Large phonon band gap in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and the vibrational signatures of ferroelectricity in $A\mathrm{Ti}{\mathrm{O}}_3$ perovskites: First-principles lattice dynamics and inelastic neutron scattering

We report on first-principles density functional perturbation theory calculations and inelastic neutron scattering measurements of the phonon density of states, dispersion relations, and electromechanical response of $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. The phonon density of states of the quantum paraelectric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ is found to be fundamentally distinct from that of ferroelectric $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ and $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ with a large, $70–90\mathrm{meV}$, phonon band gap. The phonon dispersion and electromechanical response of $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ reveal giant anisotropies. The interplay of covalent bonding and ferroelectricity strongly modulates the electromechanical response and gives 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 $A\mathrm{Ti}{\mathrm{O}}_3$ perovskites seems to be 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.

Figure 1

(Color online) Computed phonon dispersion relations (full line) of (a) tetragonal $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, (b) rhombohedral $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and (c) cubic $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ compared to reported experimental inelastic neutron scattering (INS) single crystal data (Ref. 20), optical long-wavelength data [Ref. 22a], and reported first-principles calculations (Ref. 4).

Figure 2

(Color online) Comparison of the computed generalized phonon density of states with the measured inelastic neutron spectra $(T=6\mathrm{K})$ of tetragonal $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, rhombohedral $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and the quantum paraelectric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$.

Figure 3

(Color online) The computed [(a)–(f)] charge densities and [(g)–(o)] isosurface plots of tetragonal PT, rhombohedral BT, and cubic ST displayed using the code XCRYSDEN (Ref. 37). All densities were computed from the fully relaxed zero pressure LDA structures. The charge densities in [(a)–(c)] the [010] Ti-O plane and [(d)–(f)] the [010] Pb-O plane are shown. The $0.12\mathrm{a.u.}$ isosurfaces viewed down [100] and [110] are shown in (g)–(i) and (j)–(l), respectively, while the $0.03\mathrm{a.u.}$ isosurfaces are shown in (m)–(o). (p) The symbols used in (g)–(o) above.

Figure 4

The computed total and partial densities of states of tetragonal $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, rhombohedral $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and cubic $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ (energy $E=\hslash \omega$). For cubic $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$, effects from phonon instabilities are neglected.