  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 for 1:2 chemical ordering along [111] and [001]. We used
linear response with density functional perturbation theory (DFPT) as
implemented in the code ABINIT to compute the Born effective charges,
electronic dielectric tensors, long wavelength phonon frequencies and 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 (TO) mode with E symmetry is found to be unstable in the
ferroelectric P3m1 structure and the ground state is found to be triclinic.
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.
