arXiv subjects

Christian Schröder

Publications and source records attributed to Christian Schröder.

16 recordsLinked to original sources

arXiv2026

Photoemission study of Iodoalkanes

Core level atomic photoionization is influenced by the molecular environment of the emitting atom. To probe this influence we used extreme ultraviolet (XUV) radiation to measure the I$\left(4d\to\varepsilon f \right)$ photoemission of four iodine substituted alkanes in the range from 60 eV to 160 eV photon energy. Using two detection angles relative to light polarization allowed us to extract and compare the asymmetry parameter of the investigated compounds. These results are in agreement with theory by Pi and Landsman (L.-W. Pi and A. Landsman, Attosecond time delay in photoionization of noble-gas and halogen atoms, Applied Sciences 8, 322 (2018)) and previous experiments by Olney et al. (T. N. Olney, G. Cooper, and C. Brion, Quantitative studies of the photoabsorption (4.5-488 ev) and photoionization (9-59.5 ev) of methyl iodide using dipole electron impact techniques, Chemical Physics 232, 211 (1998)) for iodomethane. 2-iodopropane behaves nearly identical to iodomethane, while for iodoethane and 1-iodopropane we find a distinct and consistent, energy dependant difference most prominent at around 130 eV photon energy. This further proves the influence of the chemical environment on core level photoionization. Due to the sensitivity on the exact positions of the carbon atoms and the energy dependence we hypothesise this difference is caused by intramolecular scattering of the outgoing photoelectron wave packet, causing changes in the angular distribution.

physics.atom-ph↗

arXiv2025

Fostering Innovation: Streamlining Magnetocaloric Materials Research by Digitalization

Refrigeration based on the magnetocaloric effect (MCE) can contribute to energysaving, environmentally friendly cooling in private households, or industrial application. The cooling is based on the reversible heat release or uptake during a phase-transformation of the materials that can be controlled by a magnetic field. This process could replace conventional compression-based refrigeration, which often relies on environmentally harmful refrigerants. Here we show, how to digitalize the process chain for the synthesis, theoretical and experimental characterization, and prototypical application of magnetocaloric alloy. Different Heusler alloys are examined experimentally as model systems for potential application in magnetic cooling. OTTR templates are used for the acquisition and semantic representation of knowledge in the development of an ontology. The ontology, when combined with unstructured data, can be exploited to train a model that can then be used to predict missing facts, which can help to gain new insights and to generate new hypotheses. Furthermore, tools are developed that automate data acquisition into ontological structures and workflows are implemented that provide an easy-to-use theoretical and experimental evaluation of the MCE from first principles and raw data.

cond-mat.mtrl-sci↗

arXiv2024

Origin of magnetic switching cascades in tetrahedral CoFe nanostructures

We present a comprehensive study of small-scale three-dimensional (3D) tetrahedral CoFe nanostructure arrays prepared by focused electron beam-induced deposition (FEBID) and placed in two distinct orientations with respect to the direction of an external magnetic field. Using ultra-sensitive micro-Hall magnetometry we obtain angular-dependent magnetic stray field hysteresis loops that show characteristic cascading magnetic switching close to zero magnetic field. By employing micromagnetic simulations we could reproduce the hysteresis loops and identify characteristic field dependent magnetic configurations including a vortex-type groundstate. From this we derive a coarse-graining macrospin model and show that the complex switching behavior can be explained by the reorientation dynamics of non-interacting uniaxial anisotropic magnetic grains modeled as a superposition of Stoner-Wohlfarth particles.

cond-mat.mes-hall↗

arXiv2022

Thermodynamics of the spin square

Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an example of a completely integrable system, in the double sense: quantum mechanical and classical. However, this does not automatically imply that the thermodynamic quantities of the classical system can also be calculated explicitly. In this work, we derive analytical expressions for the density of states, the partition function, specific heat, entropy, and susceptibility. These theoretical results are confirmed by numerical tests. This allows us to compare the quantum mechanical quantities for increasing spin quantum numbers $s$ with their classical counterparts in the classical limit $s\to \infty$. As expected, a good agreement is obtained, except for the low temperature region. However, this region shrinks with increasing $s$, so that the classical state variables emerge as envelopes of the quantum mechanical ones.

cond-mat.stat-mech↗

arXiv2022

Iterative Refinement of Schur decompositions

The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (more) accurate Schur decomposition of $A$ from a given approximate Schur decomposition. This task arises, for example, in the context of parameter-dependent eigenvalue problems and mixed precision computations. We have developed a Newton-like algorithm that requires the solution of a triangular matrix equation and an approximate orthogonalization step in every iteration. We prove local quadratic convergence for matrices with mutually distinct eigenvalues and observe fast convergence in practice. In a mixed low-high precision environment, our algorithm essentially reduces to only four high-precision matrix-matrix multiplications per iteration. When refining double to quadruple precision, it often needs only 3-4 iterations, which reduces the time of computing a quadruple precision Schur decomposition by up to a factor of 10-20.

math.NA↗

arXiv2022

Balanced Truncation Model Reduction with A Priori Error Bounds for LTI Systems with Nonzero Initial Value

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order system, if the initial condition is not zero. In the literature there are several attempts for modified reduction methods at the price of having no error bound or only a posteriori error bounds which are often too expensive to evaluate. In this work we propose a new balancing procedure that is based on a shift transformation on the state. We first derive a joint projection reduced-order model in which the part of the system depending only on the input and the one depending only on the initial value are reduced at once and we prove an a priori error bound. With this result at hand, we derive a separate projection procedure in which the two parts are reduced separately. This gives the freedom to choose different reduction orders for the different subsystems. Moreover, we discuss how the reduced-order models can be constructed in practice. Since the error bounds are parameter-dependent we show how they can be optimized efficiently. We conclude this paper by comparing our results with the ones from the literature by a series of numerical experiments.

eess.SY↗

arXiv2022

Thermodynamics of the classical spin triangle

The classical spin system consisting of three spins with Heisenberg interaction is an example of a completely integrable mechanical system. In this paper we explicitly calculate thermodynamic quantities as density of states, specific heat, susceptibility and spin autocorrelation functions. These calculations are performed (semi-)analytically and shown to agree with corresponding Monte Carlo simulations. For the long-time autocorrelation function, we find, for certain values of the coupling constants, a decay to constant values in the form of an $1/t$ damped harmonic oscillation and propose a theoretical explanation.

cond-mat.stat-mech↗

arXiv2021

Effect of a Tertiary Butyl Group on Polar Solvation Dynamics in Aqueous Solution: A Computational Approach

The current computational study investigates the changes in solvation dynamics of water when introducing hydrophobic side chains to the molecular probe N-methyl-6-oxyquinolinium betaine. High precision transient fluorescence and absorption measurements published in the companion paper revealed an influence of hydrophobic sidechain alterations on the observed solvation dynamics of a chromophore in water. As the influence of shape, size and structure of chromophores on the time-dependent Stokes shift was so far thought to play a role only in slowly rotating solvents compared to the solute or if the hydrogen bonding ability of the solute changes, this finding is quite unexpected. Analysis of the time-dependent Stokes shift obtained from nonequilibrium simulations corroborates experimental retardation factors and activation energies, and indicates that solute motion, namely vibration, is mainly responsible for the observed retardation of solvation dynamics. The faster dynamics around the smaller chromophore is in fact achieved by some normal modes located at the pyridinium part of the chromophore. Rotation also contributes to a very small extent to hydration dynamics, but for small and large derivatives alike. Local residence times furthermore reveal slight retardations in the first solvent shell around the chromophores. The current picture of the solute acting as a passive molecular probe therefore needs to be revised even for solvents like water.

physics.chem-ph↗

arXiv2021

The small impact of various partial charge distributions in ground and excited state on the computational Stokes shift of 1-methyl-6-oxyquinolinium betaine in diverse water models

The influence of the partial charge distribution obtained from quantum mechanics of the solute 1-methyl-6-oxyquinolinium betaine in the ground- and first excited state on the time-dependent Stokes shift is studied via molecular dynamics computer simulation. Furthermore, the effect of the employed solvent model - here the non-polarizable SPC, TIP4P and TIP4P/2005 and the polarizable SWM4 water model - on the solvation dynamics of the system is investigated. The use of different functionals and calculation methods influences the partial charge distribution and the magnitude of the dipole moment of the solute, but not the orientation of the dipole moment. Simulations based on the calculated charge distributions show nearly the same relaxation behavior. Approximating the whole solute molecule by a dipole results in the same relaxation behavior, but lower solvation energies, indicating that the time scale of the Stokes shift does not depend on peculiarities of the solute. However, the SPC and TIP4P water models show too fast dynamics which can be ascribed to a too large diffusion coefficient and too low viscosity. The calculated diffusion coefficient and viscosity for the SWM4 and TIP4P/2005 model coincide well with experimental values and the corresponding relaxation behavior is comparable to experimental values. Furthermore we found that for a quantitative description of the Stokes shift of the applied system at least two solvation shells around the solute have to be taken into account.

physics.chem-ph↗

arXiv2021

Computational solvation dynamics of oxyquinolinium betaine linked to trehalose

Studying the changed water dynamics in the hydration layers of biomolecules is an important step towards fuller understanding of their function and mechanisms, but has shown to be quite difficult. The measurement of the time-dependent Stokes shift of a chromophore attached to the biomolecule is a promising method to achieve this goal, as published in J. Phys. Chem. Lett. 5 (2014), 1845, where trehalose was used as biomolecule, 1-methyl-6-oxyquinolinium betaine as chromophore and water as solvent. An overall retardation of solvent molecules is then obtained by comparison of the linked system to the same system without trehalose, but contributions from different subgroups of solvent molecules, for example molecules close to or far from trehalose, are unknown. The difficulty arising from these unknown contributions of retarded and possibly unretarded solvent molecules is overcome in this work by conducting computer simulations on this system and decomposing the overall signal into contributions from various molecules at different locations. We performed non-equilibrium molecular dynamics simulation using a polarizable water model and a non-polarizable solute model and could reproduce the experimental time-dependent Stokes shift accurately for the linked trehalose-oxyquinolinium and the pure oxyquinolinium over a wide temperature range, indicating the correctness of our employed models. Decomposition of the shift into contributions from different solvent subgroups showed that the amplitude of the measured shift is made up only half by the desired retarded solvent molecules in the hydration layer, but to another half by unretarded bulk water, so that measured relaxation times of the overall Stokes shift are only a lower boundary for the true relaxation times in the hydration layer of trehalose.

physics.chem-ph↗

arXiv2021

Additive polarizabilities in ionic liquids

An extended Designed regression analysis of experimental data on density and refractive indices of several classes of ionic liquids yielded statistically averaged atomic volumes and polarizabilities of the constituting atoms. These values can be used to predict the molecular volume and polarizability of an unknown ionic liquid as well as its mass density and refractive index. Our approach does not need information on the molecular structure of the ionic liquid, but it turned out that the discrimination of the hybridization state of the carbons improved the overall result. Our results are not only compared to experimental data but also to quantum-chemical calculations. Furthermore, fractional charges of ionic liquid ions and their relation to polarizability are discussed.

physics.chem-ph↗

arXiv2017

Direct-write of free-form 3D nanostructures with controlled magnetic frustration

Building nanotechnological analogues of naturally occurring magnetic structures has proven to be a powerful approach to studying topics like geometry-induced magnetic frustration and to provide model systems for statistical physics. Moreover, it practically allows to engineer novel physical properties by realizing artificial lattice geometries that are not accessible via natural crystallization or chemical synthesis. This has been accomplished with great success in the field of two-dimensional artificial spin ice systems with important branches reaching into the field of magnetic logic devices. Although first proposals have been made to advance into three dimensions (3D), established nanofabrication pathways based on electron beam lithography have not been adapted to obtain free-form 3D nanostructures. Here we demonstrate the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures with full control over the degree of magnetic frustration. By employing micro-Hall sensing, we have determined the magnetic stray field generated by our free-form structures in an externally applied magnetic field and we have performed micromagnetic and macro-spin simulations to deduce the spatial magnetization profiles in the structures and analyze their switching behavior. Furthermore we show that the magnetic 3D elements can be combined with other 3D elements of different chemical composition and intrinsic material properties.

cond-mat.mes-hall↗

arXiv2014

Dynamics and thermodynamics of a pair of interacting magnetic dipoles

We consider the dynamics and thermodynamics of a pair of magnetic dipoles interacting via their magnetic fields. We consider only the "spin" degrees of freedom; the dipoles are fixed in space. With this restriction it is possible to provide the general solution of the equations of motion in analytical form. Thermodynamic quantities, such as the specific heat and the zero field susceptibility are calculated by combining low temperature asymptotic series and a complete high temperature expansion. The thermal expectation value of the autocorrelation function is determined for the low temperature regime including terms linear in $T$. Furthermore, we compare our analytical results with numerical calculations based on Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2008

Multiple nearest-neighbor exchange model for the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30

Our measurements of the differential susceptibility dM/dH of the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30 reveal a pronounced dependence on magnetic field (H) and temperature (T) in the low H - low T regime, contrary to the predictions of existing models. Excellent agreement with experiment is achieved upon formulating a nearest-neighbor classical Heisenberg model where the 60 nearest-neighbor exchange interactions in each molecule, rather than being identical as has been assumed heretofore, are described by a two-parameter probability distribution of values of the exchange constant. We suggest that the probability distribution provides a convenient phenomenological platform for summarizing the combined effects of multiple microscopic mechanisms that disrupt the idealized picture of a Heisenberg model based on a single value of the nearest-neighbor exchange constant.

physics.atm-clus↗

arXiv2008

Modulated spin waves and robust quasi-solitons in classical Heisenberg rings

We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuous EOM reduces to the Landau-Lifshitz equation in a particular limiting regime. The usefulness of the continuum EOM is demonstrated by the fact that the time-evolved numerical solutions of the discrete spin EOM closely track the corresponding time-evolved solutions of the continuum equation. Of special interest, our continuum EOM possesses soliton solutions, and we find that these characteristics are also exhibited by the corresponding solutions of the discrete EOM. The robustness of solitons is demonstrated by considering cases where initial states are truncated versions of soliton states and by numerical simulations of the discrete EOM equations when the spins are coupled to a heat bath at finite temperatures.

cond-mat.other↗

arXiv2005

Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron

The observation of hysteresis effects in single molecule magnets like Mn$_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T=0 this system undergoes a first order metamagnetic phase transition at a critical field $\Bcrit$ between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.

cond-mat.mtrl-sci↗