Effect of Al doping on the upper critical field of MgB$_{2}$ single crystals

We use magnetization measurements to investigate the effect of Al substitution on the temperature dependence of the upper critical field, H$_{c2}$(T), of MgB$_{2}$ single crystals. We find that as the Al concentration is increased, the shape of H$_ {c2}$(T) changes from that for dirty $\sigma$ bands to that for dirty $\pi$ bands, which verifies that Al doping enhances intraband scattering mainly in the $\pi$ bands. Thus, one of the characteristics of the two-gap nature of MgB$_{2}$, i.e., the strong temperature dependence of the H$_{c2}$(T) anisotropy $\gamma_{H} = H_{c2}^{ab}/H_{c2}^{c}$ in pure MgB$_{2}$, is drastically affected by Al doping.