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.

5 pages, 5 figures, 1 supplementary material