarization,leavingbehindhot, servedwithmetalclustersformedinheliumnanodroplets[9].unpolarized clusters that may fragment and escape out Besidesthestronglyboundclusters(covalentormetal- of the detection volume. Depolarization may be induced lic)whichareusuallyobservedinexperiments,alkaliscan by the strong second-order spin-orbit interaction present form van der Waals-type molecules and clusters in which in the heavy alkali atoms, causing spontaneous spin flip- all electrons are spin-oriented and strongly localized [5, ping into the unpolarized state. Alternatively, the local- 10].Althoughbondinginthesehigh-spinclusterswaspre- ized,spin-orientedelectronsmayevolveinto adelocalized dicted to be quite strong for lithium clusters (‘ferromag- collectivestateastheclustersizegrowslarger,whicheven- netic bonding’), sodium clusters were theoretically found tually gives rise to spin flipping [10]. 2 G. Droppelmann et al.: Stability of two-component alkali clusters formed on helium nanodroplets Based onthese findings the question ariseshow stable mixed clusters of light and heavy alkali atoms in high- spin states are. In other words, how does the binding of 5 10 one or several heavy alkali atoms (Rb or Cs) to a clus- + KN ter consistingoflightalkalis(Na orK)affectthe stability + othfitshiesscuoemwpeourenpdorctluosntear?seIrnieosrdofermteoassuhreedmseonmtseolfigahbtuonn- -1 e (s)104 KKNN--12+CCss12 dstaantceessopnectthreasoufrmfaicxeedofalhkealliiucmlusntaenrsodforrompleedtsinushiinggh-fsepmin- nt rat KN-3+Cs3 tosecond (fs) photo ionization (PI) in combination with ou 3 mass-selective ion detection. C10 2 Experimental 2 10 0 1 2 3 4 5 6 7 8 9 101112131415 Besidesnumeroustechniquesforproducingbeamsofmetal Total number N of atoms in cluster clusters [1], the aggregationof metal atoms inside helium Fig. 1. Photo ionization mass spectra of two-component nanodroplets has been established as an alternative route to forming metal clusters of well defined composition [4]. potassium-cesium clusters KN−MCsM for M = 0 to M = 3 formed on helium nanodroplets. The pure cesium clusters are Using this technique, the metalclusters are formedin the represented by hatched bars. ultracold environment of the helium droplets at temper- atures in the millikelvin range. Moreover, helium nanodroplets can be efficiently loaded with a variety of different atomic or molecular species. droplets with an average of 11 Cs atoms in a first pickup ◦ In the experiment reported here, a beam of helium cellatatemperatureof105 Candthenwith13Katoms ◦ nanodroplets is consecutively doped with two different in a second pickup cell at a temperature of 160 C. The species of alkali atoms in two separate pickup cells to errorbars reflect uncertainties resulting from background formtwo-componentclustersonthedroplets.Thegrowth countratescausedbythefollowingeffects[15]:Evenwhen statistics for alkali clusters is found to deviate from the helium droplets are doped with only one species, non- Poissoniandistribution[14].Furtherdownstreamthemixed negligible signal intensity is measured at cluster masses clusters are photo ionized by fs laser pulses from a mode- matching the ones of mixed clusters. This is due to the lockedTi:Salaser.NonresonantfsPIathighpulserepeti- fact that natural potassium has two stable isotopes 39K 41 tionrate(80MHz)isanefficientmethodofionizingalkali and K with abundances 93.3% and 6.7%, respectively. clusters largely size-independently. The experimental de- Thus, KN clusters are composed of all possible combina- tails are given elsewhere [15,16,17]. tions of K isotopes 39KM41KN, the abundances of which PI takes place inside the detection volume of a com- beinggivenbythebinomialdistribution.Besides,contam- mercialquadrupolemass spectrometer,in whichthe laser ination of the droplets mainly with water on the level of beam intersects the doped helium droplet beam perpen- 1% leads to the appearance of alkali clusters with water dicularly.The outputofthe fs laseristightly focusedinto molecules attached to them, KNH2O, or even to reaction the helium droplet beam. The laser wavelength is tuned productsofthetype KN(KOH).However,noinfluenceon to about 760nm, which corresponds to the shortest pos- cluster growth has ever been observed. sible wave length. These laser parameters are chosen on The mixed clusters, KN−1Cs1, and KN−2Cs2 plotted account of the fact that PI signals recorded at the al- in Fig. 1 as green and red bars, respectively, display a kali cluster masses generally increase with shorter wave strikinglysimilarabundancepatterncomparedtothe one lengthandwithtighterfocusingofthelaserbeam,thereby ofpureKN clusters.Theexcessenergyduetothe nonres- mostlysuppressingmass-specificresonancesofthe ioniza- onantnature ofthe ionizationprocessleads to desorption tion cross sections. andfragmentationoftheionizedclusters.Thus,theabun- dance spectra reflect the stability pattern with respect to fragmentationratherthanthe abundanceuponformation 3 Results and discussion on the helium droplets. Prominent steps at masses 3, 5 and 9 clearly reflect the electronic shell closures of the When multiply doping helium nanodroplets simultane- ionized clusters. Besides, the mass spectra display a pro- ously with Cs and either Na or K atoms, both single- nounced odd-even alternation with odd-numbered clus- component as well as two-component clusters appear in ters being more abundant. Thus, the stability of two- the mass spectrum, as shown in Fig. 1 and Fig. 2. As ab- component KN−MCsM clusters with respect to the elec- scissa we choose the total number N of atoms contained tronic structure appears to be determined by the total ineachclustertorevealsimilaritiesintheabundancepat- number of constituents and not by the number of atoms terns of pure and mixed clusters. of one species. Since under the given experimental con- The mass spectrum of mixed KN−MCsM clusters for ditions fragmentation of strongly bound metallic clusters M =0−3showninFig.1isrecordedwhendopinghelium wouldnotbe expected,weconclude thatmixedaswellas G. Droppelmann et al.: Stability of two-component alkali clusters formed on helium nanodroplets 3 5 NaN 10 NaN-1Cs -1 Count rate (s)110034 NaN-2Cs2 -1 ount rate (s)110034 KKCCK298ssC12s1 c K7Cs2 2 10 2 10 1 2 3 4 5 6 7 8 9 10 11 12 13 0.1 1 10 100 Total number N of atoms in cluster mean number of picked up K atoms Fig. 2. Mass spectra of two-component sodium-cesium clus- Fig. 3. Evolutionofintegralsignalintensitiesofselectedclus- ters NaN−MCsM for M = 0 to M = 2 formed on helium termasspeaksasafunctionofthedegreeofdopingwithpotas- nanodroplets. siumatoms.Cesiumdopingconditionsareheldconstantatan average of 11 cesium atoms perdroplet. pure alkali clusters formed on helium nanodroplets are in high-spin states [10]. is peaked at Cs2 with roughly equal signal intensities at the masses of Cs and Cs3. Interestingly, mixed clusters containing one or two Cs Inordertostudythiseffectaseriesofmeasurementsat atoms tend to fall off slightly faster with increasing num- variable K pickup conditions is depicted in Fig. 3. Shown ber of K atoms than pure KN clusters. This trend is even are count rates of a representative selection of different morepronouncedasthenumberofCsatomsgrowslarger. masspeaksasafunctionoftheapproximatemeannumber This points at the fact that mixed K-Cs clusters tend to ofpickedupKatoms.Thesevaluesarecomputedfromthe be destabilized by the presence of Cs atoms,in particular vaporpressurecurveofKusingthecalibration10−4mbar when more than one Cs atom is involved. Mixed clus- ≈b 1atomperdroplet.Thiscalibrationhasbeencheckedby ters containing one Cs atom, KN−1Cs1, are detected up to N =13,those containing two Cs atoms, KN−2Cs2, are meansoflaser-inducedfluorescencespectroscopyinearlier observeduptoN =9,andKN−3Cs3 clustersaredetected experiments. with high uncertainty up to N =5. ThedatashowninFig.3indicatethefollowinggeneral trend.BothpureCs1 andCs2 clustersaswellascombined The peak intensities of pure CsN clusters are signif- clusters K8Cs1 and K7Cs2 are suppressed in the mass icantly lower than the ones of pure KN clusters. Since spectrumuponmultiple dopingwithKatoms.Inparticu- no substantial difference in the doping efficiencies is ex- lar, abundances of clusters containing two Cs atoms, Cs2 pected, this discrepancy is attributed to a more efficient and K7Cs2, fall off more rapidly than the ones contain- PI process in the case of KN clusters. In contrast, two- ing only one Cs atom. When adding up all signals from component clusters, KN−MCsM, are expected to have PI clusters containing one, respectively two Cs atoms, (not cross sections comparable to those of pure KN clusters. showninthegraph)thesametrendholds.Thus,therapid The fact that mixed clusters KN−1Cs1 and KN−2Cs2 are disappearanceofmixed clusters ofa givensize containing significantly less abundant than pure KN clusters there- more than one Cs atom is a combined effect of the low foreimpliesthatthesemixedclustersactuallyarelesssta- stability of large pure CsN clusters and the reduction of ble. stability of mixed clusters with an increasing number of Besides the mentioned stability pattern as a function K atoms. of the number of K atoms, the more pronounced limita- Fig. 2 displays mass spectra of two-component clus- tion to maximum cluster size appears to be imposed by ters containing Na and Cs atoms. The pure NaN cluster the number ofCs atoms attachedto a mixed clusters of a abundances are dominated by the Na2 dimer mass peak givensize.E.g.,mixedclusterscontainingthreeCsatoms, due to a resonance in the PI cross section of Na2 at the KN−3Cs3,arelessabundantbyaboutoneorderofmagni- chosen laser wave length [17]. Mixed clusters composed tude compared to mixed clusters with one Cs, KN−1Cs1, of Na and Cs atoms are less abundant than pure NaN whichroughlymatchesthereducedabundanceofthepure clusters by about one order of magnitude. This is mainly Cs3 clusterascomparedtotheCsmonomer(hatchedbars due to a lower level of doping with Cs atoms compared in Fig. 1). However, this behavior is a consequence of co- to the experiment with mixed clusters made of K and doping the helium droplets with K atoms. When load- Cs, discussed above. Thus, combinations involving 2 Cs ing the droplets only with Cs atoms at the same pickup atoms,NaN−2Cs2,areonlyvisibleatselectedclustersizes cell temperature, the detected CsN abundance spectrum and NaN−3Cs3 is not present in the spectrum. Neverthe- 4 G. Droppelmann et al.: Stability of two-component alkali clusters formed on helium nanodroplets less, a faster droping off of the mixed cluster intensities the mixed clusters falls off faster as the number of Na or of NaN−1Cs1 with respect to the pure NaN mass peaks is K atoms increases than for the pure NaN of KN clusters. againclearlyvisible, indicating that NaN clusters tend to Thus,admixingheavyRborCsatomstolightNaN ofKN be destabilized by the presence of Cs atoms as it is seen clusters tends to destabilize the resulting two-component in the spectra of mixed clusters with K atoms. clusters. In addition to the mixed alkali clusters discussed so The fact that the number of heavy alkali constituents far,clusters made up ofRb andeither Na orK have been imposes the dominant limitation to the maximum size of studied. In comparison with the KN−MCsM cluster spec- stable two-componentclustersrather thanthe totalnum- trum, larger quantities of mixed clusters KN−MRbM are ber of atoms points at second-orderspin-orbit interaction observed. Clusters containing up to M =5 Rb atoms are beingthedominanteffectthatleadstodepolarizationand clearly detected. The abundance pattern both of pure an fragmentation. Delocalization of the electron wave func- mixed clusters as a function of total number of atoms, tionswhichwouldcausespontaneousdepolarizationasthe N, is modulated by the effect of shell closures and odd- high-spin clusters grow larger can therefore be ruled out. even alternations, as in the K-Cs case. Also, mixed clus- The largest two-component clusters are observed in the ter abundances fall off faster as N growslargercompared combinationofNaandRbyieldingmixedclustersofsizes to pure KN clusters, indicating the destabilizing effect of up to Na10Rb6 and Na2Rb8. No significant influence of additional heavy alkali atoms. The abundance of mixed the doping order on the mass spectra of mixed clusters, clusters of a fixed size is also reduced the more Rb atoms as studied with K-Rb clusters, is observed. are present in the clusters. However, the latter effects However,theheliumdropletsourceconditionsarefound are not as pronounced as in the K-Cs combination. Two- to crucially influence the abundance of pure and mixed componentclusterscontainingonlyoneRbatoms,KN−1Rb1,clusters.Largerdroplets havehighercoolingcapacityand appearsystematicallylessabundantthanthosecontaining therefore sustain the aggregation of larger spin-polarized moreRbatoms.Furthermore,theinfluenceoftheorderof clustersandpossiblyofmetallicclustersaswell.Therefore doping of first K atoms in a first pickup cell and then Rb studyingabundancespectraofpureandmixedalkaliclus- atomsinasecondone,andviceversa,wasalsocompared. ters at variable helium droplet beam conditions may pro- However,nosignificantdifferenceintheclusterabundance vide valuable information on the formation and stability spectra was observed. ofhigh-spinclusters.Besides,time-resolvedmeasurements The mass spectrum of mixed NaN−MRbM clusters is of the fragmentation process, e.g. using the pump-probe similar to the one of KN−MRbM except for the fact that technique, will add to the understanding of the laser in- pureNaN clustershavemuchlowerabundancescompared duceddynamics ofmany-body systems isolatedin helium to pure RbN clusters and even compared to mixed clus- nanodroplets. ters, which is due to the small ionization cross section Financialsupportby the Deutsche Forschungsgemein- of NaN for N > 2. As in the KN−MRbM mass spec- schaft is gratefully acknowledged. tra, clusters containing only one Rb atom, NaN−1Rb1, are systematically less abundant than those containing a larger number of Rb atoms. This type of mixed clusters References apparentlyhasminimumstabilityascomparedtoallother clustercompositions.Cluster sizesaslargeasNa2Rb8 are 1. Walt A.de Heer. Rev. Mod. Phys., 65:611, 1993. observed in the mass spectrum. 2. H. Haberland. Clusters of Atoms and Molecules I and II. Spinger Series in Chemical Physics, Vol. 52 and 56, Springer, Berlin, 1994. 3. W. Ekardt. Metal Clusters. Wiley,New York,1999. 4 Conclusion 4. Josef Tiggesbäumker and Frank Stienkemeier. Phys. Chem. Chem. Phys., 9:4725, 2007. Two-componenthigh-spinalkaliclusterscomposedoflight 5. S. P. de Visser, D. Danovich, and S. Shaik. Phys. Chem. (Na, K) and heavy (Rb, Cs) atoms can be formed on he- Chem. Phys., 5:158–164, 2003. lium nanodroplets with rather large abundance. The sta- 6. M. Brack. Rev. Mod. 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