  The electric coupling between surface ions and bulk ferroelectricity gives
rise to a continuum of mixed states in ferroelectric thin films, exquisitely
sensitive to temperature and external factors, such as applied voltage and
oxygen pressure. Here we develop the comprehensive analytical description of
these coupled ferroelectric and ionic ("ferroionic") states by combining the
Ginzburg-Landau-Devonshire description of the ferroelectric properties of the
film with Langmuir adsorption model for the electrochemical reaction at the
film surface. We explore the thermodynamic and kinetic characteristics of the
ferroionic states as a function of temperature, film thickness, and external
electric potential. These studies provide a new insight into mesoscopic
properties of ferroelectric thin films, whose surface is exposed to chemical
environment as screening charges supplier.
