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Out-of-plane PFM phase images of successive FE domain evolution under external (a) negative (−4.7 V) and (b) positive (3.3 V) switching voltages after an initial poling process to make the capacitor single domain. All of the PFM phase images were obtained in the same region. The scan size is . (c) and (d) were obtained by superposing the PFM phase images from (a) and (b). The FE domains grow sideway in a particular direction, indicated by the open arrows, depending on the polarity of the switching voltage. The solid dots indicate the regions where DWs become strongly pinned. and represent the direction of the upward and downward electric field induced by a negative and positive switching voltage in a BFO capacitor, respectively.
(a) Depth profiles of lattice constants along the -axis (toward the miscut direction, i.e.,  direction) and the -axis (perpendicular to the miscut direction, i.e.,  direction) in the miscut BFO(001) films, obtained from GID measurements and RSMs. The solid line and the dashed line indicate the lattice constants of bulk STO and BFO, respectively. (b) Time-dependent switched area, calculated from the PFM phase images in Fig. 1(a) (negative switching voltage) and Fig. 1(b) (positive switching voltage).
(a) A schematic diagram of the gradient of the  strain induced by the substrate’s vicinality. The magenta (dark) and white (bright) blocks represent strongly strained and relaxed BFO regions, respectively. Note that the  direction is perpendicular to the gradient directions. (b) A top view of the  strain variation in BFO regions with slanting lines in (a). (c) Variation of the double-well potential due to the strain-induced local internal field. Energy barriers for polarization switching in strongly strained, weakly strained, and relaxed BFO unit cells are schematically illustrated. “up” and “down” represent upward and downward polarization states in the double-well potentials, respectively.
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