### Abstract

We have developed and implemented a formalism for computing the structural response of a periodic insulating system to a homogeneous static electric field within density-functional perturbation theory (DFPT). We consider the thermodynamic potentials E(R, η,ε) and F(R, η,P), whose minimization with respect to the internal structural parameters R and unit cell strain 77 yields the equilibrium structure at fixed electric field ε and polarization P, respectively. First-order expansion of E(R, η,ε) in S leads to a useful approximation in which R(P) and η(P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To facilitate this minimization, we formulate a modified DFPT scheme such that the computed derivatives of the polarization are consistent with the discretized form of the Berry-phase expression. We then describe the application of this approach to several problems associated with bulk and short-period superlattice structures of ferroelectric materials such as BaTiO_{3} and PbTiO_{3}. These include the effects of compositionally broken inversion symmetry, the equilibrium structure for high values of polarization, field-induced structural phase transitions, and the lattice contributions to the linear and the nonlinear dielectric constants.

Original language | English (US) |
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Article number | 104108 |

Pages (from-to) | 1041081-10410817 |

Number of pages | 9369737 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 66 |

Issue number | 10 |

DOIs | |

State | Published - Sep 1 2002 |

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*66*(10), 1041081-10410817. [104108]. https://doi.org/10.1103/PhysRevB.66.104108