Nanoscale Polarization-Dependent Young’s Modulus of Ferroelectric BaTiO₃ Single Crystals

Flexoelectric fields produced by strong strain gradients at the nanoscale couple to ferroelectric polarization, promoting changes in the mechanical properties of ferroelectric materials as a function of the direction of the ferroelectric polarization. In this work, we calculate the asymmetry in the Young's modulus found in oppositely polarized out-of-plane domains of BaTiO₃ single crystals by means of contact resonance AFM, and we evaluate its impact on the electromechanical response as measured by piezoresponse force microscopy, both using band excitation modes. We analyze the electromechanical response of the different BaTiO₃ domains using k-means to build up their mean elastic and electromechanical features and quantify the flexoelectrically induced modulation of the Young's modulus. Finally, we discuss the use of contact Kelvin probe force microscope measurements to decouple electrostatic artifacts from purely piezoelectric ones when flexoelectric coupling appears.