Theory of structural response to macroscopic electric fields in ferroelectric systems

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, E ) and F (R, η, P), whose minimization with respect to the internal structural parameters R and unit cell strain η yields the equilibrium structure at fixed electric field E and polarization P, respectively. First-order expansion of E(R, η, E ) in E 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 BaTiO3 and PbTiO3. 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 non-linear dielectric constants.

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

“…When the system is isolated from the external circuit, an induced current accumulates an extra charge (or spin, orbital) on one side of the system, which results in a spatial polarization of charge, spin and orbital. [39] Accordingly, this type of current associated with such internal degrees of freedom is often called a polarization current. In the following, we describe the physics of polarization current using the language of non-abelian gauge field, in particular, that of F kµt .…”

Domain-size dependence of piezoelectric properties of ferroelectrics

“…Electromechanical properties of ferroelectrics have been studied theoretically using firstprinciple calculations 5,7,8 . A continuum Landau theory describing a single domain or homogeneous state has been used to study the electromechanical properties of BaT iO 3 as a function of temperature and electric field direction 9 .…”

First-principles perturbative computation of phonon properties of insulators in finite electric fields

“…(5) is evaluated by computing all needed quantities at finite electric field. However, we will also compare our approach with an approximate scheme that has been developed in the literature over the last few years, 10,11,12,13 in which the electronic contribution is neglected and the lattice contribution is approximated in such a way that the finite-electric-field approach of Refs. 7-8 is not needed.…”

“…In Ref. 10, it was shown that this theory amounts to treating the coupling of the electric field to the electronic degrees of freedom in linear order only, while treating the coupling to the lattice degrees of freedom to all orders. Such a theory has been shown to give good accuracy in cases where the polarization is dominated by soft polar phonon modes, but not in systems in which the electronic and lattice polarizations are comparable.…”

“…Such a theory has been shown to give good accuracy in cases where the polarization is dominated by soft polar phonon modes, but not in systems in which the electronic and lattice polarizations are comparable. 10,11,12,13,14 In this approximate theory, the effect of the electric field on the lattice dielectric properties 13 and phonon frequencies 12 comes about through the field-induced atomic displacements. Thus, in the notation of Eqs.…”