Reply to "comment on 'Origin of piezoelectric response under a biased scanning probe microscopy tip across a 180° ferroelectric domain wall'" COMMENTS COMMENTS

In response to the preceding Comment of Jungk et al. [Phys. Rev. B 89, 226101 (2014)PRBMDO0163-182910.1103/PhysRevB.89.226101] regarding the validity of our finite element method (FEM) modeling in quantitatively predicting the piezoelectric response behavior in piezoresponse force microscopy (PFM), particularly the lateral response, we present here our latest experiment results that show quantitative agreement between FEM predictions and experiments. An approach to decouple the vertical PFM signal into cantilever vertical deflection and buckling contribution is proposed. Combined with simultaneously obtained lateral PFM, we show the possibility of performing quantitative three-dimensional PFM measurements (two lateral and one vertical response) from one single PFM image. A method to perform background subtraction for lateral signals is now presented that eliminates the spurious background issues seen in the past experimental works cited previously by Lei et al. [Phys. Rev. B 86, 134115 (2012)PRBMDO0163-182910.1103/PhysRevB.86.134115], as well as in the new results presented in the Comment of Jungk et al. The quantitative agreement between experiments and FEM then becomes clear with such a subtraction scheme.