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

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 BiFeO3 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 BiFeO3 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 BiFeO3 grains can be determined through numerical calculations. In the polycrystalline BiFeO3 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 BiFeO3, so as to realize desirable magnetoelectric coupling.

. Schematic view of the R3c BiFeO3 (BFO) structure in the rhombohedral representation for first principles calculations.
The piezoelectric tensor of BFO is calculated using the density functional perturbation theory (DFPT), as implemented in the Vienna ab initio simulation package (VASP). The calculations were performed using the projector-augmented wave method within the local spindensity approximation plus the on-site repulsion (LSDA + U), in which Ueff = 4 eV is used on Fe3d states. We use a 5×5×5 Gamma-centered k-point sampling for the calculations, and adopt a plane-wave cutoff of 800 eV and a convergence threshold of 10 −7 eV to improve the accuracy of piezoelectric tensor. The ionic positions were first fixed to calculate the electronic contribution to the piezoelectric tensor, and then the ions were relaxed to obtain the ionic contribution to the piezoelectric tensor. The total piezoelectric tensor is the sum of the electronic and ionic contributions. In laboratory coordinate system, 10 ������⃑ becomes The transform matrix for 71° polarization switching from P1 to P2 (i.e., an anticlockwise rotation of 90° around 10 ������⃑ is And the matrix for 180° polarization switching from P2 to P6 (i.e., an inversion in the body center) is Then a 109°-switching is achieved by the combination of the above two operations from P1 to P6, with the transform matrix being A general transform matrix for all the possible switching cases starting from P1 state can be where d is the rotation angle (anticlockwise) around 10 ������⃑, and e = -1 (e = +1) represents for inversion (identity) operation, with the details listed in Fig. S2(f). Figure S3. Polarization switching in BiFeO3 under an electric field along -z axis.
The poling field tends to increase the OP polarization along -z axis. Even if the original OP polarization is along -z axis, there are still switching possibilities in BFO. Take crystal lattice as depicted in Figure S3 for instance, the OP polarization of P5-P8 is along the electric field. P8 could switch 71º to P5 and P7, or switch 109º to P6, as long as the OP polarization of P5, P6, and P7 along the field is larger than that of P8. In addition, P5 could switch 71º to P6 while the switching possibility of P6 is much less since the OP polarization of P6 along the field is the maximum among all the 8 polarization states.
Notably, 180º-switching is unlikely if the original OP polarization is along -z axis, otherwise the OP polarization would turn to antiparallel to the poling field, which is of course energetically unfavorable. Figure S4. Qualitative illustrations of the in-plane lattice distortion for different switching cases.
The grains and domains are randomly oriented in the polycrystalline sample. In the 2 μm × 2 μm scanning range of our films, the average angle θ between the polarization and the z axis over all > 0 ( < 0) regions is about 59.7º (117.6º). To qualitatively compare the IP stress for different switching cases, we suppose a crystal lattice with (001) plane of the Pseudo cubic perpendicular to z axis and the OP polarization after switching along -z direction (poling field). In this state, the angle between polarization and z axis is 54.5º (125.5º) for > 0 ( < 0), which is close to the above mentioned average θ. Besides, (001)  (a) 71º switching with original OP polarization antiparallel (+71º) and parallel (-71º) to the poling field. The latter shows more apparent in-plane distortion.
(b) 109º switching with original OP polarization antiparallel (+109º) and parallel (-109º) to the poling field. The former shows more apparent in-plane distortion.
(c) 71º, 109º, and 180º switching with original OP polarization antiparallel to the poling field.
The in-plane lattice distortion of +109º switching is the most apparent, while no additional distortion appears after 180º switching.
(d) 71º and 109º switching with original OP polarization parallel to the poling field. The in-plane lattice distortion of the former is more apparent.