Flexoelectric Effects Under an AFM Tip

The mechanical properties of materials are described by even parity tensors, therefore are believed to be insensitive to space inversion even for non-centrosymmetric materials such as ferroelectrics, i.e., for a ferroelectric material the mechanical response should not depend on whether its polarization is pointing up or down.
This situation can change, however, if flexoelectricity (a relevant phenomenon at the nanoscale) is taken into account, because deforming a ferroelectric material in an inhomogeneous way will yield two sources of polarization: the piezoelectric one due to strain, and the flexoelectric one due strain gradients. These two polarizations can be parallel or antiparallel depending on the ferroelectric polarity, which in turn will result in two different electrostatic energy costs of the deformation. [1]
At the macroscale, ferroelectric crystals are generally composed by a complex distribution of domains including domain walls. The vigorous research efforts on the functional properties of ferroelectric domain walls have already shown these almost bidimensional structures possess different functional properties from the host material, including a significant decrease of the young modulus. [2]
Overall, both factors can affect the effective mechanical properties of ferroelectric single crystals at the nanoscale. In this talk, I will show that by decoupling the mechanical stiffness from electromechanical responses at the nanoscale, it is possible to identify the asymmetry in the mechanical properties arising from the presence of strain gradients and domain walls, and its dependence on the ferroelectric polarization.[3] This has important consequences in terms of applications and devices: while the asymmetry in mechanical properties induced by the coupling of flexoelectricity to ferroelectricity leads to ferroelectrics as smart mechanical materials [1], domain wall engineering can be used to tune the mechanical properties of ferroelectrics systems. Altogether, this opens new opportunities to mechanically read ferroelectric polarization states and detect sub-resolution polarization domains.

This work was supported by Center for Nanophase Materials Sciences (CNMS), which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory.

The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

References:
[1] K. Cordero-Edwards, N. Domingo, A. Abdollahi, J. Sort, G. Catalan, Ferroelectrics as Smart Mechanical Materials, Advanced Materials, 29 (2017) 1702210.
[2] Ch.Stefani, L. Ponet, K. Shapovalov, P. Chen, E. Langenberg, D. G. Schlom, S. Artyukhin, M. Stengel, N. Domingo, and G. Catalan, Phys. Rev. X 10, 041001
[3] M. Checa, Ch. Stefani, K. Kelley, N. Balke, L. Collins, G. Catalan, S. Jesse, N. Domingo (submitted ACSNano 2024).