Equilibrium polarization of ultrathin PbTiO₃ with surface compensation controlled by oxygen partial pressure

We present a synchrotron x-ray study of the equilibrium polarization structure of ultrathin PbTiO₃ films on SrRuO₃ electrodes epitaxially grown on SrTiO₃ (001) substrates, as a function of temperature and the external oxygen partial pressure (pO₂) controlling their surface charge compensation. We find that the ferroelectric Curie temperature (T_C) varies with pO₂ and has a minimum at the intermediate pO₂, where the polarization below T_C changes sign. The experiments are in qualitative agreement with a model based on Landau theory that takes into account the interaction of the phase transition with the electrochemical equilibria for charged surface species. The paraelectric phase is stabilized at intermediate pO₂ when the concentrations of surface species are insufficient to compensate either polar orientation.