Polarization, Dynamical Charge, and Bonding in Partly Covalent Polar Insulators
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ABSTRACT We have investigated the macroscopic polarization and dynamical charges of some crystalline dielectrics presenting a mixed ionic/covalent character. First principles investigations have been done within the Hartree-Fock, LDA, and model GW approaches. All calculations have been performed on the same footing, using the all-electron FLAPW scheme. Apparently similar oxides have strikingly different behaviors: some (like the ferroelectric perovskites) have giant dynamical charges, while others (like ZnO) are quite normal and display dynamical charges close to the nominal static ones. We find the rationale for such differences.
INTRODUCTION The dynamical charges of a polar crystal (also called Born effective charges or trasverse charges) measure by definition the current flowing across the sample during a relative sublattice displacement. The dynamical charge of an ion is a tensor having its site symmetry, and is defined at zero electric field [1]. In the extreme ionic limit, and assuming a rigid-ion picture, the dynamical charge coincides with the nominal static charge of the ion. In a realistic picture, the static charge of a given ion is largely arbitrary and ill defined from first principles, whereas the dynamical charge is experimentally accessible (via phonon spectra) and microscopically well defined [2]. The modern theory of the macroscopic polarization [3] allows first-principle calculations of the dynamical charges as Berry phases. The interesting case studies are those where the polar crystal has a mixed ionic/covalent character, and the displacement of a given ion induces a nonrigid displacement of the associated electronic charge. In some of these cases (like in ZnO) the dynamical charges turn out to be very close to their nominal value (i.e. ±2), while in others (like the ferroelectric perovskites) the dynamical charges may assume giant values (more than three times the nominal value). The aim of the present study is to get physical insight into the microscopic mechanisms governing the dynamical charges, and in particular to understand the reasons for such qualitative differences. Besides the above physical motivation, the present study has also a technical motivation. So far, first-principle studies of the dynamical charges have been performed within densityfunctional theory in the local-density approximation (LDA). Since polarization phenomena are dominated by delicate hybridization mechanisms, we investigate how LDA performs in 9 Mat. Res. Soc. Symp. Proc. Vol. 408 01996 Materials Research Society
comparison with alternate schemes, where the band structure (and hence hybridization) are rather different from the LDA one. Before presenting our first-principle results, we use a highly simplified tight-binding method to show qualitatively how the covalence mechanism strongly affects the dynamical charges. A MODEL PICTURE Let us take the simple model of a one-dimensional chain with two sites per cell, sketched in Fig. 1, and whose nearest-neighbor tight-binding Hamiltonian in the centrosymmetric st
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