Generalized relation between electromechanical responses at fixed voltage and fixed electric field

TL;DR

This paper develops a comprehensive theoretical framework relating electromechanical responses at fixed voltage and electric field, including first-principles calculations, crucial for understanding giant electrostrictors with large electromechanical effects.

Contribution

It introduces a general relation between responses at fixed voltage and fixed electric field, extending the understanding of electromechanical couplings beyond previous models.

Findings

Proper and improper responses are mathematically related.

First-principles calculations demonstrate the correction from fixed field to fixed voltage responses.

The theory accurately reproduces known piezoelectric and electrostrictive responses.

Abstract

We present a general relation between the electromechanical couplings of infinitesimal strain and electric field to arbitrary order, measured at fixed voltage and at fixed electric field. We show that the improper response at fixed field can be written as the strain derivative of the $n^{\text{th}}$ order susceptibility tensor, and the proper response at fixed voltage drop can be written as the response at fixed field plus corrections for dilations and 90$^{\circ}$ rotations induced by strain. Our theory correctly reproduces the proper piezoelectric response and we go beyond with the electrostrictive response. We present first-principles calculations of the improper electrostrictive response at fixed field, and illustrate how the correction is used to obtain the proper response at fixed voltage. This distinction is of high importance given the recent interest in giant electrostrictors exhibiting electromechanical responses as large as the piezoelectric ones.