  Against expectations, robust switchable ferroelectricity has been recently
observed in ultrathin (1 nm) ferroelectric films exposed to air [V. Garcia $et$
$al.$, Nature {\bf 460}, 81 (2009)]. Based on first-principles calculations, we
show that the system does not polarize unless charged defects or adsorbates
form at the surface. We propose electrochemical processes as the most likely
origin of this charge. The ferroelectric polarization of the film adapts to the
bound charge generated on its surface by redox processes when poling the film.
This, in turn, alters the band alignment at the bottom electrode interface,
explaining the observed tunneling electroresistance. Our conclusions are
supported by energetics calculated for varied electrochemical scenarios.

Mesoscale and Nanoscale Physics