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.

<p>This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered.</p><p>The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.</p>

This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered. The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.

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.

In this work we studied magnetic properties of molecular magnets of the new heteropolyanion {Cu20}, dodecanuclear cluster {Ni12}, and the heterometallic {Cr7M} wheels, in which one of the CrIII ions of Cr8 has been replaced by a Fe, Cu, Zn, Ni, ion with this extra-spin acts as local probe for the spin dynamics.Such systems have been synthesized recently and they are well described using the Heisenberg spin Hamiltonian with a Zeeman term of an applied magnetic field along the z-axis. Using the numerical exact diagonalization method, we have calculated the energy spectrum and the eigenstates for different compounds,and we have used them for reexamining the available experimental susceptibility data to determine the values of exchange parameters.We have studied the thermodynamic properties such magnetization, susceptibility, heat-capacity. At low temperature regions molecular magnets act as individual quantum nanomagnets and can display super-paramagnetic phenomena like macroscopic quantum tunneling, ground state degeneracy, level-crossing. A crucial issue for understanding these phenomena is the coupling between magnetic molecular levels and the environment such as nuclear spins. We have modeled the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in Nuclear Magnetic Resonance (NMR) experiments.

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.