We investigate whether quantum spin rings with nearest-neighbor Heisenberg or Ising exchange interactions can host solitary states. Using complete diagonalization techniques the system is described without classical or semiclassical approximation. In this case definitions used in connection with classical solitons are not applicable, one needs to redefine what solitary objects on a quantum spin system with translational symmetry ought to be. Thus, we start our contribution by defining which quantum states possess solitary character. In addition we discuss useful observables in order to visualize solitary quantum states. Then we demonstrate for various quantum spin rings that solitary quantum states indeed exist, and that they are moving around the spin ring without changing their shape in the course of time.

Das Standart-Modell zur Beschreibung von Observablen magnetischer Moleküle ist das Heisenberg-Modell. In diesem wird der Magnetismus des Superaustausches der Elektronen durch einfache bilineare Spin-Spin-Kopplungen beschrieben. Zur genaueren Approximation experimenteller Ergebnisse können, der jeweiligen Struktur des Moleküls entsprechend, verschiedene Erweiterungen des Heisenberg-Modells verwendet werden. Diese werden, explizit für das 4-Spin-System {Ni4Mo12}, in ihren Auswirkungen auf die Hochtemperatur-Nullfeldsuszeptibilität, die Nullfeldsuszeptibilität und die Hochfeldmagnetisierung betrachtet. Die wesentlichen Erweiterungen sind dabei die Einzelionen-Anisotropie, die Dzyaloshinskii-Moriya-Anisotropie und die allgemeinen Kopplungen zweiter Ordnung. Letztere stellen eine Verallgemeinerung der bekannten biquadratischen Kopplungen dar und werden im Rahmen eines magneto-elastischen Modells hergeleitet. Dabei ergeben sich unterschiedliche Einschränkungen der Kopplungsmatrix zweiter Ordnung für starre und flexible Molekülstrukturen. Speziell für {Ni4Mo12} entsprechen die Ergebnisse numerischer Simulationen von Messwerten einer Strukturänderung im externen Magnetfeld.

In this work a numerical approach for the determination of the energy spectra and the calculation of thermodynamic properties of magnetic molecules is presented. The work is focused on the treatment of spin systems which exhibit point-group symmetries. Ring-like and archimedean-type structures are discussed as prominent examples. In each case the underlying spin quantum system is modeled by an isotropic Heisenberg Hamiltonian. Its energy spectrum is calculated either by numerical exact diagonalization or by an approximate diagonalization method introduced here. In order to implement full spin-rotational symmetry the numerical approach at hand is based on the use of irreducible tensor operators. Furthermore, it is shown how an unrestricted use of point-group symmetries in combination with the use of irreducible tensor operators leads to a reduction of the dimensionalities as well as to additional information about the physics of the systems. By exemplarily demonstrating how the theoretical foundations of the irreducible tensor operator technique can be realized within small spin systems the technical aspect of this work is covered. These considerations form the basis of the computational realization that was implemented and used in order to get insight into the investigated systems.

The details of the interplay between the electronic structure and the magnetic properties of matter represent a state of the art challenge. In the present work spectroscopic investigations on the electronic structure of some interesting materials are presented. The achieved information has been used in order to answer specific questions related to the magnetic behavior of the investigated materials. For the transition metal dicyanamide compounds it is shown that the electronic states arising from carbon and nitrogen remain roughly unchanged for all compositions. A model for the magnetic superexchange interaction was proposed. In this model the geometry of the crystallographic structure accounts for a particular interaction pattern while the occupancy of the 3d transition metal band is the factor which triggers the changeover from antiferromagnetic to ferromagnetic interaction. In the case of six-membered ferric-wheel molecules the comparison between experimental and theoretical data issued estimations for the magnitude of magnetic exchange interactions. The information on the electronic structure of the LaNi5-xMex (Me=Cu, Al) allowed a better understanding of their magnetic behavior. The changes induced in the electronic structure of the parent compound by partial substitutions of nickel by copper or aluminum are discussed.

The presented thesis includes investigations to fully characterize the electronic structure and magnetic properties ofselected manganese containing high-spin molecules by means of various X-ray spectroscopic, magnetic and theoretical methods. The investigations on the Mn4 star-shaped molecule havelead to a number of interesting results. Magneto-chemical studies exhibit very weak exchange coupling constantsbetween the four Mn(II) ions, leading to complicated low lying states in which the ground state is not well separated, resulting from a dominant weak ferromagnetic coupling and a giant moment of up to 20 µB/f.u. XMCD measurements revealed that almost the completemagnetic moment is located around the Mn(II) ions.This is in agreement with only a few charge transfer states foundwithin the detailed X-ray absorption spectroscopic study. The electronic structure and detailed magnetic properties of the star-shaped heteronuclear CrIIIMnII3 complex have been precisely investigated.With XPS the homovalency of Mn and Cr have been verified. The XA-spectra of the manganese and chromium L edges were measured and compared to earlier investigated Mn4 spectra.The combination high-magnetic field magnetic measurements and element selective XMCD of Mn and Cr L edges and quantum model calculations lead to a complete analysis of the magnetic structure of the CrMn3 magnetic core. The III valence state of the manganese ions in MnIII6O2Salox has been verified. From X-ray diffraction, typical Jahn-Teller distorted oxygen octahedra have been found for Mn(III) ions. Comparisons of XPS and XAS spectra of the complex to corresponding spectraof maganite and tetranuclear manganese(II) cluster it was definitely possible to identify MnIII6O2Salox as a pure Mn(III) compound.

Since the synthesis of Mn12, which can be regarded as the birth of the class of magnetic molecules, many different molecules of various sizes and structures have been produced. The magnetic nature of these molecules originates from a number of paramagnetic ions, whose unpaired electrons form collective angular momenta, referred to as spins. The interaction between these spins can often be described in the Heisenberg model. In this work, we use the rotational band model to predict the energy spectrum of the giant Keplerate {Mo72Fe30}. Based on the approximate energy spectrum, we simulate the cross-section for inelastic neutron scattering, and the results are compared to experimental data. The successful application of our approach substantiates the validity of the rotational band model. Furthermore, magnetic molecules can serve as an example for studying general questions of quantum mechanics. Since chemistry now allows the preparation of magnetic molecules with various spin quantum numbers, this class of materials can be utilized for studying the relations between classical and quantum regime. Due to the correspondence principle, a quantum spin system can be described exactly by classical physics for an infinitely large spin quantum number s. However, the question remains for which quantum numbers s a classical calculation yields a reasonable approximation. Our approach in this work is to develop a converging scheme that adds systematic quantum corrections to the classical density of states for Heisenberg spin systems. To this end, we establish a correspondence of the classical density of states and the quantum spectrum by means of spin-coherent states. The algorithm presented here allows the analysis of how the classical limit is approached, which gives general criteria for the similarity of the classical density of states to the quantum spectrum.