Unified ab initio formulation of flexoelectricity and strain-gradient elasticity

Abstract

The theories of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference-dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO${}_3$, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.

arXiv comment23 pages, 3 figures, 8 tables

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Cited by in corpus (24)

• Does Flexoelectricity Drive Triboelectricity?
• Giant strain gradient elasticity in SrTiO3 membranes: bending versus stretching
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Defect driven flexo-chemical coupling in thin ferroelectric films
• Macroscopic Polarization from Antiferrodistortive Cycloids in Ferroelastic SrTiO${}_3$
• The influence of elastic strain gradient on the upper limit of flexocoupling strength, spatially-modulated phases and soft phonon dispersion in ferroics
• Switching a polar metal via strain gradients
• Direct Observation of Large Flexoelectric Bending at the Nanoscale in Lanthanide Scandates
• Missed surface waves in non-piezoelectric solids
• Using high multipolar orders to reconstruct the sound velocity in piezoelectrics from lattice dynamics
• Metric-wave approach to flexoelectricity within density-functional perturbation theory
• Flexocoupling induced soft acoustic mode and the spatially modulated phases in ferroelectrics
• Lattice-mediated bulk flexoelectricity from first principles
• Dynamical manipulation of polar topologies from acoustic phonon pumping
• Large Magnetic Moment in Flexoelectronic Silicon at Room Temperature
• Ferroelectric to incommensurate fluctuations crossover in PbHfO3-PbSnO3
• Generalized Einstein's and Brinkman's solutions for the effective viscosity of nanofluids
• Lamellar fluctuations melt ferroelectricity
• Hidden Symmetry of Flexoelectric Coupling
• Flexocoupling impact on the kinetics of polarization reversal
• Size effect of soft phonon dispersion law in nanosized ferroics
• A coupled magneto-structural continuum model for multiferroic ${\mathrm{BiFeO}}_3$
• Symmetry of flexoelectric response in ferroics
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions