“…9 To parallel the spectacular developments in instrumentation, methods, and applications, significant effort has been concentrated on the theoretical description of PFM, including the image formation mechanisms, 10,11 domain wall contrast, 12,13 tip-induced polarization switching, [14][15][16] and hysteresis loop formation. 9,17 However, all theoretical efforts to date assumed ad hoc models for tip geometry, typically using either sphere-plane or point-charge-plane approximations, while the realistic tip geometry is significantly more complex. This lack of knowledge about the tip properties results in large uncertainties in the interpretation of PFM data and precludes reliable quantitative interpretation of switching data, PFM spectroscopy, and domain wall profiles in terms of material parameters.…”