Finite-temperature phonon dispersion and vibrational dynamics of ${\mathrm{BaTiO}}_3$ from first-principles molecular dynamics

A systematic investigation of the finite-temperature phonon dispersion, including its smearing and temperature effects, is carried out using autocorrelation function method together with first-principles molecular dynamics method along the [001] direction of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, as an illustrating example of entropy-stabilized structures. A unique anharmonicity in the cubic phase mainly derived from the interactions between titanium and oxygen atoms is revealed, which provides extremely strong damping and smearing to longitudinal optical phonons but no discernible effect on the shift of phonon energies. The anharmonicity gives rise to a nearly constant density distribution in a cubic region around the equilibrium position of the relative motion of titanium atoms with respect to oxygen atoms. These results may help to gain a further insight into complex interactions in entropy-stabilized structures and provide an essential benchmark reference to the development of the promising machine-learning based molecular dynamics methods for the investigation of phonon properties.

Figure 1

Schematic illustration of the primitive unit cell of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ used in FPMD simulations, where green balls represent Ba, blue ball represents Ti, and red ones are O. The [001] direction in the phonon dispersion calculation is along the $z$ axis of the coordinate system.

Figure 2

Phonon spectra at (a) 290 K in the tetragonal phase, (b) 473 K and (c) 758 K in the cubic phase along the [001] direction of the Brillouin zone. Colored maps are finite-temperature phonon spectra calculated using the autocorrelation method, and dashed lines are DFPT results. Inelastic neutron scattering measurements are displayed as dots, where diamonds are taken from the experiment of Shirane et al. [53] in 1967, circular dots come from the experiment of Bouillot et al. [54] in 1979, and pentagonal dots are the results of the experiment of Jannot et al. [55] in 1984.

Figure 3

Instantaneous polarization of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ in the ferroelectric phase, 290 K, and in the paraelectric phase, 758 K.

Figure 4

Density distribution of Ti with respect to Ba and O1 atoms along the [001] direction. (a), (b), and (c) are distributions of Ti relative to Ba. (d), (e), and (f) are distributions of Ti relative to O1.

Figure 5

Density distribution profiles of Ti in selected planes. (a), (b), and (c) are the distribution profile of Ti relative to O at 290 K, 473 K, and 758 K, respectively. (d), (e), and (f) are the Ti distribution relative to Ba at 290 K, 473 K, and 758 K, respectively. The first row is distributions in the $x-y$ plane, and the second row is those in the $x-z$ plane. Note that at 290 K, the $x-y$ plane for Ti-Ba distribution is at $z=0.05$ Å. and the $x-y$ plane for Ti-O distribution is at $z=0.12$ Å.