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Synchronization – the adjustment of rhythms among coupled self-oscillatory systems – is a fascinating dynamical phenomenon found in many biological, social, and technical systems.
The present thesis deals with synchronization in finite ensembles of weakly coupled self-sustained oscillators with distributed frequencies.
The standard model for the description of this collective phenomenon is the Kuramoto model – partly due to its analytical tractability in the thermodynamic limit of infinitely many oscillators. Similar to a phase transition in the thermodynamic limit, an order parameter indicates the transition from incoherence to a partially synchronized state. In the latter, a part of the oscillators rotates at a common frequency. In the finite case, fluctuations occur, originating from the quenched noise of the finite natural frequency sample.
We study intermediate ensembles of a few hundred oscillators in which fluctuations are comparably strong but which also allow for a comparison to frequency distributions in the infinite limit.
First, we define an alternative order parameter for the indication of a collective mode in the finite case. Then we test the dependence of the degree of synchronization and the mean rotation frequency of the collective mode on different characteristics for different coupling strengths.
We find, first numerically, that the degree of synchronization depends strongly on the form (quantified by kurtosis) of the natural frequency sample and the rotation frequency of the collective mode depends on the asymmetry (quantified by skewness) of the sample. Both findings are verified in the infinite limit.
With these findings, we better understand and generalize observations of other authors. A bit aside of the general line of thoughts, we find an analytical expression for the volume contraction in phase space.
The second part of this thesis concentrates on an ordering effect of the finite-size fluctuations. In the infinite limit, the oscillators are separated into coherent and incoherent thus ordered and disordered oscillators. In finite ensembles, finite-size fluctuations can generate additional order among the asynchronous oscillators. The basic principle – noise-induced synchronization – is known from several recent papers. Among coupled oscillators, phases are pushed together by the order parameter fluctuations, as we on the one hand show directly and on the other hand quantify with a synchronization measure from directed statistics between pairs of passive oscillators.
We determine the dependence of this synchronization measure from the ratio of pairwise natural frequency difference and variance of the order parameter fluctuations. We find a good agreement with a simple analytical model, in which we replace the deterministic fluctuations of the order parameter by white noise.
Wetting and phase transitions play a very important role our daily life. Molecularly thin films of long-chain alkanes at solid/vapour interfaces (e.g. C30H62 on silicon wafers) are very good model systems for studying the relation between wetting behaviour and (bulk) phase transitions. Immediately above the bulk melting temperature the alkanes wet partially the surface (drops). In this temperature range the substrate surface is covered with a molecularly thin ordered, solid-like alkane film ("surface freezing"). Thus, the alkane melt wets its own solid only partially which is a quite rare phenomenon in nature. The thesis treats about how the alkane melt wets its own solid surface above and below the bulk melting temperature and about the corresponding melting and solidification processes. Liquid alkane drops can be undercooled to few degrees below the bulk melting temperature without immediate solidification. This undercooling behaviour is quite frequent and theoretical quite well understood. In some cases, slightly undercooled drops start to build two-dimensional solid terraces without bulk solidification. The terraces grow radially from the liquid drops on the substrate surface. They consist of few molecular layers with the thickness multiple of all-trans length of the molecule. By analyzing the terrace growth process one can find that, both below and above the melting point, the entire substrate surface is covered with a thin film of mobile alkane molecules. The presence of this film explains how the solid terrace growth is feeded: the alkane molecules flow through it from the undercooled drops to the periphery of the terrace. The study shows for the first time the coexistence of a molecularly thin film ("precursor") with partially wetting bulk phase. The formation and growth of the terraces is observed only in a small temperature interval in which the 2D nucleation of terraces is more likely than the bulk solidification. The nucleation mechanisms for 2D solidification are also analyzed in this work. More surprising is the terrace behaviour above bulk the melting temperature. The terraces can be slightly overheated before they melt. The melting does not occur all over the surface as a single event; instead small drops form at the terrace edge. Subsequently these drops move on the surface "eating" the solid terraces on their way. By this they grow in size leaving behind paths from were the material was collected. Both overheating and droplet movement can be explained by the fact that the alkane melt wets only partially its own solid. For the first time, these results explicitly confirm the supposed connection between the absence of overheating in solid and "surface melting": the solids usually start to melt without an energetic barrier from the surface at temperatures below the bulk melting point. Accordingly, the surface freezing of alkanes give rise of an energetic barrier which leads to overheating.
In the frame of a world fighting a dramatic global warming caused by human-related activities, research towards the development of renewable energies plays a crucial role. Solar energy is one of the most important clean energy sources and its role in the satisfaction of the global energy demand is set to increase. In this context, a particular class of materials captured the attention of the scientific community for its attractive properties: halide perovskites. Devices with perovskite as light-absorber saw an impressive development within the last decade, reaching nowadays efficiencies comparable to mature photovoltaic technologies like silicon solar cells. Yet, there are still several roadblocks to overcome before a wide-spread commercialization of this kind of devices is enabled. One of the critical points lies at the interfaces: perovskite solar cells (PSCs) are made of several layers with different chemical and physical features. In order for the device to function properly, these properties have to be well-matched.
This dissertation deals with some of the challenges related to interfaces in PSCs, with a focus on the interface between the perovskite material itself and the subsequent charge transport layer. In particular, molecular assemblies with specific properties are deposited on the perovskite surface to functionalize it. The functionalization results in energy level alignment adjustment, interfacial losses reduction, and stability improvement.
First, a strategy to tune the perovskite’s energy levels is introduced: self-assembled monolayers of dipolar molecules are used to functionalize the surface, obtaining simultaneously a shift in the vacuum level position and a saturation of the dangling bonds at the surface. A shift in the vacuum level corresponds to an equal change in work function, ionization energy, and electron affinity. The direction of the shift depends on the direction of the collective interfacial dipole. The magnitude of the shift can be tailored by controlling the deposition parameters, such as the concentration of the solution used for the deposition. The shift for different molecules is characterized by several non-invasive techniques, including in particular Kelvin probe. Overall, it is shown that it is possible to shift the perovskite energy levels in both directions by several hundreds of meV. Moreover, interesting insights on the molecules deposition dynamics are revealed.
Secondly, the application of this strategy in perovskite solar cells is explored. Devices with different perovskite compositions (“triple cation perovskite” and MAPbBr3) are prepared. The two resulting model systems present different energetic offsets at the perovskite/hole-transport layer interface. Upon tailored perovskite surface functionalization, the devices show a stabilized open circuit voltage (Voc) enhancement of approximately 60 meV on average for devices with MAPbBr3, while the impact is limited on triple-cation solar cells. This suggests that the proposed energy level tuning method is valid, but its effectiveness depends on factors such as the significance of the energetic offset compared to the other losses in the devices.
Finally, the above presented method is further developed by incorporating the ability to interact with the perovskite surface directly into a novel hole-transport material (HTM), named PFI. The HTM can anchor to the perovskite halide ions via halogen bonding (XB). Its behaviour is compared to that of another HTM (PF) with same chemical structure and properties, except for the ability of forming XB. The interaction of perovskite with PFI and PF is characterized through UV-Vis, atomic force microscopy and Kelvin probe measurements combined with simulations. Compared to PF, PFI exhibits enhanced resilience against solvent exposure and improved energy level alignment with the perovskite layer. As a consequence, devices comprising PFI show enhanced Voc and operational stability during maximum-power-point tracking, in addition to hysteresis reduction. XB promotes the formation of a high-quality interface by anchoring to the halide ions and forming a stable and ordered interfacial layer, showing to be a particularly interesting candidate for the development of tailored charge transport materials in PSCs.
Overall, the results exposed in this dissertation introduce and discuss a versatile tool to functionalize the perovskite surface and tune its energy levels. The application of this method in devices is explored and insights on its challenges and advantages are given. Within this frame, the results shed light on XB as ideal interaction for enhancing stability and efficiency in perovskite-based devices.
In this thesis, the two prototype catalysts Fe(CO)₅ and Cr(CO)₆ are investigated with time-resolved photoelectron spectroscopy at a high harmonic setup. In both of these metal carbonyls, a UV photon can induce the dissociation of one or more ligands of the complex. The mechanism of the dissociation has been debated over the last decades. The electronic dynamics of the first dissociation occur on the femtosecond timescale.
For the experiment, an existing high harmonic setup was moved to a new location, was extended, and characterized. The modified setup can induce dynamics in gas phase samples with photon energies of 1.55eV, 3.10eV, and 4.65eV. The valence electronic structure of the samples can be probed with photon energies between 20eV and 40eV. The temporal resolution is 111fs to 262fs, depending on the combination of the two photon energies.
The electronically excited intermediates of the two complexes, as well as of the reaction product Fe(CO)₄, could be observed with photoelectron spectroscopy in the gas phase for the first time. However, photoelectron spectroscopy gives access only to the final ionic states. Corresponding calculations to simulate these spectra are still in development. The peak energies and their evolution in time with respect to the initiation pump pulse have been determined, these peaks have been assigned based on literature data. The spectra of the two complexes show clear differences. The dynamics have been interpreted with the assumption that the motion of peaks in the spectra relates to the movement of the wave packet in the multidimensional energy landscape. The results largely confirm existing models for the reaction pathways. In both metal carbonyls, this pathway involves a direct excitation of the wave packet to a metal-to-ligand charge transfer state and the subsequent crossing to a dissociative ligand field state. The coupling of the electronic dynamics to the nuclear dynamics could explain the slower dissociation in Fe(CO)₅ as compared to Cr(CO)₆.
Within the course of this thesis, I have investigated the complex interplay between electron and lattice dynamics in nanostructures of perovskite oxides. Femtosecond hard X-ray pulses were utilized to probe the evolution of atomic rearrangement directly, which is driven by ultrafast optical excitation of electrons. The physics of complex materials with a large number of degrees of freedom can be interpreted once the exact fingerprint of ultrafast lattice dynamics in time-resolved X-ray diffraction experiments for a simple model system is well known. The motion of atoms in a crystal can be probed directly and in real-time by femtosecond pulses of hard X-ray radiation in a pump-probe scheme. In order to provide such ultrashort X-ray pulses, I have built up a laser-driven plasma X-ray source. The setup was extended by a stable goniometer, a two-dimensional X-ray detector and a cryogen-free cryostat. The data acquisition routines of the diffractometer for these ultrafast X-ray diffraction experiments were further improved in terms of signal-to-noise ratio and angular resolution. The implementation of a high-speed reciprocal-space mapping technique allowed for a two-dimensional structural analysis with femtosecond temporal resolution. I have studied the ultrafast lattice dynamics, namely the excitation and propagation of coherent phonons, in photoexcited thin films and superlattice structures of the metallic perovskite SrRuO3. Due to the quasi-instantaneous coupling of the lattice to the optically excited electrons in this material a spatially and temporally well-defined thermal stress profile is generated in SrRuO3. This enables understanding the effect of the resulting coherent lattice dynamics in time-resolved X-ray diffraction data in great detail, e.g. the appearance of a transient Bragg peak splitting in both thin films and superlattice structures of SrRuO3. In addition, a comprehensive simulation toolbox to calculate the ultrafast lattice dynamics and the resulting X-ray diffraction response in photoexcited one-dimensional crystalline structures was developed in this thesis work. With the powerful experimental and theoretical framework at hand, I have studied the excitation and propagation of coherent phonons in more complex material systems. In particular, I have revealed strongly localized charge carriers after above-bandgap femtosecond photoexcitation of the prototypical multiferroic BiFeO3, which are the origin of a quasi-instantaneous and spatially inhomogeneous stress that drives coherent phonons in a thin film of the multiferroic. In a structurally imperfect thin film of the ferroelectric Pb(Zr0.2Ti0.8)O3, the ultrafast reciprocal-space mapping technique was applied to follow a purely strain-induced change of mosaicity on a picosecond time scale. These results point to a strong coupling of in- and out-of-plane atomic motion exclusively mediated by structural defects.
Ultrafast magnetisation dynamics have been investigated intensely for two decades. The recovery process after demagnetisation, however, was rarely studied experimentally and discussed in detail. The focus of this work lies on the investigation of the magnetisation on long timescales after laser excitation. It combines two ultrafast time resolved methods to study the relaxation of the magnetic and lattice system after excitation with a high fluence ultrashort laser pulse. The magnetic system is investigated by time resolved measurements of the magneto-optical Kerr effect. The experimental setup has been implemented in the scope of this work. The lattice dynamics were obtained with ultrafast X-ray diffraction. The combination of both techniques leads to a better understanding of the mechanisms involved in magnetisation recovery from a non-equilibrium condition. Three different groups of samples are investigated in this work: Thin Nickel layers capped with nonmagnetic materials, a continuous sample of the ordered L10 phase of Iron Platinum and a sample consisting of Iron Platinum nanoparticles embedded in a carbon matrix. The study of the remagnetisation reveals a general trend for all of the samples: The remagnetisation process can be described by two time dependences. A first exponential recovery that slows down with an increasing amount of energy absorbed in the system until an approximately linear time dependence is observed. This is followed by a second exponential recovery. In case of low fluence excitation, the first recovery is faster than the second. With increasing fluence the first recovery is slowed down and can be described as a linear function. If the pump-induced temperature increase in the sample is sufficiently high, a phase transition to a paramagnetic state is observed. In the remagnetisation process, the transition into the ferromagnetic state is characterised by a distinct transition between the linear and exponential recovery. From the combination of the transient lattice temperature Tp(t) obtained from ultrafast X-ray measurements and magnetisation M(t) gained from magneto-optical measurements we construct the transient magnetisation versus temperature relations M(Tp). If the lattice temperature remains below the Curie temperature the remagnetisation curve M(Tp) is linear and stays below the M(T) curve in equilibrium in the continuous transition metal layers. When the sample is heated above phase transition, the remagnetisation converges towards the static temperature dependence. For the granular Iron Platinum sample the M(Tp) curves for different fluences coincide, i.e. the remagnetisation follows a similar path irrespective of the initial laser-induced temperature jump.
In processing and data storage mainly ferromagnetic (FM) materials are being used. Approaching physical limits, new concepts have to be found for faster, smaller switches, for higher data densities and more energy efficiency. Some of the discussed new concepts involve the material classes of correlated oxides and materials with antiferromagnetic coupling. Their applicability depends critically on their switching behavior, i.e., how fast and how energy efficient material properties can be manipulated. This thesis presents investigations of ultrafast non-equilibrium phase transitions on such new materials. In transition metal oxides (TMOs) the coupling of different degrees of freedom and resulting low energy excitation spectrum often result in spectacular changes of macroscopic properties (colossal magneto resistance, superconductivity, metal-to-insulator transitions) often accompanied by nanoscale order of spins, charges, orbital occupation and by lattice distortions, which make these material attractive. Magnetite served as a prototype for functional TMOs showing a metal-to-insulator-transition (MIT) at T = 123 K. By probing the charge and orbital order as well as the structure after an optical excitation we found that the electronic order and the structural distortion, characteristics of the insulating phase in thermal equilibrium, are destroyed within the experimental resolution of 300 fs. The MIT itself occurs on a 1.5 ps timescale. It shows that MITs in functional materials are several thousand times faster than switching processes in semiconductors. Recently ferrimagnetic and antiferromagnetic (AFM) materials have become interesting. It was shown in ferrimagnetic GdFeCo, that the transfer of angular momentum between two opposed FM subsystems with different time constants leads to a switching of the magnetization after laser pulse excitation. In addition it was theoretically predicted that demagnetization dynamics in AFM should occur faster than in FM materials as no net angular momentum has to be transferred out of the spin system. We investigated two different AFM materials in order to learn more about their ultrafast dynamics. In Ho, a metallic AFM below T ≈ 130 K, we found that the AFM Ho can not only be faster but also ten times more energy efficiently destroyed as order in FM comparable metals. In EuTe, an AFM semiconductor below T ≈ 10 K, we compared the loss of magnetization and laser-induced structural distortion in one and the same experiment. Our experiment shows that they are effectively disentangled. An exception is an ultrafast release of lattice dynamics, which we assign to the release of magnetostriction. The results presented here were obtained with time-resolved resonant soft x-ray diffraction at the Femtoslicing source of the Helmholtz-Zentrum Berlin and at the free-electron laser in Stanford (LCLS). In addition the development and setup of a new UHV-diffractometer for these experiments will be reported.
This publication based thesis, which consists of seven published articles, summarizes my contributions to the research field of laser excited ultrafast structural dynamics. The coherent and incoherent lattice dynamics on microscopic length scales are detected by ultrashort optical and X-ray pulses. The understanding of the complex physical processes is essential for future improvements of technological applications. For this purpose, tabletop soruces and large scale facilities, e.g. synchrotrons, are employed to study structural dynamics of longitudinal acoustic strain waves and heat transport. The investigated effects cover timescales from hundreds of femtoseconds up to several microseconds.
The main part of this thesis is dedicated to the investigation of tailored phonon wave packets propagating in perovskite nanostructures. Tailoring is achieved either by laser excitation of nanostructured bilayer samples or by a temporal series of laser pulses. Due to the propagation of longitudinal acoustic phonons, the out-of-plane lattice spacing of a thin film insulator-metal bilayer sample is modulated on an ultrafast timescale. This leads to an ultrafast modulation of the X-ray diffraction efficiency which is employed as a phonon Bragg switch to shorten hard X-ray pulses emitted from a 3rd generation synchrotron.
In addition, we have observed nonlinear mixing of high amplitude phonon wave packets which originates from an anharmonic interatomic potential. A chirped optical pulse sequence excites a narrow band phonon wave packet with specific momentum and energy. The second harmonic generation of these phonon wave packets is followed by ultrafast X-ray diffraction. Phonon upconversion takes place because the high amplitude phonon wave packet modulates the acoustic properties of the crystal which leads to self steepening and to the successive generation of higher harmonics of the phonon wave packet.
Furthermore, we have demonstrated ultrafast strain in direction parallel to the sample surface. Two consecutive so-called transient grating excitations displaced in space and time are used to coherently control thermal gradients and surface acoustic modes. The amplitude of the coherent and incoherent surface excursion is disentangled by time resolved X-ray reflectivity measurements. We calibrate the absolute amplitude of thermal and acoustic surface excursion with measurements of longitudinal phonon propagation. In addition, we develop a diffraction model which allows for measuring the surface excursion on an absolute length scale with sub-Äangström precision. Finally, I demonstrate full coherent control of an excited surface deformation by amplifying and suppressing thermal and coherent excitations at the surface of a laser-excited Yttrium-manganite sample.
In this dissertation the lattice and the magnetic recovery dynamics of the two heavy rare-earth metals Dy and Gd after femtosecond photoexcitation are described. For the investigations, thin films of Dy and Gd were measured at low temperatures in the antiferromagnetic phase of Dy and close to room temperature in the ferromagnetic phase of Gd. Two different optical pump-x-ray probe techniques were employed: Ultrafast x-ray diffraction with hard x-rays (UXRD) yields the structural response of heavy rare-earth metals and resonant soft (elastic) x-ray diffraction (RSXD), which allows measuring directly changes in the helical antiferromagnetic order of Dy. The combination of both techniques enables to study the complex interaction between the magnetic and the phononic subsystems.
Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.