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Zhang et al. Microstructures 2023;3:2023046 https://dx.doi.org/10.20517/microstructures.2023.57 Page 3 of 11

EXPERIMENTAL METHODS
PMN-30PT single crystals with (100) orientation were obtained from MTI Corporation, China. The crystals
were synthesized by an improved Bridgman method. The size of the crystals is 5 mm × 5 mm × 0.2 mm,
two-sided polished with a surface roughness (Ra) less than 10 Å.

High-resolution θ-2θ XRD studies and RSMs were carried out using a PANalytical X’Pert Pro diffractometer
with CuK radiation. The optical images were taken using a Nikon ECLIPSE LV100POL optical
α-1
microscope.

All measurements were performed by two commercial AFM systems, an AIST-NT Smart scanning probe
microscopy (SPM) 1000 and an Asylum Research MFP-3D Infinity at room temperature under ambient
conditions. The IP PFM signal depends on the sample orientation with respect to the cantilever. It means
that only the projected component of the IP polarization vector perpendicular to the cantilever contributes
to the IP PFM signal, as IP PFM modes rely on the torsional vibration of the cantilever. Therefore, in order
to resolve the IP polarization vectors, angle-resolved PFM measurements were carried out by changing the
azimuthal angle between the cantilever and the sample. Consequently, the directions of the IP polarization
variants have been resolved by high-resolution PFM images acquired at the quasi-identical region by
changing the cantilever-sample orientation from 0° to 360° with an interval of 45°. To note, during the
angle-resolved PFM measurements, the orientation of the cantilever is fixed, and only the angle of the
sample is rotated with respect to the cantilever. The angle-resolved PFM measurements were performed
with an AC excitation bias between 1.0 to 2.0 V (peak to peak) with platinum-coated tips (HQ:NSC35/Pt,
Mikromasch) at an off-resonance frequency of 100 kHz to avoid any crosstalk from the topography or
resonance frequencies. For SSPFM measurements, commercial silicon tips with conductive Ti/Ir coating
(ASYELEC.01-R2, Asylum Research) were used.

RESULTS AND DISCUSSION
The composition of PMN-30PT single crystals is at the MPB that separates the rhombohedral and
tetragonal phases, and the existence of intermediate monoclinic phases at this regime is argued to facilitate
the rotation path between these two phases. To analyze the polarization variants in the sample, RSMs were
performed to determine the crystal structure. A twofold and a threefold peak splitting were observed around

3 1 0 a n d 3 1 1 r e f l e c t i o n s , r e s p e c t i v e l y , c o n f i r m i n g a m o n o c l i n i c A ( M A ) s t r u c t u r e
[Supplementary Figure 1] [34,35] .

Type 1 domain structures with a typical zigzag feature on the topography are shown in Figure 1. The long
vertical zigzag stripes [Figure 1A], with an average stripe/domain width of 2.5 mm, can be observed in the
majority of the sample regions, as evidenced by the optical image shown in Figure 1G. Coinciding with the
topography, the out-of-plane (OOP) phase shows the same zigzag domain structure, with a clear 180° phase
reversal between the adjacent two stripe domains [Figure 1B]. Such topography-domain correlation
originates from a mechanochemical polishing effect that leads to a polarization-dependent mechanical
property upon polishing. Of note, the downward polarization demonstrates a higher surface height in
comparison to the upward polarization, as confirmed in the OOP poling experiment in
Supplementary Figure 2. Two sets of IP PFM images [Figure 1C-F] were obtained by changing the tip-
sample rotation angle from 0 to 90 to resolve the IP polarization variants as the polarization component
perpendicular to the cantilever leads to a torsional movement of the cantilever that can be sensitively
detected. The 0° and 90° rotation IP PFM phase signals in Figure 1C and E show checkerboard domain
structures with four-color contrast, indicating four polarization variants. Figure 1C and E is then binarized
to Figure 1D and F with only black and white contrast. The trailing field, which is equivalent to an IP