The surface of a ferroelectric BaTiO${}_3$(001) single crystal was studied using synchrotron radiation induced x-ray photoelectron diffraction (XPD), x-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), and low-energy electron diffraction (LEED). AFM, XPS, and LEED show that the surface is BaO terminated with a (1$\times$1) reconstruction. The Ba $4d$, Ti $2p$, and O $1s$ XPD results were compared with multiple scattering simulations for out-of- (${\mathrm{P}}^{+},{\mathrm{P}}^{-}$) and in-plane (${\mathrm{P}}^{in}$) polarizations using a genetic algorithm to determine atomic rumpling and interlayer relaxation. Linear combinations of the XPD simulations of the surface structure of each polarization state allow determination of the domain ordering. The best agreement with experiment is found for 55$\%$ ${\mathrm{P}}^{+}$, 38$\%$ ${\mathrm{P}}^{-}$, and 7$\%$ ${\mathrm{P}}^{in}$. The rumpling is smaller at the surface than in the bulk, suggesting that both domain ordering and surface structural changes contribute to screening of the polarization.

• Received 30 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.184116