The tip-sample interaction and scanning tunneling microscopy atomic-force microscopy (STM-AFM) image formation on ${\mathrm{TiO}}_2\mathrm{}\left(110\right)\mathrm{}$ $1\times 1$ and $1\times 2$ surfaces are simulated by using the ultrasoft pseudopotentials plane-wave technique. The effects of spin polarization and bias voltage on the tip-sample interaction in AFM are also investigated. The calculation demonstrates that overall the tip-oxygen interaction is much stronger than the tip-Ti interaction, which determines the main feature of the AFM image formation. The present calculations provide reasonable explanations to a very recent experiment adopting the technique of the combination of STM and AFM.

• Received 19 August 2001

DOI:https://doi.org/10.1103/PhysRevB.65.125417