  First-principles calculations reported here illuminate the effects of the
interfacial properties of $\alpha$-Al$_{2}$O$_{3}$ and graphene, with emphasis
on the structural and electronic properties. Various contact interfaces and
different $\alpha$-Al$_{2}$O$_{3}$ surface terminations are considered with on
and slightly-off stoichiometric aluminium oxide. We show that depending on
whether aluminium or oxygen is in contact with graphene, an $sp^{3}$ structural
deformation and spontaneous spin-polarization may occur next to the interface
contact. Interestingly, some cases cause a $p$-type doping in the graphene band
structure, depending on the initial $\alpha$-Al$_{2}$O$_{3}$ geometry placed on
graphene. The importance of leaving the surface dangling bonds of alumina
saturated or not is also highlighted, and we show that it might be a control
mechanism for opening a gap in graphene by the influence of the $sp^{3}$ bond
between oxygen and carbon atoms at the interface. We discuss the potential of
utilizing this sensitivity for practical applications.
