Experimental verification of theoretical models on vortex matter properties of superconducting materials Summary: Applying a magnetic field to a type II superconductor opens the way to the very rich and interesting physics of the vortex matter (i.e. the properties of the flux line lattice as a function of magnetic field, temperature and material parameters). Although a large amount of work has been published in this field, many questions are still unsettled. Theories that describe the different states of the vortex matter in the superconducting phase diagram are available, but have to be verified by experiments. Unfortunately, most experiments suffer from two main problems: (i) due to very high upper critical fields in many superconductors, only a small part of the superconducting phase diagram is experimentally accessible and can be used for comparison. (ii) The defect structure responsible for vortex pinning is a crucial parameter for the vortex matter behavior and enters theory. But this information can usually not be obtained or reliably estimated in experiment. Therefore, almost all verifications of theory by experiments address only qualitative results on the temperature and / or magnetic field dependence of the vortex properties and the effects of changing defect density cannot be analyzed at all. The main goal of this project is to compare theory and experiment in a more quantitative way than available in current literature. This will be achieved by two innovations. (i) We will obtain all parameters entering theory from experiment. In particular, we will study neutron irradiated single crystals, where the radiation induced defects dominate the pinning behavior, and where the size and density of the defects can be analyzed by transmission electron microscopy. (ii) To verify also the defect density dependence of the theoretical models, samples will be exposed to different neutron fluences - usually proportional to the defect density - and analyzed after each irradiation step. The macroscopic properties of the flux line lattice (critical current density - Jc, fishtail effect,...) will be evaluated from magnetic measurements (e.g. in a SQUID), from which additionally the reversible parameters - also needed for the theoretical discussion - will be derived. The main focus will be placed on the comparison of the fishtail effect (which denotes the commonly observed second peak in Jc vs. magnetic field measurements) with theory since this feature is assumed to be a key factor in understanding vortex matter physics and on the behavior (field, temperature, and defect density dependence) and absolute values of Jc. Since most theoretical models predict different kinds of vortex matter phases, the investigations will be completed by real space imaging of the flux lines using scanning probe microscopy. We aim to compare directly the macroscopic (i.e. Jc) with the microscopic flux line state (static distribution and dynamics) at different field, temperature and defect density values with particular emphasis on the possible phase transitions and phase mixtures related to the fishtail effect. Vortex matter properties can change significantly from material to material. Furthermore theoretical models are often limited by certain parameters (e.g. the ratio of the coherence length to the defect radius). Thus it is necessary to investigate different kinds of material so that results on a wide range of parameters become available. Most experiments will be carried out on selected low temperature superconducting single crystals as these materials are expected to be most convenient for achieving our goals, but high temperature superconductors will also be considered.