Ionic Polarizability of Conductive Metal Oxides and Critical Thickness for Ferroelectricity inBaTiO3

We report a first-principles investigation of ultrathin ${\mathrm{BaTiO}}_3$ films with ${\mathrm{SrRuO}}_3$ electrodes. We find that the ionic relaxations in the metal-oxide electrode play a crucial role in stabilizing the ferroelectric phase. Comparison with frozen-phonon calculations shows that the degree of softness of the ${\mathrm{SrRuO}}_3$ lattice has an essential impact on the screening of ferroelectric polarization in ${\mathrm{BaTiO}}_3$. The critical thickness for ferroelectricity in ${\mathrm{BaTiO}}_3$ is found to be 1.2 nm. The results of our calculations provide a possible explanation for the beneficial impact of oxide electrodes on the switching and dielectric properties of ferroelectric capacitors.