Diffractive imaging of transient electronic core-shell structures in a nanoplasma
Daniela Rupp, Leonie Flückiger, Marcus Adolph, Tais Gorkhover, Maria Krikunova, Jan Phillipe Müller, Maria Müller, Tim Oelze, Yevheniy Ovcharenko, Mario Sauppe, Sebastian Schorb, David Wolter, Marion Harmand, Rolf Treusch, Christoph Bostedt, Thomas Möller
DDiffractive imaging of transient electronic core-shell structures ina nanoplasma
Daniela Rupp, ∗ Leonie Fl¨uckiger,
1, 2
Marcus Adolph, Tais Gorkhover,
1, 3
Maria Krikunova, † Jan Philippe M¨uller, Maria M¨uller, Tim Oelze, Yevheniy Ovcharenko,
1, 4
Mario Sauppe, Sebastian Schorb, David Wolter, Marion Harmand, Rolf Treusch, Christoph Bostedt,
6, 7, ‡ and Thomas M¨oller IOAP, Technische Universit¨at Berlin,Hardenbergstraße 36, 10623 Berlin, Germany ARC Centre of Excellence for Advanced Molecular Imaging,La Trobe University, Bundoora, Victoria 3086, Australia SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025, USA European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany FLASH, DESY, Notkestraße 85, 22603 Hamburg, Germany Chemical Sciences and Engineering Division, Argonne National Laboratory,9700 S. Cass Avenue, Argonne, IL 60439, USA Department of Physics and Astronomy, Northwestern University,2145 Sheridan Road, Evanston, IL 60208, USA (Dated: November 7, 2018)
Abstract
We have recorded the coherent diffraction images of individual xenon clusters with intense ex-treme ultraviolet pulses to elucidate the influence of light-induced electronic changes on the diffrac-tion pattern. Using the FLASH free-electron laser we tuned the wavelength to specific xenon atomicand ionic resonances. The data show the emergence of a transient core-shell structure within theotherwise homogeneous sample. Simulations indicate that ionization and nanoplasma formationresult in a cluster shell with strongly altered refraction. The presented resonant scattering approachenables imaging of ultrafast electron dynamics on their natural time scale. a r X i v : . [ phy s i c s . a t m - c l u s ] O c t ntense femtosecond short-wavelength pulses from free-electron lasers (FELs) open newavenues to investigate transient states and ultrafast processes with unprecedented spatialand temporal resolution [1–4]. Examples include diverse topics ranging from the first demon-stration of femtosecond coherent diffractive imaging (CDI) [5] and the 3D characterizationof isolated nanoparticles [6] to the visualization of quantum vortices in helium droplets [7],and non-equilibrium dynamics in molecules [8] and clusters [9–11].Typical CDI efforts concentrate on retrieving the atomic structure or density distribu-tion of the sample. Ultrafast photon induced changes to the sample electronic structureare mostly discussed in terms of “damage” in both, experimental [12] and theoretical [13]approaches. However, the availability of intense short-wavelength pulses also yields tremen-dous opportunity to directly image electronic structure changes with high spatial resolutionin a time-resolved manner. During the X-ray scattering process the photons interact with theelectrons that are either tightly bound to the nuclei or delocalized in the valence states. Inparticular near absorption resonances, the X-ray scattering cross-sections depend sensitivelyon the energy of the incoming photon and the electronic structure of the sample [14–16].In this letter we demonstrate how resonant elastic scattering can be used to directlyimage the spatial distribution of transient charge states in an evolving nanoplasma. Assamples we use submicron-sized clusters that are simultaneously transformed to a highlyexcited nanoplasma and imaged with a single intense femtosecond FEL pulse. On thetimescale of the pulse the position of the clusters is frozen in space and ionic motion in thegenerated nanoplasma can be neglected [17]. Nevertheless, we do observe modulations in thescattering patterns that scale with the FEL intensity and that are characteristic for core-shellstructures. As they are independent from the geometric arrangement of the atoms in thecluster, we attribute these modulations to light-induced electronic structure changes whichis supported by Mie calculations and Monte-Carlo simulations. The models indicate thatthe electronic core-shell structures exhibit surprisingly sharp boundaries that act akin to atransient mirror within the nanoplasma. The experiments show the potential of resonantcoherent diffractive imaging for taking snapshots of ultrafast ionization dynamics or chargemigration in complex samples with femtosecond time and nanometer spatial resolution.The experiments were performed at the soft X-ray free-electron laser FLASH [18] withextreme ultraviolet (XUV) pulses at 91 eV photon energy. This energy matches the giant4d resonance of neutral xenon [19] and some Xe charge states [20–25] as discussed in detail2 IG. 1. Isolated xenon clusters were irradiated with intense XUV pulses (91 eV photon energy,5 × W/cm peak intensity). All events with single clusters of (400 ±
50) nm radius wereselected for analysis (total of 94 events) by the characteristic spacing of the diffraction rings.a) Representative diffraction images, intercepted at different positions of the focal power densitydistribution. b) Corresponding ion spectra of all 94 events (shifted by an offset for better visibility).The average kinetic energy of the Xe ions was used to sort the events for FEL exposure powerdensity [17]. For the following analysis, all events were binned into categories A to F according tothe abundance of higher charge states. below. The FEL beam with 10 photons per 100 femtosecond pulse was focused into a 20 µ m(FWHM) spot, reaching power densities up to 5 × W/cm . The pulses intersected ahighly diluted jet of very large xenon clusters [26]. An adjustable piezo skimmer slit ensuredthat only one single cluster is present in the focus volume per FEL shot [27]. The scatteringpatterns were measured with a previously described [14, 28] large area scattering detector.The size of each single, mostly spherical cluster could be determined from the spacing ofthe extrema in the diffraction patterns [26]. Within the size regime of R = (400 ±
50) nm atotal of 94 diffraction images were obtained. In addition to the diffraction images, coincidentsingle-shot ion spectra were recorded [17, 29].In Fig. 1a examples for the single-shot diffraction images are displayed. The data weresorted for increasing FEL exposure intensity by the kinetic energy of the Xe ions fromthe time-of-flight spectra [17], as shown in Fig. 1b. In order to analyze only the intensitydependent changes in the patterns and to cancel out effects from irregular shapes and slightly3ifferent sizes, the data were binned into six categories A to F related to the appearance ofthe next higher charge states (see brackets on the right side of Fig. 1b) and the diffractionpatterns were averaged.The radial profiles resulting from thus averaged scattering images of each category A toF are displayed in Fig. 2a. The high-frequency modulation of the profiles reflects the clustersize information. The envelope of profile A, representing the class of clusters exposed tolowest intensities, agrees well with the expected curve for a homogeneous spherical xenoncluster, dropping linearly on a logarithmic scale. In the absence of light induced changesin the particle, the profiles from clusters irradiated with higher FEL intensity would followa similar curve, just with a proportionally higher scattering signal. In contrast, the profileenvelopes B to F develop a more and more pronounced lobe structure roughly at 15 ◦ to30 ◦ scattering angle. This evolving superstructure corresponds to the development of anadditional characteristic length scale in the sample. In a classical Mie model, the lobefeature is characteristic for a core-shell structure with strongly deviating refractive indicesin the shell compared to the core [30, 31]. We apply a core-shell model to the data to extractestimates for the thickness and optical constants of the shell. Subsequently, we develop aphysical picture of the plasma formation and discuss a possible origin of such a core-shellsystem as well as the limitations of this model.In our Mie calculations we made some simplifying assumptions, namely that the profilesA to F, obtained at different FEL-intensities, reflect the course of the same evolution, butup to different stages. Individual steps of the evolution can therefore be extracted fromthe difference between each two profiles. This approach is conceptually similar to resonantimaging of magnetic domains and their ultrafast switching, where diffraction patterns aresubtracted above and below an absorption edge [15]. In Fig. 2b the difference profiles fromFig. 2a are given (F-E, E-D, and so on). The difference spectra reveal very distinct featuresin the superstructure: With increasing FEL intensity a broad lobe appears that becomesmore and more pronounced, narrows, and shifts towards higher scattering angles.Simulated profiles matching the superstructure in Fig. 2b are shown in Fig. 2c. The sim-ulations were carried out using a code based on Mie theory and extended for spheres witha core-shell structure [30, 31, 33]. A schematic visualization in Fig. 2d illustrates this evolu-tion. The parameters of the shell used in these simulations are given in Fig. 2e, specificallyincreasing shell thickness, increasing refractive index decrement δ (the refractive index n is4 IG. 2. a) Radial profiles of averaged diffraction images from bins A to F, as indicated in Fig. 1b.The measured scattering intensities are corrected for the flat detector geometry [14] and a nonlineardetector response [6, 32], radially averaged and plotted logarithmically vs. scattering angle. ProfileA exhibits a ripple structure corresponding to the cluster size on an otherwise linearly dropping(log scale) curve, as expected from Mie theory for a homogeneous xenon cluster. Towards higherexposure power densities up to profile F, an additional large-scale structure evolves. b) Differenceprofiles from a). For better visibility the curves were shifted by multiplication with a factor. c)Matching calculated profiles obtained with a Mie-based core-shell code [33]. d) Schematic visual-ization of the spatially inhomogeneous nanoplasma evolving with increasing FEL exposure powerdensity. e) Parameters of the shell used as input for the calculations displayed in c), i.e. shellthickness d (in m), refractive index decrement δ , and absorption index β (dimensionless, with n = 1 − δ + i β ). Black lines serve as guide to the eye. The refractive index of the core was keptconstant to n = 1 . i · .
044 (neutral xenon at 91 eV [34]). given by n = 1 − δ + i β ), and a very low absorption coefficient β (factor 4 less than neutralxenon). Please note that while the tendencies found via the Mie simulations are probablycorrect, the absolute values might not match the actual optical constants in the nanoplasmabecause (i) the refractive index of the core is unknown, (ii) the nanoplasma evolution iscontinuous whereas we consider only five snapshots, and (iii) the nanoplasma structure mayconsiderably deviate from a concentric core-shell system. In fact, it can be rather expectedto be asymmetric in the direction of incident light [35]. Nevertheless, the good agreementbetween Fig. 2b and c supports the hypothesis of a strongly altered outer shell in the cluster5anoplasma. It is notable that the core-shell structure appears to be a general feature be-cause it survives the averaging over many single-cluster patters which themselves incorporatethe average scattering signal over the FEL pulse duration. This raises the question of theorigin of this refractive core shell system, i.e. the generation of a tens of nanometers thickshell of the nanoplasma with optical properties that differ so drastically from the plasmacore.The presumed origin of the core-shell structure lies in the peculiar electronic properties ofxenon atoms and ions in the vicinity of the photon energy of 91 eV. Absorption cross-sectionsfor xenon atoms and atomic ions have been measured [20–25] and are summarized in Fig. 3.There is a clear step from high to low absorption between Xe and Xe with extremelyhigh values for the charge state 4+ which exhibits a large ionic resonance at 91 eV. Corre-spondingly, the penetration depth increases from about 30 to 300 nm. To further investigatethis observation, we model a first-order picture of the radial charge state distributions for ourexperiment using a Monte Carlo approach. The propagation of photons into the clusters iscalculated starting at the cluster surface. At every atom or ion the absorption of the photonis tested, using probabilities according to the atomic and ionic cross-sections. The resultingradial charge state density distributions for an FEL intensity of 1 × W/cm are givenin Fig. 4a. The simple simulation allows to derive the average charge state as a function ofthe propagation depth and even to calculate the imaginary part of the refractive index β (cf. caption of Fig. 4). Both curves given in Fig. 4b show that an outer shell exists up toa propagation depth of about 120 nm that is exclusively populated by high charge states.Then the average charge state drastically drops in a transition region of about 100 nm while FIG. 3. Absorption of xenon at 91 eV. Total absorption cross-sections in Mbarn of neutral Xe [20]and Xe charge states 1+ [21], 2+ [22], 3+ [23], 4+ [24], 5,6,7+ [25] (colored points). Related pene-tration depth in nm (black crosses). β reveals an evenmore pronounced kink within only 50 nm, resulting in an optical core-shell system with arather transparent shell and opaque core.Our simple atomistic model is in good agreement with the results from the Mie-calculations, showing the same trend however not the same absolute shell thicknesses (cf.Fig. 2). Further, it is noted that the step in β in Fig. 4b is still to soft to explain the pro-nounced superstructure in the scattering intensity. To generate pronounced modulations,two preconditions are necessary: (i) a transparent outer shell (low absorption index) and(ii) a sharp boundary between regions of different refractive index. We have tested that themodulations would vanish in case of a rather smooth transition over several tens of nanome-ters as in Fig. 4b. The required sharp transition is puzzling. Moreover, our atomistic modelis expected to underestimate the transition regime width, as it neglects impact ionizationand other charge transfer dynamics within the cluster that would smear out the charge statedistribution.However, the model only describes the absorption of the nanoplasma, i.e. the imaginarypart β , and its radial dependence. For the optical response of the cluster both, the real andimaginary part of the refractive index δ and β are relevant, which are interrelated through theKramers-Kronig dispersions relations. In particular, a peak in β (absorption resonance) isaccompanied by a zero transition of δ . Plasma calculations of the atomic scattering factors of Xe [38] indeed indicate that between 90 eV and 98 eV the real part of the atomic scatteringfactor f (proportional to the refractive index decrement δ ) rapidly changes from stronglypositive to negative values and back several times. Based on this information, the followingconsideration may provide an explanation for the required sharp change in refraction. Wehave to expect, that the atomic/ionic resonances are shifted by the plasma in the cluster [39],possibly up to several eV [40]. Now considering the radial position of the Xe -distributionin Fig. 4a (green curve) and comparing it with the average charge states at the same radialpositions (purple curve) clearly shows that the environment of Xe ions strongly changes asa function of the propagation depth. Such a change in the plasma environment may translateinto a radially dependent plasma shift of the electronic resonances up to several eV [39], fromjust below a sharp resonance to just above the resonance. This would result in a drasticchange of the real part of the refractive index within a short distance, acting like a transient7 IG. 4. a) Simulation of the radially changing charge state densities for a 400 nm radius clusterirradiated with 1 · W/cm , corresponding to approximately 870 photons falling on the geometriccross-section of one xenon atom and propagating into the cluster from surface to core. Absorptioncross-sections from Fig. 3 are used to calculate the radial charge state densities. Only linear photoabsorption is taken into account, while nonlinear effects, light scattering and plasma processes suchas collisional ionization are neglected. b) The average charge state as derived from the radial chargestate distributions is given in purple as a function of propagation depth r . Via β = π λn a σ abs [36]also the imaginary part of the refractive index β ( r ) can be calculated (wavelength λ , n a atomicdensity [37], σ abs absorption cross-section). plasma mirror. A similar argument could be made for the xenon charge states 4+ to 6+,which also exhibit narrow and very strong absorption resonances in the vicinity of 91 eV[23, 24]. To test this hypothesis, a full description of the light propagation via sophisticatedtheoretical approaches will be needed that include impact ionization, charge transfer, plasmashifts of the energy levels, and further nanoplasma dynamics [41–43]. Nevertheless, thesegeneral considerations provide a first step towards understanding the observed results.In summary, we have presented scattering patterns of single large xenon clusters reso-nantly excited with intense XUV pulses. The patterns reveal strong intensity dependentmodulations of the scattering distribution, characteristic for core-shell systems. Mie-basedsimulations support a model of light induced electronic core-shell structures in the initiallyhomogeneous systems with an increasingly thick outer shell characterized by low absorptionand a strong and rapid change in refraction. The origin of this abrupt change in refrac-tive index can be correlated to the radially changing plasma environment of higher charge8tates, translating into a radially changing shift of the electronic resonances. Our workshows that ultrafast light scattering can map the transient spatial charge distributions ofresonant electronic states on the nanoscale. This method can be employed to develop adeeper understanding of nanoplasma formation and charge transfer dynamics which play akey role in many areas ranging from single-shot X-ray imaging to fusion and warm densematter research as well as condensed matter physics. In the future, the approach providesan avenue to resolve ultrafast electron dynamics in extended systems on their natural timescale with intense attosecond pulses currently under development at FELs and lab-basedsources [32, 44–46].The authors thank Thomas Fennel and Christian Peltz for enlightening discussions. Ex-cellent support from IOAP and DESY machine shops is acknowledged. The experimentshave received funding from BMBF (grants 05K10KT2/05K13KT2) and DFG (grants MO719/13-1 and /14-1). 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