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We have constructed the surface phase diagram of the BaTiO$_{3}$(001) surfaceby employing an evolutionary algorithm for surface structure prediction, wherethe ferroelectric polarization is included as a degree of freedom. Among over1000 candidate structures explored, a surface reconstruction of(2$\times$1)-TiO is discovered to be thermodynamically stable and have the\emph{p2mm} plane group symmetry as observed experimentally. We find that theinfluence of ferroelectric polarization on the surface free energy can beeither negligibly small or sizably large (over 1 eV per ($2 \times 1$)supercell), depending strongly on the surface structure and resulting in asignificant distinction of surface phase diagram with varying ferroelectricpolarization. It is therefore feasible to control the surface stability byapplying an external electric field. Our results may have importantimplications in understanding the surface reconstruction of ferroelectricmaterials and tuning surface properties.

Effects of ferroelectric polarization on surface phase diagram: an evolutionary algorithm study of the BaTiO$_{3}$(001) surface