Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

We report a molecular dynamics study of quality of the ferroelectric phase transition in crystalline <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>PbTi</a:mi><a:msub><a:mtext>O</a:mtext><a:mn>3</a:mn></a:msub></a:mrow></a:math>. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.