Despite the intense activity in the year since the discovery of superconductivity in MgB2, key parameters, in particular the upper and lower critical fields Hc2 and Hc1 and their anisotropies, are not well-established, largely because of the difficulty of growing MgB2 crystals. Attempts have been made to deduce these parameters from experiments on polycrystalline material, but they have substantial uncertainties. Hc2 is particularly important for applications, as it is the field which quenches bulk super-conductivity. In terms of understanding MgB2, it is now clear that the conventional electron-phonon interaction is strong enough to account for the high transition temperature Tc, but the consequences of the double super-conducting gap for the anisotropy and its dependence on temperature, are uncertain. Here we describe detailed direct measurements of Hc1(T) and Hc2(T) for the two principal crystallographic directions in a clean single crystal of MgB2. For fields in the c-direction, $mu_0 H^c_{c1}(0)$ = $0.28 +- 0.01T$ and $mu_0 H^c_{c2}(0)$ is $3 +- 0.5T$; this ratio of critical fields is rather low and implies that MgB2 is only just a Type II super-conductor. The anisotropies of both critical fields are close to 2.
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