Tuning the structural and magnetic properties of Sr 2 FeReO 6 by substituting Fe and Re with valence invariant metals

In the course of this work the effect of metal substitution on the structural and magnetic properties of the double perovskites Sr2MM’O6 (M = Fe, substituted by Cr, Zn and Ga; M’ = Re, substituted by Sb) was explored by means of X-ray diffraction, magnetic measurements, band structure calculations, Mößbauer spectroscopy and conductivity measurements. The focus of this study was the determination of (i) the kind and structural boundary conditions of the magnetic interaction between the M and M’ cations and (ii) the conditions for the principal application of double perovskites as spintronic materials by means of the band model approach. Strong correlations between the electronic, structural and magnetic properties have been found during the study of the double perovskites Sr2Fe1-xMxReO6 (0 < x < 1, M = Zn, Cr). The interplay between van Hove-singularity and Fermi level plays a crucial role for the magnetic properties. Substitution of Fe by Cr in Sr2FeReO6 leads to a non-monotonic behaviour of the saturation magnetization (MS) and an enhancement for substitution levels up to 10 %. The Curie temperatures (TC) monotonically increase from 401 to 616 K. In contrast, Zn substitution leads to a continuous decrease of MS and TC. The diamagnetic dilution of the Fe-sublattice by Zn leads to a transition from an itinerant ferrimagnetic to a localized ferromagnetic material. Thus, Zn substitution inhibits the long-range ferromagnetic interaction within the Fe-sublattice and preserves the long-range ferromagnetic interaction within the Re-sublattice. Superimposed on the electronic effects is the structural influence which can be explained by size effects modelled by the tolerance factor t. In the case of Cr substitution, a tetragonal – cubic transformation for x > 0.4 is observed. For Zn substituted samples the tetragonal distortion linearly increases with increasing Zn content. In order to elucidate the nature of the magnetic interaction between the M and M’ cations, Fe and Re were substituted by the valence invariant main group metals Ga and Sb, respectively. X-ray diffraction reveals Sr2FeRe1-xSbxO6 (0 < x < 0.9) to crystallize without antisite disorder in the tetragonal distorted perovskite structure (space group I4/mmm). The ferrimagnetic behaviour of the parent compound Sr2FeReO6 changes to antiferromagnetic upon Sb substitution as determined by magnetic susceptibility measurements. Samples up to a doping level of 0.3 are ferrimagnetic, while Sb contents higher than 0.6 result in an overall antiferromagnetic behaviour. 57Fe Mößbauer results show a coexistence of ferri- and antiferromagnetic clusters within the same perovskite-type crystal structure in the Sb substitution range 0.3 < x < 0.8, whereas Sr2FeReO6 and Sr2FeRe0.9Sb0.1O6 are “purely” ferrimagnetic and Sr2FeRe0.1Sb0.9O6 contains antiferromagnetically ordered Fe sites only. Consequently, a replacement of the Re atoms by a nonmagnetic main group element such as Sb blocks the double exchange pathways Fe–O–Re(Sb)–O–Fe along the crystallographic axis of the perovskite unit cell and destroys the itinerant magnetism of the parent compound. The structural and magnetic characterization of Sr2Fe1-xGaxReO6 (0 < x < 0.7) exhibit a Ga/Re antisite disorder which is unexpected because the parent compound Sr2FeReO6 shows no Fe/Re antisite disorder. This antisite disorder strongly depends on the Ga content of the sample. Although the X-ray data do not hint at a phase separation, sample inhomogeneities caused by a demixing are observed by a combination of magnetic characterization and Mößbauer spectroscopy. The 57Fe Mößbauer data suggest the formation of two types of clusters, ferrimagnetic Fe- and paramagnetic Ga-based ones. Below 20 % Ga content, Ga statistically dilutes the Fe–O–Re–O–Fe double exchange pathways. Cluster formation begins at x = 0.2, for 0.2 < x < 0.4 the paramagnetic Ga-based clusters do not contain any Fe. Fe containing Ga-based clusters which can be detected by Mößbauer spectroscopy firstly appear for x = 0.4.

Higher-order calculations in manifestly Lorentz-invariant baryon chiral perturbation theory

This thesis is concerned with calculations in manifestly Lorentz-invariant baryon chiral perturbation theory beyond order D=4. We investigate two different methods. The first approach consists of the inclusion of additional particles besides pions and nucleons as explicit degrees of freedom. This results in the resummation of an infinite number of higher-order terms which contribute to higher-order low-energy constants in the standard formulation. In this thesis the nucleon axial, induced pseudoscalar, and pion-nucleon form factors are investigated. They are first calculated in the standard approach up to order D=4. Next, the inclusion of the axial-vector meson a_1(1260) is considered. We find three diagrams with an axial-vector meson which are relevant to the form factors. Due to the applied renormalization scheme, however, the contributions of the two loop diagrams vanish and only a tree diagram contributes explicitly. The appearing coupling constant is fitted to experimental data of the axial form factor. The inclusion of the axial-vector meson results in an improved description of the axial form factor for higher values of momentum transfer. The contributions to the induced pseudoscalar form factor, however, are negligible for the considered momentum transfer, and the axial-vector meson does not contribute to the pion-nucleon form factor. The second method consists in the explicit calculation of higher-order diagrams. This thesis describes the applied renormalization scheme and shows that all symmetries and the power counting are preserved. As an application we determine the nucleon mass up to order D=6 which includes the evaluation of two-loop diagrams. This is the first complete calculation in manifestly Lorentz-invariant baryon chiral perturbation theory at the two-loop level. The numerical contributions of the terms of order D=5 and D=6 are estimated, and we investigate their pion-mass dependence. Furthermore, the higher-order terms of the nucleon sigma term are determined with the help of the Feynman-Hellmann theorem.

Topologically correct intersection curves of tori and natural quadrics

This thesis provides efficient and robust algorithms for the computation of the intersection curve between a torus and a simple surface (e.g. a plane, a natural quadric or another torus), based on algebraic and numeric methods. The algebraic part includes the classification of the topological type of the intersection curve and the detection of degenerate situations like embedded conic sections and singularities. Moreover, reference points for each connected intersection curve component are determined. The required computations are realised efficiently by solving quartic polynomials at most and exactly by using exact arithmetic. The numeric part includes algorithms for the tracing of each intersection curve component, starting from the previously computed reference points. Using interval arithmetic, accidental incorrectness like jumping between branches or the skipping of parts are prevented. Furthermore, the environments of singularities are correctly treated. Our algorithms are complete in the sense that any kind of input can be handled including degenerate and singular configurations. They are verified, since the results are topologically correct and approximate the real intersection curve up to any arbitrary given error bound. The algorithms are robust, since no human intervention is required and they are efficient in the way that the treatment of algebraic equations of high degree is avoided.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Feature-invariant image registration method for quantification of surgical outcomes in patients with craniosynostosis: a preliminary study

Craniosynostosis consists of a premature fusion of the sutures in an infant skull that restricts skull and brain growth. During the last decades, there has been a rapid increase of fundamentally diverse surgical treatment methods. At present, the surgical outcome has been assessed using global variables such as cephalic index, head circumference, and intracranial volume. However, these variables have failed in describing the local deformations and morphological changes that may have a role in the neurologic disorders observed in the patients. This report describes a rigid image registration-based method to evaluate outcomes of craniosynostosis surgical treatments, local quantification of head growth, and indirect intracranial volume change measurements. The developed semiautomatic analysis method was applied to computed tomography data sets of a 5-month-old boy with sagittal craniosynostosis who underwent expansion of the posterior skull with cranioplasty. Quantification of the local changes between pre- and postoperative images was quantified by mapping the minimum distance of individual points from the preoperative to the postoperative surface meshes, and indirect intracranial volume changes were estimated. The proposed methodology can provide the surgeon a tool for the quantitative evaluation of surgical procedures and detection of abnormalities of the infant skull and its development.

Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Natural variations at position 93 of the invariant Vα24-Jα18 α chain of human iNKT-cell TCRs strongly impact on CD1d binding

Human invariant natural killer T (NKT) cell TCRs bind to CD1d via an "invariant" Vα24-Jα18 chain (iNKTα) paired to semi-invariant Vβ11 chains (iNKTβ). Single-amino acid variations at position 93 (p93) of iNKTα, immediately upstream of the "invariant" CDR3α region, have been reported in a substantial proportion of human iNKT-cell clones (4-30%). Although p93, a serine in most human iNKT-cell TCRs, makes no contact with CD1d, it could affect CD1d binding by altering the conformation of the crucial CDR3α loop. By generating recombinant refolded iNKT-cell TCRs, we show that natural single-nucleotide variations in iNKTα, translating to serine, threonine, asparagine or isoleucine at p93, exert a powerful effect on CD1d binding, with up to 28-fold differences in affinity between these variants. This effect was observed with CD1d loaded with either the artificial α-galactosylceramide antigens KRN7000 or OCH, or the endogenous glycolipid β-galactosylceramide, and its importance for autoreactive recognition of endogenous lipids was demonstrated by the binding of variant iNKT-cell TCR tetramers to cell surface expressed CD1d. The serine-containing variant showed the strongest CD1d binding, offering an explanation for its predominance in vivo. Complementary molecular dynamics modeling studies were consistent with an impact of p93 on the conformation of the CDR3α loop.

Intestinal microbes affect phenotypes and functions of invariant natural killer T cells in mice

Invariant natural killer T (iNKT) cells undergo canonical, Vα14-Jα18 rearrangement of the T-cell receptor (TCR) in mice; this form of the TCR recognizes glycolipids presented by CD1d. iNKT cells mediate many different immune reactions. Their constitutive activated and memory phenotype and rapid initiation of effector functions after stimulation indicate previous antigen-specific stimulation. However, little is known about this process. We investigated whether symbiotic microbes can determine the activated phenotype and function of iNKT cells.

Light Transport in PT-invariant Photonic Structures with Hidden Symmetries

We introduce a recursive bosonic quantization technique for generating classical PT photonic structures that possess hidden symmetries and higher order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such PT-symmetric photonic networks is also presented.