Domain formation and dielectric response in PbTiO₃: A first-principles free-energy landscape analysis

We determine the relative thermodynamic stability of competing homogeneously and inhomogeneously ordered ferroelectric phases of PbTiO ₃ using its free-energy landscape, obtained from constrained- polarization molecular-dynamics simulations with a first-principles effective Hamiltonian and thermodynamic integration. While we find that the tetragonal structure is thermodynamically most stable at temperatures below the ferroelectric transition temperature (T₀=660 K), the free energy of an "orthorhombic-like" 90^â̂̃ domain phase relative to the tetragonal phase almost vanishes at T=540 K and remains small at all temperatures below T₀. In contrast to BaTiO₃, the 90^â̂̃ domain structure is an order of magnitude lower in energy than the one with 180^â̂̃ domains. We show that the dielectric response contains signatures of such a domain structure and is significantly stronger than that of the uniformly polarized tetragonal phase of PbTiO₃.