  We have conducted a detailed thin film growth structure of oxygen engineered
monoclinic HfO$_{2\pm x}$ grown by reactive molecular beam epitaxy (MBE). The
oxidation conditions induce a switching between ($\bar{1}11$) and (002) texture
of hafnium oxide. The band gap of oxygen deficient hafnia decreases with
increasing amount of oxygen vacancies by more than 1 eV. For high oxygen
vacancy concentrations, defect bands form inside the band gap that induce
optical transitions and $p$-type conductivity. The resistivity changes by
several orders of magnitude as a function of oxidation conditions. Oxygen
vacancies do not give rise to ferromagnetic behavior.
