Local Strain and Polarization Mapping in Ferrielectric Materials

CuInP₂S₆ (CIPS) is a van der Waals material that has attracted attention because of its unusual properties. Recently, a combination of density functional theory (DFT) calculations and piezoresponse force microscopy (PFM) showed that CIPS is a uniaxial quadruple-well ferrielectric featuring two polar phases and a total of four polarization states that can be controlled by external strain. Here, we combine DFT and PFM to investigate the stress-dependent piezoelectric properties of CIPS, which have so far remained unexplored. The two different polarization phases are predicted to differ in their mechanical properties and the stress sensitivity of their piezoelectric constants. This knowledge is applied to the interpretation of ferroelectric domain images, which enables investigation of local strain and stress distributions. The interplay of theory and experiment produces polarization maps and layer spacings which we compare to macroscopic X-ray measurements. We found that the sample contains only the low-polarization phase and that domains of one polarization orientation are strained, whereas domains of the opposite polarization direction are fully relaxed. The described nanoscale imaging methodology is applicable to any material for which the relationship between electromechanical and mechanical characteristics is known, providing insight on structural, mechanical, and electromechanical properties down to ∼10 nm length scales.