= Solution
A surface slope converts some vertical displacement into lateral motion of the tip and changes the normal contact geometry. Roughness also changes friction, contact area and local contact stiffness, and can mix cantilever bending, buckling and torsion. A lateral image that follows a height gradient can therefore appear even when the relevant in-plane polarization component is absent.
Record topography and both <piezoresponse force microscopy> channels simultaneously, and compare the lateral signal with the local slope rather than height alone. Reverse the scan direction to identify frictional contributions, rotate the sample relative to the cantilever, and compare the vector transformation expected for an in-plane response with the geometrical cross-talk. Repeat on a smoother region or a polished specimen, at controlled force and drive amplitude. Track contact resonance or compare sufficiently far from it so that local stiffness does not masquerade as a change in response.
A useful control is a nonpiezoelectric surface of similar roughness. Electrically switching a domain while leaving its topography unchanged provides a further comparison when feasible. \b[No single trace–retrace test proves the absence of cross-talk]: genuine in-plane response and slope-induced signals can both transform under rotation, so several controls must agree.
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