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We have developed and implemented a formalism for computing the structuralresponse of a periodic insulating system to a homogeneous static electric fieldwithin density-functional perturbation theory (DFPT). We consider thethermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization withrespect to the internal structural parameters R and unit cell strain eta yieldsthe equilibrium structure at fixed electric field e and polarization P,respectively. First-order expansion of E(R,eta,e) in e leads to a usefulapproximation in which R(P) and eta(P) can be obtained by simply minimizing thezero-field internal energy with respect to structural coordinates subject tothe constraint of a fixed spontaneous polarization P. To facilitate thisminimization, we formulate a modified DFPT scheme such that the computedderivatives of the polarization are consistent with the discretized form of theBerry-phase expression. We then describe the application of this approach toseveral problems associated with bulk and short-period superlattice structuresof ferroelectric materials such as BaTiO3 and PbTiO3. These include the effectsof compositionally broken inversion symmetry, the equilibrium structure forhigh values of polarization, field-induced structural phase transitions, andthe lattice contributions to the linear and the non-linear dielectricconstants.

Theory of structural response to macroscopic electric fields in ferroelectric systems