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.

This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems. Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry. In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique. Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally. In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states. The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.

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.