Upper critical field study of MBE grown MgB$_2$ thin films

"Normal" alloying of MgB$_2$ enhances the electron scattering, as does radiation damage. As a result, the upper critical field $H_{c2}^{\parallel}(0)$ parallel to the ab planes doubles from about 18 to 35 T. ASU has been growing films by non-equilibrium MBE methods and either intentionally doping with oxygen during growth, or by deposition at room temperature with subsequent annealing {\em ex situ} at rather low temperature: {\em e.g.} 350 $^\circ$C for 36 hrs followed by 600 $^\circ$C for 30 min. The resistive transitions of the films have been measured in fields up to 45 T at different temperatures. The measurements revealed strong enhancement of $H_{c2}^{\parallel}(0)$. In particular, the cold-deposited film remains superconducting at 45 T at 5 K, while extrapolation yields $H_{c2}^{\parallel}(0)$ higher than 65 T, almost as high as the best C-doped HPCVD films. At the same time, the film is strongly inhomogeneous, the resistivity is as high as ~30 m$\Omega$cm, while the transitions are very broad, and the critical temperature is lowered to 24 K. However, $dH_{c2}/dT$ at $T_c$ reaches a record high value of 2.7 T/K. These observations open up another way to get exceptional $H_{c2}$ values in MgB$_2$ films.