# Nonlinear Flexoelectricity in Non-centrosymmetric Crystals

## TL;DR

This paper analytically derives flexoelectric coefficients from microscopic parameters in a 2D lattice model and uses simulations to reveal how elastic asymmetries induce linear flexoelectricity, with quadratic effects dominating in non-centrosymmetric systems.

## Contribution

It provides a microscopic analytical framework for flexoelectricity and demonstrates the origin of linear and quadratic effects through simulations.

## Key findings

- Elastic constant differences induce linear flexoelectricity.
- Quadratic flexoelectric effect dominates in non-centrosymmetric systems.
- Flexoelectric coefficients depend on ionic positions and spring constants.

## Abstract

We analytically derive the elastic, dielectric, piezoelectric, and the flexoelectric phenomenological coefficients as functions of microscopic model parameters such as ionic positions and spring constants in the two-dimensional square-lattice model with rock-salt-type ionic arrangement. Monte-Carlo simulation reveals that a difference in the given elastic constants of the diagonal springs, each of which connects the same cations or anions, is responsible for the linear flexoelectric effect in the model. We show the quadratic flexoelectric effect is present only in non-centrosymmetric systems and it can overwhelm the linear effect in feasibly large strain gradients.