  Experimental efforts to stabilize ferromagnetism in ultrathin films of
transition metal oxides have so far failed, despite expectations based on
density functional theory (DFT) and DFT+U. Here, we investigate one of the most
promising materials, SrRuO$_3$, and include correlation effects beyond DFT by
means of dynamical mean field theory. In agreement with experiment we find an
intrinsic thickness limitation for metallic ferromagnetism in SrRuO$_3$ thin
films. Indeed, we demonstrate that the realization of ultrathin ferromagnetic
films is out of reach of standard thin-film techniques. Proposing charge
carrier doping as a new route to manipulate thin films, we predict room
temperature ferromagnetism in electron-doped SrRuO$_3$ ultra thin films.
