The different development of the anisotropic upper critical field in MgB$_2$ by aluminum and carbon doping

The temperature dependence of the upper critical field, $H_{c2} $, for both field directions in partially substituted polycrystalline MgB$_2$ was determined. Whereas the suppression of $T_c$ is similar for aluminum and carbon substituted samples, $H_{c2}$ is affected by the substitution in profoundly different ways. In the case of Al substitution changes can tentatively be described by intrinsic effects (shift of the Fermi level). In the C substituted samples, $H_{c2}$ is increased drastically, and extrinsic effects (disorder) have to play a major role. The strong contrast between the two substitutions is discussed, taking into account three relevant scattering rates.