“…This is evidenced by the fact that, very different models for the lateral spatial dependence of the electric field perpendicular to the surface, away from the AFM tip (Fig. 1a) have been proposed to describe the lateral expansion of the domain wall, and these models vary on the role of the film thickness [6][7][8][9][10][11][12][13][14][15]25,26 . In this paper we : (a) demonstrate that the electric field due to an AFM tip, in a thin film, in a direction perpendicular to the surface, is produced by the cone of the tip rather than the field produced by the hemisphere of the tip, beginning at a lateral distance only about one tip diameter away from the tip (Fig.…”