Microsopic modeling of low-dimensional frustrated magnets

The low-dimensional transition metal spin-1/2 systems gained highest attention due to the discovery of high temperature superconductivity in these systems. The directed search for new materials and the intense investigation of this class of compounds showed that because of low-dimensionality and the occurrence of magnetic frustration they exhibit exotic magnetic ground states governed by magnetic exchange interactions and quantum fluctuations. The study of these properties has become a new branch in solid state physics and is indeed not only of academical but also of technical importance, e.g. multiferroics are important for high-tech applications and spintronics, moreover, such systems are dealt as candidates for quantum computing. Low-dimensional spin-compounds exhibit rich phase diagrams for the magnetic ground state governed by the relative size of the single magnetic exchange couplings. Therefore, the determination of the correct magnetic ground state and the ordering temperature requires a careful and accurate analysis of the single exchange pathways. To this end, a strategy of combining theory and experiments has turned out to be of crucial importance and will be followed in this research project. The main problems in the theoretical description arise from strong electron correlations. Existing theoretical methods are either limited to small clusters, as post Hartree-Fock methods, or include correlation effects by using empirical parameters as, e.g., in hybrid functionals or LSDA+U within the scope of density functional theory (DFT). In the last years there was considerable progress in the theoretical description of strongly correlated compounds and several numerical methods have been developed which work quite well, but they still have to be improved and there are several open questions left that have to be answered. In this project solid and cluster models will be used enabling the application and comparison of different DFT exchange-correlation functionals and post Hartree-Fock methods. This will result in a comprehensive description of the magnetic properties of low-dimensional spin-systems and will also serve for improving the choice of parameters and corrections in DFT. The cluster models will further be used for model calculations to gain better insight into magneto-structural correlations and the effects of electron correlations on local geometries and orbital ordering. The obtained microscopic models will also serve as basis for quantum Monte Carlo simulations and exact diagonalization methods whose results will be compared with different experimental data. The study will start with spin-1/2 compounds, as cuprates, and will then be extended to compounds with more than one unpaired electron per magnetic center, in particular Fe- and Mn-compounds.