First-principles theory of ferroelectric phase transitions for perovskites: The case of ${\mathrm{BaTiO}}_3$

We carry out a completely first-principles study of the ferroelectric phase transitions in ${\mathrm{BaTiO}}_3$. Our approach takes advantage of two features of these transitions: the structural changes are small, and only low-energy distortions are important. Based on these observations, we make systematically improvable approximations which enable the parametrization of the complicated energy surface. The parameters are determined from first-principles total-energy calculations using ultrasoft pseudopotentials and a preconditioned conjugate-gradient scheme. The resulting effective Hamiltonian is then solved by Monte Carlo simulation. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. We find the transitions to be intermediate between order-disorder and displacive character. We find all three phase transitions to be of first order. The roles of different interactions are discussed.