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.

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{Cu20}, dodecanuclear cluster {Ni12}, and the heterometallic {Cr7M} wheels, in which one of the CrIII ions of Cr8 has been replaced by a Fe, Cu, Zn, Ni, ion with this extra-spin acts as local probe for the spin dynamics.Such systems have been synthesized recently and they are well described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.

The subject of this thesis is to study the interaction between carbon nanotubes (CNTs) and antiferromagnetic tetrametallic molecules attached to them. By employing quantum transport measurements, the sensitivity to sense the interactions is greatly increased, because the quantum dot is very susceptible to changes in its environment. The properties of carbon nanotubes can be altered by chemical functionalization with the aforementioned molecules, where the attachment is performed covalently via a ligand exchange with the CNT. The thesis is partitioned into two main parts: the first part presents experiments performed on tetramanganese functionalized CNTs, whereas for the second similar studies are conducted, except manganese is replaced by cobalt. Both complexes exhibit an antiferromagnetic ground state, yet the metal spin of manganese (S=5/2) is reduced to S=3/2 for cobalt. Additionally, an altered device preparation has been employed during the second part, leading to a strong suppression of the background signal. Quantum transport measurements at T=4K on manganese-functionalized CNTs show a very regular pattern of Coulomb diamonds, indicating only a mild disturbance of the quantum dot's electron system by the covalent bond. Moreover, the charging energy reveals a wave function extending over the entire device dimensions. However, at T=30mK in the tunneling current a strong noise emerges, when repeatedly measuring over an hour while keeping external biases constant. Additionally, these time traces are superimposed by a long-term background, which is removed by a correction algorithm plus a subsequent digitization. The remaining signal reveals a random telegraph signal (RTS) which is extensively studied and from its statistics the equivalent temperature of T=654mK for the excitation of the system is extracted. The quantum transport experiments conducted on cobalt-functionalized CNTs show a much better data quality of the coulomb diamonds, which is ascribed to the alteration in the device's preparation. From the line shape of the Coulomb oscillations as well as from the Coulomb staircases an electron temperature of about T=500mK is extracted. Moreover, a magnetic field dependence of the stability diagrams is apparent, attributable to Zeeman splitting. The respective Landé factor of g=1.73 is, compared to similar CNT quantum dot systems, unusually low. It is as attributed to an increased spin-orbit interaction between the conduction electrons and the cobalt's nuclei. The respective time traces exhibit or lack an RTS signal, depending on their external biases. Regarding the Coulomb diamonds, an essential prerequisite for the occurrence of an RTS is the proximity to a resonance, which is equatable to a high sensitivity of the quantum dot detector. Considering the available energy, the underlying process that is the cause for the emergence of the RTS is ascertained to be an internal excitation of the antiferromagnetic states of the metallic core.

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.