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Parallel and Perpendicular Susceptibility Above $T_{c}$ in La$_{2-x}$Sr$_{x}$CuO$_{4}$ Single Crystals

We report direction-dependent susceptibility and resistivity measurements on La$_{2-x}$Sr$_{x}$CuO$_{4}$ single crystals. These crystals have rectangular needle-like shapes with the crystallographic "c" direction parallel or perpendicular to the needle axis,which, in turn, is in the applied field direction. At optimal doping we find finite diamagnetic susceptibility above $T_{c}$, namely fluctuating superconductivity (FSC), only when the field is perpendicular to the planes. In underdoped samples we could find FSC in both field directions. We provide a phase diagram showing the FSC region, although it is sample dependent in the underdoped cases. The variations in the susceptibility data suggest a different origin for the FSC between underdoping (below 10%) and optimal doping. Finally, our data indicates that the spontaneous vortex diffusion constant above $T_c$ is anomalously high.