Superconducting critical fields and anisotropy of a MgB2 single crystal

Using a double axis vibrating sample magnetometer, we have made detailed magnetic measurements of the lower critical field H-c1 for fields parallel to the two crystallographic directions of MgB2, single crystals. Additionally, using a novel Hall probe magnetometer we have measured high precision magnetization loops, from which we directly determine the Lipper critical field H-c1 for both field orientations. Our results suggest that H-c2 is much larger than most previous estimates and that consequently the Ginzburg-Landau parameter kappa is very low (less than 5). We find the anisotropy parameter gamma similar to 2, independent of temperature over the measured range.