Origin of the large phonon band-gap in SrTiO3 and the vibrational signatures of ferroelectricity in ATiO3 perovskite: First principles lattice dynamics and inelastic neutron scattering of PbTiO3, BaTiO3 and SrTiO3

We report first principles density functional perturbation theory calculations and inelastic neutron scattering measurements of the phonon density of states, dispersion relations and electromechanical response of PbTiO3, BaTiO3 and SrTiO3. The phonon density-of-states of the quantum paraelectric SrTiO3 is found to be fundamentally distinct from that of ferroelectric PbTiO3 and BaTiO3 with a large 70-90 meV phonon band-gap. The phonon dispersion and electromechanical response of PbTiO3 reveal giant anisotropies. The interplay of covalent bonding and ferroelectricity, strongly modulates the electromechanical response and give rise to spectacular signatures in the phonon spectra. The computed charge densities have been used to study the bonding in these perovskites. Distinct bonding characteristics in the ferroelectric and paraelectric phases give rise to spectacular vibrational signatures. While a large phonon band-gap in ATiO3 perovskites seems a characteristic of quantum paraelectrics, anisotropy of the phonon spectra correlates well with ferroelectric strength. These correlations between the phonon spectra and ferroelectricity, can guide future efforts at custom designing still more effective piezoelectrics for applications. These results suggest that vibrational spectroscopy can help design novel materials.Comment: 11 pages, 4 color figures and 2 Table

Ab initio linear response and frozen phonons for the relaxor PMN (PbMg1/3Nb2/3O3)

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.Comment: 34 pages, 6 figures. to appear in PR

Geometric frustration in compositionally modulated ferroelectrics

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1-7. Geometric frustration gives rise to new fundamental phenomena and is known to yield intriguing effects, such as the formation of exotic states like spin ice, spin liquids and spin glasses1-7. It has also led to interesting findings of fractional charge quantization and magnetic monopoles5,6. Geometric frustration related mechanisms have been proposed to understand the origins of relaxor behavior in some multiferroics, colossal magnetocapacitive coupling and unusual and novel mechanisms of high Tc superconductivity1-5. Although geometric frustration has been particularly well studied in magnetic systems in the last 20 years or so, its manifestation in the important class formed by ferroelectric materials (that are compounds exhibiting electric rather than magnetic dipoles) is basically unknown. Here, we show, via the use of a first-principles-based technique, that compositionally graded ferroelectrics possess the characteristic "fingerprints" associated with geometric frustration. These systems have a highly degenerate energy surface and exhibit original critical phenomena. They further reveal exotic orderings with novel stripe phases involving complex spatial organization. These stripes display spiral states, topological defects and curvature. Compositionally graded ferroelectrics can thus be considered as the "missing" link that brings ferroelectrics into the broad category of materials able to exhibit geometric frustration. Our ab-initio calculations allow a deep microscopic insight into this novel geometrically frustrated system.Comment: 14 pages, 5 Figures; http://www.nature.com/nature/journal/v470/n7335/full/nature09752.htm

Phonon density of states, free energy, and anharmonicity of LiKSO<SUB>4</SUB>

LiKSO4 has been investigated extensively by a variety of techniques recently. The phonon density of states of this material is now calculated for its two phases P63 (C66) and P31c (C3v4) using the rigid molecular-ion model within the external mode formulation. The partial density of states associated with translations of each species of atoms and translations and rotations of the "molecules" SO4-2 are individually derived in the two phases. The free-energy difference and vibrational energy for the two phases are also evaluated. We have also analyzed the anharmonic behavior in the system at q&#8773; 0, using perturbation theory in order to understand its role in the rotational dynamics of SO4-2 ions

Lattice dynamics of MgSiO<SUB>3</SUB> perovskite

A lattice dynamical study of the geophysically important mineral MgSiO<SUB>3</SUB> in its orthorhombic perovskite phase, with space group Pnma (D<SUB>2h</SUB><SUP>16</SUP> ) has been carried out using a rigid ion model, with the potential consisting of Coulombic and short-ranged interactions. With the help of program DISPR, the ionic charges and radii were optimized using the equilibrium conditions. The resulting potential model is employed to predict the elastic constants and the phonon dispersion relations. The computed long wavelength optic modes are in good agreement with the corresponding experimental Raman and infrared active bands. The phonon density of states has been obtained and is used to evaluate the specific heat, the mean square displacements and thermal parameters of atoms