Analysis of ultrafast X-ray diffraction data in a linear-chain model of the lattice dynamics

Herzog, Marc; Schick, Daniel; Gaal, P.; Shayduk, Roman; Schmising, Clemens von Korff; Bargheer, Matias

doi:10.1007/s00339-011-6719-z

Cited by 39 publications

(68 citation statements)

References 19 publications

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“…The thermally expanded unit cells are only the final state of the laser-excited crystal. In order to calculate the transient lattice dynamics (including only longitudinal acoustic phonons) towards this final state, we set up a model of a linear chain of masses and springs in which each unit cell represents a mass m i that is coupled to its neighbors via springs with the spring constant k i = m i v 2 i /c 2 i (c i -lattice c-axis, v i -longitudinal sound velocity): [10] …”

Section: Lattice Dynamicsmentioning

confidence: 99%

“…x N ) and K is the tri-diagonal force matrix. [10] The matrix K can be diagonalized to obtain the eigenvectors Ξ j and eigenfrequencies ω j in order to find the general solution…”

Section: Analytical Solutionmentioning

confidence: 99%

“…[10] and in the documentation of the phononAna class. Generally, we use matlab's capability to solve the eigenproblem for K in order to get the results for X(t) for each time step.…”

Section: Analytical Solutionmentioning

confidence: 99%

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udkm1Dsim—A simulation toolkit for 1D ultrafast dynamics in condensed matter

Schick

Bojahr

Herzog

et al. 2014

Computer Physics Communications

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The udkm1Dsim toolbox is a collection of matlab (MathWorks Inc.) classes and routines to simulate the structural dynamics and the according X-ray diffraction response in one-dimensional crystalline sample structures upon an arbitrary time-dependent external stimulus, e.g. an ultrashort laser pulse. The toolbox provides the capabilities to define arbitrary layered structures on the atomic level including a rich database of corresponding element-specific physical properties. The excitation of ultrafast dynamics is represented by an N -temperature model which is commonly applied for ultrafast optical excitations. Structural dynamics due to thermal stress are calculated by a linear-chain model of masses and springs. The resulting X-ray diffraction response is computed by dynamical X-ray theory. The udkm1Dsim toolbox is highly modular and allows for introducing user-defined results at any step in the simulation procedure.

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Section: Lattice Dynamicsmentioning

confidence: 99%

“…x N ) and K is the tri-diagonal force matrix. [10] The matrix K can be diagonalized to obtain the eigenvectors Ξ j and eigenfrequencies ω j in order to find the general solution…”

Section: Analytical Solutionmentioning

confidence: 99%

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udkm1Dsim—A simulation toolkit for 1D ultrafast dynamics in condensed matter

Schick

Bojahr

Herzog

et al. 2014

Computer Physics Communications

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“…[25] These simulations are well established to predict the out-of-plane dynamics but do not consider the in-plane dynamics directly. Therefore, we employ the out-of-plane phonon damping as an adjustable parameter to couple energy to in-plane motion.…”

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confidence: 99%

Following Strain-Induced Mosaicity Changes of Ferroelectric Thin Films by Ultrafast Reciprocal Space Mapping

et al. 2013

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We investigate coherent phonon propagation in a thin film of ferroelectric PbZr0.2Ti0.8O3 (PZT) by ultrafast x-ray diffraction (UXRD) experiments, which are analyzed as time-resolved reciprocal space mapping (RSM) in order to observe the in-and out-of-plane structural dynamics simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattice dynamics on a picosecond timescale, which is not observed for out-of-plane compression.Oxides are attractive constituents of future nanoelectronic devices, because of their broad spectrum of outstanding physical properties, such as ferroelectricity and ferromagnetism, and owing to the progress made in the fabrication of high quality epitaxial heterostructures.[1] Epitaxial strain engineering and the careful choice of mechanical and electrical boundary conditions enable a direct influence on these functionalities.[2-6] Structural defects and nanoscale inhomogeneities, such as dislocations and domains, typically affect the properties of functional oxides and have been extensively studied by experiment and theory. [7,8] Ultrafast x-ray diffraction (UXRD) emerged as a powerful tool to observe lattice motion in real time [9][10][11] and has provided a deeper insight in the structure-property relations of functional oxides on ultrashort timescales. Recent femtosecond x-ray scattering experiments on ferroelectric oxides showed that electron screening induces an ultrafast piezoelectric response of the lattice [12] and that in turn the deformation leads to a change of the polarization.[13] However, these experiments were conducted on rather perfect epitaxial crystals. The influence of nano-domains has been considered in experiments on transient phases [14], but the role of static structural defects remained unexplored on such ultrafast timescale.Here we exemplify how ultrafast reciprocal space mapping (URSM) using a laser-based plasma x-ray source yields direct additional information on the reversible inplane structure dynamics in a ferroelectric perovskite PbZr 0.2 Ti 0.8 O 3 (PZT) film which is solely induced by the existence of dislocations typical of such materials. In particular, the width of the PZT Bragg reflection reports that tensile out of plane strain leads to drastically increased damping. The energy flows into in-plane strain which is evidenced by the in-plane component of the reciprocal space map. Our results indicate that in mismatched epitaxial films of oxide materials, with their high * daniel.schick@uni-potsdam.de • a-domains are embedded in the matrix of the c-axis grown tetragonal PZT film, as proved by the AFM topography image in b) as well. Misfit dislocations (MD) and threading dislocations (TD) formed at the SRO-PZT interface and across the PZT film, accounting for the lateral inhomogeneity on a sub-100 nm length scale.susceptibility to the formation of domains and dislocations, in-plane phenomena emerge on a hundred picosecond timescale. URSM yields the relevant information on lateral lattice dynamic...

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“…Coherent excitations can be controlled in amplitude and phase by series of light pulses in time domain, which is labeled temporal coherent control [19]. The main fraction of the deposited optical energy is stored in incoherent excitations of the lattice, i.e., heat [20,21] which can consequently not be controlled by a temporal sequence of light pulses. This thermal lattice excitation often generates a background which makes is difficult to precisely observe the coherent acoustic signal in purely optical experiments.…”

mentioning

confidence: 99%

Spatiotemporal Coherent Control of Thermal Excitations in Solids

et al. 2017

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X-ray reflectivity (XRR) measurements of femtosecond laser-induced transient gratings (TG) are applied to demonstrate the spatio-temporal coherent control of thermally induced surface deformations on ultrafast timescales. Using grazing incidence x-ray diffraction we unambiguously measure the amplitude of transient surface deformations with sub-Å resolution. Understanding the dynamics of femtosecond TG excitations in terms of superposition of acoustic and thermal gratings makes it possible to develop new ways of coherent control in x-ray diffraction experiments. Being the dominant source of TG signal, the long-living thermal grating with spatial period Λ can be canceled by a second, time-delayed TG excitation shifted by Λ/2. The ultimate speed limits of such an ultrafast x-ray shutter are inferred from the detailed analysis of thermal and acoustic dynamics in TG experiments. [5][6][7] or plasmonic [8,9] degrees of freedom. Strain-induced phenomena may be used to discover new material properties and develop new applications, for example the modification of optical and electronic properties in semiconductor nanostructures [10]. Surface acoustic waves (SAWs) are often employed as a source of lattice strain. They can be generated [11] and controlled [12] optically via the excitation of transient gratings (TGs) [13,14]. Recently, these TG-excitations heave been used to probe heat transport in suspended thin films [15] and magneto-elastic coupling in thin nickel films [16][17][18]. Optical excitation of a solid generates not only coherent sound waves but also incoherent thermal strain. Coherent excitations can be controlled in amplitude and phase by series of light pulses in time domain, which is labeled temporal coherent control [19]. The main fraction of the deposited optical energy is stored in incoherent excitations of the lattice, i.e., heat [20,21] which can consequently not be controlled by a temporal sequence of light pulses. This thermal lattice excitation often generates a background which makes is difficult to precisely observe the coherent acoustic signal in purely optical experiments.In this letter we demonstrate, for the first time, the coherent control of incoherent, thermal transient gratings. We apply spatio-temporal coherent control showing that the spatial part of coherent control adds a new degree of freedom to control the amplitude and the phase of a thermally deformed surface. This is clearly a new approach that introduces the concept of spatial coherent control to the dynamics of incoherent excitations on ultrafast time scales, a phenomenon impossible to achieve with temporal coherent control only. We also demonstrate the control of a transient thermal grating on a timescale faster than the oscillation of the simultaneously excited coherent acoustic modes. Our new quantitative method allows for decomposing the coherent and incoherent dynamics in the sample by measuring the amplitude of the surface excursion with sub-Å precision and ≈ 70 ps temporal resolution. The modification of x-ray diffracti...

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Analysis of ultrafast X-ray diffraction data in a linear-chain model of the lattice dynamics

Cited by 39 publications

References 19 publications

udkm1Dsim—A simulation toolkit for 1D ultrafast dynamics in condensed matter

udkm1Dsim—A simulation toolkit for 1D ultrafast dynamics in condensed matter

Following Strain-Induced Mosaicity Changes of Ferroelectric Thin Films by Ultrafast Reciprocal Space Mapping

Spatiotemporal Coherent Control of Thermal Excitations in Solids

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