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For rhombohedral multiferroelectrics, non-180° ferroelectric domain switching may induce ferroelastic and/or (anti-)ferromagnetic effect. So the determination and control of ferroelectric domain switching angles is crucial for nonvolatile information storage and exchange-coupled magnetoelectric devices. We try to study the intrinsic characters of polarization switching in BiFeO 3  by introducing a special data processing method to determine the switching angle from 2D PFM (Piezoresponse Force Microscopy) images of randomly oriented samples. The response surface of BiFeO 3  is first plotted using the piezoelectric tensor got from first principles calculations. Then from the normalized 2D PFM signals before and after switching, the switching angles of randomly oriented BiFeO 3  grains can be determined through numerical calculations. In the polycrystalline BiFeO 3  films, up to 34% of all switched area is that with original out-of-plane (OP) polarization parallel to the poling field. 71° polarization switching is more favorable, with the area percentages of 71°, 109° and 180° domain switching being about 42%, 29% and 29%, respectively. Our analysis further reveals that IP stress and charge migration have comparable effect on switching, and they are sensitive to the geometric arrangements. This work helps exploring a route to control polarization switching in BiFeO 3 , so as to realize desirable magnetoelectric coupling.

Studying the Polarization Switching in Polycrystalline BiFeO3 Films by 2D Piezoresponse Force Microscopy