Ab initiolinear response and frozen phonons for the relaxorPbMg1∕3Nb2∕3O3

Abstract

We report first principles density functional studies using plane wave basis sets and pseudopotentials and all-electron linear augmented plane wave (LAPW) of the relative stability of various ferroelectric and antiferroelectric supercells of PMN $(\mathrm{Pb}{\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3})$ for 1:2 chemical ordering along [111] and [001]. We used linear response with density functional perturbation theory as implemented in the code ABINIT to compute the Born effective charges, electronic dielectric tensors, long wavelength phonon frequencies and longitudinal optic-transverse optic (LO-TO) splittings. The polar response is different for supercells ordered along [111] and [001]. Several polar phonon modes show significant coupling with the macroscopic electric field giving giant LO-TO splittings. For [111] ordering, a polar transverse optic mode with $E$ symmetry is found to be unstable in the ferroelectric $P3m1$ structure and the ground state is found to be monoclinic. Multiple phonon instabilities of polar modes and their mode couplings provide the pathway for polarization rotation. The Born effective charges in PMN are highly anisotropic and this anisotropy contributes to the observed huge electromechanical coupling in PMN solid solutions.