Phase Transitions in BaTi${\mathrm{O}}_3$ from First Principles

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultrasoft pseudopotential calculations. This approach is applied to BaTi${\mathrm{O}}_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder versus displacive character of the transitions and the roles played by different interactions are discussed.