High-resolution angle-resolved lateral piezoresponse force microscopy: Visualization of in-plane piezoresponse vectors.

Piezoresponse force microscopy (PFM) is a widely used tool for ferroelectric domain imaging. Lateral PFM (LPFM) utilizes the torsional vibration mode of a probe cantilever; it can distinguish ferroelectric domains having different polarizations with respect to the axis perpendicular to the cantilever, but it is blind to the parallel axis innately. We introduce a high-resolution angle-resolved-LPFM technique that is capable of visualizing full two-dimensional in-plane piezoresponse vector fields. The LPFM signal is analyzed for each pixel with respect to the sample-probe orientation angle with the aid of an image registration technique, and the corresponding local in-plane piezoresponse vector is deduced from the amplitude and phase of the trigonometric curve fitting. This technique provides a pathway for the visualization of complicated ferroelectric and piezoelectric structures.