Correlated domain and crystallographic orientation mapping in uniaxial ferroelectric polycrystals by interferometric vector piezoresponse force microscopy

Abstract

Ongoing advances in scanning probe microscopy techniques are continually expanding the possibilities for nanoscale characterization and correlated studies of functional materials. Here, we demonstrate how a recent extension of piezoresponse force microscopy (PFM), known as interferometric vector PFM, can be utilized for simultaneously mapping the local crystallographic orientations and the domain structure of distributed grains in uniaxial ferroelectric polycrystals. By shifting the laser beam position on the cantilever, direction-dependent piezoresponse signals are acquired analogous to classical vector PFM, but without the need to rotate the sample. Using polycrystalline ErMnO$_{3}$ as a model system, we demonstrate that the reconstructed piezoresponse vectors correlate one-to-one with the crystallographic orientations of the micrometer-sized grains, carrying grain-orientation and domain-related information. We establish a versatile approach for rapid, multimodal characterization of polycrystalline uniaxial ferroelectrics, enabling automated, high-throughput reconstruction of polarization and grain orientations with nanoscale precision.

Figures (5)

• Figure 1: Shown in a) is a schematic drawing of the experimental setup for interferometric vPFM. Scans are performed with the laser beam (red line) sequentially positioned at each of the red dots. The position used for conventional PFM, with the beam placed directly above the AFM tip apex, is shown by a dashed line. The coordinate system is defined with $x$ along and $z$ normal to the cantilever. A schematic representation of the polycrystalline ErMnO$_3$ model system is shown in b). The hexagons represent the crystallographic orientation of the unit cells within a grain, with the polarization, $\pm P$, being parallel to the crystallographic $c$-axis. The acquired and background corrected piezoresponse amplitude $A_{\mathrm{PFM}}$ data (Supplementary Section II) shown in c–f) are recorded with the laser beam positioned at different locations along the cantilever, as indicated in the inset. The white dashed box in c) marks the area discussed in Figure \ref{['fig:2fig_pfm_feature']}.
• Figure 2: Direction-dependent piezoresponse maps, $d'_\mathrm{X}$, $d'_\mathrm{Y}$, and $d'_\mathrm{Z}$, calculated from the raw data highlighted by the dashed white box in Figure \ref{['fig:1fig_raw']}, are shown in a), c), and e), respectively. Cross sections along the arrow in a) are extracted in b), d), and f) and reveal pronounced variations in piezoresponse. The crystallographic $c_{\mathrm{X}}$ component, measured via EBSD at the same position, is shown in g), with the line-profile presented in h). A clear correlation between the $d'_\mathrm{X}$ data, obtained from interferometric vPFM in b), and $c_\mathrm{X}$, measured via EBSD in h), can be observed.
• Figure 3: The direction-dependent piezoresponse vector, $\boldsymbol{d'}$, is visualized for the entire scan area in a). The color-code using hue, represents the in-plane piezoreponse, while the brightness and saturation quantify the component directed out-of-plane, $d'_{\mathrm{Z}}$. A map visualizing the crystallographic $\boldsymbol{c}$-axis, obtained via EBSD, is included in b). The ability to resolve the 180° domain structure is demonstrated for the blue/yellow domain within one grain in a), indicated by the square and triangle on opposite sites of the color wheel. In this representation, the $d'_{\mathrm{Z}}$ is scaled to match the range of the in-plane components, as it is typically about twice as large in magnitude.proksch_3d_2025
• Figure 4: The direction-dependent distributions of the piezoresponse are displayed as a function of the corresponding EBSD components for the 15.0 mapped grains. The sampled piezoresponses reflect bimodal distributions that broaden with increasing EBSD-component magnitude, reflecting the antiparallel alignment of ferroelectric domains within one grain.
• Figure 5: From the three-dimensional piezoresponse data in Figure \ref{['fig:3fig_comparison_2D']}, the crystallographic $c$-axis direction is calculated and presented in a), with two hexagons highlighting a predominantly in-plane and a predominantly out-of-plane grain. The reference EBSD map, presented in Figure \ref{['fig:3fig_comparison_2D']} b), is displayed in b) for comparison. The in-plane component is encoded via hue (color), while the out-of-plane component is encoded by the brightness. Higher out-of-plane component corresponds to lower brightness.