Interactions of an atomic force microscope tip with a reversed ferroelectric domain

A theory of interactions between an atomic force microscope (AFM) tip and a ferroelectric domain that forms under its electric field is proposed. We show that even for low potentials these interactions are dominant compared to the van der Waals forces and the electrostatic forces, within a certain distance interval. This interval expands, almost linearly, with the applied voltage. Dependence of the critical voltage required for domain formation as a function of the tip-ferroelectric surface distance is defined. This interaction force drops abruptly with removal of the tip from the ferroelectric surface, increases with the applied voltage and the tip apex radius, and depends logarithmically weak on the tip cone length.