Two-particle excitations, such as spin and charge excitations, play a key role in high-Tc cuprate superconductors (HTSC). Due to the antiferromagnetism of the parent compound the magnetic excitations are supposed to be directly related to the mechanism of superconductivity. In particular, the so-called resonance mode is a promising candidate for the pairing glue, a bosonic excitation mediating the electronic pairing. In addition, its interactions with itinerant electrons may be responsible for some of the observed properties of HTSC. Hence, getting to the bottom of the resonance mode is crucial for a deeper understanding of the cuprate materials . To analyze the corresponding two-particle correlation functions we develop in the present thesis a new, non-perturbative and parameter-free technique for T=0 which is based on the Variational Cluster Approach (VCA, an embedded cluster method for one-particle Green's functions). Guided by the spirit of the VCA we extract an effective electron-hole vertex from an isolated cluster and use a fully renormalized bubble susceptibility chi0 including the VCA one-particle propagators.Within our new approach, the magnetic excitations of HTSC are shown to be reproduced for the Hubbard model within the relevant strong-coupling regime. Exceptionally, the famous resonance mode occurring in the underdoped regime within the superconductivity-induced gap of spin-flip electron-hole excitations is obtained. Its intensity and hourglass dispersion are in good overall agreement with experiments. Furthermore, characteristic features such as the position in energy of the resonance mode and the difference of the imaginary part of the susceptibility in the superconducting and the normal states are in accord with Inelastic Neutron Scattering (INS) experiments. For the first time, a strongly-correlated parameter-free calculation revealed these salient magnetic properties supporting the S=1 magnetic exciton scenario for the resonance mode. Besides the INS data on magnetic properties further important new insights were gained recently via ARPES (Angle-Resolved Photoemission-Spectroscopy) and Raman experiments which disclosed a quite different doping dependence of the antinodal compared to the near-nodal gap. This thesis provides an approach to the Raman response similar to the magnetic case for inspecting this gap dichotomy. In agreement with experiments and one-particle data obtained in the VCA, we recover the antinodal gap decreasing and the near-nodal gap increasing as a function of doping. Hence, our results prove the Hubbard model to account for these salient gap features. In summary, we develop a two-particle cluster approach which is appropriate for the strongly-correlated regime and contains no free parameter. Our results obtained with this new approach combined with the phase diagram and the one-particle excitations obtained in the VCA strongly constitute a Hubbard model description of HTSC cuprate materials. / Zwei-Teilchen Anregungen, darunter Spin und Ladungs Anregungen, sind von besonderer Bedeutung in Hoch-Tc Kuprat Supraleitern (HTSL). Aufgrund der antiferromagnetischen Phase bei niedrigen Dotierungen werden magnetische Anregungen direkt mit dem Mechanismus der Supraleitung in Verbindung gebracht. Gerade die sogenannte Resonanzmode ist ein vielversprechender Kandidat für den pairing glue, eine bosonische Anregung, welche die Paarung von Elektronen induziert. Weiterhin wird deren Wechselwirkung mit itineranten Elektronen verantwortlich gemacht für einige der beobachteten Eigenschaften der HTSL. Für ein tieferes Verständnis der Kuprate ist es daher unerlässlich, der Resonanzmode auf den Grund zu gehen. Um die entsprechenden Zwei-Teilchen Korrelationsfunktionen zu analysieren, entwickeln wir auf Basis des Variational Cluster Approach (VCA, eine Cluster Methode, um Ein-Teilchen Green Funktionen zu berechnen) in der vorliegenden Dissertation eine neue, nicht-perturbative und parameterfreie Technik für T=0. Im Sinne der VCA berechnen wir einen effektiven Elektron-Loch Vertex auf einem einzelnen Cluster und verwenden eine vollkommen renormierte Bubble Suszeptibilität chi0, welche die VCA Ein-Teilchen-Propagatoren beinhaltet. Mit Hilfe unserer neuen Technik können wir die magnetischen Anregungen der HTSL im Rahmen des Hubbard Modells in der stark korrellierten Phase reproduzieren. Als herausragendes Ergebnis erhalten wir die berühmte Resonanzmode im underdotierten Bereich innerhalb des von der Supraleitung induzierten Gaps der Spin-Flip Elektron-Loch Anregungen. Deren Intensität und Sanduhren-förmige Dispersion zeigen eine sehr gute Übereinstimmung mit den Experimenten. Weiterhin sind charakteristische Eigenschaften, wie die Energie der Resonanzmode oder die Differenz des Imaginärteils der Suszeptibilität in der supraleitenden und normalen Phase im Einklang mit Inelastischen Neutronenstreu (INS) Experimenten. Zum ersten Mal bringt eine stark-korrellierte und parameterfreie theoretische Rechnung diese besonderen magnetischen Eigenschaften hervor und bekräftigt damit die Erklärung der Resonanzmode als S=1 magnetisches Exziton. Neben den INS Resultaten zu magnetischen Eigenschaften wurden kürzlich weitere wichtige neue Erkenntnisse mittels ARPES (Winkelaufgelöste Photoemissionen Spektroskopie) und Raman Experimenten erhalten. Beide legten eine deutlich unterschiedliche Dotierungsabhängigkeit des anti-nodalen Gaps verglichen mit dem Gap nahe des nodalen Punktes offen. Im Rahmen dieser Dissertation wird eine der magnetischen Berechnung ähnliche Technik für den Raman Response benutzt, um dieses unterschiedliche Verhalten des Gaps zu untersuchen. Übereinstimmend mit den Experimenten und Ein-Teilchen Ergebnissen aus VCA Rechnungen bekommen wir ein Abfallen des anti-nodalen Gaps und Ansteigen des Gaps nahe dem nodalen Punkt als Funktion der Dotierung. Folglich zeigen unsere Ergebnisse, dass das Hubbard Modell diese besonderen Eigenschaften des Gaps beinhaltet. Zusammenfassend entwickeln wir eine Zwei-Teilchen Cluster Technik, welche für stark korrellierte Systeme geeignet ist und keine freien Parameter enthält. Unsere Ergebnisse mit dieser neuen Technik in Verbindung mit dem Phasendiagramm und Ein-Teilchen Anregungen der VCA Rechnungen bekräftigen mit Nachdruck eine Beschreibung der HTSL Kuprate auf Basis des Hubbard Modells.

The present work gives an overview of the authors work in the field of electronic structure calculations. The main objective is to show how electronic structure methods in particular density functional theory (DFT) can be used for the description and interpretation of experimental results in order to enhance our understanding of physical and chemical properties of materials. The recently found superconductor MgB2 is an example where the electronic structure was the key to our understanding of the surprising properties of this material. The experimental confirmation of the predicted electronic structure from first principles calculations was very important for the acceptance of earlier theoretical suggestions. Molecular crystals build from magnetic clusters containing a few transition metal ions and organic ligands show fascinating magnetic properties at the nanoscale. DFT allows for the investigation of magnetic ordering and magnetic anisotropy energies. The magnetic anisotropy which results mainly from the spin-orbit coupling determines many of the properties which make the single molecule magnets interesting.

Stuttgart, Univ., Diss., 2003.

Stuttgart, Univ., Diss., 2006.

This thesis deals with solving stationary magnetic field in material with non-constant magnetic reluctivity in realistic geometry. To this end, we extended adgfem software. Software adgfem implements discontinuous Galerkin method and so far has been used mainly to solve convection- diffusion problems and lacked streamlined approach to computational mesh generation. This thesis contains step-by-step guideline to creation of complex geometry using software SALOME. This mesh is then converted to format suitable for adgfem using newly written convertor datToAdgfem. Mesh created in this way is then used for calculation of non-linear static magnetic field.

III-Mn-V dilute ferromagnetic semiconductors (DFSs) have been treated as a candidate material for semiconductor spintronics due to their intrinsic ferromagnetism mediated by holes. In this thesis, three different Mn doped III-V DFSs, (In,Mn)As, (Ga,Mn)As, and (Ga,Mn)P, have been produced by ion implantation and pulsed laser melting. The comparison of magnetic anisotropy, magnetization, Curie temperature, as well as the electrical property is performed between three different materials to understand the nature of hole-mediated ferromagnetism in DFSs. An in-plane magnetic easy axis is observed in (Ga,Mn)As and (Ga,Mn)P, while an out-of-plane magnetic easy axis is found in (In,Mn)As due to the contribution of different inner strain resulting from the lattice mismatch between the DFS layer and the corresponding substrate. Most importantly, the direct proof of interplay between localization and magnetism is provided by a systematic comparison between (Ga,Mn)As and (In,Mn)As. When the Mn concentration is increased in the regime of the insulator-metal transition, the long-range ferromagnetic coupling is gradually built up accompanied with the appearance of metallic features. The generation of long-range global ferromagnetism is strongly influenced by the p-d coupling between hole and Mn local spins: The global ferromagnetism (metallic feature) happens at lower Mn concentration in (In,Mn)As than in (Ga,Mn)As due to the stronger p-d coupling from the smaller lattice parameter of GaAs. Moreover, for the case of (Ga,Mn)P with the strongest p-d coupling in comparison with (In,Mn)As and in (Ga,Mn)As, the super-exchange model has to be considered, since metallic features does not appear at the highest obtainable Mn concentration. Through the comparison between three different DFS materials, our findings strongly advocate for the heterogeneous model of electronic states at the localization boundary and point to the crucial role of weakly localized holes in mediating efficient spin-spin interactions even on the insulator side of the insulator-metal transition at least for (In,Mn)As and in (Ga,Mn)As.

This work reports on physical properties of a novel CeCo0.715Si2.285 compound. The compound crystallizes in the I-4m2 space group structure with extremely elongated unit cell (a = 4.13˚A , c = 32.84˚A) containing BaAl4 structural patterns. In zero magnetic field it orders antiferromagnetically at TN = 10.0K. Under application of magnetic field along the c-axis it manifests numerous magnetic transitions in small fields (B < 0.5T), resembling the so-called 'devil's staircase' behaviour (e.g. CeSb, CeCoGe3). The magnetization is almost constant from 1T up to 45T for H||c but considerably reduced (0.3µB/Ce) with respect to the free Ce3+ ion. For fields applied along the a-axis typical behaviour for a hard axis in a material with uniaxial anisotropy is observed. The performed single crystal neutron diffraction experiment did not allow complete determination of magnetic structure. 1

Title: Critical behavior in magnetic phase diagrams of uranium compounds Author: Bc. Petr Opletal Department: Department of Condensed Matter Physics Supervisor: RNDr. Jan Prokleška, Ph.D., Department of Condensed Matter Physics Abstract: This work is focused on study of phase diagrams and related critical effects in the pseudoternary UCo1-xRuxAl compound. Three single crystals of nominal composition UCo0.99Ru0.01Al, UCo0.995Ru0.005Al and UCo0.9975Ru0.0025Al have been prepared by Czochralski method in triarc furnace. Quality of single crystals was checked by EDX analysis, Laue method and XRPD. For UCo0.99Ru0.01Al Curie temperature was determined as TC = 16 K. UCo0.995Ru0.005Al shows transition from paramagnetic to ferromagnetic phase at TC= 4.5 K and at higher temperatures we observe a metamagnetic transition of first order with a critical field HC = 0.04 T. UCo0.9975Ru0.0025Al is paramagnetic to low temperatures with metamagnetic transition of first order and critical field HC = 0.55 T. Experiments in hydrostatic pressure on UCo0.995Ru0.005Al and UCo0.9975Ru0.0025Al showed decay of ferromagnetism and increase of critical field. This behavior is similar to evolution of magnetism in UCoAl and URhAl in applied hydrostatic pressure. Keywords: UCoAl, URuAl, ferromagnetism, metamagnetism

Title: Electron properties of the substituted cerium compounds Author: Milan Klicpera Department: Department of Condensed Matter Physics Supervisor: doc. Mgr. Pavel Javorský Dr. Abstract: The subject of this work is the study of vibron states in tetragonal CeCuAl3 and CePd2Al2 compounds and their development with the substitution of constituent elements. After the preparation of single crystals and polycrystalline samples, the careful chemical and structural characterization was done. The structural, magnetic and superconducting phase transitions in samples were observed and thoroughly investigated. The crucial experiments were performed using the elastic and inelastic neutron scattering techniques leading to the refinement of magnetic structures in CeCuAl3, CePd2Al2 and CePd2Ga2. The energy spectra of substituted Ce(Cu,Al)4 and CePd2(Al,Ga)2 compounds were studied as well allowing to determine the crystal field excitations and their interaction with phonons (vibron states) in these materials. Keywords: cerium internetallic compounds, vibron states, electronic properties, neutron scattering

The thesis is focused on the physics of magnetic nanoparticles (NPs), starting from the solution of magnetic structure, internal alignment within the single particle and role of interactions and particle structure in magnetic response of systems of the NPs. Moreover, the macroscopic arrangement of the NPs and its effect on the properties of system containing the NPs are discussed. The work brings several new results and concepts, such as the solution of magnetic structure of the ε-Fe2O3 phase, methods of proper detection and description of magnetic metal catalyst in carbon nanotubes and role of the NP arrangement and their effect on graphene placed on the top of substrates decorated with the NPs. 1